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2021 Moderator Election Q&A - Questionnaire Asked 1 year, 10 months ago In connection with the moderator elections, we are holding a Q&A thread for the candidates. Questions collected from an earlier thread have been compiled into this one, which shall now serve as the space for the candidates to provide their answers. Not every question was compiled - as noted, we only selected the top 8 questions as submitted by the community, plus 2 pre-set questions from us. As a candidate, your job is simple - post an answer to this question, citing each of the questions and then post your answer to each question given in that same answer. For your convenience, I will include all of the questions in quote format with a break in between each, suitable for you to insert your answers. Just copy the whole thing after the first set of three dashes. Please consider putting your name at the top of your post so that readers will know who you are before they finish reading everything you have written, and also including a link to your answer on your nomination post. Once all the answers have been compiled, this will serve as a transcript for voters to view the thoughts of their candidates, and will be appropriately linked in the Election page. Good luck to all of the candidates! Oh, and when you've completed your answer, please provide a link to it after this blurb here, before that set of three dashes. Please leave the list of links in the order of submission. To save scrolling here are links to the submissions from each candidate (in order of submission): Asaf Karagila Daniel Loughran Carl-Fredrik Nyberg Brodda Liviu Nicolaescu Alec Rhea Tim Campion Pedro Tamaroff Stefan Kohl For pseudonymous candidates, Are you a professional mathematician? In what capacity? Should there be a term for which moderators are elected? If elected, how long do you envision serving as a moderator? There has been extensive discussion on MO Meta on how to make the MathOverflow community more welcoming and inclusive. How do you think the community should approach this issue, and what role (if any) do you think moderators should play in this regard? What time zone are you in? Assuming a notion of "culture" as explained here, what would a newly elected moderator do to preserve it? Will there be more efforts to preserve the culture, or more to steer it toward things nearer to "what a Stack Exchange forum should be?" As MathOverflow is growing, the diversity of the moderator team might become an issue of interest. As I understand, the present moderators have much in common, and women are, to say it that way, underrepresented. In which way do you think would you contribute to the diversity of the moderator team? What do you see as the biggest challenge for MathOverflow as a site and as a community in the next few years? Do you think women are underrepresented in the MO community compared to the mathematical community as a whole? Is this a problem for MO? If so, what would you do about it as a moderator? How would you deal with a user who produced a steady stream of valuable answers, but tends to generate a large number of arguments/flags from comments? How would you handle a situation where another mod closed/deleted/etc a question that you feel shouldn't have been? Catija CatijaStaffModCatija I'm using my real name. I have a permanent lectureship at the University of Bath. I think terms are a good idea in general, as they stop the power being concentrated and allow a variety of members to have a go. It also puts in a safety mechanism in the rare case that a moderator lapses. Though certainly moderators should be able to be re-elected once their term has come to an end provided their work is appreciated by the community. I'd happily serve for a couple of years then see how I get on after that. I do feel that new users are often marginalised as they are not familiar with the standards of the community. I would help by encouraging patience amongst the current members, and use my moderators abilities to edit posts to improve the exposition as appropriate so that new users get an idea of the kind of style which mathoverflow uses. I really like mathoverflow and think that it has a great culture. The questions should be overall research level, where I interpret research level to mean PhD level and above. Certainly I think that PhD students can ask questions which more advanced researchers would find naive/basic, but I think mathoverflow should be used for this purpose. I certainly learnt a lot on mathoverflow as a PhD student, even though I cringe at some of the questions I asked back in the day (which were all part of the learning process). My understanding is that there are no moderators in Europe at the moment, so I would be able to make sure that more time zones were covered. I would make sure that mathoverflow is open to all, and particularly encourage women to participate and feel welcome. I think keeping up the momentum that it has and making sure that questions and answers are high-quality. I think that it is a substantial problem in mathematics in general that women are underrepresented, but I would agree that the situation is even worse on mathoverflow than the real world. I would make sure that mathoverflow is open to all, and particularly encourage women to participate and feel welcome. Discreetly contact this user to point out the large number of flags and offer advice on how to improve their MO etiquette. Contact the moderator in question to discuss the situation and try to find out why they decided it should be closed. Through objective civil discussions we should be able to come to a joint conclusion as to what to do with the question. Daniel LoughranDaniel Loughran 19k1313 silver badges66 bronze badges $\begingroup$ LIES! You're in BST right now which is GMT+1!!! :-) $\endgroup$ – Asaf Karagila Mod $\begingroup$ Did you follow meta discussions in the past? It seems that this is your first active participation on meta (at least on the SE 2.0 meta, although you may have participated on the old meta, now known as "tea"). $\endgroup$ $\begingroup$ @AsafKaragila: I'm not really sure how appropriate it is for one potential candidate to grill another. But I have placed more focus on the actual mathematical questions and answers which is what I believe mathoverflow is really about. Though one of the reasons I'm applying for moderator is that I want to play a more active role in how the site is run and would play an active role on meta. $\endgroup$ – Daniel Loughran $\begingroup$ I'm not "grilling" you. I'm sincerely asking. Moderating is a meta-activity. You haven't been active on meta. And I felt that this was important enough to bring up. Thanks for the answer! $\endgroup$ $\begingroup$ As a point of order, it's quite common for candidates to be questioned about their answers in the comments on their questionnaire or on their nomination. While we certainly want these questions to be civil and fair, people have often responded to such questions in the comments or by editing their answer to cover their response more fully. Particularly in an election for three positions, I feel that it's perfectly fine for this to happen between candidates since they may be co-moderators in the future. $\endgroup$ – Catija StaffMod $\begingroup$ @DanielLoughran I notice that after completing only a handful of reviews for your first 11 years on the site, just yesterday you went on a blitz and completed about 20 of them in one day. This reviewing pattern seems a bit irregular -- could you say something about it? (Personally, I think my own lack of review experience is a black mark on my own candidacy, but I don't think I'd have held your lack of reviewing experience against you.) Also, I applaud you for being one of the first to put your name forward. Could you expand a bit on what serving as moderator would mean to you? $\endgroup$ – Tim Campion Mod $\begingroup$ @TimCampion: Well I thought that if I'm going to take being a moderator seriously then I better get more experience at doing moderator activities, with doing more reviewing being an obvious place to improve as I expect I would be doing a lot of this should I be elected as a moderator. $\endgroup$ $\begingroup$ As for what being a moderator would mean to me: I really love MO and have got a lot out of it and learnt so much mathematics. I have mostly focused so far on the Question and Answer side, but I feel that the time is really right for me to give more back to the community and play a more active role on the meta and behind the scenes of MO. I want to move my participation on mathoveflow to the next level and becoming a moderator would mean a lot to me, and I would feel very honoured if the community decided to put their trust in me to perform this role. $\endgroup$ $\begingroup$ I feel like I should add that I would also view being a moderator as part of my professional activities as a professional mathematician, rather than just being a "hobby". $\endgroup$ $\begingroup$ Thanks, I think all of that is very admirable! $\endgroup$ $\begingroup$ Discretely or discreetly? :-) $\endgroup$ – Rand al'Thor $\begingroup$ @Rand al'Thor: Ha good catch! Corrected. $\endgroup$ Here is a link to my candidate statement. I use my real name, Tim Campion (I may sometimes publish as Timothy Campion). I am currently a 6th year math PhD student at the University of Notre Dame working with Chris Schommer-Pries. In the fall, I will start a postdoc at Johns Hopkins University with Emily Riehl. I'm of two minds on this question. Certainly if elected, I would be happy to serve for a finite period of time. I did notice during the nomination phase that several excellent moderator candidates were suggested who declined to run because of the level of responsibility involved. If term lengths were imposed, I suspect that the pool of qualified candidates interested in running would grow because the commitment would be less open-ended. So if we were to decide that it's desirable to have more rotation on the moderation team, I think that having finite term lengths would probably be an effective strategy. On the other hand, I think the current moderation team does a generally excellent job -- if it ain't broke, why fix it? I would suggest that if term lengths were to be imposed, then we should grandfather in the current moderation team, allowing them to serve indefinitely barring specific issues, or take some similar sort of measures to preserve the benefits of the current system, such as not limiting the number of terms for which a moderator might serve. On balance, I tentatively think that it would indeed be desirable to have more rotation on the moderation team, much as we do with departmental administrative positions in academia. As I understand it, moderators play several roles in the functioning of MO: Dealing with flagged posts and problem users. Facilitating meta discussions by sharing specific information they are privy to. Leading by example in helping to define the culture of MO. (Typically) serving on the board of MO and helping to shape long-term MO strategy. For each of these roles, the benefits of cultivating a core of long-serving, experienced moderators are clear, but the benefits of continuously refreshing the workforce are equally clear. In summary, finite term lengths sound like a pretty good idea to me, but only if the benefits of the current stability enjoyed by the moderation team can be maintained. In my answer to Question (8) below, I discuss making MO more welcoming to and inclusive of women and other underrepresented groups. Much of what I say there is applicable here: moderators can lead by example, be gentle to newcomers, and take corrective action when others fall short of such standards. Moderators can also do things like help new users to clean up their questions to make them more palatable to the MO audience. Most of these measures are not specific to moderators, but a moderator's actions in such regards do carry extra weight. I am in EST (UTC-5)/EDT (US Eastern time zone). This will continue to be the case when I change positions in the fall. I have difficulty parsing the description of "culture" discussed by Gerhard at the linked post, but I take this to be a question about some of the unique aspects of the culture at MO setting us apart from other SE sites. To be honest, I have only limited familiarity with other SE sites, so I don't have a deep grasp of which aspects of our culture stand in contrast to them. MO's situation is of course unique in that we were founded independently from SE and continue to be an independent entity hosted on the SE network. We have cultivated a space specifically for research mathematics, which is fantastically valuable. Compared to other sites, this makes our community more "targeted", which has allowed us, for instance, to welcome more open-ended questions than are typically permitted on other sites. These aspects of our culture are to be treasured. Perhaps this is an appropriate place to say something about our relationship with the SE network more broadly. I feel that the relationship could use a bit more structure. For instance, when SE redid the theme of the site last year, and when they announced the new rich text editor a few months ago, I felt we were caught both times a bit flat-footed. For instance, it's been a year, and we still haven't implemented a background color for the site in the new theme! One measure I think could help would be to have a specific individual MO user (a moderator or otherwise) designated as the "point person" for communication with SE. We would expect this person to be given a heads-up about major changes like these two before they were publicly announced, and this person would have the authority "make official requests" about such matters from the MO community to SE. I've spoken about the value of diversity in the moderator team in answer to (2) above. In many respects I would be a regressive moderator choice as regards diversity. One aspect I do bring to the table concerns my early years on MO. I joined MO within a few months of its founding, and for many years was mostly a lurker on the site, before becoming increasingly active as I've matured mathematically. But in those early years, I was between my undergraduate and graduate school, working in industry, and not sure what role math would play in my future. MO was instrumental in helping me sustain my interest in mathematics and eventually return to academia. So I do bring a bit of an outsider's perspective. I think things have been working pretty well for many years now. The balance of questions on this questionnaire suggests that issues of inclusiveness and diversity in our community are on many people's minds. I agree that such issues should be at the forefront of discussions about the future of MO going forward. I object to one premise of the question. Women (as well as numerous other demographic groups) are underrepresented in mathematics as a whole, and this is an issue for mathematics as a whole. The question asks about the extent to which the problem is worse on MO than in mathematics as a whole; I believe it is a nonzero extent, but it doesn't matter. MO is part of the mathematics community, and as such, any problem for the mathematics community is a problem for MO. As a moderator, there are various things to do in terms of leading by example in being welcoming to newcomers, which we've discussed ad nauseum over the past few months. One thing we haven't done is to systematically seek out women (and members of other underrepresented demographic groups) and ask them about MO. In dealing with problems of underrepresented groups, it doesn't seem very productive to me to have those who are represented bandying about ideas bout addressing such issues. I think it's high time we do something a little more proactive -- perhaps create some sort of survey or something like that. This is the sort of thing that a moderator's behind-the-scenes role could be helpful in facilitating. I suspect the current moderation team has some internal guidelines on such matters, to which I would defer. Common sense says that the user should be contacted privately with a gentle explanation of the problems with their conduct and suggestions on how to fix them, gradually escalating if necessary to more formal interventions like suspensions. Again I suspect the current moderation team has their own well-established norms on such matters, to which I would defer. Common sense suggests contacting the mod privately and discussing the issue as human beings, trying to find some consensus. Tim CampionModTim Campion $\begingroup$ Since you engaged with the other candidates, I can ask you "difficult questions" without backlash, I hope. Why being a moderator is going to be any different to being a high-reputation user (which can partake in moderation tasks such as reviews, closure, deletion, etc.) $\endgroup$ $\begingroup$ @AsafKaragila I appreciate the question! (I kinda wish there more questions, to be honest!). I'm not completely clear on this. There was very little feedback when I asked about it over here. I would look to the current moderators for guidance, but my understanding is that the primary responsibility of a moderator is to review flagged posts. I do not claim to be uniquely suited to this task, but I am willing to put in some effort at it. Perhaps some of the issues discussed above are irrelevant to moderation. $\endgroup$ $\begingroup$ Thanks. I agree that it'd be ideal for the moderator to tell us about what they actually do before the election. I don't think that a lot of it is reviewing posts directly, rather it's dealing with the controversial issues (e.g. things that are closed/reopened or deleted/undeleted) or problematic users. I know that on MSE there's a lot more low quality material, but we don't intervene too often with that level of moderation. It's mainly things that the community can't do by itself. $\endgroup$ $\begingroup$ "systematically seek out women (and members of other underrepresented demographic groups) and ask them about MO." <-- the best idea. I believe it's already been done a little bit, but more data is better, and more representative of the breadth of views out there. $\endgroup$ – David Roberts Mod $\begingroup$ @theHigherGeometer actually, for once I'd like to see someone say that they would like to act on the responses coming from asking underrepresented or minority groups instead of just asking them about their experiences. it might seem like a minor difference, but it's the difference between lip-service and action so... it's not that minor. I should also say that I think Tim has provided a thoughtful and considered response to the questions though, and he's on my shortlist of people to vote for. $\endgroup$ – postmortes $\begingroup$ regarding the integration of underrepresented groups I think it will not suffice to invite members of the respective groups to ask or answer questions on MO but also questions and answers regarding their experience with the "organs" of mathematical research like journals, institutions, forums,etc. should be welcomed and taken serious. Maybe installing something like awareness events on meta could be a first idea for MO to take an active part in that respect. $\endgroup$ – Manfred Weis $\begingroup$ @postmortes (and Manfred) I definitely agree, and I suspect some moves are being made. Awareness events seem like a very reasonable idea. $\endgroup$ $\begingroup$ @postmortes I absolutely agree about words vs. action. Perhaps I'm betraying my own ignorance, but my perception of the state of things on MO is that we basically haven't done that first step of finding out what the suggestions of various underrepresented groups would actually be -- we just keep recycling discussion of being welcoming to newcomers, etc. After that first step, it is of course important to actually act on such suggestions. $\endgroup$ $\begingroup$ @ManfredWeis I don't know what an awareness event would entail, but it sounds interesting! I'd be interested in finding out more. $\endgroup$ $\begingroup$ I think I agree with a feeling of repeating the same initial steps over and over -- and I am certain that any discussion on how to welcome minorities and underrepresented groups more will be difficult both to start and to manage. So... I welcome your intention to tackle this :) $\endgroup$ $\begingroup$ @TimCampion what I could imagine would be to encourage questions that bring e.g. women mathematicians to the attention of the mathematical community and/or general public; there is for example that movie about the African American women at NASA, but I can't remember having seen questions regarding these pioneering women on MO. I think an inherent "problem" in attracting e.g. women as contributors to MO is that the focus is on math, problems and solutions whereas the people behind the math are hardly of interest. $\endgroup$ $\begingroup$ In line with what postmortes is saying, I wholeheartedly welcome and support your intention to tackle acting on such suggestions! $\endgroup$ – Carl-Fredrik Nyberg Brodda I am using my real name. I am Professor of Mathematics at the University of Notre Dame. I believe that there should be a term. I would serve a 3 year term I have to admit I have not followed that discussion. Perhaps one should define more precisely the term inclusive. I do like the current warning "New Contributor". We do not want to scare new users away. This is inclusive. I believe MP should remain a site for research level mathematics. This in itself is a bit exclusive and I am not comfortable broadening the scope. Eastern Time Zone US Speaking from my own experience, I like that in the current format MO offers access to an amazing community of experts asking and answering questions. I hope it will stay that way and even more, it increases. I like this "culture" and I would like to preserve it. I honestly do not have a good idea. I do not even know the gender of many of the contributors. As a moderator I would try to keep the contributions/ discussions strictly academic, where mathematics plays a central role. Abusive and discriminating language should not find a place on this site in my time here the dialogue has mostly been like that. In the few instances when I noticed that the language became heated the moderators intervened to cool it down and I appreciated that. The issue of underrepresentation of women and minorities in the mathematical community is real deserve addressing but I do not feel that MO is the optimal avenue. You got me here. I do not know about the costs of maintaining this site and about how difficult it would be to maintain the current sources of funding. Since this site does not deal in controversial issues I believe that the risk of it being polluted/trolled is minimal but vigilance needs to be maintained. I have noticed that the frequency of homework-like questions has increased. This is bad for two reasons: it dilutes the quality of this site and it might inadvertently make this site complice to the academic dishonesty that seems to have grown substantially in campuses during the pandemic. I do not know what is the percentage of women on this site so I cannot give you an informed answer. Some contributors want to preserve their anonymity and I respect that. This make it difficult (at least for me) to have an idea of the demographics of this site and how it impacts its quality. I would first send an email warning the person that this is unacceptable behavior on this site and if this continued measure would be taken. Measures would range from temporary restricting the right to comment and a penalty of $x_1$ points removed from his/her reputation, temporary restricting the right to ask or answer questions and a penalty of $x_2>x_1$ points removed from the reputation. If the comments continue to receive many flags even after warnings and penalties then we as a community we have to judge the costs vs the benefits of having such a person contribute to this site. I would try to resolve this in private with the other moderators and present my best arguments why the question deserves attention. I've only encountered few situations of this kind and in some cases, when the user seemed to be MO-inexperienced, I helped "save" the question, by voting it up and editing it to highlight the features I found interesting. Liviu NicolaescuLiviu Nicolaescu $\begingroup$ Do moderators have the power to remove reputation points? $\endgroup$ – Thomas Browning $\begingroup$ @ThomasBrowning I honestly do not know. In any case this is an issue that only the community can decide it's worth pursuing if abusive language/behavior becomes a serious issue. $\endgroup$ – Liviu Nicolaescu $\begingroup$ @ThomasBrowning As far as I can tell, the possible sanctions include suspensions and account deletion / destruction, but not loss of points or restricting the right to comment without general suspension. $\endgroup$ – Stefan Kohl Mod $\begingroup$ @StefanKohl: When an account is deleted the votes given by that account are usually removed (the dreaded "User removed" notice), since moderators can delete user accounts, that's one more way of removing points. $\endgroup$ $\begingroup$ I think that the range of punishments is rather limited as is since there is little in between a warning and expulsion. Whether this is good or bad is a matter of debate. $\endgroup$ I am using my real name (though I publish as Nyberg-Brodda rather than Nyberg Brodda). I am currently a final year PhD student. Yes, I think term limits is part of a healthy democratic process, and can help boost engagement between the community and the moderators. I do think that re-election should be significantly easier than initial election for moderators whose work is appreciated by the community. The time itself is not as important, but I might envision myself working for a couple of years. I think it is important to reward genuine curiosity and attempt at engagement from new users, even if it is not quite to the standard we are used to. Of course, this does not mean that questions about "checking my proof of the Riemann hypothesis using antimatter" should be treated with great patience and explanation, but rather that new users are treated with a greater deal of flexibility and forgiveness, treating these as part of the learning process. An analogy: if a new PhD student were to ask a "stupid" or "obvious" question to a well-known and friendly professor in the tea room after a seminar, I would wish the community to react in a similar way that the professor might react. To me, a moderator's role in this regard is to ensure that the community as a whole keeps this goal in mind, and to step in with a soft touch to steer back any discussions that divert from this goal, or directly work against it. BST (UTC+1). I think the unique culture of MathOverflow is, beyond any doubt, something that should be preserved, while keeping in mind that certain aspects of it will naturally be evolving as it becomes more inclusive and diverse (see below). I would almost certainly be the youngest member of the moderator team, both academically and age-wise. Coming from a progressive background in Sweden, I would also be strongly motivated and driven to work towards goals of diversity and equal representation on the moderator team. Preserving the aforementioned culture of MathOverflow, and ensuring the continued development of the community's diversity and inclusivity (these challenges are, as mentioned before, quite interlinked!). Yes, and yes. As a moderator, my work would primarily be reactive (welcoming new users on their first posts; steering diverging conversations; pointing out and taking action, if necessary, to unwelcome behaviour, etc), and so my main contribution to this issue would be in line with this, rather than proactive measures. However, this is not to say that it would only be reactive; for example, I might raise meta issues about certain posts and how (un)welcome these are in our community, as we have seen in the past (e.g. about sexist jokes). I would likely raise the issue with the user in question in private, to remind them of the community guidelines, and to ensure that they are aware of the effect their comments have on other users. I would first and foremost ask the moderator in question in private. I would not override any decision before getting a very clear idea of all variables involved in the decision, which I trust was not made lightly. Carl-Fredrik Nyberg BroddaCarl-Fredrik Nyberg Brodda $\begingroup$ I think that it could be a good idea to have a Ph.D. student on the moderator team. Let me take the liberty to ask you a somehow provocative question. Assume (as a thought experiment) that some senior mathematician, that you know very well and could have an influence on your career, posts something inappropriate (for instance, a sexist joke), that some controversy arises, and that you must be the one taking action. What would you do? $\endgroup$ – Francesco Polizzi $\begingroup$ @FrancescoPolizzi This is a very good question. Of course, the reality of that situation would mean that it might at first be difficult to see the situation entirely objectively (I am only human!). However, through careful deliberation, including with other moderators, seeing the reactions and opinions presented by the community, and careful (and transparent!) assessment of the facts, this initial difficulty disappears. A sexist joke (for instance) is equally unwelcome regardless of who makes it. My role as a moderator would be to serve the community, not myself. $\endgroup$ $\begingroup$ these are thoughtful answers, thank you; since you are in your final year of your Ph.D., I imagine your situation will change quite substantially in the near future; are you planning on staying in academia? $\endgroup$ – Carlo Beenakker $\begingroup$ @CarloBeenakker Thank you! Yes, I am planning on staying in academia (job market permitting). $\endgroup$ $\begingroup$ @Carl-FredrikNybergBrodda I notice that you have by far the most MO reviewing experience of any of the candidates, which is fantastic! Could you say a few words about your reviewing experience? What draws you to it? What are some of the considerations at the top of your mind when reviewing? How do you think this experience would inform your work as a moderator? $\endgroup$ $\begingroup$ @TimCampion Thank you! To me, reviewing (especially first posts) means doing the kind of "small nudges to make the site slightly better" that I really enjoy. Seeing other members' reactions on posts when I am uncertain of the quality has also really helped me get a feel for e.g. what qualifies as "research level" or "on-topic". There are still some posts where I feel unable to accurately decide; in those cases, I skip the question and let the other reviewers decide. This gives me a small boost of "community spirit" endorphins, which is great for wanting to review more later that day :-) $\endgroup$ I am using my real name. I am a final year PhD student, I will defend my thesis in a few weeks from today, and begin a job as a professional mathematician shortly thereafter. Two years seems like a fair amount of time for a newly elected moderator, upon which the moderator may choose to re-run or leave the post. For moderators that have been on the site for many years, I believe the situation may be different, and community may already have absolute trust in their abilities, in which case a probation period may not longer be necessary. This issue is of course still outstanding in other sites, such as the sister site math.SE. It is surely impossible to guarantee hundreds of thousands of users are constantly behaving in a civil fashion, but I believe as moderators we should set the example, such as looking out for posts by new users (highlighted by the system) and making sure that if one of us (moderator or otherwise) has interacted with the user, such interaction has indeed been welcoming and civil. In a site such as MO, where professionals interact, there is definitely no place for disrespect, intolerance, or other such behaviour. At the same time, some users may come off as terse or unkind even if there is not ill-will: it is hard to communicate through text, where the nuance of spoken word is lost. Because of this, moderators should be ready to mediate interactions between new users and existing users that may have escalated due to a simple misunderstanding. This does happen often and, quite likely, more often that the former situation. At the moment, I am in GMT+01:00 (Irish Standard Time). Each community in SE has its own ways and its own idiosyncrasies, in particular when it comes to commenting, answering and weighing on the value of these interactions. As long as these have positive outcomes and do not produce a harmful environment, the community is free to find its own way. For example, more experienced users tend to be reticent on giving an answer when they deem it "easy enough" or "well known", which is not useful for record-keeping. As a moderator in math.SE, I usually kindly request such comments be made into answers. If this does not work (for whatever reason, which is at any rate irrelevant) I tend to cite these replies and add them to the answers as community wiki. This helps the site keep track of those questions that have been answered, and avoid duplication. I do not know the moderators personally, so I'll just tell you a bit about myself. I am from Argentina, where I spent most of my formative years, graduated from a public university where students from multiple backgrounds are educated, and where I also worked as a teacher assistant. I also worked part-time in a private university where I taught math for students without a mathematical background. I emigrated to Ireland almost four years ago. I have been working with undergraduate students in Ireland for the last four years, taught around 24 courses during this time as a TA, and had the opportunity to (if perhaps briefly) interact with hundreds of students from many different countries and backgrounds. This has helped me become more aware of existing diversity issues, and learn how to help students (and in this case, users) have a better experience. On another level, I have actively participated in many mathematics-related events in Europe and South America where I (usually indirectly) learned from organizers about how to foster diversity in such events. I most strongly believe that MO should be a place where every mathematician (or mathematics-adjacent professional) feels welcome to participate, and I am ready to contribute to this effort. Certain interactions I have had in the past make me believe a large amount of mathematics-adjacent internet users have a negative (or very negative) opinion of MO and the sister site math.SE, in particular with regards to the experience of new users, for example, and the way these users are treated. It would be good to understand how we can help improve the image of the site (and not in a cosmetic way!), specially if future professional mathematicians have such view of the site. Compared to workshops, conferences and other similar events (where in many cases they are still underrepresented), women participate in MO much less than usual: by looking at the first few pages of users, organized by reputation, where almost all users have public names, one can count exactly one username with an identifiable female name out of about 300+. This is of course an issue in that many early researchers miss out on using the forum (assuming they would agree using the forum is a good use of their time!), while MO misses out on the invaluable input it could receive from the many leading experts that are not participating. The site has established itself as an important piece of the mathematical community to many, and I believe we should make sure it keeps up to the standard we would expect from workshops, say, and does its best to attract mathematicians independent of their background. I would like to help with the efforts. We have dealt with this issue in math.SE a few times (I have been a moderator there for about 7 years). Sometimes the user did improve their behaviour after we contacted them and made them aware of the issue, making it clear that we valued their input to the site but that we could not tolerate disruptive behaviour. Sometimes we had to escalate and suspend them. As any other site, there's a code of conduct, and every user ---independent of their prowess--- should adhere to it. This has also happened a few times in math.SE. The moderators involved should discuss the matter privately, and aim to come to an agreement. If no agreement is reached, I believe moderators should withdraw from the situation and let the community decide. Ideally, this kind of situation would not happen regularly, and I believe moderators should be the last ones to decide to close a question, and let trusted users do the voting. After all, moderators can take unilateral action, and this (if not always, quite often) leads to discussion unless the course of action is clear cut (say if a user posted spam, or a solution to an open problem which is clearly bogus.) Could you expand a bit on the similarities and differences between MO and MSE, both in general, and with regard to the way you personally use them? If elected moderator, how would you split your time between the two sites? Both forums are similar in their Q&A format, the more experienced users from math.SE are either professional mathematicians, educators, former mathematicians, or a mix of these, as it happens in MO. The main difference is the influx math.SE experiences from new users that are very unfamiliar with the way the site works, use of LaTeX, and other issues, and the level of the questions, along with a perhaps more collegial environment in MO. In this way, math.SE requires more intense moderator activity, which is backed up by many highly active users that help with the efforts, while MO tends to see just a handful of "lost" users and perhaps sometimes more serious issues that have to be dealt with. I enjoy using math.SE to provide help to people that are learning a subject and, perhaps less than before, to get some help on non-research level questions that I bump into every now and then. During last year of my PhD, I started using it very little, answering questions seldomly. I use MO to consult with experts and try to find answers to questions that may appear during my research, though I have used it very passively lately, and read rather than contribute with answers. I am looking forward to spending more time on the site, and hopefully contributing to it more meaningfully. PedroPedro $\begingroup$ I understand that you are a moderator and extremely active user at MSE, but comparatively less active on MO. Could you expand a bit on the similarities and differences between MO and MSE, both in general, and with regard to the way you personally use them? If elected moderator, how would you split your time between the two sites? Also: for how long have you been a moderator at MSE? $\endgroup$ $\begingroup$ Thanks, I just noticed your edit in response to my comment -- it's clarifying! $\endgroup$ $\begingroup$ Not at all active user on math.se, @Tim, for some years now. Not even an active moderator. (Also, please know that mathematics.se is math.se, capital letters or not, whereas MSE is meta.se. I only learned of that distinction a year ago.) $\endgroup$ – amWhy $\begingroup$ @amWhy (I only became aware of the usage of MSE for meta stack exchange recently too -- I was figuring it was safe to use MSE for math.se in this context, but you're right -- best be consistent!) Pedro Tamaroff is a 100k+ rep user all time on Math.SE and has 1000+ rep on the year. By MO standards, that's quite active. It's difficult to gauge moderator activity from public information as so much of the work is apparently behind the scenes. I do see that Pedro hasn't posted or commented on Math.SE meta since 2017. I for one appreciate your perspective, yourself being an active Math.SE user. $\endgroup$ $\begingroup$ I was in the same position, not knowing math.se wasn't seen as MSE outside of the two math sites, but folks on meta.se wasted no time at all, when I posted a general question on meta.se, and cited two examples on "MSE"... Best to avoid clashing with those folks. If it's any consolation, I knew, and I'm sure everyone here knows, your use of MSE was meant to refer to math.se. And as for 1000 rep in a year? that often comes with an occasional post + "royalties" earned with continued upvotes of past posts. I can vouch for that. $\endgroup$ I use my real name here, but I am currently a voluntary college dropout studying math independently. This could potentially present an issue, since someone like me with no formal prestige to their name moderating this site could give an impression of reduced professionalism at MO to the mathematical community at large. MO seems to be taking a more center stage in mathematics at large (being mentioned in papers and at conferences etc.), and I wouldn't want to risk damaging that momentum in any way. That being said, I have consistently participated here since I dropped out back in 2018; I left as an undergrad because I wanted to focus on research related to the surreal numbers, but my university wanted me to spend another 1.5 years and $50,000+ for the privilege of taking religious studies classes (it was an American Lasallian Christian university) and general ed credits to complete requirements for my degree. I had taken all available upper division math and physics classes and maintained a 4.0 by the the end of my first semester as a junior, and the prospect of slowing down for a year and a half to check off 'religion class' boxes rubbed me the wrong way. I do intend to return to academia and complete a PhD, but I would first like to finish what I left college to finish and get a paper submitted for publication. Mathoverflow has been essential for me these past few years; I could not have come as far as I have without the help I've received from members of this site. Irrespective of how my academic career progresses, I intend to leave plenty of room for participation here at MO; my situation is such that I don't have to worry about income, so I won't be leaving academia any time soon. I think the newly available positions should rotate once every year/few years, so that parts of the moderation team can accurately reflect the feelings of the community as they evolve. It may be that someone who seems to reflect the communities values during the lead-up to an election phase turns out to be a flawed match as the landscape of the community changes, or that someone who was initially a poor choice matures and becomes a paragon of potential moderation. This would also prevent, to some extent, the possibility of attitudes along along the lines of, "I'm a moderator so I don't have to listen to you, you have to listen to me". Although I haven't seen anything close to this on MO from the current moderators, we are all flawed humans; putting safeguards up against our baser natures is a good idea in my opinion, even if we couldn't imagine falling prey to them. The current moderation team, however, should remain on permanently or until they choose to leave in my opinion. I think everyone currently moderating has given the community ample evidence that they are the kind of moderators we want on this site, and they could serve as an 'old guard' of sorts to help guide newer moderators in the subtle methods of their craft. This is something I'm particularly sensitive to due to the situation outlined in my answer to question 1; for the last 3+ years, MO has been my only formal connection to the academic mathematical world and has consequently weighed heavily on my self-image as a mathematician. If I had a PhD position, or a temporary/permanent job in academia, and I were to suddenly find MO too unwelcoming for me, I could simply turn to the other institutions around me and use them for support. With nowhere else to turn, the times when I felt unwelcome by the community here (which only happened rarely) were extremely disheartening, and could have been rectified pretty simply via the correct type of proactive moderation. I think it is easiest to explain my position using the metaphor of "MO as a tea room for professional mathematicians to discuss research mathematics". Taking this view, all the regular participants here at MO are standing around a swanky lounge, sipping exotic teas and having scintillating conversation about arcane topics unheard of by the common man. An outsider walks in and is initially blown away by the scale of it all; who knew that things could even get this abstract and complicated! They initially float around a bit, listening in on conversations where perhaps every fifth word makes sense, until they finally reach a point of excitement and offer their first input into the conversation at hand. This is where things can go wrong in the current culture in a way that moderators could fix. Let us assume that their input, whatever it was, was not sufficient to be of interest to anyone else involved in the conversation. The current cultural norm is the equivalent of everyone falling silent for a moment and giving the newcomer a dirty look, before continuing on with the conversation as if they hadn't blurted anything out in the first place. If the newcomer continues to try to offer input, the standard response is increasingly dirtier looks eventually followed by a comment, muttered into someones hand but spoken to the crowd at large, along the lines of 'you don't belong here and you should know that you don't belong here'. Where a moderator can fix this situation, sticking with the above metaphor, is by playing the role of a good host. They could proactively identify newcomers like the one outlined above and glide around the room, close enough to hear them, waiting to see what their input level is. If it becomes apparent that they aren't quite ready to converse in this tea room the moderator could quietly pull them aside, introduce themselves and briefly explain the ethos of the room, then politely suggest other rooms that they might be more comfortable in until they mature to a point where they should return. Also, if something untoward is said before moderators can step in, they could make a point of telling the newcomer that these opinions are not universal -- from someone with a diamond next to their name, comforting words like this can have significant psychological impact. This added personal touch would alleviate much of the perceived unfriendliness in my opinion. GMT-5, St. Louis currently, but I'm engaged to be married the 15th of may and we're looking at moving to Ireland so my time zone may change soon. The kind of 'culture' outlined by Gerhard above is something I think is incredibly valuable and rare here at mathoverflow, and something naturally engendered by the nature of high-level mathematical discussion. I think moderators role in 'culture influence' should, to some extent, require a split personality on the part of the moderator. On the one hand moderators (like Todd for example) are themselves accomplished mathematicians and should be allowed to contribute freely and in an unrestricted capacity as a mathematician on the site, implicitly influencing the cultural norms in the same way we all do by communal participation in them combined with individual evaluations of their significance and importance. On the other hand, as a moderator they should not strive to directly influence cultural norms beyond their normal capacity as a participant of the site, and instead strive to allow the community to decide its own culture (with moderators viewed as community participants on equal footing with everyone else). Moderators aren't elected to be tastemakers for the site. This is a delicate line to walk, but I think finding it and balancing is one of the more difficult and important jobs for a prospective moderator. I am a white man, so I am definitely not contributing to diversity via my race or sex. I have suffered from mental health issues in the past to the point of inpatient care however, and have a permanent diagnosis of generalized anxiety disorder, so I may be able to offer more diversity in understanding potential mental health issues from a moderating perspective. I think things are looking up for MO on average as I mentioned in my response to question 1, but the potential problems I see on the horizon are primarily the ones I see outlined in other questions about welcoming newcomers and participation from women. One potential problem not mentioned in other questions is how the increasing polarity of the outside world right now might gradually seep in and influence interactions here on MO. We live in a world that is increasingly full of disagreement and refusal to see eye-to-eye; we've already seen some of that enter MO in the form of the recent drama culminating in a suspension. I think that it's incumbent upon moderators to acknowledge this increasing polarity, and proactively make an effort to identify and stamp out any extraneous politicking here to keep things as math-content oriented as possible. It is also important to not simply label any opposing opinions as politicking that must be squashed, but I think that by consulting other moderators and the community at large we should be able to discern a bright red line between friendly discussion and deliberate flaming. This question doesn't ask us if we think women are underrepresented in math, but wether MO is worse than the math community at large as far as female representation is concerned. I definitely think there are fewer women here than there are in the math community at large; two of my five total professors as an undergrad were women, whereas the proportion of women to men here seems to skew more than 90% in the male direction. I think this is certainly a problem, for the same reason it would be a problem that approximately 50% of the math community was not participating in MO for some reason or another; we aren't hearing input from valuable voices on topics they might be leading experts on in the world. Despite this being a problem for MO, I think it is rooted somewhat in the unfriendliness of online communities towards women in general. I am not aware of any online math/science forum where participation by women approaches 50%, and I would go farther and say that outside of forums specifically dedicated to predominately classically feminine topics males tend to dominate the conversation online. I definitely feel that it is a moderators responsibility to try to alleviate this issue, but the obvious tools at hand seem insufficient to the challenge. I would say that encouraging our female colleagues in real life to participate and making sure to moderate carefully for any shenanigans is probably the most I can think of off the top of my head, but I do think this is a topic worth investing further collaborative thought in for whatever the moderation team is moving forwards. I would begin by alerting them to the situation and asking what their take on the conflict was. If where they're coming from is understandable but they have a brash tone that is creating friction, I might try to keep an eye out for conflicts with other users and step in to clarify positions and de-muddy waters when necessary. On the other hand, if they're coming from somewhere that is ultimately deemed unreasonable or unworkable for the community by myself and other moderators consulted about the user (moderators would presumably be discussing the situation if it was a repeated issue with flags), I would inform them in a firm but friendly manner that the nature of their current interactions with the site are unacceptable and ask them to recalibrate or risk having punitive action taken against them. If they proceed to cause problems without showing improvement, I would implement short suspensions with explanations initially, and gradually increase the length of suspensions as necessary to get the point across. If nothing seems to work after a significant amount of time trying this process, I would ban the user. I would ask that moderator in private about why they closed the question, and if I disagreed with the closure I would explain why and ask for their take on my opinion. Hopefully we could resolve it between the two of us, either me agreeing that it should have been closed or them agreeing that it can be reopened, but if we're really at a loggerheads I would try to consult other moderators and get a consensus opinion. I would respect whatever that consensus was, irrespective of my own personal opinions. Alec RheaAlec Rhea $\begingroup$ Congratulations on your upcoming nuptials and the move to Ireland! $\endgroup$ $\begingroup$ @AsafKaragila Thank you, I'm pretty excited about it :). $\endgroup$ – Alec Rhea $\begingroup$ Congratulations - Ireland is lovely! $\endgroup$ – Vladimir Dotsenko $\begingroup$ Congratulations on your upcoming marriage! I would like to ask you a question related to your anxiety issue. Of course, this not intended to be personal, but just to understand if it can impact the community in some ways, as moderation implies a lot of interactions with the other users. Feel free not to answer if the question makes you feel uncomfortable. As far as I know, anxiety can be exacerbated by stressful situations. Did you think about ways to cope with this, especially when some potentially stressful situations occur during the controversies among users? $\endgroup$ $\begingroup$ @FrancescoPolizzi Thank you for asking, it is a relevant question. Yes, stressful situations can exacerbate anxiety and historically even social things online could cause me some degree of increased anxiety. Further, my anxiety usually makes me more confrontational as opposed to less confrontational, which would be very bad for moderating. I have considered these things and had to deal with them even as a non-moderator interacting on the site, and I do have coping mechanisms for the stress-inducing times. (cont.) $\endgroup$ $\begingroup$ @FrancescoPolizzi Aside from the obvious, like reminding myself that none of this is personal and that I respect everyone contributing here, I've found that getting married and building a life with my partner has done a great deal to calm my anxiety about... pretty much everything. It's hard not to feel ridiculous stressing about interactions online (and many other small things) when you have a wife to build a future with and kids on the horizon, and this is my ultimate secret weapon against unnecessary anxiety related to moderation. $\endgroup$ $\begingroup$ @AlecRhea: thank you for the thoughtful answers. $\endgroup$ $\begingroup$ This person made some good job with reviews. But Ī̲'d wish to see somewhat more such a good job. $\endgroup$ – Incnis Mrsi $\begingroup$ @IncnisMrsi Thank you Incnis; yes, I agree that I should participate more in review activity and I intend to. I have been having issues with the review interface which has prevented me from participating recently, but I hope to find a solution soon so I can get some hours in. $\endgroup$ I am using my real name. Yes, I think there likely should be such term, though my feeling for this is not strong. Similarly as common in politics, something like 4 or 5 years may be appropriate, with the possibility of re-election. If moderators are elected for an indefinite time, by the time one may perhaps see an increasing number of moderators elected a long time ago, in all stages of becoming inactive. Candidating for re-election means actively offering one's services again, as opposed to merely not stepping back. As to myself -- I'd be happy to serve for a couple of years, quite possibly more. I think the MathOverflow community should be as welcoming as possible to every potential contributor of interesting, on-topic questions or valuable answers to on-topic questions -- no matter whether they initially need guidance or not. On the other hand, I think it should not become 'more inclusive' in the sense of broadening the scope of the site, and it should continue to be not welcoming to people who obviously cannot contribute on-topic posts or who even actively try to disrupt normal operation of the site. Central European Time = UTC + 1 hour in winter and UTC + 2 hours in summer. In my opinion, the specific culture of MathOverflow which gives the site the feeling of a global mathematics department in which experts for every topic can be found and talked to in a friendly atmosphere definitely needs to be preserved. -- It is what makes this site unique, and which gives it most of its value and fascination. I would contribute to the diversity of the moderation team merely by being European. That said -- as I was the one who proposed this question for the last moderator election back in 2013 -- I hesitated to post my candidacy until now in the hope that this time not all candidates would be male again. Preserving the specific culture and atmosphere of the site. Increasing the participation of female colleagues. Increasing the participation of mathematicians from all parts of the world, in particular those which are currently underrepresented. I would appreciate it very much if both genders would be represented more equally in the MO community, and I think the site would clearly benefit from this. When reading the list of users sorted by decreasing number of points, it is depressing how long it takes until one finds the first names who are not clearly male -- and how long it even takes until one finds the first who are clearly female. Unfortunately the reality is that what a moderator can do to change this gender disbalance is relatively limited. -- A moderator can neither change the society, nor the general way the StackExchange software works. Nevertheless, I would at least do the small things which a moderator can do in this respect -- like being kind and welcoming, and whenever there is a good occasion, invite female colleagues to participate. First of all, I would contact them, and kindly explain to them how their behavior is perceived by colleagues. If that doesn't resolve the issue, further steps would depend on the outcome of an exchange of opinions with the fellow moderators and on a careful consideration of all aspects of the case. As to my experience on the site so far, it happens very rarely that a moderator closes / deletes etc. a question which I strongly feel shouldn't have been closed / deleted etc.. In cases of doubt, sometimes I would have tended to decide the other way -- but without strong feelings in that direction. That said, if the described situation should ever occur, I would certainly talk to the fellow moderator about the issue, and see what they and the other members of the moderation team think about the question. Stefan KohlModStefan Kohl $\begingroup$ I didn't find your name in the thread meta.mathoverflow.net/questions/4926/…. By whom have you been suggested? $\endgroup$ – Todd Leason $\begingroup$ @ToddLeason: You don't need to be suggested to nominate yourself or to be a good candidate. $\endgroup$ $\begingroup$ @Stefan Kohl: Concerning quest 1: Do you have a position in academia? $\endgroup$ $\begingroup$ @StefanKohl You are an extremely experienced reviewer of posts on MO, which is fantastic! Could you say a few words about this? What sorts of concerns are at the forefront of your mind when reviewing posts? Has your approach evolved over the years? What have you learned from this work? $\endgroup$ $\begingroup$ As to my experience with reviewing -- there are not much surprising things to be said in general. I didn't make a statistics -- but as likely everyone would expect, a part of the posts appearing in the review queues is good as they are, another part of the posts are good after some polishing or clarification, and yet another part cannot be rescued (e.g. calculus homework, and sometimes spam). Over the years I became more careful with my judgments as to which questions can perhaps still be 'repaired' and be made on-topic, and which really cannot. $\endgroup$ $\begingroup$ What I noticed is that there is a steady stream of questions with no positive and no negative feedback which after a year fall victim to auto-deletion, in a part of the cases likely just due to inappropriate tagging. -- I sometimes went through the list of such questions to see which of them could be improved and should be brought back to attention, and edited and sometimes upvoted them. $\endgroup$ I am using my real name. I am a professional mathematician. I recently started a permanent position. No. I think that moderators should serve for as long as they want, provided that they do a good job. There are protocols in place for moderators to be removed, and these can and should be used when appropriate. But if a moderator is doing a good job overall (even if infrequent a times), that's not a problem. I think that the moderators should lead by example. But I think that the moderators' role is probably more focused on making sure that users with history of harassment are dealt with, since this is in part the main power difference of moderators from standard users. In the context of MO, however, inclusiveness can also be understood as also being more welcoming to graduate students and perhaps advanced hobbyists. This is a razor thin line, and I think that the moderators' role here is probably more fundamental in shaping policy via meta discussions. UK timezone. But I'm active most of the time. I am a very firm believer that the culture of MathOverflow is great, and that it should keep this identity rather than becoming a "more normative SE site". That means allowing somewhat more open-ended questions, for example. At the same time, we need to remember that as time passes by and the community grows bigger the culture changes. From a village to a town to a city. Nevertheless, I think we can preserve this culture. But this requires participation from all the core members of the community, not just the moderators. So far we're doing a good job. I lived in Israel until I finished my Ph.D., so my cultural background is very different from those who grew up in the English speaking world. I think that with respect to the current moderator team, I'm a "generation younger", at least in academic terms. The preservation of the unique community that we have here. I wrote more in the answers to questions 3 & 5. Yes, and I think that women are underrepresented in the mathematical community to begin with. I think it's a problem for the same reason that the low numbers of women in mathematics is a problem. Unfortunately, I don't think there is a lot that a moderator can do about it. We can, should, and presumably do remove content that can be viewed as offensive (e.g. some jokes from the old math jokes thread), and we should try to make the site more hospitable. But having a nice restaurant is not enough to guarantee that people show up to buy the food. If this is a continuing issue, escalate in the standard procedure of warnings and suspensions. If this is a relatively new issue, I'd try to contact them first to see if everything is okay or if something happened. I've experienced that before on Math.SE. The solution is simple: open communications. Unless something is in a time crunch, don't override other moderators without discussing it first. Tim Campion asked: I understand that you are a moderator and extremely active user at MSE, while also being an active and respected member of the MO community. Could you expand a bit on the similarities and differences between MO and MSE, both in general, and with regard to the way you personally use them? If elected moderator, how would you split your time between the two sites? Also: for how long have you been a moderator at MSE? Let's start from the top. Both sites are of course sites about mathematics, but MathOverflow is a site [mainly] for professional mathematician. We should, of course, be welcoming to everyone, but the main target crowd is professional mathematicians (academic or otherwise). As such, MO is much more a friendly interaction between colleagues, whereas MSE is closer to office hours, in some extent. (Of course, in reality neither is an accurate description and many exceptions on both ends of the spectrum can be easily found on both sites.) In terms of my personal usage the most striking difference is that I hardly ask questions on MSE at this point. I find it easier to answer questions on MSE, simply by sheer volume of questions and their level (where I can easily pull an answer out of a hat, as opposed to thinking about it for longer in the case of MO). Finally, if elected moderator, the time splitting is not going to be any different. I tend to check both sites very very often most of the time. I will simply have more to interact with on this site, even when there's no new set theory questions for me to look at. I've been a moderator on MSE for just over two and a half years now. I expect the moderation on MO to be very different: less intense in volume, but perhaps more intricate in the subtle issues as dealing with people. Asaf KaragilaModAsaf Karagila $\begingroup$ Congrats on the permanent position! $\endgroup$ – Noah Snyder $\begingroup$ Thanks :) ${}{}$ $\endgroup$ $\begingroup$ Would you plan to continue making jokes as a moderator? I enjoy some of the jokes around here, but I think from a moderator they'd be unhelpful. E.g. mathoverflow.net/questions/378692/… $\endgroup$ – Matt F. $\begingroup$ @Matt: Probably, yes. Maybe to a lesser degree, but I think that some humour in the comments is a good thing. I think that part of the independent sense of community we have here is due to the lax settings in which jokes can be made, and I don't think this should change (regardless to whether or not I'm elected). $\endgroup$ $\begingroup$ Frankly, I'm not sure how to interpret the downvotes. Are they telling me to withdraw from the race? Is there a specific disagreement? Is it because I dared exercise my right as a user and engage with a candidate? $\endgroup$ $\begingroup$ the way I would interpret them, is that a confrontational attitude is totally OK for a regular user, but it is not what we would expect from a moderator (as the name says: a person who moderates = mitigates/restrains) $\endgroup$ $\begingroup$ @Carlo: Someone needs to ask questions. I don't know some of the other candidates well enough, and I also want to vote in this election. What happened to due diligence? $\endgroup$ $\begingroup$ I assume whoever downvoted this answer, simply upvoted another one. Which means showing support for that candidate's nomination. So it doesn't seem to be a big deal. By the way, you have done a good job on MSE imo. I sometimes feel uncomfortable with the jokes and sarcasm in your comments. But overall, I think your pros outweigh the cons by a fair margin. Good luck! $\endgroup$ – polfosol $\begingroup$ @polfosol: Thanks. I find it odd to downvote one over the other since there are three seats open in this election. We're far from competing for votes here. Which, again, had me confused. $\endgroup$ $\begingroup$ @Yemon: There's no real written rule. If you support a candidate, and you think they wrote compelling answers to their questions, upvote. If you think they did a bad job answering those questions, downvote. If you're not sure, don't vote. These answers have no real bearing on the election itself, but they do signal something about the support to the nominee. As for the actual election, you have three votes and you rank your top three candidates, the voting is an STV method and in this case (three candidates) I think it practically means you vote for the three people you want in. $\endgroup$ $\begingroup$ @AsafKaragila That's not quite correct, either in this specific case or in general - Voters have a single vote but they may choose who to award it to in a cascading order - it's Single Transferable vote. And, while you're correct that in the past you were able to only rank your top three choices, this election will be the first on the network where you can rank all candidates you wish to support, not merely the top three. $\endgroup$ $\begingroup$ @Catija: You have blown my mind. And the dominoes that fell from the shockwave made sense in the whole idea of STV. So double-thanks! $\endgroup$ $\begingroup$ @Catija I hope this voting method is clearly explained on the voting page; this seems important information. $\endgroup$ – Federico Poloni $\begingroup$ @FedericoPoloni You can see the current version (that aligns with the current default of three slots to rank your choices) on the election tab of the election - mathoverflow.net/election/2?tab=election There are some links to outside resources there, too. Meeks STV is a fairly standard methodology. The new voting page will be up on Monday as the election transitions into the voting phase (provided we don't end up with a primary). It will have some new text explaining that you may rank as many as you choose but cautioning you to only vote for candidates you think would be good mods. $\endgroup$ $\begingroup$ However you interpret these downvotes, please don't withdraw from the race, and please don't try to change your local attitudes. Imo a mod like you would be good for health of this place. $\endgroup$ – მამუკა ჯიბლაძე This site is for discussion about MathOverflow. You must have an account there to participate. 2021 Moderator election: suggestions for nominees? 2021 Moderator Election Q&A - Question Collection MathOverflow updated site theme is ready for testing! Nudge: the new Stacks editor has significant implications for this site What do moderators do these days? Can't submit edit review 2013 Community Moderator Election 2021 Community Moderator Election Results 2022 Moderator Election Q&A – Question Collection	CommonCrawl
Home Journals EJEE Life evaluation method for alternating current contactor of electrical multiple unit Submisssion Achive Life evaluation method for alternating current contactor of electrical multiple unit Feng Kong \| Haiming Shi \| Zhiyuan Wei \| Changying Liu* Changchun Railway Vehicles Co., Ltd, National Railway Engineering Research Center, Changchun 130000, China Central South University, Changsha 410083, China College of Instrumentation & Electrical Engineering, Jilin University, Changchun 130000, China [email protected] https://doi.org/10.3166/EJEE.19.31-42 https://ejee.revuesonline.com/accueil.jsp With the aid of the Weibull distribution analysis for contactor life, this paper attempts to accurately evaluate the service life of the alternating current (AC) contactor of electrical multiple unit (EMU). Specifically, the structure, working principle and failure mechanism of EMU AC contactor were determined, and the failure mode of AC contactor was identified, together with its judgment basis. On this basis, the author built a simulation system for EMU AC contactor life evaluation in light of the requirements of the evaluation task. Then, the reliability of EMU AC contactor was evaluated by Weibull distribution method. The results on contactor life and reliability show that the proposed method enjoys high feasibility and satisfies the technical requirements of EMU maintenance for AC contactor service life assessment. The research findings provide strong technical support to EMU operation and maintenance. electrical multiple unit (EMU), service life assessment, failure mechanism, Weibull distribution; alternating current (AC) contactor High-speed EMUs have the advantages of rapidity, convenience, comfort and safety. They are playing an important role in people's travel activities. The fast, stable and safe operation of the vehicle is related to the safety of people's lives and property, so it has special requirements for its reliability, availability, maintainability and safety. AC contactor is one of the most widely used auxiliary devices in high-speed motor vehicles. Its reliability and service life are directly related to the operation stability, safety and cost of vehicles. Therefore, it is very important to study its reliability and service life, and provide reliable technical support for vehicle operation and maintenance. The life test of electrical appliances is an important process to evaluate the life of contactors. Domestic and foreign research institutes have always attached great importance to the research of test methods and devices. Since the 1960s, scientists and technicians in various countries have developed computer-based testing techniques and devices for automatic measurement and data processing of the performance parameters of contactors, and for testing the contact reliability and mechanical life of contactors (Schoepf et al., 2009). In recent years, contactor service life detection device based on virtual instrument technology has been developed to realize real-time on-line detection of dynamic performance parameters of contactor (Tang & Su, 2008). Although a great deal of research work has been done on AC contactor life test at home and abroad, the research on AC contactor life of high-speed EMUs is still in the initial stage, and there is no fully formed reliable technology and device available. A service life evaluation method for AC contactor of high speed EMUs is presented in this paper. 2. Failure mechanism analysis of AC contactor of EMU 2.1 AC contactor structure and working principle AC contactors can be mainly divided into electromagnetic mechanism, contact system, arc extinguishing device and other components (Yuan & Gao, 2008). Wherein, the electromagnetic mechanism is composed of a coil, a moving iron core (armature iron) and a static iron core; the contact system is composed of a main contact and an auxiliary contact. The specific structure is shown in Figure 1. When the contactor is working, the coil electrifying causes the static iron core to produce the electromagnetic suction, overcomes the spring reaction force, causes the moving armature to drive the contact mechanism to the static contact movement, realizes the dynamic contact and the static contact closing, completes the contactor closing action, the circuit is connected. When the coil is powered down, the spring reaction force causes the moving armature to drive the contact mechanism to return to its original position, the moving contact and the static contact are separated, the release action is completed, and the circuit is disconnected (Yang & Yang, 2011). 1.Main contact 2. Normally closed auxiliary contact 3. Normally open auxiliary contact 4. Moving iron core 5. Coil 6. Static iron core 7. Arc shield 8. Spring Figure 1. Structure diagram of AC contactor 2.2. Failure mode of AC contactor As defined in the national standard GB3187-82, failure means that the product loses the specified function, and the product failure mainly emphasizes the functional state of the product (Leung & Streicher, 2002; Pecht & Dasgupta, 1995). Product failure analysis is to conduct in-depth physical, chemical, and use of the product analysis. The failure mode of products mainly refers to the external visual failures, cash realisation forms and process rules of products. The failure modes of electrical products are mainly embodied in physical structure failure, performance failure and contact failure. Failures of physical structures, such as structural loosening, part breakage, coil breakage and short circuit, can be determined by physical analysis. The main performance failure phenomena are the increase of closed voltage/current, the decrease of disconnection voltage/current, the increase of contact resistance, the inflexibility of operation and the abnormal time parameters. Contact failure is caused by abnormal electrical parameters of contacts and frequent failures of products due to a combination of factors such as humidity, temperature and vibration. In this paper, through in-depth study and analysis of the working characteristics of the AC contactor, the contact failure of the contactor is determined as the final failure form to evaluate the reliability of the contactor. The contactor pressure drop value is taken as the static parameter of its reliability determination, and the contactor pressure is observed. The trend of the measured value is measured to determine the reliability of the contactor and the life expectancy. 2.3. Analysis and criterion of contact failure mechanism of AC contactor There are many reasons for the contactor failure. The failure mechanism analysis of the contactor is to analyze the failure mechanism of the contactor during the service life test. The failure mechanism of contactor can be divided into hard failure mechanism analysis and soft failure mechanism analysis. The hard failure of AC contactor is mainly due to the unreliable operation of its closure and disconnection. The hard failure of the contactor will be caused by the influence of the structural parameters of the contactor, the material of the contactor and the external environment factors, and the erosion of the contact surface by the arc during the working process. When the contactor can still complete the function of disconnection and closure, but its contactor voltage drop and open circuit voltage have obvious change trend, contactor soft failure occurs. Figure 2 is a classification of failure modes and hard failure mechanisms of AC contactors in an action cycle. Figure 2. Failure mode and hard failure accumulation classification diagram The EMU AC contactor life evaluation test studied in this paper collects the dynamic waveform data of the current and voltage signals of the coil and the contact during the closing and opening process of the contactor, and calculates the arcing time by processing the waveform data obtained by the analysis. And performance parameters such as bounce time to determine the soft failure. The failure criterion is an important factor in the life assessment and reliability determination test. Different failure criteria in the same test process will make the test conclusions different. Therefore, it is of great significance to determine failure criteria reasonably in the service life evaluation test. In this paper, through the in-depth study and analysis of the failure mode and failure mechanism of the contactor, the following methods are used as the basis for judging the failure of the test product during the test: - Contact pressure drop of the closed contact Uj>5%Ue; - Disconnect the voltage between the contacts Uj>90%Ue; - Contact occurs in fusion or other forms of bonding; - The contactor coil does not act when the coil is energized. - Contactor coil does not return when power fails. - Defective damage to test parts, loose connecting wires and parts. - Mechanical components are blocked and stuck. - After the contactor is energized, there is obvious noise. After testing, the test results of any item are not in conformity with the product standards. 3. Design of contactor service life simulation system 3.1. Hardware system design The service life simulation system of EMU contactor is the precondition of system function realization. The system composition and realization method directly determine the operation principle and performance of the system. Figure 3. System composition principle During the simulation test of EMU contactor service life, it is necessary to control the contactor sample to close and disconnect automatically according to the requirement. At the same time, it is necessary to collect the voltage and current of the coil and the main contact during the load on-off process quickly, real-time and accurately. The system is mainly composed of master computer, data acquisition circuit, signal conditioning circuit, coil drive circuit, PLC control circuit, load circuit and input power excitation. As shown in Figure 3. (1) The main control computer is the control core of the test system. Each part of the control system works according to a certain time sequence and order, and processes, analyzes and judges the collected data information. (2) The coil drive circuit is mainly composed of a PLC and a solid state relay. The digital I/O port of the PLC is used to control the on/off action of the solid state relay, thereby controlling the contactor to perform the closing and opening operations according to the set operating frequency. (3) The data acquisition circuit takes the data acquisition board as the core, and carries out real-time and high-speed acquisition of the data obtained by amplitude transformation and filtering of the conditioning circuit. (4) The coil drive circuit drives the contactor coil to generate electricity and generate electromagnetic attraction force, which drives the contactor movable contact to perform closing and opening operations. The action of the contactor is controlled by the controllable switch, and the controllable switch has a certain load carrying capacity. (5) Signal conditioning circuit converts the signal that the system needs to collect into the voltage signal acceptable to the data acquisition circuit, and has some filtering function. 3.2. Software system design Figure 4. Software block diagram The software of AC contactor service life simulation system for EMU is developed on the basis of LabVIEW environment under Windows operating system. Based on the structure of hardware system and according to different service life simulation test modes, the simulation test of contactor under various service conditions is realized. The software system designed in this paper includes test conditions and parameters setting, failure mechanism discrimination, service life prediction and reliability evaluation. As shown in Figure 4. 4. Contactor life Weibull distribution analysis Through the mathematical analysis of the reliability of the product, the distribution of product life is found out from the results of mathematical statistics analysis, and the rationality of life distribution can be judged by comparing it with the phenomenon and cause of failure. In this paper, the Weibull distribution method is used to evaluate the service life of the contactor. 4.1. Point estimate of the parameter In product reliability analysis techniques, the failure distribution type is the failure time distribution function. Many reliability feature quantities are closely related to the failure function density, and the parameter estimation method can be used to solve the reliability feature quantity (Zuo et al., 1999; Marković et al., 2009). Natural logarithmic form of Weibull function $\ln [\ln \frac{1}{1-F(t)}]=m\ln t-m\ln \eta $ (1) where $y=\ln [\ln \frac{1}{1-F(t)}]$, x=lnt, a=m, b=-mlnη, then equation 4.1 is converted to $y=ax+b$ (2) Using the method of median rank and fitting straight line, the parameter values of Weibull are calculated by least square estimation of regression coefficients $\overset{\wedge }{\mathop{a}}\,$ and $\overset{\wedge }{\mathop{b}}\,$. If the error between Equation 4.2 and the test value is the smallest, then it must be satisfied: $Q=\sum{{{({{y}_{i}}-a{{x}_{i}}-b)}^{2}}}=\min $ (3) Then parameters a and b should satisfy: $\left\{ \begin{align} & \frac{\partial Q}{\partial a}=-2\sum\limits_{i=1}^{r}{{{x}_{i}}}({{y}_{i}}-a{{x}_{i}}-b)=0 \\ & \frac{\partial Q}{\partial b}=-2\sum\limits_{i=1}^{r}{{{x}_{i}}}({{y}_{i}}-a{{x}_{i}}-b)=0 \\\end{align} \right.$ (4) Solutions have to $\left\{ \begin{align} & a=\frac{n\sum\limits_{i=1}^{r}{x{}_{i}{{y}_{i}}}-\sum\limits_{i=1}^{r}{x{}_{i}}\sum\limits_{i=1}^{r}{{{y}_{i}}}}{r\sum\limits_{i=1}^{r}{x_{i}^{2}-{{(\sum\limits_{i=1}^{r}{x{}_{i}})}^{2}}}} \\ & b=\frac{1}{n}\sum\limits_{i=1}^{r}{{{y}_{i}}-\frac{a}{n}\sum\limits_{i=1}^{r}{x{}_{i}}} \\\end{align} \right.$ (5) $\left\{ \begin{align} & m=a \\ & \eta ={{e}^{-(\frac{b}{a})}} \\\end{align} \right.$ (6) A. Interval estimation of parameters Since the parameter satisfies m=1/σ, η=eμ, the given confidence level is γ, due to $\gamma =P\left\{ {{\omega }_{(1+\gamma )/2}}\le \frac{\overset{\wedge }{\mathop{\sigma }}\,}{\sigma }\le {{\omega }_{(1-\gamma )/2}} \right\}=P\left\{ {{\omega }_{(1+\gamma )/2}}/\overset{\wedge }{\mathop{\sigma }}\,\le m\le {{\omega }_{(1-\gamma )/2}}/\overset{\wedge }{\mathop{\sigma }}\, \right\}$ (7) Therefore, the confidence interval for the parameter m is $[{{\omega }_{(1-\gamma )/2}}/\overset{\wedge }{\mathop{\sigma ,}}\,{{\omega }_{(1+\gamma )/2}}/\overset{\wedge }{\mathop{\sigma }}\,]$ (8) Similarly, for a given confidence level of γ, using the confidence interval of the parameter $\mu $, the confidence interval for the confidence level of the parameter η is γ. $[\exp (\overset{\wedge }{\mathop{\mu }}\,-\overset{\wedge }{\mathop{\sigma }}\,{{\upsilon }_{(1+\gamma )/2}}),\exp (\overset{\wedge }{\mathop{\mu }}\,-\overset{\wedge }{\mathop{\sigma }}\,{{\upsilon }_{(1-\gamma )/2}})]$ (9) $\overset{\wedge }{\mathop{\sigma }}\,=\underset{i=1}{\overset{r}{\mathop{\sum }}}\,C(n,r,i)\ln {{t}_{i}},\overset{\wedge }{\mathop{\omega }}\,=\underset{i=1}{\overset{r}{\mathop{\sum }}}\,D(n,r,i)\ln {{t}_{i}}$. 4.2. One-sided confidence limit for reliable life and reliability When the product is subject to the Weibull distribution, the corresponding reliable lifetime for a given credibility is: ${{t}_{R}}=\eta {{(-\ln R)}^{1/m}}=\eta {{(-\ln R)}^{\sigma }}=\exp [\mu +\sigma \ln (-\ln R)]$ (10) $V(R)=\frac{\overset{\wedge }{\mathop{\mu }}\,-\ln {{t}_{R}}}{\overset{\wedge }{\mathop{\sigma }}\,}=\frac{\overset{\wedge }{\mathop{\mu }}\,-\mu -\sigma \ln (-\ln R)}{\overset{\wedge }{\mathop{\sigma }}\,}=\frac{\overset{\wedge }{\mathop{\mu }}\,-\mu }{\overset{\wedge }{\mathop{\sigma }}\,}-\frac{\sigma }{\overset{\wedge }{\mathop{\sigma }}\,}\ln (-\ln R)$ (11) It can be seen that the random variable V(R) is the axial pivot of the reliable life tR, and the standard random distribution of n random numbers U1,U2,…Un is generated on the computer, where n is the sample size of the fixed censored life test, and the simulation is performed by the Monte-Carlo method. The distribution of the axis pivot amount V(R), while obtaining the confidence level of its tR confidence level is γ: ${{t}_{RL}}=\exp [\overset{\wedge }{\mathop{\mu }}\,-\overset{\wedge }{\mathop{\sigma }}\,{{\omega }_{1-r}}(R)]$ (12) For a given time td, let xd=lntd, therefore have $\begin{align} & \ln [-\ln \overset{\wedge }{\mathop{R}}\,({{t}_{d}})]=\frac{{{x}_{d}}-\overset{\wedge }{\mathop{\mu }}\,}{\overset{\wedge }{\mathop{\sigma }}\,}=\frac{\sigma }{\overset{\wedge }{\mathop{\sigma }}\,}(\frac{{{x}_{d}}-\mu }{\sigma }-\frac{\overset{\wedge }{\mathop{\mu }}\,-\mu }{\sigma }) \\ & =\{\frac{\overset{\wedge }{\mathop{\mu }}\,-\mu }{\overset{\wedge }{\mathop{\sigma }}\,}-\frac{\sigma }{\overset{\wedge }{\mathop{\sigma }}\,}\ln [-\ln R({{t}_{d}})]\}=-{{V}_{[R({{t}_{d}})]}} \end{align}$ (13) Obtained by the above formula ${{V}_{R({{t}_{0}})}}=\frac{\overset{\wedge }{\mathop{\mu }}\,-{{x}_{d}}}{\overset{\wedge }{\mathop{\sigma }}\,}$ (14) When the significant level is 1-α, use the quantile table of V1-p to find the values of two VR(td) adjacent to V1-p,1-α, and then use linear interpolation to find the RL(t) corresponding to VL(td). 5. Experiment and data analysis In order to verify the feasibility of the EMU AC contactor life evaluation method proposed in this paper, the service life evaluation simulation experiment was carried out on the EMU AC contactor by using the built system, and the life assessment analysis was carried out. The contactor model used in the experiment is LC1-D 0910. Figure 5 shows the AC contactor main contact and coil voltage and current waveform signal acquisition. Table 1 shows the reliability life prediction distribution table of the high-speed motor AC contactor. Through the analysis of the experimental data, it can be seen that the reliability of the AC contactor of EMU can approach 100% for 100 000 times, almost without failure. The reliability of the action is more than 60% in the one million time. With the increase of the number of actions, the reliability decreases quickly. After 2 million actions, only 10 may be left at work, almost all of them fail. Take the frequent action of the system door control and air conditioning 100 times a day as an example, to ensure the reliability of more than 60%, it can work for 10,000 days. Figure 5. AC contactor main contact and coil waveform measurement results Table 1. EMU AC contactor reliability life prediction distribution table Life h Aiming at the requirement of correctly predicting the service life of AC contactor in EMU operation and maintenance, this paper presents a simulation method for the service life of AC contactor in EMU. Firstly, the failure mechanism of AC contactor of EMU is studied and analyzed. Then the service life simulation platform of AC contactor of EMU is built. Then the reliability evaluation method of contactor based on Weibull distribution method is studied. Finally, the feasibility of the proposed method is verified by experiments. Leung C., Streicher E. (2002). Material transfer in dynamic welding of Ag and Ag/SnO2 contact material. Proceedings of the 48th IEEE Holm Conference on Electrical Contacts, pp. 21-28. https://doi.org/10.1109/HOLM.2002.1040818 Marković D., Jukić D., Benšić M. (2009). Nonlinear weighted least squares estimation of a three.parameter weibull density with a nonparametric start. Journal of Computational and Applied Mathematics, Vol. 288, No. 1, pp. 304-312. https://doi.org/10.1016/j.cam.2008.09.025 Pecht M., Dasgupta A. (1995). Physics.of.failure: An Approach to Reliable Product Development. Journal of the Institute of Environmental Sciences, No. 38, pp. 30-34. https://doi.org/ 10.1109/IRWS.1995.493566 Schoepf T. J., Boudina A., Rowlands R. D., Repp B. T. (2009). Pre.conditioning automotive relay contacts to increase their resistance to dynamic welding. IEICE Transactions on Electronics, Vol. 90C, No. 7, pp. 1441-1447. https://doi.org/10.1093/ietele/e90-c.7.1441 Tang J., Su T. S. (2008). Estimating failure time distribution and its parameters based on intermediate data from a wiener degradation model. Naval Research Logistics, Vol. 55, No. 3, pp. 265-276. https://doi.org/10.1002/nav.20280 Yang Y., Yang X. (2011). Electronic equipment reliability test. Digital Communication. Vol. 38, No. 6, pp. 66-69. https://doi.org/10.3969/j.issn.1001-3824.2011.06.018 Yuan X. Q., Gao P. (2008). Talking about the structure, application and development of AC contactor. Electrical Manufacturing, Vol. 2008, No. 1, pp. 34-36. https://doi.org/10.3969/j.issn.1673-5471.2008.01.006 Zuo M. J., Jiang R. Y., Richard C. M. Yam. (1999). Approaches for reliability modeling of continuous.state devices. IEEE Transactions on Reliability, Vol. 48, No. 1, pp. 9-18. https://doi.org/10.1109/24.765922	CommonCrawl
Sunday, June 30, 2019 ... / / Sane, genuine libertarian system wouldn't enable peaceful mass migration Last night, I accidentally watched Soph's gaming streaming channel – again, for an hour – and while I didn't find it too important that Kabbalah in Minecraft has frozen over, I did want to learn something new. And it's just my conclusion that this 15-year-old girl is more likely to teach me new things about politics, society, and Generation Z than the likes of Ben Shapiro or even Jordan Peterson. First of all, she must share some rare genes with me – I would like to know what they are. It's not just about the identical views on political issues but also the authentic, natural individualism, lack of desire to integrate into herds, and the related pattern of smiles and non-smiles and many other things. OK, fine, so she has often agreed to be called a libertarian. So have I. It's normal. We're supporters of the individual freedoms, abolition of the government, and stuff like that. It's somewhat accidental that this label gets appropriate at some point – classical liberalism has meant almost the same thing but the term "liberalism" has been hijacked by the far left, anti-liberal folks. In the U.S., libertarians often look like a minority of fringe whackos which is strange because as I see it, much of America has been built on libertarianism. Other texts on similar topics: freedom vs PC, politics Higgs mass from entropy maximization? As you know, the Higgs boson is the most recently discovered fundamental particle (next Thursday, it will be 7 years from the discovery) and its mass seems to be $m_H=125.14\pm 0.24\GeV$ or so. In various models, supersymmetric or scale-invariant or otherwise, there exist partial hints why the mass could be what it is and what this magnitude qualitatively means. Reader T.G. had to be blacklisted because he was too vigorous and repetitive in defending the highly provoking 2014 Brazilian paper Maximum Entropy Principle and the Higgs Boson Mass (by Alves+Dias+DaSilva, about 12 citations now) which claims to calculate the almost identical value $125.04\pm 0.25\GeV$ using a new assumption, entropy maximization. What are they doing? Look at this chart which they omitted, for unknown reasons, so this blog post is more comprehensible than the paper. The horizontal axis is the Higgs boson mass $m_H$ and the vertical axis shows the branching ratios of Higgs decays – the probability that the Higgs decays to some final products or others. You may see that near the observed value $m_H \sim 125\GeV$, there are relatively many decays that are relatively close to each other. None of them is dominant and beating all others etc. Other texts on similar topics: LHC, string vacua and phenomenology Saturday, June 29, 2019 ... / / Boss of "miraculous socialist" farm JZD Slušovice died A Czechoslovak communist company was a source of universal admiration and was considered a miracle. I think that you're really among the first non-Czechoslovak people who learn something about that phenomenon – which may be interpreted as a sign of the director's (and/or Czechs') amazing skills or as an example of the truly bizarre anomalies that the suppression of the free markets sometimes creates. Most recently, František Čuba (1936-2019) was a Czech Senator for President Zeman's small party, SPO (formerly SPOZ). That agronom, pedagogue, and politician has been mostly known as the director of JZD Slušovice, the most famous farm of the Soviet bloc. Čuba, a communist cadre, has been the boss of JZD Slušovice (founded in 1952) since 1963 (when he was a 28-year-old ambitious commie) but it was the last years of communism in which the success of JZD Slušovice became stunning. Other texts on similar topics: Czechoslovakia, markets Friday, June 28, 2019 ... / / Smolin's wrong and vacuous would-be philosophical slogans Amanda Gefter has written a text for the Quanta Magazine How to Understand the Universe When You're Stuck Inside of It attempting to persuade the reader that Lee Smolin has a "radical idea". She hasn't convinced me. Instead, I want to explain why the physics value of this would-be philosophical talk is at most zero. First, the subtitle says: Lee Smolin has a radical idea for how to understand an object with no exterior: Imagine it built bit-by-bit from relationships between events. OK, building the Universe from relationships is nothing new let alone radical. To one extent or another, numerous well-established insights as well as numerous proposed extensions of the status quo may be said to match these vague words. Special relativity says that most quantities, including time, are relative and depend on the chosen reference frame. Only some invariants – such as the relative speed between two observers – are absolute. Because we need two observers to define their relative speed, we may say that it's their relationship that is the "actually real" information according to relativity. John Wheeler has talked about "It from Bit" which is a similar sequence of words as those above. Phil Gibbs has proposed – much more mathematically concrete – event-symmetric spacetime where the information has to be invariant under all permutations of spacetime points. We could enumerate tons of people who have said various things about "relational" descriptions of the world, starting with Leibniz. The value added by Lee Smolin is non-existent. Also, he seems to share the misconception that Nature's information is naturally divided to bits, binary digits. It's not. A bit is a very unnatural measure of the information – we could say a man-made or an anthropogenic one. Information comes in continuous quantities in Nature and the natural unit is one nat. Twitter's Trump rule, Putin+Dalai Lama against multiculturalism Donald Trump is having a good time at G20. In this video, a left-wing U.S. journalist "asked" Trump: "Will you tell Putin not to meddle in the 2020 elections?" But for Trump, a good entertainer, it was more than a rhetorical question. He said "Of course I will", turned to Putin, and told him "Don't meddle in the 2020 elections". ;-) I think that Putin liked the stunt, too. Russians aren't this good at similar American humorous responses. There are objective reasons why Hollywood is still ahead of Volgawood. Some left-wing talking head at CNN seemed utterly shocked by Trump's response – it was a "fact stranger than fiction". Not really. It was a witty reaction to an annoying repetitive conspiracy theory and in a very pleasant, friendly way, Trump has expressed the view or the fact that the conspiracy theory and its believers are dumb. Meanwhile, Trump told Sánchez to sit down and the Spanish prime minister smiled and complied. Much of the Spanish press was hysterical about that "humiliation", too! Again, Trump's theater was mostly a joke but there was an underlying alpha-male reality behind it – alpha-male reality elevating both Trump personally and the U.S. That's how America is led today, get used to it. Other texts on similar topics: freedom vs PC, politics, Russia A three-parameter jungle of F-theory Standard Models I want to mention two cool new papers now. First, a paper showing that natural supersymmetry is alive and well. The current status of fine-tuning in supersymmetry Melissa, Sascha Baron-Cohen (Borat), and Roberto (Holland+Kazakhstan+Spain – and I've sent a few more people to arXiv.org again LOL) have analyzed the degree of fine-tuning in supersymmetric models using two widely accepted formulae. They found out that totally natural SUSY models are compatible with the LHC exclusion limits – the degree of fine-tuning is just 3-40 or 60-600 for low-scale measure or high-scale measure, respectively. The models get particularly viable if you look at the pMSSM (phenomenological minimal supersymmetric standard model – parameterized by a limited number of parameters close to the observations; I think it should have been expected) and the pMSSM-GUT is doing much better in fine-tuning than other GUT models. And when the fine-tuning depends primarily on the higgsino mass which may still be very low, and it's possible in huge regions of the parameter space, the fine-tuning may be very low. Tons of writers if I avoid the more accurate term "lying or deluded inkspillers" have persuaded some 97% of the Internet users who care – it's my estimate based on the comments I am receiving – that the LHC has excluded natural supersymmetry. Well, the calculations in the actual experts' papers show something very different. This 39-page-long paper with 9 MB of graphs concludes in the abstract: "We stress that it is too early to conclude on the fate of supersymmetry/MSSM, based only on the fine-tuning paradigm." So when someone tells you that the LHC has said something fatal about supersymmetry or naturalness, don't forget you are being lied to. Other texts on similar topics: mathematics, string vacua and phenomenology Top female German left-wing politicians plan a semi-ban of SUVs Echoing the self-confidence of Adolf Hitler's, these fundamentally misguided individuals would love to impose it on all of Europe These days, Germany's politics is largely controlled by the people whose skulls are filled with sawdust. But things will be worse if and when the truly left-wing parties take over Germany. Material scientists among the TRF readers are urged to figure out what is worse than sawdust. For years, we mocked the unhinged green extremists' for their efforts to demonize the sports utility vehicles, the SUVs. Those were killing the planets, right? We allowed the unhinged people to be legitimized and many of them can already pretend to be mainstream. They are no longer satisfied with demonizing SUVs; they want to mostly ban it. Three days ago, Die Welt (German) described a plan of some top ladies in all the three main German left-wing parties. See stories in Jalopnik (English) and Autoforum (Czech) for some coverage in more friendly languages. Other texts on similar topics: cars, climate, Europe, science and society Wednesday, June 26, 2019 ... / / Are feeling-based popular articles about symmetries helpful? K.C. Cole is one of the better science writers – who is surely choosing better sources for her texts than almost all other writers about physics – and she just published a new text in the Quanta Magazine: The Simple Idea Behind Einstein's Greatest Discoveries The title is friendly towards symmetries, as you can see, and many parts of her text try to suggest details about the importance of symmetry in the 20th and 21st century physics. The subtitle is unfriendly, however: Lurking behind Einstein's theory of gravity and our modern understanding of particle physics is the deceptively simple idea of symmetry. But physicists are beginning to question whether focusing on symmetry is still as productive as it once was. I concluded that the real intended story is that the symmetries are no longer considered as fundamental as they used to be. And I think that such a statement would be correct – although this transition wasn't really taking place in 2019 but rather in the 1990s or 1980s. However, I don't think that the body of Cole's article actually contains evidence that a rational reader could consider a justification of her subtitle. Other texts on similar topics: mathematics, string vacua and phenomenology, stringy quantum gravity Greenpeace girls invaded a shareholders' meeting, faced a backlash ČEZ, the Czech Energy Works (České energetické závody), is the main Czech power utility company. It runs most of the Czech power plants, a big part of the grid, also sells gas to the consumers, and does other things. It's just sold its business in Bulgaria but it is generally trying to invest abroad, too. The market cap of ČEZ is some $12 billion. OK, today, we have the warmest day of the year so far, with temperatures reaching 35 °C – it seems unlikely that the "absolute" records will be broken today, as promised yesterday; in August 2012, Dobřichovice near Prague saw 40.4 °C. Next week, the temperature high should be just 25 °C. (Update: Pilsen-Bolevec, 2 miles from me, saw Czechia's highest temperature today, 37.9 °C. The absolute Czech record safely survived.) PM Babiš is going to survive another no-confidence vote. And ČEZ has a shareholder's meeting, also deciding about the dividend. ČEZ is also planning to sell Počerady, a brown coal power plant, to the billionaire and "coal baron" Mr Pavel Tykač – which would extend its lifetime – according to an agreement from 2013. Greenpeace Czechia doesn't seem to like it. Other texts on similar topics: climate, Czechoslovakia, Europe, Kyoto, politics, science and society Taxonomic ranks: lots of arbitrary conventions but also some real useful information Quanta Magazine's Christie Wilcox has talked to comparative biologist Andreas Hejnol and others when she was writing What's in a Name? Taxonomy Problems Vex Biologists In 1735, Carl von Linné (1707-1778) published Systema Naturae where he introduced the clumping of species into groups and subgroups. That was done more than a century before the evolution theory emerged – but Linné has surely noticed some "family relationships" between organisms on Earth which could have allowed him to rediscover Darwin's theory well before others. The English names of these categories are memorized by the poem Dear King Phillip Came Over For Great Spaghetti While Queen Elizabeth Always Prefers To Devour the Nuts in the Living Room OK, the female part was added by your humble correspondent because of affirmative action (but the assertion is more accurate than the proposition about her husband). The categories are domain, kingdom, phylum, division, class, order, family, genus, species which is almost exactly copied from Latin: regio, regnum, phylum, divisio, classis, ordo, familia, genus, species. Note that a "family" and others are sometimes generalized to "superfamilies" and "subfamilies" or "infrafamilies", groups that are larger or smaller or much smaller than the original ones. Only the first two ranks in the list above, domain and kingdom, are slightly different in English and Latin. The others are Anglicized versions of the Latin words – in the last cases (genus, species), they are completely identical. The first words related to the empires are a bit different in Latin. English biologists could have picked "region" and "reignerdom" to follow the Latin roots chosen for the kings (yes, Russians use "tsarstvo" for the kingdom, from a Tsar). Other texts on similar topics: biology, science and society Tuesday, June 25, 2019 ... / / George Rosenkranz: 1916-2019 Guest blog by Charles Wilson George Rosenkranz has died and, if you needed a reminder, Great Lives are lived fully, taking what is presented and Apprehending what is given – using that word in a very acquisitive sense. The mind does not float above the world of "Mere Appearances". It is an agent in this world and actively engages the surroundings. Rosenkranz and his associates changed the world. When I taught High School Math (A fellow teacher referred to it as "Warehousing and Crowd Control") I would tell my students that, "Math is something that you do, not something you think about". Rosenkranz lived his life that way and it is worth examining, if only for a few moments. Other texts on similar topics: experiments, guest, science and society SJWs at Google are training AI to maximize bias, spreading of lies ...an internally open goal is to prevent a second Trump term... John, your humble correspondent, and probably many of us have watched a breathtaking 25-minute-long Project Veritas video Insider blows whistle & exec reveals Google plan to prevent "Trump situation" in 2020 on hidden cam (Bitchute) A hidden cam has recorded Ms Jen Gennai, a Google boss for innovations, who openly bragged that Google was a big enough company that has the power to define "fairness" and decide who will be the U.S. president. Donald Trump and his supporters don't obey the Google SJWs' definition of "fairness". Other texts on similar topics: computers, freedom vs PC, politics Monday, June 24, 2019 ... / / Turok et al.: a quantum fluctuation complaint against inflation ...and like most of Turok's papers, it's fundamentally wrong... Most of the arXiv.org papers that I cover are papers that I consider good – innovative, interesting, correct, solving something, presenting real possibilities. But I am not one of those people who think that people's judgement should be censored so that only "nice" appraisals are heard. In a healthy scientific process, one must unavoidably hear about wrong and bad papers. The elimination of wrong things is actually the primary procedure that the scientific method revolves around. One very bad hep-th paper today is Quantum Incompleteness of Inflation by Di Tucci, Feldbrugge, Lehners, and Turok (Potsdam+Perimeter). Helpfully enough, the alphabetic sorting of the author names coincides with the sorting according to the increasing age or experience. Neil Turok is obviously the "boss". The last, oldest three authors have written numerous wrong papers criticizing the Hartle-Hawking paradigm for the initial wave function of the Universe. Now, Alice Di Tucci, the most junior member, was added to write a very similar criticism of cosmic inflation, too. Other texts on similar topics: astronomy, string vacua and phenomenology, stringy quantum gravity Biggest Czech protest since 1989 ends up as a mostly SJW event In the recent year, I participated at two anti-Babiš rallies in Pilsen – although my presence was always a bit experimental (well, comparably experimental to my "attendance" of the anti-Iraq-War rallies in Boston in late 2002) – because I think it's wrong for him to bend the court system, it's wrong to get billions of crowns in subsidies, and I am not excited about a former communist as a prime minister with an extremely primitive, purely material way of thinking about everything. But I saw the folks who seem to be the actual drivers behind these events – and what is the possible alternative that they could give us instead of Babiš. In many cases, I must say "No, thank you." You know, I applauded many people's clichés and they were nice or touching. But it seemed obvious to me that they were guests, not the drivers. The drivers seem to be far left SJWs. Right now, the biggest rally in Czechia since 1989 is taking place in the Letná Plain in Prague – an elevated empty place above the Moldau River, not far from the Prague Castle (3D map, street view). The world's biggest Stalin statue was standing there up to the 1960s. The name "Letná" is an adjective seemingly related to "let" which means "a flight" but "Letná" actually comes from old Slavic "Leteň" which is a place illuminated by the Sun – and I happen to live meters from Pilsen's own Letná. ;-) See the live video now. Organizers and others agree with the estimate of 200,000-250,000 people. Well, T-Mobile has "calculated" the number to be 258,000 – not sure since when phone providers are experts in this calculation, especially given the fact that one phone doesn't translate to one person and the ratio may depend on the situation. Sullivan witch hunt: top Czech attorneys vs Harvard Some individual Western public intellectuals – folks like Roger Scruton – used to help the dissidents in the communist Europe before the fall of communism. These days, it's especially Western Europe and Northern America that is falling into a totalitarian system that is analogous to what we used to have before 1989. It's natural that some public intellectuals and otherwise visible pundits from the post-communist Europe are repaying the debt and trying to intervene into some egregious cases of the abuse of power in the West. Czech Protestant education guru John Amos Comenius (1592 Eastern Moravia – 1670 Amsterdam exile), once asked by John Winthrop to become the president of Harvard. Six weeks ago, I discussed the case of Ronald Sullivan, a top black American attorney and a former aide of Obama's, who has become a far right heretic according to an unhinged student mob at Harvard because he dared to accept the request of Harvey Weinstein to become one of his attorneys. The mob found it politically incorrect for a lawyer to defend their officially declared villain-in-chief of the hypocritical and unhinged "#MeToo" movement. Harvard's administrators caved to the hysterical mob – one could say that they seemed happy to do so – and fired both Sullivan and his wife as housemasters of the Winthrop House. Other texts on similar topics: Czechoslovakia, freedom vs PC, politics A ghost told a science writer that quantum mechanics is the Inquisition, has to be defeated Michael Brooks is a far left British journalist and a consultant of Nude Socialist who has promoted homeopathy and celebrated that "scientists" are finally angry about global warming, among other things. Two days ago, in Nautil.us, he has presented a very clear proof that the critics of quantum mechanics are just another branch of the loony far left activists: The Spirit of the Inquisition Lives in Science Well, Brooks has a particular idiosyncrasy. The left-wing activism is hybridized with his speaking to the ghosts. Other texts on similar topics: philosophy of science, quantum foundations Carbon neutrality 2050: Visegrád saves Europe again As The Guardian and others have complained, four post-communist European countries have blocked a crazy statement that "Europe should be carbon-neutral by 2050" on a Thursday meeting in Brussels. The heroic quartet turned out to be a "genetically modified Visegrád Group": Poland, Czechia, Hungary (we're in Central Europe), and... Estonia (the Easternmost among the three Baltic states) that has replaced Slovakia. Especially after the election of Ms Zuzana Čaputová as the Slovak president, Slovakia solidified its role as the Brussels' fifth column within the Visegrád Group. Fortunately, they could be replaced with a more sensible country this time! Thankfully, Čaputová didn't break the tradition and her first foreign visit was one to Prague yesterday. She charmed most of the people and met our president who is no longer in his best Olympic shape. Even though many people dreamed about them, there have been no controversies coming from the Zeman-Čaputová meeting at all. But you could see a clash of two paradigms, an apolitical babe (who is working hard to disprove the proverb that women above 40 can't play hide-and-seek because no one would be searching for them) vs an achieved political veteran. McAllister et al.: weak gravity makes some low-volume cycles mandatory Out of the 14 new primarily hep-th papers today, about 8 (a majority) may be counted as "string theory" which is great. Even more impressively, 4 papers are about Calabi-Yau manifolds. Let me look at the first one – which was posted at 18:00:00 UTC, guaranteeing the first place. These guys may have mastered the correct calculation of the delay after you press the enter key and after the packets get to the arXiv. A counting problem involving the Calabi-Yau manifolds is one of the most popular examples of the deep implications that string theory has for the world of mathematics. A real-six-dimensional manifold of a particular topology, the quintic (or the quintic hypersurface), has some non-contractible lower-dimensional manifolds in it. Some of them are (complex) "lines" in some algebraic sense. Their number has been known to be 2875 for quite some time. The more complex submanifolds, the "conics", are more numerous. Mathematicians have only known that their number was 609,250 since 1986. To count the higher-degree curves seemed like an impossibly difficult problem for the mathematicians. Suddenly, string theorists arrived and claimed that the Calabi-Yau manifold above was a mirror dual to another – string theory on both manifolds may be exactly physically equivalent – and physicists were therefore able to easily compute as many numbers in the sequence as they wanted, thus proving that string theorists are better mathematicians than the mathematicians. As all TRF readers surely know by heart, the next two entries are 317206375 and 242467530000. Baer et al.: stringy naturalness prefers less usual but accessible SUSY scenarios, risky electroweak symmetry breaking In early February, I discussed a paper by Howard Baer and 4 co-authors which made some steps to update the estimates of superpartner masses and other parameters of new physics – by replacing naturalness with the string naturalness which takes "the number of string vacua with certain properties" as a factor that makes a vacuum more likely. Ace of Base, Living in Danger – recorded decades before the intense Islamization of Sweden began. In the eyes of a stranger, such as a Czech, Swedes are surely living in danger. The relevance will become clear later. They have claimed that this better notion of naturalness naturally drives cubic couplings $A$ to large values (because those are more represented in the string vacua, by a power law) which means a large mixing in the top squark sector and stop masses that may exceed $1\TeV$. Also, the other (first two generation squarks...) scalars are "tens of ${\rm TeV}$ in mass". The lightest two neutralinos should be close to each other, with a mass difference around $5\GeV$. Most encouraging is the derivation that the Higgs mass could be pushed up towards the observed $125\GeV$, plus minus one. Second Bell's theorem and the irrational cult around it Off-topic, climate bragging: Steve Koonin is an NYU physics professor and a high-tier DOE official under Obama who proposed to introduce "the red team, the blue team" to the climate debate. I successfully urged him to respond to Gavin Schmidt's attack against a Koonin's talk at Purdue University – attack posted at RealClimate.ORG – and made sure he knew the address to submit it to the Anthony Watts' blog where it became the most successful text in quite some time. A stupid 1976 paper by Bell did more than anything else for the deluded anti-quantum zealots to explode Five days ago, I reviewed Bell's theorem. Two spins that are entangled – in a singlet state – produce a simple correlation $\langle \sigma_a \sigma'_b\rangle=-\cos\vartheta_{a,b}$ between the measurements of projections of the two spins along axes $\hat a,\hat b$, respectively. This nice and simple quantum mechanical prediction cannot be reproduced by a local classical theory (even with hidden variables) because such a local classical theory implies inequalities for correlations involving three axes that the (experimentally verified) cosines do not obey. A voodoo doll. Anti-quantum zealots believe that quantum mechanics must enable some magic action-at-a-distance (and break Einstein's relativity, at least in principle) but it doesn't. My blog post was a polished, more effective version of a 1964 paper by Bell. That paper made some sense, Bell has proven an actual result that was somewhat analogous to no-go theorems banning hidden variables. In fact, it was technically a more correct paper than John von Neumann's theorem on the same topic from the 1930s. Although he wasn't terribly clear, it was implicit in the 1964 paper that the class of theories that was ruled out was composed of theories that were (1) classical theories with hidden variables that simultaneously (2) interacted locally. But John Bell continued to write... and drift towards the confusion and ideologically motivated stupidity. So the misinterpreters of quantum mechanics love to say that he's proven not one Bell's theorem but two Bell's theorems. The second theorem was described in a 1976 paper "The Theory of Local Beables" – although my CERN version of that preprint was already written in 1975. Acharya: string/M-theory probably implies low-energy SUSY Bobby Acharya is a versatile fellow. Whenever you search for the author Acharya, B on Inspire, you will find out that "he" has written 1,527 papers which have earned over 161,000 citations which would trump 144,000 citations of Witten, E. Much of this weird huge number actually has some merit because Acharya is both a highly mathematical theorist – an expert in physics involving complicated extra-dimensional manifolds – as well as a member of the ATLAS experimental team at the LHC. Today, he published Supersymmetry, Ricci Flat Manifolds and the String Landscape. String theory and supersymmetry are "allies" most of the time. Supersymmetry is a symmetry that first emerged – at least in the Western world – when Pierre Ramond was incorporating fermions to the stringy world sheet. (In Russia, SUSY was discovered independently by purely mathematical efforts to classify Lie-algebra-like physical symmetries.) Also, most of the anti-string hecklers tend to be anti-supersymmetry hecklers as well, and vice versa. On the other hand, string theory and supersymmetry are somewhat independent. Bosonic string theory in $D=26$ has no SUSY – and SUSY is also broken in type 0 theories, some non-supersymmetric heterotic string theories, non-critical string theory, and more. Also, supersymmetry may be incorporated to non-gravitational field theories, starting with the Wess-Zumino model and the MSSM, which obviously aren't string vacua – because the string vacua make gravity unavoidable. μνSSM produces nice neutrino masses, new 96 GeV Higgs The most interesting new hep-ph preprint is Precise prediction for the Higgs-Boson Masses in the μνSSM with three right-handed neutrino superfields (58 pages) by Sven Heinemeyer (CERN) and Biekötter+Muñoz (Spain) – BHM. They discuss some remarkable combined virtues of a non-minimal supersymmetric model of particle physics. Note that none of the so far observed elementary particles – bosons or fermions – seems to be a superpartner of another observed fermion or boson, respectively. But for theoretical reasons, it is more likely that these superpartners exist and a supersymmetric Standard Model is a more accurate description of Nature than the Standard Model – the minimum model encompassing the currently observed particles. A pocket magnet with 45.5 tesla: a revolution for LHC/FCC? Pavel has pointed out that I overlooked a remarkable paper on experimental physics in Nature: 45.5-tesla direct-current magnetic field generated with a high-temperature superconducting magnet (by Hahn, Kim, 9 more) Magnets are cool. When we were 10 or so, our class would work in nearby gardens. Some of the greenhouses were covered by plastic films that were attached by... wonderful square magnets, 10 x 10 x 2 cm or so. I was facing a dilemma: on one hand, the founder of Czechoslovakia Prof Thomas Garrigue Masaryk taught us "don't be afraid and don't steal". On the other hand, the magnets were wonderful and I was a curious kid. A few times, my curiosity prevailed over Masaryk. By taking a few magnets, I was helping to disassembly the communist regime – some four years before I became a full-time dissident. Other texts on similar topics: experiments, LHC, science and society Jesus had a reason for a men-only last supper The amount of censorship by the Big Tech companies that have teamed up with each other and with the totalitarian Left has been incredible in recent weeks. Last night, Soph's new YouTube videos were erased within a day. A 100% polite vegan who loves black pigeons was also silenced for "extreme or repeated hate speech" for a day, before the YouTube account was restored in the wake of a huge backlash. Pinterest has internally and indefensibly labeled a pro-life group, Live Action, as "pornography" to be capable of erasing it from their platform. Eric Cochran was the whistleblower at Pinterest who was immediately fired and escorted by guards, without an explanation. Project Veritas, a news group that just tried to cover the Pinterest censorship, was silenced on YouTube: their video was blurred in an Orwellian way. The number of such stories is huge. It's impossible to enumerate them, let alone write detailed accounts of each. Professor Ricardo Duchesne was fired from University of New Brunswick because his books dared to provide the reader with deep evidence that the Western civilization had some traits that no other – and Asian – civilizations could boast. That's white supremacy and it is apparently banned! His dismissal was guaranteed by a mob that doesn't do much scholarly work and may be summarized as a bunch of malicious, lying, and useless parasites sucking dollars from the stupid Canadian taxpayer. Lots of worrisome news of this new totalitarian type are served by Paul Joseph Watson on his @prisonplanet Twitter account and his new summit.news website. Just the top 5 news in a list over there: Facebook bans comments that only say "Honk". A Brazilian duo of Lesbians has first castrated a boy (plus created a hole which they called the "vagina") and they murdered him – certain feminists aren't just like the Nazis, they're like the Nazi killers from concentration camps. A supporter burned thousands of Brexit Party votes. A Muslim invited to Germany by Angela Merkel has aggressively attacked a random German lad with a bottle – a "revenge for Afghanistan". A female left-wing comedian urged milkshake to be replaced with a battery acid in the milkshake attacks. And so on and so on. Other texts on similar topics: freedom vs PC, politics, religion Bell's inequality is straightforward, the quantum world is local "Quantum Strangeness: Wrestling..." by George Greenstein is another deeply flawed book on the foundations of quantum mechanics that was recently published. It talks about Bell's experiment all the time – which is lame because that experiment is neither very interesting nor very special or pedagogically useful. The text of the book seems very unprofessional. For example, the sentence "It was many years ago that I first encountered the Great Predictor" appears at the beginning of three chapters, 1,9,16. At least, the author suggests that he decided to be happy about the Copenhagen Interpretation but doesn't make it very clear why it's the right answer and I wouldn't say that his description what the Copenhagen Interpretation really says is quite accurate. So much of the book is communicating some subjective religious emotions of the writer. I find it totally bizarre how many people are so confused about such an elementary exercise which is included in both graduate and undergraduate courses of quantum mechanics – and the lecture about Bell's inequality is in no way among the hardest ones. The September 9th asteroid should be nuked The contemporary public discussions are largely dominated by people who are either totally dishonest, or lack the basic education or intelligence, or have lost any sense of proportion, usually because of some intense ideological brainwashing they have been subjected to. A comparison to show that point: several U.S. presidential candidates want to spend $5 trillion over a decade (just in the U.S.) to fight a completely non-existent threat of "climate change". On the other hand, some people who have never dared to criticize the climate hysteria are fighting against a $29 billion spending (over the same decade) to build a new generation of particle colliders, the mankind's most characteristic direction to advance the experimental pure science by brute force. What is wrong with all these people, which clearly include Alessandro Strumia as I learned in recent days? Incidentally, I had to close the discussion because Alessandro was evolving it in totally nutty directions, both when it comes to the anthropic memes and the anti-collider jihad? How can they be so totally messed up not to resist to write a daily dose of lies and demagogy directed against pure science and its value which only costs a few billion dollars per year; while they are silently endorsing the wasting of trillions of dollars for complete stupidities? Other texts on similar topics: astronomy, experiments, science and society Tricolor Movement: I am a voter again A new party that finally includes the fight against postmodern far left excesses into the core program A few months ago, the center right Civic Democratic Party (ODS) – that was founded as a full-blown right-wing party by Václav Klaus Sr, the most important Czech politician after 1989, in the early 1990s – has expelled its most popular member according to polls, Václav Klaus Jr, the ex-president son, for his colorful but apt metaphors criticizing the dictatorial trends in the European Union. He dared to point out similarities between Macron's and Hitler's plans for Europe; and he dared to point out that most of the laws discussed by Czech lawmakers are forced on us by the EU, a situation that resembles Jews' committees that were "generously" allowed to vote about their own distribution to buses going to concentration camps. From my perspective, that expulsion was way too much of a collaboration with the evil. And although I still think that folks at ODS are better than the generic SJWs in parties such as TOP 09, I viewed those steps as a betrayal and stopped being a voter of ODS – which I had been from the beginning of that party. Because I am a homo politicus, I didn't choose "abstain" in the European Union elections and picked the nationalist party SPD as a temporarily good proxy for the right direction that the European Union needs. Two days ago or so, Klaus Jr – the experienced high school principal and mathematics teacher whose face is a textbook on the spontaneous symmetry breaking and I hope the TRF readership is mature enough not to turn this triviality into the main topic of the comment section – and his allies have finally founded a new party, The Tricolor Movement of Citizens (THO). So I registered as a supporter. Other texts on similar topics: Czechoslovakia, education, Europe, freedom vs PC, politics Direct anthropic bound on the weak scale from supernovæ explosions – or how I learned to stop worrying and love the Higgs Guest blog by Prof Alessandro Strumia, not only a famous misogynist but also a physicist ;-) I thank Luboš for hosting this post, where I present a strangelove-like idea that might be the long-sought explanation of the most puzzling aspect of the Standard Model (SM) of the Fundamental Interactions: the existence of two vastly different mass scales. The electro-weak Fermi scale (set by the Higgs mass, that controls the mass of all other elementary Standard Model particles) is 17 orders of magnitude smaller than the gravitational Planck scale (the mass above which any elementary particle is a black hole, according to Einstein Relativity and Quantum Mechanics). The puzzle is that, according to many theorists, the Standard Model Higgs is unnatural because its squared mass receives Planck-scale quantum corrections, so that cancellations tuned by one part in $10^{34}$ are needed to get the small Fermi scale. This naturalness argument lead theorists to expect that the Higgs cannot be alone, that it must exist together with new physics that protects its lightness. Theorists proposed concrete examples of new physics that makes the Higgs natural: supersymmetry, technicolor, extra dimensions... Dozens of thousands of research publications studied these ideas and supersymmetry seemed to work so beautifully that most theorists expected that the Fermi scale is the scale of supersymmetry breaking. Other texts on similar topics: astronomy, guest, landscape, string vacua and phenomenology Most laymen have a remarkable psychological problem with the universe born out of nothing The criticism of Hartle-Hawking by Turok et al. is demonstrably wrong In the Quanta Magazine, Natalie Wolchover published a new article Physicists Debate Hawking's Idea That the Universe Had No Beginning about the controversies surrounding the Hartle-Hawking "wave function of the Universe" which quantifies the philosophical guess that "the Universe was born out of nothing". In the "story", there must be two opposing sides – that's how journalism likes to work. So the "other side" standing against the Hartle-Hawking school is Neil Turok and a few sycophants. If I am overlooking someone on his side who is more than just a sycophant of Turok's, please let me know. Physics normally predicts "what an initial state evolves into". Given an initial state $\ket\psi$ or $\rho$ at time $t_1$, assuming that we have already accepted quantum mechanics, we may calculate the probabilities of measuring $L(t_2)=\lambda_j$ at a later time $t_2$. In quantum mechanics, all this evolution is encoded in unitary evolution operators $U$ – which is called $S$ if we evolve from $-\infty$ to $+\infty$. So we explain why something occurred later – by reducing it (in the case of quantum mechanics, probabilistically) on the laws of evolution in physics combined with some knowledge about the state at an earlier time. Other texts on similar topics: astronomy, science and society, stringy quantum gravity Penington vs information loss MmanuF has pointed out that I forgot to discuss an impressive preprint Entanglement Wedge Reconstruction and the Information Paradox by Geoffrey Penington. He's still a Stanford graduate student but it's totally plausible that he understands the subtle ways how at least AdS/CFT resolves the information loss paradox more than any other physicist in the world. After a long search for the most illuminating video to embed, I chose Angelique de Peyrac because MmanuF is French while Peyrac was also Geoffrey. Too bad that things like Angelique are no longer sufficiently politically correct in California. The 73-page-long paper has everything to convince me that the man knows everything that is really important for the resolution of the information loss paradox – and the related firewall paradox: the paper agrees with all the qualitative assumptions that I have convinced myself to be irrevocable; and it contains additional 164 equations that seem totally relevant and a dozen of somewhat randomly ones have passed my nontrivial examination. ;-) YouTube's income should be treated as donations to a far left party Demonetization of YouTube is needed if the server wants to be used a media department of left-wing and Islamist groups John Archer and Johnny Liu have pointed out that after a pro-censorship campaign by Vox Media, a sibling of Daily Kos, YouTube has just changed and escalated its censorship policies, it has been doing so for years, and it will continue to do so: Our ongoing work to tackle hate Using some obnoxious language that is widespread among far left individuals who have no positive moral or other qualities, the cowardly writer of that seemingly official text declares that YouTube will be removing all contents that has any traces of common sense, the truth, conservative values, or respect for the civilization and those who have built it. Other texts on similar topics: computers, politics Experimenters and especially journalists can't write good far-reaching interpretations of QM experiments Sinclair QL (Quantum Leap). Sometimes in the 1980s, I was so attracted by an article about that computer that I memorized a long 1-page article about it. With hindsight, my worshiping seems rather irrational. By some technical measures, it could have been a stronger computer than Commodore C64 that I used to have – but it turned out to be unsuccessful and less software had existed for QL. Philip Ball wrote a text for the Quanta Magazine Quantum Leaps, Long Assumed to Be Instantaneous, Take Time which makes semi-covert statements that an experiment has allegedly disproved the basic principles of quantum mechanics. That much is clear from the title. The subtitle is even a bit more radical than that: An experiment caught a quantum system in the middle of a jump — something the originators of quantum mechanics assumed was impossible. Another text saying that the founding fathers of quantum mechanics were not only wrong but idiots, as some current geniuses revealed. In reality, it's the other way around, of course. Other texts on similar topics: experiments, philosophy of science, quantum foundations EU has turned Czech PM into a full-blown EU hater In politics, I increasingly have to choose the lesser evil. ODS has betrayed me so for the first time, I voted for the nationalist SPD in the recent European Union elections – although I am far from being a fan of their views on direct democracy, welfare, and other things. But among the parties that would get an MEP, SPD was the only clear non-communist party opposing the terrifying trends of the present EU. Don't get me wrong: it may have been just a temporary punishment of ODS by one voter, me. I still think that the actual MEPs representing ODS are much better than the average MEPs – and maybe better than SPD's MEPs. Because these trends seem so terrible, my criticisms against the Czech PM, former communist oligarch Andrej Babiš, correspondingly weakened. In December 2018, the European Parliament pointed out that Babiš was in a conflict of interests. Last weekend, right after the EU elections (so that Babiš couldn't possibly complain about the timing), a report of an EU audit was released. See the 71 pages in English. Unsurprisingly, the European Commission-hired auditors concluded that he is in a complete clash of interests. They have audited 39 projects out of 101 since early 2017 – when Babiš placed his Agrofert Corporation into two trust funds with the purpose of formally "cutting his ties" from the company – and 19 of them have been found in the violation of the law. Again: about one-half of subsidized projects in Czechia are criminal. CZK 282 million (€11 million) of EU subsidies was found to be illegitimate because of his conflict of interests. Aside from the conflict of interests laws, Agrofert's companies have violated many other laws, however (some of them could lead to new criminal investigations against both Agrofert managers and Babiš himself), so in total, CZK 451 million (€17 million) in subsidies was paid illegally. These funds should be returned. Clearly, the whole "trust funds" are just a farce invented by Babiš's lawyers – that may have been a "sufficiently good farce" to please the Czech voters and silence Babiš's critics but that doesn't solve anything from an impartial person's viewpoint. He is still the factual beneficiary of the subsidies and he's controlling everyone who matters inside the "trust funds". He may always remove the "protectors" of the trust funds and other things. So placing Agrofert in the "trust funds" hasn't solved a damn thing and the EU audit agrees with this common sense statement of mine. In practice, Babiš doesn't want to return a penny so the EU – when they make the statement final in 3 months or so, and the conclusion will almost certainly be the same – will simply take the money from the future subsidies for Czechia. It's being rumored that another report from the second audit is on its way and it will demand CZK 2 billion ($100 million or so) of Czech agricultural subsidies to be returned by Agrofert to the Czech state. Note that his net worth is about $4 billion, just like Trump's, and the subsidies have always been crucial for that agricultural and chemical business. Wednesday afternoon update: The second audit report (about Agrofert's purely agricultural subsidies – the first one was about subsidies unrelated to agriculture) has been sent to Czech government authorities and rumors say that it's equally brutal and will demand billions of crowns to be returned by Agrofert. Babiš is almost certainly the most subsidized politician in the history of the mankind. Soph takes on Greta ...and Gretinism... Great minds think alike. When I talked to Murray Gell-Mann years ago, it was clear to us that we had a similar thinking about many issues – and we were excited and upset about similar things and for similar reasons, too. This YouTube copy of Soph's "Greta" video may disappear but so far, it's there and useful for Australia where BitChute is behind the Great Mao Australian Firewall. On June 13th, Soph posted a brand new remake of her climate video on YouTube – without a hat, with a new outfit, new music, new – and less emotional – reading, new background pictures and animations, fewer details about the way to get rid of counterproductive politicians. So when Stephen Wolfram remembered Gell-Mann, I appreciated Wolfram's intelligence, ego, and unusual stories from Wolfram's life but I also felt like being almost in Gell-Mann's skin. Gell-Mann would be annoyed by that text by Wolfram, I am sure – so I exploited the opportunity to be somewhat annoyed on behalf of Gell-Mann. If you ask me, I can enumerate the places where Wolfram is just wrong. There's one unlikely person whom I spiritually identify with: Soph, a 14.7-year-old girl from the wealthiest suburb of the Bay Area (although she has moved there from New York). Incidentally, I am proud to have had 18 visits from Larkspur (a town with 12k inhabitants where Soph attends the Redwood High School) just today – Larkspur beats all of Stanford today! ;-) When I wrote about her for the first time almost three weeks ago, I immediately mentioned a comparison with Greta Thunberg because it seems particularly apt and shocking. Greta – Soph's "fellow squarehead" (slang for Scandinavians) – is a mediocre, dumb hired gun working for the left-wing establishment (which starts with her parents, folks who are obviously on her side of the ideological disputes) while pretending to be a revolutionary. In Soph's delicious jargon, Greta is "one opinionated š*thead who is enough to completely destabilize democracy". Soph is a younger, creative, smart, self-made, ingenious kid who is an actual rebel and the true mastermind behind her YouTube (990k followers) and BitChute videos. It has always been obvious to me that Soph must see Greta as her arch-nemesis. Soph feels very similarly to your humble correspondent about similar things – so she must be profoundly angry about a "premium unleaded autist" (Soph's creative words) Swedish girl who is being praised by all the left-wing media while Soph is described as some kind of trash. It should be the other way around and Soph knows it. Well, in some interviews, Soph did refer to Greta. But I knew that the sentiment had to be much stronger. Other texts on similar topics: climate, politics, science and society, video Wolfram on Gell-Mann I got a permission to post a very interesting text by Stephen Wolfram so if you're thirsty for some intellectual adrenaline and if you can survive without tons of writers' humility ;-), keep on reading. Remembering Murray Gell-Mann (1929–2019), Inventor of Quarks Guest blog by Stephen Wolfram In the mid-1970s, particle physics was hot. Quarks were in. Group theory was in. Field theory was in. And so much progress was being made that it seemed like the fundamental theory of physics might be close at hand. Right in the middle of all this was Murray Gell-Mann—responsible for not one, but most of the leaps of intuition that had brought particle physics to where it was. There'd been other theories, but Murray's—with their somewhat elaborate and abstract mathematics—were always the ones that seemed to carry the day. It was the spring of 1978 and I was 18 years old. I'd been publishing papers on particle physics for a few years, and had gotten quite known around the international particle physics community (and, yes, it took decades to live down my teenage-particle-physicist persona). I was in England, but planned to soon go to graduate school in the US, and was choosing between Caltech and Princeton. And one weekend afternoon when I was about to go out, the phone rang. In those days, it was obvious if it was an international call. "This is Murray Gell-Mann", the caller said, then launched into a monologue about why Caltech was the center of the universe for particle physics at the time. Other texts on similar topics: computers, experiments, guest, science and society, string vacua and phenomenology Sane, genuine libertarian system wouldn't enable p... 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Volume 20 Supplement 13 Proceedings of the 2018 International Conference on Intelligent Computing (ICIC 2018) and Intelligent Computing and Biomedical Informatics (ICBI) 2018 conference: genomics An efficient simulated annealing algorithm for the RNA secondary structure prediction with Pseudoknots Zhang Kai1,2, Wang Yuting1, Lv Yulin1, Liu Jun1,2 & He Juanjuan1 BMC Genomics volume 20, Article number: 979 (2019) Cite this article RNA pseudoknot structures play an important role in biological processes. However, existing RNA secondary structure prediction algorithms cannot predict the pseudoknot structure efficiently. Although random matching can improve the number of base pairs, these non-consecutive base pairs cannot make contributions to reduce the free energy. In order to improve the efficiency of searching procedure, our algorithm take consecutive base pairs as the basic components. Firstly, our algorithm calculates and archive all the consecutive base pairs in triplet data structure, if the number of consecutive base pairs is greater than given minimum stem length. Secondly, the annealing schedule is adapted to select the optimal solution that has minimum free energy. Finally, the proposed algorithm is evaluated with the real instances in PseudoBase. The experimental results have been demonstrated to provide a competitive and oftentimes better performance when compared against some chosen state-of-the-art RNA structure prediction algorithms. RNA is a linear molecular compound formed by polymerization of ribonucleotides with phosphodiester bonds, the ribonucleotides are composed of phosphoric acid, ribose and bases. The RNA sequence consists of Adenine (A), Uracil (U), Guanine (G) and Cytosine (C), the four-base arrangement allows RNA to have a variety of functions that can play great role in genetic coding, translation, regulation, and gene expression. The search for the secondary structure of RNA sequence has been widely used as the first step to understand biological functions [1]. Pseudoknot is a special RNA secondary structure that is found in many important biologically molecules [2, 3], it usually contains not well-nested base pairs. These non-nested base pairs make the presence of pseudoknots in RNA sequences more difficult to be predicted by dynamic programming, which use a recursive scoring system to identify paired stems. The general problem of predicting minimum free energy (MFE) structures with pseudoknots is NP-complete problem [4]. In general, researchers apply the principle of MFE to evaluate RNA secondary structure. When the RNA sequence is freely folded in space to form the secondary structure of MFE under fixed experimental conditions, the change is stopped, meanwhile, the stable state of the RNA sequence is formed. For the calculation of the free energy of RNA secondary structure, the stem energy is defined as a negative, the energy of loop is defined as a positive, and the free single strand does not participate. Deng found that the molecular free energy is related to a single complementary base pair, but adjacent base pairs also affect the free energy calculation of the molecule [5]. In the secondary structure prediction, if the free energy calculation of each part does not affect each other, the free energy of the entire structure is accumulated form the energy of each part, and the calculation principle is shown in Eq. (1). $$ \varDelta G=\sum \varDelta {G}_S+\sum \varDelta {G}_H+\sum \varDelta {G}_I+\sum \varDelta {G}_B+\sum \varDelta {G}_M+\sum \varDelta {G}_P+\varDelta \delta $$ In the above formula, ΔGS means the stem free energy; ΔGH, ΔGI, ΔGB, and ΔGM represent the free energy of hairpin, internal, bulged, and multi-branch loop, respectively; ΔGP represent the pseudoknot free energy, which is generally split into loop for calculation to simplify the calculation process; Δδ is a threshold set to balance the error during the experiment process. After the RNA secondary structure is calculated in the Eq. (1), researcher can objectively evaluate whether the current structure is stable by numerical changes. At present, existing algorithms for the prediction of RNA secondary structure with pseudoknots can be classified into two categories. The first category is dynamic programming (DP) based approaches. DP is the initial computational approach used to predict RNA structure [6]. The idea of dynamic programming is to divide a complex problem into many simple sub-problems to facilitate their treatment [7]. Combining the DP idea with the principle of MFE, researchers have proposed many RNA secondary structure prediction algorithms. Rivas and Eddy [8] proposed pknots-RE algorithm that can predict RNA sequence with pseudoknot structure. Dirks and Pierce [9] proposed NUPACK algorithm which calculate a series of recursion probabilities that can be used to compute base-pairing probabilities with or without pseudoknots. However, these algorithms are very time-consuming to predict long-chain sequence, and its maximum predictive sequence length cannot exceed 150. The second category is Heuristic based approaches, which can handle long RNA sequences and obtain high quality feasible solution efficiently [10]. Ren et al. [11] proposed HotKnots to build up candidate secondary structures by adding substructures one by one to partially formed structures. Zuker et al. [12] and Turner et al. [13] integrate thermodynamic model into their algorithms to search for secondary structure with minimal free energy. SARNA-predict-pk [14] algorithm is an extended version of SARNA-Predict [10] which predicts RNA secondary structures with pseudoknots. This algorithm employs a new thermodynamic model that was described by Rastegari and Condon [15] and implemented in the HotKnots software. The model can be used to evaluate RNA sequences with pseudoknots. IPknot [16] algorithm proposed a computational method for predicting RNA secondary structures with pseudoknots based on maximizing the expected accuracy of a predicted structure. Iterative HFold [17] takes as input a pseudoknot-free structure, and produces a possibly pseudoknotted structure whose energy is at least as low as that of any (density-2) pseudoknotted structure containing the input structure. It leverages strengths of earlier methods, namely the fast running time of HFold, a method that is based on the hierarchical folding hypothesis and the energy parameters of HotKnots V2.0. Fatmi et al. [18] proposed a new algorithm that combines between the Greedy Randomized Adaptive Search Procedure (GRASP) and the Genetic Algorithm (GA) principle. This method repeats a process consisting of two phases: the construction phase and the local search phase. During the construction phase, a list of feasible solutions is iteratively constructed. The local search phase comes with the wake of the construction step; it aims to improve the solution obtained from the first phase by launching a local search to find the local optimum solution. In this paper, a novel efficient simulated annealing (SA) algorithm is proposed to predict RNA secondary structure with pseudoknot. Firstly, an efficient base pairing method is designed, which is based on the minimum stem length and the minimum loop length, and a completed conflict resolution is provided for the conflicting bases; Then a simple and effective fitness function is proposed, and the number of stem and the total number of base pairs of the RNA sequence is used as metrics for evaluating the secondary structure of RNA; Finally, the annealing schedule is selected to systematically decrease the temperature as the algorithm proceeds, the final solution is the structure with MFE. In this paper, eighteen test sequences are randomly selected from the PseudoBase [19], and the results are compared with other leading prediction algorithms such as HotKnots [11], IPknot [16], TT2NE [20], CombFold [21], RnaStructure [22], CyloFold [23] and RNAflod [24] which shows, the effectiveness of our algorithm. The RNA secondary structure folds itself by forming hydrogen bonds between G-C, A-U, and G-U. Therefore, the prediction of all hydrogen connections among the primary structure of the sequence become the first in predicting RNA secondary structure. Many components can be identified in the secondary structure, such as stem, hairpin loop, multi-branched loop or multi-loops, bulge loop, internal loop, and pseudoknot, as shown in Fig. 1. RNA Secondary Structure and Substructures For a given RNA sequence X = 5′-x1x2…, xi, … xn-3′ of length n, i is defined as the initial index of the current base and Y(X) is the mapping string of consecutive complementary base pairs of X, Y(X) = (y1, y2, …, yi, …, yn), yi is assigned to be j, if base xi bond with base xj, as shown in Eq. 2. $$ {y}_i=\Big\{{\displaystyle \begin{array}{c}j,\mathrm{if}\;{x}_i\;\mathrm{paired}\kern0.17em \mathrm{with}\;{x}_j\\ {}i,\mathrm{else}\kern6em \end{array}} $$ As shown in Fig. 2, when the base is paired, the sequence numbers of the paired bases are exchanged and stored in Y(X), then Y(X) = (1, 14, 13, 12, 5, 6, 7, 8, 9, 10, 11, 4, 3, 2, 15). Each mapping string Y(X) is a candidate solution, the solution with MFE is the optimal solution, which is the most stable secondary structure. One of the mapping string Y(X) for sequence X In order to better simulate the folding process of RNA secondary structure in the program, we define each part of the RNA secondary structure as follows: Definition 1: X = 5′-x1x2…xn-3′, xi ∈ {A, U, G, C}, Sequence X is called an RNA sequence of length n. Definition 2 (stem): xixi + 1…xi + k-1 and xj-k + 1…xj-1xj is two sub-segments in sequence X, (xi, xj) ∈ W = {(A, U), (U, A), (G, C), (C, G), (G, U), (U, G)}, 1 ≤ i < j ≤ n, j − i≥ 3, then the structure of consecutive base pairing by {(xi, xj), (xi + 1, xj-1),…, (xi + k-1, xj-1)} is called the stem of length k (k ≥ 2). To simplify calculations, stem can be expressed as a mi = (i, j, k), where parameters i and j are the index of beginning base and ending base, and parameter k is the length of this stem. Definition 3 (hairpin Loop): There must be at least MinLoop (MinLoop ≥ 3) unpaired bases in any hairpin loop structure. Definition 4 (consecutive complementary base paired set): The complete RNA secondary structure of a sequence X is called a consecutive complementary base pair set, recorded as M(X), M(X) = (m1, m2,…, mi, …,mn). Each mi represents a stem, according to the above definition, any mi can be recorded as (i, j, k). In the sequence X, the secondary structure formed by the pairing of M(X) is represented by Y(X). Definition 5 (pseudoknot): ∀ xp, xq, xr, xs, ∈ X, (xp, xq), (xr, xs) ∈ W, and the number of four bases in X satisfies 1 ≤ p < r < q < s ≤ n or 1 ≤ r < p < s < q ≤ n, then the structure formed by these two base pairs is called a pseudoknot structure, as shown in Fig. 3. A arc representation for pseudoknot structure According to the above definition, the secondary structure prediction problem with pseudoknot can be converted to find the number of stems in all possible stem of the X sequence. These stems are so unique that secondary structure formed by their base complementarity has MFE state. Thus, an efficient Prediction algorithm of RNA secondary structure with pseudoknot based on SA (PRSA) is proposed. Set of K consecutive base pairs Since single base pairs cannot contribute to the reduction of free energy, the PRSA algorithm considers consecutive base pairs. In order to find all the stem structures, we defined the minimum stem length (MinStem ≥ 2) and the minimum loop length (MinLoop ≥ 3) parameters, as shown in Fig. 4. Consecutive paired MinStem and unpaired MinLoop After initially setting the parameters MinStem and MinLoop, all the reasonable mi can be calculated. Parameters i, j and k need to satisfy the following three constraints: $$ 1\le i\le n-2\ast MinStem- MinLoop+1 $$ $$ i+2\ast MinStem+ MinLoop-1\le j\le n $$ $$ MinStem\le k\le \frac{j-i- MinLoop+1}{2} $$ For example, Mengo_PKB is an RNA molecule from the PseudoBase, whose sequence is 5′ − ACGUGAAGGCUACGAUAGUGCCAG − 3′. Let MinStem and MinLoop be 3, all possible triplets (i, j, k) are (2,14,3), (2,14,4), (2,20,3), (3,13,3), (3,21,3), (8,22,3), (9,19,4), (10,18,3), (11,20,3). The pseudo code of calculation consecutive base pairs is shown as Algorithm 1. But in all base pairs, the same position of bases may have different consecutive base pair numbers, we need to merge these same positions. Like the above Mengo_PKB sequence, the set of base pairs after the merge is (2, 14, (3, 4)), (2, 20, (3)), (3, 13, (3)), (3, 21, (3)), (8, 22, (3)), (9, 19, (3, 4)), (10, 18, (3)), (11, 20, (3)). The pseudo code that saves the merged result to the K consecutive base pair set is shown in Algorithm 2. As known that most predicted algorithms require more effort to calculate the MFE structure after calculating the free energy of the current prediction, which makes their algorithm converge very slowly. A pool of candidate structures is generated by constructing a set of K consecutive base pairs, which makes the PRSA algorithm converge faster than other prediction algorithms. This also makes each iteration more valuable because each iteration generates a new structure from the candidate pool. Neighbor state and its conflict When the secondary structure prediction is performed on any of the RNA molecules, the PRSA algorithm would first calculate the K consecutive base pair set by parameter preprocessing, and then generate a neighbor state through a random function in the simulated annealing algorithm. Taking the TMEV molecule as an example, after the preprocessing process of the upper section 'Set of K consecutive base pairs', a K consecutive base pairs set of TMEV molecules is obtained, as shown in Fig. 5. K consecutive base pairs set of TMEV molecules Divided according to the base start position and end position of stem, this set contains 13 elements. Since the base start and end positions of the stem are the same, different stem lengths may exist, so the algorithm determines one stem by generating two random numbers. The first random number is between 1 and 13, and the second random number is related to its corresponding set of K consecutive base pairs. For example, take two random values as 10 and 1, respectively. At this time, m1 = (9, 19, 3), a local RNA secondary structure is formed. In order to be recorded in the programming, this section of the algorithm has been processed in 4 steps: (1) The paired base numbers are exchanged as shown in Fig. 6, m1 is added to the consecutive base pair set M(X), at this time M(X) = {m1 = (9, 19, 3)}, and the secondary structure corresponding to M(X) is represented by Y1(X). m1 base number exchange process (2) A randomly generated mi that may conflict with elements in the set M(X). When the algorithm program performs the next iteration of the loop, a new stem m2 = (2, 20, 3) is generated. At this time, a base pairing conflict occurs, that is, the bases originally numbered 18 and 19 have been paired with the bases at other positions, and the base complementary pairing conflicts are shown in Fig. 7. New neighboring state generation process (3) If there is a conflict, the position number of the conflicting base is exchanged again to remove the conflict, and the m1 in the M(X) is updated, and the schematic diagram of removing the base pairing conflict is shown in Fig. 8. The M(X) is updated to {m1 = (11, 17, 1)} after removal. Remove base pairing conflicts (4) Determine whether the updated mi meets the constraint. If it does not, remove it; if it does, it will not be considered. When the constraint is initialized, the algorithm program sets the minimum length of the stem to be no smaller than MinStem. Assume that the initial value of MinStem is 3, therefore, the remaining pairing mode of m1 needs to be removed, and the element is deleted from M(X), and M(X) is an empty set. The operation process is shown in Fig. 9. Check the rationality of remaining mi After the conflicts and constraints are resolved, the base pairing is performed in the new stem and added to M(X), as shown in Fig. 10. At this time, M(X) = {m2 = (2, 20, 3)}, the secondary structure corresponding to M(X) is represented by Y2(X), and Y2(X) is the neighbor state of Y1(X). m2 base number exchange Fitness function For most MFE based RNA secondary structure prediction algorithm, the complex thermodynamic model is often used to evaluate candidate solutions [21]. However, there is no useful information to guide the candidate solution to find lower neighbor energy state. Consequently, the convergence of these MFE based prediction algorithms is very slow. Actually, only the consecutive base pairs stem ∆GS provide negative free energy which contributes to the reduction of free energy. The stability of RNA sequence can also be approximately evaluated by consecutive base pairs stem. Where Group is the number of stems of the secondary structure of the RNA sequence, TP is the sum of the number of all base pairs in the sequence, TP divided by Group is the average number of base pairs (AP), PG is the predicted number of pseudoknots by the algorithm, MG is the expected number of pseudoknots, and k is the length of the stem. The evaluation function for random candidate M(X) can be seen in the following Equation: $$ F\left(M(X)\right)=\Big\{{\displaystyle \begin{array}{cc} TP\times A{P}^2,& PG\le MG\\ {} TP\times A{P}^2\times \frac{Group- PG}{Group},& PG> MG\end{array}} $$ $$ TP=\sum \limits_{i=1}^n{m}_i.k $$ $$ AP=\frac{TP}{Group} $$ The two structures of the BCRV1 molecule are evaluated using the custom fitness function, M1(X) = {m1 = (5,47,6), m2 = (14,80,6), m3 = (20,38,5), m4 = (26,98,7), m5 = (53,74,9)}, as shown in Fig. 11a; M2(X) = {m1 = (4,48,8), m2 = (19,39,6), m3 = (26,98,7), m4 = (52,75,10)}, as shown in Fig. 11b. We produce the images of RNA structure with jViz. Rna [25]. Two different secondary structures of BCRV1 After evaluation, the calculated data of the secondary structure of BCRV1 molecule are shown in Table 1. According to the fitness function values of the two structures, it indicates that M2 is better than M1. Table 1 Evaluation results Overall algorithm The PRSA algorithm initializes the parameters to determine the constraints of the RNA sequence, thereby calculating a set of K consecutive base pairs. According to this set, the neighbor state is randomly generated, and the custom fitness function is adopted to evaluate the quality of the current solution (CurrentPairs) and the previous generation solution (MaxPairs). If the CurrentPairs performs better, it would replace the MaxPairs directly. Otherwise, it will determine whether to accept the new pairing structure based on probability from Boltzmann distribution. The final predicted solution structure is stored in MaxPairs, which has MFE and includes pseudoknot. The pseudo-code of the overall algorithm is shown in Algorithm 3. In section 'method', Predicting RNA secondary structures with pseudoknots is implemented using the PRSA algorithm. In the following, we first present the datasets, the exiting methods and accuracy measures we use for the evaluation of the algorithm, then the prediction performance of the PRSA algorithm is demonstrated by comparative experiments. The eighteen benchmark instances from PseudoBase were used to test the proposed method. The characteristic of each sequence is shown in Table 2. The second column is the Abbreviation of the RNA sequence, the third column is the RNA PKB number, the fourth column is the RNA type, the fifth column is the sequence length and the last column is the number of base pairs in the known structure. The predicted structure should be similar to the base pairs of the known structure. Table 2 Benchmark Instances from RNA PseudoBase Accuracy measures The prediction accuracy is calculated by comparing the predicted structure with the known structure. In order to assess the quality of the results produced, three evaluation criteria were used: sensitivity (SN%), specificity (SP%) and F-measure(%) [26]. The evaluation criteria are as follows: $$ SN= TP\div \left( TP+ FN\right) $$ $$ SP= TP\div \left( TP+ FP\right) $$ $$ F- measure=2\ast SP\ast SN\div \left( SN+ SP\right) $$ Where TP represents the number of correctly predicted base pairs; FP represents the number of incorrectly predicted base pairs; FN represents the number of unpredicted base pairs compared with the known structure. When the prediction results are accurate, both SN and SP should be close to 100%. Comparison with existing methods To better reflect the accuracy of the algorithm proposed in this paper, the computational results of the PRSA algorithm are compared with seven state-of-the-art algorithms, including HotKnots [11], IPknot [16], TT2NE [20], CombFold [21], RnaStructure [22], CyloFold [23] and RNAflod [24]. Among these algorithms, the HotKnots algorithm and the IPknot algorithm use heuristic ideas to predict the secondary structure. The names of the seven algorithms and the website links to the algorithm-based Web sites are listed in Table 3. Table 3 State-of-the-art RNA structure predication algorithms The comparisons of the proposed method with the other methods are shown in Tables 4, 5 and 6. If the value in the table is "#", it means that the algorithm does not support the prediction of the length of the sequence, such as TT2NE. The results of the proposed method and the compared methods are all run 10 times for each sequence. Table 4 Sensitivity Comparison Results Table 5 Specificity Comparison Results Table 6 F-measure Comparison Results From Table 4, in terms of sensitivity, the proposed method provides the best results in nineteen sequences, of which 9 sequences predict 100%. In addition, there are 3 sequences predicting with sensitivities greater than 90%. In terms of specificity, the specificity of 8 sequences in Table 5 is more than 90%, including that the specificity of 6 sequences is 100%. For F-measure, there are 14 sequences exceeding 82%, including 9 sequences above 90%. The proposed method has average sensitivity, specificity, and F-measure of 91.1, 86.9, and 88.0%, respectively. In addition, the average sensitivity of the proposed method is better than the CyloFold method by 7%, better than the TT2NE method by 4.4% and better than the HotKnots method by 12.3%. In case of the average of specificity, the proposed method is better than the CyloFold method by 3.2%, better than the TT2NE method by 13.7% and better than the HotKnots method by 13.1%. In case of the average of F-measure, the proposed method is better than the CyloFold method by 5.3%, better than the TT2NE method by 8.9% and better than the HotKnots method by 13.1%. According to Section 'Accuracy comparison tests', we can find that the PRSA algorithm has obvious advantages in the quality of the solution compared with other algorithms. Taking the BCRV1 molecule as an example, the sequence of this method is predicted by the PRSA algorithm and the CyloFold algorithm, respectively. The arc representation of the obtained secondary structure is shown in Fig. 12. It can be seen from the figure that the secondary structure predicted by the algorithm in this paper has become infinitely close to the real structure. Comparison of predicted secondary structure by PRSA and CyloFold algorithm In this paper, we propose an efficient simulated annealing algorithm for the RNA secondary structure predicting with pseudoknots, combined with the evaluation function to compensate for the high time complexity of the free energy calculation model. The algorithm sets the MinStem and MinLoop parameters to determine the pseudoknot structure formed by the base pair cross-combination, and optimizes the pool of candidate solutions, thereby reducing the time cost of the algorithm. The custom evaluation function is used to improve the efficiency of RNA secondary structure prediction algorithms. Moreover, the performance of the PRSA algorithm is compared with state of art algorithms including eighteen PseudoBase benchmark instances, and the comparison results show that the PRSA algorithm is more accurate and competitive with higher sensitivity and specificity values. However, as the size of RNA molecules becomes larger, this superiority will gradually disappear. The reason for the analysis may be that the algorithm for evaluating individuals is based on the average base pairs length rather than the standard thermodynamic model. As the length of the RNA molecule increases, the number of groups of complementary bases M(X) will become larger, so that the effect of average base-pairs on prediction results becomes weaker, the accuracy of the PRSA algorithm will be reduced. Besides, the parameter settings of the PRSA algorithm will also affect the prediction results, which will be studied further in the future. Pseudoknots sequencing data are available from the PseudoBase database (http://www.ekevanbatenburg.nl/PKBASE/PKB.HTML). DP: Guanine GA: Genetic Algorithm GRASP: Greedy Randomized Adaptive Search Procedure MFE: minimum free energy NP: Non-deterministic Polynomial RNA: Simulated Annealing Tinoco I, Bustamante C. How RNA folds. 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The author would like to thank the editors and reviewers for their suggestions, which is a great help for this article. About this supplement This article has been published as part of BMC Genomics Volume 20 Supplement 13, 2019: Proceedings of the 2018 International Conference on Intelligent Computing (ICIC 2018) and Intelligent Computing and Biomedical Informatics (ICBI) 2018 conference: genomics. The full contents of the supplement are available online at https://bmcgenomics.biomedcentral.com/articles/supplements/volume-20-supplement-13. This work was supported by the National Natural Science Foundation of China (Grant Nos. 61702383, U1803262, 61602350). School of Computer Science, Wuhan University of Science and Technology, Wuhan, 430081, China Zhang Kai, Wang Yuting, Lv Yulin, Liu Jun & He Juanjuan Hubei Province Key Laboratory of Intelligent Information Processing and Real-time Industrial System, Wuhan, 430081, China Zhang Kai & Liu Jun Zhang Kai Wang Yuting Lv Yulin Liu Jun He Juanjuan Conceived and developed the algorithm: ZK and WYT. Performed the experiments: WYT, LYL and LJ. Analyzed the data: ZK and HJJ. Wrote the article: ZK, WYT, and LYL. The manuscript has been read and approved by all named authors. Correspondence to He Juanjuan. Kai, Z., Yuting, W., Yulin, L. et al. An efficient simulated annealing algorithm for the RNA secondary structure prediction with Pseudoknots. BMC Genomics 20, 979 (2019). https://doi.org/10.1186/s12864-019-6300-2 RNA secondary structure Pseudoknot Simulated annealing algorithm	CommonCrawl
How is prestressing with losses self-balanced? By definition, prestressing is a self-balanced load. This is because it is in fact merely an applied state of internal stresses. This can also be demonstrated mathematically (in this case for a simple parabolic cable) via Lin's load-balancing method. For a cable which follows the layout given by $$ y(x) = \dfrac{4e}{L^2}x^2 $$ where $e$ is the vertical distance between the maximum and minimum points of the parabola, $L$ is the span of the cable, and $x=y=0$ is located at the minimum point of the layout, the equivalent load is $$ q = \dfrac{8Pe}{L^2}$$ where $P$ is the prestress force. Therefore, the total vertical load given by the distributed load is $\dfrac{8Pe}{L}$. This force is countered by the vertical forces applied at the anchors. These are equal to $P\sin(\theta) \approx P\theta$ and $y'(x) \approx \theta$, so the forces are each equal to $Py'\left(\frac{L}{2}\right) = \dfrac{4Pe}{L}$ and combined are equal (and opposite) to the total distributed load. So the total global load applied is null. Now, what if we consider friction losses between the cable and the duct in a post-tensioned beam? Then the combined forces at the extremities remain equal to $\dfrac{8Pe}{L}$, but the total distributed load will be reduced by the losses, implying in a non-balanced load, which is impossible. This may be adjusted by the anchorage slip losses, but what if we assume a hypothetical anchor which doesn't slip? Is this impossible and slippage is necessary to make the load balanced? And how are the remaining losses (elastic deformation, creep, shrinkage and relaxation) affected? civil-engineering structural-engineering concrete prestressed-concrete Wasabi♦Wasabi $\begingroup$ By friction losses, what exactly do you mean? Bond between the prestressing strands and the concrete/grout? $\endgroup$ – grfrazee $\begingroup$ Ah, this is for post-tensioned cables, not pre-tensioned. It is the friction between the cable and the duct at the moment of jacking. @grfrazee $\endgroup$ – Wasabi ♦ $\begingroup$ Ok, I see. Your title is a little misleading, then :-) $\endgroup$ $\begingroup$ Well, post-tensioning is still considered prestress ("prestressing with post-tensioned cables"). @grfrazee $\endgroup$ $\begingroup$ Understood. I'll admit that my experience with pre/post-tensioning isn't all that great. It's weird for me to call post-tensioned structures "prestressed" since you're applying the tensioning after construction, but I suppose "prestressing" really just means that the stress is applied before the load occurs. Ah, the wonderful vagaries of the English language... $\endgroup$ Comments by @Mr.P nudged me to realize that there is a redistribution of equivalent loads due to losses which cannot be trivially encompassed by Lin's method. To demonstrate this, take the following simply-supported beam (ignore all concepts of units or scale here, this is a thought exercise). The bending moment diagram solely due to prestress for this beam will be the following polygonal diagram (before any losses, assuming $P\cos\theta \approx P$): This is equivalent to the diagram obtained by a concentrated vertical load at midspan equal to $F = 2P\sin\theta \approx 40$, which is balanced out by the two vertical loads at the supports, each equal to $P\sin\theta \approx 20$ (in the opposite direction). However, let us now consider friction losses. Let's assume they cause a 10% reduction to the stress in the tendon at midspan. This implies that the bending moment at midspan will also be reduced by 10%, and will therefore equal 90. However, the diagram's profile is no longer polygonal. That can be easily observed by looking at the bending moment at any other point. In an isostatic structure, the bending moment is simply equal to $P \cdot e$, where $e$ is the distance between the cable and the centroid. Looking at quarter-span, the bending moment before losses was equal to $100\cdot0.5=50$, or exactly half of the mid-span moment. To calculate after losses, however, we need to calculate the force at this point. Simplifying things considerably, let's assume the loss here is half of that at midspan, so only 5%.1 In that case, the bending moment at quarter-span will be equal to $95\cdot0.5=47.5$, which is not equal to half of the mid-span moment of 90. Indeed, the bending moment diagram from support to midspan becomes of the form $$M = Pe\left(\dfrac{2x}{L}-0.1\left(\dfrac{2x}{L}\right)^2\right)$$ where $e$ is the distance of the cable to the centroid at midspan, $L$ is the span, and $0.1$ represents the 10% loss of prestress at midspan. Getting the first and second derivatives of this equation gives us the equivalent concentrated load at midspan and the uniform load distributed along the entire span, respectively: $$\begin{align} M' = Q &= Pe\left(\dfrac{2}{L} - 0.2\dfrac{4x}{L^2}\right) \\ Q\left(\dfrac{L}{2}\right) &= \dfrac{1.6Pe}{L} \therefore F = 2Q\left(\dfrac{L}{2}\right) = 32 \\ M'' = q &= \dfrac{0.8Pe}{L^2} = 0.8 \end{align}$$ Therefore, the equivalent loading which generates the correct (simplified) bending moment diagram after friction losses is the following: This implies in a new uniform load which did not appear before losses, a representation of the load redistribution described by @Mr.P. The equivalent concentrated load at midspan is also no longer equal to $F = 2P\sin\theta$, which would have resulted in $F \approx 36$. The prestress, however, is balanced, since $32 + 0.8\cdot10 = 40$, as expected. The same reasoning can be applied to parabolic cables. For the following beam: the uniform equivalent load is $q = \dfrac{8Pe}{L^2} = 2$, which generates a total upwards force of $2\cdot32=64$, to be cancelled out by the concentrated downwards forces of 32 at each support. The bending moment diagram before any losses is: However, assuming once again a 10% loss due to friction at midspan, and that the friction-loss profile is linear, the bending moment diagram becomes: which has the following cubic equation (with $x=0$ at the midspan): $$M = 2.00\cdot128\left(1-\left(\dfrac{2x}{L}\right)^2\right)\left(0.9+0.1\dfrac{2x}{L}\right)$$ getting the first and second derivatives, I can find the equivalent loading, which in this case is equal to: Given what we saw with the first example, it comes as no surprise that there's an increase in the distributed load near the supports. It also makes intuitive sense that the distributed load is reduced near the midspan. How that concentrated load at midspan comes to be, however, I have no idea. However, once again the prestress is self-balanced: $\dfrac{1.8+2.4}{2}\cdot32-3.2=64$. This answer therefore answers the question posed of how prestressing with losses is self-balanced: the equivalent load is redistributed, but the total value is not modified. That being said, I cannot explain how to calculate this redistribution in a general case because, well, I don't know how that's done. 1 Though friction losses are usually quite linear (or polygonal), this is a poor assumption. After all, the 10% loss at midspan must include the effect of the concentrated angle change at that point. At quarter-span, the losses are only due to linear friction loss, and will therefore probably be substantially lower than 5%. That being said, we can just state that 10% is at the point immediately before the angle change, where the bending moment approaches 100 but where only linear friction losses have occurred. All diagrams obtained with Ftool, a free 2D frame analysis tool. $\begingroup$ Nice write-up! In theory you could produce a tendon profile that gives you a perfectly even equivalent load. It was way too long ago since I took my heavy calculus classes to even begin figuring out how to do it though. It would also look quite daunting once you take slip, staggered tensioning, etc. into account. Luckily for me, since the reality of our business is quite brutish, there's usually diminishing returns trying to find the perfect solution rather than settling for something close enough :) $\endgroup$ – Mr. P Not the answer you're looking for? Browse other questions tagged civil-engineering structural-engineering concrete prestressed-concrete or ask your own question. How accurately are moveable span bridges balanced? How is the design life of a reinforced concrete structure calculated? How is a self-locking hex nut (ISO 7040) used? Is the order of operations in jacking a cable relevant? (Non)simultaneous prestressing anchorage slip losses Axial deformation of variable cross-section member do prestressing tendons located in the compression zone contribute to compression reinforcement? Custom heavy gauge machine table to support clothes dryer How to calculate the required prestressed jacking pressure to apply to a pre-tension concrete beam?	CommonCrawl
Optimal design for dynamical modeling of pest populations MBE Home The role of structural viscoelasticity in deformable porous media with incompressible constituents: Applications in biomechanics August 2018, 15(4): 961-991. doi: 10.3934/mbe.2018043 Quantifying the survival uncertainty of Wolbachia-infected mosquitoes in a spatial model Martin Strugarek 1,2,, , Nicolas Vauchelet 3, and Jorge P. Zubelli 4, AgroParisTech, 16 rue Claude Bernard, 75231 Paris Cedex 05, France Sorbonne Université, Université Paris-Diderot SPC, CNRS, INRIA, Laboratoire Jacques-Louis Lions, équipe Mamba, F-75005 Paris, France LAGA - UMR 7539 Institut Galilée, Université Paris 13, 99, avenue Jean-Baptiste Clément 93430 Villetaneuse, France IMPA, Estrada Dona Castorina, 110 Jardim Botânico 22460-320, Rio de Janeiro, RJ, Brazil * Corresponding author: M. Strugarek. Received July 24, 2017 Accepted January 03, 2018 Published March 2018 Figure(6) Artificial releases of Wolbachia-infected Aedes mosquitoes have been under study in the past yearsfor fighting vector-borne diseases such as dengue, chikungunya and zika.Several strains of this bacterium cause cytoplasmic incompatibility (CI) and can also affect their host's fecundity or lifespan, while highly reducing vector competence for the main arboviruses. We consider and answer the following questions: 1) what should be the initial condition (i.e. size of the initial mosquito population) to have invasion with one mosquito release source? We note that it is hard to have an invasion in such case. 2) How many release points does one need to have sufficiently high probability of invasion? 3) What happens if one accounts for uncertainty in the release protocol (e.g. unequal spacing among release points)? 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Discrete & Continuous Dynamical Systems - A, 2006, 14 (1) : 93-116. doi: 10.3934/dcds.2006.14.93 Samira Boussaïd, Danielle Hilhorst, Thanh Nam Nguyen. Convergence to steady state for the solutions of a nonlocal reaction-diffusion equation. Evolution Equations & Control Theory, 2015, 4 (1) : 39-59. doi: 10.3934/eect.2015.4.39 Maho Endo, Yuki Kaneko, Yoshio Yamada. Free boundary problem for a reaction-diffusion equation with positive bistable nonlinearity. Discrete & Continuous Dynamical Systems - A, 2019, 0 (0) : 0-0. doi: 10.3934/dcds.2020033 Tarik Mohammed Touaoula, Mohammed Nor Frioui, Nikolay Bessonov, Vitaly Volpert. Dynamics of solutions of a reaction-diffusion equation with delayed inhibition. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020193 Henri Berestycki, Luca Rossi. Reaction-diffusion equations for population dynamics with forced speed I - The case of the whole space. Discrete & Continuous Dynamical Systems - A, 2008, 21 (1) : 41-67. doi: 10.3934/dcds.2008.21.41 Henri Berestycki, Luca Rossi. Reaction-diffusion equations for population dynamics with forced speed II - cylindrical-type domains. Discrete & Continuous Dynamical Systems - A, 2009, 25 (1) : 19-61. doi: 10.3934/dcds.2009.25.19 Martin Strugarek Nicolas Vauchelet Jorge P. Zubelli	CommonCrawl
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Sine-Gordon wobbles through Bäcklund transformations DCDS-S Home Variational approximations of bifurcations of asymmetric solitons in cubic-quintic nonlinear Schrödinger lattices October 2011, 4(5): 1033-1046. doi: 10.3934/dcdss.2011.4.1033 The VES hypothesis and protein misfolding Leonor Cruzeiro 1, CCMAR and FCT, Universidade do Algarve, Campus de Gambelas, Faro 8005-139, Portugal Received September 2009 Revised October 2009 Published December 2010 Proteins function by changing conformation. These conformational changes, which involve the concerted motion of a large number of atoms are classical events but, in many cases, the triggers are quantum mechanical events such as chemical reactions. Here the initial quantum states after the chemical reaction are assumed to be vibrational excited states, something that has been designated as the VES hypothesis. While the dynamics under classical force fields fail to explain the relatively lower structural stability of the proteins associated with misfolding diseases, the application of the VES hypothesis to two cases can provide a new explanation for this phenomenon. This explanation relies on the transfer of vibrational energy from water molecules to proteins, a process whose viability is also examined. Keywords: neurodegenerative diseases, ice worm., Davydov/Scott model. Mathematics Subject Classification: Primary: 92C05, 82C10; Secondary: 92C3. Citation: Leonor Cruzeiro. The VES hypothesis and protein misfolding. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1033-1046. doi: 10.3934/dcdss.2011.4.1033 J. Abrahams, A. Leslie, R. Lutter and J. Walker, Structure at 2.8 Å resolution of F1-ATPase from bovine heart mitochondria,, Nature, 370 (1994), 621. doi: 10.1038/370621a0. Google Scholar P. W. Anderson, Absence of diffusion in certain random lattices,, Phys. 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An Improved PSO Algorithm for the Classification of Multiple Power Quality Disturbances Liquan Zhao* and Yan Long** Corresponding Author: Liquan Zhao* ([email protected]) Liquan Zhao, School of Electrical Engineering, Northeast Electric Power University, Jilin, China, [email protected] Yan Long, Information & Telecommunication Group, Beijing Smart-Chip Microelectronics Technology Company Limited, Beijing, China, [email protected] Revision received: July 17 2017 Accepted: July 20 2017 Abstract: In this paper, an improved one-against-one support vector machine algorithm is used to classify multiple power quality disturbances. To solve the problem of parameter selection, an improved particle swarm optimization algorithm is proposed to optimize the parameters of the support vector machine. By proposing a new inertia weight expression, the particle swarm optimization algorithm can effectively conduct a global search at the outset and effectively search locally later in a study, which improves the overall classification accuracy. The experimental results show that the improved particle swarm optimization method is more accurate than a grid search algorithm optimization and other improved particle swarm optimizations with regard to its classification of multiple power quality disturbances. Furthermore, the number of support vectors is reduced. Keywords: Classification Accuracy , Classification of Power Quality Disturbance , Particle Swarm Optimization , Support Vector Machine The larger number of loads accessing the power system has caused a variety of problems for the power grids, resulting in economic losses and having a strong social impact in recent years. This has made the power providers and their customers more and more concerned about the problems of power quality. Therefore, the classification of power quality disturbances (PQDs) is required in order to solve power quality problems [1]. Frequently, a power quality disturbance is not just a single disturbance but is comprised of a variety of disturbances. In the latter cases, this disturbance is called multiple disturbances [2]. The classification of multiple PQDs includes extracting feature vectors and optimizing classifiers. At present, the main methods of classifying multiple power quality disturbances include: neural network [3], decision tree [4], and support vector machine (SVM) [5,6]. These classification methods are reliable but the processes of feature extraction and construction of the classifier are complex, there is a long training time for a neural network classifier and it is easy to fall into the local minimum. Although the decision tree classifier can be accomplished quickly, the rules are complex and the model is difficult to deal with. The SVM method is widely used to solve pattern recognition problems. SVM overcomes the disadvantages of the artificial neural network, which easily relapses into the local optimal solution and has a long training time [7], and thus, we used SVM as the classifier in this paper. However, the SVM classifier has currently not been matched with the best method to optimize the parameters. Based on this problem, a new method of power quality disturbance classification method is proposed based on an improved particle swarm optimization (PSO) algorithm for parameter optimization of the SVM classifier. The SVM method is used as a classifier to classify the PQDs in this paper. First, we use the wavelet transformation method to extract and input the features of PQDs into the classifier. After this, the improved PSO algorithm that we proposed is used to optimize the SVM. Finally, the power quality disturbances are classified by using SVM classifier. The main difference between our approach and previous approaches is that we proposed an improved PSO algorithm to optimize the SVM and applied this improved SVM to classify PQDs to further improve the classifier performance. 2. Support Vector Machine The SVM-based learning technique is slightly different from pattern-recognition problems in which the desired output is a discrete value instead of the real value function. The SVM utilizes a linear function set most problems are nonlinear in practice. The nonlinear separable problem can be mapped to a high dimensional space by the kernel function, which can be divided into a linear separable problem. The separation of two classes is performed by the optimal hyper plane [8]. The data set is [TeX:] $$T = \left\{ x _ { i } , y _ { i } \right\} , x _ { i } \in R ^ { n }$$ is the input vector and [TeX:] $$y _ { i } \in \{ + 1 , - 1 \}$$ is the output vector. The fuzzy one-class SVM searches for a crisp hyperplane that separates the image of the target class from the origin: [TeX:] $$f ( x ) = w ^ { T } x + b$$ where w is weight and b is base [9]. Eq. (1), which is namely the hyperplane, is considered to be optimal when the separating margin between two classes is at its maximum, which is achieved by computing: [TeX:] $$\varphi ( w ) = \min \frac { 1 } { 2 } \\| w \\| ^ { 2 }$$ which is subject to: [TeX:] $$y _ { i } \left( w ^ { T } x + b \right) \geq 1 , i = 1,2 , \cdots , N$$ Lagrange function method is used to optimize the above problem, which can be expressed as followings: [TeX:] $$\mathrm { L } ( w , b , a ) = \frac { 1 } { 2 } \\| w \\| ^ { 2 } - \sum _ { i = 1 } ^ { \mathrm { N } } a _ { \mathrm { i } } \left[ y _ { i } \left( w ^ { T } x _ { i } + b \right) - 1 \right]$$ where ai is a Lagrange multiplier and xi that corresponds to a non-zero ai is known as the support vector [10]. When the data set is not linearly separable, a slack variable is introduced. Thus, Eq. (2) is converted to Eq. (5). [TeX:] $$\varphi ( w , \xi ) = \left\{ \begin{array} { l } { \min ( 0.5 \\| \left. w \right\|\| ^ { 2 } + C \sum _ { i = 1 } ^ { N } \xi _ { i } ) } \\ { \text { s.t. } y _ { \mathrm { i } } \left( w ^ { T } x _ { i } + b \right) \geq 1 - \xi _ { i } \quad \xi _ { i } \geq 0 } \end{array} \right.$$ where C and [TeX:] $$\xi _ { i }$$ is the cost factor and slack variable, respectively. When the data set is not linearly separable, the original data space is transformed into a high dimensional space by using a conversion method. These transformations are performed by using kernel functions. Therefore, Eq. (5) can be converted to the following expression: [TeX:] $$Q ( a ) = \max \sum _ { i = 1 } ^ { N } a _ { i } - \frac { 1 } { 2 } \sum _ { i , j = I } ^ { N } a _ { i } a _ { j } y _ { i } y _ { j } K \left( x _ { i } \cdot x _ { j } \right)$$ subject to: [TeX:] $$\sum _ { i = 1 } ^ { N } y _ { i } a _ { i } = 0$$ [TeX:] $$0 \leq \alpha _ { i } \leq C , i = 1,2 , \cdots , N$$ where [TeX:] $$K \left( x _ { i } \cdot x _ { j } \right)$$ is the kernel function. The polynomial function, Gaussian function and radial basis function (RBF) are the most commonly used kernel functions. We selected the Gaussian kernel function as the kernel function of SVM, which can be expressed as follows: [TeX:] $$K \left( x \cdot x _ { i } \right) = \exp \left( - \frac { \left\\| x - x _ { i } \right\\| ^ { 2 } } { 2 \sigma ^ { 2 } } \right)$$ where σ is the bandwidth. Since SVM is originally designed for the binary classification, when we use it to deal with the multiclass problem, such as the classification of multiple PQDs that results in the observed power signals containing several disturbance components at the same time, we should use a combination of several binary classifiers to construct multiple classifiers. There are several methods of combining binary classifiers in order to construct multiclass classifications. The most commonly used multiclass classification method include the one-against-one method and the one against all method. This paper uses the one-against-one method. However, the parameters σ and C have uncertain values in SVM, and the selection of σ and C has a great impact on the classification results of the SVM method. Therefore, this paper uses an improved PSO method to optimize the parameters σ and C in the SVM method. The classification accuracy of power quality disturbances is used as the performance index for optimization. 3. Particle Swarm Optimization Algorithm The PSO method that was first proposed in 1995. It is motivated by simulating the way in which a swarm of birds search for food. The PSO method firstly randomly initializes the value of positions and velocities for each particle, before every particle adjusts its velocity according to its neighbors and flying experiences. This process can be expressed as the following: [TeX:] $$v _ { i d } ^ { t + 1 } = w v _ { i d } ^ { t } + c _ { 1 } r _ { 1 } \times \left( p _ { i d } - x _ { i d } ^ { t } \right) + c _ { 2 } r _ { 2 } \times \left( p _ { g d } - x _ { i d } ^ { t } \right)$$ [TeX:] $$x _ { \mathrm { id } } ^ { \mathrm { t } + 1 } = x _ { \mathrm { id } } ^ { \mathrm { t } } + v _ { \mathrm { id } } ^ { \mathrm { t } + 1 }$$ where [TeX:] $$v _ { i d } , x _ { i d } , p _ { i d } \text { and } p _ { g d }$$ are the velocity of particle, the current position of particle, best position of single particle and the best position of the population respectively [11]. The parameters w and t are the inertia weight and current iteration number, respectively. The parameters r1 and r2 are random positive values that are less than one. The parameters c1 and c2 are constants. The PSO method is a type of adaptive search optimization algorithm based on a group. The potential solution of each optimization problem in the algorithm is called a "particle". The objective function determines the fitness value of each particle. We use the classification accuracy of multiple QPDs as the fitness value. The process of particle swarm algorithm is expressed as follows: 1) Initialize all parameter values. 2) Calculate the fitness value of each particle. 3) Compare the fitness value of each particle with the optimal location of the history. The best fitness value of the particle is used as pid. 4) If the fitness value of every particle is better than the best position of the population. The current value is set to be pgd. 5) According to Eqs. (10) and (11), update the velocity and position of each particle. 6) If the number of iterations reaches its maximum, stop the algorithm. Otherwise, return to step 2. Although the standard PSO has many advantages, it is very random and the diversity is poor. In particular, it is difficult to obtain the global optimum solution for the PSO methods [12,13]. To overcome this problem, we proposed an improved PSO method. 4. Improved Particle Swarm Optimization Algorithm The inertia weight is one of the most important parameters for the PSO method, and it controls the degree of historical factors in the current state. Different inertia weights have different effects on the efficiency of the PSO. An increased inertia weight value will accelerate the speed of convergence. However when this value becomes smaller, it will make the convergence efficiency of the PSO more accurate. Setting the parameters properly can greatly improve the efficiency of the PSO method. Most researchers use the linearly decreasing method to calculate the inertia weight in order to improve the performance of the PSO method. These methods have better performance than the methods based on a fixed inertia weight. Furthermore, it can also adjust the local and global optimization ability of the PSO method. However, there are some disadvantages to linear transition as it does not truly reflect the particle search process and the achieved results are not satisfactory. This paper puts forward an exponential decreasing function in the iterative process. The basic idea behind this method is described as follows. In the initial stage of the algorithm, particles have a rapid searching speed. They expand into the global search space and determine the approximate location of the optimal solution in the shortest time. As the inertia weight gradually decreases, the speed of particles also slows. As the number of iteration increases, the inertia weight also gradually decreases. The exponential inertia weight formula is shown as follows: [TeX:] $$w = A ^ { - 1 } \exp \left[ \left( 1 - \frac { k } { T } \right) ^ { 2 } \right]$$ where A, T, and k are the amplitude modulation factor, the maximum iteration number, and current iteration number, respectively. Fig. 1 shows the inertia weight value with the change in the number of iterations. Where A = 3 and T = 100 . It can be seen from Fig. 1 that the improved inertia weight has a rapid decline rate in the initial stage, which results in the particles having a rapid searching speed and determining the approximate location of the optimal solution in the shortest time. As the number of iteration increases, the value of inertia weight gradually decreases which is good for fine search in a local area and improves the performance of the algorithm. The curve diagram of the change in the inertia weight with the iteration number. Fig. 2 shows the fitness value with the change in the number of iterations. As shown in Fig. 2, in early iterations, the fitness value obtained by the PSO method is bigger than our proposed PSO method, but after 20 iterations, the fitness value obtained by the improved PSO is bigger than the PSO. This means that the improved PSO method has better performance than the traditional PSO method. This shows that our proposed PSO algorithm is effective. The curve diagram of the change in the fitness with the iteration number. 5. Parameters Optimization of SVM based on Improved PSO The penalty parameter σ and bandwidth parameter C have uncertain values in the SVM classifier. Therefore, we use the improved PSO method to optimize these parameters to obtain the optimal value. xi1 and xi2 are used to express the bandwidth parameter and penalty parameter, respectively. The range of σ and C is set to [0.1, 100] and [0.1, 100], respectively. Furthermore, we set the maximum number of iterations as 100 and the number of particles as 20. The optimization of SVM parameters based on the improved PSO involves the follows: 1) Initialize the speed and position of the particle. 2) The corresponding A and B of each particle at the beginning are used in the SVM classifier. Calculate the initial fitness value of each particle and the fitness value is the classification accuracy of the disturbance. 3) Compare the individual fitness value and the historical optimal fitness value of each particle. If the current fitness value is good, record the current σ and C values and update the system. Otherwise, the σ and C values are unchanged. 4) Compare the current fitness values and the optimal fitness values of population of each particle. If the current fitness value is good, record the current σ and C values and update the system. Otherwise, the σ and C values are unchanged. 5) Update the velocity and position information of each particle according to the velocity and position formula. 6) If the number of iterations reaches the preset maximum, the algorithm stops and outputs the global optimal solution and the corresponding global optimal value. Otherwise, return to step (2) and repeat. 6. Simulation and Analysis We use 11 types of disturbance as the signals to be classified in this paper [14]. In this paper, the extracted features of the above-mentioned 11 types of PQDs signals are input into the SVM classifier, which uses our proposed PSO method to optimize the parameters of the SVM. Finally, the multiple PQDs are classified by the improved SVM. The process of classification involves the following steps: 1) The normalized processed data is selected as the training sample while the bandwidth parameters and the penalty parameters are given; 2) Use proposed PSO algorithm to optimize the above mentioned parameters and obtain the optimal value; 3) Training samples are trained by the SVM model and the classification model is obtained; 4) Finally, the remaining samples are input into the trained classification model as test samples, and the classification accuracy is obtained. Table 1 provides the mathematical expression of the 11 types of disturbances. (D1) to (D11) are the mathematical models of voltage sag, voltage interruption, voltage swell, harmonic, impulsive transient, transient oscillation, voltage flicker, voltage sag with flicker, voltage swell with flicker, voltage sag with harmonic and voltage swell with harmonic respectively. In the experiment, we set [TeX:] $$\omega = 100 \pi , t _ { 1 } = 0.071,$$, [TeX:] $$t _ { 2 } = 0.142 \text { and } T = 2 \pi / \omega$$. In the mathematical model, the u(t) is a step function, and the parameters B, [TeX:] $$\alpha _ { 3 } , \alpha _ { 5 } , \alpha _ { 7 } , \alpha \text { and } \beta$$ are randomly generated from the specified ranges that are given in (D1) to (D11), respectively. In this paper, 11 types of PQDs that are constructed according to the above mentioned model are used as the source signals to test the performance of the proposed classification method. The grid search algorithm [15] and the improved PSO algorithm [16,17] are compared against the multiple power quality disturbances classifications. We mainly focus on PSO algorithm so we did not compare the other swarm intelligence algorithms [18-21] that can also be used to optimize the SVM and classify quality disturbances. Mathematical models of power quality disturbance Table 2 provides the comparison of average accuracy and the total number of support vectors of multiple PQDs using the original PSO and improved PSO with different amplitude modulation factors A. The A is a parameter of inertia weight as shown in Eq. (12). There were 80 training samples for each disturbance and 120 test samples. From Table 2, we can see that the average classification accuracy of method based on the original PSO is 93.9394% and the total number of support vectors is 478. However, for the method based on the improved PSO method, when A=2.9 , the average classification accuracy is 94.3182% and the total number of support vectors is 369. Furthermore, when A=3.0 , the average accuracy of the method based on the improved PSO method is 94.7727% and the total number of support vectors is 325. When A=3.1 , the average classification accuracy of the improved PSO method is 94.4697% and the total number of support vectors is 386. When A=3.2 , the average classification accuracy of the improved PSO method is 94.3939% and the total number of support vectors is 406. Although the classification accuracy of the method based on the improved PSO method and the number of support vector vary with different A values, all accuracy values were higher for our PSO method compared to the method based on the original PSO method while the number of support vectors is less than the original method. This shows that the performance of classification method based on the improved PSO is better than the original PSO in terms of accuracy and running time. Comparison results of different A values When the value of A is greater than 3 or less than 3, the classification accuracy will be reduced and the number of support vectors will increase. This is because the value of A becomes larger and the maximum and minimum values of the inertia weight will be larger. However, literature has shown that the optimal value of the inertia weight is between 0.4 and 0.9 so the value of A was chosen to be 3 in this paper. Classification accuracy of various disturbance signals The classification accuracy of power quality disturbances based on different methods is shown in Table 3. There were 80 training samples of each disturbance and 120 test samples. As shown in Table 3, the accuracies of voltage sag and harmonic disturbance are the same for different methods. For the voltage swell disturbance, impulsive transient disturbance, voltage sag+harmonic, the proposed method has the same accuracy as the grid search method, which is higher than others. For the voltage interruption disturbance, the proposed method has the same accuracy of 88.3333% as the SVM method based on the improved PSO [16] method, which is higher than others. For the transient oscillation disturbance and voltage swell+harmonic, the proposed method has the same accuracy as the SVM methods based on the improved PSO [16] and improved PSO [17] method, which is higher than others. For the voltage sag+flicker, the proposed method has higher accuracy than the others. For the voltage flicker and voltage swell+flicker, the proposed method has lower accuracy than other methods. Although our method has lower accuracy for two types of disturbance signals, our method has the same or higher accuracy for the other nine types of disturbance signals and the average classification accuracy of our method is 94.7727%. This is higher than the accuracy of other methods, which is 93.9394%, 94.1667%, 94.1667% and 94.0909%, respectively. This shows that our method has better performance. In this paper, an improved PSO method is proposed and used to optimize the parameters of the SVM to improve the performance of the power quality disturbances classification. The improved PSO algorithm utilizes a new exponential function formula for determining inertia weight. In the initial stage of the algorithm, a particle has a rapid searching speed. With a gradual decrease in the inertia weight, the speed of the particles will be reduced and in the later stage, the rate of inertia weight gradually decreases. This is advantageous in allowing for a continuous search of a local area and improving the performance of the algorithm. The parameters of the SVM are optimized by the improved PSO algorithm before the multiple power quality disturbances are classified. Compared with other improved PSO algorithms and grid search algorithms, the average classification accuracy is enhanced by using the improved PSO method. In addition, the total number of support vectors is also reduced. This paper is supported by the National Natural Science Foundation of China (Grant No. 61271115). 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Houhe, "Planning of distributed energy storage system for improving low voltage and network loss in rural network," Journal of Northeast Electric Power University, vol. 37, no. 5, pp. 19-24, 2017.custom:[[[-]]] Disturbance type Mathematical model Voltage swell [TeX:] $$X ( t ) = \left( 1 + B \left[ u \left( t _ { 2 } \right) - u \left( t _ { 1 } \right) \right] \right) \sin \omega t , T \leq t _ { 2 } - t _ { 1 } \leq 9 T , 0.1 \leq B \leq 0.8$$ (D1) Voltage sag [TeX:] $$X ( t ) = \left( 1 - B \left[ u \left( t _ { 2 } \right) - u \left( t _ { 1 } \right) \right] \right) \sin \omega t , T \leq t _ { 2 } - t _ { 1 } \leq 9 T , 0.1 \leq B \leq 0.8$$ (D2) Voltage interruption [TeX:] $$X ( t ) = \left( 1 - B \left[ u \left( t _ { 2 } \right) - u \left( t _ { 1 } \right) \right] \right) \sin \omega t , T \leq t _ { 2 } - t _ { 1 } \leq 9 T , 0.9 \leq B \leq 1$$ (D3) Harmonic [TeX:] $$\begin{array} { l } { X ( t ) = \sin \omega t + \alpha _ { 3 } \sin ( 3 \omega t ) + \alpha _ { 5 } \sin ( 5 \omega t ) + \alpha _ { 7 } \sin ( 7 \omega t ) } \\ { 0.05 \leq \alpha _ { 3 } \leq 0.15,0.02 \leq \alpha _ { 5 } \leq 0.1,0.02 \leq \alpha _ { 7 } \leq 0.1 } \end{array}$$ (D4) Impulsive transient [TeX:] $$\begin{array} { l } { X ( t ) = \sin \omega t + B \left[ u \left( t - t _ { 1 } \right) - u \left( t - t _ { 2 } \right) \right] } \\ { 1 \leq B \leq 3,1 m s \leq t _ { 2 } - t _ { 1 } \leq 3 m s } \end{array}$$ (D5) Transient oscillation [TeX:] $$\begin{array} { l } { X ( t ) = \sin \omega t + B e ^ { - 10 \left( t _ { 2 } - t _ { 1 } \right) } \sin 10 \omega t \left[ u \left( t _ { 2 } \right) - u \left( t _ { 1 } \right) \right] } \\ { 0.5 T \leq t _ { 2 } - t _ { 1 } \leq 3 T , 0.1 \leq B \leq 0.8 } \end{array}$$ (D6) Voltage flicker [TeX:] $$X ( t ) = [ 1 + \alpha \sin ( \beta \omega t ) ] \sin \omega t , 0.05 \leq \alpha \leq 0.1,0.1 \leq \beta \leq 0.3$$ (D7) Voltage swell+harmonic [TeX:] $$\begin{array} { l } { X ( t ) = \left( 1 + B \left[ u \left( t _ { 2 } \right) - u \left( t _ { 1 } \right) \right] \right) \sin \omega t + \sin ( \omega t ) + \alpha _ { 3 } \sin ( 3 \omega t ) + \alpha _ { 5 } \sin ( 5 \omega t ) + \alpha _ { 7 } \sin ( 7 \omega t ) } \\ { 0.1 \leq B \leq 0.8 , T \leq t _ { 2 } - t _ { 1 } \leq 9 T , 0.05 \leq \alpha _ { 3 } \leq 0.15,0.02 \leq \alpha _ { 5 } \leq 0.1,0.02 \leq \alpha _ { 7 } \leq 0.1 } \end{array}$$ (D8) Voltage sag+harmonic [TeX:] $$\begin{array} { l } { X ( t ) = \left( 1 - B \left[ u \left( t _ { 2 } \right) - u \left( t _ { 1 } \right) \right] \right) \sin \omega t + \sin ( \omega t ) + \alpha _ { 3 } \sin ( 3 \omega t ) + \alpha _ { 5 } \sin ( 5 \omega t ) + \alpha _ { 7 } \sin ( 7 \omega t ) } \\ { 0.1 \leq B \leq 0.8 , T \leq t _ { 2 } - t _ { 1 } \leq 9 T , 0.05 \leq \alpha _ { 3 } \leq 0.15,0.02 \leq \alpha _ { 5 } \leq 0.1,0.02 \leq \alpha _ { 7 } \leq 0.1 } \end{array}$$ (D9) Voltage swell+flicker [TeX:] $$\begin{array} { l } { X ( t ) = \left( 1 + B \left[ u \left( t _ { 2 } \right) - u \left( t _ { 1 } \right) \right] \right) \sin \omega t + [ 1 + \alpha \sin ( \beta \omega t ) ] \sin \omega t } \\ { T \leq t _ { 2 } - t _ { 1 } \leq 9 T , 0.05 \leq \alpha \leq 0.1,0.1 \leq B \leq 0.8,0.1 \leq \beta \leq 0.3 } \end{array}$$ (D10) Voltage sag+flicker [TeX:] $$\begin{array} { l } { X ( t ) = \left( 1 - B \left[ u \left( t _ { 2 } \right) - u \left( t _ { 1 } \right) \right] \right) \sin \omega t + [ 1 + \alpha \sin ( \beta \omega t ) ] \sin \omega t } \\ { T \leq t _ { 2 } - t _ { 1 } \leq 9 T , 0.05 \leq \alpha \leq 0.1,0.1 \leq B \leq 0.8,0.1 \leq \beta \leq 0.3 } \end{array}$$ (D11) Algorithm Average classification accuracy (%) Total number of support vectors Original PSO 93.9394 478 Improved PSO A = 2.9 94.3182 369 Disturbance type Classification accuracy (%) Original PSO Grid search Others improved PSO [16] Others improved PSO [17] Improved PSO Voltage sag 100 100 100 100 100 Voltage swell 88.3333 90.8333 89.1667 89.1667 90.8333 Voltage interruption 86.6667 85.8333 88.3333 86.6667 88.3333 Harmonic 100 100 100 100 100 Impulsive transient 97.5 98.3333 97.5 97.5 98.3333 Transient oscillation 99.1667 99.1667 100 100 100 Voltage flicker 95 92.5 95 94.1667 94.1667 Voltage sag+harmonic 90 91.6667 90.8333 90.8333 91.6667 Voltage swell+harmonic 90 90 91.6667 91.6667 91.6667 Voltage sag+flicker 90 90.8333 89.1667 90 92.5 Voltage swell+flicker 96.6667 96.6667 94.1667 95 95 Average classification accuracy 93.9394 94.1667 94.1667 94.0909 94.7727	CommonCrawl
$\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\\| #1 \\|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$ 3.2: The Mean Value Theorem [ "article:topic", "mean value theorem", "instantaneous velocity", "Rolle\u2019s Theorem", "authorname:apex", "showtoc:no", "license:ccbync" ] Book: Calculus (Apex) 3: The Graphical Behavior of Functions Contributed by Gregory Hartman et al. Associate Professor (Mathematics) at Virginia Military Institute $ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $ $ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} $ We motivate this section with the following question: Suppose you leave your house and drive to your friend's house in a city 100 miles away, completing the trip in two hours. At any point during the trip do you necessarily have to be going 50 miles per hour? In answering this question, it is clear that the average speed for the entire trip is 50 mph (i.e. 100 miles in 2 hours), but the question is whether or not your instantaneous speed is ever exactly 50 mph. More simply, does your speedometer ever read exactly 50 mph?. The answer, under some very reasonable assumptions, is "yes."' Let's now see why this situation is in a calculus text by translating it into mathematical symbols. First assume that the function $y = f(t)$ gives the distance (in miles) traveled from your home at time $t$ (in hours) where $0\le t\le 2$. In particular, this gives $f(0)=0$ and $f(2)=100$. The slope of the secant line connecting the starting and ending points $(0,f(0))$ and $(2,f(2))$ is therefore \frac{\Delta f}{\Delta t} = \frac{f(2)-f(0)}{2-0} = \frac{100-0}{2} = 50 \, \text{mph}. The slope at any point on the graph itself is given by the derivative $f'(t)$. So, since the answer to the question above is "yes," this means that at some time during the trip, the derivative takes on the value of 50 mph. Symbolically, f'(c) = \frac{f(2)-f(0)}{2-0} = 50 for some time $0\le c \le 2.$ How about more generally? Given any function $y=f(x)$ and a range $a\le x\le b$ does the value of the derivative at some point between $a$ and $b$ have to match the slope of the secant line connecting the points $(a,f(a))$ and $(b,f(b))$? Or equivalently, does the equation \[f'(c) = \frac{f(b)-f(a)}{b-a}\] have to hold for some $a < c < b$? Let's look at two functions in an example. Example $\PageIndex{1}$: Comparing average and instantaneous rates of change Consider functions $$f_1(x)=\frac{1}{x^2}\quad \text{and} \quad f_2(x) = \|x\|$$ with $a=-1$ and $b=1$ as shown in Figure $\PageIndex{1}$ (a) and (b), respectively. Both functions have a value of 1 at $a$ and $b$. Therefore the slope of the secant line connecting the end points is $0$ in each case. But if you look at the plots of each, you can see that there are no points on either graph where the tangent lines have slope zero. Therefore we have found that there is no $c$ in $[-1,1]$ such that $$f'(c) = \frac{f(1)-f(-1)}{1-(-1)} = 0.$$ Figure $\PageIndex{1}$: A graph of $f_1(x) = 1/x^2$ and $f_2(x) = \|x\|$ in Example $\PageIndex{1}$. So what went "wrong"'? It may not be surprising to find that the discontinuity of $f_1$ and the corner of $f_2$ play a role. If our functions had been continuous and differentiable, would we have been able to find that special value $c$? This is our motivation for the following theorem. Theorem $\PageIndex{1}$: The Mean Value Theorem of Differentiation Let $y=f(x)$ be continuous function on the closed interval $[a,b]$ and differentiable on the open interval $(a,b)$. There exists a value $c$, $a < c < b$, such that f'(c) = \frac{f(b)-f(a)}{b-a}. That is, there is a value $c$ in $(a,b)$ where the instantaneous rate of change of $f$ at $c$ is equal to the average rate of change of $f$ on $[a,b]$. Note that the reasons that the functions in Example $\PageIndex{1}$ fail are indeed that $f_1$ has a discontinuity on the interval $[-1,1]$ and $f_2$ is not differentiable at the origin. We will give a proof of the Mean Value Theorem below. To do so, we use a fact, called Rolle's Theorem, stated here. Theorem $\PageIndex{2}$: Rolle's Theorem Let $f$ be continuous on $[a,b]$ and differentiable on $(a,b)$, where $f(a) = f(b)$. There is some $c$ in $(a,b)$ such that $f'(c) = 0.$ Consider Figure $\PageIndex{2}$ where the graph of a function $f$ is given, where $f(a) = f(b)$. It should make intuitive sense that if $f$ is differentiable (and hence, continuous) that there would be a value $c$ in $(a,b)$ where $f'(c)=0$; that is, there would be a relative maximum or minimum of $f$ in $(a,b)$. Rolle's Theorem guarantees at least one; there may be more. FIgure $\PageIndex{2}$: A graph of $f(x) = x^3-5x^2+3x+5$, where $f(a) = f(b)$. Note the existence of $c$, where $a<c<b$, where $f'(c)=0$. Rolle's Theorem is really just a special case of the Mean Value Theorem. If $f(a) = f(b)$, then the average rate of change on $(a,b)$ is $0$, and the theorem guarantees some $c$ where $f'(c)=0$. We will prove Rolle's Theorem, then use it to prove the Mean Value Theorem. Proof of Rolle's Theorem Let $f$ be differentiable on $(a,b)$ where $f(a)=f(b)$. We consider two cases. Case 1: Consider the case when $f$ is constant on $[a,b]$; that is, $f(x) = f(a) = f(b)$ for all $x$ in $[a,b]$. Then $f'(x) = 0$ for all $x$ in $[a,b]$, showing there is at least one value $c$ in $(a,b)$ where $f'(c)=0$. Case 2: Now assume that $f$ is not constant on $[a,b]$. The Extreme Value Theorem guarantees that $f$ has a maximal and minimal value on $[a,b]$, found either at the endpoints or at a critical value in $(a,b)$. Since $f(a)=f(b)$ and $f$ is not constant, it is clear that the maximum and minimum cannot both be found at the endpoints. Assume, without loss of generality, that the maximum of $f$ is not found at the endpoints. Therefore there is a $c$ in $(a,b)$ such that $f(c)$ is the maximum value of $f$. By Theorem 3.1.2, $c$ must be a critical number of $f$; since $f$ is differentiable, we have that $f'(c) = 0$, completing the proof of the theorem. We can now prove the Mean Value Theorem. Proof of the Mean Value Theorem Define the function $$g(x) = f(x) - \frac{f(b)-f(a)}{b-a}x.$$ We know $g$ is differentiable on $(a,b)$ and continuous on $[a,b]$ since $f$ is. We can show $g(a)=g(b)$ (it is actually easier to show $g(b)-g(a)=0$, which suffices). We can then apply Rolle's theorem to guarantee the existence of $c \in (a,b)$ such that $g'(c) = 0$. But note that $$0= g'(c) = f'(c) - \frac{f(b)-f(a)}{b-a} \ ;$$ $$f'(c) = \frac{f(b)-f(a)}{b-a},$$ which is what we sought to prove. Going back to the very beginning of the section, we see that the only assumption we would need about our distance function $f(t)$ is that it be continuous and differentiable for $t$ from 0 to 2 hours (both reasonable assumptions). By the Mean Value Theorem, we are guaranteed a time during the trip where our instantaneous speed is 50 mph. This fact is used in practice. Some law enforcement agencies monitor traffic speeds while in aircraft. They do not measure speed with radar, but rather by timing individual cars as they pass over lines painted on the highway whose distances apart are known. The officer is able to measure the average speed of a car between the painted lines; if that average speed is greater than the posted speed limit, the officer is assured that the driver exceeded the speed limit at some time. Note that the Mean Value Theorem is an existence theorem. It states that a special value $c$ exists, but it does not give any indication about how to find it. It turns out that when we need the Mean Value Theorem, existence is all we need Example $\PageIndex{2}$: Using the Mean Value Theorem Consider $f(x) = x^3+5x+5$ on $[-3,3]$. Find $c$ in $[-3,3]$ that satisfies the Mean Value Theorem. The average rate of change of $f$ on $[-3,3]$ is: $$\frac{f(3)-f(-3)}{3-(-3)} = \frac{84}{6} = 14.$$ We want to find $c$ such that $f'(c) = 14$. We find $f'(x) = 3x^2+5$. We set this equal to 14 and solve for $x$. \[ \begin{align} f'(x) &= 14 \\ 3x^2 +5 &= 14\\ x^2 &= 3\\ x &= \pm \sqrt{3} \approx \pm 1.732 \end{align}\] We have found 2 values $c$ in $[-3,3]$ where the instantaneous rate of change is equal to the average rate of change; the Mean Value Theorem guaranteed at least one. In Figure $\PageIndex{3}$ $f$ is graphed with a dashed line representing the average rate of change; the lines tangent to $f$ at $x=\pm \sqrt{3}$ are also given. Note how these lines are parallel (i.e., have the same slope) as the dashed line. Figure $\PageIndex{3}$: Demonstrating the Mean Value Theorem in Example $\PageIndex{2}$. While the Mean Value Theorem has practical use (for instance, the speed monitoring application mentioned before), it is mostly used to advance other theory. We will use it in the next section to relate the shape of a graph to its derivative. Gregory Hartman (Virginia Military Institute). Contributions were made by Troy Siemers and Dimplekumar Chalishajar of VMI and Brian Heinold of Mount Saint Mary's University. This content is copyrighted by a Creative Commons Attribution - Noncommercial (BY-NC) License. http://www.apexcalculus.com/ Integrated by Justin Marshall. 3.1: Extreme Values 3.3: Increasing and Decreasing Functions Gregory Hartman (Apex) CC BY-NC instantaneous velocity Rolle's Theorem © Copyright 2019 Mathematics LibreTexts	CommonCrawl
Letter to the editors in chief KRM Home Global regularity for a model of Navier-Stokes equations with logarithmic sub-dissipation February 2018, 11(1): 191-213. doi: 10.3934/krm.2018010 Asymptotic behavior of the compressible non-isentropic Navier-Stokes-Maxwell system in $\mathbb{R}^3$ Zhong Tan and Leilei Tong , School of Mathematical Sciences and Fujian Provincial Key Laboratory, on Mathematical Modeling & High Performance Scientific Computing, Xiamen University, Xiamen 361005, China *Corresponding author: Leilei Tong Received June 2015 Revised February 2017 Published August 2017 Fund Project: This work is Supported by the National Natural Science Foundation of China (Grant Nos. 11271305,11531010) The compressible non-isentropic Navier-Stokes-Maxwell system is investigated in $\mathbb{R}^3$ and the global existence and large time behavior of solutions are established by pure energy method provided the initial perturbation around a constant state is small enough. 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Research \| Open \| Published: 06 May 2016 Predicting the dynamics of a native Araucaria forest using a distance-independent individual tree-growth model Enrique Orellana1, Afonso Figueiredo Filho1,2, Sylvio Péllico Netto2 & Jerome Klaas Vanclay3 Forest Ecosystemsvolume 3, Article number: 12 (2016) \| Download Citation In recent decades, native Araucaria forests in Brazil have become fragmented due to the conversion of forest to agricultural lands and commercial tree plantations. Consequently, the forest dynamics in this forest type have been poorly investigated, as most fragments are poorly structured in terms of tree size and diversity. We developed a distance-independent individual tree-growth model to simulate the forest dynamics in a native Araucaria forest located predominantly in southern Brazil. The data were derived from 25 contiguous plots (1 ha) established in a protected area left undisturbed for the past 70 years. The plots were measured at 3-year intervals from their establishment in 2002. All trees above a 10-cm diameter at breast height were tagged, identified as to species, and measured. Because this forest type comprises hundreds of tree species, we clustered them into six ecological groups: understory, subcanopy, upper canopy shade-tolerant, upper canopy light-demanding, pioneer, and emergent. The diameter increment, survival, and recruitment sub-models were fitted for each species group, and parameters were implemented in a simulation software to project the forest dynamics. The growth model was validated using independent data collected from another research area of the same forest type. To simulate the forest dynamics, we projected the species group and stand basal areas for 50 years under three different stand-density conditions: low, average, and high. Emergent species tended to grow in basal area, irrespective of the forest density conditions. Conversely, shade-tolerant species tended to decline over the years. Under low-density conditions, the model showed a growth tendency for the stand basal area, while under average-density conditions, forest growth tended to stabilize within 30 years. Under high-density conditions, the model indicated a decline in the stand basal area from the onset of the simulation, suggesting that under these conditions, the forest has already reached its maximum-stock capacity. The model validation using independent data indicated close agreement between the observed and estimated values, suggesting the model is consistent in projecting species-group and stand growth. The methodology used in this study for developing the growth model should be tested in other species-rich forests. The humid subtropical forests in South America exhibit a structure similar to that of tropical forests, but with fewer species and a lower tree density (Sands 2005). One of these subtropical forests is the Araucaria forest located primarily in southern Brazil between 20 and 30° south latitude (Behling and Pillar 2007) and comprised of hundreds of tree species. Araucaria angustifolia (Bert.) O. Kuntze is the most important species of this forest type and is regarded as Brazil's most important native conifer. Extensive commercial logging has left this forest type in fragments surrounded by agricultural crops, pasture, and grasslands (Koch and Corrêa 2002; Sands 2005). Between 1915 and 1960, Brazil exported 18.5 billion cubic meters of wood, most of it from Araucaria forests. Between 1960 and 1970, over 200,000 ha of Araucaria species were deforested. Today, this ecosystem is considered one of the most threatened in Brazil (Carlucci et al. 2011), and Araucaria angustifolia appears on the IUCN (International Union for Conservation of Nature and Natural Resources) red list of threatened species as critically endangered. Research on the forest dynamics of native araucarian forests is still incipient, mainly because most of the forest fragments are poorly structured. To gain a better understanding of the forest dynamics, growth models have been developed to evaluate the structure and composition of the forest over time. These powerful tools can be used to explore how the forest will change in response to adversity and stand conditions (Newton 2007). Because of inherent limitations, modelling approaches such as transition matrices and stand-table projections are no longer recommended to predict stand development in species-rich forests, except where the stand data are available only in summarized form (Vanclay 1994, p.55). Nevertheless, these approaches have been widely applied to simulate the forests dynamics in Brazilian Araucaria forests (Sanquetta 1999; Mello et al. 2003; Stepka et al. 2010; Ebling et al. 2012; Dalla Lana et al. 2015). Compared to matrix models, individual tree-growth models provide more versatility and a greater richness of detail to simulate growth in mixed forests (Zhao et al. 2004). Many individual tree-growth models have been developed to predict forests dynamics, particularly in the last two decades (Botkin 1993; Liu and Ashton 1998; Chave 1999; Huth and Ditzer 2000; Köhler et al. 2001; Tietjen and Huth 2006; Pütz et al. 2011). Some of these individual tree-based growth models have been used to evaluate the dynamics in tropical forests, but few have been constructed to investigate succession in conifer-angiosperm mixed forests in subtropical regions. This study is the first application of these modeling approaches to araucarian forest fragments in Brazil. The aim was to simulate the dynamics of the ecological species groups and the forest as a whole by using a distance-independent individual tree-growth model constructed for Brazil's native Araucaria forests. Experimental site The study area is part of the Irati National Forest (FLONA; 25.4° S, 50.6° W), a conservation unit that has been protected for over 70 years to encourage research in the forests of southern Brazil. Before the creation of the National Forest, the area underwent selective logging, but it has since been preserved. The climate is "Cfb" according to the Köppen classification system, with an average annual rainfall of 1442 mm and no dry season. The average temperatures are 22 °C in January and 10 °C in July, with more than five frosts a year. The study area was composed of 25 ha sampled as a series of contiguous 1-ha plots (100 m × 100 m), each subdivided into four 2500-m2 (50 m × 50 m) plots. Beginning in 2002, these plots were measured every 3 years. All trees with a diameter at breast height (DBH) greater than 10 cm were tagged, measured, and identified to the species level (Figueiredo Filho et al. 2010). Grouping species For highly diverse forests, it is often impractical to fit mathematical models to each species. To reduce the number of parameters, the species should therefore be grouped according to common characteristics (Vanclay 1991a; Purves and Pacala 2008). The species grouping is a key process in developing growth models for natural forests (Alder and Silva 2000), and several authors have discussed the best way to group them for modeling natural forest dynamics (Vanclay 1991a; Köhler and Huth 1998; Phillips et al. 2002; Gourlet-Fleury et al. 2005; Picard et al. 2010, 2012). We followed the methodology suggested by Alder et al. (2002) which has also been found useful by Lujan-Soto et al. (2015) in Mexican natural forests. This particular method defines ecological groups according to the position of the tree species on a two-axes graph with the average diameter increment (cm · yr−1) plotted against the 95th percentile of the diameter distribution (Fig. 1) when the diameters at breast height are sorted in ascending order (Alder et al. 2002). The maximum tree size was represented by the 95th percentile of the size distribution rather than the maximum observed size (King et al. 2006) to prevent bias from any errors or outliers. Araucaria forest data displayed using the two-dimensional species-classification system proposed by Alder et al. (2002). Upp. Can. Shade Tol. = upper canopy shade-tolerant; Upp. Can. Light Dem. = upper canopy light-demanding; incr, increment Alder's approach clustered species into six ecological groups: understory, subcanopy, upper canopy shade tolerant, upper canopy light demanding, pioneer and emergent. For example, understory species present low diameter growth rates (Y-axis of the graph) and do not reach big sizes (observed on the 95th percentile of diameter distribution, X-axis), pioneers present high diameter growth rates and do not reach big sizes. Conversely, emergents present high diameter growth rates and attain big sizes. While Alder et al. (2002) used cluster analysis to define the species groups, we defined them by plotting the data for the 107 species present in the sample area (25 ha) with more than 10 observations as described above (Fig. 1) and visually compared it to the two-axis graph proposed by Alder et al. (2002). For the species with few observations (n < 10), Alder's approach did not correspond to any known ecological groups in araucarian forests. Therefore, rare species (n < 10) were included in the group that most resembled the ecological description of the species as reported in the literature. The complete list of tree species and their ecological groups are presented in the Appendix. Sub-models to predict forest dynamics Sub-models of the diameter increment, survival, and recruitment were fitted for each of the six ecological groups formed. When analyzing forest growth, it is convenient to distinguish one- and two-sided competition. One-sided competition refers to resources such as light, which may be intercepted by overtopping trees and denied to overtopped. In contrast, two-sided competition refers to competition for other resources such as nutrients (Vanclay 1994, p. 161–162; Weiskittel et al. 2011). One-sided competition is well represented by the variable BAL (basal area in larger trees), which indicates the "sociological ranking" of the trees within the plot (Ledermann and Eckmüllner 2004). The diameter increment sub-model employed an equation (Eq. 1) suggested by Vanclay (1994), p.166, $$ \ln \left(\varDelta {d}_i+0,2\right)={\beta}_0+{\beta}_1.{\mathrm{DBH}}_i+{\beta}_2. \ln \kern0.5em {\mathrm{DBH}}_i+{\beta}_3.{\mathrm{BAL}}_i+{\beta}_4.G $$ where ln is the natural logarithm, Δd i is the diameter increment (cm · yr−1) of tree i, DBH is the diameter at breast height (cm) of tree i calculated for the middle of the interval (Vanclay 1994, p. 158), BAL is the basal area in larger trees (m2 · ha−1) of tree i, G is the plot basal area (m2 · ha−1), and β i are the estimated parameters. This is an easily fit and robust model whose trend line is very similar to those of other models that represent the biological behavior of the diameter increment (Vanclay 2012). A value of 0.2 was added when fitting the diameter increment to accommodate negative or zero increments (common in tropical forests) and enable the logarithmic transformation of null and negative values, because omitting these observations would have introduced bias and resulted in overestimates of the diameter increment (Vanclay 1991a). Because zero and negative increments are related to several factors that vary among the different data surveys, other studies have used offsets smaller (Vanclay 1991a) or larger than 0.2 (Kariuki et al. 2006; Easdale et al. 2012). A graphical analysis of the data offers an effective way to define the best value to use. The design of the plots in the sampled area with blocks (1 ha) divided in quadrats (2500 m2) allowed us to test different plot sizes when fitting diameter increment models. The p-value of the variable BAL revealed that quadrats were more effective than blocks when fitting diameter increment, whereas 1-ha blocks were more representative for plot basal area (G). This reflects the reality that competition for water and nutrients may extend over a much larger area than competition for light. Recruitment was estimated at plot level based on 1-ha plots. All recruitment trees are set to start with 10 cm of DBH, as this is the minimum-recorded tree size. The number of recruitment trees for each species group are estimated depending on two variables: group basal area (G g ) and stand basal area (G). Group basal area was chosen because more trees of a particular species group will recruit if more density of that group is present within the plot. Stand basal area was included in the model because species groups behave differently according to the density of trees. For example, shade-tolerants tend to benefit in crowded stands compared to light-demandings. Recruitments were estimated by (Eq. 2) $$ \ln \left(N+1\right)={\beta}_0+{\beta}_1.{G}_g+{\beta}_2.{G_g}^2+{\beta}_3.G $$ where ln is the natural logarithm, N is the number of trees per plot, G g is the basal area of the group g in the plot (m2 · ha−1), and G is the plot basal area (m2 · ha−1). This approach is consistent with other recruitment models (Vanclay 1992). Natural variability was included in the model by combining compatible deterministic and stochastic components to estimate tree survival. The deterministic estimate of tree survival was performed conventionally (Vanclay 1991b) with logistic regression using the same competition variables (BAL and G) employed in the diameter increment sub-model as the independent variables. Several transformations of DBH, such as DBH0.5, DBH2, and DBH−1 were examined to achieve a suitable response curve, with the resulting equation (Eq. 3) $$ p={\left[1+{ \exp}^{\left(-\left({\beta}_0+{\beta}_1.{X}_1+{\beta}_2.{X}_2+{\beta}_3.{\mathrm{BAL}}_i+{\beta}_4.G\right)\right)}\right]}^{-1} $$ where p is the survival probability in three years, X 1 and X 2 are transformations of DBH, BAL i and G are as defined above. At each time step of the model, six new records (one for each species group) are added to represent recruitment, with the number of recruit trees in each record estimated by Eq. 2. The survival of each record depends on the number of individuals represented by the record, with mortality simulated deterministically when stem counts are high, and implemented stochastically when stem counts fall below a user-specified threshold (termed 'granularity', and usually set between 0 and 1 per ha). The higher the threshold (granularity), the more run-to-run variation there will be in predictions. If the model-user sets the threshold to 0 the tree survival will be estimated deterministically. ARC statistical software (Cook and Weisberg 1999) was used to estimate the parameters, which were subsequently included in the simulation software Simile (Muetzelfeldt and Massheder 2003) to model the forest dynamics at the species-group and stand levels by projecting the basal areas. Simile is a useful tool to simulate forest dynamics, because it has several advantages in comparison to other simulation software (Vanclay 2003), particularly the visual interface that makes models accessible to those who are unfamiliar with computer programming (Muetzelfeldt and Massheder 2003). Evaluation and model validation The validation of the growth model was performed with data from another sampled area approximately 100 km from our study area and located in the protected National Forest (FLONA) of Três Barras in Santa Catarina state, where 26 1-ha permanent plots were established and measured once in 2004 and again in 2009. The structure of the forest where the data was collected to validate the model is similar to the structure of the sampled area used to parameterize the model, presented in an advanced stage of succession. The data observed in the field in 2009 were compared to the data projected by the model using the data from the first survey (2004) conducted in the sampled area as input. The comparisons between the projected and observed values were performed in the last survey year (2009), by calculating bias, (ē) precision (s e ) and accuracy (m x ), as suggested by Pretzsch (2009). $$ \overline{e}=\frac{{\displaystyle {\sum}_{i=1}^n\left({x}_i-{X}_i\right)}}{n}\kern3em {\overline{e}}_{\%}=\frac{\overline{e}}{\overline{X}}\times 100 $$ $$ {s}_e=\sqrt{\frac{{\displaystyle {\sum}_{i=1}^n{\left({x}_i-\overline{e}-{X}_i\right)}^2}}{n-1}}\kern2em {s}_{e\%}=\frac{s_e}{\overline{X}}\times 100 $$ $$ {m}_x=\sqrt{{\left({s}_e\right)}^2+{\left(\overline{e}\right)}^2}\kern3em {m}_{x\%}=\frac{m_x}{\overline{X}}\times 100 $$ where x i is the predicted value of plot i, X i is the observed value of plot i and n is the number of plots. Bias corresponds to a systematic deviation between observed and estimated values and is calculated by the mean difference between them. The precision indicates the concentration of predicted values around the arithmetic mean of the simulations. It is calculated from the deviation of the simulation from the observed values. The accuracy is calculated from the bias and precision and represents the degree to which the estimation approximates the reality. It can be unsatisfactory or poor when bias and low precision occurs, respectively (Pretzsch 2009). Simulating forest dynamics The model has a 1-ha spatial resolution and a temporal resolution (time-step) of 1 year. We selected three 1-ha plots that have different characteristics in terms of density—the plot with the lowest basal area (15.5 m2 · ha−1) in the sampled area, a plot with an average basal area (29.2 m2 · ha−1), and the plot with the highest basal area (39.1 m2 · ha−1) in the sampled area—to start the model. This allowed us to check its behavior under different conditions in terms of initial density. Basal area projections were made for the species groups (G g ) and stand (G) for a period of 50 years. The diameter increment, survival, and recruitment sub-model parameters that were fitted for the species groups are shown in Table 1. Table 1 Coefficients of the fitted models for diameter increment, survival, and recruitment for each species group For the diameter-increment models, only the independent variables of the pioneer group (Group 5) were not significant (p > 0.05), but they were nevertheless included in the model since the signs of the coefficients exhibited biological consistency. As expected, BAL and G had negative signs, indicating that the increased competition reduced the diameter increment. However, a significant BAL was expected for the pioneer group, as this group has high light demands. One hypothesis to explain the lack of significance of these variables for the pioneers may be that this group contains few observations due to the forest being at an advanced stage of succession. As for survival, the BAL variable was only being significant (p < 0.05) for the three shade-tolerant groups, suggesting that larger trees such as the representatives of the emergent and upper canopy light-demanding groups cause mortality in the three shade-tolerant groups. The stand basal area variable (G) was only significant for the understory, indicating that this is the group most affected by density. With respect to recruitment, G was insignificant for the tested models, but because the coefficients were consistent with biological expectations and experience elsewhere (Weiskittel et al. 2011), the variable was retained in the model. Validation of the growth model and simulations of forest dynamics The errors in bias, precision, and accuracy were calculated as percentages (Pretzsch 2009) and are shown in Table 2. Table 2 Percentage error in the bias, precision, and accuracy for the species-group and stand basal areas Errors greater than 11 % for the bias, precision, and accuracy were observed in three groups: the understory (G1), upper canopy shade-tolerant (G3) and pioneer groups (G5), but those for the stand basal area (G) did not exceed 3 %. Pioneer groups (G5) exhibited in the largest errors among the species groups, because this is the most diverse species group. Conversely, emergents (G6) exhibited the smallest errors in bias, precision and accuracy as this group is mainly represented by one tree species, namely Araucaria angustifolia (see Appendix). Simulation of forest dynamics After validating the model, it was used to predict the basal area of the species groups and stand (Fig. 2) with 50-year simulations using three plots with different densities: the plot with the lowest basal area (Fig. 2a and b), a plot with an average basal area (Fig. 2c and d), and the plot with the highest basal area (Fig. 2e and f). Fifty-year projections for the species group and stand basal areas. Plot simulations are for low (a, b), average (c, d), and high densities (e, f). The curves are averages from 20 simulations (granularity = 0.2), and the vertical bars indicate one standard deviation above and below the mean. G1, understory; G2, subcanopy; G3, upper canopy shade-tolerant; G4, upper canopy light-demanding, G5, pioneer; G6, emergent; G, stand basal area For the three plots analyzed, the projections indicated that the basal area tends to grow in emergent species, while that of the shade-tolerant species tends to decline (understory, subcanopy, and upper canopy shade-tolerant) (Fig. 2a, c and e). The model did not show any major change in the basal area of the light-demanding upper canopy over the simulated period. However, the growth of emergent species is not indefinite, and stabilization occurred close to 200 years after beginning the simulations. This estimate is consistent with the reality observed in the field given that the emergent group is composed solely of Araucaria angustifolia and Ocotea porosa, two of the most long-lived species of this forest type. Ocotea porosa is possibly the most long-lived species and can live for more than 500 years (Carvalho 1994). Studies based on stem analysis (counting annual rings) showed that Araucaria angustifolia can grow for up to ~300 years (Carvalho 2003). In the plot with low density, the model showed a growth trend in the stand basal area (Fig. 2b) over the 50-year simulation. The stand basal area growth stabilized in a period similar to that of the emergent species, that is, 200 years after the onset of the simulations. In the plot with average density, the model indicated a growth trend for the first 30 years after initiating the simulation (Fig. 2d), after which the growth stabilized. In the plot with the highest density, the model indicated a decline in stand basal area from the onset of the simulations (Fig. 2f), which was justified by the sharp decline in the basal area of two shade-tolerant groups, the subcanopy and the shade-tolerant upper canopy (Fig. 2e). This decline in the basal area in the high-density plot indicates high mortality rates, suggesting it has already reached its maximum stock. Other studies have been conducted to evaluate the forest dynamics for different species groups in species-rich forests by using individual tree-growth models (Köhler and Huth 1998; Huth and Ditzer 2000; Tietjen and Huth 2006; Groeneveld et al. 2009). In most cases, the emergent or climax species showed a growth tendency after 50-year simulations (Köhler and Huth 1998; Huth and Ditzer 2000; Tietjen and Huth 2006), corroborating our results, even though most of these studies applied process-based models. It is important to consider that comparisons between the results of different models are difficult, because they are constructed for different purposes, parameterized for forests that differ in typology and structure, and reported according to their objectives (Phillips et al. 2004). Overall, however, the methodology used in this study to project the forest dynamics using an empirical independent-distance individual tree-growth model constructed specifically for Araucaria forests has proven to be an effective means of assessing the forest dynamics in this forest type. We recommend testing the methodology applied in this study with other species-rich forests. The validation of the model we constructed using independent data collected from another research area indicated consistency within the model in projecting the stand and ecological species-group growth in the Araucaria forest. The method for grouping the species proposed by Alder et al. (2002) was efficient and, according to the literature, consistent with the ecological characteristics of the main species of the forest. The 50-year projections for the three plots of the study area revealed that the emergent-species group tends to grow in basal area, irrespective of forest density. Conversely, the model indicated that the shade tolerant-species groups tend to decline in basal area over time, which was more pronounced in the high-density plot. Regarding projections for the stand basal area, the model indicated more vigorous growth in the low-density plot over the simulated period. Conversely, a decline of basal area was observed over time in the high-density plot, suggesting that this plot has already reached its maximum stock, probably due to mortality in the shade-tolerant species. In conclusion, we recommend that the growth model we constructed be used to investigate the forest dynamics in Brazilian native Araucaria forests. The methodology used for developing this growth model, particularly the method applied for grouping the species in this study, can also be tested in other species-rich forests. Alder D, Silva J (2000) An empirical cohort model for management of Terra Firme forests in the Brazilian Amazon. 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Wiley-Blackwell, Chichester Zhao D, Borders B, Wilson M (2004) Individual-tree diameter growth and mortality models for bottomland mixed-species hardwood stands in the lower Mississippi alluvial valley. For Ecol Manage 199:307–322. doi:10.1016/j.foreco.2004.05.043 We thank CNPq (Brazilian National Council for Scientific and Technological Development) for providing a scholarship to the first author. This research was funded by CNPq (Brazilian National Council for Scientific and Technological Development). Midwest State University-UNICENTRO-PR, PR 153, Km 7, Riozinho, Irati, Paraná, 84500-000, Brazil Enrique Orellana & Afonso Figueiredo Filho Federal University of Paraná, UFPR. Av. Pref. Lothário Meissner, 900, Jardim Botânico, Curitiba, Paraná, 80210-170, Brazil Afonso Figueiredo Filho & Sylvio Péllico Netto Southern Cross University (SCU), PO Box 157, Lismore, NSW, Australia Jerome Klaas Vanclay Search for Enrique Orellana in: Search for Afonso Figueiredo Filho in: Search for Sylvio Péllico Netto in: Search for Jerome Klaas Vanclay in: Correspondence to Enrique Orellana. EO constructed the model and wrote the manuscript. AFF was responsible for collecting data since the first survey and he suggested the inclusion of the analysis presented on the paper. SPN suggested the inclusion of the statistical indices used in this research and helped with English editing. JKV taught the first author how to build the growth model and did the last review in the English version. All authors read and approved the final manuscript. Table 3 List of tree species classified in order of abundance for each group Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. https://doi.org/10.1186/s40663-016-0071-x Forest succession Araucaria angustifolia	CommonCrawl
Effect of Segment-Body Vibration on Strength Parameters Ruben Tobias Goebel1, Heinz Kleinöder2, Zengyuan Yue3, Ranajay Gosh4 & Joachim Mester2 An Erratum to this article was published on 09 September 2015 In this study, we examine the biomechanical advantage of combining localized vibrations to hamstring muscles involved in a traditional resistance training routine. Thirty-six male and female participants with at least 2 years of experience in resistance training were recruited from the German Sport University Cologne. The participants were randomized into two training groups: vibration training group (VG) and traditional training group (TTG). Both groups underwent a 4-week training phase, where each participant worked out at 70 % of the individual 1 repeat maximum (RM—maximum load capacity of a muscle for one lift to fatigue) (4 sets with 12 repetitions each). For participants in the VG group, local vibration was additionally applied directly to hamstring muscles during exercise. A 2-week examination phase preceded the pretests. After the pretests, the subjects underwent a prescribed training for 4 weeks. At the conclusion of the training, a 2-week detraining was imposed and then the study concluded with posttests and retest. The measured parameters were maximum isometric force of the hamstrings and maximum range of motion and muscle tension at maximum knee angle. The study revealed a significant increase in maximum isometric force in both training groups (VG = 21 %, TTG = 14 %). However, VG groups showed an increase in their range of motion by approximately 2 %. Moreover, the muscle tension at maximum knee angle increased less in VG (approximately 35 %) compared to TG (approximately 46 %). We conclude that segment-body vibrations applied in resistance training can offer an effective tool to increase maximum isometric force, compared to traditional training. The cause for these findings can be attributed to the additional local vibration stimulus. Maximum isometric force, range of motion, and muscle tension of hamstring muscle were compared between training regimes incorporating localized vibrations and traditional leg curl. The vibrational training group showed statistically significant improvements in maximum isometric force after the first week of training compared to 3 weeks for the traditional training regimen. The vibrational training group retained gain in performance for a longer time after the testing regimen than traditional training. The range of motion was improved, and muscle tension increase was less for the vibrational training group compared to the traditional training group. Resistance training is considered as the bedrock for improving neuromuscular performance for both athletic and preventive health [1–7]. Over the recent past, establishing additional training protocols over a traditional resistance training routine has been a key focus of sports and conditioning experts [8–11]. In this paper, we specifically focus on enhancement through vibration training method which has recently emerged as an effective and convenient technique in improving neuromuscular performance especially when combined with a strength training program. Underscoring this trend, whole-body vibration, which is easy to administer through a vibrating platform, has gained tremendous popularity over the last decade for neuromuscular improvements [12–14]. For instance, it was found that when whole-body vibrations were induced through the feet using a vibrating platform into resistance training individuals, maximum isometric force of the corresponding muscle group improved between 6.5 % and approximately 40 % (for example, see [15, 16]). Two effects are believed to be the primary reasons for the increase of maximum force of vibration training compared to traditional training. First, Martin and Park [17] and Mester et al. [18] found that reflectory muscle contractions take place during the vibration stimulus. The sensitivity of muscle spindles increases during vibration training, and their effects on the stretch-shortening cycle are acute responses of the skeleton muscles to vibration training. It is assumed that consequently the reaction time and the threshold to create an action potential are decreased [19–21]. Park and Martin [22] identified an increase of muscle strength in hand flexor muscles while introducing segment-body vibrations to the tendons of the same muscles. Second, Eklund and Hagbarth [23] showed the antagonistic muscle relaxation during vibration, which improves motor coordination between agonist and antagonist [17]. As a consequence, the synchronization of neuronal activity between the muscles was improved, which resulted in increased maximum force [24, 25]. Rehn et al. [20] showed in their rating of 19 studies " […] that there is strong to moderate evidence that long-term whole body vibrations can have positive effects regarding leg muscular performance" ([20], p. 4–5). It is furthermore reported that muscle tension (MT) increases after a traditional resistance training program [26]. No publication in English language could be identified to correlate muscle tension and vibration training. In contrast to whole-body vibration, which only indirectly influences the training muscle groups, direct stimulation of a specific muscle group can be a good alternative candidate due to specificity and greater control. Only few studies examined the effect of vibration training called segment-body vibration on muscle strength and athletic performance [27]. These studies have reported an increase of the maximum force between 5 and 50 % (e.g., [24, 28, 29]). Therefore, the present study examined the effects of a special local vibration training, in which local segment-body vibrations were directly induced into the belly of the hamstring muscles in comparison to an identical training regime without vibrations. Both maximum isometric force and maximum flexibility as well as MT of the trained muscles were measured following a predefined period and regimen of training. Approved by the Ethics-Committee of the German Sport Univeristy Cologne. In the present intervention study, the leg flexor muscles were strengthened unilaterally. A total of 36 healthy subjects with at least 2 years' experience in resistance training were selected for the study and randomized into a vibration training group (VG) and traditional training group (TTG). Note that no special prescriptions on diet and other behavioral activities were imposed for this study on any of the subjects. Additional informed consent was obtained from all patients for whom identifying information is included in this article. All procedures followed were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1975, as revised in 2008 [5]. The matched-pair technique [30] has been applied after the sixth pretest measurement to establish the two training groups. This technique assigned eight female subjects (44 %) to the VG and six female subjects (33 %) to the TTG. Both study groups performed the same exercise (leg curl) for the hamstrings on the right leg only. The setup of the leg curl machine in combination with the vibration generator physically only allowed superimposed vibrations during exercise of the right leg. The leg curl was performed on a lying leg curl machine (Gym 80, Signum Standart line, International Products, Gelsenkirchen, Germany [31]) with a standardized deadweight of 320 kg and a serially standardized weight stack of 85 kg. The weight stack did not limit the training load of any of the subjects. In addition to the regular resistance training machine, vibration was administered using a Medic Swing vibration generator (Mechatronic, Hamm, Germany). The device was convex and could be adjusted in height and angle, which allows its usage for local vibrations of lower body segments. Before participation, all subjects were fully informed of the purpose, experimental procedures, possible risks, and their rights and gave their written consent to participate. Variables and Statistics The comparative performance metric for the current experiment was set to the following variables: isometric force, maximum range of motion (ROM), and maximum MT. The reliability of the measurements was measured beforehand in a test-retest design with 12 test persons during the pretests. The results of the test-retest scenario are as follows: isometric force r = 0.75, ROM r = 0.79, and MT r = 0.69 where r describes the correlation coefficient. Means and standard deviations were calculated by ANOVA with repeated measurements. Differences were tested with the Tukey post hoc test. Moreover, the different values between pre- and posttests were examined by dependent t test as well. The progression from pretest to retest (six measurements) within the two study groups was also recorded. Finally, the 1-Pearson correlation as a measure of similarity between the time course of the individual changes has been calculated at VG and TTG to present the means of maximum isometric force development from pretest to retest. Ward's cluster algorithm has been applied at VG and TTG to present individual cases [32]. Sociometrical and anthropometrical data for this experiment are displayed in Table 1. Table 1 Sociometrical and anthropometrical data of the subjects in study 1 ($ \overline{\mathrm{x}} $ = mean, s x = standard deviation) During the 2 weeks of pretesting phase, each subject additionally performed six measurements of all variables in order to exclude adaptations due to the familiarization of the testing protocol by the subjects. These test results are not part of the pretest. The actual pretest was performed prior to the first training with a rest interval of 72 h before the first session of training commenced. First, second, and third measurements and posttest have been performed after each training week with at least 24 h rest after the last training session. After 2 weeks of detraining, the same tests were repeated during the retest to measure changes in performance. Note that during this phase of testing, no vibrations were provided to the VG. The maximum isometric force of the leg flexors was measured using a leg curl machine (Gym 80 International, Gelsenkirchen, Germany), which was equipped with a force sensor (Mechatronic) (see Fig. 1, right part). The sample rate of the force sensor was 100 Hz, and the accuracy of measurement was 0.01 N. The time frame, during which the force was recorded, covered 5 s. Subjects took a facedown position during the measurement. The inner knee angle during measurements was 160° (see Fig. 1, left part). Measurement of maximum isometric force. Left: measurement position; right: leg curl machine with force sensor In order to determine the range of motion of the knee joint, the following novel setup has been applied considering the anatomical structures of the knee joint. To the best of our knowledge, no references record this setup. Subjects lay on their backs with the counter-lateral knee protruding over the edge of the bench. This leg was fixed with a belt (see Fig. 2b) to avoid evasive movement of the hip joint. The leg to be studied was brought to maximum flexion in the hip joint (hip angle β; see Fig. 2). The two-joint hamstring muscles (m. semitendinosus, m. semimembranosus, m. biceps femoris (caput longum)) were fixed in their final position at the hip joint (see Fig. 2a). The hip angle β was measured taking the horizontal plane and the distal end of the condylus lateralis as reference points and trochanter major as pivot point. The maximum hip angle β of the pretest is re-established during all following measurements and therefore standardized the measurement. While the hip joint angle is fixed, subjects used a cable winch to bring the leg to be studied into a stretching position. Consequently, the hamstring muscles experience an extension. The distal end of the condylus lateralis, the trochanter major of the hip joint, and the malleolus lateralis of the ankle form the reference points for the knee angle α (see Fig. 2). The measurement accuracy of the goniometer was 1°. Angles were recorded after 3 s in the maximum joint angle. The maximum knee angle was self-determined by the subjects and defined as a position which the volunteer felt discomfort, but no pain. The knee angle α of the pretest served as reference value for the muscle tension and therefore was established in all following measurements. After this standard value was achieved, subjects are asked to reach their maximum possible knee angle. This novel setup to measure the ROM of the knee joint to determine the extensibility of the hamstring muscles was applied to eliminate the pain that occurs while stretching the hamstring muscles with full knee extension [33–36]. Measurement station and measurement procedure of muscle tension. A: fixation of the leg to be tested, B: fixation of the counter-lateral leg, C: adjustment pole, D: direction of traction, E: force sensor, target angle α, hip angle β, 90° between lower leg and cable winch While stretching the hamstrings, the muscle tension was measured using a force sensor (Mechatronic), which was located between the cable winch and foot loop. The force sensor and the lower leg of the subject were in a rectangular position. The force was recorded over a period of 5 s. The effect of gravity and the weight of the leg were eliminated from the maximum value measured in Newton. The following formula was used to calculate the actual muscle tension (the symbols explained in Table 2): Table 2 Explanation of the parts of the formula used to convert the measured muscle tension into the actual muscle tension and their units $$ \mathrm{Muscle}\ \mathrm{Tension}=\frac{F1L+fL* \cos \left(\alpha +\beta \right)}{\delta }. $$ Both study groups performed the same exercise (leg curl) for the hamstrings on the right leg only. The subjects executed 4 training sets of 12 repetitions with 90 s pause between sets for all individuals of both groups. A total of three training sessions per week was carried out for a total of 4 weeks. The resistance progression was tracked using repeated measurements of the maximum isometric force as the test progressed. The VG group, in addition to the abovementioned protocol, also underwent vibrational loading on their hamstring. For the test persons in VG, the vibration area was placed directly on the center of the hamstrings (Fig. 3, right part). This device worked with a constant amplitude of 4 mm and allows a variable frequency between 18 and 38 Hz. Only the VG group trained with additional segment-body vibrations. Table 3 describes and summarizes in greater detail the training parameters for hamstring strengthening in both groups. Left: vibration trainer Medic Swing (Mechatronic). Right: vibration training of the hamstrings Table 3 Training parameters The initial training load was determined at the end of the pretest phase, applying a test procedure previously described in detail [37]. The relative resistance was kept at 70 % of 1 RM for the whole training period in order to maintain a training load recommended for hypertrophy in resistance training [37, 38]. Consequently, the effective training load was adjusted according to the weekly measured maximum isometric force of the subject. The resistance training followed a 5-min general warm-up procedure for both groups which included 3 min of treadmill running at 8 km/h, stretching of quadriceps and hamstring muscles (twice holding each stretch for 15 s alternating between each leg), and jumping exercises, which included skipping (6 m), two foot ankle hops (6 reps), and split squat jump (5 reps) [39]. Maximum Isometric Force The progression of the mean maximum isometric force (in percent) over the duration of the study is plotted in Fig. 4. The mean of the pretest values for both groups was normalized to 100 %. The force (F) values of 10.22 in the VG and 8.19 in the TTG became significant in the one-way ANOVA with repeated measurements. Thus, both interventions, i.e., strengthening with and without vibration, produced a significant increase on maximum force. However, more useful information could be gleaned using the post hoc test (Tukey) which provides information about the effects of the training time on maximum force. Development of maximum isometric force (Fmax) in VG and TTG (Tukey post hoc test). Significant differences (α = 5 %) between mean values of measurements were marked with an asterisk Next, we studied at the t test for dependent samples for the changes in the groups from pretest to posttest (see Table 4). Both training groups showed significant changes between pretest and posttest. The mean maximum isometric force in the VG was 523 N in the pretest and 636 N in the posttest. For the TTG, the values were 567 N (pretest) and 648 N (posttest), respectively. Table 4 Result of the t test for dependent samples for VG and TTG with increases of isometric maximum force Results for Maximum Knee Angle The variance analyses only revealed one significant F value (2.69) for the VG. The value calculated for the TTG (1.53) was not significant. Based on this result, we can assume that vibration-supported maximal strength training has an impact on the maximum knee angle. For the TTG, neither time of measurement nor training stimuli influenced the development of the maximum knee angle significantly. The Tukey post hoc test for the VG showed that the development of maximum ROM shows only one significant difference. Thus, we can conclude that a vibration training of the hamstrings only has a limited impact on the maximum flexibility of the same musculature. The following t test for dependent samples provides more information about the development of the maximum knee angle over the duration of the training period (see Table 5). Table 5 Result of the t test for dependent samples for the VG and TTG with increases in maximum knee angle (ROM) Maximum Muscle Tension Figure 5 illustrates the course of the mean muscle tension (MT) at maximum knee angle over the duration of the study. The conclusion we can draw from the significant F values for both groups (F = 8.1 for the VG; F = 6.91 for the TTG) is that maximal strength training with and without vibration influences the maximum ROM and maximum MT of the trained musculature. The Tukey post hoc test showed that the increase of MT in the posttest differed significantly from all previous measurements of VG. This is also true for the retest values of VG when compared to all other measurements except for the pretest. Similarly, we cannot assess any changes in MT for the TTG's first 3 weeks of training (i.e., the pretest period). Statistically significant differences were measured between the pretest, first and third measurements, and posttest. These changes indicate an increase in MT at maximum knee angle. Finally, a significant decrease in MT can be ascertained between posttest and retest. The significant changes from the post hoc analysis were illustrated in Fig. 5. The subsequent t test for dependent samples showed the changes in both groups from pretest to posttest (see Table 6). Development of maximum MT (muscle tension) of VG and TTG and results of the Tukey post hoc test. Significant differences (α = 5 %) between mean values of measurement are marked with an asterisk Table 6 Results of the t test for dependent samples for VG and TTG with increases in MT These results, on maximum isometric force illustrated in Fig. 4, indicated significant variations over the whole training period. The results indicate that the maximum isometric force of the VG increased significantly from the pretest value even after the first training week. Thereafter, compared to the pretest, all the following measurements became significant. This can be contrasted with the TTG which achieved statistically relevant maximal force improvements only between the last three measurements and the pretest. Furthermore, the first significant difference in TTG is between the second measurement and posttest. This indicates that—in comparison to the VG—the improvement of maximum force occurred at a later time in the TTG. A possible reason for the faster response can be explained by an acute increase of training intensity through superimposed segment-body vibrations in VG [22]. The resulting higher load on the neuromuscular system in VG explained by the reflectory response forced by the vibration stimulus [18] may have caused a faster neuromuscular adaptation in VG compared to TTG. The t test (Table 4) shows that the mean increases in maximum force of 21.4 % (VG) and 14.2 % (TTG) were significant. A possible cause for this higher improvement rate of the VG likely stems from the additional vibration stimulus. In order to work out the practical relevance of this study, a cluster analysis was performed, and the results are summarized in Figs. 6 and 7. As a result, three groups (see Fig. 6, right) with distinct development levels became visible. The different courses of the mean values of all groups [1–3] are presented in Fig. 6 (right). For group A (four subjects), an initial decrease in maximum isometric force after the first week of training was observed. From the second measurement onwards, the maximum force value steadily increased compared to the posttest. In contrast to this development, group B (five subjects) showed a steady increase of the maximum force from pretest to retest. Finally, group C (nine subjects) experienced an initial steep increase in maximum force compared to the first measurement, which was subsequently followed by stagnation until the posttest. Left: tree diagram of Ward's cluster analysis. Representation of groups of subjects (groups A, B, C) with similar maximum isometric force development from pre-retest of VG—group segregation after cluster analysis. Abscissa lists the subjects; ordinate shows the 1-Pearson correlation coefficient value (r) [31]. Segregation line was set at linkage distance 0.95. Right: presentation of mean maximum isometric force development of the three groups Left: tree diagram of Ward's cluster analysis. Representation of groups of subjects (groups A, B, C) with similar maximum isometric force development from pre-retest of TTG—group segregation after cluster analysis. Abscissa lists the subjects; ordinate shows the 1-Pearson correlation coefficient value (r) [31]. Segregation line was set at linkage distance 0.9. Right: presentation of mean maximum isometric force development of the three groups The results for TTG subjects are plotted in Fig. 7 (left) with the dividing line at 0.9. Similar to VG subjects, TTG subjects were split up into three observational groups. The mean values for group A (two subjects) revealed an initial increase in maximum isometric force until the values dropped below the initial level in the post- and the retest. The slope of group B (four subjects) first showed a decrease in maximum isometric force to the second measurement. Afterwards, the maximum isometric force increased until it reached the peak at the posttest. Similar to group B of the VG, group C of the TTG (12 subjects) showed a continuously increasing maximum isometric force until the posttest. In summary, superimposed vibration during a submaximal resistance training on individuals with a comparably high strength level in hamstring muscles can initially decrease isometric force. A possible reason for this development is to be found in the higher absolute load of this training group, which might have caused an initial musculoskeletal overtraining to muscles, bones, and joints of the subjects [40]. In contrast, the same training method applied to individuals with a comparably average or lower strength level leads to an increase of isometric force after three training units. The effect of vibration training lasts also after 2 weeks of detraining for individuals of all entry levels. In comparison, a traditional submaximal strength training improves isometric force initially but reveals a potential loss of isometric force for comparably well-trained individuals after the third training week. Those results have to be treated with care, because the subjects have not been distributed equally in numbers to the groups A–C. The cluster analysis gives an overview about possible inter-individual different adaptations to a submaximal resistance training with and without superimposed segment-body vibrations. Further studies have to reveal the physiological reasons behind those differences. Finally, the increase of maximum isometric force after 2 weeks of detraining at the retest remains significant at 22 % for the VG. Those results are in accordance with other findings [41–43], although little is known about the effects of segment vibration training on the magnitude and rate of strength loss during detraining. In contrast, the TTG significantly decreases the maximum isometric force during the same time period by 6 %. It is possible that the cause of the sustainability of the isometric maximum force level in VG can be found in the higher training intensity through the superimposed vibrations, and therefore a different regeneration time compared to the TTG of this population. It can be assumed that a change in isometric force manifested either earlier or later to the retest. Future studies should provide evidence for the effects of different detraining phases of vibration training. With regard to the maximum knee angle, from Table 5, a significant change from pretest to posttest can be noticed in the VG. Maximal strength training with induced vibration causes a higher increase in maximum ROM than traditional resistance training. However, the statistically relevant increase in the range of motion of 2 % plays a minor role in sports practice. Finally, for the maximum muscle tension, the data from Table 6 shows that the significant difference between pretest and posttest values becomes obvious in both groups. The mean increases in MT at maximum knee angle in VG (34.3 %) and TTG (46.0 %) were significant. This study reveals that a maximal strength training of the hamstrings brings about a significant increase of MT of this musculature. These results thus indicate that dynamic strength training with additional local vibration stimulation represents an effective means to an increase of maximum isometric force of the hamstrings. In the VG, 21.4 % (112 N) of maximum isometric force was gained from pretest to posttest in contrast to 14.2 % (81 N) in the TTG. This vast increase of the VG is consistent with results reported in different sources (e.g., [44]; Knauf 1999, unpublished). Single cases with additional vibration stimulation show even higher increases between 13 % and 60 % of this parameter (e.g., [45, 16]). Clearly, the additional local vibration stimulus can be considered to be the reason for the much higher increase of maximum isometric force compared to the TTG. The fact that the vibrations are induced directly into the target muscle ensures that the generated amplitude and frequency reached the trained muscle without major transmission loss [46]. Moreover, since the frequency in the present study ranged between 18 and 36 Hz, a harmonic reflectory response of the involved muscles seems plausible [17] as well as a substantial relaxation of the antagonist [23]. Another explanation for the higher force development can be attributed to the reflectory contractions which lead to higher muscular activity [18]. In combination with submaximal loads (e.g., 70 % of the 1 RM), this causes an increase in force in the stimulated muscles [17] and a synchronization of muscular activity [24, 25]. Another important finding of this study was the long-term effects due to vibration training. In the retest, the maximum isometric force of the VG was still 22.7 % higher than at the time of the pretest (Römpke 2004 unpublished, [41]). In contrast to this, maximum isometric force of the TTG was 4 % lower in the retest than in the pretest. Since the training load was comparable in both groups, the increased intensity, which results from the additionally induced segment-body vibrations, obviously triggers a memory effect in the nerve-muscle system. The cluster analysis illustrated differences in the development of maximum isometric force between vibration training and traditional strengthening. Subjects of VG with high maximum force values in the pretest experience an initial decrease before they reach their late maximum in the retest. In contrast to this, the maximum force of the hamstrings of the subjects with high force values within TTG increased remarkably already after the first week of training. Another difference within TTG was the considerable decrease in the last week of training below the pretest value. Subjects with a low maximum isometric force showed an increase of this parameter within the first week of training (VG) and subsequently stagnated until the posttest, whereas the TTG revealed a continuous increase until the posttest. Obviously, the weaker athletes have difficulties coping with the vibration training stimulus. In the VG, the maximum knee angle increased significantly 2 % (2°) from pretest to posttest. The results of the TTG are almost identical (2.5 %, 3°). As a consequence, there were no better results produced using the additional vibration input. Among other factors, submaximal strength training generally improves recruitment, frequency (e.g., [47–49]), and synchronization of muscles and muscle groups. If the relaxation potential of the hamstrings can be thus enhanced, we can assume that the maximum range of motion increases. For the purpose of this study, the development of flexibility was of great importance. By means of repeated measurement, Mall et al. [50] were able to prove an increase in range of motion of 3.4°. Likewise, a study by Wydra et al. [51] showed an increase in passive range of motion of 8° within 2 weeks time. In this study, the tested leg performed a total number of 12 muscle stretches with a small improvement of 2°–2.5°. So the main reason for changes in maximum knee angle in this study can be found in the total number of 6 measurements during the whole study. MT at maximum knee angle also developed similarly in both training groups. MT remained almost unaltered from pretest until the third measurement, but increased afterwards. The increase increment of 34.3 % in the VG and 46.0 % in the TTG between pretest and posttest became significant in the t test. Since the maximum range of motion does not increase considerably between the third measurement and posttest, the development of MT must have a different cause. Submaximal strength training leads to both neuronal and structural adaptation processes in the musculature [52]. One of the results of muscle hypertrophy is an increase in parallel or serial sarcomere number, and thus an increase in the number of titin-myosin-complex filaments in the musculature which are part of every sarcomere [53]. The effects are supposedly related to an activation of more titin-myosin-complex filaments within one muscle (-group) which themselves increase the maximum MT [53]. As the maximum isometric force increases from the pretest to every measurement that follows and the MT increases after the third measurement, it is safe to assume that the process of muscle hypertrophy (consequently the changes in muscle structure) occurs following after the second training week. Since the time of the increase in MT is the same in both groups, it is also safe to assume that muscle hypertrophy occurs independently of the different training stimuli. To the best of our knowledge, this is the first study to explore the effects of segment muscle vibrations superimposed to the muscle belly of the agonist muscle. The findings demonstrated that segment-body vibrations may improve muscle coordination, increasing the activation of the agonist muscle, resulting in an increase of maximum force. Therefore, we conclude that initially, the neuronal adaptations to submaximal strength training lead to an increase in maximum isometric force, but not to a significant increase in MT before the third measurement. This method thus offers to athletes a short-term increment of maximum force, which has the potential to improve overall performance in force-dependent sports. Resistance training in sports already covers a significant part of the training schedule. The application of segment muscle vibration in the present study increases the quality of the resistance training by achieving the same effects with segment muscle vibrations in shorter training time or achieving a higher isometric muscle force in the same training time. Moreover, evidence of positive effects of the application of whole-body vibrations in rehabilitations has been reported. Vibration training has been successfully applied in the rehabilitation process of anterior cross-ligament injuries [54–56], in treatment of knee ostearthritis [57], in rehabilitation of spina bifida [58], etc. In contrast, no evidence can be found that supports the use of vibration training in the rehabilitation process of stroke patients [59]. Those above rehabilitation applications are based on whole-body vibration. To the best of our knowledge, no studies about segment-body vibrations and rehabilitation exist. It is to be assumed that similar and more specific effects in rehabilitation can be achieved with segment-body vibrations. The role of muscle tension in static and dynamic force development is still under investigation. Force measurement under isometric conditions is influenced by muscle properties and neural factors [60]. The key limitation brought about due to lack of a control group can be alleviated if more studies are conducted, which include a control group and EMG. This can further reveal the role of muscle tension and would be the subject of future research. We will also like to point out another limitation of the study which stems from the fact that the bilateral effects of two different training methods of the two arms have not been controlled. It is known that unilateral resistance training of the elbow flexor muscles of the non-dominant arm of a test person can have a significant increase of isometric maximum force of 5.3 % at the contralateral elbow flexor muscles [61]. 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The statements made herein are solely the responsibility of the authors. Sport Science Program, Qatar University, P.O. Box 2713, Doha, Qatar Ruben Tobias Goebel Institute of Training Science and Sport Informatics, German Sport University Cologne, Cologne, Germany Heinz Kleinöder & Joachim Mester The German Research Center, Center of Elite Sport, German Sport University Cologne, Cologne, Germany Zengyuan Yue Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA, USA Ranajay Gosh Heinz Kleinöder Joachim Mester Correspondence to Ruben Tobias Goebel. RG is the main and corresponding author of this publication. He carried out the studies on the effects of segment-body vibrations on resistance training parameters of the hamstring muscles. He made substantial contribution in all areas of the published study, such as conception, design, data acquisition, analysis, and interpretation. Furthermore, he drafted and finalized the manuscript. HK contributed substantially to the concept of the study and the study design. He conceptualized the training intervention protocol and the measurement protocol. He furthermore has been involved in revising the manuscript critically for important intellectual content. ZY contributed specifically in data acquisition, statistical analysis, and result presentation. In particular, he developed the mathematical formula to calculate the muscle tension. RG has been involved in drafting and critically revising the manuscript's content and participated in the sequence alignment. JM conceived the study, supervised and coordinated the study, and helped to draft the manuscript. All authors read and approved the final manuscript. Dr. RG is the Acting Director of the Sport Science Program, College of Arts and Sciences, Qatar University, Doha, Qatar. Dr. HK is the Head of Strength Diagnostics and Motion Analysis in the Institute of Training Sciences and Sport Informatics, German Sport University Cologne, Cologne, Germany. Dr. ZY is from The German Research Center, Center of Elite Sport, Cologne, Germany. Dr. RG is an associate research scientist in Mechanical and Industrial Engineering, Northeastern University, Boston, MA, USA. Univ.-Prof. JM is the Director of the Institute of Training Sciences and Sport Informatics, German Sport University Cologne, Cologne, Germany, and the Chairman of The German Research Center, Center of Elite Sport, Cologne, Germany. An erratum to this article is available at http://dx.doi.org/10.1186/s40798-015-0028-6. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Goebel, R.T., Kleinöder, H., Yue, Z. et al. Effect of Segment-Body Vibration on Strength Parameters. Sports Med - Open 1, 14 (2015). https://doi.org/10.1186/s40798-015-0022-z Received: 30 December 2014 DOI: https://doi.org/10.1186/s40798-015-0022-z Segment-body vibration Maximum range of motion	CommonCrawl
Home Journals IJHT Transition to Chaotic Natural Convection of Cu-water Nanofluid in an Inclined Square Enclosure Transition to Chaotic Natural Convection of Cu-water Nanofluid in an Inclined Square Enclosure Bilal Boudjeniba \| Abdelghani Laouer \| Salah Laouar* \| El Hacene Mezaache Département de Physique, Faculté des Sciences, Université de Skikda, B.P. 26, 21000, Algérie Département de Physique, Université Mohamed seddikBenYahia - Jijel, B.P.98, Jijel 18000, Algérie Laboratoire de Recherche en Physico-chimie des Surfaces et Interfaces, Université de Skikda, B.P.26, 21000, Algérie [email protected] In this paper, the scenario leading to chaos in natural convection of Cu-water nanofluid inside an inclined square enclosure with the aspect ratio equal to unity is numerically investigated. The enclosure is heated from one part of the side and cooled through two other opposite half sides. The governing equations and the corresponding boundary conditions are solved numerically using the finite difference method. The effect of Rayleigh number and the volume fraction on natural convection flow are analyzed. The obtained results indicate that the mode of fluid flow which is initially stationary, passes by a periodic mode across a supercritical Hopf bifurcation, then quasi periodic at two incommensurable frequencies, before reaching the final stage of chaotic convection for both pure fluid and nanofluid. The sequences of bifurcation are presented graphically; it was found that the presence of suspended nanoparticles inside the base fluid causes significantly the delay of this transition. heat transfer, natural convection, nanofluid, enclosure, Hopf Bifurcation, phase trajectory, Lyapunov exponent, chaos Transient natural convection inside the closed enclosures containing pure fluids has many practical engineering applications, the cases of electronic components cooling and especially the heat exchangers are among the most referenced applications. In all cases of the proposed topic, experimental studies and numerical computations aimed to clarify the flow regime and to determine the temperature field with both stable and instable boundary conditions. It should also to characterize the scenario leading to chaos and turbulence in relation with the nature of the fluid, the geometrical configuration of the enclosure and the initial and boundary conditions. In this context, we note the existence of some excellent research works related to this subject, which spans over sixty years. Nevertheless, the low thermal conductivity of fluids limits the performance of heat transfer inside enclosures. However, it should be noted that the presence of metal, metallic oxide or non-metallic nanometer-sized particles (referred to as MNS-particles, MONS-particles or NMNS-particles for convenience) in the fluid (named nanofluid firstly by Choi, 1995 [1]) contributes substantially to increase the heat transfer rate. As far as we know, turbulent or chaotic natural convection in closed enclosures containing nanofluids has not been studied sufficiently, although this regime of flow seems to be very interesting. This implies that the solid particles neither settle at the bottom of a fluid nor in clustering. Sadik et al. [2] summarize some important published works on the effect of MNS-particles, MONS-particles and NMNS-particles suspended in the base fluid on the forced convection heat transfer inside the enclosures. In the literature they include analytical models that agree with experimental data of several physical properties such as thermal conductivity, effective viscosity, density and effective heat capacity. In the same way, Motevasel et al. [3] investigate experimentally at low concentration the effect of MgO-nanoparticles aggregation on the nanofluid's thermal conductivity and viscosity and a relatively good agreements was found between the proposed fractal models and the experimental values. Oztop et al. [4] considered rectangular enclosures partially heated and filled with nanofluid in natural convection. The finite volume method was used to solve the governing equations. For different types of nanoparticles: Cu, Al2O3 and TiO2, an increase in the mean Nusselt number was found with respect to the volume fraction andwith Rayleigh number inthe range of 1000-500000. Also, by using nanofluids, the heat transfer is more pronounced at low aspect ratio than at high ones, a value of 25 % can be reached. Maiga et al. [5] studied numerical thermal forced convection of water/gAl2O3 and ethylene-glycol/gAl2O3 nanofluids inside cylindrical configuration with uniform heat flux at borders. For the turbulent flow, a Launder-Spalding k-e model was used with specific combined thermal and physical properties of the base fluids and nanoparticles. The solutions were validated by experimental data, it is noticed that the presence of particles affects the wall friction, this latter increases with the particle volume fraction. In another study, Maiga et al. [6] considered two systems uniformly heated with Dirichelet and Neumann boundary conditions: the structure consists of a tube and parallel coaxial disks. They used two types of nanofluids in laminar forced convection flow regime, namely water/gAl2O3 and ethylene-glycol/gAl2O3. They noticed that this last nanofluid provides a better heat transfer. The presence of nanoparticles in the base fluid increases the wall shear stress substantially. The authors proposed two correlations for the averaged Nusselt number in relation with Reynolds number and Prandtl number to analyze the heat transfer in a tube using water as base fluid. In the same geometrical configuration of uniformly heated tube, Maiga et al. [7] explored numerically the effect of Al2O3 volume fraction on the hydrodynamic and thermal behavior of turbulent flow regime. The mathematical model based on the non-linear and coupled momentum of the energy and mass equations has been solved by a finite difference algorithm. The differential equations are discretized over a control volume. They supposed a single phase approach (e.g. fluid phase and particles in thermal equilibrium and move with the same velocity) and it was found that the wall shear stress increases with particle volume fraction and Reynolds number. Elahmer et al. [8], on the effect of nanofluids in forced convective heat transfer in a tube, concludes thatethylene-glycol/CNT-Ag hybride nanofluid seems to be more advantageous for the enhancement of convective heat transfer than ethylene-glycol/CNT nanofluid. The case of two-phase approach (each phase with his own velocity) has been used to study both forced and mixed convection of nanofluid in a tube [9-10] and in inclined square cavity [11]. Some of the researchers consider that it is the appropriate approach to investigate in this novel kind of fluids. But there are some parameters which appear when using nanofluids, like gravity, Brownian motion, nanoparticles clustering and the friction between the fluid and the particles. Due to the lack of appropriate theoretical studies and experimental data in the literature to investigate in this issue, the existence of macroscopic two-phase approach is not applicable for analyzing heat transfer process [12-14]. Moreover, the single-phase approach is less complicated for modeling and more computationally efficient. In order to maintain a nanofluid in homogeneous state and to maximize their capacity to evacuate heat, it is essential to maintain the nanofluid in the chaotic state. The aim of the present numerical study is to investigate on the different ways leading to chaos for Cu-water nanofluid in order to improve heat transfer by natural convection throughout closed enclosure and to avoid nanoparticles clustering and sedimentation. In this paper it is supposed that the fluid and the nanoparticles are in a single phase and homogeneous state. We consider an inclined closed square enclosure heated partially from one side and cooled at two opposite walls, while the rest of boundaries are adiabatic. 2. Mathematical Formulation The geometry of the present study is an inclined enclosure filled with a Cu-water nanofluid, this is shown in Figure 1. It consists of an H and L as enclosure dimensions. The half wall located at $x=0$ and the opposite one located at $x^{\prime}=L$ are maintained at the constant cold temperature $T_{c},$ whereas one part of wall located at $y^{\prime}=0$ is maintained at a constant hot temperature $T_{h},$ while the other borders of enclosure are adiabatic. The nanofluid in the cavity is considered to be newtonian, it is incompressible and laminar with constant physical properties except the density variation due to the Boussinesq approximation. The thermo-physical properties of the base fluid and the Cu-nanoparticles are listed in Table 1. It is considered that the viscous dissipation, thermal radiation and the work due to the volume expansion are negligible. Figure 1. Geometry of the problem and coordinate system. Table 1. Thermophysical properties of the fluid and the nanoparticles, from [4] Fluid phase (water) Copper (Cu) $c_{p}\left(J k g^{-1} K^{-1}\right)$ $\rho\left(k g . m^{-3}\right)$ $k\left(W . m^{-1} . K^{-1}\right)$ $\alpha\left(m^{2} s^{-1}\right)$ $1.47 \times 10^{-7}$ $11.631 \times 10^{-5}$ $\beta\left(K^{-1}\right)$ $21 \times 10^{-5}$ Regarding the above assumptions, the dimensional governing equations using the vorticity stream-function formulation can be written in Cartesian coordinates as follows: $\frac{\partial^{2} \psi^{\prime}}{\partial x_{l^{2}}}+\frac{\partial^{2} \psi^{\prime}}{\partial y^{\prime 2}}=-\omega^{\prime}$ (1) $\frac{\partial \omega^{\prime}}{\partial t^{\prime}}+\frac{\partial}{\partial x^{\prime}}\left(u^{\prime} \omega^{\prime}-\frac{\mu_{n f}}{\rho_{n f}} \frac{\partial \omega^{\prime}}{\partial x^{\prime}}\right)+\frac{\partial}{\partial y^{\prime}}\left(v^{\prime} \omega^{\prime}-\frac{\mu_{n f}}{\rho_{n f}} \frac{\partial \omega^{\prime}}{\partial y^{\prime}}\right)$ $=\left(\frac{\varphi \rho_{s} \beta_{s}+(1-\varphi) \rho_{f} \beta_{f}}{\rho_{n f}}\right) g\left(\cos \theta \frac{\partial T^{\prime}}{\partial x^{\prime}}-\sin \theta \frac{\partial T^{\prime}}{\partial y^{\prime}}\right)$ (2) $\frac{\partial T^{\prime}}{\partial t^{\prime}}+\frac{\partial}{\partial x}\left(u^{\prime} T^{\prime}-\alpha_{n f} \frac{\partial T^{\prime}}{\partial x \prime}\right)+\frac{\partial}{\partial y^{\prime}}\left(v^{\prime} T^{\prime}-\alpha_{n f} \frac{\partial T^{\prime}}{\partial y^{\prime}}\right)=0$ (3) With the appropriate initial and boundary conditions: For $t^{\prime}=0$ : $\left\{\begin{array}{c}{u^{\prime}=v^{\prime}=0} \\ {T^{\prime}=\frac{1}{2}\left(T_{c}+T_{h}\right)}\end{array}\right.$ (4) For $t^{\prime}>0$: $\left\{\begin{array}{c}{u^{\prime}=v^{\prime}=0} \\ {\frac{\partial T^{\prime}}{\partial y^{\prime}}=0}\end{array}\right.$ at $\left[\begin{array}{c}{\left\{\begin{array}{c}{y^{\prime}=H} \\ {0 \leq x^{\prime} \leq L} \\ {y^{\prime} \leq 0} \\ {x^{\prime}<x_{p}^{\prime}-h^{\prime} / 2} \\ {x^{\prime}>x_{p}^{\prime}+\frac{h^{\prime}}{2}}\end{array}\right.}\end{array}\right.$ $\left\{\begin{array}{c}{u^{\prime}=v^{\prime}=0} \\ {\frac{\partial T^{\prime}}{\partial x^{\prime}}=0}\end{array} \text { at }\left\{\begin{array}{l}{x^{\prime}=0, x^{\prime}=L} \\ {0 \leq y^{\prime}<H / 2}\end{array}\right.\right.$ $\left\{\begin{array}{c}{u^{\prime}=v^{\prime}=0} \\ {T^{\prime}=T_{h}}\end{array} \text { at }\left\{\begin{array}{c}{y^{\prime}=0} \\ {x^{\prime}>x_{p}^{\prime}-\frac{h^{\prime}}{2}} \\ {x^{\prime}<x_{p}^{\prime}+\frac{h^{\prime}}{2}}\end{array}\right.\right.$ $\left\{\begin{array}{c}{u^{\prime}=v^{\prime}=0} \\ {T^{\prime}=T_{c}}\end{array} \text { at }\left\{\begin{array}{l}{x^{\prime}=0, x^{\prime}=L} \\ {H / 2 \leq y^{\prime} \leq H}\end{array}\right.\right.$ (5) $\alpha_{n f}=\frac{k_{e f f}}{\left(\rho C_{p}\right)_{n f}}$ (6) The effective thermal conductivity of the nanofluid $k_{e f f}$ is approximated by Maxwell-Garnetts model as cited in $[2,23],$ see Table 1 for calculations: $\frac{k_{e f f}}{k_{f}}=\frac{k_{n f}}{k_{f}}=\frac{k_{s}+2 k_{f}-2 \varphi\left(k_{f^{-}}-k_{S}\right)}{k_{S}+2 k f^{+\varphi}\left(k_{f}-k_{S}\right)}$ (7) We considered a spherical shape of copper nanoparticles [2, 4, 14, 22, 23]. This model is well adapted to evaluate the enhancement of the heat transfers. Other models exist in the literature, such as: the model of Hamilton-Crosser and the model of Yu-Choi, cited in [2], which takes into account the nonspherical form of the particles. For our case the use of the equation (7) is relatively satisfactory. The specific heat of the nanofluid is expressed as [12, 15]: $\left(\rho c_{p}\right)_{n f}=\varphi\left(\rho c_{p}\right)_{s}+(1-\varphi)\left(\rho c_{p}\right)_{f}$ (8) The effective viscosity can be defined as follows [4]: $\mu_{n f}=\frac{\mu_{f}}{(1-\varphi)^{2.5}}$ (9) Concerning the velocity field, it is related to the stream function by: $\left\{\begin{array}{c}{u^{\prime}=\frac{\partial \psi^{\prime}}{\partial y^{\prime}}} \\ {v^{\prime}=-\frac{\partial \psi}{\partial x^{\prime}}}\end{array}\right.$ (10) By introducing the following dimensionless variables: $\left\{\begin{array}{c}{(x, y)=\left(\frac{x^{\prime}}{H}, \frac{y}{H}\right) ; t=\frac{t^{\prime} \alpha_{f}}{H^{2}} ;(u, v)=\left(\frac{u^{\prime} H}{\alpha_{f}}, \frac{v^{\prime} H}{\alpha_{f}}\right)} \\ {\psi=\frac{\psi^{\prime}}{\alpha_{f}} ; \omega=\frac{\omega^{\prime} H^{2}}{\alpha_{f}} ; \quad T=\frac{T^{\prime}-T_{c}}{T_{h}-T_{c}}}\end{array}\right.$ (11) The governing equations (1)-(3) can be rewritten in dimensionless form as: $\frac{\partial^{2} \psi}{\partial x^{2}}+\frac{\partial^{2} \psi}{\partial y^{2}}=-\omega$ (12) $\frac{\partial \omega}{\partial t}+\frac{\partial}{\partial x}\left(u \omega-\operatorname{Prm} \frac{\partial \omega}{\partial x}\right)+\frac{\partial}{\partial y}\left(v \omega-\operatorname{Prm} \frac{\partial \omega}{\partial y}\right)=$ $R a . \operatorname{Pr} . \operatorname{Pnfr}\left(\cos \theta \frac{\partial T}{\partial x}-\sin \theta \frac{\partial T}{\partial y}\right)$ (13) $\frac{\partial T}{\partial t}+\frac{\partial}{\partial x}\left(u T-t d r \frac{\partial T}{\partial x}\right)+\frac{\partial}{\partial y}\left(v T-t d r \frac{\partial T}{\partial y}\right)=0$ (14) With the corresponding boundary conditions For $t=0$: $\left\{\begin{array}{c}{u=v=0} \\ {T=\frac{1}{2}}\end{array}\right.$ (15) For $t>0$: $\left\{\begin{array}{c}{u=v=0} \\ {\frac{\partial T}{\partial y}=0}\end{array}\right.$ at $\left[\begin{array}{c}{\left\{\begin{array}{c}{y=1} \\ {0 \leq x \leq A} \\ {y=0}\end{array}\right.} \\ {\text {and}\left\{\begin{array}{c}{y=0} \\ {x>x_{p}-h / 2} \\ {x>x_{p}+\frac{h}{2}}\end{array}\right.}\end{array}\right.$ $\left\{\begin{array}{c}{u=v=0} \\ {\frac{\partial T}{\partial x}=0 \quad \text { at }\left\{\begin{array}{l}{x=0, x=A} \\ {0 \leq y<1 / 2}\end{array}\right.}\end{array}\right.$ $\left\{\begin{array}{c}{u=v=0} \\ {T=1}\end{array} a t\left\{\begin{array}{c}{y=0} \\ {x>x_{p}-\frac{h}{2}} \\ {x<x_{p}+\frac{h}{2}}\end{array}\right.\right.$ $\left\{\begin{array}{c}{u=v=0} \\ {T=0}\end{array} \text { at }\left\{\begin{array}{l}{x=0, x=A} \\ {1 / 2 \leq y \leq 1}\end{array}\right.\right.$ (16) The dimensionless parameters appearing in the equations (13-14) are defined as $t d r=\frac{\alpha_{n f}}{\alpha_{f}}=\frac{k_{n f}}{k_{f}} \frac{1}{(1-\varphi)+\varphi \frac{\left(\rho c_{p}\right)_{S}}{\left(\rho c_{p}\right)_{f}} )}$; $\operatorname{Pr} m=\frac{\operatorname{Pr}}{(1-\varphi)^{2.5}\left((1-\varphi)+\varphi \frac{\rho_{S}}{\rho_{f}}\right)}$ ; $R a=\frac{g \beta \Delta T L^{3}}{v_{f} \alpha_{f}}$; $\operatorname{Pnfr}=\frac{1}{1+\frac{1-\varphi \rho_{f}}{\varphi \rho_{S}}} \frac{\beta_{s}}{\beta_{f}}+\frac{1}{1+\frac{\varphi \rho_{s}}{1-\varphi \rho_{f}}}$ For the estimation of the intensities of the heat transfers, the calculation of Nusselt number related to its local evaluation through the hot wall and its global evaluation along this wall. While referring to [4] and [16], it can be written as: $N u_{l o c a l}(x)=-\frac{k_{n f}}{k f} \frac{\partial T}{\partial y} )_{h o t w a l l}$ (17) Concerning the calculation of the averaged Nusselt number, this can be given as: $N u_{A v g}=\int_{\text {hot wall}} N u(x) d x$ (18) 3. Numerical Method The vorticity and energy equations are transformed into their finite difference equations by employing the ADI-method, which is adapted for the transient solutions. This formulation leads to a tri-diagonal matrix at each half time step that is solved using a TDMA algorithm. For this method, it is possible to use a relatively large time steps, in this case the numerical stability conditions are easy to satisfy. To solve the stream function equation, the SOR-method is used. First of all, to satisfy the mass continuity, the convergence criterion of the stream function (e.g. the relative gap between the previous stream function at each point and their new values) is chosen less than 10-5. Secondly, the velocity components are computed with a central finite-difference approximation of the stream function. In the past, computational method has been tested for different mesh sizes (more than 121x121 nodes) and different time steps, thereafter, the validity of the computer program was tested for pure fluid in steady state by simulating the bench mark numerical solution [17]. All results were considered to be very satisfactory (the relative gap less than 1 %). Other tests were carried out in oscillatory regimes and good agreement of frequencies is obtained. In addition, the results obtained by the present algorithm concerning the study of a nanofluid in a closed cavity with horizontal thermal walls are in good agreement with those presented by Oztop et al. [4]. 4. Validation To test the accuracy of the present numerical study, the average values of Nusselt number for wide range of Rayleigh numbers are given in Table 2 and compared with previous works. As it can be seen, the obtained results are in good agreements with those given by the literature. Table 2. Comparison of average Nusselt number with those published in several references Oztop [4] Khanafir [12] Davis [17] Tiwari [14] Esmaeil [18] Barakos [19] Present work Figure 2. Temperature profile at the horizontal mid-plane of the enclosure $R a=1.8910^{5}, P r=0.71$ Figure 3. Velocity profile at the horizontal mid-plane of the enclosure $R a=10^{5}, h=0.5, y_{p}=0.5$ Another validation as shown in Figure 2, concerning natural convection in a square enclosure, differentially heated and filled with air. One can observe the obtained results of the computed temperatures, regarding the horizontal midline of the enclosure, comparison with the results of Oztop et al. [4], Khanafer et al. [12] and Krane et al. [20] gives excellent agreement. The results obtained by simulation are validated with the result of Oztop et al. [4] for natural convection in a square enclosure filled with three types of nanoparticles showed in Figure 3. It is clear that the vertical velocity profile along the horizontal midline of the enclosure for Ra=105, h=0.5 and yp=0.5 is in good agreement with our numerical simulation. As matter of comparison with Oztop et al. [4], a slight change in the volume fraction from zero to 0.20 causes a significant increase of average Nusselt numbers throughout a heated element as showed in Figure 4. Furthermore, it also considerable with increasing Rayleigh number. It is clear that all results of the present code (the one used for simulation) are in good agreement with those proposed by Oztop et al. [4]. Figure 4. Average Nusselt numbers versus volume fraction The numerical code is used to make a number of simulations for various ranges of controlling parameter, such as Rayleigh number, $10^{3} \leq R a \leq 3.510^{7}$. The enclosure is partially heated at one side and partially cooled at two other opposite sides. Concerning the volume fraction, the used values are 10 % and 20 % in addition to the case of pure fluid. 5.1 Bifurcation to oscillatory convection Figure 5, shows the temporal stream function signals at the mid-point of the enclosure (first line) in addition to the streamlines, the isotherms and the phase space trajectories at the second, third and fourth lines respectively. The first column refers to pure fluid $\left(R a=8.2010^{4}\right),$ the second column to Cu-water nanofluid with $\varphi=0.1\left(R a=1.9110^{5}\right)$ and the third column to Cu-water nanofluid with $\varphi=0.2$ $\left(R a=4.5210^{5}\right) .$ As indicated by this figure, the temporal signal shows a sharply decrease and then trend to an asymptotic limit of stationary heat transfer mode. We note that all physical properties of the system follow this evolution for studied cases. Figure 5. Temporal stream function signals $\psi_{m i d}$ (line 1), streamlines (line 2), isotherms (line 3) and phase space trajectories $\left(T_{m i d}, \psi_{m i d}\right)$ (line 4). For streamlines, the first number gives the minimum value, the second one, the maximum value and the third one is the gap between two successive streamlines. The isotherms are equally spaced from the hot wall (T=1) to cold one (T=0), with a gap of 0.1 According to the streamlines, one can observe a dominate monocellular flow turning in the counterclockwise direction for all cases, whereas, a small counter rotating cell appears at the top corner of the enclosure, which grow up proportional with volume fraction. The corresponding isotherms show the characteristics of conduction for dominated regime except at the central part of the cavity, because they are distributed approximately parallel to the active walls. The stationarity of the regime can be confirmed through the layout of the phase plan trajectory ( $\left(T_{m i d}, \psi_{m i d}\right)$ for the threecases. Line four of Figure 5 shows that this is a limit point attractor. When increasing Rayleigh number until obtaining an oscillatory convection mode, before reaching this situation precisely, we expect to find the breaking value of Rayleigh number, where there is a complete alteration of stationary regime behavior. We highlight that despite of increasing the Rayleigh number, the frequency of the cycle deduced by the Fourier spectrum remains almost invariant and the time required for the establishment mode becomes much longer near this value. Figure 6. Temporal signals of $\psi_{m i d}$ (first line), Phase space trajectories $\left(T_{m i d}, \psi_{m i d}\right)$ (second line), Amplitude spectra (third line) and the amplitude of $\psi_{\text { mid }}$ versus $\left(R a-R a_{c}\right)^{1 / 2}$ beside the bifurcation point (fourth line), respectively for Pure fluid (first column; Ra=8.40 104), nanofluid with φ=10 % (second column; Ra=1.97 105) and nanofluid with φ=20 % (third column Ra=4.60 105) Figure 7. Streamlines over one complete cycle: (a) Pure fluid at Ra=8.45 104; (b) Cu-water nanofluid with $\varphi=0.1$ at Ra=2.0 105; (c) Cu-water nanofluid with $\varphi=0.2$ at Ra=4.64 105 After several tests, we can determine with a good approach the value of Rayleigh number, at which there is a topological change of the temporal signals of stream function (first line, Figure 6) for several Rayleigh numbers, the signals become periodic. In the same way, sketch of phase space trajectories (second line, Figure 6) at the same values of Rayleigh numbers confirm the existence of a limiting cycle representing the phase portrait of stream function versus temperature at the mid-point of the cavity $\left(T_{\operatorname{mid}}, \psi_{\operatorname{mid}}\right)$. The third line illustrates the amplitude spectra with the non-dimensional frequencies values. Apparently, there is only one single frequency component for each case: $f=34.17, f=52.49$ and $f=0.1$ and $f=0.1$ and $f=0.1$ and Cu-water nanofluid with $\varphi=0.2$ respectively. In the fourth line, from Figure 6, we show the amplitude of the stream function at the mid-point of the cavity for various Rayleigh numbers near the first critical point versus the square root differences between all used values of Rayleigh number and critical Rayleigh number for all cases studied here. Apparently, for the three cases, the evolution is linear, consequently, we deduce that there is a supercritical Hopf bifurcation $[21]$ located near $R a=8.3510^{4}$ for pure fluid, $R a=1.9510^{5}$ for Cu-water nanofluid with $\varphi=0.1,$ and $R a=4.5610^{5}$ for Cu-water nanofluid with $\varphi=0.2$ . Note that these values were extracted by a linear fitting. Figure 8. Temporal signals of $\psi_{m i d}$ (first column) and amplitude spectra (second column): First line: Pure fluid; Second line: Cu-water nanofluid with $\varphi=0.1$ ; Third line: Cu-water nanofluid with $\varphi=0.2$ Figure 7 shows streamlines over one complete cycle for pure fluid (a) $R a=8.4510^{4},$ Cu-water nanofluid (b) $R a=$ $210^{5} \varphi=0.1$ and Cu-water nanofluid (c) $R a=4.6410^{5} \varphi=$ 0.2 respectively at specific moments of the cycles (referring to 1-5, from Figure 8). One can observe mainly a single circulation cell turning in the counterclockwise direction in all cases and at the top corner of the enclosure one observes a small cell turning in the clockwise direction and growth at a specific moment of the cycle. In addition, Figure 8 shows that the flow is characterized by the presence of only one fundamental frequency with one small harmonic. Through these results, it is quite clear that the physical system has a periodic behavior. 5.2 Bifurcation to chaos The bifurcation sequences are observed numerically until the onset of chaos, this is illustrated in Figure 9 (pure fluid), Figure 10 (Cu-water nanofluid with $\varphi=0.1$ ) and Figure 11 (Cu-water nanofluids with $\varphi=0.2$ ), where: the first column shows the time evolution of the temperature at the mid-point of the cavity, the second column presents the amplitude spectra of stream function, we note that the fast Fourier transform (FFT) algorithm is used to evaluate the amplitudes in the frequency domain, mostly 213 and 214 points, they were checked out from the temporal signals. Eventually, the third column shows the phase space trajectory in the plane $\left(T_{m i d}, \psi_{m i d}\right)$. 5.2.1 Bifurcation for pure fluid According to Figure 9, the frequency amplitude spectrum for Ra=8.70 104 (first line) shows the non-dimensional fundamental peak frequency with order 35.4 and one significant harmonic of this peak is obvious. In addition, the phase space trajectory is a limit cycle, corresponding to a periodic state, related to the temporal signal of temperature at the mid-point of the cavity. Figure 9. Bifurcation sequence to chaos for pure fluid As Rayleigh number increased further, we observe in the second line at Ra=8.25 106 that the amplitude spectrum resulting from FFT method includes a second frequency $f_{2}$ . It is noted that the ratio $f_{1} / f_{2}=1.354$ is irrational, where f1=578.61, f2=427.24; we define this situation as incommensurability, so the attractor is a T2 torus. As expected, this second bifurcation occurs for Rayleigh number ranging from 8,062,500 to 8,125,000. The quasi periodic mode with two observable incommensurable frequencies is still existing for Ra=9.70 106 where f1=629.882, f2=463.867 and $f_{1} / f_{2} \cong 1.357$ and all the rest of peaks are: f1-f2, 2(f1-f2), 2f1, f1+f2. We note that the spectrum is highly noisy, which is precursor to pseudo-chaotic behavior. The transition from quasi-periodic to chaotic flow can be clearly visualized in third line, where the Rayleigh number is 107, apparently the temporal signal of temperature has a non-periodic evolution, in addition the phase space trajectory is fully disturbed. We further note that the spectrum amplitude is continuous, which is similar to the characteristic exhibited by all chaotic regimes. 5.2.2 Bifurcation for Cu-water nanofluid In this section, we will explore the way towards the chaotic mode undergo by water containing copper nanoparticules with a volume fraction in the range [10-20 %], and see the influence of additional nanoparticles on the flow mode and we will try to compare with the base case, i.e., water that is presented in the first part. Figure 10. Bifurcation sequence to chaos for Cu-water nanofluid with According to Figure 10, the frequency amplitude spectrum for Ra=1.97 105 (first line) shows the non-dimensional fundamental peak with order 52.49, since the temporal signal of temperature at the mid-point of the cavity have a periodic evolution, but no significant harmonic is obvious. In addition the phase space trajectory is a limit cycle, which is corresponding to the periodic state. At Ra=106, we note also that the flow is strictly periodic containing one fundamental frequency. Similarly, the appearance of a single harmonic, has a frequency of a doubled value compared to the first one. As the Rayleigh number is increased to 1.109 107, we observe in the second line two distinct frequencies having irrational ratio, at which the periodic mode submits a second transition leading into a T2 torus. In this case harmonics are obtained from their linear combinations. In this region the flow is fully quasi-periodic as expected, since the second bifurcation occurs for Rayleigh number included in the interval [10,615,000; 11,090,000]. The quasi periodic mode with 2 observable incommensurable frequencies is still existing until Ra=1.35 107. chaotic state occurs for Rayleigh number $R a>1.35$ 107, as an indication, Ra=1.40 107 in the last line. The amplitude spectrum has a continuous nature similar to the characteristic exhibited by all chaotic regimes. We note also, that the temperature signal is nonperiodic. Figure 11. Bifurcation sequence to chaos for Cu-water nanofluid with $\varphi=0.2$ From Ra number equal to 4.565 105 the regime is periodic, the dimensionless fundamental peak frequency is of the order of 84.22. At the first line, from Figure 11, Ra=5.0 106, it shows two harmonics in addition to fundamental one. The phase portrait shows a closed trajectory, corresponding to a periodic regime. For Ra=2.60 107, by utilizing FFT method, we found in the second line from Figure 11 two distinct incommensurate frequencies: f1=700.68 and f2=637.20. In this case all harmonics can be expressed by linear combinations of these fundamental frequencies set as $m_{1} f_{1}+m_{2} f_{2}$ where $m_{1}$ and $m_{2}$ being positive integers. Consequently, the regime is quasi-periodic.. We observe in third line for Ra=2.80 107 that the temperature signal is non-periodic. The transition to chaotic flow can be clearly visualized through the phase space maps and from amplitude spectrum which has a continuous nature. 6. Sensitivity to the Initial Conditions The sensitivity to the initial conditions of our system is highlighted following by a change of the initial temperature of the enclosure of the order of 10-6. Figure 12 gives the examples for various pertinent numbers of Rayleigh, (a): pure fluid, (b): Cu-water nanofluid with $\varphi=0.1$ , and (c): Cu-water nanofluid with $\varphi=0.2$ , where it is seen that the signals have the same shape until a given time, where the two signals become separate, this behavior is a sign of all chaotic systems. Figure 12. Sensitivity to the initial conditions for: (a) pure fluid; (b) nanofluid with $\varphi=0.1$ ; (c) nanofluid with $\varphi=0.2$ ; Solid line, T01=0.5; dashed line, T02=0.5+10-6 The obtained results seem to be confirmed by the estimated largest Lyapunov exponent values Ly [19], where is defined by: $\begin{aligned}\left[\psi_{\operatorname{mid}}\left(T_{01}, t\right)-\psi_{\operatorname{mid}}\left(T_{02}, t\right)\right] & \\=&\left[\psi_{\operatorname{mid}}\left(T_{01}, 0\right)-\psi_{\operatorname{mid}}\left(T_{02}, 0\right)\right] \exp \left(L_{y} t\right) \end{aligned}$ (19) As it is shown in table 3, all values being positive and were proved to increase when Rayleigh number increases for both pure fluid and nanofluid. In the same way, calculations show that more increasing in Rayleigh number more the separation time occurs earlier. Table 3. The estimated largest Lyapunov exponent values as a function of Rayleigh number Lyapunov exponent $\varphi=0$ $\varphi=0.1$ Figures 13 summarize the study, in such way that, the transition from a regime of flow to another depends primarily on two parameters: Rayleigh number and volume fraction of the nanoparticules. Whereas, the addition of nanometric particle size to base fluid enables the slow downing of this transition in a proportional manner. So that, the attractor alters from limit point to a limit cycle via a supercritical Hopf bifurcation, and the values of Rayleigh numbers corresponding to this first bifurcation are 8.35 104, 1.95 105, 4.56 105 for the pure fluid, nanofluid with $\varphi=0.1$ and nanofluid with $\varphi=0.2$ , respectively. In the same way, the values of Rayleigh numbers agree with the two other transitions, i.e., transition from periodic to quasi periodic mode and quasi periodic to chaos for the three cases quoted previously. Figure 13. Bifurcation sequences observed numerically. (a): pure fluid, (b): nanofluid with $\varphi=0.1$ , (c): nanofluid with $\varphi=0.2$ . S=steady state, P= periodic, QP2=quasi-periodic with two incommensurate frequencies, C= chaotic According to Figure 13, we can also note that the quasi periodic regime exists in a narrow field of Rayleigh number, in such way, the chaotic mode is very close from this region. 7. Heat Transfer Improvement Figure 14. Mean Nusselt number variation along the hot wall according to Rayleigh number and various volume fraction In this section, the effect of volume fraction of copper nanoparticles on heat flow by natural convection in the cavity is studied, we have plotted various values of the mean Nusselt number along the hot wall for various volume fraction using different values of Rayleigh number as illustrated on Figure14. Since, the strength of natural convection is characterized by magnitude of a dimensional Nusselt number that compares a convective heat flow with reference to typical conductive heat flow. According to Figure 14, we notice that for three cases the heat transfer in the cavity is proportional to Rayleigh number. Let us indicate that the improvement of heat transfer is in relation with the volume fraction of copper nanoparticles, which is sustained by a wide range of authors [4, 12, 14]. The improvement of heat transfer when increasing volume fraction of nanoparticles is very evident. For example when Ra=106 and $\varphi=0 .1$ , the improvement is 10.39% compared to pure fluid, and it becomes 20.42% for $\varphi=0 .2$ . The study proposed in this paper is carried out aiming to find out the physical instabilities for Cu-water nanofluid that occur in a square inclined cavity of $45^{\circ}$, heated partially from one side and cooled partially from two other opposite side. From the investigation carried out in this paper, we were able to visualize the transition from steady state regime for low Rayleigh numbers until the onset of chaos when Ra increases. The problem was treated using a numerical approach, based on the finite difference method and by using our own developed code, which is validated with experimental and numerical results, some of which are well explained in this study. The scenario borrowed up to the chaos by the two systems (pure fluid and nanofluid) is according to that proposed by Curry and York [21], i.e., quasi-periodicity at two incommensurable frequencies. The transition from laminar natural convection to chaos is affected by the presence of nanoparticles, so that the volume fraction causes backwardness in the transition to chaotic regime, this is well explained from the diagram of Figure 13; but on the other hand an improvement in heat transfer inside the cavity was found. A later study on unsteady natural convection in differentially heated cavities may be extended for other types of nanoparticles, taking into account other inclinations and various shape factors. The authors would like to acknowledge Professor Mohamed Lashab from Larbi Ben M'hidi university, Algeria for his given assistance, we are extremely grateful to him for his help. geometric aspect ratio, L/H specific heat at constant pressure, J.kg-1K-1 acceleration due to gravity, m.s-2 Exponential function nondimensional length of partial heater, h'/L length of heater, m length of enclosure along y', m thermal conductivity, W.m-1.K-1 length of enclosure along x', m Nusselt number nondimensional time nondimensional temperature hot wall temperature, K cold wall temperature, K nondimensional velocity components, x, y nondimensional cartesian coordinates Nondimensional position of the heater element along x Nondimensional position of the heater element along y thermal diffusivity, m2.s-1 coefficient of thermal expansion, K-1 inclination angle, rad dynamic viscosity, kg. m-1.s-1 density, kg.m-3 nanoparticle volume fraction nondimensional stream function nondimensional vorticity Exponent and subscripts for dimensional quantities [1] Choi, U.S., Eastman, J.A. 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Ali Taghavi Department of Mathematics, Faculty of Mathematical Sciences University of Mazandaran P. O. Box 47416-1468 Babolsar, Iran. Mojtaba Nouri Vahid Darvish Home > Vol 26, No 3 (2018) > Taghavi Korean J. Math. Vol 26, No 3 (2018) pp.459-465 DOI: https://doi.org/10.11568/kjm.2018.26.3.459 A note on nonlinear skew Lie triple derivation between Prime $\ast$-algebras Ali Taghavi, Mojtaba Nouri, Vahid Darvish Recently, Li et al proved that $\Phi$ which satisfies the following condition on factor von Neumann algebras $$\Phi([[A,B]_{},C]_{})=[[\Phi(A),B]_{},C]_{}+[[A,\Phi(B)]_{},C]_{}+[[A,B]_{},\Phi(C)]_{}$$ where $[A,B]_{}=AB-BA^{}$ for all $A,B\in\mathcal{A}$, is additive $\ast$-derivation. In this short note we show the additivity of $\Phi$ which satisfies the above condition on prime $\ast$-algebras. Lie triple derivation, Prime *-algebra, additive map. 46J10, 47B48, 46L10. Z. Bai and S. Du, The structure of non-linear Lie derivations on factor von Neumann algebras, Linear Algebra Appl. 436 (2012), 2701–2708. (Google Scholar) J. Cui and C.K. Li, Maps preserving product XY −Y X∗ on factor von Neumann algebras, Linear Algebra Appl. 431 (2009), 833–842. (Google Scholar) C. Li, F. Lu and X. Fang, Nonlinear ξ−Jordan ∗-derivations on von Neumann algebras, Linear and Multilinear Algebra. 62 (2014), 466–473. (Google Scholar) C. Li, F. Lu and X. Fang, Nonlinear mappings preserving product XY + Y X∗ on factor von Neumann algebras, Linear Algebra Appl. 438 (2013), 2339–2345. (Google Scholar) C. LI, F Zhao and Q. Chen, Nonlinear Skew Lie Triple Derivations between Factors, Acta Mathematica Sinica 32 (2016), 821–830. (Google Scholar) L. Moln ́ar, A condition for a subspace of B(H) to be an ideal, Linear Algebra Appl. 235 (1996), 229–234. (Google Scholar) A. Taghavi, V. Darvish and H. Rohi, Additivity of maps preserving products AP ± PA∗ on C∗-algebras, Mathematica Slovaca 67 (2017), 213–220. (Google Scholar) A. Taghavi, H. Rohi and V. Darvish, Non-linear ∗-Jordan derivations on von Neumann algebras, Linear Multilinear Algebra 64 (2016), 426–439. (Google Scholar) W. Yu and J. Zhang, Nonlinear ∗-Lie derivations on factor von Neumann algebras, Linear Algebra Appl. 437 (2012), 1979–1991. (Google Scholar)	CommonCrawl
Optimal renewable resources mix for low carbon production energy system in Morocco Omar Benzohra1, Sidi Salah Ech-Charqaouy1, Fouzia Fraija1 & Dennoun Saifaoui1 The production of electrical energy has always been a subject of debate to fight against climate change and preserve natural resources. Several countries, including Morocco, have proposed ambitious policies to develop renewable energy sources of production in the short and medium term. The major problem of renewable sources production is their intermittent nature. Using storage units, particularly PETS' and molten salt technologies, will increase the penetration rate of renewable energies. The balance between production and consumption will optimize production, and it represents an important aspect of smart grids. In this article, an electrical energy consumption prediction was developed for the period 2019-2025, and optimization of the renewable energies injected within the grid was made by introducing the algorithm used. The results show that the use of storage units will increase the rate of renewable energies integration to 47.189% of the total installed capacity. Electrical power is a major factor for the social and economic development of the countries. The consumption of electrical energy will reportedly be doubled in 2040 (IEA, 2018), where comes the need to install new electrical infrastructure. In Morocco, electricity demand (ED) is experiencing an average increase of 6-7% annually, and the expected electricity consumption in 2030 is 95 TWh. Currently, Morocco consumes 37 TWh for an installed capacity of 9GW. The electricity production field has made it possible to meet 86% of the national ED, and the difference is compensated via the Moroccan Algerian (MA) and Moroccan Spanish (MS) interconnection (www.one.org.ma). The Moroccan network is mono-directional, radial, and not robust. As more energy enters the market, the transition to a more efficient network with more flexible infrastructures becomes paramount, and the solution is the Smart Grid (SG) (Morad et al. 2013). There is no absolute definition to describe SG, but it can be characterized by its two-way communication, reliability and safety, ability to reduce peak power consumption via Demand Side Management Tool (DSM), ability to provide environmental benefits, locate and repair defects, integrate renewable energies, and manage storage units (Warren 2014) (Wu and Xia 2017). The SG can be summed up by a combination of electrical infrastructure and embedded intelligence associated with the software, automation, transmission, and information processing (Torriti 2012). This intelligence can be deployed at various levels of a network (Galván-López et al. 2015), and this network will be able to integrate data that control the operations that will be assigned to them (Sahbani et al. 2016) (Kuzemko et al. 2017). The basic essential element of SGs is to measure the real needs of consumers to produce the quantity they need. Electricity is very difficult to store. It is, therefore, necessary at all times to balance the network, to ensure that the production is equal to the consumption. If the gap between production and consumption increases too much, the network suffers from frequency deviations and damaging voltages for the network equipment and those of the consumers. The consequences can go as far as the disconnection of certain branches of the network, or even the generalized incident blackout. Where comes the need for DSM and Demand Response (DR). This shifting can effectively reduce the aggregate energy load during peak hours (Alasseri et al. 2017). In Europe, the consumption of electrical energy is more interesting in winter than in summer, and this is due to the excessive use of heating. The electric variation varies from one country to another. The Belgian electricity sector is liberalized and unbundled. The country is using several business models, as the peak electricity consumption is around 13 GW. The Belgian electricity grid is quite advanced in the market, including decentralized generation, and the government plans to a possible phase-out of the nuclear power plants at the end of their lifetime. DR products are available for ancillary services and strategic reserve. Boogen et al. (2017) have conducted a study on the impact of DSM activities on residential ED in Switzerland. It has been found that the presence of DSM has a significant impact on the consumption of electricity, and their presence reduces the ED by 5%. (Paulus and Borggrefe 2009). Barbato et al. (2015) have proposed a distributed DSM system for SG infrastructure, specially adapted to reduce the demand for residential users using a dynamic pricing strategy. The authors used energy rates as a function of the overall power demand of customers. Mellouk et al. (2018) have used a genetic algorithm method to solve DSM and dynamic economic dispatch problems. In North America, the specific needs of electric power reveal so many winter peaks that are due to the use of heating means in winter and air conditioning in summer. The American power grid is centralized, fragile, and old, and this makes it rather vulnerable. On August 14, 2003, the American power grid experienced a blackout in California affecting 55 million people and causing $ 6 trillion in losses (Gillingham et al. 2009). US utility grid-initiated DSM program that initially focused on load shifting and their increasing on electric end-use efficiency. Several studies were elaborate to a better implementation of demand-side management programs and modeling their roles to reach a balance between demand and supply in the presence of renewable energies generation considering their stochastic behavior. Alavi et al. (2015) have proposed the point estimate model for modeling wind and solar power uncertainties, and have made a comparison between deterministic and probabilistic management. Zakariazadeh et al. 2014a, 2014b have developed a conceptual model for a DR management system with an optimization tool using a stochastic multiobjective. The objective is to schedule distributed energy resources and aims at minimizing the total operational costs and emissions. Siano (2014) have presented a survey of DR potentials and benefits in SG. Zakariazadeh et al. (2014a, 2014b) have used a stochastic multi-objective economic and environmental operational scheduling method to minimize the total operational costs and emissions and to generate a Pareto-optimal solution for the energy and reserve scheduling problem. Mohamed and Koivo (2010) have used the mesh adaptive direct search algorithm to minimize the cost function of the system. Cicek and Delic (2015) have studied DRM in a smart micro-grid (SMG) with wind power and founded the optimal deficit limiting conventional power production and consumption schedules. Rahimi et al. (2013) have investigated to compensate wind intermittency by introducing various technologies such as pumped hydro storage/ plug-in hybrid electric vehicle (HEV), solar energy, and batteries. Aghajani et al. (2017) have proposed a study of stochastic programming model to optimize the performance of a SMG in a short-term to minimize operating costs, and emissions with RES. The authors' used probabilistic density function to predict climatic data (wind speed, solar irradiation … ), and DR programming with the participation of residential, commercial, and industrial customers. In Morocco, where air conditioning is very widespread, the seasonal peak takes place in summer. Electricity consumption also varies significantly on the scale of a day: As we can see from the data collected for the ED, there are two-peak consumption per day; Midday peak: this one reflects the launch of the economic and industrial works. Evening peak: begins at around 19h, corresponds to the increase in household consumption and coincides with the end of economic activity. Network balancing is particularly crucial at the peak. The value of this peak that sizes the electricity network by ensuring the security of the network. The historical holder of most of the means of production is the National Office of Electricity and Water (NOEW). The transmission system operator provides the long-distance transport of large quantities of electricity on high and very high voltage lines. It is responsible for the overall balance of the network, and the instant equilibrium between supply and demand of electricity. The distribution network operator provides the connection and daily distribution of electricity to all consumers. This activity, also considered as monopoly, is under the responsibility of NOEW, and the suppliers are the companies responsible for marketing and billing electricity to consumers. This activity is open to competition in Morocco, and several boards hold the market such as LYDEC, AMENDIS, REDAL, RADEEMA ... At the end of the chain, electricity consumers can be different in nature, from very large industrial consumers to residential customers, though consumers in the tertiary sector. The main contribution made in this paper is to consolidate a low-carbon energy mix by promoting renewable energies integration into the power grid by: Modeling and predicting monthly ED in Morocco by 2025 Propose a flexible and low carbon demand model by promoting the contribution of renewable energies within the power grid by 48% in 2025 The remainder of this paper is organized as follows: section 2 describes the problem and presents the data. In section 3, the regression model was studied and a 2025 ED forecasting scenario was elaborated. The proposed algorithm is analyzed in section 4, and the results are presented in section 5. The last section summarizes the results and draws conclusions. In this study, a regression model is proposed for long-term energy management in order to promote the contribution of renewable energies resources in a SG. Due to the stochastic behavior of wind and solar energies, their accurate prediction is not possible and is always associated with uncertainties. The predictability of the data is analyzed to evaluate the relevance of keeping the parameters that have a low potential for the predictability. This is intended to determine carefully which criteria have a negative or negligible contribution to prediction accuracy. Therefore, to provide more compliance between planning and reality.The application and integration of ED prediction and generation of RES to SGs will optimize the management of the network. However, it is assumed that the distribution system's operator, which has the possibility of managing and controlling the grid using distribution management systems, performs planning for generation resources and consumer demands in a SMG and advanced metering infrastructure. The following section is dedicated to data examinations. Analyzing and modeling monthly electricity demand Figure 1 presents the evolution of ED in Morocco from 2000 until 2017. First, the figure shows a slight increase during the first seven years. Then a strong increase is observed since 2007. This may be due to several factors, direct and indirect, such as the increase in the exploitation rate of electronic equipment, climate change, and the acceleration of growth dynamics and modernization. Monthly ED in Morocco (2000-2017) Figure 2 displays the annual evolution of the demand for electric energy in Morocco during the period 1971-2017. It can be seen that the series reveals a growing trend over the years. Modelling monthly electricity demand Annual ED in Morocco (1971-2017) In the literature, several prediction methods are available according to prediction horizons. Every method has its strengths, weaknesses, and changes according to the context and environment of prediction. It is often difficult to identify a prediction method that differs widely from others (Doucouré 2015). Forecasting techniques are ranging from time series to hybrid models. Reviews research is presented by Bohi and Zimmerman (1984), and by Suganthi and Samuel (2012). In this study, a regression-based model has been used to predict electricity consumption in Morocco in the long-term. The main objective of multiple regression is to learn more about the relationship between several independent or predictive variables and a dependent or criterion variable. A straight line in a two-dimensional space is defined by the equation (1) $$ Y=a+b\ast X $$ where Y is the variable described by a constant 'a' and slope 'b' multiplied by the variable X. Multiple regression is where a dependent variable is described by several parameters, as is shown in equation (2): $$ Y=a+b\ast {X}_1+c\ast {X}_2+d\ast {X}_3+\dots +n\ast {X}_n $$ Where (b, c, d … , n) are the coefficients of the regression R2 describe the model fit goodness. If R2 adjusted is close to one, it indicates that the model has managed to explain almost all the dispersion thanks to the independent's variables. In this paper, a regression-based model has been used introducing gross national product (GNP), population, and 11monthly dummy variables as explanatory variables. The model development was done in excel, and the results are summarized in Table 1. Table 1 Multiple regression coefficient & probabilities The P value designates the probability that measures certainty with which it is possible to invalidate the null hypothesis. The more P valued tends to one, the more the null hypothesis is invalidated with more certainty. Table 1 reports that the intercept coefficient with GNP and population are all highly significant with a confidence level of 99%. The coefficient for May is not significant which indicates that ED this month is similar to that of December. All the other dummy variables for the other months are significant, which means that more or less electricity is consumed during the corresponding months than in December. However, the model still contains a large serial correlation despite its high predictive power. Autocorrelation occurs when the error term observations in regression are correlated. If those values follow a pattern, it means that the model contains autocorrelation. The Durbin-Watson (D-W) is widely used to test the first-order residues independence. The D-W statistic is calculated as follow: $$ d=\frac{\sum \limits_{i=2}^n\left({e}_i-{e}_{i-1}\right)2}{\sum \limits_{i=1}^n\left({e}_i\right)2} $$ Where ei describe the residuals and n is the number of elements in the sample. D-W statistic value varies between zero and 4. If it is equal 2, it means that the model has no autocorrelation. If'd' is less than 2, especially a value less than 1, means that the data is positively autocorrelated. If'd' is substantially above 2 means that the data is negatively autocorrelated. The D-W statistic calculated in this model is estimated at 0.79730711, indicating the presence of positive autocorrelation. In theory, if the residuals are serially correlated, then the estimate of the coefficients may be unstable. In this study, all the independent variables are statistically significant at a 1% error level. However, autocorrelation could be affecting the results, making it appear significant when it is not. Back in reviews, two approaches can be used to deal with serial autocorrelation. The first method is eliminating the symptoms of autocorrelation by using another estimation method. Otherwise, preventing autocorrelation from occurring in the first place by adding relevant missing independent variables. There are situations in which autocorrelation cannot be eliminated if the omitted independent variable is not available or cannot be found. To reduce autocorrelation, several methods are presented in reviews, such as the AR (1) method used by (Mirasgedis et al. 2006), and Henley and Pierson (1994). Cochrane-Orcutt Method, feasible generalized least squares (FGLS) or estimated generalized least squares (EGLS). Cochrane-Orcutt regression is an iterative version of the FGLS method for addressing autocorrelation. This approach uses the following steps for estimating rho. Step 1: Run Ordinary Least Square (OLS) regression on eq (2) and calculate the residualse1, e2… en Step 2: Using these sample residuals ei, find an estimate for ρ using OLS regression on $$ {\varepsilon}_i=\rho {\varepsilon}_{i-1}+{\delta}_i $$ Step 3: Substitute this estimate for ρ in the generalized difference equation $$ {y}_i^{\prime }={\beta}_0^{\prime }+{\beta}_1{x}_{i1}^{\prime }+\dots +{\beta}_k{x}_{ik}^{\prime }+{\delta}_i $$ Step 4: Based on step 3, new residuals can be calculated. Go to Step 2. Continue this iteration until the change in the estimated value of 'ρ' is less than some predetermined amount. Note that an iterative approach is used since regression coefficient 'r' in step 2 is not necessarily an unbiased estimate of 'ρ' although it is known to be a consistent estimate of 'ρ'. The use of the Cochrane-Orcutt method has eliminated the first-order autocorrelation. The new statistical value of the Durbin-Watson test is around 2.03, showing that the model has no longer autocorrelation in the error term. Fig. 3 represents the distribution of the error against time, the new distribution is rather random, and it oscillates around zero. Error terms distribution The coefficient of May is not significant, which means that electricity consumed in that month is similar to that of December, or less. All the other coefficients are significant, which indicates that more or less electricity is consumed during these months than in December. The adjusted R² has been updated and has increased slightly from (94.6%) to (96.23%), which designate an improvement of the predictive power of the model. Both RMSE and MAPE are calculated for the model, and the results are summarized in Table 2. Evaluation of the model Table 2 MAPE & RMSE calculated for the regression based model Historical electricity consumption data for the period 01/2000-12/2017 has been used to evaluate the regression-based model. The sample period 01/2000-12/2016 were used in training the model used in equation (3). The results of the computation are summarized in Table 3. Table 3 Forecasting ED for 2017 for the training set 2000-2016 The model shows a very high predictive power as the overall prediction error is 0.3%. The maximum prediction error is 4%. However, the estimations' deviation between actual and forecasted monthly ED is 1% or less for 6 out of 12 months. On an annual basis, the model has shown a high predictive power as the forecasted ED is very close to the actual data. Fig. 4 shows forecasted electricity consumption against real electricity consumption for 2017. Forecasting electricity demand for the period 2019-2025: Real electricity consumption against forecasted electricity consumption After executing the model on the desired period, the results summarized in Table 4 shows the electricity consumption values and their rate of increase. The model rate of increase is compared to what was published by the utility grid in (www.onee.org.ma) Table 4 Forecasted electricity consumption for 2019 and 2025 and the rate of increase compared to 2017 With the 2025 forecasting done, the scaling consists of converting the values obtained into time powers for the 8760 hours of the year, by taking account of the types of the days, the time and seasonal variations. J. Torriti (2017), A.Pimm et al. (2018) and Ma et al. (2017) have used this approach in their studies. Monthly electricity consumption is modeled as the addition of 4 variables; monthly electricity consumed during working days, holidays, days near holidays and Saturdays. Eq (6) represent the modeled electricity consumption function. $$ {E}_{mi}={E}_{wd}{n}_{wd}+{E}_h{n}_h+{E}_{nh}{n}_{nh}+{E}_s{n}_s $$ Where Em, is the monthly electricity consumption, and 'i' vary from 1 to 12 Ewd: Monthly electricity consumption during working days nwd: Number of working days during a month Eh: Monthly electricity consumption during holidays nh: Number of holidays during a month Enh: Electricity consumption during days near holidays nnh: Number of days near holidays during a month Es: Electricity consumption during Saturdays ns: Number of Saturdays during a month Equation (6) can also be written in the following form: $$ {E}_{mi}={E}_{wd}\ast \left[{n}_{wd}+{r}_h{n}_h+{r}_{nh}{n}_{nh}+{r}_s{n}_s\right] $$ Where, $ {r}_h=\raisebox{1ex}{$\overline{E_h}$}\!\left/ \!\raisebox{-1ex}{$\overline{E_{wd}}$}\right. $ is the rate of holidays $ {r}_{nh}=\raisebox{1ex}{$\overline{E_{nh}}$}\!\left/ \!\raisebox{-1ex}{$\overline{E_{wd}}$}\right. $ rate days near holidays $ {r}_s=\raisebox{1ex}{$\overline{E_s}$}\!\left/ \!\raisebox{-1ex}{$\overline{E_{wd}}$}\right. $ rate of Saturdays After calculating these rates, they will be used to calculate the hourly power of each type of day of the year. Once the daily energy of the working day is determined, the other values are multiplied by the corresponding ratio of the type of the day. Therefore, daily ED is summarized in Table 5. Table 5 Forecasted daily power consumption depending on the type of days The conversion of energy into power is done by calculating the hourly effect of the day when the consumption is maximum (Table 6). This method was used by Grand et al. (2015) and aimed to extrapolate the hourly load deducing by homothetic from the previous years, and it is calculated as is shown by the equation (7) Table 6 Daily ratio $$ {e}_h=\frac{E_i}{\sum \limits_{i=1}^{24}{E}_i} $$ Where, eh is the hourly ratio Ei hourly energy $ \sum \limits_{i=1}^{24}{E}_i $ daily consumption Scaling is the multiplication of these factors by the corresponding daily energy for each category of days. Hourly energy consumption is summarized in Fig. 5: Generation-demand balance in 2025 Hourly needs for the period 2025 Conventional generation sources A very large part of electricity generation is provided by conventional generation sources, including coal-fired power plants where the fuel is burned in a boiler using the heat generated either by combustion, or in a combustion turbine. In Morocco, the power supplied by coal-fired power plants is 1785 MW (2017). Oil-based production unit's burn oil in a boiler producing steam that turns a turbine, which drives an alternator and produces electricity. The power supplied by these units is 600 MW (2017). Combined-cycle power plants use natural gas as a fuel in a two-stage production system: the first step is to put the alternator in motion by burning natural gas. Then, in a second cycle, the heat from the first cycle is recovered to the max to generate steam that rotates a second steam turbine to generate additional electricity. The total power of the system is defined in equation (8) $$ {\boldsymbol{P}}_{\boldsymbol{cc},\boldsymbol{tot}}=\frac{\mathbf{2}}{\mathbf{3}}{\boldsymbol{P}}_{\boldsymbol{cc},\boldsymbol{gt}}+\frac{\mathbf{1}}{\mathbf{3}}{\boldsymbol{P}}_{\boldsymbol{cc},\boldsymbol{st}} $$ The efficiency of the system is around 59%. In Morocco, 1184 MW is installed in a combined cycle for the production of electrical energy. A gas turbine power plant is a heat engine performing the various stages of its thermodynamic cycle in a succession of members traversed by a gaseous fluid in a continuous flow. In Morocco, a gas turbine power plant is functional and develops a power of 315 MW. Renewable energy sources generation Renewable sources of production, particularly solar and wind have great potential. The installed capacity of the wind power plant will reach 2000 MW in 2020, spread over several sites. With a very strong solar field, Moroccan kingdom can produce a power of 20 GW just by solar, (www.onee.org.ma) but this capacity is not exploited yet. However, 2 GW of solar is planned to be operational by 2020 divided into concentrating thermal power plants and photovoltaic power plants. Hydroelectric generation A hydroelectric power plant is the process of producing electricity by using water as the driving force to turn the turbines that drive generators to produce electrical power. These stations can also be used for energy storage as a pumped energy transfer station. The total installed capacity of these units in Morocco should be around 1400 MW around 2020. Generation-consumption balance Electricity consumption is highly unsteady, and this variability is sensitive during a season with peaks of consumption, more or less strong, this variation can also be on the scale of the day. In Morocco, generally warm country, widely equipped in air conditioner, the peak in electrical consumption is in summer. Network balancing is crucial at the peak. Consumption peak value sizes the network to ensure electricity energy quality and complementary production capacities. Moroccan production units currently in operation are summarized in Fig. 6. Percentage of different production sector in Morocco (2017) The forecasted ED is denoted as (Fi, i=1 … .m). The devices that produce electricity are divided into three groups. Basic production units, decentralized production units, and peak production units. They are classified according to their priority. High, medium, low. When the demand is low, the manager would use the base source (coal = low), the more the demand increases, the more the manager would have to resort to another source of production, notably RES and gas-based production (Table 7). Table 7 Production units' priorities Basic production units are scheduled to be operational in full-time. These units require a very high investment cost, but the operating cost is relatively low. In Morocco, as shown in Fig. 6, a preponderance of the production sources are based on coal and oil, 50% of the total installed capacity. During an electrical peak, utility grid manager uses auxiliary sources to meet ED. Those capacities have a fast startup and a high operating cost which explains the high cost during peak hours. Production group maintenance is a periodic action programmed to detect latent anomalies in equipment and guarantee their proper functioning. Maintenance can reduce the probability of failure and increase equipment life. In this study, the maintenance schedule is supposed to be known. The proposed algorithm is based on the promotion of renewable sources integration. The base capacities will be coal power plants operating with the minimum technical requirements. Coal plants are chosen because of their stability, reliability, and low production costs, where RES will be connected to be injected to meet required consumption in mid-peak time. The gas-based production units are characterizing by their fast start and flexibility, denoted as high because its request arrival time is in peak hour. The objective of shifting electricity consumption can be various. The objective of electricity suppliers is to avoid the appearance of high peak load demand. In consumers' point of view, the objective is to minimize electricity bill, and offer a better electricity quality. In order to provide optimal schemes to regulate controllable devices to meet some desired properties, the demand load is forecasted based on the previous usage. The period of estimation is a forecasted window. It can be one day, a week, or even longer. In that case, the algorithm can run beforehand to generate a scheme for organizing the production units. In this paper, the algorithm is designed for one day ahead of planned load shifting, and it can be easily extended to the other sizes of forecasted windows. Utility grid manager objective is to balance ED and production, to smooth the load curve by eliminating electrical peaks, and regress the energy bill. The approach used in this paper is to predict daily consumption by 2025, transform energy into hourly power, and optimize the use of conventional power sources. The algorithm is based on the use of coal-based sources of production with their technical minimum to ensure the base, and adding production units when needed by promoting RES injection. $$ \left\{\begin{array}{c}{P}_n=a\ast {P}_{jlec}+b\ast {P}_{abm}+c\ast {P}_{eet}+d\ast {P}_{ctm}+e\ast {P}_{ctj}+f\ast {P}_{cts}+g\ast {P}_{ctk}+h\ast {P}_{hyd}+i\ast {P}_{wt}+\\ {}j\ast {P}_{solar}+k\ast {P}_{IMS; IMA}\kern14.75em \\ {}\mathit{\operatorname{maximize}}\ {F}_{d,\mathit{\min}}-{P}_{wt}-{P}_{solar}\ge {P}_{n,\mathit{\min}}\kern6.5em \\ {}\ f:=h+i+j\le 0.48\kern18.25em \end{array}\right. $$ Eq (9) describes the distribution of national production according to different sources of production. 'a, b, c ... k' are the coefficients that describe each source of production. Eq (9) is the equation to be maximized; with 'i' the coefficient of wind turbines production and 'j' is the coefficient of solar energy production. The objective is to integrate renewable energies into the power grid, without exceeding 48% of the total production due to technical standard. Implementation of the proposed algorithm In this paper, an algorithm was implemented by programming language C to address the optimization problem in the power grid by shifting RES to start working at the appropriate time. The flowchart of the proposed algorithm is presented in the illustration below Fig. 7. The initialization step initializes the parameters, time, type of day, the forecasted electricity consumption, coal production, RES production, gas production, Spain-Morocco interconnection, Algeria-Morocco interconnection. In each iteration, the priority change according to the required demand and the utility grid react according to the available sources of production. The flowchart of the proposed algorithm The program starts with the initialization of the inputs: the day Ti, month Mi, forecasted consumption Fd, available production units Ai, their degree of importance Ii, and their downtime Ci. With day and month acknowledged, the forecasted electricity consumption would be determined, consequently, the production units' status: low, medium, and high, as needed. After the determination of production units' status, the connected units will be chosen according to the need for consumption. If all the objectives were realized, the program would shut down showing the results. Otherwise, an incremental loop is created to continue the calculation. When the production meets the demand, the program will stop, print results, and shows the percentage of renewable energies integration within the power grid. Fig. 8 shows that the use of RES production varies according to the hours of the years. The graph represents a monotonous hourly load, classified from the greatest to the smallest value. Based on equation (9), the max of production to be connected is 40% in 2019, 48% in 2025 (www.one.org.ma). Hourly monotonous electric load for 2025 Figure 9 represents the load monotone expected in 2025 in hourly volume, represented in the descending curve. The bottom of the graph represents basic generation power plants that operate in technical minimum during the same period. Monotonous electric load for the period 2025 with basic generation power plants After the execution of the program, the calculation of the small integrable value by renewable energies over the whole period was calculated, Pres, min=1248.793 MW. This value represents a penetration rate of 17.54502 % of the total installed capacity, distributed on wind farms and solar fields. The integrable capacity of renewable energies can be increased by adding storage capacity, PETS' to store the energy produced by wind turbines, and molten salt technology to store solar energy. The capacity of the storage units in Morocco in 2025 will reach 2110 MW, 1110 MW of PETS', 1000 MW of molten salts (www.onee.org.ma). RES are intermittent, so their storage is mandatory for better utilization of these resources. The integrable RES capacity is 3358,793 MW, which corresponds to a maximum penetration rate of 47,189%. The capacity of the electrical system to absorb the surplus of RES generation is increased. As a result, demand increases and the maximum power that can be produced by RES power plants increase, and the penetration rate is improved. In order to define relevant scenarios, several factors are relative and which must be taken into account. The total character of the energy system will impose the elected choice. The world price of the energy that depends directly on the estimated balance offers and demand on a world level. The second character refers to the relations foreign of Morocco and the evolution of its integration in various regional contexts. This variable is particularly determining for the future of the Moroccan energy system that suffers from a notorious insufficiency of primary resources in this sector. The process of decarbonizing of the electrical supply network bases the fall of price by putting in exploitation new technologies of production of electrical energy leading in the long term to a surplus of offer and capacity installed. The electricity production field in Morocco is mainly based on centralized production based on coal, while the production based on renewable energies does not exceed 13%, Fig. 10. Injected power by sources After the implementation of the program, the share of renewable energies has increased. By regressing the share of decentralized generation sources and putting them in technical minimum, the production of renewable energy injected into the network has reached 17,545 %. Storage units represent an effective way to increase the percentage share of renewable energies. The aim of these units is to store the excess of production from REPP, and use it when needed. By adding the generation stored in these units, the share of renewable energies has increased to 47.18963%. By using thermal sources of production with their nominal values, production would exceed demand in 42.796% of the time, and only 1.554% of the time when thermal production would be in line with consumption, Fig. 11. The renewable energy threshold was calculated for the remaining 55.650% of the sample, and the calculated value vary between 0.36% and 31.7%. Monotonous electric charge for 2025 The program used will help to manage the production units better, to promote renewable energy integration, and to reduce greenhouse gas emissions. First, reduce the nominal power of the thermal power plants, and use them with their technical minimums, Fig. 12. The insufficiency, in this case, will be compensated by means of renewable energies. The integrable capacity calculated is 17.545% over the entire period. By adding the storage units, which totalize 2110 MW, Table 8, the integrable threshold will increase to 47.189%. Table 8 Storage units available by 2025 Forecasted load monotone with basic power plants working with minimum technic power Installed power distribution without optimization Installed power distribution after optimization The program has therefore helped to increase the renewable energy threshold in 2025 from 31.733% out of 4875 hours, Fig. 13, to 47.189% out of 8760 hours, Fig. 14. This value corresponds to a significant decrease in conventional sources, and the decrease of the energetic mix cost, since the cost of the kWh produced from renewable energies is cheaper than the one produced by TPP. Summarizing what was done, the regression-based model was used to predict electricity demand in Morocco for 2025. The method has shown a high predictive capacity with a significant adjusted R², 96.23%. The forecasted energy was scaled by converting the values obtained into time powers, for the 8760 hours of the year, based on the type of days, the time and seasonal variations. An algorithm based on the promotion of renewable sources integration was elaborated. After the integration of basic power plant, the program has to promote directly the integration of renewable energies within the power grid and indirectly via storage units. The calculated integrable threshold is 17.545%. With storage capacities added, the new integrable power by renewable energies will border 3358.793 MW, with a percentage of integration of 47,189%. A value that converges with the policy of the country who have proposed 42% of the installed capacity power of RES by 2020, and 52% by 2030. Among the perspectives that can be identified on the purpose of this work would be to develop more complex modeling of the intermittency, and the balance of the electrical network by integrating the hourly climatic and meteorological data to calculate the electric power generated by the natural flow. Thus, our study will allow developing more deeply the economic and environmental consequences. The datasets generated and analyzed during the current study are not publicly available due confidentiality issues, but are available from the corresponding author on reasonable request. $ \overline{E} $ : Mean Electricity power E m, i : Monthly Electricity consumed in 'i' hour ABM: Ain Beni Mathar power plant BPP: Basic Power Plant Combined cycle CTJ: Thermal Power plant Jerada CTK: Thermal Power plan Kenitra CTM: Thermal Power plant Mohamedia CTS: Thermal Power plant Safi DR: DSM: DW: Durbin Watson ED: EET: Electric Energy Tahadart GPP: Gas Power Plant GT: GWh: Giga Watt-hour HEV: Hybrid Electric Vehicle JLEC: Jorf Lasfer Electricity Company Morocco-Algeria Interconnection MAPE: Mean Absolute Percentage Error MS: Morocco-Spain Interconnection NH: Near holidays NOEW: National Office of Electricity and Water Pumped Energy Transfer Station R2 : Coefficient of determination REPP: Renewable Energy Power Plant RMSE: Root Mean Square Error SG: SMG: Smart Micro Grid Steam Turbine TPP: Thermal Power Point TWh: Tera Watt-hour WD: WT: Aghajani GR, Shayanfar HA, Shayeghi H (2017) Demand side management in a smart micro-grid in the presence of renewable generation and demand response. 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Energy Conversion Manag 78:151–164 Zakariazadeh A, Jadid S, Siano P (2014b) Stochastic multi-objective operational planning of smart distribution systems considering demand response programs. Electric Power Systems Res 111:156–168 The authors would like to thank the National Office of Electricity and Water (ONEE/BE) for providing data which give the authors the opportunity to pursue research in this area. Faculty of Sciences, Hassan II University, Casablanca, Morocco Omar Benzohra, Sidi Salah Ech-Charqaouy, Fouzia Fraija & Dennoun Saifaoui Omar Benzohra Sidi Salah Ech-Charqaouy Fouzia Fraija Dennoun Saifaoui SE provided the data used in the study. OB analyzed and interpreted electricity demand data, programmed the algorithm, and was a major contributor in writing the manuscript. DS revised the program with OB. DS and FF have revised the work. All authors read and approved the final manuscript, and agreed both to be personally accountable for the author's own contributions and to ensure that questions related to the accuracy or integrity of any part of the work, even ones in which the author was not personally involved, are appropriately investigated, resolved, and the resolution documented in the literature. Correspondence to Omar Benzohra. Benzohra, O., Ech-Charqaouy, S.S., Fraija, F. et al. Optimal renewable resources mix for low carbon production energy system in Morocco. Energy Inform 3, 3 (2020). https://doi.org/10.1186/s42162-020-00105-9 demand-side management low carbon system	CommonCrawl
Home Journals JESA Modeling of the Inking Apparatus of the Sheet Printing Machine Modeling of the Inking Apparatus of the Sheet Printing Machine Eldar A. Aliyev Department of Theory of Mechanisms and Machines, Azerbaijan Technical University, H. Javid Ave. 25. Baku, AZ1073, Azerbaijan [email protected] The ink apparatus was considered as a dynamic system formed by a combination of rollers and cylinders. The transition characteristic of the ink apparatus was considered as a natural reaction of this model to various external influences. For research, a single-capacitance model of an ink apparatus is proposed. The flow of ink through a series of rollers and cylinders that form a baseline is considered. To determine the amount of ink, the power conditions of the ink machine are considered. Presumably, the power of the ink unit is pulsed. The amount of ink passing through each contact node in one printing cycle. A model of the distribution of ink layers in the ink apparatus of a sheet printing machine is built. A method for calculating the distribution of ink layers in the ink apparatus for letterpress and offset printing machines has been developed. The regularity of the distribution of ink across the maximum and minimum layers is established. Also determined the total amount of ink accumulated in the ink apparatus. For the unsteady mode, the change in the volume of ink in the stream was characterized by the equation of a single-capacitance model of the ink apparatus. The equation of non-stationary mode is obtained. The dynamic characteristic of a single-capacitance model made it possible to determine the unevenness of the ink layer on the form in the case of a pulsed power supply of the ink apparatus. The extension of the proposed methodology to ink apparatus with branched streams of ink makes it possible to use this method for the study of ink apparatus of different designs. Also, the presentation of an ink apparatus in the form of a single-capacitance object creates the prerequisites for a more accurate description of its properties in transition modes. inking apparatus, offset printing, distribution model, dynamic characteristic It is known that the main purpose of the ink printing system is to provide a given thickness of the ink layer on the prints when printing different types of products. Therefore, the ink system can be considered as an object of regulation. Adjustable, that is, the initial, value is the thickness of the layer of ink on the prints, the input is the supply of ink. Changing the type of printed matter requires changing the printing form. This can be considered as a change in the nature of the disturbance and the load on the inking system. Inking devices of offset printing machines [1] are the most important technological units, the dynamic and static properties of which significantly affect the print quality. Therefore, the urgent task is to develop mathematical methods for researching the work and further model-oriented design of inking devices based on software and hardware. The purpose of this work is to create a scientific basis for structural and mathematical modeling of a high-pressure and high-sheet offset printing apparatus for printing machines. To achieve this goal, the following tasks were set: Modeling of the inking apparatus as a control object associated with the movement and ink flow of the printing process; Determination of the nutritional condition for the development of a single-capacitive mathematical model of the inking apparatus; Development of methods for the distribution of ink layers in an inking apparatus for high and sheet offset printing machines. 2. Literature Review and Problem Statement To describe the dynamics of the inking apparatus in work [2], approximate mathematical models with pure delay were used, which are obtained by the experimental study of several prototypes of the inking apparatus or one variable prototype. The theoretical path corresponds to modeling the processes of transferring ink and a moisturizing solution in the inking apparatus by describing physical processes with the subsequent use of software implemented on a computer. However, the model of the inking apparatus is not described in the work. Using a high-precision force measuring device manufactured in the laboratory [3], a method for measuring the adhesion force when the ink film is torn from a blanket is developed. Using the proposed method, the adhesionproperties of industrial inks of Ag nanoparticles, varying the film thickness and solids content, were evaluated. Howeverin this work, individual ink-transporting units of the ink apparatus during ink transfer were not considered. To improve the quality of color offset printing and to learn the process of ink transfer, the article [4] uses the method of theoretical analysis and experiment. The speed and pressure of the ink flow field are analyzed by deformation of the rubber roller and rotation of the two rollers. The effective ink layer thickness is removed when the ink transfer rate can be obtained. The authors obtained the deformation of the rubber roller and the ink transfer rate under various conditions, and analyzed factors such as rotational speed, deformation of the rubber roller, the thickness of the ink layer between the two rollers, which affect the ink flow and transfer speed. Verkhola et al. [5] developed mathematical models of the elements of inking devices and based on them a model of the ink-printing system of a printing offset machine from Heidelberg GTO 52 was compiled. This mathematical model describes the process of rolling and transferring ink from an ink-spraying device to prints. In addition, the model makes it possible to take into account the different modes of operation of the spray device. Based on the mathematical model, an information technology for research and analysis of the nature of the distribution of ink and its effect on the thickness of the layer, which is transmitted to the output of the ink-printing system, was created. However, the proposed model is intended for small-format machines with a simple inking device. A number of scientists have revealed various approaches to the mathematical description of inking devices. Thus, the calculation was based on a system of algebraic equations that reflects the addition and division of ink layers in contact zones [6-8]. The use of these equations makes it possible to solve the static problem of the distribution of ink along the inking apparatus, as well as the dynamic problem of transferring layers of ink to the form and print; moreover, to solve the dynamic problem, it is proposed to consider systems of algebraic equations composed for a series of sequential cycles. Considering the duration of establishing a stationary mode, ranging from several tens to several hundreds of cycles, one can judge the great complexity and complexity of the computational work associated with this method. A model of an inking device was proposed by Alekseyev [9], based on the consideration of the operations of splitting individual volumes of ink into many discrete strips and forming a continuous non-uniform layer from them by summing. The mathematical model of the inking apparatus is represented in matrix form, and its transformation is carried out by methods of vector algebra. The complexity of these calculations is such that the use of computer technology is also required. However, in this work this path is not investigated and structural modeling of the inking apparatus is not considered. Ink transfer to a printing form was studied taking into account the surface roughness of the printing form [10]. However, the paper does not consider structural modeling of the inking apparatus. The Reynolds equation for ink transfer was derived on the basis of the theory of elastohydro dynamic lubrication, and a model of the relationship between the roller parameters, speed, pressure and ink thickness in the gap of the rollers was established using the Hertz contact theory [11, 12]. The influence of the speed, pressure and size of the roller on the thickness of the ink in the gaps of the rollers was analyzed. In addition, the ink transfer model was modified subject to the retention of ink in the roller gaps. The effect of print speed on ink performance was analyzed using computer simulation. However, in these works, structural modeling of the inking apparatus was not considered. The discrepancy between the various structures and parameters of the inking system of modern offset printing was investigated [13]. The surfaces of the inking rollers and cylinders were discretized using computer simulation, on the basis of which a mathematical model of constant time was created in a system of periodic and continuous ink supply. And then the feed system and the vibration system are analyzed. The simulation result shows that the ink supply system, the method of vibration of the vibrator, the coating of the plate has a great influence on the dynamic properties. However, in this work, structural modeling of the inking apparatus is also not considered in studying the influence of the inking supply system. Based on a non-oriented graph [14], a system for manual input of offset printing was considered as a complex non-oriented graph and a network diagram was created. On this basis, in accordance with the distribution of the surface of the ink roller and the creation of a dynamic two-dimensional array for recording changes in the thickness of the ink on the ink roller, the process of ink transfer during printing was really and intuitively reproduced. However, in this work, the structural modeling of the inking apparatus was also not investigated. Based on the analysis of published scientific papers, the following conclusion can be made about the state of the problem of mathematical modeling by the printing process. The development of methods for the mathematical description of the printing process, in relation to sheet offset printing, goes in several directions. One of which is a mathematical study of the movement of ink and a moisturizing solution in the ink and moisturizer and their interaction on a printed form in order to determine the conditions for obtaining high-quality prints. Study of the movement and interaction of the main material flows during sheet offset printing by traditional methods of mathematical analysis and theoretical mechanics is not able to cover complex and diverse dynamic phenomena and cannot give a complete mathematical description of the printing process as an automatic object management. 3. Single-Capacitance Model of the Inking Apparatus Suppose that the movement of ink on the surface of a roller or cylinder is characterized by a flow Q through a cross-sectional area S=ljh. $Q=\iint_{S} V_{n} d S$ (1) Under these conditions, we take the printing speed constant vn=const and limit the flow to the width of the elementary zone lj=const. Then we find that the flow of ink is uniquely determined by the thickness of the ink layer Consider the flow of ink through a sequential chain of rollers and cylinders 1,2, ..., k, k + 1, k + 2, which form a baseline (Figure 1a). We accept the following modeling conditions: when leaving any node i in the direction of direct flow, the contact layer hi is multiplied by the transmission coefficient βi, and in the direction of the return flow, by the coefficient (1-βi) (Figure 1b). The ratio of the formed layers is characterized by a splitting coefficient. $B_{i}=\left.\frac{\beta_{i}}{1-\beta_{i}}\right\|_{\beta_{i=0,5}}=1$ (2) When transferring ink from the knurling roller (k) to the plate cylinder (k+1) with a fill factor σ (provided that the relief is level). Figure 1. Ink flow model: а- baseline; b- ink transfer through the roller; c- pulse power mode; d- continuous power $B_{k}=\left.\frac{\sigma \beta_{k}}{1-\sigma \beta_{k}}\right\|_{\beta_{k=0,5}}=\frac{\sigma}{2-\sigma}$ (3) When transferring ink from a mold to rubber and from rubber to paper $B_{k+1}=\frac{\beta_{k+1}}{1-\beta_{k+1}}$; $B_{k+2}=\frac{\beta_{k+2}}{1-\beta_{k+2}}$ (4) in letterpress– $B_{k+1}=B_{p}=\frac{\beta_{p}}{1-\beta_{p}}$ in offset printing- $B_{k+2}=B_{p}=\frac{\beta_{p}}{1-\beta_{p}}$ To determine the amount of ink supplied to the inking apparatus in the average for one printing cycle and the amount of ink transferred to the print, it is necessary to consider the power conditions of the inking apparatus. 3.1 Determining the power condition of the inking apparatus Suppose that the power of the ink unit is pulsed by the oscillating transfer roller: T=m$\tau_{0}$ - the power cycle, where - m is the number of printing cycles $\tau_{0}$; γT power pulse duration - the time it takes for the duct cylinder to rotate a certain angle; $\delta_{0}$- pulse amplitude - the thickness of the supplied portion of ink, which is determined by the equation (Figure 1c). $\delta_{0}=h_{D}-(1-\beta) h_{0}$ (5) The amount of ink supplied on average per print cycle is $g_{0}=\frac{1}{m} \gamma \delta_{0}=\gamma_{0} \delta_{0}=\gamma_{0} h_{D}-(1-\beta) \gamma_{0} h_{0}=$ $=\beta \gamma_{0} h_{0}-(1-\beta) \gamma h_{1}$ (6) Whence it follows that pulse power with an amplitude $\delta_{0}$, period T and duty cycle γ is equivalent to pulse power with a period $\tau_{0}$ and duty cycle $\gamma_{0}=\gamma /m$ or continuous power supply with a thickness of the supply layer $\gamma_{0} \delta_{0}$ (Figure 1d). Assuming that the amount of ink entering node i is equal to the amount of ink being drawn from the node, we can write (Figure 1b). $g_{i}=\beta_{i-1} h_{i-1}-\left(1-\beta_{i}\right) h_{i}=\beta_{i} h_{i}-\left(1-\beta_{i+i}\right) h_{i+1}$ (7) In stationary mode, the amount of ink gi passing through each contact node for one printing cycle is constant and equal to the amount of ink supplied to the ink supply g0 unit on average for one printing cycle and the amount of ink transferred to the print: $g_{0}=\delta_{0} \gamma_{0}=\ldots=\beta_{i-1} h_{i-1}-\left(1-\beta_{i}\right) h_{i}=$ $=\beta_{i} h_{i}-\left(1-\beta_{i+i}\right) h_{i+i}=\ldots=\sigma h$ (8) where, h is the thickness of the ink layer on the print. 3.2 The study of modeling the inking apparatus and the method of calculating the distribution of layers of ink the inking apparatus Based on Eq. (8) taking into account the splitting coefficients $B_{i}$ build a model of the distribution of ink layers: $\frac{\beta_{i} h_{i}}{h}=\frac{\left[1-\left(1-\beta_{i}\right)\right] h_{i}}{h}=$ $=\sigma\left[1+\frac{1}{B_{i+1}}\left(1+\frac{1}{B_{i+2}}\left(1+\ldots+\frac{1}{B_{k}}\left(1+\frac{1}{B_{k+1}}\left(1+\frac{1}{B_{k+2}}\right) \cdots\right)\right)\right)\right]$ (9) At $\beta_{i}$=0,5 (i=1,2,…k) formula (9) gets a simple form $\frac{\beta_{i} h_{i}}{h}=\sigma(k-i)+\frac{c_{0}}{2}(2-\sigma)$ (10) where, $C_{0}=2 / \beta_{p}$, for letterpress machines ($\beta_{k+1}=\beta_{p}$; $1+\frac{1}{\beta_{k+2}} \equiv 1$) $C_{0}=2 \frac{2+\beta_{p}}{1-\beta_{p}}$-for offset printing machines ($\beta_{k+1}$=0,5; $\beta_{k+2}=\beta_{p}$) Ink distribution in inking devices under conditions $h_{i}=\beta_{i} h_{i}+\left(1-\beta_{i}\right) h_{i} ; \left(1-\beta_{i}\right) h_{i}=\frac{1}{B_{i}} \beta_{i} h$ (11) $h_{i}^{\alpha v e}=\frac{1}{2 \pi}\left[\alpha_{i} \beta_{i-1} h_{i-1}+\left(1-\alpha_{i}\right)\left(1-\beta_{i}\right) h_{i}\right]$ (12) $\frac{\beta_{i} h_{i}}{g_{0}}=1+\frac{1}{B_{i+1}}\left(1+\frac{1}{B_{i+2}}\left(1+\ldots+\frac{1}{B_{k}}\left(1+\frac{1}{B_{k+1}}\left(1+\frac{1}{B_{k+2}}\right) \cdots\right)\right)\right)$ (13) $B_{0}=\ldots=B_{i}=\ldots=B_{k-1}=\frac{\beta}{1-\beta}=1; \quad B_{k}=\frac{\sigma}{2-\sigma};$ $B_{k+1}=\frac{\beta_{k+1}}{1-\beta_{k+1}}$;$B_{k+2}=\frac{\beta_{k+2}}{1-\beta_{k+2}}$ (14) where, $\alpha_{i}$- the displacement coefficient, which characterizes part of the ink path along the periphery of the roller between the contact nodes when the flow is moving in the forward direction; define in the following form: For letterpress machines: $\frac{\beta_{k+1} h_{k+1}}{g_{0}}=1$ $\frac{\sigma \beta h_{k}}{g_{0}}=1+\frac{1}{B_{k+1}}$ $\frac{\beta h_{k-1}}{g_{0}}=1+\frac{1}{B_{k}}\left(1+\frac{1}{B_{k+1}}\right)$ $\frac{\beta h_{i}}{g_{0}}=k-i+\frac{1}{B_{k}}\left(1+\frac{1}{B_{k+1}}\right)$ (15) $\frac{\beta \gamma h_{1}}{g_{0}}=k-i+\frac{1}{B_{k}}\left(1+\frac{1}{B_{k+1}}\right)$ $\frac{\beta \gamma h_{0}}{g_{0}}=k+\frac{1}{B_{k}}\left(1+\frac{1}{B_{k+1}}\right)$ $\frac{\gamma h_{d}}{g_{0}}=k+1+\frac{1}{B_{k}}\left(1+\frac{1}{B_{k+1}}\right)$ Also for offset printing machines: $\frac{\beta_{k+1} h_{k+1}}{g_{0}}=1+\frac{1}{B_{k+2}}$ $\frac{\sigma \beta h_{k}}{g_{0}}=1+\frac{1}{B_{k+1}}\left(1+\frac{1}{B_{k+2}}\right)$ $\frac{\beta h_{k-1}}{g_{0}}=1+\frac{1}{B_{k}}\left(1+\frac{1}{B_{k+1}}\left(1+\frac{1}{B_{k+2}}\right)\right)$ (16) $\frac{\beta h_{i}}{g_{0}}=k-i+\frac{1}{B_{k}}\left(1+\frac{1}{B_{k+1}}\left(1+\frac{1}{B_{k+2}}\right)\right)$ $\frac{\beta \gamma h_{0}}{g_{0}}=k+\frac{1}{B_{k}}\left(1+\frac{1}{B_{k+1}}\left(1+\frac{1}{B_{k+2}}\right)\right)$ $\frac{\gamma h_{D}}{g_{0}}=k+1+\frac{1}{B_{k}}\left(1+\frac{1}{B_{k+1}}\left(1+\frac{1}{B_{k+2}}\right)\right)$ Based on the data obtained, we construct an ink flow distribution diagram for the baseline (Figure 2). With $\sigma$=0 on all rollers $i \leq k$ a constant layer is established C0; at i>k the layer is equal to zero (there is no transfer of ink to the form, since $\sigma$=0). With $\sigma$=1, the distribution diagram is a descending step line with step I. At $\sigma$<1, the step decreases proportionally to the value s. When passing through the node i=k, the diagram undergoes a jump, which is greater, the smaller $\sigma$. Regardless of i0=k-C0/2, a constant layer C0, is always set on the roller C0, i.e. all distribution curves merge here. The layer C0 becomes larger in the presence of an offset cylinder and with a decrease in the coefficient of transition of ink to paper $\beta_{p}$. Figure 2. The distribution of layers of ink in the inking apparatus: a- motion scheme; b - distribution diagram in the direction of direct flow Using the formula (9), the regularity of the ink distribution over the maximum layers in the direction of the direct flow, and the minimum layers in the direction of the reverse flow $\left(1-\beta_{i}\right) h_{i / h}$ are established. Also, for each roller, the middle layer characterizing the amount of ink accumulated on the roller can be calculated. For simplicity of calculation, it is assumed that the path sections of the forward and reverse flows are equal to each other: $\frac{\widetilde{h}_{l}}{h}=\frac{\beta_{i-1} h_{i-1}+\left(1-\beta_{i}\right) h_{i}}{2 h}$ (17) Imagine the distribution of the middle layer $\tilde{h}_{1}$/h along the sections of the ink path li/l0 (l0- the length of the print). The total amount of ink accumulated in the inking apparatus is determined by the amount characterizing the area under the distribution curve: $N_{0}=\sum_{i=1}^{k+2} \frac{\tilde{h}_{l}}{\mathrm{h}} \frac{l_{i}}{l_{0}}=C_{0} \bar{d} k+\frac{1}{2}\left(2 i_{0}-k\right) \sigma \bar{d} k+\left(2+\frac{3}{\beta_{p}}\right) \sigma$ (18) The first term of the sum characterizes the capacity of the rollers under the condition of uniform distribution ($\bar{d}$ is the ratio of the average diameter of the roller to the diameter of the plate cylinder); the second term takes into account the uneven distribution; the third is related to the capacity of the plate and offset cylinders. The proposed method extended to inking devices with branched streams of ink (as shown in Figure 3). Figure 3. The distribution of ink in the inking apparatus of complex structure: a- motion scheme; b- distribution diagram; DL baseline AL I, AL II - additional lines For this purpose, a scheme for branching ink flows passing through contact nodes is constructed (the sum of the components is equal to the total flow). A baseline is highlighted through which the ink enters the plate cylinder in the shortest possible way. For the baseline, the ink is distributed taking into account the attenuation of the ink flow due to branches. At the nodes where the ink flow branches, there are supply layers that serve as the beginning of additional lines. All additional lines end at node k+1. The distribution of layers in additional lines gives the necessary number of equations for determining the components of the total flow. For non-stationary mode, the change in the volume of ink in the stream is characterized by the equation of the single-capacitance model (the time is counted in printing cycles n). $\frac{d V}{d n}=q_{t}-q_{f}$ (19) where, qt=ht the supply of ink to the site I x I, qf=h - is the total consumption of ink from the site I x I taking into account the transfer of ink to the print elements of the print q=$\sigma$h and returning the remaining amount of ink q'=(1-$\sigma$)h to the ink tank. In a similar equation by Mill [7], the return of ink q' was not taken into account. Given the amount of ink accumulated in the stream V=N0h . Where N0- is the constant of the ink unit, we obtain the equation of the non-stationary mode. $N_{0} \frac{d h}{d n}+h=h_{t}\left(n-n_{0}\right)$ (20) where, n0- is the transport delay; the expression for the transient response takes the form. $h(n)=h+\left(h_{t}+h_{0}\right)\left(1-e^{-\frac{n-n_{0}}{N_{0}}}\right)$ (21) The constant N0 is determined taking into account the actual distribution of inking the stream in accordance with the formula (18). The dynamic characteristic (20) of the single-capacitance model allows one to determine the unevenness of the ink layer on the form in the case of pulsed power supply of the inking apparatus ht(t). Considering the inking apparatus as an open pulse system [15], using the discrete Laplace transform to solve Eq. (20), we find the amplitude of the pulsations with respect to the average layer thickness $\Delta=\frac{h_{\max }-h_{\min }}{2 h_{\text {ave}}}=\frac{1-e^{-\frac{1-\gamma_{0}}{N_{0}}}}{1+e^{-\frac{1-\gamma_{0}}{N_{0}}}}$ (22) Given an acceptable value $\Delta_{0}$, you can determine the required value of the constant N0 of the inking apparatus. As a result of the studies, the regularity of the distribution of the layers of ink in the inking apparatus was determined. To study the movement of ink, a single-capacitive model of an inking apparatus was developed. For this purpose, the flow of ink roughs a series of rollers and cylinders that form a baseline is considered (Figure 1a). Modeling was carried out under certain conditions. The ratio of the formed layers was characterized by a splitting coefficient Bi which are determined by formulas (2), (3), (4). To determine the amount of ink gi, passing through each contact node in the stationary mode, the power conditions of the ink apparatus are considered. The amount of ink g0, supplied to the inking apparatus in the average for one printing cycle and the amount of ink transferred to the print is determined by equation (8). Based on this equation, taking into account the splitting coefficients, a mathematical model of the distribution of ink layers (formula 9) is constructed, and a method for calculating the distribution of ink layers in an inking apparatus of high (15) and offset (16) printing machines is also developed. The regularity of the distribution of ink on the maximum and minimum layers is established. For each roller, the middle layer characterizing the amount of ink accumulated on the roller is calculated by formula (17). Based on theoretical studies, a diagram of the distribution of ink flow for the baseline is built (Figure 2). It was found that the C0 layer becomes larger in the presence of an offset cylinder and with a decrease in the ink-to-paper transfer coefficient $\beta_{p}$. The developed methodology for calculating the distribution of ink layers in an inking apparatus of high and offset printing machines can be extended to inking devices with branched streams of ink. To calculate the distribution of ink layers in this inking device, it is necessary to determine the pattern of branching of the ink flows passing through the contact nodes. Select the baseline through which the ink enters the mold cylinder in the shortest way. The supply layers located in the nodes, the branching of the ink flow is considered the beginning of additional lines. Based on the fact that all additional lines end at the node k+1, the distribution of layers in additional lines gives the necessary number of equations to determine the components of the total flow. It is established that in an unsteady mode, a change in the volume of ink in the stream is also characterized by the equation of a single-capacitance model. The ink volume is determined by formula (19), taking into account the transfer of ink to the printing elements and returning the remaining amount of ink to the ink tank. In a similar equation, the return of ink was not taken into account, which led to erroneous results. Studies have also established that the unevenness of the ink layer on the form in the case of pulsed power of the inking apparatus can be determined by the dynamic characteristic of the single-capacitance model, which is determined by formula (20). The advantages of this study compared to analogs can be considered that, in contrast to analogs, a fundamentally different approach to the mathematical description of inking devices based on the method of structural and mathematical modeling is proposed. The inking apparatus was considered as a dynamic system formed by a combination of rollers and cylinders and converting the input action (continuous or discrete portions of ink) into a time-varying thickness of the intermediate and output layers. The mathematical description is based on a system of difference or differential equations that adequately reflect the structure of the inking apparatus and the dynamic processes that occur in its links. The transitional characteristic of the inking apparatus was considered as a natural reaction of this model to various external influences (ink supply, shape relief, etc.). 1. It has been established that a single-capacitance model represents an inking apparatus as a single continuous flow, characterized by a change in the layer thickness along the line of ink movement, as well as in time. 2. It was found that the pulsed power supply at the input of this model makes it possible to determine the unevenness of the ink layer on the form 3. The calculations established that in stationary mode the amount of ink gi passing through each contact node for one printing cycle is constant. The amount of ink gi is equal to the amount of ink g0 supplied to the inking apparatus on average for one printing cycle and the amount of ink transferred to the print. 4. The proposed methodology for calculating the distribution of ink layers can be extended to inking devices with branched streams of ink. 5. The change in the volume of ink in the stream in an unsteady mode and the unevenness of the ink layer on the form in the case of pulsed power of the inking apparatus is characterized by the equation of a single-capacitance model. [1] Bobrov, V.I., Kulikov, G.B. (2012). Problems of creating and using effective printing and finishing systems. Proceedings of Universities, Problems of Printing and Publishing, 2: 12-14. [2] Wilson, D.J. (2007). Web offset printing machine: mechanisms, operation, maintenance. ed. V.N. Rumyantsev. M.: Print-Media Center. https://books.google.az/books/about/.html?id=_yDfNwAACAAJ&redir_esc=y. [3] Lee, A.R., Kim, I., Kim, K.Y., Nam, S.Y., Choi, Y.M. (2015). Quantitative measurement of ink-blanket adhesion for contact transfer printing inks. International Journal of Precision Engineering and Manufacturing. 16(1): 151-156. https://doi.org/10.1007/s12541-015-0019-z [4] Su, L., Chu, H.Y., Cai, L.G., Zhao, J.T. (2012). Research of elastic deformation of rubber ink roller and ink flow characteristics on two ink rollers. Applied Mechanics and Materials, 220-223: 1703-1710. https://doi.org/10.4028/www.scientific.net/AMM.220-223.1703 [5] Verkhola, M.I., Panovik, U.P. (2015). Information technology for the analysis of ink transfer in ink printing systems of offset printing machines. Transactions of BSTU. Publishing and Printing, 9(182): 18-23. [6] Morozov, M.G. (1968). Calculation of ink supply in letterpress and flat printing machines. part I, MSH, 19: 84-102. [7] Mill, K.K. (1964). Experimental verification of the theory of ink distribution. In the Book: Printing Inks and Color, 366-385. [8] Ruder, R. (1965). Unter suchungenzur Farbverteilungim Farbwerken von Rotationsmaechinen des Hoch-und Flachdruckes. T.H. Karl¬Marx-Stadt, 32-34. [9] Alekseyev, G.A. (1980). Inking machines of rotational letterpress and flat printing machines. M.: Book, 74-82. [10] Aliyev, E.A. (2017). Influence microgeometry offset printing plates for transfer ink from the printing form on Dekel. Proceedings of the International Symposium of Mechanism and Machine Science, AzCIFToMM-Azerbaijan Technikal University, Baku, Azerbaijan, pp. 201-202. [11] Liu, L.L., Li, K.K., Lu, F. (2016). Dynamic simulation modeling of inking system based on elastohydrodynamic lubrication, International Journal of Heat and Technology, 34(1): 124-128. https://doi.org/10.18280/ijht.340118 [12] Liu, L.L., Lu, F., Bai, J.Y. (2011). Simulation of inking system based on elastohydrodynamic lubrication. 2nd International Conference on Frontiers of Manufacturing and Design Science (ICFMD 2011). Applied Mechanics and Materials, 121-126: 2883-2886. https://doi.org/10.4028/www.scientific.net/AMM.121-126.2883 [13] Zhao, M.L. (2011). The dynamic property analysis of ink system in offset press. 2nd International Conference on Manufacturing Science and Engineering. Advanced Materials Research, 199-200: 132-136. https://doi.org/10.4028/www.scientific.net/AMR [14] Yan, Z.H., Hui, R.L., Ling, H.Y. (2009). Dynamic simulation of offset printing inking system based on undirected graph. ETP / IITA World Congress in Applied Computing, Computer Science and Computer Engineering (ACC 2009), Sanya, Peoples R. China, pp. 193-196. [15] Dittkin, Y.Z. (1963). Theory of linear impulse systems. M.: Fizmatiz, 164-176.	CommonCrawl
Grade 1 - Geometry 1.G.A Reason with shapes and their attributes. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size) ; build and draw shapes to possess defining attributes. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.Students do not need to learn formal names such as "right rectangular prism." Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. 1.MD Grade 1 - Measurement and Data 1.MD.A Measure lengths indirectly and by iterating length units. 1.MD.A.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. 1.MD.B Tell and write time. Tell and write time in hours and half-hours using analog and digital clocks. 1.MD.C Represent and interpret data. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. 1.NBT Grade 1 - Number and Operations in Base Ten 1.NBT.A Extend the counting sequence. 1.NBT.A.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. 1.NBT.B Understand place value. 1.NBT.B.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: 1.NBT.B.2.a 10 can be thought of as a bundle of ten ones–-called a "ten." 1.NBT.B.2.b The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. 1.NBT.B.2.c The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols $>$, $=$, and $<$. 1.NBT.C Use place value understanding and properties of operations to add and subtract. 1.NBT.C.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 1.OA Grade 1 - Operations and Algebraic Thinking 1.OA.A Represent and solve problems involving addition and subtraction. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.See Glossary, Table 1. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 1.OA.B Understand and apply properties of operations and the relationship between addition and subtraction. 1.OA.B.3 Apply properties of operations as strategies to add and subtract.Students need not use formal terms for these properties. Examples: If $8 + 3 = 11$ is known, then $3 + 8 = 11$ is also known. (Commutative property of addition.) To add $2 + 6 + 4$, the second two numbers can be added to make a ten, so $2 + 6 + 4 = 2 + 10 = 12$. (Associative property of addition.) Understand subtraction as an unknown-addend problem. For example, subtract $10 - 8$ by finding the number that makes 10 when added to 8. 1.OA.C Add and subtract within 20. 1.OA.C.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., $8 + 6 = 8 + 2 + 4 = 10 + 4 = 14$); decomposing a number leading to a ten (e.g., $13 - 4 = 13 - 3 - 1 = 10 - 1 = 9$); using the relationship between addition and subtraction (e.g., knowing that $8 + 4 = 12$, one knows $12 - 8 = 4$); and creating equivalent but easier or known sums (e.g., adding $6 + 7$ by creating the known equivalent $6 + 6 + 1 = 12 + 1 = 13$). 1.OA.D Work with addition and subtraction equations. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? $6 = 6$, $7 = 8 - 1$, $5 + 2 = 2 + 5$, $4 + 1 = 5 + 2$. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations $8 + ? = 11$, $5 = \boxvoid - 3$, $6 + 6 = \boxvoid$. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.Sizes are compared directly or visually, not compared by measuring. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. Measure and estimate lengths in standard units. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. Estimate lengths using units of inches, feet, centimeters, and meters. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Relate addition and subtraction to length. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram. Work with time and money. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using \$ and $¢$ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? 2.MD.D 2.MD.D.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problemsSee Glossary, Table 1. using information presented in a bar graph. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 2.NBT.A.1.a 100 can be thought of as a bundle of ten tens–-called a "hundred." 2.NBT.A.1.b The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). Count within 1000; skip-count by 5s, 10s, and 100s. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using $>$, =, and $<$ symbols to record the results of comparisons. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Add up to four two-digit numbers using strategies based on place value and properties of operations. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. Explain why addition and subtraction strategies work, using place value and the properties of operations.Explanations may be supported by drawings or objects. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.See Glossary, Table 1. Fluently add and subtract within 20 using mental strategies.See standard 1.OA.6 for a list of mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. Work with equal groups of objects to gain foundations for multiplication. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape. Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).Excludes compound units such as $\hbox{cm}^3$ and finding the geometric volume of a container. Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.Excludes multiplicative comparison problems (problems involving notions of "times as much"); see Glossary, Table 2. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units–-whole numbers, halves, or quarters. Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Recognize area as an attribute of plane figures and understand concepts of area measurement. 3.MD.C.5.a A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area. 3.MD.C.5.b A plane figure which can be covered without gaps or overlaps by $n$ unit squares is said to have an area of $n$ square units. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). Relate area to the operations of multiplication and addition. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. 3.MD.C.7.c Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths $a$ and $b + c$ is the sum of $a \times b$ and $a \times c$. Use area models to represent the distributive property in mathematical reasoning. 3.MD.C.7.d Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. Use place value understanding and properties of operations to perform multi-digit arithmetic. Use place value understanding to round whole numbers to the nearest 10 or 100. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., $9 \times 80$, $5 \times 60$) using strategies based on place value and properties of operations. 3.NF Grade 3 - Number and Operations---Fractions 3.NF.A Develop understanding of fractions as numbers. Understand a fraction $1/b$ as the quantity formed by 1 part when a whole is partitioned into $b$ equal parts; understand a fraction $a/b$ as the quantity formed by $a$ parts of size $1/b$. Understand a fraction as a number on the number line; represent fractions on a number line diagram. 3.NF.A.2.a Represent a fraction $1/b$ on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into $b$ equal parts. Recognize that each part has size $1/b$ and that the endpoint of the part based at 0 locates the number $1/b$ on the number line. 3.NF.A.2.b Represent a fraction $a/b$ on a number line diagram by marking off $a$ lengths $1/b$ from 0. Recognize that the resulting interval has size $a/b$ and that its endpoint locates the number $a/b$ on the number line. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize and generate simple equivalent fractions, e.g., $1/2 = 2/4$, $4/6 = 2/3$. Explain why the fractions are equivalent, e.g., by using a visual fraction model. 3.NF.A.3.c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express $3$ in the form $3 = 3/1$; recognize that $6/1 = 6$; locate $4/4$ and $1$ at the same point of a number line diagram. 3.NF.A.3.d Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols $>$, =, or $<$, and justify the conclusions, e.g., by using a visual fraction model. Represent and solve problems involving multiplication and division. Interpret products of whole numbers, e.g., interpret $5 \times 7$ as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as $5 \times 7$. Interpret whole-number quotients of whole numbers, e.g., interpret $56 \div 8$ as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as $56 \div 8$. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.See Glossary, Table 2. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations $8 \times ? = 48$, $5 = \boxvoid \div 3$, $6 \times 6 = ?$ Understand properties of multiplication and the relationship between multiplication and division. Apply properties of operations as strategies to multiply and divide.Students need not use formal terms for these properties. Examples: If $6 \times 4 = 24$ is known, then $4 \times 6 = 24$ is also known. (Commutative property of multiplication.) $3 \times 5 \times 2$ can be found by $3 \times 5 = 15$, then $15 \times 2 = 30$, or by $5 \times 2 = 10$, then $3 \times 10 = 30$. (Associative property of multiplication.) Knowing that $8 \times 5 = 40$ and $8 \times 2 = 16$, one can find $8 \times 7$ as $8 \times (5 + 2) = (8 \times 5) + (8 \times 2) = 40 + 16 = 56$. (Distributive property.) Understand division as an unknown-factor problem. For example, find $32 \div 8$ by finding the number that makes $32$ when multiplied by $8$. Multiply and divide within 100. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that $8 \times 5 = 40$, one knows $40 \div 5 = 8$) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. Solve problems involving the four operations, and identify and explain patterns in arithmetic. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations). Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs $(1, 12)$, $(2, 24)$, $(3, 36)$, … Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. Make a line plot to display a data set of measurements in fractions of a unit $(1/2, 1/4, 1/8)$. Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles. An angle that turns through $n$ one-degree angles is said to have an angle measure of $n$ degrees. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. Generalize place value understanding for multi-digit whole numbers. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that $700 \div 70 = 10$ by applying concepts of place value and division. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using $>$, =, and $<$ symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Extend understanding of fraction equivalence and ordering. Explain why a fraction $a/b$ is equivalent to a fraction $(n \times a)/(n \times b)$ by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols $>$, =, or $<$, and justify the conclusions, e.g., by using a visual fraction model. 4.NF.B Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 4.NF.B.3 Understand a fraction $a/b$ with $a > 1$ as a sum of fractions $1/b$. 4.NF.B.3.a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. 4.NF.B.3.b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: $\frac38 = \frac18 + \frac18 + \frac18$; $\frac38 = \frac18 + \frac28$; $2 \frac18 = 1 + 1 + \frac18 = \frac88 + \frac88 + \frac18.$ 4.NF.B.3.c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. 4.NF.B.3.d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction $a/b$ as a multiple of $1/b$. For example, use a visual fraction model to represent $5/4$ as the product $5 \times (1/4)$, recording the conclusion by the equation $5/4 = 5 \times (1/4).$ Understand a multiple of $a/b$ as a multiple of $1/b$, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express $3 \times (2/5)$ as $6 \times (1/5)$, recognizing this product as $6/5$. (In general, $n \times (a/b) = (n \times a)/b.$) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? 4.NF.C Understand decimal notation for fractions, and compare decimal fractions. 4.NF.C.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. For example, express $3/10$ as $30/100$, and add $3/10 + 4/100 = 34/100$. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite $0.62$ as $62/100$; describe a length as $0.62$ meters; locate $0.62$ on a number line diagram. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols $>$, =, or $<$, and justify the conclusions, e.g., by using a visual model. Interpret a multiplication equation as a comparison, e.g., interpret $35 = 5 \times 7$ as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.See Glossary, Table 2. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Gain familiarity with factors and multiples. Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. Generate and analyze patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g.,$x$-axis and $x$-coordinate, $y$-axis and $y$-coordinate). Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. 5.G.B 5.G.B.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy based on properties. Convert like measurement units within a given measurement system. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using $n$ unit cubes is said to have a volume of $n$ cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. Apply the formulas $V = l \times w \times h$ and $V = b \times h$ for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Understand the place value system. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., $347.392 = 3 \times 100 + 4 \times 10 + 7 \times 1 + 3 \times (1/10) + 9 \times (1/100) + 2 \times (1/1000)$. Compare two decimals to thousandths based on meanings of the digits in each place, using $>$, =, and $<$ symbols to record the results of comparisons. Use place value understanding to round decimals to any place. Perform operations with multi-digit whole numbers and with decimals to hundredths. Fluently multiply multi-digit whole numbers using the standard algorithm. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Use equivalent fractions as a strategy to add and subtract fractions. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, $2/3 + 5/4 = 8/12 + 15/12 = 23/12$. (In general, $a/b + c/d = (ad + bc)/bd$.) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result $2/5 + 1/2 = 3/7$, by observing that $3/7 < 1/2$. Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret a fraction as division of the numerator by the denominator $(a/b = a \div b)$. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret $3/4$ as the result of dividing $3$ by $4$, noting that $3/4$ multiplied by $4$ equals $3$, and that when $3$ wholes are shared equally among $4$ people each person has a share of size $3/4$. If $9$ people want to share a $50$-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product $(a/b) \times q$ as $a$ parts of a partition of $q$ into $b$ equal parts; equivalently, as the result of a sequence of operations $a \times q \div b$. For example, use a visual fraction model to show $(2/3) \times 4 = 8/3$, and create a story context for this equation. Do the same with $(2/3) \times (4/5) = 8/15$. (In general, $(a/b) \times (c/d) = ac/bd$.) Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence $a/b = (n \times a)/(n \times b)$ to the effect of multiplying $a/b$ by $1$. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for $(1/3) \div 4$, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that $(1/3) \div 4 = 1/12~$ because $(1/12) \times 4 = 1/3$. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for $4 \div (1/5)$, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that $4 \div (1/5) = 20~$ because $20 \times (1/5) = 4$. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Write and interpret numerical expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add $8$ and $7$, then multiply by $2$" as $2 \times (8 + 7)$. Recognize that $3 \times (18932 + 921)$ is three times as large as $18932 + 921$, without having to calculate the indicated sum or product. Analyze patterns and relationships. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. 6.EE Grade 6 - Expressions and Equations 6.EE.A 6.EE.A.1 Write and evaluate numerical expressions involving whole-number exponents. Write, read, and evaluate expressions in which letters stand for numbers. 6.EE.A.2.a Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "Subtract $y$ from 5" as $5 - y$. 6.EE.A.2.b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression $2 (8 + 7)$ as a product of two factors; view $(8 + 7)$ as both a single entity and a sum of two terms. 6.EE.A.2.c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas $V = s^3$ and $A = 6 s^2$ to find the volume and surface area of a cube with sides of length $s = 1/2$. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression $3 (2 + x)$ to produce the equivalent expression $6 + 3x$; apply the distributive property to the expression $24x + 18y$ to produce the equivalent expression $6 (4x + 3y)$; apply properties of operations to $y + y + y$ to produce the equivalent expression $3y$. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions $y + y + y$ and $3y$ are equivalent because they name the same number regardless of which number $y$ stands for. 6.EE.B 6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Solve real-world and mathematical problems by writing and solving equations of the form $x + p = q$ and $px = q$ for cases in which $p$, $q$ and $x$ are all nonnegative rational numbers. Write an inequality of the form $x > c$ or $x < c$ to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form $x > c$ or $x < c$ have infinitely many solutions; represent solutions of such inequalities on number line diagrams. 6.EE.C Represent and analyze quantitative relationships between dependent and independent variables. 6.EE.C.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation $d = 65t$ to represent the relationship between distance and time. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas $V = l w h$ and $V = b h$ to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. Grade 6 - The Number System 6.NS.A Apply and extend previous understandings of multiplication and division to divide fractions by fractions. 6.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for $(2/3) \div (3/4)$ and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that $(2/3) \div (3/4) = 8/9$ because $3/4$ of $8/9$ is $2/3$. (In general, $(a/b) \div (c/d) = ad/bc$.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? 6.NS.B Compute fluently with multi-digit numbers and find common factors and multiples. 6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express $36 + 8$ as $4 (9 + 2)$. 6.NS.C Apply and extend previous understandings of numbers to the system of rational numbers. 6.NS.C.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 6.NS.C.6.a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., $-(-3) = 3$, and that 0 is its own opposite. 6.NS.C.6.b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. 6.NS.C.6.c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Understand ordering and absolute value of rational numbers. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret $-3 > -7$ as a statement that $-3$ is located to the right of $-7$ on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write $-3^\circ C > -7^\circ C$ to express the fact that $-3^\circ C$ is warmer than $-7^\circ C$. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of $-30$ dollars, write $\|-30\| = 30$ to describe the size of the debt in dollars. 6.NS.C.7.d Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than $-30$ dollars represents a debt greater than 30 dollars. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 6.RP Grade 6 - Ratios and Proportional Relationships 6.RP.A Understand ratio concepts and use ratio reasoning to solve problems. 6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was $2:1$, because for every $2$ wings there was $1$ beak." "For every vote candidate A received, candidate C received nearly three votes." Understand the concept of a unit rate $a/b$ associated with a ratio $a:b$ with $b \neq 0$, and use rate language in the context of a ratio relationship. \$Expectations for unit rates in this grade are limited to non-complex fractions. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 6.RP.A.3.a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. 6.RP.A.3.b Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? 6.RP.A.3.c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. 6.RP.A.3.d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. 6.SP Grade 6 - Statistics and Probability 6.SP.A 6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 6.SP.B 6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. Summarize numerical data sets in relation to their context, such as by: 6.SP.B.5.a Reporting the number of observations. 6.SP.B.5.b Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. 6.SP.B.5.c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. 6.SP.B.5.d Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Use properties of operations to generate equivalent expressions. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, $a + 0.05a = 1.05a$ means that "increase by $5\%$" is the same as "multiply by $1.05$." Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. 7.EE.B.4.a Solve word problems leading to equations of the form $px + q = r$ and $p(x + q) = r$, where $p$, $q$, and $r$ are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is $54$ cm. Its length is $6$ cm. What is its width? 7.EE.B.4.b Solve word problems leading to inequalities of the form $px + q > r$ or $px + q < r$, where $p$, $q$, and $r$ are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. \$ Draw, construct, and describe geometrical figures and describe the relationships between them. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. 7.NS.A.1.a Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. 7.NS.A.1.b Understand $p + q$ as the number located a distance $\|q\|$ from $p$, in the positive or negative direction depending on whether $q$ is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. 7.NS.A.1.c Understand subtraction of rational numbers as adding the additive inverse, $p - q = p + (-q)$. Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. 7.NS.A.1.d Apply properties of operations as strategies to add and subtract rational numbers. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as $(-1)(-1) = 1$ and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If $p$ and $q$ are integers, then $-(p/q) = (-p)/q = p/(-q)$. Interpret quotients of rational numbers by describing real-world contexts. Apply properties of operations as strategies to multiply and divide rational numbers. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Solve real-world and mathematical problems involving the four operations with rational numbers.Computations with rational numbers extend the rules for manipulating fractions to complex fractions. Analyze proportional relationships and use them to solve real-world and mathematical problems. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks $1/2$ mile in each $1/4$ hour, compute the unit rate as the complex fraction $\frac{1/2}{1/4}$ miles per hour, equivalently $2$ miles per hour. Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by equations. For example, if total cost $t$ is proportional to the number $n$ of items purchased at a constant price $p$, the relationship between the total cost and the number of items can be expressed as $t = pn$. Explain what a point $(x, y)$ on the graph of a proportional relationship means in terms of the situation, with special attention to the points $(0, 0)$ and $(1, r)$ where $r$ is the unit rate. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Use random sampling to draw inferences about a population. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Draw informal comparative inferences about two populations. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. 7.SP.C 7.SP.C.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. 7.SP.C.7.a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event. 7.SP.C.8.c Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? Work with radicals and integer exponents. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, $3^2\times3^{-5} = 3^{-3} = 1/3^3 = 1/27$. Use square root and cube root symbols to represent solutions to equations of the form $x^2 = p$ and $x^3 = p$, where $p$ is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that $\sqrt{2}$ is irrational. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as $3 \times 10^8$ and the population of the world as $7 \times 10^9$, and determine that the world population is more than $20$ times larger. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Understand the connections between proportional relationships, lines, and linear equations. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Use similar triangles to explain why the slope $m$ is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation $y = mx$ for a line through the origin and the equation $y = mx + b$ for a line intercepting the vertical axis at $b$. Analyze and solve linear equations and pairs of simultaneous linear equations. Solve linear equations in one variable. 8.EE.C.7.a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form $x = a$, $a = a$, or $a = b$ results (where $a$ and $b$ are different numbers). 8.EE.C.7.b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Analyze and solve pairs of simultaneous linear equations. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, $3x + 2y = 5$ and $3x + 2y = 6$ have no solution because $3x + 2y$ cannot simultaneously be $5$ and $6$. 8.EE.C.8.c Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. 8.F Grade 8 - Functions 8.F.A Define, evaluate, and compare functions. 8.F.A.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Function notation is not required in Grade 8. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. Interpret the equation $y = mx + b$ as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function $A = s^2$ giving the area of a square as a function of its side length is not linear because its graph contains the points $(1,1)$, $(2,4)$ and $(3,9)$, which are not on a straight line. 8.F.B Use functions to model relationships between quantities. 8.F.B.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two $(x, y)$ values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Understand congruence and similarity using physical models, transparencies, or geometry software. Verify experimentally the properties of rotations, reflections, and translations: 8.G.A.1.a Lines are taken to lines, and line segments to line segments of the same length. 8.G.A.1.b Angles are taken to angles of the same measure. 8.G.A.1.c Parallel lines are taken to parallel lines. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. Understand and apply the Pythagorean Theorem. Explain a proof of the Pythagorean Theorem and its converse. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 8.G.C Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. 8.G.C.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Know that there are numbers that are not rational, and approximate them by rational numbers. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., $\pi^2$). For example, by truncating the decimal expansion of $\sqrt{2}$, show that $\sqrt{2}$ is between $1$ and $2$, then between $1.4$ and $1.5$, and explain how to continue on to get better approximations. Investigate patterns of association in bivariate data. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? Counting and Cardinality HSA-APR Algebra - Arithmetic with Polynomials and Rational Expressions HSA-APR.A Perform arithmetic operations on polynomials. HSA-APR.A.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. HSA-APR.B Understand the relationship between zeros and factors of polynomials. HSA-APR.B.2 Know and apply the Remainder Theorem: For a polynomial $p(x)$ and a number $a$, the remainder on division by $x - a$ is $p(a)$, so $p(a) = 0$ if and only if $(x - a)$ is a factor of $p(x)$. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. HSA-APR.C Use polynomial identities to solve problems. HSA-APR.C.4 Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity $(x^2 + y^2)^2 = (x^2 - y^2)^2 + (2xy)^2$ can be used to generate Pythagorean triples. Know and apply the Binomial Theorem for the expansion of $(x + y)^n$ in powers of $x$ and $y$ for a positive integer $n$, where $x$ and $y$ are any numbers, with coefficients determined for example by Pascal's Triangle.The Binomial Theorem can be proved by mathematical induction or by a com- binatorial argument. HSA-APR.D Rewrite rational expressions. HSA-APR.D.6 Rewrite simple rational expressions in different forms; write $\frac{a(x)}{b(x)}$ in the form $q(x) + \frac{r(x)}{b(x)}$, where $a(x)$, $b(x)$, $q(x)$, and $r(x)$ are polynomials with the degree of $r(x)$ less than the degree of $b(x)$, using inspection, long division, or, for the more complicated examples, a computer algebra system. Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. HSA-CED Algebra - Creating Equations HSA-CED.A Create equations that describe numbers or relationships. HSA-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law $V = IR$ to highlight resistance $R$. HSA-REI Algebra - Reasoning with Equations and Inequalities HSA-REI.A Understand solving equations as a process of reasoning and explain the reasoning. HSA-REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. HSA-REI.B Solve equations and inequalities in one variable. HSA-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Solve quadratic equations in one variable. HSA-REI.B.4.a Use the method of completing the square to transform any quadratic equation in $x$ into an equation of the form $(x - p)^2 = q$ that has the same solutions. Derive the quadratic formula from this form. HSA-REI.B.4.b Solve quadratic equations by inspection (e.g., for $x^2 = 49$), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as $a \pm bi$ for real numbers $a$ and $b$. HSA-REI.C Solve systems of equations. HSA-REI.C.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line $y = -3x$ and the circle $x^2 + y^2 = 3$. Represent a system of linear equations as a single matrix equation in a vector variable. Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension $3 \times 3$ or greater). HSA-REI.D Represent and solve equations and inequalities graphically. HSA-REI.D.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Explain why the $x$-coordinates of the points where the graphs of the equations $y = f(x)$ and $y = g(x)$ intersect are the solutions of the equation $f(x) = g(x)$; find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where $f(x)$ and/or $g(x)$ are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. HSA-SSE Algebra - Seeing Structure in Expressions HSA-SSE.A Interpret the structure of expressions. HSA-SSE.A.1 Interpret expressions that represent a quantity in terms of its context. HSA-SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients. HSA-SSE.A.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret $P(1+r)^n$ as the product of $P$ and a factor not depending on $P$. Use the structure of an expression to identify ways to rewrite it. For example, see $x^4 - y^4$ as $(x^2)^2 - (y^2)^2$, thus recognizing it as a difference of squares that can be factored as $(x^2 - y^2)(x^2 + y^2)$. HSA-SSE.B Write expressions in equivalent forms to solve problems. HSA-SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. HSA-SSE.B.3.a Factor a quadratic expression to reveal the zeros of the function it defines. HSA-SSE.B.3.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. HSA-SSE.B.3.c Use the properties of exponents to transform expressions for exponential functions. For example the expression $1.15^t$ can be rewritten as $(1.15^{1/12})^{12t} \approx 1.012^{12t}$ to reveal the approximate equivalent monthly interest rate if the annual rate is $15\%$. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments. HSF-BF Functions - Building Functions HSF-BF.A Build a function that models a relationship between two quantities. HSF-BF.A.1 Write a function that describes a relationship between two quantities. HSF-BF.A.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context. HSF-BF.A.1.b Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. HSF-BF.A.1.c Compose functions. For example, if $T(y)$ is the temperature in the atmosphere as a function of height, and $h(t)$ is the height of a weather balloon as a function of time, then $T(h(t))$ is the temperature at the location of the weather balloon as a function of time. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. HSF-BF.B Build new functions from existing functions. HSF-BF.B.3 Identify the effect on the graph of replacing $f(x)$ by $f(x) + k$, $k f(x)$, $f(kx)$, and $f(x + k)$ for specific values of $k$ (both positive and negative); find the value of $k$ given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Find inverse functions. HSF-BF.B.4.a Solve an equation of the form $f(x) = c$ for a simple function $f$ that has an inverse and write an expression for the inverse. For example, $f(x) =2 x^3$ or $f(x) = (x+1)/(x-1)$ for $x \neq 1$. HSF-BF.B.4.b Verify by composition that one function is the inverse of another. HSF-BF.B.4.c Read values of an inverse function from a graph or a table, given that the function has an inverse. HSF-BF.B.4.d Produce an invertible function from a non-invertible function by restricting the domain. Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. HSF-IF Functions - Interpreting Functions HSF-IF.A Understand the concept of a function and use function notation. HSF-IF.A.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If $f$ is a function and $x$ is an element of its domain, then $f(x)$ denotes the output of $f$ corresponding to the input $x$. The graph of $f$ is the graph of the equation $y = f(x)$. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by $f(0) = f(1) = 1$, $f(n+1) = f(n) + f(n-1)$ for $n \ge 1$. HSF-IF.B Interpret functions that arise in applications in terms of the context. HSF-IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function $h(n)$ gives the number of person-hours it takes to assemble $n$ engines in a factory, then the positive integers would be an appropriate domain for the function. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. HSF-IF.C Analyze functions using different representations. HSF-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. HSF-IF.C.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima. HSF-IF.C.7.b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. HSF-IF.C.7.c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. HSF-IF.C.7.d Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. HSF-IF.C.7.e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as $y = (1.02)^t$, $y = (0.97)^t$, $y = (1.01)^{12t}$, $y = (1.2)^{t/10}$, and classify them as representing exponential growth or decay. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. HSF-LE Functions - Linear, Quadratic, and Exponential Models HSF-LE.A Construct and compare linear, quadratic, and exponential models and solve problems. HSF-LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. HSF-LE.A.1.a Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. HSF-LE.A.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. HSF-LE.A.1.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. For exponential models, express as a logarithm the solution to $ab^{ct} = d$ where $a$, $c$, and $d$ are numbers and the base $b$ is 2, 10, or $e$; evaluate the logarithm using technology. HSF-LE.B Interpret expressions for functions in terms of the situation they model. HSF-LE.B.5 Interpret the parameters in a linear or exponential function in terms of a context. HSF-TF Functions - Trigonometric Functions HSF-TF.A Extend the domain of trigonometric functions using the unit circle. HSF-TF.A.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. Use special triangles to determine geometrically the values of sine, cosine, tangent for $\pi/3$, $\pi/4$ and $\pi/6$, and use the unit circle to express the values of sine, cosines, and tangent for $\pi - x$, $\pi + x$, and $2\pi - x$ in terms of their values for $x$, where $x$ is any real number. Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. HSF-TF.B Model periodic phenomena with trigonometric functions. HSF-TF.B.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. HSF-TF.C Prove and apply trigonometric identities. HSF-TF.C.8 Prove the Pythagorean identity $\sin^2(\theta) + \cos^2(\theta) = 1$ and use it to find $\sin(\theta)$, $\cos(\theta)$, or $\tan(\theta)$ given $\sin(\theta)$, $\cos(\theta)$, or $\tan(\theta)$ and the quadrant of the angle. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. HSG-C Geometry - Circles HSG-C.A Understand and apply theorems about circles HSG-C.A.1 Prove that all circles are similar. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Construct a tangent line from a point outside a given circle to the circle. HSG-C.B Find arc lengths and areas of sectors of circles HSG-C.B.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. HSG-CO Geometry - Congruence HSG-CO.A Experiment with transformations in the plane HSG-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. HSG-CO.B Understand congruence in terms of rigid motions HSG-CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. HSG-CO.C Prove geometric theorems HSG-CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to $180^\circ$; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. HSG-CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. HSG-CO.D Make geometric constructions HSG-CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. HSG-GMD Geometry - Geometric Measure and Dimension HSG-GMD.A Explain volume formulas and use them to solve problems HSG-GMD.A.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. HSG-GMD.B Visualize relationships between two-dimensional and three-dimensional objects HSG-GMD.B.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. HSG-GPE Geometry - Expressing Geometric Properties with Equations HSG-GPE.A Translate between the geometric description and the equation for a conic section HSG-GPE.A.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. Derive the equation of a parabola given a focus and directrix. Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. HSG-GPE.B Use coordinates to prove simple geometric theorems algebraically HSG-GPE.B.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point $(1, \sqrt{3})$ lies on the circle centered at the origin and containing the point $(0, 2)$. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Find the point on a directed line segment between two given points that partitions the segment in a given ratio. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. HSG-MG Geometry - Modeling with Geometry HSG-MG.A Apply geometric concepts in modeling situations HSG-MG.A.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). HSG-SRT Geometry - Similarity, Right Triangles, and Trigonometry HSG-SRT.A Understand similarity in terms of similarity transformations HSG-SRT.A.1 Verify experimentally the properties of dilations given by a center and a scale factor: HSG-SRT.A.1.a A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. HSG-SRT.A.1.b The dilation of a line segment is longer or shorter in the ratio given by the scale factor. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. HSG-SRT.B Prove theorems involving similarity HSG-SRT.B.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. HSG-SRT.C Define trigonometric ratios and solve problems involving right triangles HSG-SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. Explain and use the relationship between the sine and cosine of complementary angles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. HSG-SRT.D Apply trigonometry to general triangles HSG-SRT.D.10 Prove the Laws of Sines and Cosines and use them to solve problems. Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). HSG-SRT.D.9 Derive the formula $A = 1/2 ab \sin(C)$ for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. Number and Quantity HSN-CN Number and Quantity - Complex Numbers HSN-CN.A Perform arithmetic operations with complex numbers. HSN-CN.A.1 Know there is a complex number $i$ such that $i^2 = -1$, and every complex number has the form $a + bi$ with $a$ and $b$ real. Use the relation $i^2 = -1$ and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. HSN-CN.B Represent complex numbers and their operations on the complex plane. HSN-CN.B.4 Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, $(-1 + \sqrt{3} i)^3 = 8$ because $(-1 + \sqrt3 i)$ has modulus $2$ and argument $120^\circ$. Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. HSN-CN.C Use complex numbers in polynomial identities and equations. HSN-CN.C.7 Solve quadratic equations with real coefficients that have complex solutions. Extend polynomial identities to the complex numbers. For example, rewrite $x^2 + 4$ as $(x + 2i)(x - 2i)$. Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. HSN-Q Number and Quantity - Quantities HSN-Q.A Reason quantitatively and use units to solve problems. HSN-Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. Define appropriate quantities for the purpose of descriptive modeling. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. HSN-RN Number and Quantity - The Real Number System HSN-RN.A Extend the properties of exponents to rational exponents. HSN-RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define $5^{1/3}$ to be the cube root of $5$ because we want $(5^{1/3})^3 = 5^{(1/3)3}$ to hold, so $(5^{1/3})^3$ must equal $5$. Rewrite expressions involving radicals and rational exponents using the properties of exponents. HSN-RN.B Use properties of rational and irrational numbers. HSN-RN.B.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. HSN-VM Number and Quantity - Vector and Matrix Quantities HSN-VM.A Represent and model with vector quantities. HSN-VM.A.1 Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., $\textbf{v}$, $\|\textbf{v}\|$, $\|\|\textbf{v}\|\|$, $v$). Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. Solve problems involving velocity and other quantities that can be represented by vectors. HSN-VM.B Perform operations on vectors. HSN-VM.B.4 Add and subtract vectors. HSN-VM.B.4.a Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. HSN-VM.B.4.b Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. HSN-VM.B.4.c Understand vector subtraction $\textbf{v} - \textbf{w}$ as $\textbf{v} + (-\textbf{w})$, where $-\textbf{w}$ is the additive inverse of $\textbf{w}$, with the same magnitude as $\textbf{w}$ and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise. Multiply a vector by a scalar. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as $c(v_x, v_y) = (cv_x, cv_y)$. Compute the magnitude of a scalar multiple $c\textbf{v}$ using $\|\|c\textbf{v}\|\| = \|c\|v$. Compute the direction of $c\textbf{v}$ knowing that when $\|c\|{v} \neq 0$, the direction of $c\textbf{v}$ is either along $\textbf{v}$ (for $c > 0$) or against $\textbf{v}$ (for $c < 0$). HSN-VM.C Perform operations on matrices and use matrices in applications. HSN-VM.C.10 Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. Work with $2 \times2$ matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area. HSN-VM.C.6 Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. Add, subtract, and multiply matrices of appropriate dimensions. Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. HSS-CP Statistics and Probability - Conditional Probability and the Rules of Probability HSS-CP.A Understand independence and conditional probability and use them to interpret data HSS-CP.A.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not"). Understand that two events $A$ and $B$ are independent if the probability of $A$ and $B$ occurring together is the product of their probabilities, and use this characterization to determine if they are independent. Understand the conditional probability of $A$ given $B$ as \$, and interpret independence of $A$ and $B$ as saying that the conditional probability of $A$ given $B$ is the same as the probability of $A$, and the conditional probability of $B$ given $A$ is the same as the probability of $B$. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. HSS-CP.B Use the rules of probability to compute probabilities of compound events in a uniform probability model HSS-CP.B.6 Find the conditional probability of $A$ given $B$ as the fraction of $B$'s outcomes that also belong to $A$, and interpret the answer in terms of the model. Apply the Addition Rule, \$, and interpret the answer in terms of the model. Apply the general Multiplication Rule in a uniform probability model, \$, and interpret the answer in terms of the model. Use permutations and combinations to compute probabilities of compound events and solve problems. HSS-IC Statistics and Probability - Making Inferences and Justifying Conclusions HSS-IC.A Understand and evaluate random processes underlying statistical experiments HSS-IC.A.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population. Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability $0.5$. Would a result of $5$ tails in a row cause you to question the model? HSS-IC.B Make inferences and justify conclusions from sample surveys, experiments, and observational studies HSS-IC.B.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. Evaluate reports based on data. HSS-ID Statistics and Probability - Interpreting Categorical and Quantitative Data HSS-ID.A Summarize, represent, and interpret data on a single count or measurement variable HSS-ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. HSS-ID.B Summarize, represent, and interpret data on two categorical and quantitative variables HSS-ID.B.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. HSS-ID.B.6.a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. HSS-ID.B.6.b Informally assess the fit of a function by plotting and analyzing residuals. HSS-ID.B.6.c Fit a linear function for a scatter plot that suggests a linear association. HSS-ID.C Interpret linear models HSS-ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Compute (using technology) and interpret the correlation coefficient of a linear fit. Distinguish between correlation and causation. HSS-MD Statistics and Probability - Using Probability to Make Decisions HSS-MD.A Calculate expected values and use them to solve problems HSS-MD.A.1 Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes. Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households? HSS-MD.B Use probability to evaluate outcomes of decisions HSS-MD.B.5 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. HSS-MD.B.5.a Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant. HSS-MD.B.5.b Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident. Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). K.CC Kindergarten - Counting and Cardinality K.CC.A Know number names and the count sequence. K.CC.A.1 Count to 100 by ones and by tens. Count forward beginning from a given number within the known sequence (instead of having to begin at 1). Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20 (with 0 representing a count of no objects). K.CC.B Count to tell the number of objects. K.CC.B.4 Understand the relationship between numbers and quantities; connect counting to cardinality. K.CC.B.4.a When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. K.CC.B.4.b Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. K.CC.B.4.c Understand that each successive number name refers to a quantity that is one larger. Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects. K.CC.C Compare numbers. K.CC.C.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.Include groups with up to ten objects Compare two numbers between 1 and 10 presented as written numerals. K.G Kindergarten - Geometry K.G.A Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). K.G.A.1 Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. Correctly name shapes regardless of their orientations or overall size. Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid"). K.G.B Analyze, compare, create, and compose shapes. K.G.B.4 Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/"corners") and other attributes (e.g., having sides of equal length). Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. Compose simple shapes to form larger shapes. For example, "Can you join these two triangles with full sides touching to make a rectangle?" K.MD Kindergarten - Measurement and Data K.MD.A Describe and compare measurable attributes. K.MD.A.1 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. K.MD.B Classify objects and count the number of objects in each category. K.MD.B.3 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.Limit category counts to be less than or equal to 10. K.NBT Kindergarten - Number and Operations in Base Ten K.NBT.A Work with numbers 11--19 to gain foundations for place value. K.NBT.A.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. K.OA Kindergarten - Operations and Algebraic Thinking K.OA.A Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. K.OA.A.1 Represent addition and subtraction with objects, fingers, mental images, drawingsDrawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., $5 = 2 + 3$ and $5 = 4 + 1$). For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. Fluently add and subtract within 5. NBT Number and Operations in Base Ten Number and Operations---Fractions The Number System Ratios and Proportional Relationships	CommonCrawl
Printed from https://ideas.repec.org/a/kap/theord/v79y2015i4p639-666.html An experiment on case-based decision making Brit Grosskopf Rajiv Sarin Elizabeth Watson We experimentally investigate the disposition of decision makers to use case-based reasoning as suggested by Hume (An enquiry concerning human understanding, 1748 ) and formalized by case-based decision theory (Gilboa and Schmeidler in Q J Econ 110:605–639, 1995 ). Our subjects face a monopoly decision problem about which they have very limited information. Information is presented in a manner which makes similarity judgements according to the feature matching model of Tversky (Psychol Rev 84:327–352, 1977 ) plausible. We provide subjects a "history" of cases. In the $$2\times 2$$ 2 × 2 between-subject design, we vary whether information about the current market is given and whether immediate feedback about obtained profits is provided. The results provide support for the predictions of case-based decision theory, particularly when no immediate feedback is provided. Copyright Springer Science+Business Media New York 2015 Brit Grosskopf & Rajiv Sarin & Elizabeth Watson, 2015. "An experiment on case-based decision making," Theory and Decision, Springer, vol. 79(4), pages 639-666, December. Handle: RePEc:kap:theord:v:79:y:2015:i:4:p:639-666 Itzhak Gilboa & David Schmeidler, 1995. "Case-Based Decision Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 110(3), pages 605-639. Itzhak Gilboa & David Schmeidler, 1992. "Case-Based Decision Theory," Discussion Papers 994, Northwestern University, Center for Mathematical Studies in Economics and Management Science. Itzhak Gilboa & David Schmeidler, 1995. "Case-Based Decision Theory," Post-Print hal-00753144, HAL. Gayer Gabrielle & Gilboa Itzhak & Lieberman Offer, 2007. "Rule-Based and Case-Based Reasoning in Housing Prices," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-37, April. Gabrielle Gayer & Itzhak Gilboa & Offer Lieberman, 2004. "Rule-Based and Case-Based Reasoning in Housing Prices," Cowles Foundation Discussion Papers 1493, Cowles Foundation for Research in Economics, Yale University. Itzhak Gilboa & Gabrielle Gayer & O. Lieberman, 2007. "Rule-Based and Case-Based Reasoning in Housing Prices," Post-Print hal-00481229, HAL. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212. Wolfgang Ossadnik & Dirk Wilmsmann & Benedikt Niemann, 2013. "Experimental evidence on case-based decision theory," Theory and Decision, Springer, vol. 75(2), pages 211-232, August. Rajiv Sarin & Farshid Vahid, 2004. "Strategy Similarity and Coordination," Economic Journal, Royal Economic Society, vol. 114(497), pages 506-527, July. Vahid, F. & Sarin, R., 2001. "Strategy Similarity and Coordination," Monash Econometrics and Business Statistics Working Papers 8/01, Monash University, Department of Econometrics and Business Statistics. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2006. "Empirical Similarity," The Review of Economics and Statistics, MIT Press, vol. 88(3), pages 433-444, August. Itzhak Gilboa & Offer Lieberman & David Schmeidler, 2004. "Empirical Similarity," Cowles Foundation Discussion Papers 1486, Cowles Foundation for Research in Economics, Yale University. Itzhak Gilboa & David Schmeidler & Offer Lieberman, 2006. "Empirical Similarity," Post-Print hal-00746558, HAL. Matsui, Akihiko, 2000. "Expected utility and case-based reasoning," Mathematical Social Sciences, Elsevier, vol. 39(1), pages 1-12, January. Itzhak Gilboa & David Schmeidler, 1996. "Act similarity in case-based decision theory (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 47-62. Itzhak Gilboa & David Schmeidler, 1994. "Act-Similarity in Case-Based Decision Theory," Discussion Papers 1081, Northwestern University, Center for Mathematical Studies in Economics and Management Science. Itzhak Gilboa & David Schmeidler, 1997. "Act Similarity in Case-Based Decision Theory," Post-Print hal-00753126, HAL. Herbert A. Simon, 1955. "A Behavioral Model of Rational Choice," The Quarterly Journal of Economics, Oxford University Press, vol. 69(1), pages 99-118. repec:kap:expeco:v:1:y:1998:i:1:p:43-62 is not listed on IDEAS Rubinstein, Ariel, 1988. "Similarity and decision-making under risk (is there a utility theory resolution to the Allais paradox?)," Journal of Economic Theory, Elsevier, vol. 46(1), pages 145-153, October. Reinhard Selten, 1998. "Axiomatic Characterization of the Quadratic Scoring Rule," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 43-61, June. Sarin, Rajiv & Vahid, Farshid, 1999. "Payoff Assessments without Probabilities: A Simple Dynamic Model of Choice," Games and Economic Behavior, Elsevier, vol. 28(2), pages 294-309, August. Mengel, Friederike & Sciubba, Emanuela, 2010. "Extrapolation in Games of Coordination and Dominance Solvable Games," Sustainable Development Papers 98475, Fondazione Eni Enrico Mattei (FEEM). Mengel Friederike & Sciubba Emanuela, 2010. "Extrapolation in Games of Coordination and Dominance Solvable Games," Research Memorandum 034, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR). Friederike Mengel & Emanuela Sciubba, 2010. "Extrapolation in Games of Coordination and Dominance Solvable Games," Working Papers 2010.148, Fondazione Eni Enrico Mattei. Roxane Bricet, 2018. "Precise versus imprecise datasets: revisiting ambiguity attitudes in the Ellsberg paradox," THEMA Working Papers 2018-08, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise. repec:kap:jrisku:v:59:y:2019:i:1:d:10.1007_s11166-019-09309-1 is not listed on IDEAS Han Bleichrodt & Martin Filko & Amit Kothiyal & Peter P. Wakker, 2017. "Making Case-Based Decision Theory Directly Observable," American Economic Journal: Microeconomics, American Economic Association, vol. 9(1), pages 123-151, February. Benjamin Radoc & Robert Sugden & Theodore L. Turocy, 2019. "Correlation neglect and case-based decisions," Journal of Risk and Uncertainty, Springer, vol. 59(1), pages 23-49, August. Benjamin Radoc & Robert Sugden & Theodore L. Turocy, 2017. "Correlation neglect and case-based decisions," Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) 17-11, School of Economics, University of East Anglia, Norwich, UK.. Case-based decision making; Case-based reasoning ; Heuristics; Limited information environments; Similarity; All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:theord:v:79:y:2015:i:4:p:639-666. See general information about how to correct material in RePEc.	CommonCrawl
Category Archives: Quantum Computing Quantum Gates: Single Qubit Gates A classical computer is built from electrical circuits that consist of logic gates and wires. The logic gates perform intended logical operations of information and wires pass information between logic gates. Similarly, a quantum computer would be built from quantum circuits that consist of quantum gates and wires. However, when it comes down to comparing how operations are performed at elementary gates level, there is no similarity between classical logic gates and quantum gates. Unlike classical logic gates, quantum gates operate not according to logical rules but to physical (quantum mechanical) laws. A single qubit gate acts on not only on qubits $\|0\rangle=\begin{bmatrix}1\\0\end{bmatrix}$ and $\|1\rangle=\begin{bmatrix}0\\1\end{bmatrix}$ but also on a superposition of $\|0\rangle$ and $\|1\rangle$, $\alpha\|0\rangle+\beta\|1\rangle$, where $\alpha$ and $\beta$ are complex numbers. For an obvious reason, single qubit gates are $2\times 2$ matrices. Furthermore, a quantum gate operation is performed through a unitary time evolution, and this means that they are required to be unitary matrices. Recall that a matrix $U$ of complex entries is unitary if $UU^\dagger=I$ where $\dagger$ denotes transpose conjugate i.e. $U^\dagger = \bar U^t$. If we write $U=\begin{bmatrix}a & b\\c & d\end{bmatrix}$, then $U$ is unitary if and only if $\|a\|^2+\|b\|^2=\|c\|^2+\|d\|^2=1$ and $a\bar c+b\bar d=0$. Any unitary matrix is qualified to be a quantum gate but not all unitary matrices would be interesting or useful gates. For practical purposes, it is important to see which gates are universal if there are any and that which gates are physically implementable. The following are some examples of well-known single cubit gates. Pauli-X, Pauli-Y, Pauli-Z gates. A matrix $H$ is Hermitian if $H=H^\dagger$. Hermitian matrices play a crucial role in quantum mechanics as Hamiltonians are required to be Hermitian. The eigenvalues of a Hamiltonian are the energies of the corresponding quantum system and of course they all have to be real. Hermitian matrices are guaranteed to have all real eigenvalues. A $2\times 2$ Hermitian matrix can be written in the form $H=\begin{bmatrix}x_0+x_3 & x_1-ix_2\\x_1+ix_2 & x_0-x_3\end{bmatrix}$ where the $x_i$ are all reals. The matrices \begin{equation}\label{eq:pauli}\sigma_0=\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix},\ \sigma_1=\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix},\ \sigma_2=\begin{bmatrix}0 & -i\\i & 0\end{bmatrix},\ \sigma_3=\begin{bmatrix}1 & 0\\0 & -1\end{bmatrix}\end{equation} form a basis for the space of all Hermitian matrices. The $\sigma_i$ in \eqref{eq:pauli} are called the Pauli spin matrices in physics. $\sigma_0$ is just the identity matrix but notice that $\sigma_1,\sigma_2,\sigma_3$ are also unitary matrices. They are called Pauli-X, Pauli-Y, Pauli-Z gates, respectively. Pauli-X gate is also called NOT gate as it acts like the classical NOT gate. \begin{align}\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\begin{bmatrix}1\\0\end{bmatrix}&=\begin{bmatrix}0\\1\end{bmatrix}\\\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}\begin{bmatrix}0\\1\end{bmatrix}&=\begin{bmatrix}0\\1\end{bmatrix}\end{align} Square root of NOT gate. The gate $$\sqrt{\mathrm{NOT}}=\frac{1}{2}\begin{bmatrix}1+i & 1-i\\1-i & 1+i\end{bmatrix}$$ is called square root of NOT gate because $$\sqrt{\mathrm{NOT}}\cdot\sqrt{\mathrm{NOT}}=\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}$$ $\sqrt{\mathrm{NOT}}$ is one of the gates that are truly quantum because there is no classical counterpart. Hadamard gate. $$H=\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1\\1 & -1\end{bmatrix}$$ is called the Hadamard gate. It turns $\|0\rangle$ to $\frac{\|0\rangle+\|1\rangle}{\sqrt{2}}$ and $\|1\rangle$ to $\frac{\|0\rangle-\|1\rangle}{\sqrt{2}}$. Michael A. Nielsen and Isaac L. Chung, Quantum Computation and Quantum Information, Cambridge University Press, 2000. Colin P. Williams and Scott H. Clearwater, Explorations in Quantum Computing, Spinger Telos, 1998. This entry was posted in Quantum Computing on November 7, 2020 by Sung Lee. The Tensor Product Let $V$ and $W$ be two vector spaces of dimensions $m$ and $n$, respectively. The tensor product of $V$ and $W$ is a space $V\otimes W$ of dimension $mn$ together with a bilinear map $$\varphi: V\times W\longrightarrow V\otimes W;\ \varphi(v,w)=v\otimes w$$ which satisfy the following universal property: For any vector space $X$ and any bilinear map $\psi: V\times W\longrightarrow X$, there exists uniquely a linear map $\gamma : V\otimes W\longrightarrow X$ such that $\psi(v,w)=\gamma(u\otimes w)$ for all $v\in V$ and $w\in W$. $$\begin{array}[c]{ccc}V\otimes W & & \\\uparrow\scriptstyle{\varphi} & \scriptstyle{\gamma}\searrow& \\V\times W & \stackrel{\psi}\rightarrow & X\end{array}\ \ \ \gamma\circ\varphi=\psi$$ Often, we use more down to earth definition of the tensor product. Let $\{e_1,\cdots,e_m\}$ and $\{f_1,\cdots,f_n\}$ be bases of $V$ and $W$, respectively. The tensor product $V\otimes W$ is a vector space of dimension $mn$ spanned by the basis $\{e_i\otimes f_j: i=1,\cdots,m,\ j=1,\cdots,n\}$. Let $v\in V$ and $w\in W$. Then $$v=\sum_i v_ie_i\ \mbox{and}\ w=\sum_j w_jf_j$$ The tensor product $v$ and $w$ is then given by $$v\otimes w=\sum_{i,j}v_iw_je_i\otimes f_j$$ It can be easily shown that this definition of the tensor product in terms of prescribed bases satisfies the universality property. Although this definition uses a choice of bases of $V$ and $W$, the tensor product $V\otimes W$ must not depend on a particular choice of bases, i.e. regardless of the choice of bases the resulting tensor product must be the same. This also can be shown easily using some basic properties from linear algebra. I will leave them for exercise for readers. The tensor product can be used to describe the state of a quantum memory register. A quantum memory register consists of many 2-state systems (Hilbert spaces of qubits). Let $\|\psi^{(1)}\rangle$ and $\|\psi^{(2)}\rangle$ be qubits associated with two different 2-state systems. In terms of the standard orthogonal basis $\begin{pmatrix}1\\0\end{pmatrix}$ and $\begin{pmatrix}0\\1\end{pmatrix}$ for each 2-state system, we have \begin{align}\|\psi^{(1)}\rangle&=\begin{pmatrix}\omega_0^{(1)}\\\omega_1^{(1)}\end{pmatrix}=\omega_0^{(1)}\begin{pmatrix}1\\0\end{pmatrix}+\omega_1^{(1)}\begin{pmatrix}0\\1\end{pmatrix}\\\|\psi^{(2)}\rangle&=\begin{pmatrix}\omega_0^{(2)}\\\omega_1^{(2)}\end{pmatrix}=\omega_0^{(2)}\begin{pmatrix}1\\0\end{pmatrix}+\omega_1^{(2)}\begin{pmatrix}0\\1\end{pmatrix}\end{align} Define $\otimes$ on the basis members as follows: \begin{align}\|00\rangle&=\begin{pmatrix}1\\0\end{pmatrix}\otimes\begin{pmatrix}1\\0\end{pmatrix}=\begin{pmatrix}1\\0\\0\\0\end{pmatrix},\ \|01\rangle=\begin{pmatrix}1\\0\end{pmatrix}\otimes\begin{pmatrix}0\\1\end{pmatrix}=\begin{pmatrix}0\\1\\0\\0\end{pmatrix}\\\|10\rangle&=\begin{pmatrix}0\\1\end{pmatrix}\otimes\begin{pmatrix}1\\0\end{pmatrix}=\begin{pmatrix}0\\0\\1\\0\end{pmatrix},\ \|11\rangle=\begin{pmatrix}0\\1\end{pmatrix}\otimes\begin{pmatrix}0\\1\end{pmatrix}=\begin{pmatrix}0\\0\\0\\1\end{pmatrix}\end{align} These four vectors form a basis for a 4-dimensional Hilbert space (a 2-qubit memory register). It follows that \begin{align}\|\psi^{(1)}\rangle\otimes\|\psi^{(2)}\rangle&=\omega_0^{(1)}\omega_0^{(2)}\|00\rangle+\omega_0^{(1)}\omega_1^{(2)}\|01\rangle+\omega_1^{(1)}\omega_0^{(2)}\|10\rangle+\omega_1^{(1)}\omega_1^{(2)}\|11\rangle\\&=\begin{pmatrix}\omega_0^{(1)}\omega_0^{(2)}\\\omega_0^{(1)}\omega_1^{(2)}\\\omega_1^{(1)}\omega_0^{(2)}\\\omega_1^{(1)}\omega_1^{(2)}\end{pmatrix}\end{align}Similarly, to describe the state of a 3-qubit memory register, one performs the tensor product $\|\psi^{(1)}\rangle\otimes\|\psi^{(2)}\rangle\otimes\|\psi^{(3)}\rangle$. Quantum memory registers can store an exponential amount of classical information in only a polynomial number of qubits using the quantum property the Principle of Superposition. For example, consider the two classical memory registers storing complimentary sequences of bits $$\begin{array}{\|c\|c\|c\|c\|c\|c\|c\|}\hline1 & 0 & 1 & 1 & 0 & 0 &1\\\hline 0 & 1 & 0 & 0 & 1 & 1 & 0\\\hline\end{array}$$ A single quantum memory register can store both sequences simultaneously in an equally weighted superposition of the two states representing each 7-bit input $$\frac{1}{\sqrt{2}}(\|1011001\rangle+\|0100110\rangle)$$ A matrix can be considered as a vector. For example, a $2\times 2$ matrix $\begin{pmatrix}a & b\\c & d\end{pmatrix}$ can be identified with the vector $(a, b, c, d) \in \mathbb{R}^4$. Hence one can define the tensor product of two matrices in a similar manner to that of two vectors. For example, $$\begin{pmatrix}a_{11} & a_{12}\\a_{21} & a_{22}\end{pmatrix}\otimes\begin{pmatrix}b_{11} & b_{12}\\b_{21} & b_{22}\end{pmatrix}:=\begin{pmatrix}a_{11}b_{11} & a_{11}b_{12} & a_{11}b_{21} & a_{11}b_{22}\\a_{12}b_{11} & a_{12}b_{12} & a_{12}b_{21} & a_{12}b_{22}\\a_{21}b_{11} & a_{21}b_{12} & a_{21}b_{21} & a_{21}b_{22}\\a_{22}b_{11} & a_{22}b_{12} & a_{22}b_{21} & a_{22}b_{22}\end{pmatrix}$$ [1] A. Yu. Kitaev, A. H. Shen and M. N. Vyalyi, Classical and Quantum Computation, Graduate Studies in Mathematics Volume 47, American Mathematical Society, 2002 [2] Colin P. Williams and Scott H. Clearwater, Explorations in Quantum Computing, Springer TELOS, 1998 This entry was posted in Linear Algebra, Quantum Computing on August 27, 2020 by Sung Lee.	CommonCrawl
Journal of Behavioral Data Science, 2022, 2 (2), 1–22. DOI: https://doi.org/10.35566/jbds/v2n2/p1 Disentangling the Influence of Data Contamination in Growth Curve Modeling: A Median Based Bayesian Approach Tonghao Zhang$^{1}$ , Xin Tong$^{2}$ , and Jianhui Zhou$^{1}$ $^1$Department of Statistics, University of Virginia $^2$Department of Psychology, University of Virginia [email protected] Abstract. Growth curve models (GCMs), with their ability to directly investigate within-subject change over time and between-subject differences in change for longitudinal data, are widely used in social and behavioral sciences. While GCMs are typically studied with the normal distribution assumption, empirical data often violate the normality assumption in applications. Failure to account for the deviation from normality in data distribution may lead to unreliable model estimation and misleading statistical inferences. A robust GCM based on conditional medians was recently proposed and outperformed traditional growth curve modeling when outliers were present resulting in nonnormality. However, this robust approach was shown to perform less satisfactorily when leverage observations existed. In this work, we propose a robust double medians growth curve modeling approach (DOME GCM) to thoroughly disentangle the influence of data contamination on model estimation and inferences, where two conditional medians are employed for the distributions of the within-subject measurement errors and of random effects, respectively. Model estimation and inferences are conducted in the Bayesian framework, and Laplace distributions are used to convert the optimization problem of median estimation into a problem of obtaining the maximum likelihood estimator for a transformed model. A Monte Carlo simulation study has been conducted to evaluate the numerical performance of the proposed approach, and showed that the proposed approach yields more accurate and efficient parameter estimates when data contain outliers or leverage observations. The application of the developed robust approach is illustrated using a real dataset from the Virginia Cognitive Aging Project to study the change of memory ability. Keywords: Robust methods · Growth curve modeling · Conditional medians · Laplace distribution Longitudinal data track the same subjects across different time points. In contrast to cross-sectional data, longitudinal data allow for measuring the within-subject change over time, capturing the duration of events, and recording the timing of various events. Growth curve modeling is one of the most frequently used analytical techniques for longitudinal data analysis (e.g., McArdle & Nesselroade, 2014), due to its abilities to examine within-subject change over time, and to investigate into differences of the change patterns among individuals. In growth curve modeling, estimation methods that are based on the normality assumption in data distribution are widely accepted, and have been incorporated in many statistical software packages. When data all come from a normal population, those methods are able to provide consistent and efficient parameter estimators. However, practical data are often contaminated with outlying observations in social and behavioral sciences, so that the normality assumption is violated in real data analysis. For example, Micceri (1989) investigated 440 large-scale data sets in psychology and found that almost all of them were significantly nonnormal. When the normality assumption does not hold, traditional growth curve modeling which focuses on conditional means of the outcome variables may lead to inefficient and even biased model estimation (e.g., Yuan & Bentler, 2001). To disentangle the influence of data contamination, the cause of the contamination needs to be understood. Reflected in growth curve modeling, data contamination may be caused by extreme scores in either random effects or within-subject measurement errors. The former is referred to as leverage observations and the latter is called outliers (Tong & Zhang, 2017). It is necessary to distinguish these two types of outlying observations since their influences on the estimation of growth curve models (GCMs) are different. Although techniques to detect leverage observations and outliers have been developed (e.g., Tong & Zhang, 2017), it has been shown that outlying observation detection in longitudinal data is a challenging problem whose sensitivity and specificity are difficult to guarantee. Even if the leverage observations and outliers are correctly identified, simply deleting them could result in decreased statistical efficiency (Lange, Little, & Taylor, 1989). To address the issue of data contamination, various robust estimation methods have been proposed to produce reliable analysis in the presence of data nonnormality. Some of them rely on making distributional assumptions that are more reasonable to the dataset, such as using Student's t distributions or mixture of normal distributions (Lu & Zhang, 2014; Reich, Bondell, & J., 2010; Tong & Zhang, 2012). However, those methods are sensitive to the choice of the assumed distribution, which is difficult to specifiy a priori and verify afterwards, especially for small sized data. Another genre of robust methods assign weights to observations according to their distances from the center of the majority of data so that extreme cases are downweighted (e.g., Pendergast & Broffitt, 1985; Singer & Sen, 1986; Yuan & Bentler, 1998a; Zhong & Yuan, 2010). Those weighting methods may have limitations under certain conditions, e.g., in general, they do not take the leverage observations into consideration (Zhong & Yuan, 2011). Median-based regression and its generalization, quantile regression (Koenker, 2004), have emerged as another genre of robust methods. Such methods are distribution free, and have been extended to many topics such as penalized regression and time series models. Although the median-based methods are still not widely applied to longitudinal research (Geraci, 2014), they are getting more and more attention (e.g., Cho, Hong, & Kim, 2016; Galvao & Poirier, 2019; Huang, 2016; Smith, Fuentes, Gordon-Larsen, & Reich, 2015; Zhang, Huang, Wang, Chen, & Langland-Orban, 2019). Recently a robust growth curve modeling approach using conditional medians was proposed (Tong, Zhang, & Zhou, 2021). Although this robust approach outperformed traditional conditional mean-based growth curve modeling in the presence of outliers, it still yielded biased parameter estimates when leverage observations exist. It is crucial to have a robust estimator for growth curve models when data are contaminated with both outliers and leverage observations in longitudinal studies. To obtain such an estimator, we develop a DOuble MEdian-based structure (DOME) to mitigate potential distortion in both distributions of random effects and of within-subject measurement errors in growth curve modeling. When random effects and measurement errors are symmetrically distributed, the estimates based on the developed method will be very close to the ones obtained by traditional growth curve modeling estimation method. It is expected that DOME growth curve modeling is more robust against nonnormal data than traditional conditional mean-based method, and also outperforms the median-based growth curve modeling in Tong et al. (2021). Bayesian methods are used for DOME GCM estimation because they can conveniently infer parameters that do not have symmetric distributions (e.g., variance parameters), incorporate prior information to make parameter estimates more efficient, naturally accommodate missing data without requiring new techniques, and are powerful to deal with complex model structures. In sum, the purpose of this work is to develop a robust Bayesian growth curve modeling approach that is effective to analyze longitudinal data that are contaminated with both outliers and leverage observations in general. In the following sections, the idea of the proposed robust approach, DOME GCM, will be introduced, Monte Carlo simulation studies are conducted to evaluate the numerical performance of the developed method and compare its performance with those of traditional growth curve modeling and the median-based method developed by Tong et al. (2021), and an empirical example is provided to illustrate the application of DOME GCM to study the change of memory scores using a real dataset from the Virginia Cognitive Aging Project (Salthouse, 2014, 2018). We conclude this article with discussions and suggestions on future research directions. 2 DOME Growth Curve Modeling In longitudinal studies, the same subjects are measured repeatedly over time. Suppose that a longitudinal study is conducted on a cohort of individuals, indexed by $i=1,...,N$. Let $\boldsymbol {y}_{i}=(y_{i1},...,y_{iT_i})^\intercal $ be a $T_i \times 1$ vector, where $y_{it}$ is the observation on individual $i$ at time $t$ for $t=1,...,T_i$ with $T_i$ being the maximum follow-up time for this individual. A typical form of the unconditional GCMs can be formulated as where $\boldsymbol {X}_i$ is a $T_i\times q$ factor loading matrix recording the time of measurements. It can be different across individuals when they are not measured at a common set of time. The vector $\boldsymbol {b}_{i}$ is a $q\times 1$ vector of random effects, and $\boldsymbol {\epsilon }_{i}$ is a vector of within-subject measurement errors. The vector of random effects $\boldsymbol {b}_{i}$ varies across individuals, and $\boldsymbol {\beta }$ represents the fixed effects for the population. The residual vector $\boldsymbol {u}_{i}$ represents the random component of $\boldsymbol {b}_{i}$. Without loss of generality, we assume the number of measurement occasions to be the same for all individuals, i.e., $T_i \equiv T$. Traditional GCMs typically assume that both $\boldsymbol {\epsilon }_{i}$ and $\boldsymbol {u}_{i}$ follow multivariate normal (MN) distributions, where the subscripts of MN distributions imply the dimensionalities of the random vectors. The covariance matrix $\boldsymbol {\Phi }$ is usually assumed to be diagonal $\boldsymbol {\Phi }=\sigma _{\epsilon }^{2}\boldsymbol {I}$, indicating that measurement errors have equal variance and are independent across different time points. Traditional GCMs focus on modeling the conditional means of the outcome variables, $E(\boldsymbol {y}_{i}\|\boldsymbol {b}_i)=\boldsymbol {X}_i\boldsymbol {b}_{i}$, and estimating the common growth parameters, $E(\boldsymbol {b}_{i})=\boldsymbol {\beta }$. However, it is well known that mean is sensitive to outlying observations. Tong et al. (2021) proposed a median-based GCM where the conditional medians of the outcome variables $Q_{0.5}(\boldsymbol {y}_i\|\boldsymbol {b}_i)$, are examined instead of the conditional means $E(\boldsymbol {y}_{i}\|\boldsymbol {b}_i)$. Their numerical results showed that this approach is only robust against outliers, but not against leverage observations. This is as expected because an outlier is caused by an extreme score in $\boldsymbol {\epsilon }_i$ and a leverage observation is caused by an extreme score in $\boldsymbol {u}_i$. The robust approach in Tong et al. (2021) only models the conditional medians of the outcome variables at the level-one model. Although it seems to be a natural extension to model conditional medians of the level-two model as well to address the influence of leverage observations, the extension is not straightforward because within-subject measurement errors $\boldsymbol {\epsilon }_{i}$ were assumed to be independent across different time points and can be modeled as univariate random variables, whereas $\boldsymbol {u}_i$ has to be specified as a multivariate variable with dependent components. In this paper, we tackle the complicated multivariate problem and propose a robust method by adopting two median structures as alternatives, $Q_{0.5}(\boldsymbol {y}_i\|\boldsymbol {b}_i)$ replacing $E(\boldsymbol {y}_{i}\|\boldsymbol {b}_i)$ and $Q_{0.5}(\boldsymbol {b}_i)$ replacing $E(\boldsymbol {b}_{i})$. We call this new model a double medians growth curve model (DOME GCM). 2.1 DOME GCM specification As discussed previously, outlying observations in longitudinal data can be either outliers as a result of extreme measurement errors, or leverage observations due to extreme scores in random effects (Tong & Zhang, 2017). The proposed DOME GCM aims to handle the presence of data nonnormality due to both types of outlying observations. DOME growth curve modeling is an extension of traditional mean-based method, where medians for vector are taken entry-wise. In this multilevel modeling framework, at the first level, the relationship between $\boldsymbol {X}_i$ and the outcome variable $\boldsymbol {y}_i$ is based on the conditional median function $Q_{0.5}(\boldsymbol {\epsilon }_i\|\boldsymbol {u}_i) = \boldsymbol {0}$. At the second level, random effect $\boldsymbol {b}_i$ varies around the median $\boldsymbol {\beta }$, the fixed effects for the population. The random residuals $\boldsymbol {u}_i = [u_{i1}, u_{i2}, \dots , u_{iq}]^\intercal $ are the random components of $\boldsymbol {b}_i$. Since no distributional assumption is imposed on $\boldsymbol {\epsilon }_i$ or $\boldsymbol {u}_i$, the proposed DOME growth curve model is distribution-free. The multilevel structure in Equation (2) can be expressed compactly as where $Q_{0.5}({\epsilon }_{it}\|\boldsymbol {u}_i) = 0$ and $Q_{0.5}(\boldsymbol {u}_{i}) = 0$. Here $\boldsymbol {x}_{it}$ is the transpose of the $t$th row of $\boldsymbol {X}_i$. The population regression coefficient $\boldsymbol {\beta }$ is the main parameter of interest in the DOME GCM model. 2.2 Estimation of the DOME GCM Recall that in traditional regression based on conditional means, we minimize the sum of squared residuals to estimate model parameters. Similarly, in a median-based regression, estimation is carried out by minimizing the sum of absolute residuals, However, this minimization involves the sum of absolute values, which is not differentiable at zero, meaning that explicit solutions to the minimization problem are unavailable. Moreover, when more than one median constraints are introduced, as in the case of the DOME GCM model in Equations (2), defining an objective function similar to Equation (4) becomes difficult, for the reason that the objective function should be marginalized and involves integration. The computational challenge can be overcome by introducing Laplace distributions to make a connection between the estimation of DOME GCM in Equations (2) and the maximum likelihood principle (Geraci, 2014). The Laplace distribution has a relationship with the $l_{1}$-norm loss function described in Koenker and Bassett (1978). This relationship is best demonstrated by the probability density function for a unidimensional Laplace distribution $X \sim Laplace(\mu ,\sigma )$, where $\mu \in R$ is the location parameter and $\sigma \in R_{+}$ is the scale parameter. The mean and variance of the distribution are given by respectively. Laplace distribution is also known as the standard double exponential distribution. The univariate Laplace distribution can be extended to the multivariate Laplace distribution (Kozubowski & Podgorski, 2000). The marginal distributions of a multivariate Laplace distribution variable are unidimensional Laplace distributions. A multivariate Laplace distribution is parameterized by location $\boldsymbol {\mu }$ and covariance matrix $\boldsymbol {\Sigma }$, denoted as $\boldsymbol {Y} \sim Laplace(\boldsymbol {\mu }, \boldsymbol {\Sigma })$. For a $n$-dimensional Laplace distribution, if $\boldsymbol {\mu } = 0$, the probability density function of the multivariate Laplace distribution is given by where $v = \frac {2-n}{2}$ and $K_v$ is the modified Bessel function of the second kind. We employ Laplace distributions to convert the problem of estimating DOME GCM into a problem of obtaining the maximum likelihood estimator (MLE) for a transformed model. For the purpose of demonstration, we focus on a linear GCM in this paper, so that the random effect is two-dimensional where $L_i$ is the initial level and $S_i$ is the rate of change over time for the $i$th individual, respectively. The transformed model for the DOME GCM in Equations (2) is Note that the median structures are applied for the measurement errors using a univariate Laplace distribution, and for the random effects using a bivariate Laplace distribution. Since the median of a Laplace distribution is the location parameter $\mu $, it can be verified that so that parameter estimation of DOME GCM in Equations (2) can be obtained by estimating the transformed model in Equations (5), for which the likelihood function for $T$ observations across $N$ subjects is where $p(\boldsymbol {y}_i\|\boldsymbol {b}_i, \boldsymbol {\beta }, \sigma _\epsilon )$ is the conditional probability density function of $\boldsymbol {y}_i$ and $p(\boldsymbol {b}_i\|\boldsymbol {\beta }, \Sigma )$ is the probability density function for multivariate Laplace distribution. The solution of the maximum likelihood problem is difficult to derive analytically, or numerically under the frequentist framework, as $\boldsymbol {b}_i$'s need to be integrated out. Alternatively, the estimation can be carried out naturally under the Bayesian framework, as Bayesian methods with data augmentation techniques are flexible and computationally more powerful in such settings. Monte Carlo Markov Chain (MCMC) algorithms can be applied here, using empirical integration to approximate the exact integration. The basic idea of Bayesian methods is to obtain the posterior distributions of model parameters based on the likelihood function and the priors. Since the Laplace distribution can be constructed using a normal distribution and an exponential distribution, the data augmentation technique is used here to simplify the procedure to obtain posterior distributions. Specifically, to simulate a Laplace distribution with location $\boldsymbol {\mu }$ and covariance matrix $\boldsymbol {\Sigma }$, we can generate, independently, two augmented variables $W \sim exp(1)$ and $\boldsymbol {X} \sim N(0, \boldsymbol {\Sigma })$. As a result, the variable follows the $Laplace(\boldsymbol {\mu }, \boldsymbol {\Sigma })$ distribution. The augmented representation provides an efficient method to draw MCMC from the posterior distribution. Particularly, if conjugate priors are used, we can derive conditional posterior distribution for the model parameters. Gibbs sampling then can be utilized, where samples of parameters are drawn iteratively from the conditional posterior distribution. This way we obtain the empirical marginal distribution of model parameters, with which model estimation and statistical inference can be performed. Noninformative conjugate priors are used in our study because of their advantage in easy Gibbs sampling derivation. Other priors, especially informative priors when previous information is available, can also be used and may be more advantageous, on potentially reducing convergence issue or decreasing computation time (e.g., Depaoli, Liu, & Marvin, 2021). 3 Performance Evaluation of DOME GCM through a Simulation Study In this section, a simulation study is conducted to evaluate the numerical performance of the robust Bayesian DOME growth curve modeling in analyzing contaminated data with outliers and/or leverage observations, which correspond to extreme scores in measurement errors and random effects, respectively. Comparisons are drawn among the developed DOME GCM, traditional growth curve modeling based on conditional means, as well as the robust Bayesian method in Tong et al. (2021) where the median structure is only applied in the first level of GCM, referred to as the median-based method hereafter. To directly compare with the study in Tong et al. (2021), we follow their simulation design and focus on the linear GCM as discussed in the previous section. The number of measurement occasions is set at 5, the population parameter values for the fixed effects are set as $\boldsymbol {\beta } = (\beta _L, \beta _S)^\intercal = (6.2, 1.5)^\intercal $, the variance of latent intercept $\sigma _L^2 = 0.5$, the variance of latent slope $\sigma _S^2 = 0.1$, the covariance between intercept and slope is 0, and the measurement error variance $\sigma _\epsilon ^2=0.1$. In the simulation, we vary the sample size ($N = 200, 500$), the percentage of outlying observations ($10\%, 25\%$), and the types of outlying observations (outliers and leverage observations). Given a specific sample size and the percentage of outlying observations $r\%$, we first generate normally distributed measurement errors $\boldsymbol {\epsilon }_i \sim MN_5(0, \sigma _\epsilon ^2\boldsymbol {I})$ and random effects $\boldsymbol {u_i} \sim MN_2(0, \Phi )$. Then $r\%$ of subjects are randomly selected to be contaminated by outlying observations in three scenarios; all selected subjects are contaminated by outliers, all selected subjects are contaminated by leverage observations, and the selected subjects are randomly contaminated with outliers or leverage observations with equal probabilities. To generate outliers, we randomly select 2 out of the 5 observations for one subject, and replace them by data generated from $N(0, 0.1)$. To generate leverage observations, the random slopes of the contaminated subjects are set to follow the distribution $N(-3, 0.1)$, instead of $N(1.5, 0.1)$ for the population. For each data condition, a total of 500 datasets are generated. Each dataset is analyzed using the three methods. Traditional growth curve modeling with normality assumptions is conducted under the structural equation modeling framework, using the "lavaan" package in R (Rosseel, 2012). The median-based method and the proposed DOME growth curve modeling are implemented with the "rstan" package (Stan Development Team, 2019). The Markov chain length is set to be 15,000, and the burn-in period is 7,500. A set of commonly used priors are specified for model parameters. A multivariate normal distribution prior is assumed for $\boldsymbol {\beta }$. The measurement error variance $\sigma ^2_\epsilon $ is given an inverse gamma prior, and inverse Wishart distribution is assumed for the covariance of random effect $\boldsymbol {\Sigma }$. More details can be found in the R code for implementation in the appendix. 3.1 Evaluation criteria We obtain parameter estimation based on the three methods. Estimation bias, empirical standard error (ESE), average standard error (ASE), and mean squared error (MSE) for each parameter are calculated and used to evaluate the numerical performances of those methods. Let $\theta $ denote a parameter and also its population value, and let $\hat {\theta }_k$ and $SE_k$ denote its estimate and the corresponding estimated standard error in the $k$th replication. Then the parameter estimate of $\theta $, $\hat {\theta }$, is calculated as the average of parameter estimates of 500 simulation replications The bias of $\hat {\theta }$ is $bias(\hat {\theta }) = \hat {\theta } - \theta $. The empirical standard error is defined by The average standard error is When standard errors are estimated accurately in model estimation by the developed method, ASE should be very close to ESE. The mean squared error is calculated by $MSE(\hat {\theta }) = bias^2 + ESE^2$. A smaller MSE indicates a more accurate and precise estimator. When Bayesian methods are applied, Geweke tests (Geweke, 1992) are used to assess the convergence of Markov chains for all simulation replications. After the burn-in period, if sample parameter values are drawn from the stationary distribution of the chain, the means of the first and last parts of the Markov chain (by convention the first 10% and the last 50 %) should be equal, and the Geweke statistic asymptotically follows a standard normal distribution. We report the convergence percentage of the 500 replications by Geweke test, and the summarized model estimation results are based only on converged replications. In practice, if the MCMC procedure does not converge, we may adopt longer Markov chains, or choose different starting values or prior distributions to yield convergent Markov chains. The model estimation time, in the number of seconds, is reported for the two Bayesian methods. The median estimation time (MET) is the median of the estimation time for the converged replications. When there are no outlying observations, traditional mean-based growth curve modeling and the two robust median based growth curve modeling approaches perform equally well. Tables 1 - 2 summarize the parameter estimation results for the overall latent slopes ($\beta _S$) and the variance of latent slopes ($\sigma _S^2$), respectively, with the sample size $N = 200$. The overall latent slope and variance of latent slopes are chosen as the parameters of interest, based on the presumption that substantive researchers using growth curve models are most often interested in assessing changes over time. Results for other model parameters and for $N=500$ have similar patterns and are given in the supplementary file: https://github.com/CynthiaXinTong/DOME. When the sample size is 200, Geweke tests suggest that at least $91\%$ replications converged. We summarize the estimation results based on those converged Markov chains. Table 1: Estimation results for $\beta _S$ under different types of data contamination when N = 200 Type r% Method Est Bias MSE ASE ESE CR MET Mean 1.33 -0.17 29.5 4.62 3.07 NA Median 1.48 -0.02 1.21 2.50 2.42 94.2 1149 DOME 1.48 -0.02 1.28 2.77 2.65 96 1551 Mean 1.06 -0.44 194.6 6.30 3.62 NA Median 1.44 -0.06 4.73 3.19 2.78 94.4 740 DOME 1.43 -0.07 5.17 3.35 3.05 95.8 1362 Mean 1.05 -0.45 202 9.82 2.26 NA Median 1.05 -0.45 204 8.39 2.64 94.6 2583 Mean 0.37 -1.13 1269 14.0 2.35 NA Median 0.37 -1.13 1270 10.8 3.02 95.6 2963 DOME 1.29 -0.21 47.1 7.35 4.09 94.6 2674 50-50 Mix Median 1.21 -0.29 86.2 7.05 5.40 95.0 2200 Mean 0.72 -0.78 611 11.1 5.67 NA Note. Est = Estimate; CR = convergence rate; MET = median estimation time in seconds; 50-50 Mix: data contain outliers and leverage observations with equal probabilities. MSE was multiplied by 1000 and ASE and ESE were multiplied by 100. Table 2: Estimation results for $\sigma _S^2$ under different types of data contamination when N = 200 Mean 0.25 0.15 26.36 4.71 5.60 NA DOME 0.16 0.06 8.98 3.21 6.92 95.4 1263 Median 0.06 -0.04 1.66 1.53 1.07 94.8 619.28 DOME 0.13 0.03 1.51 4.68 11.97 93.6 1154 Mean 1.92 1.82 3326 19.32 6.33 NA Median 1.93 1.83 3350 19.27 6.68 94.6 2253 DOME 0.96 0.86 750 13.78 4.43 94.0 2087 Mean 3.90 3.80 14440 39.08 9.90 NA Median 3.91 3.81 14503 38.74 11.46 94.8 2792 DOME 3.64 3.55 12592 51.48 13.78 96.0 2279 Mean 1.13 1.13 1098.89 12.30 20.06 NA Median 0.11 0.01 10.32 34.41 10.13 91.0 2196 DOME 0.18 0.08 41.08 57.74 18.41 93.0 2071 Mean 2.26 2.16 4737.37 216.05 26.35 NA Median 0.11 0.01 15.65 1.05 12.47 92.6 1819 DOME 0.51 0.41 277.74 41.60 32.35 94.4 1968 Note. Same as Table 1 When data contain outliers but no leverage observation exists, our proposed DOME growth curve modeling yields parameter estimates that are very similar to those from the conditional median-based method, and are less biased than those from traditional mean-based method. Both MSEs and standard errors from the two robust Bayesian methods are smaller than those from the traditional mean growth curve model, indicating that the proposed method is on par with conditional median-based method, and is more efficient than traditional growth curve modeling. This pattern is more salient when the proportion of outliers increases. Note that for DOME growth curve modeling, standard errors of $\sigma _S^2$ are underestimated, as ASEs are smaller than ESEs. This may be due to the autocorrelations of the Markov chains, and could potentially be overcome by thinning the Markov chains. In sum, the DOME growth curve modeling is more robust against outliers than traditional mean-based growth curve modeling. It provides less biased and more efficient parameter estimators. The conditional median-based method performs similarly as the DOME growth curve modeling on handling outliers. When data contain leverage observations but no outliers, the advantage of the DOME GCM becomes apparent. In this situation, both traditional mean-based method and the conditional median-based growth curve modeling break down, yielding similar parameter estimates. But the estimates by DOME GCM are much less biased. For example, as shown in Table 1, when the proportion of leverage observations is $10\%$, the estimation bias for $\beta _S$ is -0.45 for both traditional mean-based method and the robust median-based method. DOME growth curve modeling can substantially reduce the bias to -0.06. This is mainly because the conditional median-based method only applies medians in the first level of the growth curve model, whereas leverage observations are extreme values in the second level. Note that standard errors in the DOME growth curve modeling is overestimated as ASEs are larger than ESEs. However, ASEs estimated by the DOME GCM method are still closer to their corresponding ESEs than the ASEs estimated by the other two methods. When data contain both outliers and leverage observations, DOME growth curve modeling still performs much better than the mean-based method and the median-based method in terms of estimation bias and efficiency. In general, when data are suspected to be contaminated, DOME GCM should be a preferred method than the traditional GCM and conditional median-based GCM. It is probably counter-intuitive that the MET is shorter when the proportion of outliers is higher. This is consistent with the findings in Tong et al. (2021). In MCMC sampling, Markov chains typically have trouble exploring high curvature regions. A small proportion of outliers (e.g., 10%) creates a steep and high curvature region for the chain to enter, and thus the computing time tends to be longer. As the proportion increases, the curvature becomes smoother and the MCMC procedure is faster. 4 A Real Data Application To demonstrate its application, we apply the proposed DOME GCM to a subset of data from the Virginia Cognitive Aging Project (VCAP; Salthouse 2014, 2018). VCAP, starting in 2001, is currently one of the largest active longitudinal studies of aging involving comprehensive cognitive assessments in adults ranging from 18 to 99 years of age. Over 5,000 adults have participated in the three-session (6-8 hours) assessment at least once, with about 2,500 participating at least twice, and about 1300 participating three or more times. The subset we used contains observations on 338 participants, who made 5 visits to the assessment sessions. The change of memory scores over time is studied in this illustrative example. Traditional mean-based method and the conditional median-based method in Tong et al. (2021) are also applied to fit the dataset for comparison. The trajectory plot for the memory scores (Figure 1) suggests a linear growth curve structure for the development of memory abilities. In the Bayesian estimation of DOME GCM, we assign a normal prior for the location vector $\boldsymbol {\beta }$, an inverse-gamma distribution for the measurement error variance $\sigma _\epsilon ^2$, and an inverse-Wishart for the random effect covariance $\Sigma $. For both the conditional median-based GCM and DOME GCM estimation, the total length of Markov chains is set as 15,000, with the first 7,500 draws being the burn-in period. Geweke statistics suggest that the Markov chains are stable after the burn-in period. The trace plots (Figures 2- 3) also suggest the convergence of the Markov chains. Figure 1: The trajectory plot for memory scores. Each lines is formed by connecting the consecutive measurements on the same individual. Figure 2: MCMC trace plot for the DOME growth curve modeling. Each line is formed by connecting consecutive draws of the same parameter. Only the draws after burn-in period of MCMC is used. Figure 3: MCMC trace plot for the conditional median-based method. Each line is formed by connecting consecutive draws of the same parameter. Only the draws after burn-in period of MCMC is used. The parameter estimates using the three methods are summarized in Table 3, and they differ a lot. The estimated rate of change $\hat {\beta }_S$ is 0.021 based on the traditional mean-based method. The estimates coming from the robust methods are much smaller, 0.003 from the conditional median-based approach, and 0.005 from the DOME growth curve modeling. Also, the $95\%$ credible interval of $\hat {\beta }_S$ from traditional mean-based method is $[0.001, 0.042]$, suggesting the memory ability for the investigated population (median age of the group is 55) has a significant increasing trend. In contrast, the intervals produced by the two robust methods all cover zero, which is more reasonable and interpretable as most participants in the dataset are elderly. The parameter estimates from the two robust methods are similar. Based on our simulation results, when there is no leverage observation in the dataset, conditional median-based method and DOME growth curve modeling are expected to give similar results. That is most likely the case in this illustrative example. The difference between traditional method and the robust methods is the result of the presence of outliers in the dataset. As suggested in our simulation study, we should generally trust the results from DOME. The results from DOME show that the initial median memory ability is about 0.203. The credible intervals indicate that there are significant between-subject differences in both initial ability and the change over time. The covariance between the two random effects is -0.009, and is significantly different from 0, meaning that a higher initial level is associated with a slower rate of change in general. Table 3: The estimates of memory ability real data application. Estimate SE CI Geweke Statistic Mean GCM $\beta _{L}$ 0.186 0.037 [0.114, 0.258] $\beta _{S}$ 0.021 0.011 [0.001, 0.042] $\sigma _{L}^{2}$ 0.374 0.036 [0.304, 0.444] $\sigma _{LS}$ -0.014 0.008 [-0.031, 0.002] $\sigma _{S}^{2}$ 0.016 0.004 [0.001, 0.023] Median GCM $\beta _{L}$ 0.217 0.039 [0.139, 0.289] -0.337 $\beta _{S}$ 0.003 0.007 [-0.010, 0.017] 0.709 $\sigma _{L}^{2}$ 0.089 0.023 [0.052, 0.140] -0.707 $\sigma _{LS}$ -0.009 0.003 [-0.016, -0.003] 1.001 $\sigma _{S}^{2}$ 0.003 0.001 [0.002, 0.005] -0.603 Double Median GCM $\beta _{L}$ 0.203 0.038 [0.127, 0.278] 0.108 5 Discussion Growth curve modeling based on conditional medians has been developed to disentangle the influence of data contamination. In this paper, we developed a DOME GCM, a double medians based structure, to handle both outliers and leverage observations in longitudinal data. A simulation study was conducted to compare the numerical performances of traditional mean-based growth curve modeling, a median-based growth curve modeling, as well as the proposed DOME growth curve modeling. Results showed that when data were normally distributed, the three methods performed equally well. When data contain outliers but not leverage observations, the median-based method and DOME growth curve modeling yielded similar parameter estimates, which were less biased and more efficient than those from traditional growth curve modeling. When leverage observations existed, DOME growth curve modeling outperformed the other two approaches, providing much less biased parameter estimates. We therefore recommend to use DOME growth curve modeling in general as it can effectively handle both leverage observations and outliers. As pointed out in Tong and Zhang (2017), outliers and leverage observations are equally likely to exist in samples in practice, but they affect model estimation differently. Although various methods have been developed to identify outliers and leverage observations separately, the accuracy and effectiveness of those methods were not guaranteed, especially in longitudinal studies. Tong and Zhang (2017) suggested that a final detection decision should rely on a combination of multiple methods. Our work in this paper indirectly provided an approach to imply whether data contain leverage observations or not, by comparing the estimation results from the median-based growth curve modeling and the DOME growth curve modeling. If their results greatly deviate from each other, we can conclude that leverage observations exist. Note that estimations of the random effects parameters (e.g., $\sigma _S^2$) are not as good as those for the fixed effects (e.g., $\beta _S$) in general. This is consistent with the literature; namely, although the median has a higher breakdown point of 50%, it can be less efficient than the mean under some conditions. Thus, we need to carefully examine the estimated random effects parameters to determine whether there are significant between-subject variations in the within-subject change. One alternative approach is to extend the current approach based on conditional medians to approaches based on conditional quantiles. Such extension is natural with the assistance of asymmetric Laplace distributions, and we would be able to investigate the change pattern at different quantile levels inferring between-subject differences without investigating the random effects parameters. In this study, we evaluated the performance of DOME growth curve modeling when data were contaminated. We want to point out that the data distribution nonnormality may be due to data contamination or nonnormal population distributions. 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Multivariate Behavioral Research, 46, 229–265. doi: https://doi.org/10.1080/00273171.2011.558736 Appendix: Implementation The "rstan" package (Stan Development Team, 2019) is used in our study. Below we provide the annotated R code for the real data analysis. DOME<-" data{ int<lower=0> N; int<lower=0> T; vector[NT] X; vector[NT] y; // fixed inv_gamma parameter, prior of epsilon variance real shape; real inv_scale; // beta prior information, the global slope&intercept vector[2] beta_0; cov_matrix[2] Var_beta0; // hyper parameter's value for Var_b cov_matrix[2] Var_b0; transformed data{ int len; len = NT; parameters{ real<lower=0> sigma; //epsilon variance vector<lower=0>[len] v; // data augmentation, represent // Laplace epsilon in expo vector<lower=0>[N] vb; // data augmentation, MLD b vector[2] beta; vector[2] b_star[N]; cov_matrix[2] Var_b; cov_matrix[2] Var_beta; transformed parameters{ vector[len] mu; vector[len] sigma_y; vector[N] vb_root; vb_root = sqrt(vb); for(i in 1:N){ for(j in 1:T){ mu[T(i-1)+j] = beta[1] + b_star[i,1]vb_root[i] + (beta[2] + b_star[i, 2]vb_root[i]) X[T(i-1)+j]; sigma_y = sqrt(sigmav); model{ // model y ~ normal(mu, sigma_y); // data augmentation sigma ~ inv_gamma(shape, inv_scale); v ~ exponential(1); vb ~ exponential(1); // priors beta ~ multi_normal(beta_0, Var_beta); // b_star * sqrt(vb) is b, written this way to vectorize b_star ~ multi_normal([0, 0], Var_b); Var_beta ~ inv_wishart(3, Var_beta0); Var_b ~ inv_wishart(3, Var_b0); #load VCAP data and prepare intial values for MCMC y<-as.vector(y) X<-as.vector(time) N<-length(y)/5 lm_est<-lm(y~X) beta_0<-c(lm_est$coefficients[1],lm_est$coefficients[2]) Var_beta0<-matrix(c(0.5,0,0,0.1),ncol = 2) Var_b0<-matrix(c(0.5,0,0,0.1),ncol = 2) dat<-list(N=N, T=T, y=y, X=X, beta_0=beta_0, shape=0.1, inv_scale=0.1, Var_beta0=Var_beta0, Var_b0=Var_b0) v_initial<-rep(1,NT) vb_initial<-rep(1,N) b_initial<-matrix(rep(0, N2), N, 2) intial<-list(list(sigma=runif(1,0.5,2), beta=beta_0, b=b_initial, v=v_initial, vb=vb_initial, Var_beta=Var_beta0, Var_b=Var_b0)) #fit the DOME model using rstan package fit_DOME<-stan(model_code=double_quantile, model_name="DOME", init=intial, pars=c("beta","Var_b"), data=dat, iter=15000, chains=1) summary(fit_DOME)$summary //check convergence via geweke test content<-extract(fit_double_median) geweke.diag(content$beta[,1])$z geweke.diag(content$Var_b[, 1, 1])$z #draw traceplot for MCMC, serving as reference for convergence color_scheme_set('mix-blue-red') mcmc_trace(fit_DOME, pars = c("beta[1]","beta[2]", "Var_b[1,1]", "Var_b[1,2]", "Var_b[2,2]"), facet_args = list(ncol = 1, strip.position = "left"), iter1 = 7500)	CommonCrawl
Molecular detection of the causative agent of the potato soft rot, Pectobacterium carotovorum, in Egypt and essential oils as a potential safe tool for its management Mohamed Hamed El-habbak1 & Mohamed Hassan Refaat2,3 Egyptian Journal of Biological Pest Control volume 29, Article number: 5 (2019) Cite this article Forty-two bacterial isolates were collected from soft-rotted potato tubers originating from four governorates in Egypt. Their phenotypic and genetic characteristics were studied. The phenotypic identification resulted in grouping the studied isolates into five different species and/or genera including Pectobacterium sp., Bacillus sp., Dickeya sp., Pseudomonas sp. (1), and Pseudomonas sp. (2). The molecular identification of the 10 isolates of them were pathogenic to potato tubers and other hosts. More specific identification of the later 10 isolates, using two specific primers for P. carotovorum subsp. carotovorum (Pcc) and the reference strain PccY46 (Acc. No. KP187511.1), revealed that all these isolates had yielded 220–272-bp DNA fragments identical to the 16S rRNA gene of PccY46. Phylogenetic analysis showed sequence similarity ranging from 87 to 98%, which confirmed the genetic variation among the 10 tested strains of Pcc. The isolates were distributed in four major clusters, each subdivided into a few sub-clusters. In another experiment, two different essential oils (peppermint and clove oils) plus a nano-Cu-based fungicide (Tango®), in comparison to the two different antibiotics and the two copper fungicides, were evaluated for their potential management on the three most severe bacterial isolates (Pcc1, Pcc5, and Pcc10). Results of in vivo experiment showed that clove oil was the most effective, where it caused a reduction of disease severity (0.0%) on potato tubers, 4 days post artificial inoculation. In terms of food crops such as rice (Oryza sativa L.), maize (Zea mays L.), and wheat (Triticum aestivum L.), potato (Solanum tuberosum) has so far been ranked fourth in the world, and regarding its remarkable nutritive value, its total world acreage gets far beyond any other cultivated crop (Douches et al. 1996). In 2016, Egypt was ranked 14th in the world, with 5.0 million tons of potatoes produced (FAO 2016). The blackening of potato tuber in field and the tuber soft rot in storage, transit, and field are all caused by Pectobacterium carotovorum subsp. carotovorum (Pcc), which causes a great loss (Nabhan et al. 2011). Perombelon and Kelman (1980) referred the main causes of tuber bacterial soft rot to either unsuitable environmental conditions during growth or a bad storage state or to both. Among the members of the species Pectobacterium, which infect a wide range of vegetable crop hosts, Pectobacterium atrospeticum was identified as the main potato pathogen (Gardan et al. 2003). Many strains of Pectobacterium atrosepticum have been subjected to genetic analyses, which suggested that almost all were, to a great extent, quite close to the other species, Pectobacterium atrosepticum (Avrova et al. 2002). Ma et al. (2007) reported that despite the close resemblance, any good reason(s) to explain how the Pectobacterium spp. members uniquely infect different vegetable crops still has not been genetically figured out yet. Controlling bacterial potato bacterial soft rot is a real challenge for producers. Many control strategies have been developed and applied. Using, for example, protective chemicals make ware tubers unsafe for consumption. In addition, Crépin et al. (2012) stated that although biological control techniques have recently progressed so far to control to some extent disease severity, they argued that their use, however, is still limited. Though certified, tubers are subject to the occurrence of soft rot during later tuber handling, which leads to severe disease infection loss. So, it is quite crucial to measure, in these tubers, both disease severity and incidence (Czajkowski et al. 2011). The application of plant resistance elicitors, as a complementary option to trigger preventive defense reactions, might aid in controlling the disease; however, this control strategy is not a top priority, since plants lack highly efficient defense elicitors (Deravel et al. 2014). Using chemical resistance, inducer technique has been proved effective in controlling P. carotovorum and other bacterial species, which cause soft rot disease (Farrar et al. 2009). Bokshi et al. (2003) showed that acetyl-salicylic acid (ASA) enhanced resistance against E. carotovora subsp. carotovora which causes the disease. In addition, there are other compounds that can inhibit plant pathogens and/or suppress toxin production by pathogens, for example, organic and inorganic salts (Olivier et al. 1998). Benzoic acid and sodium benzoate at the rates of 1.0, 5.0, and 10.0 mM, as reported by Saleh and Huang (1997), relatively minimized soft rot disease infection. Acetic and boric acid and bleaching powder are also effective against onion soft rot, Burkholderia cepacia (Rahman et al. 2013). Some essential oils and hemp flower water extract were tested against Erwinia carotovora, a potato bacterial pathogen (Krebs and Jaggir 1999). Simeon and Abubakar (2014) recommended aqueous extracts of each of the lemon grass ( Cymbopogon schoenanthus ), Aloe vera ( Arabian peninsula ), and neem (Azadirachta indica), as well as borax salt, as all had inhibitory effects on Pectobacterium spp. and could be used for managing the tuber soft rot. This present study aimed to isolate the potato soft rot disease isolates found in Egypt and to identify these isolates through morphological, physiological, and molecular (PCR) techniques, as well as to test some essential oils as natural safe materials to control the disease. Isolation and purification of bacteria associated with soft-rotted potato tubers Isolation of the causal bacterium was done to potato tubers (Solanum tuberosum) showing symptoms of the soft rot disease, cultivated in four different farms located in Sinai, Sharqia, Gharbia, and Beheira governorates, Egypt. The infected tuber samples with bacterial lesions were picked and washed with tap water to get rid of adherent soil and then were air-dried. The samples were cut into small slices, with 1–2 cm thickness each; each one was surface-sterilized for 2 min with 2% sodium hypochlorite solution, rinsed three times in sterile distilled water, and then dried in-between two sterilized filter papers. Then, each sample was transferred onto nutrient agar medium (NA) plates. The inoculated plates were incubated at 30 °C for 48 h. Randomly, initiated bacterial colonies were picked and transferred to new NA medium plates for purification (Barker 2005). The resulting bacterial colonies were further purified and sub-cultured repeatedly, until pure cultures were obtained (Yuan et al. 2004). Identification of the pathogenic bacteria Morphological, nutritional, and physiological identification A primary identification of the bacterial isolates was conducted on the bases of their morphological, nutritional, and physiological characteristics according to the schemes suggested by Murray and Holt (2001). Preparation of bacterial inoculum Under laboratory conditions, bacterial suspensions of the aforementioned purified bacterial isolates were prepared as described by Desender et al. (2006) with some modifications. Each of the tested bacterial isolate was grown in and sub-cultured on King's B medium for 24 h at 30 °C and then suspended in sterile distilled water and centrifuged at 3000 rpm/min for 30 min. The pellets were re-suspended in distilled water and adjusted turbidimetrically (O.D. at 580 nm) to approximately the density of 108 CFU/ml, using a spectrophotometer. The bacterial concentration was estimated from O.D580 data using a standard curve. Pathogenicity test Potato tubers had been flame antisepticised prior to cutting into 1-cm-thick slices using a sterile knife. Each slice was placed on a moistened sterilized filter paper in a Petri dish. A volume of 0.50 ml of bacterium inoculum of each isolate was pipetted into the center of the five slices to induce artificial infection. Distilled water was used as the control treatment. All treatments were incubated at 30 °C for 4 days, then pathogenicity was examined on a daily basis. According to Lelliott and Stead (1987) disease infection ranking of rotted potato slices was recorded on a scale of negative (−), low (+), moderate (++), and high (+++) infection. Host range Tubers, fruits, bulbs, and corms, for 30 different host plants, were inoculated with each of the 10 tested bacterial isolates. Equal slices of each tested plant material were inoculated with 0.5 ml of each isolate at a rate of 108 CFU ml−1 by pipetting into the center of each of five slices. For the control, sterilized water was pipetted as well into the center of five slices. Disease rating, as explained, was measured following all treatment incubation at 30 °C for a 4-day period. Molecular identification of the pathogenic bacteria DNA was extracted from 24-h-old pure bacterial cultures of 12 bacterial isolates grown on NA medium at 37 °C. These isolates were primarily identified as P. carotovorum (Pc). Pure bacterial colonies were picked by a sterile loop and mixed in 4 ml of nutrient broth media in a sterile labeled culture tubes (Velp, Italy) and incubated overnight at 37 °C, with shaking at 150 rpm. DNA was extracted, using DNeasy Blood and Tissue Kit (Qiagen, China). The protocol was performed according to the manufacturer's instructions. The quantity and quality of the extracted DNA were measured, using the UV-spectrophotometer (T80 plus, PG Instruments Limited, England), and DNA was visualized by electrophoresis (Cleaver, power PAC300) in 1% agarose gel in 1X Tris-Acetate-EDTA (TAE) (Promega, Madison, Wisconsin) buffer stained with ethidium bromide (0.5 μg/ml) (Sambrook 2001). The DNA was stored at − 20 °C for further PCR work. The primers used in this study were synthesized by Thermo Fisher Scientific Inc., as described by Yuan et al. (2004). The PCR specific primers (Fs1: CAGAGTTTGATCCTGGCTCAG) and (Rs1: AAGGAGGTGATCCAGCC) used herein were designed based on the region of the 16S ribosomal RNA gene of P. carotovorum subsp. carotovorum (Pcc) strain Y46 (Acc. No. KP187511.1). The primers amplified a 220 to 272-bp PCR amplicon unique to P. carotovorum, compared to all known DNA sequences in the available databases, and showed homology only to P. carotovorum subsp. carotovorum. DNA amplification was performed according to the non-conventional method (De-Boer and Ward 1995), and the PCR reaction mix (25 μl) contained 5.0 μl 5X Crimson Taq buffer, 1.1 μl 25 mM MgCl2, 0.5 μl 10 mM dNTPs, 0.13 μl 5 U/μl Taq polymerase, 1.25 μl 10 μM of each primer, and 2.0 μl DNA template finalized to 25 μl by adding 13.77 NFW. PCR was performed in a thermal cycler TProfessional (Biometra, Germany) using the following protocol: denaturation (94 °C, 5 min), followed by 35 cycles of denaturation (94 °C, 1 min), annealing (55 °C, 1 min), and extension (72 °C, 1 min) with a final extension (72 °C, 7 min), and adjusted as needed. DNA sequencing and phylogenetic analysis PCR product was recognized, and nucleotide sequencing was performed in each direction by Macrogen Korea (Seoul, Rep. of Korea). The similarity search of the PCR product was performed with a Basic local alignment searching tool (BLAST) at the NCBI server (http://blast.ncbi.nlm.nih.gov/Blast.cgi). A Blast search was performed for nucleotide, using BLASTn. Biological evolutionary trees for the data were reconstructed, using MEGA (Kumar et al. 2001), using the Neighbor-Joining (NJ) method. In vitro antibacterial assay of tested essential oils Antibacterial activity was in vitro assayed for the three most virulent P. carotovorum isolates Pcc1, Pcc5, and Pcc10 (the causal pathogen of potato tubers rot) for two essential oils, two antibiotics, and three fungicides, as well as for a systematic fungicide. The two oils were (peppermint, Mentha piperita, and clove, Syzygium aromaticum) each at a rate of 1.5, 3.0, and 5.0% (vv−1). The two antibiotics were tetracycline and erythromycin, using rates of 100, 200, and 500 ppm for each. The two fungicides were Galben-Cu (Benallxyl Cu 54% WP) and Copper oxychloride (48% WP), using rates of 250, 500, and 750 ppm for each. In addition to the above, the systematic fungicide Tango® 23% (copper sulfate 8% + sulfur 28%) was tested. All treatments were tested using nutrient agar (NA) plates. For the control treatment, paper disks were immersed in distilled water. For all treatments, the NA plates were inoculated with 0.5 ml of the tested pathogenic bacterial suspension of 108 CFU dilution for 24 h. For each bacterial isolate, four 5-mm filter paper disks, for each treatment, were placed onto the surface of each inoculated plate and later on all plates were incubated at 28 °C for 72 h. Within the inhibition zone surrounding disks, the bacterial growth was an indication of treatment effect (Fatmi and Schaad 1988). In vivo antibacterial assay of tested essential oils in potato tubers Seven treatments were tested in this experiment using the concentration which gave the highest inhibition zone; two essential oils (peppermint and clove) each at a rate of 5%, two antibiotics (tetracycline and erythromycin) each at a rate of 500 ppm, and three fungicides (Copper oxychloride, Benalaxyl-Cu, and systemic fungicide Tango®) each at a rate of 750 ppm. The effects of these materials were relatively compared on the three virulent isolates of bacterial potato tubers' rot (Pcc1, Pcc5, and Pcc10 as mentioned above). Five potato tubers cv. Spunta, previously inoculated with the pathogenic strains, were treated with each treatment in a completely randomized design (CRD). Nine (30 × 40 × 10 cm) boxes were used. In the first three-box set, each box contained five tubers treated with each of the two essential oils. In the second set, five tubers were treated with each of the two antibiotics. In the last set, five tubers were treated with the three fungicides. In addition to another five inoculated tubers used as controls. All boxes incubated at 28 ± 2 °C where soft rot disease severity was estimated after 2 and 4 days based on a 0–5 ranking scale (Bdliya and Langerfeld 2005) where 0 = no symptom, 1 = 1–15% rotten tuber, 2 = 16–30%, 3 = 31–45%, 4 = 46–60%, and 5 ≥ 61%. The severity was then computed, using the following formula: $$ Disease\ Severity=\frac{\sum nv}{5N}\times 100 $$ where n = number of infected tubers in each category, v = numerical values of each category, N = total number of the infected tuber, and 5 = highest score on the severity scale. Frequency of the isolated bacteria from potato tubers showing soft rot symptoms Isolation trials from potato tubers showing bacterial soft rot, collected from Sinai, Sharqia, Gharbia, and Beheria governorates, yielded 42 bacterial isolates. The isolates were distributed among five species, belonging to four genera grouped as Pectobacterium sp., Bacillus sp., Dickeya sp., Pseudomonas sp. (1), and Pseudomonas sp. (2) at the frequency of (10, 13, 5, 8, and 6 isolates), respectively. Different governorates did not show much difference in the frequency of the isolated species, being 10, 13, 11, and 9 isolates from Sinai, Sharqia, Gharbia, and Beheira, respectively. Van der Wolf and De Boer (2007) reported that the main bacteria causing potato tuber soft rot were Pectobacterium atrosepticum, P. carotovorum subsp. carotovorum, and Dickeya spp. (Table 1). Potato seed lots were tested for the soft rot pathogen and found impure with Dickeya spp. and P. carotovorum subsp. carotovorum, but not with P. atrosepticum. High concentrations of both Dickeya spp. and Pcc were found in the stolon ends, whereas relatively low densities were found in the peel and in deeper located potato tissue (Czajkowski et al. 2009). Pseudomonas syringae van Hall was found only as a species of Gram-negative bacteria isolated from rotted potatoes, collected from clamps in England in 1945–1947 (Jones and Dowson 1950). The isolates of Bacillus spp. are thought to be saprophytic rather than pathogenic, as Bacilli are not formerly reported to be the primary causal agents of soft rots. Lund and Wyatt (1979) highlighted that potato tubers may harbor pectolytic saprophytic bacteria (Bacillus spp., Clostridium spp., Flavobacterium spp., and Pseudomonas spp.) which, if given the opportunity, can also cause rotting. Table 1 Frequency of the isolated bacteria from potato tubers showing soft rot collected from four governorates Pathogenicity and host range of isolated bacteria The pathogenicity of obtained isolates was examined on diverse plant hosts (Table 2). Results showed that each of the tested isolates was pathogenic on potato tubers. Out of them, solely three isolates (1, 5, and 10) caused extremely severe symptoms of soft rot on potato tubers; meanwhile, isolates 2, 3, 7, 8, and 9 showed moderate severity and isolates 4 and 6 showed low severity on potato tubers once tested for their pathogenicity. On the other hand, on all tested host plants, except sugar beet, isolates 1, 5, and 10 were extremely pathogenic, while isolates 2, 3, 4, 6, 7, and 8 showed low to moderate severity. Table 2 Severity of soft rot caused by confirmed isolates of Pectobacterium carotovorum on different hosts Obtained results indicate that there was a correlation between the host plant and the disease severity of some bacterial isolates as potato tubers were highly vulnerable to Pcc1, Pcc5, and Pcc10 and squash fruits were lowly vulnerable to most isolates, while sugar beet was not vulnerable to the majority of them. The present results are in harmony with those reported by Frampton et al. (2012) who confirmed that P. carotovorum was the main causal agent of soft rot disease on potato tubers. Identification of isolated bacteria Morphological, physiological, and biochemical identification Morphological, physiological, and biochemical assays by traditional identification of the 10 strains of the presumptive pathogen Pectobacterium spp. isolates confirmed that all of them were P. carotovorum, as they showed the following features: creamy, short rods, and Gram negative, and did not have the ability to produce any pigment in Kings B medium. All the tested isolates were positive for motility, starch hydrolysis, growth at 37 °C, growth in 5% NaCl and 7% NaCl, catalase activity, pectate degradation, fried egg in PDA, and relation O2 but negative for KOH 3% and pigment production. The strains also induced typical bacterial soft rot symptoms on tuber slices of cv. Spunta (Table 3). Table 3 Morphological, physiological, and biochemical characters of isolated bacteria (Pectobacterium sp.) Molecular identification of the pathogenic isolates Detection of bacterial 16S rRNA gene Amplifications with the Fs1 and Rs1 primers were positive in all strains also the Fs1 and Rs1 primers discovered P. carotovorum subsp. carotovorum DNA in the 10 tested strains (Fig. 1). A sequence similarity was undertaken by using the Blast server at the National Center for Biotechnology Information. It was found that PCR product was 220–272 bp long, the same size as the region on the P. carotovorum subsp. carotovorum 16S rRNA gene between the two primers. An alignment of the nucleotide sequence of the eventual PCR product and the region confined with the two primers of the P. carotovorum 16S rRNA gene showed an exact size and typical sequence match. Results presented in Table 4 showed the sequence of this 210–250 bp PCR amplicon. The latter PCR amplicon was obtained by the phenotypically identified P. carotovorum subsp. carotovorum strains only, but in the other examined strains, the PCR products were not observed. These results agree with those obtained by Weisburg et al. (1991) who reported that for definitive identification of P. carotovorum strains, 16S rRNA gene analysis was carried out, using two PCR primers for the specific 16S rRNA gene of P. carotovorum (GenBank Accession No. KP187511.1). The obtained nucleotide sequence of the 16S rRNA PCR product was in alignment with that of P. carotovorum 16S rRNA gene sequence. These results are in harmony with those obtained by Toth et al. (2001) who proved that the 16SrRNA analysis was used to identify the isolated bacterial strains at the molecular level. Yap et al. (2004) had similar results and identified a single amplicon produced by specific primers; however, Zhu et al. (2010) obtained four amplicons produced by the designed 16S rRNA gene primers. PCR amplified DNA in 10 indigenous isolates of Pectobacterium carotovorum (Pcc), using Fs1 and Rs1 primers Table 4 Homology search (BLAST) results of all sequenced samples Searching nucleotide database, using a nucleotide query (BLASTn) of all isolates' sequences, obtained from 10 isolates that amplified with Fs1 and Rs1 set of primers, showed a high similarity with different strains of Pcc deposited in the GenBank (Accession No. KP187511.1). The nucleotide sequence similarity percentage ranged from 87 to 98%, which confirms a variation among the 10 isolates (Fig. 2a–d). Phylogenetic analysis of nucleotide sequences of Pectobacterium carotovorum isolates (Pcc) detected, based on sequences of Pc.c1 = 250 bp (a), Pc.c2 = 240 bp (b), Pc.c5 = 240 bp (c), and Pc.c7 = 210 bp (d) and aligned on different regions of the 16S ribosomal gene, with close species. The branching pattern was generated by the Neighbor-Joining method; stability of the tree was assessed by 1000 bootstrap replication Isolates Pcc1, Pcc2, Pcc3, and Pcc4 clustered closely to reference strains Y46 (Acc. No. KP187511.1) with 87 to 99% bootstrap value, whereas isolates Pcc6 and Pcc8 clustered individually and were closer to the Pcc strain Y46 (Acc. No. KP187511.1) with 100% bootstrap value. Moreover, isolates Pcc5 and Pcc7 clustered to the reference strain Y46 (Acc. No. CP001657.1) and Erwinia carotovorum (Acc. No. KP405846.1) with 90 to 92% and 95 to 99% bootstrap value, respectively. In the present study, PCR was carried out for all DNA extracts of bacterial soft rot isolates that were identified by biochemical tests as Pcc. The results of the 10 isolates examined detected the presence of the desired DNA fragments of 1530 bp, using the 16S rDNA set of primers Fs1 and Rs1 resembling the positive DNA extract of the reference strain Pcc Y46 (Acc. No. KP187511.1), which gave a product size of 1530 bp. The 16S rDNA sequences were conserved with stable copies, and their analysis were characteristic than other ribosomal regions. In general, 16S rDNA was amplified and sequenced by universal primers to identify species and subspecies (De Boer et al. 2012). In the homology search, BLASTn of Pcc isolates sequenced on the bases of the 16S rDNA showed high similarity, with diverse reference strains at the GenBank (Acc. No. KP187511.1 and Acc. No. KP405846.1) that were closely related to the sequences of other bacterial rotting causal agents such as Pseudomonas spp., Bacillus spp., Serratia spp., and Enterobacter spp. In fact, the Fs1 and Rs1 primers that were used in the study were general primers, which can detect different bacterial causal agents (Shrihari and Negi 2011) and could be used as an exploratory step in bacterial identification. In the majority of the cases, genotypic isolates were more carefully related than those isolated from different geographical regions. However, the similarity among the groups of isolates separated from several regions suggested the same genetic origin of these isolates. Soft rot disease is widely common in different potato-growing areas in Egypt, and the results of biochemical and physiological experiments confirmed that the main causative agent of bacterial soft rot in Egypt is P. carotovorum subsp. carotovorum, while using the PCR primer pair Fs1/Rs1 was authoritative in detection and identification of all the soft rot Egyptian isolates of Pcc. DNA sequencing was found to be the most reliable way in specific detection and affirmation of the causal agent of soft rot. Furthermore, studies to assay soft rot disease etiology and epidemiology are needed. Compared to diversified DNA sequence analysis, used in this study, biochemical experiments were able to identify most isolates but misidentified others. Effect of essential oils, antibiotics, and fungicides on the P. carotovorum in vitro Assays of potential management materials in vitro and in vivo were carried out on the three most virulent isolates of Pcc (Pcc1, Pcc5, Pcc10), as confirmed by the pathogenicity test. The different isolates varied in their sensitivity to the examined materials. Notably, there is a positive correlation between the growth inhibition and the concentration increase of all examined materials. At the highest concentrations, most of them positively inhibited the growth of the pathogen (Fig. 3). Peppermint oil showed the greatest inhibitory effect among all the examined materials. Surprisingly, the effect caused by the highest concentration of the nano-copper-based fungicide Tango was worthless. Among the tested antibiotics, tetracycline showed higher inhibitory effect than erythromycin that equals nearly a twofold increase. Preferable control of E. carotovora by erythromycin and tetracycline and partial control with copper compound were also reported by Mills and Hurta (2006). In vitro inhibitory effect of essential oils, antibiotics, and fungicides on the growth of P. carotovorum isolates, 2 days after incubation at 28 ± 2 °C The antibiotics tetracyclines and oxytetracycline stimulate their bactericidal effect by the inhibition of protein synthesis; present studies also approved the bactericidal efficiency of such chemicals against P. carotovorum subsp. carotovorum. Among the examined fungicides, Galben-Cu was nearly had equal effect as copper oxychloride. Tango showed three- to fourfold decrease in inhibition than the former two fungicides (Fig. 3). Concerning safety, peppermint oil is considered the preferable treatment for controlling Pcc isolates in vitro. In vivo management trials of Pcc soft rot disease on potato The results showed that the effect of the same examined compounds in vivo behaved differently than they did in in vitro assays when tested on the same isolates. The results in Table 5 indicate that percentages of disease severity (DS) and disease incidence (DI) were significantly affected by tested treatments. The disease severity values obtained by peppermint oil reached 0.0 to 6.5%, while the values of disease incidence reached 0.0 to 17.5%, recorded as the highest significant decrease as compared to control and depending on the isolate. Meanwhile, clove oil in this experiment reduced the disease severity and disease incidence significantly to be 0.0%. As for the two antibiotics, tetracycline reduced the disease severity significantly to be 0.0% as compared to control, which was better than the effect of erythromycin that reached 0.0 to 1.5% without any significant differences in-between them. In respect of the disease incidence, the same trend was noticed. The tested commonly used copper fungicides equalled in their effect and reduced the soft rot severity (0.0 to 1.5%) as compared to control. Contrary to its effect in vitro, the nano-Cu fungicide Tango reduced the disease severity to 0.0% than in the control. Gakuubi et al. (2016) obtained a strong antibacterial activity with the essential oil of Mexican marigold (Tagetes minuta L.) against bacterial plant pathogens, i.e., P. savastanoi pv. phaseolicola, Xanthomonas axonopodis pv. phaseoli, and X. axonopodis pv. maanihotis. In another study, T. minuta also showed antibacterial activity against P. carotovorum in potatoes grown in the field and in storage (Al Abbasy et al. 2015). The antibacterial activity in the essential oils of several medicinal plants has been related to the attack on the phospholipids in the cell membranes of the microbes, which causes increased permeability and leakage of cytoplasm thereby killing the bacteria. Table 5 Effect of different materials on soft rot severity on potato tubers 2 and 4 days after storage Studies of 10 isolates of P. carotovorum (soft rot) showed pathogenicity to potato tubers and other hosts. P. carotovorum, in the reference strain Pcc Y46 in PCR experiments and the sequencing that followed, revealed that all the isolates yielded 220–272-bp DNA fragments identical to the 16S rRNA gene of Pcc Y46. Potential management against the disease was evaluated by testing two essential oils, i.e., peppermint and clove, and a nano-Cu-based fungicide, i.e., Tango, which were compared to two different antibiotics and two different commonly used copper fungicides. In vitro assays, peppermint oil at the highest tested concentration was the best treatment, giving higher inhibition zones than the antibiotics and copper fungicides. PCR-based assay made it easy and accurate to identify Egyptian isolates of the soft rot causative agent P. carotovorum subsp. carotovorum from diseased potato tubers. Clove essential oil was a new safe material for the management of soft rot disease of potato tubers in storage. Al Abbasy DW, Pathare N, Al-Sabahi JN, Khan SA (2015) Chemical composition and antibacterial activity of essential oil isolated from Omani basil (Ocimum basilicum Linn.). Asian Pac J Trop Dis 5(8):645–649 Avrova AO, Hyman LJ, Toth RL, Toth IK (2002) Application of amplified fragment length polymorphism fingerprinting for taxonomy and identification of the soft rot bacteria Erwinia carotovora and Erwinia chrysanthemi. Appl Environ Microbiol 68(4):1499–1508 Barker K (2005) At the Bench: A laboratory navigator, Update Edition. Cold Spring Harbor Laboratory Press. Cold Spring Harbor, New York Bdliya B, Langerfeld E (2005) A semi-selective medium for detection, isolation and enumeration of Erwinia carotovora ssp. carotovora from plant materials and soil. Trop Sci 45(2):90–96 Bokshi A, Morris S, Deverall B (2003) Effects of benzothiadiazole and acetylsalicylic acid on β-1, 3-glucanase activity and disease resistance in potato. Plant Pathol 52(1):22–27 Crépin A, Barbey C, Cirou A, Tannières M, Orange N, Feuilloley M, Dessaux Y, Burini J-F, Faure D, Latour X (2012) Biological control of pathogen communication in the rhizosphere: a novel approach applied to potato soft rot due to Pectobacterium atrosepticum. Plant Soil 358(1–2):27–37 Czajkowski R, Grabe GJ, van der Wolf JM (2009) Distribution of Dickeya spp. and Pectobacterium carotovorum subsp. carotovorum in naturally infected seed potatoes. Eur J Plant Pathol 125(2):263–275 Czajkowski R, Perombelon MC, van Veen JA, van der Wolf JM (2011) Control of blackleg and tuber soft rot of potato caused by Pectobacterium and Dickeya species: a review. Plant Pathol 60(6):999–1013 De Boer S, Li X, Ward L (2012) Pectobacterium spp. associated with bacterial stem rot syndrome of potato in Canada. Phytopathology 102(10):937–947 De-Boer SH, Ward J (1995) PCR detection of Erwinia carotovora subsp. atroseptica associated with potato tissue. Phytopathology 85:854–858 Deravel J, Krier F, Jacques P (2014) Biopesticides, a complementary and alternative approach to the use of agrochemicals. A review Biotechnologie, Agronomie, Société et Environnement 18(2):220–232 Desender S, Klarzynski O, Potin P, Barzic MR, Andrivon D, Val F (2006) Lipopolysaccharides of Pectobacterium atrosepticum and Pseudomonas corrugata induce different defence response patterns in tobacco, tomato, and potato. 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Am J Essent Oils Nat Products 4(2):27–36 Gardan L, Gouy C, Christen R, Rg S (2003) Elevation of three subspecies of Pectobacterium carotovorum to species level: Pectobacterium atrosepticum sp. nov., Pectobacterium betavasculorum sp. nov. and Pectobacterium wasabiae sp. nov. Int J Syst Evol Microbiol 53(2):381–391 Jones DR, Dowson WJ (1950) On the bacteria responsible for soft rot in stored potatoes, and the reaction of the tuber to invasion by Bacterium carotovorum (Jones) Lehmann & Neumann. Ann Appl Biol 37(4):563–569 Krebs H, Jaggir W (1999) Effect of plant extracts against soft rot of potatoes: Erwiniacarotovora Flora and Fauna n industrial crops. Agrarforschung 6(1):17–20 Kumar S, Tamura K, Jakobsen IB, Nei M (2001) MEGA2: molecular evolutionary genetics analysis software. Bioinformatics 17(12):1244–1245 Lelliott RA, Stead DE (1987) Methods for the Diagnosis of Bacterial Diseases of Plants. Blackwell Scientific Publications, Oxford. p. 216 Lund BM, Wyatt G (1979) A method of testing the effect of antibacterial compounds on bacterial soft rot of potatoes, and results for preparations of dichlorophen and sodium hypochlorite. Potato Res 22(3):191–202 Ma B, Hibbing ME, Kim H-S, Reedy RM, Yedidia I, Breuer J, Breuer J, Glasner JD, Perna NT, Kelman A (2007) Host range and molecular phylogenies of the soft rot enterobacterial genera Pectobacterium and Dickeya. Phytopathology 97(9):1150–1163 Mills A, Hurta R (2006) Sensitivity of Erwinia spp. to salt compounds in vitro and their effect on the development of soft rot in potato tubers in storage. Postharvest Biol Technol 41(2):208–214 Murray RGE, Holt JG (2001) The History of Bergey's Manual. In: Boone DR, Castenholz RW, Garrity GM, editors. Bergey's Manual® of Systematic Bacteriology. Springer, New York Nabhan S, Wydra K, Linde M, Debener T (2011) The use of two complementary DNA assays, AFLP and MLSA, for epidemic and phylogenetic studies of pectolytic enterobacterial strains with focus on the heterogeneous species Pectobacterium carotovorum. Plant Pathol 61(3):498–508 Olivier C, Halseth DE, Mizubuti ES, Loria R (1998) Postharvest application of organic and inorganic salts for suppression of silver scurf on potato tubers. Plant Dis 82(2):213–217 Perombelon MC, Kelman A (1980) Ecology of the soft-rot Erwinias. Annu Rev Phytopathol 18(1):361–387 Rahman MM, Khan AA, Akanda AM, Mian IH, Alam MZ (2013) Chemical control of bacterial soft rot of onion. Bangladesh J Plant Patholol 29(1&2):1–4 Saleh O, Huang J (1997) Bacterial soft rot disease of tomato fruits in Florida, USA: identification, response of some American and Egyptian cultivars of solanaceous plants and chemical control. Assiut J Agric Sci 28(2):11–26 Sambrook J RD (2001) Rapid isolation of yeast DNA. In: DW SJR (ed) Molecular Cloning, a Laboratory Manual. New York: Cold Spring Harbor Laboratory Press, pp 631–632 Shrihari RY, Negi PS (2011) Detection, identification and characterization of staphylococci in street vend foods—characterization of staphylococcus isolates. Food Nutr Sci 2(4):304–313 Simeon AU, Abubakar A (2014) Evaluation of some plant extracts for the control of bacterial soft rot of tubers. Am J Exp Agric 4(12):1869–1876 Toth I, Avrova A, Hyman L (2001) Rapid identification and differentiation of the soft rot Erwinias by 16S-23S intergenic transcribed spacer-PCR and restriction fragment length polymorphism analyses. Appl Environ Microbiol 67(9):4070–4076 Van der Wolf J, De Boer S (2007) Bacterial pathogens of potato. In: Vreugdenhil D, Bradshaw J, Gebhardt C et al (eds) Potato biology and biotechnology: advances and perspectives. Elsevier, Oxford, pp 595–619 Weisburg WG, Barns SM, Pelletier DA, Lane DJ (1991) 16S ribosomal DNA amplification for phylogenetic study. J Bacteriol 173(2):697–703 Yap M-N, Barak JD, Charkowski AO (2004) Genomic diversity of Erwinia carotovora subsp. carotovora and its correlation with virulence. Appl Environ Microbiol 70(5):3013–3023 Yuan F, Qu S, Cui C, Cao MQ, Ma RC (2004) A new strain of Erwinia carotovora subsp. carotovora isolated from soft-rotted Chinese Cabbag. Acta Microbiol Sin 44(2):136–140 Zhu L, Xie H, Chen S, Ma R (2010) Rapid isolation, identification and phylogenetic analysis of Pectobacterium carotovorum ssp. J Plant Pathology 92(2):479–483 The authors would like to thank Dr. Eman O. Hassan, Assoc. Prof. of Plant Pathol., Plant Pathol. Dept., Fac. of Agric. at Moshtohor, Benha Univ., Egypt, Sincere thanks are also given to Moshtohor Research Park, Molecular Biology Lab., Benha Univ., Egypt. Not applicable for this section. Plant Pathology Department, Faculty of Agriculture at Moshtohor, Benha University, Moshtohor, Tukh, Qalubia, 13736, Egypt Mohamed Hamed El-habbak Genetics and Genetic Engineering Department, Faculty of Agriculture at Moshtohor, Benha University, Moshtohor, Tukh, Qalubia, 13736, Egypt Mohamed Hassan Refaat Moshtohor Research Park, Molecular Biology Lab, Benha University, Tukh, Qalubia, 13736, Egypt Search for Mohamed Hamed El-habbak in: Search for Mohamed Hassan Refaat in: All authors equally contributed in all the article parts. All authors read and approved the final manuscript. Correspondence to Mohamed Hassan Refaat. El-habbak, M.H., Refaat, M.H. Molecular detection of the causative agent of the potato soft rot, Pectobacterium carotovorum, in Egypt and essential oils as a potential safe tool for its management. Egypt J Biol Pest Control 29, 5 (2019) doi:10.1186/s41938-019-0104-1 Accepted: 03 January 2019 Pectobacterium carotovorum Molecular detection Nano-cu Safe control	CommonCrawl
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Copyright © 2014, Paul Lutus — Message Page Introduction \| Modeling Biological Growth \| Modeling Nonrenewable Resources \| Analysis \| Technical Note \| References Most recent revision: 08.14.2014 Click here for a PDF version of this article. (double-click any word to see its definition) Figure 1: Peak population with nonrenewable resources This article analyzes a mathematical modeling problem in human population studies. Most mathematical treatments of population include unrealistic assumptions to make the mathematics simple enough to be understandable and useful. One such assumption is an unchanging source of sustenance for a growing population — a population's growth is constrained by a limited resource pool, but, contrary to real-world experience, the resource isn't diminished by its exploitation. In this article I present a mathematical treatment that dynamically models the relationship between a growing population and two kinds of resource commonly seen in real-world environments: renewable and nonrenewable. Renewable resources are those that tolerate being exploited, examples solar energy and wind energy. Nonrenewable resources are those that are depleted by exploitation and eventually vanish, examples oil, minerals obtained by mining, water pumped from a water table at a rate that exhausts the table, and others. By accounting for both renewable and nonrenewable resources, this article's model predicts that the human population will reach a numerical peak and then decline as nonrenewable resources are exhausted (Figure 1). The height of the population peak above the ultimate stable population size, the velocity of the change in population and the eventual sustainable population value depend on the rate of exploitation of nonrenewable resources and the ratio of renewable to nonrenewable resources. The model accepts values for these quantities and predicts outcomes on that basis. The idea of a population peak isn't original, but this article mathematically quantifies such a peak, using an algorithm based on the Logistic function expanded to accommodate the effect on population of nonrenewable resources. This issue has a serious side. Unless corrective steps are taken, if nature is allowed to run her course, the post-peak decline in human numbers shown in Figure 1 may prove to be one of the worst catastrophes in human history. The alternative is a planned, gradual reduction in our numbers through voluntary population control measures, for which the Chinese one-child policy might serve as a model. This article relies on mathematics to make its points. Readers with no interest in mathematics can skip over the mathematical sections but, by examining the graphs and text, can still follow the article's key points. (I had considered breaking this article into a nonmathematical section followed by a more technical exposition, an approach taken in some of my other articles, but the ideas presented are too dependent on mathematics for this to be practical.) Modeling Biological Growth This section describes a mathematical model able to predict the behavior of an environment composed of a growing population and a mix of renewable and nonrenewable resources. It is derived from earlier mathematical work meant to model populations, in particular the Logistic function. The Logistic function is limited to describing the relationship between a growing population and a fixed resource limit, an approach having the advantage of being relatively simple, but with the drawback that it cannot accurately model many real-world biologiocal systems. Simple Growth For the benfit of curious readers I intend to offer a detailed explanation of this class of mathematical model, by building progressively from the simplest mathematical expressions. Again, readers with no interest in mathematics may skip over these parts of the article and still understand the points made with the graphs and text. A growth pattern called simple growth shows a linear increase over time. A typical function would be: (1) $p(t) = (1 + r) t$ $p(t)$ = population at time t $r$ = rate of increase in population $t$ = time in consistent units Here's a graph of equation (1): $r$ = 0.5 Figure 2: Linear growth Compound Growth Equation (1) is simple and easy to understand, but biological populations grow in a different way. Because each member of a growing population can join in procreation, any increase in population is compounded over time, with an exponentially increasing source of new members. This is called compound growth or exponential growth. A typical function would be: (2) $p(t) = p_0 (1+r)^t$ $p(t)$ = population at time t. $p_0$ = population at time zero. $r$ = rate of change per unit of time. $t$ = time in consistent units. $p_0$ = 1 \| $r$ = 0.5 Figure 3: Exponential growth Constrained Growth Equation (2) models a population increase unconstrained by resource limitations, one that can expand indefinitely. But in the real world, any such population growth must eventually collide with limited resources. The classic way to model the role of environmental limitations is to apply the Logistic function: (3) $ \displaystyle p(t) = \frac{k p_0 e^{r t}}{k+p_0 (e^{r t}-1)}$ $k$ = environmental carrying capacity. $r$ = population growth rate. About equation (3) it is important to note that: (4) $\displaystyle \lim_{t \to \infty} p(t) = k$ In other words, over time the population $p(t)$ converges on the environmental carrying capacity $k$. $p_0$ = 1 \| $k$ = 100 \| $r$ = 0.1 Figure 4: Constrained growth Examine the graph of equation (3). At the left (0 <= t <= 40), the curve shows the unconstrained growth of equation (2). In the middle the growth rate becomes linear as resource limitations become important, and at the right (60 <= t <= 100), environmental constraints prevent a population greater than carrying capacity k. Modeling Nonrenewable Resources Above we modeled population growth in the classic way, by setting a fixed resource limit / upper population bound. In this section we will model a system having a mixture of renewable and nonrenewable resources. This system has the following properties: Population increase follows the general pattern set out above — an exponential increase until resource limitations prevent further growth. A renewable carrying capacity $k_r$ exists as in equation (3) above, a value that does not change. A nonrenewable carrying capacity $k_n$ behaves in much the same way as $k_r$, except that over time the increasing population exhausts it, usually reducing it to zero. The presence of a nonrenewable capacity allows an unsustainable population peak that must eventually decline along with the nonrenewable resources (Figures 1 and 6). The long-term outcome should agree with equation (3), i.e. $ \displaystyle \lim_{t \to \infty} p(t) = k_r$. Because of the complexity of this system, and because one of the variables ($k_n$) declines to zero and then stops changing, there's no closed-form expression to describe it — it must be modeled numerically. For maximum portability I've chosen Python to express the numerical algorithm. Here's an excerpt from a Python program able to model the described system (click here for the full listing): kr = 100 # renewable carrying capacity kn = 300 # nonrenewable carrying capacity nr = .04 # nonrenewable rate of consumption p = 1 # initial population r = .05 # population growth rate per period for t in range(101): p = 1 + r (kn+kr-p)/kr # see note 2 below kn = max(kn-p * nr,0) # see note 3 below If the nonrenewable capacity value is set to zero, the above numerical algorithm produces essentially the same results as the closed-form Logistic function, for given input values and using suitably small increments of time. This code line increases the population size by the rate of increase multiplied by a normalized capacity value from which the prior population size has been subtracted. This code line reduces the nonrenewable capacity value $k_n$ in proportion to population, times a nonrenewable consumption constant $n_r$. Over time this reduces the nonrenewable capacity value to zero, after which the max() function prevents it from falling below zero. Here's a graph of the result generated by this Python program: Renewable capacity \| Nonrenewable capacity \| Population $p_0$ = 1 \| $k_r$ = 100 \| $k_n$ = 300 \| $n_r$ = 0.04 \| $r$ = 0.05 Figure 6: Peak population Interested readers are encouraged to run the provided program and change its values to see how this changes the modeled outcome. Again, if $k_n$ is set to zero and if sufficiently small time steps are used, the algorithm's results converge with that from the closed-form Logistic function, showing that it accurately reflects the outcome of the classic population function. Now that we can use cheap computer power to model the real-world dynamics created by a mixture of renewable and nonrenewable carrying capacity, we should choose realistic values for the model. What's the true ratio of renewable ($k_r$) to nonrenewable ($k_n$) capacity? How much nonrenewable capacity consists of luxuries and how much is critical to human survival? What's the true consumption rate ($n_r$) for nonrenewable capacity? None of these questions have clear answers. The model presented here can generate useful predictions, but only with reliable values for its parameters. Unfortunately, virtually every aspect of this issue is distorted by politics and emotion. One regularly hears claims about future human numbers without discussing sustainability, and without acknowledging that we may already be beyond a sustainable human population size. Recent population studies conclude that the present (2014) human population may be as much as three times its sustainable value, which means the example graphs in this article may accurately reflect our future. Population and birthrate are classic examples of problems that are easy to state but very difficult to solve. History teaches us that large-scale social solutions to population problems tend to be undermined by partisan politics and racism. It's my view that individual choices, accompanied by full rights and universal education, are the only civilized solutions to this problem. There's a technical issue that's not addressed in the above exposition, and that is the identity of the new function. If this new function is a consistent extension of the Logistic function with an added nonrenewable resource term, then by setting the initial nonrenewable value to zero it should produce the same results as the classic Logistic function. If the new function were expressible in closed form, the task of demonstrating the relationship between the two functions would be much easier, but the Logistic function is a classic closed-form solution to a differential equation, and the new function is a numerical differential equation, an algorithm, that is inexpressible in closed form. This means a comparison between the two functions must be carried out numerically, by comparing results rather than equations. In this section I will numerically compare the results for the classic and revised functions. To acquire a meaningful comparison, I will run the algorithm with many very small increments, and show a sample of comparisons between the revised function and the classic Logistic function. The logic behind a large number of increments is that, as one approaches an infinite number of infinitesimal steps, the relationship between a summation and a definite integral converge: (5) $ \displaystyle \displaystyle \lim_{n \to \infty} \frac{b-a}{n+1} \sum_{x = 0}^n f((b-a)\frac{x}{n}+a) = \int_a^b f(x)\, dx$ For this Python test program, we get this result: t \|1-a/b\| 0 0.00000099 1000000 0.00000050 10000000 0.00000001 t = Time argument. \|1-a/b\| = Absolute difference (error value) between classic Logistic function result and that for the extended Logistic function presented here. In further tests, as the number of iterations is increased, the results show a convergence between the classic and extended forms of the Logistic equation. Logistic Function — a key mathematical method used to model growing populations. Exponential Growth — also known as compound growth. One-child policy — a moderately successful Chinese population control program. Human overpopulation \| Carrying capacity — this article suggests that the present (2014) human population may be three times greater than a sustainable value.	CommonCrawl
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Highly Sensitive Tri-Path Photonic Crystal Fiber Plasmonic Sensor Based on Hybrid Layer of Gold / Platinum Diselenide Vijayalakshmi Dhinakaran, C.T. Manimegalai, Natesan Ayyanar, Truong Khang Nguyen, and 1 more https://doi.org/10.21203/rs.3.rs-419957/v1 Read the published version in Optical and Quantum Electronics → posted 16 Apr, 2021 Platinum Diselenide, PtSe2 is becoming highly trending owing to its fascinating optoelectronic, thermoelectric and semiconductor properties. They are non-toxic, chemically inert and allow high biomolecule absorption which makes them highly applicable in sensors to boost the sensing performance. Here, we propose Surface Plasmon Resonance (SPR) based Photonic Crystal Fiber (PCF) sensor for enhanced refractive index sensing at mid infrared wavelengths. In order to achieve this, tri-path PCF coated with hybrid layer of gold/PtSe2 which allows light to travel freely through the cladding and interact with the plasmonic material to create strong coupling effect. Finite Element Method is used for numerical examination and investigation of the sensing performance for the designed tri-path sensor. The optimized proposed sensor exhibits maximum wavelength sensitivity of 42,000 nm/RIU and maximum wavelength resolution of 2.4 x 10-6 within the analyte range from 1.33 to 1.38, which almost covers the unknown analytes of chemical, bio and gas. Further, we achieve very low loss and unique design to accomplish high sensitivity which makes it applicable to be a future candidate in various sensing applications. Cell Communication and Signaling Surface Plasmon Resonance Tri-path photonic crystal fiber Coupling effect Platinum Diselenide Photonic Crystal Fiber (PCF) is highly trending in photonics which is a single material providing a platform for sensing (Wei et al. 2013). They offer high design flexibility which creates high birefringence, high confinement field, endlessly single material, tunable dispersion, compact sensing and many more. When this PCF material is combined with plasmonic science, high sensitivity results will be achieved which paves way for being a potential future candidate in various fields (Vigneswaran et al., 2018). Surface Plasmon Resonance (SPR) is a promising sensing technique that detects the minimum variation in refractive index (RI) when there is an interaction with the metal film. They expose high sensitivity results which makes it trending and highly applicable in various sensing fields. As SPR is label free and real time detection process which produces high sensitivity, intensive research curiosity for the scientists has been highly stimulated for making more advancements in the sensors (Rahman et al., 2020). They are growing tremendously from the scientific region as there are extensive applications that also include temperature monitoring (Luan et al. 2017), multi analyte sensing (Otupiri et al., 2015), biosensing (Akowuah et al., 2012), liquid sensing (Kaur et al., 2019), disease diagnosis (Jabin et al., 2019) and many more. The most popularly used plasmonic is gold as it is chemically stable, provide long resonant shift, biocompatible and is prone to oxidation (Singh et al., 2020 & Hasan et al. 2017). Lately, along with the plasmonics, flimsy oxide layers are added such as aluminium oxide (Al2O3), indium-tin oxide (ITO), titanium dioxide (TiO2) to elevate the sensing performance of the sensor. They assist in robust SPR effect which aid to improve the sensing range along with sensitivity for the sensor (Mahfuz et al., 2019). But these plasmonics and additional coating layers also face a drawback where they have very low biomolecule absorption capability in biosensors. To defeat this drawback, it was suggested to use biomolecule recognition elements as Transition Metal Dichalcogenide (TMDC) materials along with the plasmonics (Singh et al., 2020). TMDC materials are also known as 2D materials which is a huge family that have intriguing features and unique structure that have made them highly attractive and significant in various industrial applications owing to its capability for biomolecule recognition and sensitivity enhancement (Wu et al., 2016). 2D materials limit the transport of heat and charge in their unique layered structure which is an exceptional property capable, making them enticing for optoelectronic and electronic applications (Gong et al., 2020). One of the leading factors for determining the properties and applications in 2D materials is the bandgap. These 2D materials have tunable finite band gap which make them to be a promising candidate in numerous applications (Zhang et al., 2020). These materials exhibit exclusive properties as large absorption of light, high charge mobility and transitional behavior which build them more appropriate for fabricating high performance electronic and optoelectronic devices (Guo et al., 2020). Graphene was the first man-made and discovered 2D nanomaterial in 2004. Due to its inter-band transition, it exposes good optical conductivity from near to mid infrared frequency, produces huge surface to volume ratio aiding high biocompatibility (Singh et al., 2020). There are many other 2D materials as MoS2 (Radisavljevic et al., 2011), WO3 (Wang et al., 2014), WS2 (AlaguVibisha et al., 2016), PtSe2 (Xie et al., 2019), etc which are recently trending in the research field. These materials have excellent properties as optical, thermal, electronics, optoelectronics, catalytic, super conductivity and energy-storage (Zhang et al., 2020). The investigation and analysis of the 2D materials along with its properties was first initiated by coating them over the prism as sensors (Ouyang et al., 2016). In 2016, highly sensitive prism based SPR sensor was reported using 2D materials. It is heterostructured configuration where the arrangement was made as MoS2/Aluminium/MoS2/Graphene. The sensor exposes a maximum sensitivity of 190.83 ͦ /RIU (Wu et al., 2016). Specifically, Platinum Diselenide (PtSe2) is a group ten monolayer material in 1T phase and it is highly preferred owing to their exclusive features (Guo et al., 2020). They resemble the structure of phosphorene and graphene and also reveals admirable thermoelectric, optoelectronic and semiconductor properties making it more unique. Owing to its robust interlayer interaction, the 2D material PtSe2 exposes high tunable bandgap. Moreover, this material is observed to have good chemical stability with also less toxic which makes it highly applicable for practical usage (Jia et al., 2020). Recently, a sensor was proposed where PtSe2 was selected to attain maximum Goos-Hanchen shift. The sensor has gold and titanium coating along with PtSe2 and three layers of graphene is added in BK7 prism. The results revealed the Goos-Hanchen shift sensitivity shows an increment four times when compared with the plain gold coating. The detection limit is very low as 5 x 10−7 RIU which is diminished by 2 order of magnitude and sensitivity elevates by 1000-fold when compared with plain gold coating (Guo et al., 2020). Hence, 2D material based SPR sensors are recommended for RI sensing as they exhibit highly improved sensitivity (Jia et al., 2020). The PCF combined with SPR sensing method along with various additional coating materials were investigated extensively as it was perceived to reveal superior sensitivity for the sensors. In 2016, SPR combined with D-shape PCF was mentioned with plasmonic metal employed as gold and additional coating layer of ITO for RI ranging from 1.28 to 1.34. The sensor gains a high sensitivity of 6000 nm/RIU (Huang et al., 2017). In 2018, PCF combined with SPR sensor was reported with bimetallic coating of new plasmonic material as niobium nanofilm along with additional covering of flimsy Al2O3 for organic and biochemical sensing. The sensor functions for analyte RI 1.36 to 1.41 and reveals a maximum sensitivity of 8000 nm/RIU (Hasan et al., 2018). Highly birefringent and simple design PCF-SPR was presented with gold as plasmonic and TiO2 as additional thin layer forming the bimetallic structure. The sensor operates for RI range from 1.33 to 1.38 and exposes a high sensitivity of 25,000 nm/RIU making it highly suitable in numerous sensing applications (Islam et al., 2019). Recently, dual core PCF-SPR sensor with bimetallic coating layers of gold and TiO2 was described for numerous biochemical analytes and bio-organic molecules RI detection. The sensor functions for analyte RI range of 1.33 to 1.42, disclosing a maximum sensitivity of 28,000 nm/RIU (Al Mahfuz et al., 2020). But these plasmonics with additional layers have low capability of biomolecule absorption. So, 2D materials were recommended to be used as additional covering layers along with plasmonics over PCF as they are excellent in biomolecule recognition (Singh et al., 2020). The real time PCF based modal interferometer was mentioned for auditing the concentration of dissolved hydrogen in the transformer oil. The sensor was coated with Pd/WO3 film over PCF by employing dip-coating technique. For the range 0–10 000 µl/l, the sensitivity acquired is 0.109 µl/l with response time below 33 minutes (Zhang et al., 2016). Further, D-shape PCF was described with monolayer MoS2 which was accumulated at the plane surface to boost the sensitivity of the sensor. The sensor functions for analyte RI range of 1.33 to 1.36 and attains a maximum sensitivity of 2000 nm/RIU (Nivedha et al., 2017). In 2019, PCF sensor combined with SPR was presented where thin film of gold was employed as the plasmonic along with flimsy graphene layer for detection of RI in liquid sample. The sensor operates for analyte RI range from 1.33 to 1.38. With the addition of graphene layer, the sensor improvises by 84.66% and reveals a maximum sensitivity of 8600 nm/RIU (Lou et al., 2019). Lately, a D-shaped PCF-SPR sensor with coating layers of gold/MoS2/graphene was reported. The sensor was applicable for biomedical and biochemical analyte detection for the analyte RI ranging from 1.33 to 1.40. The sensor exposes a maximum sensitivity of 14,933.34 nm/RIU (Singh et al., 2020). The above reported papers along with additional layer covering exhibit high loss and less sensitivity. So, for the first time in this work, 2D material PtSe2 is integrated through plasmonics over the outer surface of PCF to upsurge the sensitivity which reveals the novelty for this work along with which the designed tri-path sensor exposes a low loss. We present a tri-path PCF sensor which is integrated with PtSe2 through plasmonic gold to achieve high sensitivity for the designed sensor. The tri-path structure is introduced for the evanescent field to move freely through the cladding and interact with the metal region to create strong plasmonic coupling effect. This assists in reaching enhanced sensitivity for the designed sensor. External sensing is approached which removes the fabrication complexities for the sensor. Gold along with PtSe2 is employed as it reveals excellent sensitivity and unique properties which make the sensor a potential future candidate in many fields. The next, Sect. 2 discusses about the design and its novelty. Further, in Sect. 3, the coupling characteristics and results will be mentioned. Finally, in Sect. 4, the optimizations done for the geometrical parameters will be elaborately discussed. 2 Structural Design The schematic view of designed tri-path PCF sensor is displayed in Fig. 1. There are two air hole rings present which are organized in hexagonal lattice. The center air hole along with three air holes from first ring are removed. Further, three air holes from second ring are also scaled down. This arrangement is done for light to travel in an effective path. This arrangement leads to the formation of tripath structure which paves way for the light to travel easily. The guided evanescent field from core move freely through the cladding and strikes the metal region, creating strong coupling effect. This boosts the sensing performance of the designed tri-path PCF sensor making the sensor to attain high sensitivity. The diameter of big sized air hole, d is 1.4 µm and the diameter of scaled down air hole is symbolized as ds which is 0.2 µm. Pitch is represented as Λ which is the distance from center of one air hole to another. Silica is used as the background element for the designed sensor whose RI is dependent on wavelength and expressed using Sellmeier equation (Ayyanar et al., 2018); $${n}^{2}=1+ \sum {i=1}^{3}\frac{{N}{i}{\lambda }^{2}}{{\lambda }^{2}-{\lambda }_{i}^{2}} \left(1\right)$$ where refractive index of silica is denoted by n, λi and Ni are the appropriate constants, where λ1 = 0.0684043, λ2 = 0.1162414, λ3 = 9.8961611 and N1 = 0.6961663, N2 = 0.4079426, N3 = 0.8974794. The plasmonic material preferred for the designed sensor is gold whose thickness is denoted as tg = 40 nm. Drude Lorentz model is used to obtain the dielectric gold constant which is expressed as (Vial et al., $${\epsilon }{gold}\left(\omega \right)={\epsilon }{\infty }-\frac{{{\omega }{D}}^{2}}{\omega (\omega +i{\gamma }{D})}-\frac{ \varDelta \epsilon .{\varOmega }{L}^{2}}{\left({\omega }^{2}-{\varOmega }{L}^{2}\right)+i{\varGamma }_{L}\omega }$$ where, the permittivity of gold is εgold, angular frequency is ω = 6.283c/λ, ε∞ = 5.9673 is high frequency permittivity, and Δε = 1.09 is the weighing factor. The damping frequency and plasma is denoted as γD = 2π 15.92 THz and ωD = 2π 2113.6 THz respectively. Moreover, oscillator strength is ΩL = 2π650.07 THz and the spectral width is ΓL = 2π104.86 THz of the Lorentz oscillators. Gold is applied with the help of various methods as thermal evaporation (Barnes et al., 2000), wet chemistry deposition (Sioss et al., 2005) and radio sputtering technique (Armelao et al., 2005). These methods result in extreme surface roughness which diminishes the usage of these coating methods. To solve the issue of rough uneven surface, another coating method known as chemical vapour deposition (CVD) (Sazio et al., 2006) is employed which offers minimum roughness along with even coating on the surface. Further, PtSe2 was glazed over the plasmonic gold metal whose thickness is taken to be 4 nm. The RI for PtSe2 is obtained from the cited paper (Guo et al., 2020) which involves both real and imaginary parts. Gold is applied at the outer region of PCF along with PtSe2 and sensing analyte by approaching external sensing technique which removes the fabrication complexities. Perfectly Matched Layer (PML) along with scattering boundary conditions are added which protects from removing the radiant energy from fiber axis. Further, numerical study is done through Finite Element Method (FEM) which is associated with COMSOL Multiphysics software and results are discussed in upcoming sections. The proposed model sensing mechanism is based on the coupled mode theory (Ayyanar et al., 2018) which takes place amongst the evanescent field from the core mode that interacts with plasmonic mode at gold/Ptse2 layer to produce robust coupling effect. Figure 2 illustrates the electric field distribution where figure 2(a) as well as (b) displays the field distribution for fundamental core mode and plasmonic mode. Figure 2(c) reveals the coupling effect for the analyte 1.36. The designed tri-path sensor functions for the sensing range from 1.33 to 1.38 where the shift in wavelength and variation in peak intensity is observed when the analyte RI is varied. Figure 3 illustrates the dispersion relation and loss spectrum of core mode and plasmonic mode. When the interaction takes place amidst the fundamental core and SPP mode, phase matching condition occurs at a specific wavelength which is termed as resonant wavelength. The confinement loss is calculated by (Xie et al., 2019); where, λ indicates the input wavelength in microns, the effective RI of the imaginary part is signified by Im (neff) and k0=2π/λ denotes free space number. Maximum loss peak is attained in this resonant wavelength and while shift occurs in this wavelength towards shorter or longer wavelength, the anonymous sample can be detected. By the collision within core and SPP mode for the designed tri-path sensor, the maximum peak reached is 14.10 dB/cm at the wavelength 0.84 µm for the analyte 1.36. Figure 4 depicts the loss spectrum for analyte RI varied from 1.33 to 1.38. The peak loss attained for the designed tri-path sensor with gold/PtSe2 layer coating is 1.36 dB/cm, 2.14 dB/cm, 2.76 dB/cm, 2.97 dB/cm, 4.55 dB/cm and 12.82 dB/cm at their corresponding resonance wavelength 0.72 µm, 0.74 µm, 0.79 µm, 0.85 µm, 0.96 µm and 1.38 µm respectively. This shows that the loss attained for the designed sensor is also very low making it more efficient and practical. Figure 5 portrays the polynomial fit characteristic analysis for analyte RI altered from 1.33 to 1.38 for the designed tri-path sensor with coating of gold/PtSe2. For this range, the degree relation amidst the resonant wavelength and analyte RI is estimated by R2. The R2 value acquired for the designed tri-path sensor is 0.91438. High polynomial regression charecteristic is revealed which proves the quality of the designed tri-path sensor that can be employed for precise analyte RI identification. Wavelength ssensitivity is significant parameter that is employed to calculate the sensing performance for the designed tri-path sensor. The wavelength sensitivity is estimated by (Chakma et al., 2018); Where Δna is change in RI of analyte and Δλpeak is the discrepancy in shift of wavelength peak. The wavelength sensitivity calculated and obtained for the designed tri-path sensor with gold/PtSe2 coating is 2000 nm/RIU, 5000 nm/RIU, 6000 nm/RIU, 11,000 nm/RIU and 42,000 nm/RIU for its corresponding RI analyte 1.33, 1.34, 1.35, 1.36 and 1.37. Further, resolution is another important parameter that is needed to measure the sensing performance of the designed sensor. It is the efficiency to sense slight alterations in RI of analyte and is realized by (Haider et al., 2018); where, Δλmin is 0.1 nm which denotes the minimum spectral resolution which, Δλpeak denotes the difference in wavelength amongst the loss peak shift and Δna is 0.01 which denotes the analyte RI alteration. From simulation and result analysis, we observe that the maximum sensitivity attained for designed tri-path sensor is 42,000 nm/RIU along with maximum wavelength resolution of 2.4 x 10-6 RIU for the analyte 1.37. Table 1 gives the synopsis of sensing performance of designed tripath sensor for the RI of analyte altered from 1.33 to 1.38. Table 1: Sensing performance synopsis of designed tri-path sensor with gold/Ptse2 for analyte RI altered from 1.33 to1.38. Analyte RI Resonance Peak Wavelength (µm) Peak loss (dB/cm) Peak wavelength shift (µm) Wavelength Sensitivity (nm/RIU) Wavelength Resolution (RIU) 5.0E-05 Further optimizations and its analysis are done with coating of gold/PtSe2 layer where the geometrical parameters are scrutinized and adjusted to attain high sensitivity for the designed tri-path sensor. The scrutiny of optimization and its results are discussed elaborately below. Primarily, the values of parameters were considered scaled down air hole diameter (ds) as 0.2 µm, as diameter of big air hole is 1.4 µm, gold layer thickness of gold coating (tg) as 40 nm and PtSe2 thickness as 4 nm. These parameters are scrutinized and investigated to achieve maximum sensitivity for the designed tri-path sensor. The scaled down air hole diameter is optimized as 0.2 µm, 0.3 µm and 0.4 µm for analyte RI 1.36 and 1.37 respectively. The effect of this alteration is illustrated in Figure 6. The obtained loss peak for analyte 1.36 is 37.68 dB/cm, 14.10 dB/cm and 6.24 dB/cm and for analyte 1.37 it is attained as 50.47 dB/cm, 20.54 dB/cm and 9.27 dB/cm. It is evident from this investigation that the loss spectrum for analyte 1.36 transpires at 0.84 µm and for analyte 1.37 it occurs at 0.93 µm. It is noticed that the loss occurs at the same resonant wavelength for the RI 1.36 and 1.37 as mentioned above where there is no wavelength shift revealed for these alterations made. The main purpose of the scaled down air hole is to create path for the light to interact with the plasmonic region and elevate the coupling effect. So, the size of the scaled down air hole cannot be incremented above certain value as it will diminish the space for the light to pass through which will weaken the coupling effect and reduce the sensing performance of the designed sensor. Thus, we choose optimum value of 0.4 µm as the scaled down air hole diameter which is low peak loss for the designed tri-path sensor. Next, the ratio amongst the diameter of big air hole and pitch (d/Λ), was modified and analyzed for analyte RI 1.36 and 1.37 as 0.8 µm, 0.85 µm and 0.9 µm. The examinations were done for the mentioned modifications where loss peak of 5.67 dB/cm, 4.97 dB/cm and 6.24 dB/cm was attained for the analyte RI 1.36 at wavelength of 0.76 µm, 0.79 µm and 0.84 µm. Similarly, for analyte 1.37, the loss peak attained is 8.22 dB/cm, 7.38 dB/cm and 9.27 dB/cm at wavelength of about 0.81 µm, 0.85 µm and 0.93 µm respectively. The modification in d/Λ is depicted in Figure 7. From this scrutiny, we can observe that the wavelength swings towards longer wavelength which is termed as red shift. The shift takes place from 0.76 µm to 0.84 µm and 0.81 µm to 0.93 µm for analyte RI 1.36 and 1.37 respectively. The obtained wavelength sensitvity is 5000 nm/RIU for 0.8 µm, 6000 nm/RIU for 0.85 µm and 9000 nm/RIU for 0.9 µm. We can conclude from the results that the highest wavelength sensitivity is reached for 0.9 µm as 9000 nm/RIU which is decided to be the optimum value. Further modifications and elevations cannot be done for d/Λ as the designed tri-path sensor does not allow design flexibilty above this. So, from scrutiny, we opt 0.9 µm as the ratio amongst diameter of big air hole and pitch for further study. The further study analysis is done for changes in thickness of gold layer tg. For analyte RI 1.36 and 1.37, the changes done in tg is 30 nm, 40 nm and 50 nm. The results are displayed in Figure 8. It is noticed that the loss peak obtained is 10.91 dB/cm, 6.24 dB/cm and 2.97 dB/cm for analyte RI 1.36 at 0.8 µm, 0.84 µm and 0.85 µm respectively. This shows that as thickness of gold rises, the loss decreases correspondingly. Further, for analyte 1.37, the loss peak reached is 16.81 dB/cm, 9.27 dB/cm and 4.55 dB/cm at 0.88 µm, 0.93 µm and 0.96 µm respectively. The shift is observed to move towards larger wavelength from 0.8 µm to 0.85 µm and from 0.88 µm to 0.96 µm for analyte RI 1.36 and 1.37 respectively. This exposes that red shift takes place and loss peak correspondingly diminishes when thickness of plasmonic gold covering layer is incremented. For the changes made in tg as 30 nm, 40 nm and 50 nm, the wavelength sensitivity gained is 8,000 nm/RIU, 9,000 nm/RIU and 11,000 nm/RIU. So it is revealed from the investigation that highest wavelength sensitivity is gained as 11,000 nm/RIU for 50 nm thickness which is preferred as the optimum value after optimization analysis and study. The thickness should be selected in right amount for efficient functioning of the sensor. If the thicknesss is too low, then the plasmonic effect will be very less which will not be applicable for coupling to transpire. Similarly, if the thickness is surged too high, then the plasmonic effect would get very robust which would weaken the coupling effect as the evanescent field decays while reaching the thick plasmonic coating and highly increment the loss. Thus, precise thickness should be opted for the designed sensor to make the sensor operate efficiently. Hence, we select 50 nm as thickness of gold coating for further analysis. The final scrutinization is for the thickness of PtSe2 material. The thickness of PtSe2 is adjusted as 2 nm, 4 nm and 6 nm for analyte RI 1.36 and 1.37. The loss acquired is 2.66 dB/cm, 2.97 dB/cm and 3.27 dB/cm for the analyte RI 1.36 at 0.78 µm, 0.85 µm and 1 µm respectively. Similarly, at 0.82 µm, 0.96 µm and 1.06 µm the loss peak attained is 4.26 dB/cm, 4.55 dB/cm, 4.43 dB/cm for analyte 1.37 respectively. This is portrayed in the Figure 9. It is noticed that the wavelength swings towards larger wavelength for both RI of analyte 1.36 and 1.37 from 0.78 µm to 1 µm and from 0.82 µm to 1.06 µm respectively which depicts the red shift occurance. Further, wavelength sensitivity has been estimated for the adjustmaents made with thickness of PtSe2 material as 2 nm, 4 nm and 6 nm as 4000 nm/RIU, 11,000 nm/RIU and 6000 nm/RIU. From this we can conclude that for 4 nm of PtSe2 thickness, maximum sensitivity of 11,000 nm/RIU is attained. The thickness of 2D material, PtSe2 is fixed to be 4 nm as it exposes the maximum sensitivity for the designed tri-path sensor. The other optimizations of 2 nm and 6 nm reveal a lower sensitivity when compared to 4 nm. Hence, we decide 4 nm as thickness of PtSe2 material. Finally, we have completed the optimization analysis and have selected the optimized parameters as ds = 0.4 µm, d/Λ = 0.9 µm, tg = 50 nm and Ptse2 thickness = 4 nm with which the designed tri-path sensor reaches maximum sensitivity as 42,000 nm/RIU. Moreover, we have examined the sensing performance of the designed tri-path sensor by eliminating the PtSe2 coating layer. Figure 10 portrays the loss spectrum for analyte RI varied from 1.33 to 1.38 for the designed tri-path sensor without PtSe2 coating. At wavelength 0.63 µm, 0.64 µm, 0.66 µm, 0.69 µm, 0.74 µm and 0.84 µm the loss obtained for the designed sensor when PtSe2 material is detached is 1.47 dB/cm, 1.79 dB/cm, 1.90 dB/cm, 3.07 dB/cm, 3.47 dB/cm and 5.78 dB/cm respectively. Figure 11 portrays the polynomial fitting analysis for analyte RI altered from 1.33 to 1.38 for the designed tri-path sensor when PtSe2 material is removed and attained R2 value is 0.98267. The wavelength sensitivity is 1000 nm/RIU, 2000 nm/RIU, 3000 nm/RIU, 4000 nm/RIU and 11,000 nm/RIU for analyte RI 1.33, 1.34, 1.35, 1.36 and 1.37 respectively. Through this simulation and study analysis, we can witness that the sensitivity attained for designed tri-path sensor with no PtSe2 material is 11,000 nm/RIU with maximum wavelength resolution of 1 x 10-5 for the analyte 1.37. Table 2 gives an overall sensing performance of designed tripath sensor when PtSe2 material is removed for the RI analyte ranging from 1.33 to 1.38. Table 2: Overall sensing performance of designed tri-path sensor with no PtSe2 material coating for analyte RI varied from 1.33 to 1.38. While comparing both the performances of designed tri-path sensor with gold/PtSe2 layer and when PtSe2 coating layer is removed, we can conclude from the investigation done that the sensing performance is highly enhanced while 2D material PtSe2 is added. While gold/PtSe2 layer is glazed, the sensitivity reaches much higher sensitivity of 42,000 nm/RIU. Further, there is also a shift that takes place towards larger wavelength with gold/PtSe2 coating layer. The entire wavelength spectrum for gold/PtSe2 layer coating ranges from 0.72 µm to 1.38 µm which aids the sensor to operate in mid infrared frequency owing to its inter-band transition. The wavelength spectrum range when PtSe2 coating layer is eliminated for the designed tri-path sensor occurs from 0.63 µm to 0.84 µm respectively. Table 3 is displayed below which gives a ephemeral comparitive study about previously done research works with various materials used for additional coating layer along with our designed tri-path sensor which is intergrated with PtSe2 material through plasmonic gold. From this study analysis, we can conclude that the designed tri-path sensor reaches maximum sensitivity along with low loss which makes it to be anticipated as a budding applicant in various sensing domains. Table 3: Comparitive study of previously reported research works with different materials for additional coating layer with designed tri-path sensor intergrated with PtSe2 through plasmonic gold. Structure Types Range of RI (dB/cm) Wavelength Sensitivity (nm/RIU) Wavelength Resolution (RIU) D-shape PCF with gold/MoS2/graphene (Singh et al., 2020) 6.69 x 10-6 Dual core PCF with gold/Tio2 (Al Mahfuz et al., 2020) Four channel PCF with gold /Tio2 (Islam et al., 2019) PCF with gold /2D graphene (Lou et al., 2019) Two open channels PCF with silver/gold ( Liu et al., 2020) Tri-path sensor with gold/PtSe2 [ proposed work] 2.4 x 10-6 We propose a tri-path PCF intergrated with SPR sensor along with gold/PtSe2 coating layer. The sensor is simple in design where tri-path is formed to make the light pass through the cladding in the scaled down path and interact with the plasmonic surface which produces enhanced coupling effect. FEM is employed for analyzing the sensing performance and numerical simulation investigation for the deisgned tri-path sensor. Gold/PtSe2 coating layer for the designed tri-path sensor reveals superior sensing performance when compared with removal of PtSe2 coating layer. They are externally coated over the PCF which makes the sensor economical and reduces the difficulties faced by fabrication. The proposed sensor shows an excessive rise in wavelength sensitivity as 42,000 nm/RIU with maximum resolution of 2.4 x 10-6 RIU in range of RI analyte 1.33 to 1.38. Further, when study was done where PtSe2 layer coating was removed, the sensor attains sensitivity of 11,000 nm/RIU along with resolution of 1 x 10-5 RIU. The simple designed tri-path sensor also achieves low loss which makes it highly applicable and potential candidate in various fields. Funding : No funding was received to assist with the preparation of this manuscript. Conflicts of interest/Competing interests : The authors have no conflicts of interest to declare that are relevant to the content of this article. 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Parametric study of glycerol and contaminants removal from biodiesel through solvent-aided crystallization Mohd. Afnan Ahmad1,2, Arun Letchumanan1, Shafirah Samsuri ORCID: orcid.org/0000-0001-9395-99201,2, Wan Nur Athirah Mazli1,2 & Juniza Md Saad3 At present, biodiesel is known as an alternative fuel globally. It is also known that the purification of biodiesel before consumption is mandatory to comply with international standards. Commonly, purification using water washing generates a massive amount of wastewater with a high content of organic compounds that can harm the environment. Therefore, this study applied and tested a waterless method, i.e., the solvent-aided crystallization (SAC), to remove glycerol and other traces of impurities in the crude biodiesel. The parameters of coolant temperature, crystallization time, and stirring rate on the SAC system were investigated. It was discovered that with 14 °C coolant temperature, 300 RPM and higher cooling time result in the highest percentage of FAME up to 99.54%, which indicates that contaminants' presence is limited in the purified biodiesel. The use of 1-butanol as the solvent for crystallization process remarkably enhanced the separation and improved the higher biodiesel quality. The rise in the economy concerning transportation as well as environmental awareness leads to the use of petroleum-derived fossil fuels. The term biodiesel is referred to as renewable and biodegradable fuel that functions as an alternative in traditional engines (Tyson and McCormick 2006). Vegetable oil, animal fats, and waste cooking oil can be used as feedstock in producing biodiesel such as soybean oil (55%), canola oil (10%), corn oil (12%), recycled used cooking oils, and yellow greases (13%) in the United States in 2016 (Ambat et al. 2018). Oils from rapeseed, sunflower, palm kernel, and animal fats such as beef tallow and pork lard are also considered significant sources to produce biodiesel. To reserve the decreasing of traditional world fuel and promote sustainability to avoid environmental effects, biodiesel is preferred, and it has served as a prominent alternative source of fuel. Compared to petroleum fuel, the use of biodiesel also reduces the greenhouse effects, which can minimize the threat of global warming. Other than that, gasses emitted from biodiesel's combustion have low carbon monoxide content, contributing to the controlled carbon dioxide emissions and air pollution (Mohammed and Bandari 2017). The process of transesterification is one of the simplest and quickest ways of producing biodiesel. The procedure still induces glycerol as a by-product. Unreacted methanol, residual catalyst, soap, and water are also present in production. After the reaction, glycerol and other by-products are removed from the reaction mixture by a simple gravitational settling process, and the FAME phase washed to remove impurities. However, biodiesel cannot be used directly without purification, which can cause engine knocking or choking on the injector. In addition, the glycerol may accumulate around the injector valve heads and affect engine performance (Saleh et al. 2010; Atadashi et al. 2011). In the American Society for Testing and Materials (ASTM D6751), the removal of glycerol and other by-products from the fatty acid methyl ester (FAME) process is mandatory because the purity of the final FAME product is highly stressed. Despite the fact that biodiesel is the only substitute form of fuel that has been recognized in the testing requirements of the 1990 Clean Air Act Amendment and legally registered as a legal motor fuel with the Environmental Protection Agency, ASTM D6751, and EN 14,214 standards ensure the presence of impurities is limited in the FAME layer of biodiesel (Shah and Porter 2014). Conventionally, biodiesel is purified using water washing, acid washing, and washing with ether and absorbents (Bateni et al. 2017; Berrios and Skelton 2008). Until recently, water washing is the common method for biodiesel purification, but the method uses large quantities of water. Significantly, water use produces a massive amount of polluted effluent. The contaminated wastewater needs to be treated before it is released to the environment due to high pH values, high biological oxygen demand (BOD), and chemical oxygen demand (COD) contents (Wall et al. 2011; Atadashi 2015). Consequently, a large amount of water consumption is not feasible in treating the produced wastewater (Samsuri et al. 2017). One of the alternatives to replace the water washing process is by using the dry washing method. This method uses solid adsorbents or ion exchange resins to purify biodiesel. Although it can replace the water washing process, the knowledge of its chemistry and the regeneration of spent adsorbent is still lacking (Atadashi 2015). Besides, a filter is needed to increase the effectiveness of this method in purifying biodiesel. Some researchers have been developing a membrane technology system to purify biodiesel (Torres et al. 2017; Kusworo et al. 2020). Many efforts have been made in controlling membrane fouling. However, the membrane fouling process causes the membrane to have low membrane flux and permeability, which increases the cleaning chemical costs, energy demand, and operating cost of the membrane system and shortens the lifetime of the membrane. Therefore, solvent-aided crystallization (SAC) is introduced to replace the water washing to minimize the difficulties encountered in biodiesel purification. In this study, SAC was used to purify the biodiesel. SAC is a crystallization method that uses additional assisting agents (e.g. solvents). The use of assisting agent assists and affects the crystallization kinetics favorably. Although this type of crystallization can produce high-purity products, the viscosity of the melt has a negative effect on separation efficiency and the growth rates of the crystal (Eisenbart et al. 2017). The viscous product has difficulty with the nucleation process, growth, and post-treatment process. It will slow the diffusion rate and natural convection and subsequently develop the impure melt layer. Besides, the conventional melt layer crystallization is only suitable for a sample with lower viscosity. The sample used in this study is high in viscosity (i.e. biodiesel and glycerol) (Binhayeeding et al. 2017). In addition, researchers used liquid ammonia and 1-butanol as the additional assisting agents to purify glycerol via crystallization. As a result, both solvents can enhance crystal formation in suspension crystallization, but a 1-butanol solution can decrease the viscosity without affecting the vapor pressure of crystallization substances (Hass and Patterson 1941). Recent studies have reported that the addition of 1-butanol has altered the kinetics of crystallization by lowering glycerol viscosity, improving melt agitation while stirring and enhancing purification with a high crystal growth rate (Thongboonkerd et al. 2006; Eisenbart and Ulrich 2015). The studies also proved that 1-butanol is the most suitable solvent, which significantly impacts the separation of glycerol and water; therefore, SAC is seen as a feasible glycerol method purification. On top of that, the traces of 1-butanol can be easily removed completely via evaporation from the mixtures because 1-butanol is discovered to remain largely in the liquid phase (Eisenbart and Ulrich 2016). The purification method via SAC was conducted right after the transesterification process in previous literature, which replaced gravitational settling and water washing (Singh 2011). As a result, high purity of biodiesel (% FAME purity) was obtained, which confirmed the capability of SAC in removing the contaminants that exist in the biodiesel. Nevertheless, the information of free glycerol content in purified biodiesel is not mentioned, but the higher the FAME purity percentage means, the lesser the contaminants present in the biodiesel and the limitation of the glycerol content (Singh 2011). Therefore, this study attempts to remove free glycerol from FAME using the SAC method. The SAC method was done right after removing glycerol and contaminants by gravitational settling. The remaining free glycerol and other impurities left in the biodiesel were then removed using this SAC method. The composition of FAME in biodiesel and the total content of free glycerol were determined by using gas chromatography–mass spectrometry (GC–MS). Consequently, by measuring the purity of FAME, the percentage of glycerol and another contaminant such as K or Na also can be known. In addition, thermal analysis using differential scanning calorimetry (DSC) and rheometer was also used to analyze biodiesel and glycerol characteristics. Cooking oil from Buruh brand was purchased from a local market. Methanol (99.97% purity) and potassium hydroxide (KOH) pellets were supplied by Avantis Laboratory Supply. Meanwhile, ethylene glycol and 1-butanol were provided by Benua Sains Sdn. Bhd. Ethylene glycol solution of 50% (v/v) with water was used as the coolant inside the refrigerated bath. Synthesis of biodiesel via transesterification method Figure 1 shows the experimental setup of the transesterification method. About 460 g of palm oil from Buruh brand was heated in the three-necked flask up to 60 °C. The temperature of palm oil was maintained between 55 and 60 °C using a recirculating water bath facility. The stirring speed and temperature were controlled by heating and stirring the mantle. About 3.5 g of KOH was measured using an enclosed electronic measuring cylinder and dissolved in 79.2 g of methanol. Then, the methoxide solution was added to the heated palm oil, and the reaction mixture was stirred rapidly for 20 min at 500 rpm using a magnetic stirrer. Then, the crude biodiesel was transferred into a separatory funnel and left for one day. After the gravitational settling process, the bottom glycerol layer was drained using a stop cock, and the volume of glycerol was recorded. The same step was repeated by draining the remaining biodiesel layer, and the volume was recorded. Transesterification reactor setup for biodiesel production Glycerol removal via solvent-aided crystallization Figure 2 shows the experimental apparatus setup for the SAC system using a cylindrical vessel (13.5 × 17 cm). A stainless-steel cylindrical vessel was used for solvent added with crystallizer to avoid the vessel from corroding and minimize the presence of foreign compounds in the solution (Samsuri et al. 2014). The vessel was equipped with a stirrer (EURO-ST 40 D S002, IKA, Malaysia) to stir the crude biodiesel at the solid–liquid interface. This is to allow the user to set the torque and speed for consistent mixing of the solution. Besides, it is to enhance the separation of glycerol as the FAME movement at solid–liquid was well promoted. A refrigerated bath (EYELA Cool ACE CA-1111, TOKYO RIKAKIKAI CO., LTD) was used to maintain the desired temperature sample. Then, the refrigerated bath was turned on, and the temperature was set at 8 °C. SAC system setup A 500 ml volume of crude biodiesel and 1-butanol solvent with 1 wt. % of concentration was poured into the attached cylindrical vessel inside the refrigerated bath. Then, the stirrer was turned on, and the crystallization time was set for 35 min. Afterwards, stirring was stopped at the designated time, and the vessel was taken out from the refrigerated bath. Two phases of the sample were observed: the solid phase (the glycerol and other impurities) and the liquid phase (the pure biodiesel). The purified biodiesel was collected for further analysis using GC–MS. The experiment was repeated using different operating conditions such as different coolant temperatures (10, 12, 14, and 16 °C), stirring speed (100, 200, 400, and 500 rpm), and cooling time (20, 25, 30, and 40 min). All the biodiesel samples were evaluated using GC–MS to determine the FAME content as the purity of biodiesel. As shown in Fig. 3a before the purification via the SAC method and Fig. 3b the pure biodiesel remained in the liquid phase, and the solidified free glycerol and other contaminant attached to the vessel surface after SAC. a Sample solution before SAC method and b solidified free glycerol attached on vessel surface, and pure biodiesel remained in liquid phase after SAC The GC–MS Shimadzu (GC–MS QP 2020, Shimadzu, Kyoto, Japan) was used to determine the total FAME content in the biodiesel. A column with an internal diameter of 30 mm and a film thickness of 0.25 µm from SGE and BP-20 (WAX)-polyethylene glycol was used. The chromatogram peaks were generated using the GC–MS solution equipped with 250 °C of injector temperature, 23 °C/min of oven temperature, and increase to 250 °C and 200 °C of ion source temperature. Helium gas was also used as the carrier gas, while n-heptane was used as the diluent. The purity of each process of purification was calculated using Eq. (1): $$\% ~{\text{Composition~of~FAME}} = ~\frac{{{\text{Peak~are~of~individual~component}}}}{{{\text{Sum~of~correction~area}}}}~ \times 100\% ~$$ To determine crystallization temperature, both biodiesel and glycerol samples were analyzed using DSC Q2000 (TA Instrument-Waters, LLC, USA). The thermograms for both samples' heat flow were generated using the Q series (Q2000-2580-DSCQ2000) software. Biodiesel was calibrated to 30 °C and cooled to − 15 °C at a rate of 5 °C/min. Meanwhile, the temperature range for the glycerol sample was 0 to 30 °C at the same heating rate of 5 °C/min. DSC analysis is essential to determine biodiesel and glycerol's crystallization temperatures so that the suitable cooling temperature range can be used during purification via SAC. Rheometer analysis Discovery Hybrid Rheometer, DHR-1 (TA Instrument, Elstree, UK)) rotational rheometer with a single wall rotor and the concentric cylinder was used to determine the rheological properties such as viscosity, shear stress, and a shear rate of biodiesel and glycerol. Besides, TA Instrument Trios version 4 software with a flow temperature ramping method. The purpose of this analysis was to justify that the viscosities of biodiesel and glycerol are higher than 0.1 Pa∙s. Therefore, this purification method via SAC can be used or suitable for highly viscous liquids sample (Eisenbart and Ulrich 2016). The analysis of variance (ANOVA) was utilized to find the significant difference error in this research by using STATISTICA software Version 8.0 Inc., USA. The experiment was conducted with a stirring speed of 100–500 RPM, a coolant temperature of 8–16 °C, and a crystallization period of 20–40 min. The experiment was repeated three times, with the average values determined. The correlation coefficient (R2) was used to assess the accuracy of the curves, and a value 0.05 of p-value was considered significant. An amount of sample (biodiesel) was employed in this lab-sized experiment as the energy consumption of the biodiesel is determined by SAC method. The SAC's energy consumption is concentrated on the cooling energy (refrigerated bath) and the stirring energy (propeller). As the system carries out the operation, both types of equipment employ the same equation for specific energy consumption (kWh/m3). The specific energy consumption was calculated using Eq. (2), and (3) was used to compute the digital stirrer's power (Power-Torque. 2002; Samsuri et al. 2020): $${\text{SEC}}_{{{\text{equipment}}}} = \frac{{P_{{{\text{equipment}}}} \times \eta _{{{\text{equipment}}}} }}{{V_{{{\text{sample}}}} }}$$ $$P_{{{\text{propeller}}}} = \frac{{T \times N_{{{\text{rpm}}}} }}{{9548.8}}.$$ The power of equipment (kW) indicates as P, followed by η is the efficiency of the equipment, which has been set at the minimal point (80%) for both equipment. V is the volumetric flowrate (m3/h) in Eq. (2). Next, in Eq. (3) T indicates the torque of the propeller (0.4 Nm), and Nrpm referred the speed of the propeller for each run of experiment. The overall specific energy consumption is shown in Eq. (4), which is the sum of the refrigerated bath and propeller's specific energy consumption: $${\text{SEC}}_{{{\text{Total}}}} = {\text{SEC}}_{{{\text{refrigerated~bath}}}} + {\text{SEC}}_{{{\text{propeller}}}}$$ Biodiesel analysis by GC–MS The purity of FAME content after the gravitational settling process was identified using the GC–MS. The chromatogram of crude biodiesel with a graph of intensity versus retention time is plotted in Fig. 4, followed by the peak data in Table 1 to determine the systematic names of fatty acids found in the palm oil-based crude biodiesel. GC–MS chromatogram of crude biodiesel Table 1 GC–MS results for crude biodiesel separated from glycerol after gravitational settling Table 1 shows the peak number, systematic name (Library/ID), trivial name, and the percentage of FAME composition in palm oil-based biodiesel. According to the Palm Oil Research Institute of Malaysia (PORIM), the type of fatty acids present in palm oil are lauric, myristic, palmitic, palmitoleic, stearic, oleic, linoleic, linolenic, and arachidic. Based on Table 1, the total percentage composition of FAME or biodiesel produced from the gravitational settling method was 98.96%. In Table 1, the total amount of saturated fatty acid and unsaturated fatty acid was 43.25% and 55.71%, respectively. The percentage values mostly are between the range specification of biodiesel by PORIM as in Table 2 (Crabbe et al. 2001). Table 2 PORIM specification of biodiesel composition (Crabbe et al. 2001) The info such as correction area of individual component and sum of correction area is provided from the table. Thus, the percentage composition of individual FAME can be calculated using Eq. (1). Both data can be obtained from Table 3. Table 3 GC–MS peak data For Peak 3, lauric: $${\text{\% Composition~of~FAME~}} = {\text{~}}\frac{{240375}}{{77540202}} \times 100\% = 0.31\%$$ Figures 5 and 6 show the thermogram of biodiesel and glycerol. The green line indicated heat flow, and the blue line indicated heat capacity, respectively. The analysis was done for the biodiesel sample which was cooled from 30 to − 15 °C at a constant rate of 5 °C/min (green line) in Fig. 5. The appearance of the exothermic peak was due to the heat flow out of the sample because the sample is cooling specifically during crystallization. Crystallization consists of a two-step process, which is nucleation and solid growth (Çaylı and Küsefoğlu 2008). The graph shows that the onset temperature was 7.68 °C, indicating that the crystallization of the biodiesel started to occur. Then, it reached 5.47 °C show the maximum or peaks as the maximum crystallization temperature of biodiesel. DSC thermogram for crude biodiesel DSC thermogram for crude glycerol On the contrary, no visible peaks were observed in the thermogram for the glycerol sample in Fig. 6. The cooling rate for biodiesel was also used on glycerol with a different temperature range (30 to − 20 °C) and fixed heat flow. The result is also supported by a recent study on the cold properties of fuel mixture and crude glycerol using the DSC analysis, which reported that glycerol has a melting point of 17.8 °C, and no peak was observed during the DSC analysis due to the occurrence of supercooling (Gao et al. 2017). Rheological properties Figure 7 shows that the viscosity of biodiesel at 8.92 °C was 20.1 Pa∙s. The biodiesel was cooled to − 10 °C and heated up to 35 °C. Viscosity curve of biodiesel Meanwhile, Fig. 8 shows that the viscosity of glycerol at 12.6 °C was 0.189 Pa∙s, which was heated from 10 to 20 °C. Biodiesel and glycerol viscosity decreased as temperature increased (Björn et al. 2018; Silva et al. 2015). This is because as temperature rises, fluid flow in a system is increased. Thus, it is proven that the SAC process can be used for highly viscous liquid irrespective of the impact of temperature on viscosity as the viscosity of biodiesel and glycerol was higher than 0.1 Pa∙s (Eisenbart and Ulrich 2016). Viscosity curve of glycerol Effect of coolant temperature on SAC Figure 9 shows that the FAME purity increased when the temperature increased from 8 to 14 °C, and this increase is statistically significant (p < 0.05) and show an R2 value of 0.89. The lowest percentage of 99.17% at 8 °C was due to the coolant temperature, which is very close to the crystallization temperature of biodiesel as mentioned in Fig. 5. As a result, the lowest FAME purity was obtained by solidifying certain fatty acids due to the slight differences range of temperature between coolant and crystallization temperature of biodiesel. Graph of FAME Purity against coolant temperature In addition, the rate of ice crystals or solid growth is controlled by coolant temperature (Amran and Jusoh 2016; Jusoh et al. 2014a). When the temperature is close to the crystallization point, the likelihood of FAME being trapped is higher within the solid layer formed by glycerol and other impurities. Under lower coolant temperature, solid growth rate tends to be greater, which induced a higher methyl ester incorporation into contaminants solid (Samsuri et al. 2017). In addition, the thickness of the solid formed increases as the temperature of the coolant reduces. Nevertheless, the formation of a thicker solid led to high product purity (Mohamad et al. 2017). Hence, the coolant temperature influences the purity of FAME produced. In contrast, the highest purity of FAME was achieved at 99.46% at 14 °C, because this temperature is considered as the favorable coolant temperature. In this state, the FAME did not form in the solid phase and stayed in the liquid phase, while other impurities, including glycerol, were attached to the wall. As observed, solid growth was in an ordered pattern as temperature rises (Romli et al. 2009). In fact, at a higher coolant temperature, the solid can grow in the ordered pattern that enables the pure FAME to free from contaminants and accumulate in the solution and elevates the purity of FAME (Samsuri et al. 2017). However, too high of coolant temperature can affect the solid formation. At higher temperature, the inclusion of solutes can melt and dilute into the solution (Bagdasarov 1988). As a result, the percentage of FAME decreased to 99.34% at 16 °C. Thus, the coolant temperature of 14 °C is considered the ideal temperature to obtain high-purity FAME (FAME yield = 99.32 ± 0.11%). Effect of stirring rate on SAC Solution movement assistance is crucial in enhancing the solid to be formed. A propeller was used to perform this SAC system. Besides, a gentle motion is required to maintain the uniform distribution of temperature and the flow of the system (Mohamad et al. 2017). In Fig. 10, an increasing trend observed from (100 to 300 rpm) and decreases gradually at 400 and 500 rpm. Fig. 10 Graph of FAME purity against stirring speed Accordingly, 300 rpm of stirring rate produced a higher percentage of FAME purity (99.54%) due to the suitable agitation speed to diminish the build-up or accumulation of solute near the liquid–solid interface (Ab. Hamid et al. 2015). Flowrate is closely associated with the circulation of fluid, whereby an increase in flowrate will eventually decrease the advanced rate of the solid front (Miyawaki et al. 2005). As a result, the increase in FAME percentage indicates a better separation efficiency from glycerol and other contaminants. Furthermore, a high circulation flowrate also imposes the development of a high shear force, which can separate the solute from the solution (Jusoh et al. 2014b). High shear force due to high flowrate enables the contaminants solid formed to be carried away easily from the solution, leaving the biodiesel with a higher percentage of FAME. On top of that, the FAME purity was the lowest at 100 rpm (99.40%). A slower stirring speed induces slower movement of solutions and reduces the efficiency of separation. Thus, it explains that mild agitation is preferred compared to slower stirring speed. For the stirring rate of 400 and 500 rpm, the reduction of FAME purity was 99.49% and 99.42%, respectively. The FAME yield was significant (p < 0.05) with the R2 value of 0.96. This is because the higher stirring speed can erode the solid formed onto the vessel wall (Romli et al. 2009). The turbulence flow was created inside the system when the agitation was more heightened. Thus, the solidified contaminant was mixed with the biodiesel, eventually reducing the FAME purity. Besides, vigorous stirring will promote a slower solidification rate and reduce the liquid phase's final concentration (Mohamad et al. 2017; Ab. Hamid et al. 2015). Consequently, the contaminants crystallization rate is slowed down, limiting the heat transfer, and finally decreases the final concentration of FAME (FAME yield = 99.47 ± 0.06%). Effect of crystallization time on SAC The plot (p < 0.05) in Fig. 11 shows that FAME purity increased when the temperature increased up to 99.46% (R2 = 0.93). This is because longer crystallization time enhances the crystallization process. When a solution is stirred for adequate time, it provides longer residence time to be in the crystallizer and allows thicker solid layer formation (Jusoh et al. 2014b). Thus, more contaminants were trapped within the thick solid layer and left the unfrozen biodiesel with higher FAME purity. At 20 and 25 min, the FAME purity remained unchanged with 99.37%, indicating that the crystallization process just started to occur (FAME yield = 99.40 ± 0.04%). Therefore, sufficient cooling time is needed for better purity of biodiesel. However, a crystallization time longer than 40 min was not conducted further in this study. Graph of FAME purity against crystallization time In the F-test, the coefficients are added to the system and being analyzed. The experiment results might lead to improvements in system parameters and make the system better match in the experiment. The calculated F-value was 4.84, as shown in Table 4, which is greater than the tabulated F-value of 95% confidence (F0.05, 3, 11) which is 3.587 thus, that the regression model as a whole is statistically significant. Table 4 ANOVA result for regression Nowadays, the most challenging part for the industry is reducing energy consumption to reduce operational costs (Innocenzi and Prisciandaro 2021). The energy consumption for SAC method was calculated using the power of equipment measured through the term of the energy used for the contaminant removal. The energy consumption was varied for each run by the formation of the solid. The highest total energy consumption 323.0072360 kWh/m3 was achieved due to the longer time of the experiment conducted. The optimum parameter for total energy consumption is the highest number of energies consumed. Thus, based on the analysis of the energy consumption of contaminant removal at the lower crystallization time 161.5036180 kWh/m3 of energy consumption was achieved. This shows that the crystallization time was the crucial parameter to be considered. To conclude that, to compare both results, the lower energy value should be taken into account as both FAME purity show almost similar numbers (Table 5). Table 5 Calculation of energy consumption The SAC system has proven to remove contaminants from crude biodiesel, which is applicable as a waterless method for biodiesel purification. This study aims to determine the effectiveness of free glycerol from FAME using the SAC method. The highest FAME purity and the lower energy consumption removal of contaminants from biodiesel was 99.37% and 161.5036180 kWh/m3. Therefore, SAC must be operated at a coolant temperature of 14 °C, stirring rate of 300 rpm, and crystallization time of 20 min. 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All sources of funding for the research have been declared in the "Acknowledgements". Chemical Engineering Department, Universiti Teknologi PETRONAS, 32610 Seri Iskandar, Perak, Malaysia Mohd. Afnan Ahmad, Arun Letchumanan, Shafirah Samsuri & Wan Nur Athirah Mazli HICoE Centre for Biofuel and Biochemical Research (CBBR), Universiti Teknologi PETRONAS, 32610 Seri Iskandar, Perak, Malaysia Mohd. Afnan Ahmad, Shafirah Samsuri & Wan Nur Athirah Mazli Department of Science and Technology, Faculty of Humanities, Management and Science, Universiti Putra Malaysia, Nyabau Road, 97008, Bintulu, Sarawak, Malaysia Juniza Md Saad Mohd. Afnan Ahmad Arun Letchumanan Shafirah Samsuri Wan Nur Athirah Mazli MAA wrote the manuscript, AL performed experiments and analyzed data, SS supervised the works done by MAA and AL. WNAM and JMdS revised the manuscript. All authors read and approved the final manuscript. Correspondence to Shafirah Samsuri. The manuscript does not involve human participants, human data, or human tissue. Ahmad, M.A., Letchumanan, A., Samsuri, S. et al. Parametric study of glycerol and contaminants removal from biodiesel through solvent-aided crystallization. Bioresour. Bioprocess. 8, 54 (2021). https://doi.org/10.1186/s40643-021-00409-y Biodiesel purification Solvent-aided crystallization Fatty acid methyl esters	CommonCrawl
Bialgebras with Hopf restricted (or Sweedler) duals It is known from the general theory that, given a bialgebra (over a field $k$) \begin{equation} \mathcal{B}=(B,\mu,1_B,\Delta,\epsilon) \end{equation} the Sweedler's dual $\mathcal{B}^0$ (called also Hopf or restricted dual, i.e. the space of linear functionals $f\in B^$ such that $f\circ\mu\in \mathcal{B}^\otimes_k \mathcal{B}^$) is a bialgebra (with the transposed elements). It seems that it can happen that $\mathcal{B}$ admit no antipode whereas $\mathcal{B}^0$ does (and then be a Hopf algebra). My evidence (however neither an example nor a counterexample) is the following : Let $k$ be a field and $q\in k^\times$. On the usual algebra of polynomials, $(k[x],.,1)$, let us define a structure of bialgebra by $$ \Delta(x)=x\otimes 1+ 1\otimes x + q x\otimes x $$ one checks easily that $\mathcal{B}=(k[x],.,1,\Delta,\epsilon)$ ($\epsilon(P)=P(0)$ as usual) is a bialgebra and, as $g=(1+qx)$ (which is group-like) has no inverse, $\mathcal{B}$ is a bialgebra without antipode. However all the elements of $\mathcal{B}$ are dualizable (indeed, the dual of $\Delta$ is the infiltration product of Chen, Fox and Lyndon, Free differential calculus) within $k[x]$ and the bialgebra so obtained $\mathcal{B}^\vee=(k[x],\mu_\Delta,1,\Delta_{conc},\epsilon)$ admits an antipode. Remarks i) (Foissy). The Hopf algebra $\mathcal{B}^\vee$ can be considered as a subbialgebra of $\mathcal{B}^0$ (the full Sweedler's dual) which is NOT a Hopf algebra. To see this, remark that the characters of $\mathcal{B}$ are in $\mathcal{B}^0$ and the values of a character $\chi$ are fixed by $\chi(x)$. Call $F_a$ be the character s.t. $F_a(x)=a$. Convolution of characters satisfies $F_aF_b(x)=a+b+qab$. Now, for all $b\in k$, we have $F_{-1/q}F_b=F_{-1/q}$ which proves that the set of characters (i.e. group-like elements of $\mathcal{B}^0$) is NOT a group under convolution. ii) The comultiplication above was introduced, for $q=1$, by Chen, Fox, and Lyndon, Free differential calculus IV, Ann. Math. 1958. It can be defined on a noncommutative alphabet $X$ (i.e. to complete as a bialgebra a free algebra $A\langle X\rangle$) by $$ \Delta_{\uparrow}(x):=x\otimes 1+ 1\otimes x + q x\otimes x $$ forall $x\in X$. remark that it is compatible with all types of commutation between the letters. The comultiplication of such an infiltration bialgebra $(A\langle X\rangle,conc,1_{X^},\Delta_{\uparrow},\epsilon)$ has a pretty combinatorial expression. It reads, on a word $w\in X^$, $$ \Delta_{\uparrow}(w)=\sum_{I\cup J=[1..n]}\,q^{\|I\cap J\|}w[I]\otimes w[J] $$ where $n=\|w\|$ is the length of the word. My questions are the following (bwa=bialgebra without antipode, ha=Hopf algebra) Q1) Are there significant families of examples of the situation ($\mathcal{B}$ bwa and $\mathcal{B}^0$ ha) known ? (combinatorial, easy to check examples are preferred) Q2) Are there general statements ? ($\mathcal{B}$ bwa +some condition $\Longrightarrow$ $\mathcal{B}^0$ ha) rt.representation-theory examples hopf-algebras counterexamples Duchamp Gérard H. E. Duchamp Gérard H. E.Duchamp Gérard H. E. $\begingroup$ That's a rather interesting example. I suspect you might find some more in the recent work by Patrias, Lam Pylyavskyy ( arxiv.org/abs/1404.4340v1 , arxiv.org/abs/1501.00710 , arxiv.org/abs/0705.2189v1 ). $\endgroup$ – darij grinberg $\begingroup$ I will go across these references, thank you. Originally, the infiltration is defined for an arbitrary noncommutative set of variables. I will try to complete my example in readable way. $\endgroup$ – Duchamp Gérard H. E. $\begingroup$ @DuchampGérardH.E. Off-topic: ping. $\endgroup$ – Francois Ziegler $\begingroup$ @FrancoisZiegler Dear François, I think I know how "Chiinese Monoid" came in the game (due to Schützenberger). Do you have an email ? $\endgroup$ Actually your guess is true. Consider the left Hopf algebra $\widetilde{SL_q(2)}$ from Iyer, Taft, The dual of a certain left quantum group. This is constructed essentially as $SL_q(2)$, but imposing just half of the relations. Namely, if $SL_q(2)$ is given by $\Bbbk\langle X_{i,j}\mid i,j=1,2\rangle$ with relations \begin{gather} X_{21}X_{11}=qX_{11}X_{21}, \tag{$\star$}\\ X_{12}X_{11}=qX_{11}X_{12}, \\ X_{22}X_{12}=qX_{12}X_{22}, \tag{$$}\\ X_{22}X_{21}=qX_{21}X_{22}, \\ X_{22}X_{11}=qX_{12}X_{21}+1, \tag{$\circ$} \\ X_{21}X_{12}=qX_{11}X_{22}-q\cdot 1, \tag{$\bullet$} \\ X_{21}X_{12}=X_{12}X_{21}, \\ \end{gather} then $\widetilde{SL_q(2)}$ is obtained by just requiring $(\star),(*),(\circ)$ and $(\bullet)$. It turns out that $\widetilde{SL_q(2)}$ admits a left convolution inverse of the identity which is not a right convolution inverse (hence it is not an antipode). However, its Sweedler dual coincides with $SL_q(2)^\circ$, whence it is Hopf. Ender WigginsEnder Wiggins $\begingroup$ Very interesting (+1), thanks. Let me some time to digest it. $\endgroup$ Not the answer you're looking for? Browse other questions tagged rt.representation-theory examples hopf-algebras counterexamples or ask your own question. How to show that the graded dual of the universal enveloping algebra of a free Lie algebra on a finite set is the shuffle algebra If associated-graded of a filtered bialgebra is Hopf, does it follow that the original bialgebra was Hopf? Is a bialgebra pairing of Hopf algebras automatically a Hopf pairing? Twist of a group Hopf-algebra Is a bialgebra with all group-like elements invertible a Hopf algebra? Identities that connect antipode with multiplication and comultiplication Antipode of Hopf algebra in braided monoidal category is an algebra antihomomorphism?	CommonCrawl
Approximate kernel reconstruction for time-varying networks Gregory Ditzler ORCID: orcid.org/0000-0001-6890-09351, Nidhal Bouaynaya2, Roman Shterenberg3 & Hassan M. Fathallah-Shaykh4 BioData Mining volume 12, Article number: 5 (2019) Cite this article Most existing algorithms for modeling and analyzing molecular networks assume a static or time-invariant network topology. Such view, however, does not render the temporal evolution of the underlying biological process as molecular networks are typically "re-wired" over time in response to cellular development and environmental changes. In our previous work, we formulated the inference of time-varying or dynamic networks as a tracking problem, where the target state is the ensemble of edges in the network. We used the Kalman filter to track the network topology over time. Unfortunately, the output of the Kalman filter does not reflect known properties of molecular networks, such as sparsity. To address the problem of inferring sparse time-varying networks from a set of under-sampled measurements, we propose the Approximate Kernel RecONstruction (AKRON) Kalman filter. AKRON supersedes the Lasso regularization by starting from the Lasso-Kalman inferred network and judiciously searching the space for a sparser solution. We derive theoretical bounds for the optimality of AKRON. We evaluate our approach against the Lasso-Kalman filter on synthetic data. The results show that not only does AKRON-Kalman provide better reconstruction errors, but it is also better at identifying if edges exist within a network. Furthermore, we perform a real-world benchmark on the lifecycle (embryonic, larval, pupal, and adult stages) of the Drosophila Melanogaster. We show that the networks inferred by the AKRON-Kalman filter are sparse and can detect more known gene-to-gene interactions for the Drosophila melanogaster than the Lasso-Kalman filter. Finally, all of the code reported in this contribution will be publicly available. Understanding the dynamical behavior of living cells from their complex genomic regulatory networks is a challenge posed in systems biology; yet it is one of critical importance (i.e., morphogenesis). Gene expression data can be used to infer, or reverse-engineer, the underlying genomic network to analyze the interactions between the molecules. Unfortunately, most of the existing work on reverse-engineering genomic regulatory networks estimates one single static network from all available data, which is often collected during different cellular functions or developmental epochs. The idea that molecular networks are remodeled as a function of time and stage is well understood; this conclusion is supported by the developmental networks of sea urchin embryos [1]. Throughout a cellular process, such as cancer progression or anticancer therapy, there may exist multiple underlying "themes" that determine the functionalities of each molecule and their relationships to others, and such themes are dynamic. In signal processing terms, summarizing gene expression data, that comes from different cellular stages, into one network would be similar to characterizing a non-stationary signal by its Fourier spectrum. Biologically, static networks cannot reveal regime-specific or key transient interactions that lead to biological changes. One of the challenges of inferring a time-varying network is that there are only a few observations available at each time point. This small sample size is amplified by the high dimension of every sample, leading to a small n large p problem (i.e., more variables than observations). In particular, the system is under-determined. However, exploiting the fact that molecular networks are sparse, one can use compressive sensing to find a solution. Compressive sensing is concerned with the optimal reconstruction of a sparse signal from an under-determined linear system [2, 3]. Under-determined systems are quite common in computational biology/ecology, and the application of compressive sensing to solve these under-determined systems in nature has been a popular solution [4–6]. Compressive sensing theory states that, under the restricted isometry property (RIP), the optimal sparsest solution of a linear system is equivalent to the minimum l1-norm solution [2, 3]. Unfortunately, it is almost impossible to check whether a linear system satisfies the RIP condition. In general, the minimum l1-norm solution can be far from the optimal sparse solution. In our previous work [4], we addressed the problem of under-sampled sparse systems by proposing a new energy-weighted likelihood function that ensures the convergence of the likelihood function for under-determined systems with unknown covariance. The approach was coined Small sample MUltivariate Regression with Covariance estimation (SMURC) and was applied to infer the wing-muscle gene regulatory networks of the Drosophila Melanogaster during the four phases of its development [4]. However, the estimated networks at every epoch used only the data in the corresponding epoch. In particular, the larval network ignored all the measurements in the previous embryonic phase, and so was the case for the subsequent stages. Other research efforts have been proposed to address the problem of recovering time-varying gene regulatory networks by using dynamic Bayesian models [7], non-parametric Bayesian regression [8], and random graph models [9]. In this contribution, we introduce a new approach to modeling sparse time-varying networks and their applications to gene regulatory networks that are based on our recent work [10, 11]. We start by projecting the Kalman solution onto an "approximately sparse" space by using l1-regularization. We further expand upon our previous work by using a Kalman smoother. We then explore the l1-neighborhood for sparser solutions by leveraging our recent compressive sensing technique known as Kernel RecONstruction (KRON) [12]. KRON recovers the optimal sparsest solution whether the RIP condition is satisfied or not. However, KRON's computational complexity is still exponential in the number of parameters p. We, therefore, advance Approximate KRON (AKRON) [11], which builds growing neighborhoods of the l1 solution that moves towards the optimal sparsest solution and eventually reaches it. The size of the neighborhood is tunable depending on the computational resources available. We derive theoretical bounds of optimality. The AKRON Kalman filter is validated on synthetic and real-world data sets. The state-space model and Kalman filter Following the works in [4, 13], we model the network dynamics using a state space model. The system equation is given by a random walk model, which reflects a lack of prior knowledge of the network topological changes. The observation equation is given by a first-order differential equation, whose parameters reflect the strength and sign of interactions (positive and negative are activating and repressing, respectively) [14]. The state space model of the incoming edges, $\mathbf {a}_{i} \in \mathbb {R}^{p}$, for gene i can be shown to be [13] $$\begin{array}{{20}l} \mathbf{a}_{i}(k+1) =& \mathbf{a}_{i}(k)+\boldsymbol{w}_{i}(k). \end{array} $$ $$\begin{array}{{20}l} \mathbf{y}_{i}(k) =& \mathbf{X}^{\mathrm{T}}(k)~ \mathbf{a}_{i}(k)+\boldsymbol{v}_{i}(k), \end{array} $$ where i=1,⋯,p and p is the number of genes. $\boldsymbol {X}(k) \in \mathbb {R}^{p \times n}$ is the gene expression matrix at time k. yi(k) is the rate of change of expression of gene i at time k. wi(k) and vi(k) are the process and observation noise, respectively. These noise processes are assumed to be zero mean Gaussian noise processes with the known covariances Qk and Rk, respectively, and uncorrelated to the state vector ai(k). The full connectivity matrix, A(k), can be recovered by simultaneous parallel recovery of its rows $\boldsymbol {a}_{i}^{t}(k)$ at every time instant k. Thus, we can process each gene in parallel. The Kalman filter can be used to track a(k) [13, 15]; however, this is only if the system is observable. The problem with using a Kalman filter in our setting is that the system is under-determined (i.e., more variables than equations, p>n). This problem, however, can be circumvented by taking into account the sparsity of the vector ai(k). Since each gene in the genomic regulatory network is governed by only a small number of other genes, these networks are known to be sparse. Furthermore, we have also experimented with a Kalman Smoother that is applied after the Kalman filter. Note that the Kalman Smoother is optional. A Kalman smoother can reduce the covariance of the optimal estimate. We implemented Rauch et al.'s Kalman smoothing algorithm [16] and we compared AKRON-Kalman both with and without smoothing. The pseudo code for the proposed Kalman filtering approach is shown in Fig. 1. AKRON-Kalman Tracker+Smoother Constrained Kalman filtering It is known that the connectivity of the edges in gene regulatory networks [13] is sparse. Unfortunately, the output of the Kalman filter is likely not going to be sparse. We first start by projecting the Kalman solution at time k, ak\|k, onto the set of "approximately sparse" vectors by solving the following Lasso problem [17]: $$ \boldsymbol{a}_{k\|k}^{} = \arg\min_{\boldsymbol{a}\in \mathbb{R}^{p}} \left\{(1 - \alpha) \left\\|\boldsymbol{a}_{k\|k} - \boldsymbol{a}\right\\|_{2}^{2} + \alpha \\|\boldsymbol{a}\\|_{1}\right\}, $$ where α∈[0,1] controls the tradeoff between the Kalman estimate and sparsity. An α close to zero will result in a solution that is close to the Kalman estimate, but that may not be sparse. The opposite happens when α is close 1, which will produce a sparser solution, but may be far from the Kalman estimate. This is achieved by minimizing the reconstruction error (i.e., the first term in (3)). AKRON: a search for a sparser solution Consider the following l0-optimization problem, which finds the optimal sparsest solution in a linear under-determined system. $$\begin{array}{{20}l} \boldsymbol{x}^{} = &\arg \min_{\boldsymbol{x} \in \mathbb{R}^{p}} \\|\boldsymbol{x}\\|_{0} \\ & \text{s.t.} \; \boldsymbol{\Phi}\boldsymbol{x} = \boldsymbol{y} \end{array} $$ where ∥·∥0 is the l0-norm, which is defined as the support of the vector, $\boldsymbol {x} \in \mathbb {R}^{p}$, $\boldsymbol {y} \in \mathbb {R}^{n}$, and $\boldsymbol {\Phi } \in \mathbb {R}^{n \times p}$. We consider the scenario where p≫n and denote in the sequel s=p−n. Without loss of generality, Φ is assumed to be full-rank. Compressive sensing theory [3] shows that, under the Restricted Isometry Property (RIP) condition on the matrix Φ, the l1-norm solution is equivalent to the l0-norm solution. Unfortunately, it is impossible to check if the RIP condition is satisfied for a given matrix. Despite this strict condition, l1 has been routinely used to find a sparse solution in systems of the form (4). The proposed Approximate Kernel RecONstruction (AKRON) is an approximation to computationally complex Kernel RecONstruction (KRON) problems [12]. KRON is able to achieve an exact solution to (4), but the algorithm becomes computationally expensive for typically p>15. AKRON, detailed below, is introduced to balance the trade-off between the computational resources that are available and the accuracy of the reconstruction. The Kalman filter estimate is first sparsified by incorporating l1 regularization in (3) (line 5 of Fig. 1). However, the l1 projection is not guaranteed to be the optimal sparsest solution. AKRON-Kalman filter (AKRON-KF) starts off from the l1-regularized Kalman estimate in (3). Then, the s=p−n smallest elements of the l1 projection in (3) are set to zero. The logic behind this strategy is to use the l1-projection to guess the position of the zeros in the optimal solution. Given that the kernel of the system matrix Φ in (3) has dimension s, we know that if s zero locations are correctly set, then the optimal sparsest solution can be exactly found by solving the linear system in (4) [12]. Following this reasoning, AKRON finds a sparser solution by exploring δ-neighborhoods of the l1-projection. The central idea behind AKRON's δ-neighborhoods is as follows: (i) find the indices with the (s+δ) smallest magnitudes of the l1 solution, (ii) set exactly s of these indices to zero, (iii) re-solve the system Φx=y. All the possible $s+\delta \choose s$ combinations of the smallest elements in the solution of (3) are evaluated. This idea can also be viewed as a "perturbation" of the l1 approximation to make it closer to the l0-norm. The size of the neighborhood δ is tunable depending on the computational power available, and vary from 0 (l1-approximation) to n (KRON, i.e., perfect reconstruction). Example: To understand the AKRON algorithm and illustrate the importance of the δ-neighborhoods, we present a simple numerical example. Consider the following randomly generated noiseless system as in (4): $$\begin{array}{{20}l} \boldsymbol{\Phi} =& \left(\begin{array}{ccccc} -0.4588 & 1.5977 & -0.8724 & -0.1121 & -1.3068 \\ 0.2942 & 3.0954 & -1.0530 & 0.3454 & 1.5257 \\ -0.1948 & -0.7558 & -0.9756 & 0.1549 & 0.9586 \\ \end{array} \right); \\ \boldsymbol{y} =& \left(\begin{array}{ccc} -1.2316 & 1.1739 & 0.8135 \\ \end{array} \right)^{T} \end{array} $$ The optimal ℓ0-norm sparsest solution is given by $$ \boldsymbol{x}^{} = \left(\begin{array}{ccccc} 0 & 0 & 0 & -1.2372 & 1.04858 \\ \end{array} \right)^{T} $$ The ℓ1 solution, which solves (4), is given by $$ \widehat{\boldsymbol{x}}_{1} = \left(\begin{array}{ccccc} 0.0 & -0.034 & 0.047 & 0.0 & 0.870 \\ \end{array} \right)^{T} $$ Clearly, the l1-solution is not as sparse as the optimal solution and has incorrect zero locations. We have n=3,p=5 and thus s=2. If we choose δ=1 the AKRON considers the s+δ=3-smallest magnitudes of $\widehat {\boldsymbol {x}}_{1}$, which are located at indices 1, 2 and 4. We set s=2 locations to zero among these 3 indices. We consider all ${s+\delta \choose s} = {3 \choose 2} = 3$ combinations of two zeros in indices 1, 2 and 4 of $\widehat {\boldsymbol {x}}_{1}$. The combination of indices 1 and 2 set to zero leads to the sparsest optimal solution x∗ in (5). Thus, in this case, the ℓ1-norm solution is sub-optimal; but by considering a δ=1-neighborhood of this approximation, AKRON is able to exactly recover the sparsest optimal l0-solution. In the noisy case, where the constraint in (4) is replaced by ∥Φx−y∥≤ε, with ε being a given noise threshold level, the neighborhood δ is chosen adaptively as follows: set the s smallest magnitudes of the l1 solution to zero; compute the observation error ∥Φx−y∥. If this error is smaller than the energy of the noise, we adopt this solution. Otherwise, the next smallest element is set to zero and the error is recalculated. In the following propositions, we investigate under which assumptions on the entries of the l1 solution and its closeness to the l0 solution, will AKRON yield the optimal l0 solution. Proposition 1 Consider the system in (4) with the optimal l0-solution x∗ having k>s zeros. Consider the l1-solution, x1, and assume that ∥x1−x∗∥2≤ε. Let J denote the number of indices j such that $$\begin{array}{{20}l} \|(\boldsymbol{x}_{1})_{j}\| \leq \frac{\epsilon}{\sqrt{k-s+1}}. \end{array} $$ Then, by choosing δ≤J−s, AKRON yields the optimal l0-solution. Let Θ and $\overline {\Theta }$ be the index sets of zero and non-zero entries in the l0-solution x∗, respectively. We have \|Θ\|=k. We need to show that at least s indices in Θ are where (6) holds. To prove this fact, assume the opposite, i.e., at least (k−s+1) indices in Θ are such that $$\|(\boldsymbol{x}_{1})_{j}\| > \frac{\epsilon}{\sqrt{k-s+1}}. $$ However, in this case, we have $$\\|\boldsymbol{x}_{1} - \boldsymbol{x}^{}\\|_{2} > \sqrt{k-s+1}\frac{\epsilon}{\sqrt{k-s+1}} = \epsilon, $$ which contradicts the assumption ∥x1−x∗∥2≤ε. □ The following proposition derives an upper bound for $\delta \in \mathbb {N}_{+}$ when the non-zero elements of the optimal l0-solution are bounded from below. We first need the following Lemma. Consider the system in (4) with the optimal l0-solution x∗ and approximate l1-solution x1. Denote by Θ and $\overline {\Theta }$ the index sets of zero and non-zero entries in x∗, respectively. Assume that ∥x1−x∗∥2≤ε. Let R be the number of indices $j \in \overline {\Theta }$ such that \|(x1)j\|≤ε. If δ=R, then AKRON yields the optimal solution. To obtain the sparsest l0-solution, it is sufficient to choose s zeros in "correct places", i.e., with indices in Θ. Recall that AKRON sets s out of the smallest-magnitude (s+δ) entries in x1 to zero. Therefore, AKRON will yield the optimal solution if out of these (s+δ) smallest-magnitude entries, there are at least s entries from Θ. But all entries from Θ have \|(x1)j\|≤ε, for otherwise the assumption ∥x1−x∗∥2≤ε would be violated. This means that only those entries from $\overline {\Theta }$, which also satisfy \|(x1)j\|≤ε, could be chosen by AKRON, and there are only R of them. Hence δ=R will yield the optimal l0-solution. Lemma 1 provides a sufficient condition on δ for optimality of AKRON, namely, if δ=R, then we are guaranteed the optimal l0-solution. Since this condition is not necessary, we could reach optimality with δ≤R. □ Consider the system in (4) with the optimal l0-solution x∗ and approximate l1-solution x1. Let $\overline {\Theta }$ be the set of indices of non-zero elements in x∗. Assume that the non-zero entries of x∗ are bounded from below, i.e., $$\left\|\left(\boldsymbol{x}^{}\right)_{j}\right\| \geq \eta,~ \text{for all}~ j \in \overline{\Theta}~ \text{and for some}~ \eta > 0. $$ Assume further that ∥x1−x∗∥2≤ε. If ε<η, then $\delta \leq \left (\frac {\epsilon }{\eta - \epsilon }\right)^{2}$ yields the optimal l0-solution. In particular, if $\epsilon < \frac {\eta }{2}$ then δ=0 suffices. Since \|(x∗)j\|≥η for $j \in \overline {\Theta }$, we have $$\left\\|\boldsymbol{x}_{1}-\boldsymbol{x}^{} \right\\|_{2} \geq (\eta-\epsilon)\sqrt{R}\geq(\eta-\epsilon)\sqrt{\delta}, $$ where we used the fact that δ≤R from Lemma 1. Thus, $\epsilon \geq \left \\| \boldsymbol {x}_{1}-\boldsymbol {x}^{} \right \\|_{2} \geq (\eta -\epsilon)\sqrt {\delta }$, which completes the proof. □ Although Propositions 1 and 2 derive theoretical bounds for the choice of the neighborhood radius δ to recover the optimal sparsest solution, we found in our experiments below that relatively small values of δ are sufficient to achieve a balance between desired accuracy and computational complexity. In this section, we present an empirical analysis of the AKRON-KF and its smoother, including comparisons to other approaches proposed for detecting the relationships between different genes in a molecular network. The experiments include a number of carefully designed synthetic data sets, as well as a real-world data set, namely the fruit fly. Overview of experimental protocols Our experiments are conducted on real-world and synthetic data. The advantage of the synthetic data are that the ground truth networks are known; therefore, we can calculate different statistics about the reconstruction error of the network. Unfortunately, we do not have a clear view of the "ground truth" for real-world data. Therefore, we use findings from the life sciences that have studied these networks and were able to infer gene-to-gene relationships that are well established [18]. Our experiments make use of the following algorithms for a sparse reconstruction of a time-varying network: l1-KF(S): This algorithm is the output of the Kalman filter with the l1 projection applied to the state vector. The (S) indicates whether the smoother was implemented. AKRON-KF(S): This is the proposed approach using the output of l1-KF(S) to seed AKRON. It is also implemented with and without the smoother. Both of the above algorithms can reconstruct a network that represents the interactions between genes. We compute the true positive (TP), true negative (TN), false positive (FP) and false negative (FN) rates. These rates are summarized through accuracy (acc), sensitivity (sen), specificity (spe), and Matthew's correlation coefficient (mcc), which are defined below. $$\begin{array}{*{20}l} \text{acc} &= \frac{TP + TN}{TP+TN+FP+FN}, \\ \text{sen} &= \frac{TP}{TP+FN}, \\ \text{spe} &= \frac{TN}{TN+FP}, \\ \text{mcc} &= \frac{TP \cdot TN - FP \cdot FN}{\sqrt{(TP+FP)\cdot(TP+FN)\cdot(TN+FP)\cdot(TN+FN)}}. \end{array} $$ Matthew's correlation coefficient provides a more balanced statistic for examining the overall trade-offs between the different rates (i.e., TP, TN, FP, and FN). Results on synthetic data Synthetic time-varying networks are simulated to evaluate the efficacy of the proposed AKRON-KF(S) on data that we have complete control over. All results in this section are presented as the average over 25 monte carlo simulations. Averaging is performed because there could be a large degree of variation in the time-varying networks that are randomly generated. First, we evaluate the impact of α in (3) on the estimation of ak\|k and the reconstruction errors of l1-KF and AKRON-KF. The experiment is configured as follows: a 25-gene network evolves over four-time points by simulating a random walk; all networks being 85% sparse. At each time step, there are nine observations that are available. Figure 2 shows the effect of α on the reconstruction errors of AKRON-KF and l1-KF. Clearly, AKRON-KF is the better performer across the statistics that we collected. Thus, AKRON significantly improves the previous implementation of sparse Kalman filters for time-varying networks. Furthermore, AKRON-KF detects the location of the edges in the simulated networks (see Fig. 2b). Simply using the solution from l1-KF for a small α is not enough to find the location of the zeros. In fact, α needs to be close to one to achieve a high accuracy at edge detection (i.e., (3) will place a large weight on the l1 penalty and a small weigh on the error). Given these results, we choose α=0.2 for the remainder of the experiments since this value provides a reasonable trade-off between the different statistics that were assessed. Figure 2e shows that AKRON-KF is also superior to Lasso-KF as assessed by Matthew's correlation coefficient, which provides a balanced measure. Comparison of AKRON-KF and l1-KF on a synthetic data with 25 genes over four time points and with 85% sparsity. All results are averaged over 25 monte carlo simulations. a Error. b Accuracy. c Sensitivity. d Specificity. e MCC Second, we expand the synthetic experiments to evaluate the impact of δ in AKRON and the dimensionality of the kernel of X, and we also evaluate the impact that the smoothing has on the reconstruction of the networks. We simulated three different kernel dimensions and values for δ. Table 1 shows the outcome of these experiments. The entries in the table are presented as A/B, where A and B are the results from AKRON-KF and l1-KF, respectively. The table is also divided in half to separate the results for the Kalman filter and Kalman smoother. Similar to the first experiment, we observe that AKRON-KF typically outperforms l1-KF in nearly every statistic and the results can be quite significant. Furthermore, systems with a large kernel dimension (i.e., large p small n) benefit significantly from a larger value of δ. For example, consider a network that is 9×50×4. δ=1 provides a little reduction in error; however, increasing δ to 3, significantly reduces the error and increases the other statistics. Finally, we observe that smoothing improves the error of the system; however, we should note that this improvement comes at a computational cost. Table 1 Results on simulated networks Results on Flybase The application of interest is the inference of the time-varying wing-muscle genomic network of the Drosophila Melanogaster (fruit fly). The Drosophila's microarray dataset originally consists of 4028 genes taken over 66 different time points [18]. The data includes 4 stages of the Drosophila's life: embryonic (samples 1 through 30), larval (samples 31 through 40), pupal (samples 41 through 58), and adulthood (samples 59 through 66). Flybase hosts a list of undirected gene interactions [19]. We set α=0.2 based on the experiments in the previous section for l1-KF and AKRON-KF. In this application, we considered a list of 11 genes that are responsible for the wing muscle development, which has been considered by many researchers before [7–9, 20]. The embryonic, pupal, and larval stages are undersampled to 9 observations in each stage that were used in the reconstruction of the 11-gene network in each developmental epoch. All 8 time points were used in the adulthood period. To summarize, the reconstruction of the connectivity matrix uses 9 samples in the embryonic, pupal, and larval developmental stages and 8 samples in the adulthood developmental stage. The 11 gene network was reconstructed throughout each of the four developmental stages using AKRON-KF and AKRON-KFS. The networks reconstruction using the l1-KF and AKRON-KF are shown in Figs. 3a-d and 4a-d, respectively. For clarity, the displayed networks do not show the strength of the interaction, only that there is an interaction detected by one of the algorithms. The AKRON-KF tracker results in clearly sparser networks than the l1-KF. AKRON-KF was able to find all the connections reported in Flybase: (Actn,prm) appears in the embryonic, larval, and pupal stages, (Actn,up) appears in all four stages, (up,mhc) appears in the embryonic, larval, and pupal stages, (up,sls) appears in the embryonic, larval, and pupal stages and (sls,mhc) appears in the embryonic and larval stages. The other two connections appear through one medium gene (Actn,sls) appears in the embryonic, pupal and adulthood phases through one additional gene and (twin, eve) appears through one or more additional genes only in the embryonic and larval phases. Reconstructed networks for the l1-KF across the four time stages. Edges in the network represent either the suppression of a gene or excitation of a gene, or one gene excites while the other suppresses. a Embryonic. b Larval. c Pupal. d Adult Reconstructed networks for the AKRON-KF across the four time stages. Edges in the network represent either the suppression of a gene or excitation of a gene, or one gene excites while the other suppresses. a Embryonic. b Larval. c Pupal. d Adult The networks reconstruction using the l1-KF and AKRON-KF with smoothers are shown in Figs. 5a-d and 6a-d, respectively. The smoothing provides very similar network topologies to the ones without the smoother; however, we did observe that the networks were sparser in the larval stage (see Figs. 4b and 6b). Note that while Fig. 7 is considered the ground truth, the could exist relationships that have not yet been discovered. These statistics are shown in Table 2, which again shows the benefit of using the AKRON-KF over the l1-KF. Reconstructed networks for the l1-KF with a smoother across the four time stages. Edges in the network represent either the suppression of a gene or excitation of a gene, or one gene excites while the other suppresses. a Embryonic. b Larval. c Pupal. d Adult Reconstructed networks for the AKRON-KF with a smoother across the four time stages. Edges in the network represent either the suppression of a gene or excitation of a gene, or one gene excites while the other suppresses. a Embryonic. b Larval. c Pupal. d Adult The known undirected gene interactions in the Drosophila's 11-gene wing muscle network as determined from Flybase [18] Table 2 Results of the AKRON-KF and l1-KF on the real-world Drosophila Melanogaster data set Table 3 lists all previous algorithms that were applied to this genetic network. Only the AKRON-KF, l1-KF [13], SMURC [4] and Dynamic Bayesian networks [7] considered time-varying networks; and, hence, were able to distinguish the different phases in the network. The other algorithms (minimum description length [20], random graph model [9], and nonparametric Bayesian regression [8]) assumed a stationary network, and hence it is not clear at which stage the detected connections develop. The AKRON-KF along with the l1-KF are the only algorithms able to recover all known interactions and specify the developmental stage where these interactions occur. Although the l1-KF also finds all reported interactions, the networks are denser (less sparse) than the AKRON-KF. With regard to the MDL results in Table 2, we have not reported the interations. The MDL authors in [20] inferred a single network, using all 66 time points, that characterizes the entire Drosophila's life cycle. In particular, the MDL approach is stationary and does not differentiate between the phases or time-varying epochs of the data. We wanted to report the MDL findings as they are in the literature. Notice that AKRON used less points and found more correct interactions. Table 3 Detection of the known gene interactions in Flybase (E: embryonic, L: larval, P: pupal and A: adulthood) In this work, we addressed the problem of inferring time-varying molecular networks as a tracking problem that can be solved using the Kalman filter. The major difficulty, however, is that there is not a sufficient number of observations at each time point, which makes the state-space model unobservable and the tracking senseless. Fortunately, molecular networks are known to be sparse because the dynamics of every gene are governed by only a small number of genes. By incorporating the sparsity condition, we show that the tracking problem becomes feasible. We presented the AKRON Kalman filter, which builds on our previous work on the Lasso-Kalman filter (l1-KF). Our proposed approach leverages the AKRON algorithm to find a sparser solution that is more representative of the ground truth. The proposed tracker/smoother first computes the output of l1-KF; then explores growing neighborhoods of the l1-projection to look for sparser solutions, eventually reaching the optimal sparsest estimate. The size of these neighborhoods is a tunable parameter that depends on the computational power available. AKRON-KF was benchmarked on synthetic and real-world data against l1-KF. The results demonstrate that the proposed approach is better at recovering sparse time-varying networks than l1-KF. Not only was the reconstruction error of the proposed approach lower than l1-KF, but it was also better at detecting whether an edge exists in a network. AKRON-KF tracker was applied to infer the wing muscle gene regulatory network of the Drosophila Melanogaster during four developmental phases of its life cycle, and successfully identified all seven known interactions reported in Flybase. 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Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the funding agencies. Code and reproducibles will be made available on Github if accepted for publication. Department of Electrical and Computer Engineering, University of Arizona, Tucson, AZ, USA Gregory Ditzler Department of Electrical and Computer Engineering, Rowan University, Glassboro, NJ, USA Nidhal Bouaynaya Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL, USA Roman Shterenberg School of Medicine, University of Alabama at Birmingham, Birmingham, AL, USA Hassan M. Fathallah-Shaykh GCD, NCB and RS developed the AKRON Kalman filter and the theory of AKRON. GCD, NCB, RS and HMF-S participated in the design of the study. GCD and NCB implemented the study. GCD, NCB, RS and HMF-S analyzed and interpreted the data. GCD and NCB prepared the manuscript and revised it. All authors read and approved the final manuscript. Correspondence to Gregory Ditzler. Ditzler, G., Bouaynaya, N., Shterenberg, R. et al. Approximate kernel reconstruction for time-varying networks. BioData Mining 12, 5 (2019). https://doi.org/10.1186/s13040-019-0192-1 Time-varying network Compressive sensing Gene regulatory Gene regulatory networks	CommonCrawl
An optimization-based approach for efficient network monitoring using in-band network telemetry Jonatas Adilson Marques ORCID: orcid.org/0000-0002-7757-65051, Marcelo Caggiani Luizelli2, Roberto Irajá Tavares da Costa Filho1 & Luciano Paschoal Gaspary1 In recent years, as a result of the proliferation of non-elastic services and the adoption of novel paradigms, monitoring networks with high level of detail is becoming crucial to correctly identify and characterize situations related to faults, performance, and security. In-band Network Telemetry (INT) emerges in this context as a promising approach to meet this demand, enabling production packets to directly report their experience inside a network. This type of telemetry enables unprecedented monitoring accuracy and precision, but leads to performance degradation if applied indiscriminately using all network traffic. One alternative to avoid this situation is to orchestrate telemetry tasks and use only a portion of traffic to monitor the network via INT. The general problem, in this context, consists in assigning subsets of traffic to carry out INT and provide full monitoring coverage while minimizing the overhead. In this paper, we introduce and formalize two variations of the In-band Network Telemetry Orchestration (INTO) problem, prove that both are NP-Complete, and propose polynomial computing time heuristics to solve them. In our evaluation using real WAN topologies, we observe that the heuristics produce solutions close to optimal to any network in under one second, networks can be covered assigning a linear number of flows in relation to the number of interfaces in them, and that it is possible to minimize telemetry load to one interface per flow in most networks. Monitoring is an essential component of network operation and management tasks. In recent years, monitoring networks with high level of detail (e.g., per-packet hop-by-hop delays, instantaneous queue size) is becoming crucial to correctly identify and characterize network events related to faults, performance, and security. This new requirement can be attributed, in part, to the proliferation of non-elastic services (e.g., telesurgery, virtual reality video streaming) that demand timely, fine-grained and accurate monitoring to identify and quickly react to sources of substantial delay and jitter [1]. The adoption of novel technologies and paradigms, such as network virtualization and software-defined networking (SDN), also demands more detailed information about network state and behavior to allow more informed decisions (e.g., routing, buffer sizes). Traditional tools fall short at correctly dealing with the new monitoring demands or at providing the necessary level of detail while keeping reasonable overheads since these tools were not designed with those requirements in mind. Recent efforts have explored new monitoring opportunities that arise in the context of SDN to provide better visibility into the network. NetSight [2], Everflow [3] and Stroboscope [4] considered the use of packet mirroring to create packet histories that indicate paths and estimate hop-by-hop delays. Payless [5] and AdaptiveSampling [6] proposed dynamically adjusting the frequency of flow record polling from OpenFlow switches to manage overheads. All of these investigations have important limitations. First, when several switches in the path of a packet mirror it, the copies need to be transmitted through the network. Thus, the monitoring data is considerable and can become a significant source of degradation depending on the network size and level of activity. Second, these approaches have limited accuracy and level of detail. For example, in the case of Payless and AdaptiveSampling, even if the polling frequency is very high, the level of detail of the data would not be sufficient to detect situations such as intermittent congestion events in the order of microseconds. Finally, all these studies have limited their scope to traditional SDN, and do not consider recent advances in data plane programmability [7–9]. More recently, a new monitoring concept has been proposed: In-band Network Telemetry (INT) [10–12]. It makes use of new capabilities of emerging programmable switches [7, 9, 13] to encapsulate processing metadata information (e.g., queue occupancy, processing time, policy rules) into "production traffic" packets (i.e., packets originated at the application layer). This information is accumulated in a packet along its path and, at some point in the network, extracted and reported to a monitoring control entity. The collection of this information has the objective of continuously identifying state, behavior, and performance of a network as perceived by its traffic. INT may be applied to produce monitoring data with an unparalleled level of accuracy and detail [11, 14]. That is because instead of relying on active probes, which may be subject to forwarding and routing behaviors different from those of the traffic of interest, the production packets themselves can be used to probe the network. Moreover, for metadata that changes over time (e.g., queue occupancy), measurements can be made precisely during the instants when certain packets of interest are being processed at a device. This level of detail and accuracy makes possible to detect and pinpoint network events that were previously imperceptible, such as microsecond congestion. Although INT brings new opportunities regarding accuracy and level of detail, to be able to use it in practice, there is the need to understand the trade-offs between quality and costs involved in employing it. Executing this type of telemetry involves modifying production packets traversing the network, which may significantly degrade the performance of end-user applications. In a previous work [15], we have made an initial effort to identify and characterize the limitations associated with it and the factors that impact performance. The amount of metadata that may be inserted into a packet is restricted by its original size and the network maximum transmission unit (MTU). The level of degradation is a consequence of factors such as in-flight packet size variation, sharing level of device and link resources between application and monitoring data, and the processing demand imposed by metadata report packets. We argue that these factors need to be carefully considered when monitoring networks using in-band network telemetry. In this work, we introduce the In-band Network Telemetry Orchestration (INTO) problem, which is focused on optimizing the use of network resources for INT. Our ultimate goal is to minimize overheads while obtaining high-quality monitoring data. We formalize two variations of the INTO problem as mathematical programming models and prove that both are NP-Complete problems. We also introduce heuristic algorithms designed to generate high-quality polynomial computing time solutions to the variations of the INTO problem. We evaluate the quality and costs of the proposed strategies under realistic scenarios, and compare their results to allow identifying what types of networks they are better suited to monitor. The remainder of the paper is organized as follows. We start, in Section 2, by briefly reviewing data plane programmability and INT concepts. We also revisit the challenges and degradation factors associated with the use of INT. In Section 3, we formally define the In-band Network Telemetry Orchestration (INTO) problem and propose mathematical programming models to solve the two optimization variations of it. In Section 4, we introduce the proposed heuristic algorithms. In Section 5, we evaluate the proposed mathematical programming models and heuristic algorithms and compare the two variations of the problem. In Section 6, we discuss the related work. And in Section 7 we present our concluding remarks. Recently, data plane programmability has emerged as a novel concept for evolving the software-defined networking paradigm [7]. It allows network operators to specify how the forwarding devices in a network should parse packet headers (standard or custom) and process packets using a domain-specific programming language such as P4 [8]. This new level of flexibility decouples the development of network protocols and the design of switching chips [8, 10] thus enabling quicker deployment of new services. One example of concept service that has been facilitated by programmable data planes is In-band Network Telemetry (INT) [10, 11]. It makes use of the opportunity to define custom headers, tables, and processing logic to insert information about the network state (e.g., link utilization, switch buffer occupancy, hop-by-hop delays) into "production traffic" packets [11]. This telemetry data is subsequently and transparently extracted by a switch and reported to a monitoring sink/analyzer, while the packets with their original content are delivered to the recipient hosts [12]. INT provides a way for monitoring networks and services with high accuracy and level of detail [16]. Despite these benefits, because it uses production traffic, it is important to consider constraints imposed by the traffic and potential impacting factors to perform it effectively and efficiently. The key constraint of INT is that packets cannot exceed the network MTU. Therefore, the length of the telemetry data that can be embedded into a packet is limited by the difference between its original size and the MTU. The smaller the packet, the larger its telemetry capacity (i.e., the number of metadata items it can transport). All orchestration strategies have to comply with this constraint, which may limit the number of interfaces that can be monitored in a network. Next, we present and discuss the main factors that may lead to network performance degradation, as identified in our previous work [15]. Embedding telemetry data into packets causes their size to increase along their paths. Making packets increase in size may cause jitter in their transmission. Jitter may degrade the QoS of many applications, specially of non-elastic ones (e.g., VoIP, virtual reality video streaming). Packet forwarding devices have limited processing capacity. The generation of telemetry report packets uses this capacity, thus, forwarding too many reports may saturate devices. Monitoring sinks and analyzers have limited processing capacity. Receiving too many report packets and too many telemetry data may saturate these machines, which could impair their capacity to properly monitor the network. Network links have limited bandwidth. The telemetry data transported in production packets uses the bandwidth of links in the network. If too much data is inserted into packets and reported to sinks, the growth in data volume may saturate links and devices. The level of impact of the factors mentioned above is intrinsically related to the assignment of INT tasks to the traffic in the network. Figure 1 illustrates the "full" assignment of telemetry tasks, which is a straightforward method to carry out INT. The network in Fig. 1 is composed of five forwarding devices and has endpoints to four other networks (e1−e4). Moreover, there are four packet flows of the same traffic type: f1:e1⇔e4, f2:e1⇔e2, f3:e2⇔e3, and f4:e3⇔e4. The full assignment represents a scenario where every flow in the network would collect (and transport) metadata items from all device interfaces in its path. For example, the packets of flow f4 collect information about interfaces J, K, M, and N, as it is indicated by the orange circles in the figure. Example of full assignment The full assignment has significant drawbacks. First, it is not aware of telemetry demands and capacities. For example, consider the case where interfaces J, K, M, and N had each four telemetry items to be collected, and the telemetry capacity of flow f4 was 12 items (according to the typical size of packets). In this case, the full assignment would be unfeasible, because by the time packets coming from e3 arrived at interface N they would not have enough space to collect the four items from it. Therefore, the full assignment does not guarantee that, in practice, flows will cover all interfaces in their paths. Second, all flows are subject to the performance degradation factors discussed previously in this section, as the full assignment is not selective in its choices. Third, all telemetry supporting tasks (i.e., telemetry header creation and extraction, report packet generation and transmission) tend to be executed by edge devices, increasing their probability of being saturated. Fourth, device interfaces are often monitored by multiple flows, each of them collecting the instantaneous value of same metadata items. Previous work [11, 14] has shown that it is possible to obtain instantaneous metadata with microsecond granularity using only one out of all flows traversing an interface or forwarding device. Furthermore, since all flows are of the same traffic type, behavioral and performance metadata (e.g., forwarding rules, queue delay) is expected to be similar. Finally, in this assignment the INT overhead is highly influenced by the level of activity in the network (i.e., the number of flows). Thus, an increase in network activity may inadvertently saturate its links and devices. In summary, we advocate that network monitoring through INT requires some sort of task orchestration to be viable in practice. In the next sections, we present our proposed solution, starting, next, with the formalization of INT orchestration as an optimization problem. In-band network telemetry orchestration optimization In general terms, the problem under study – entitled In-Band Network Telemetry Orchestration (INTO) problem – consists in monitoring network device interfaces effectively (covering all monitoring demands) and efficiently (minimizing resource consumption and processing overheads). We start the problem definition by formally describing the input and output of our optimization models. For convenience, Table 1 presents the complete notation used in the formulation. Table 1 Summary of symbols The INTO problem considers a physical network infrastructure G=(D, I) and a set of network flows F. Set D in network G represents the programmable forwarding devices D={1,2,...,\|D\|}. Each device d∈D has a set of network interfaces that are connected to other devices in the network. We denote the interface of a device da that is connected to a device db by the tuple (da,db). Similarly, the interface of db that is connected to da is denoted by (db,da). The set of all device interfaces in the network is denoted by I. For each interface i∈I, there is an associated monitoring demand, a fixed number of telemetry items $\delta (i) \in \mathbb {N}^{+}$ that need to be collected periodically by flows in F. The interface telemetry demands are determined by monitoring policies, which are influenced by, for example, the level of activity of each interface or a previously detected event of interest. The set F represents a group of aggregate packet flows of the same traffic type that are active in the network. In the case where the operator wants to monitor different types of traffic (e.g., scientific computing, video streaming, VoIP), a separate problem instance could be created for each one with their respective flows. This is done because the metadata values observed by a flow may be different from the values observed by other flows, specially for performance-related metadata [17]. For example, if a network prioritizes forwarding VoIP traffic in detriment of Web traffic, the queueing time observed by packets of each type may be different. Thus, if an operator wants to obtain metadata that is highly consistent with a specific type of traffic, the best approach to guarantee this would be to create a problem instance for each type of traffic. We note that the INTO problem definition and our solutions do not preclude operators from treating all traffic as a single type. Creating separate instances is therefore a recommendation for the obtention of more consistent monitoring data. Each flow f∈F has two endpoints (ingress and egress) and is routed within the network infrastructure G using a single path. We denote the path ρ(f) of a specific flow f as a list of interfaces through which its packets are forwarded. For example, a network flow f from endpoint s to t routed through forwarding devices 1, 3, and 4 has ρ(f)=(1,s),(1,3),(3,1),(3,4),(4,3),(4,t). The first forwarding device interface visited is that of device 1 connected to the ingress endpoint (s), and the last is that of device 4 connected to the egress endpoint (t). Associated with each flow f is also a telemetry capacity $\kappa (f) \in \mathbb {N}^{+}$, which is the maximum number of items each packet of the flow may transport. The capacity of the flows is determined by factors such as forwarding protocols (e.g., IPv4, IPv6, NSH [18]), packet sizes, and network monitoring policies. The telemetry capacity may differ from packet to packet in a single flow, but we expect that the distribution of sizes is stable to be estimated with historic data. The capacity of (aggregate) flows can be defined according to percentile values of the distribution of sizes in order to guarantee that most (e.g., 90%) of the packets will have enough space to collect the metadata of the interfaces they are assigned to cover. Given the problem input, an INTO optimization model will try to find a feasible assignment Φ:I→F that optimizes a specific objective function, where Φ(i)=f indicates that flow f∈F should cover interface i∈I. A feasible assignment is one where (i) each interface is covered by exactly one of all flows in F that pass through it and (ii) no flow f∈F is assigned to cover more interfaces than its capacity allows, i.e., the sum of demands from all interfaces covered by a flow does not exceed its capacity. We highlight two important design decisions in our models. First, assignment function Φ does not enable partitioning the demand of an interface across multiple flows. We chose this type of assignment because some of the items to be collected on an interface are interdependent. For example, when collecting the transmission utilization it is also necessary to collect the ID of the respective interface. Enabling items to be balanced in different flows would require adjusting the models to assign flows to cover individual items instead of interfaces and introducing additional restrictions to force certain assignments in order to satisfy interdependency requirements. At this point, it is not clear that enabling such granularity in assignment would bring advantages enough to counter the complexity that would be introduced to the models, but we do consider further investigating this possibility in a future work. Second, our model assigns a single aggregate flow per interface. We observe that, in some cases, it may be useful to introduce limited assignment redundancy. For example, to guarantee coverage and reduce the number of necessary configuration updates in a scenario of highly frequent changes in the set of flows. In our work, this redundancy is implicitly achieved through the employment of the "grain" of aggregate flows traversing a network core, which tend to present small and few changes over time. We leave exploring alternative options for both of these design decisions for future work. Considering the key traffic constraint and main performance influencing factors discussed in Section 2, we define two optimization problems, namely, INTO Concentrate and INTO Balance. Next, we present the two optimization problems. For each problem we describe its objective function, propose an optimization model to solve it and prove that it is an NP-Complete problem. INTO concentrate optimization problem The number of flows participating in monitoring the network via INT dictates the number of telemetry report packets generated periodically since a report is sent for each packet of each telemetry-active flow. As previously discussed, creating too many report packets may saturate the forwarding devices that are tasked with their generation and the machines tasked with their analysis. Therefore, one possible optimization goal is minimizing the number of telemetry-active flows. That is the objective of the INTO Concentrate problem. Example assignment Figure 2 shows an example "Concentrated assignment", i.e., an assignment that uses the optimal number of telemetry-active flows for our running example previously presented in Fig. 1 of Section 2. The example assignment shows that it is possible to cover all device interfaces using only three out of the four flows in the network. Flows f1 and f3 are assigned to cover six interfaces each, {A, B, E, H, L, N} and {J, I, G, F, C, D}. Flow f4 is assigned to monitor the remaining two uncovered interfaces K and M, while flow f2 is not assigned to cover any interface. Concentrated assignment example Optimization model The proposed optimization model to solve INTO Concentrate is presented next as an integer linear program. Variable xi, f indicates whether flow f should cover interface i∈I. The values of all variables xi,f define the assignment function Φ, i.e., xi, f=1→Φ(i)=f. Variable yf indicates whether flow f is a telemetry-active flow (i.e., if it covers at least one interface). This second set of variables is necessary to compute the objective function of the problem, the number of telemetry-active flows (Eq. 1). $$\begin{array}{{20}l} \text{min} & \Phi_{c} = \sum\limits_{f \in F} y_{f} \end{array} $$ $$\begin{array}{{20}l} \text{s.t.} & \sum\limits_{f \in F} x_{i, f} = 1, & \forall i \in I, \delta(i) > 0 \end{array} $$ $$\begin{array}{{20}l} & \sum\limits_{i \in \rho(f)} x_{i,f} \cdot \delta(i) \leq y_{f} \cdot \kappa(f), & \forall f \in F \end{array} $$ $$\begin{array}{{20}l} & x_{i,f} \in \{0, 1\}, & \forall i \in I, \forall f \in F \end{array} $$ $$\begin{array}{{20}l} & y_{f} \in \{0, 1\}, & \forall f \in F \end{array} $$ The objective function (Eq. 1) defines the minimization of the number of telemetry-active flows by the sum of the y variables. Constraint set in Eq. 2 ensures that all interfaces i∈I with positive demand are covered by some flow f∈F. Constraint set in Eq. 3 bounds the number of telemetry items each flow f∈F can be assigned to collect and transport according to its capacity κ(f). Equation 3 also activates yf when any telemetry item is assigned to flow f∈F. Constraint sets in Eqs. 4 and 5 define the domains of variables xi,f and yf, which are binary. Proof of NP-completeness We will now prove that the decision version of the INTO Concentrate problem is an NP-Complete problem. Given a network infrastructure G=(D, I), the set of network flows F, and an integer number n; the goal of the decision version of the problem is to determine whether there exists a feasible assignment Φ where no more than n flows are used to transport telemetry items. Lemma 1 INTO Concentrate belongs to the class NP. We prove that the decision version of the INTO Concentrate problem is in NP by way of a verifier. Given any assignment Φ:I→F, the verifier needs to check three conditions. First, that the number of telemetry-active flows is indeed at most n (in $\mathcal {O}(\|F\|)$ time). Second, that every interface is covered (in $\mathcal {O}(\|I\|)$ time). Third, that no flow collects more telemetry items than its capacity (in $\mathcal {O}(\|I\|\|F\|)$). For a yes instance (G, F, n), the certificate is any feasible assignment using n flows in F; the verifier will accept such an assignment. For a no instance (G, F, n), it is clear that no assignment using n flows of F will be accepted by the verifier as a feasible assignment. Any Bin Packing problem instance can be reduced in polynomial time to an instance of the INTO Concentrate Decision problem. An instance of the Bin Packing Problem (BPP), which is a classical NP-Complete problem [19], comprises a set A of items, a size sa for each item a∈A, a positive integer bin capacity C, and a positive integer n. The decision version of the BPP asks if its possible to pack all items into n bins, i.e., if there is a partition of A into n disjoint sets (B1,B2,...,Bn) such that the sum of sizes of the items in each subset is at most C. The INTO Concentrate problem is a generalization of the BPP where bins may have different capacities and each item may only be put on a specific subset of all bins. We reduce any instance of the BPP to an instance of the INTO Concentrate problem using the following procedure. The reduction has polynomial time complexity $\mathcal {O}(n\|A\|)$. An infrastructure G is created with \|A\| forwarding devices and two endpoints es and et. See example in Fig. 3, device numbers are shown in bold. The devices are connected in line, i.e., device a∈A is connected to device b=a+1,b∈A. Devices a=1 and a=\|A\| are also connected to endpoints es and et, respectively. The interface of each device a=1,2,...,\|A\| that is connected to the next device (or to endpoint et in the case of device a=\|A\|) has telemetry demand equal to sa, while the other interface has no telemetry demand. The interface demands are shown in italics in the figure. Example BPP reduction to INTO Concentrate. A BPP instance with \|A\|=3 items, bin capacity C=4, and number of bins n=2 is reduced to an INTO Concentrate instance with 3 forwarding devices and 2 flows with telemetry capacity equal to 4 items Next, n flows (B1,B2,...,Bn) are created. Each flow has endpoints es and et and is routed through a path comprising all forwarding device interfaces in G, i.e., ρ(Bi)=(1,es),(1,2),(2,1),...,(\|A\|,et),i=1,2,...,n. The telemetry capacity of all flows is C. Theorem 1 The INTO Concentrate decision problem is NP-Complete. By the instance reduction presented, if a BPP instance has a solution using n bins, then the INTO Concentrate problem has a solution using n flows. Consider that each item a of size sa packed into a bin Bi corresponds to the coverage of the interface of device a with positive telemetry demand by flow Bi. Conversely, if the INTO Concentrate problem has a solution using n flows, then the corresponding BPP instance has a solution using n bins. Covering the positive demand interface of device a with flow Bi corresponds to packing an item of size sa into bin Bi. Lemmas 1 and 2 complete the proof. □ INTO balance optimization problem The number of telemetry items to be collected by each flow determines how much a packet will grow in size during its forwarding inside the network. If too many telemetry items are concentrated into one flow, the links through which its packets are forwarded may be saturated by significant growth in data volume. Consequently, another optimization goal would be to balance the telemetry demands among as many flows as possible. This assignment strategy would minimize the probability of saturating any single link because the variation in data volume becomes minimal for each flow. The INTO Balance objective is to minimize the maximum number of telemetry items transported (i.e., telemetry load) by any single flow. Figure 4 illustrates a possible Balanced assignment, i.e., one that achieves the optimal telemetry load balance, for the example scenario previously presented in Figs. 1 and 2. This example assignment shows that it is possible to cover all device interfaces in the network while assigning no more than four interfaces (i.e., collecting 4×4=16 items) per telemetry-active flow. The optimal load balance value is determined by three factors: (i) the maximum telemetry demand per single interface, (ii) the fraction between the sum of all interface demands and the number of flows, and (iii) the different flow to interface assignment options. In the example, all interfaces have equal demand of four items. The total sum of demands 14interfaces×4 items=56 items divided by the four flows equals 14 items per flow. Since a flow must collect all (or none) of the items of an interface, the optimal load balance is found when two flows are assigned to collect 16 items each (i.e., cover four interfaces) and the other two are assigned to collect 12 items (i.e., cover three interfaces). The assignment shown in Fig. 4 follows this distribution. Flows f2 and f3 are assigned to four interfaces each, {A, B, D, F} and {C, G, I, J}. Likewise, f1 and f4 are assigned to three interfaces each, {E, H, L} and {K, M, N}. Balanced assignment example Next, we present the integer linear program to solve the INTO Balance optimization problem. Variable xi, f indicates whether flow f∈F should cover interface i ∈ I. As was the case with the Concentrate model, the values of variables xi, f define the assignment function Φ, i.e., xi, f=1→Φ(i)=f. Variable k indicates the maximum number of telemetry items assigned to be collected and transported by a single flow. $$\begin{array}{{20}l} \text{min} & \Phi_{b} = k \end{array} $$ $$\begin{array}{{20}l} & \sum\limits_{i \in \rho(f)} x_{i,f} \cdot \delta(i) \leq \kappa(f), & \forall f \in F \end{array} $$ $$\begin{array}{{20}l} & \sum\limits_{i \in \rho(f)} x_{i,f} \cdot \delta(i) \leq k, & \forall f \in F \end{array} $$ $$\begin{array}{*{20}l} & k \geq 0 \end{array} $$ The objective function (Eq. 6) defines the minimization of k, the maximum telemetry load of each flow. Constraint set in Eq. 7 ensures that all interfaces i∈I (with positive demand) are covered by some flow f∈F. Constraint set in Eq. 8 bounds the number of telemetry items each flow f∈F can be assigned to collect and transport according to its capacity κ(f). Constraint set in Eq. 9 guarantees that k is at least the maximum number of items to be collected by any single flow. Constraint set in Eq. 10 defines the domains of variables xi,f, which are binary. The constraint in Eq. 11 defines the domain of variable k. We now prove that the decision version of the INTO Balance problem is an NP-Complete problem. Given a network infrastructure G=(D, I), the set of network flows F, and an integer number n; the goal of the decision version of the problem is to determine if there exists a feasible assignment Φ where no flow is assigned to transport more than n telemetry items. INTO Balance belongs to the class NP. Similarly to Lemma 1, we prove that the decision version of the INTO Balance problem is in NP by way of a verifier. Given any assignment Φ:I→F, the verifier needs to check two conditions. First, that no flow collects more than n telemetry items and than its capacity (in $\mathcal {O}(\|I\|\|F\|)$). Second, that every interface is covered (in $\mathcal {O}(\|I\|)$ time). For a yes instance (G, F, n), the certificate is any feasible assignment where each telemetry-active flow transports at most n items; the verifier will accept such an assignment. For a no instance (G, F, n), it is clear that no assignment making each telemetry-active flow collect at most k items will be accepted by the verifier as a feasible assignment. Any Multiprocessor Scheduling problem instance can be reduced in polynomial time to an instance of the INTO Balance Decision problem. An instance of the Multiprocessor Scheduling Problem (MSP), which is a known NP-Complete problem [19], comprises a set J of jobs, a length lj for each job j∈J, a set of m processors, and a deadline n (a positive integer). The goal of the decision version of the MSP is to decide whether there exists a scheduling of jobs on the m processors (P1,P2,...,Pm) such that all jobs finish before elapsed time n. We reduce any instance of the MSP to an instance of the INTO Balance problem using the following procedure. The reduction has polynomial time complexity $\mathcal {O}(m\|J\|)$. An infrastructure G is created with \|J\| forwarding devices and two endpoints es and et. See example in Fig. 5, device numbers are shown in bold. The devices are connected in line, i.e., device j∈J is connected to device k=j+1,k∈J. Devices 1 and \|J\| are also connected to endpoints es and et, respectively. The interface of each device j=1,2,...,\|J\| that is connected to the next device (or to endpoint et for device \|J\|) has telemetry demand equal to lj, while the other interface has no telemetry demand. The interface demands are shown in italics in the figure. Example MSP reduction to INTO Balance. An MSP instance – with \|J\|=3 jobs, number of processors m=2, and deadline n=6 – is reduced to an INTO Concentrate instance – with 3 forwarding devices and 2 flows with telemetry capacity equal to 6 Next, m flows P1,P2,...,Pm are created. Each flow has endpoints es and et and is routed through a path comprising all device interfaces in G, i.e., ρ(Pi)=(1,es),(1,2),(2,1),...,(\|J\|,et),i=1,2,...,m. The telemetry capacity of all flows is n. The INTO Balance decision problem is NP-Complete. By the instance of the reduction presented, if an MSP instance has a solution schedule where all jobs finish within n time units, then the INTO Balance problem has a solution with no more than n items assigned to be transported by any single flow. Consider that each job j of length lj scheduled to a processor Pi corresponds to the coverage of the interface of device j (with positive telemetry demand) by flow Pi. Conversely, if the INTO Balance problem has a solution where each flow is assigned to collect no more than n telemetry items, then the corresponding MSP instance has a solution where every job complete within n time units. Covering the positive demand interface of device j with flow Pi corresponds to scheduling a job of length lj to process Pi. Lemmas 3 and 4 complete the proof. □ Heuristic algorithms for in-band network telemetry orchestration In this section, we propose and formalize two heuristic algorithms (Concentrate and Balance) designed to produce high-quality solutions to the two optimization problems (INTO Concentrate and INTO Balance, respectively) in a timely manner. Concentrate heuristic algorithm As mentioned in Section 3.1, given the challenge of optimizing in-band telemetry orchestration, one possible strategy is to minimize the number of flows that will be used to transport telemetry data. In this section, we propose Concentrate, a heuristic algorithm focused on minimizing this number. Algorithm 1 shows the pseudo-code of Concentrate. Next, we detail its procedures. The algorithm has two input parameters: the set I of all active device interfaces and the set F of all packet flows in the network. The algorithm maintains two main data structures, CoveredBy and Monitors, that indicate which flow covers each interface (i.e., function Φ) and which interface is to be monitored by each flow, respectively. These data structure also constitute the algorithm's output that is used to generate packet processing rules and configure a network. Initially, no flow has been assigned to monitor any interface yet; in Lines 1-2, CoveredBy and Monitors are initialized to reflect this. The algorithm also maintains four other auxiliary variables: κr (Line 3), NIFs (Line 4), SIFs (Line 5), and UFs (Line 6). Variable κr indicates the remaining telemetry capacity available for each flow. It is initialized with the telemetry capacity κ of the flows and is updated as assignments are made by the algorithm. NIFs indicates, for each flow, the number of interfaces not yet covered in its path. Variable SIFs keeps a sorted list of the interfaces in the path of a flow ordered non-decreasingly by the number of flows passing through them (and by the telemetry demand in case of a tie). Set UFs consists of all currently unassigned flows, initially UFs =F. Lines 7-16 contain the main repeat loop of the algorithm. At each iteration of the outermost loop, the algorithm first selects the unassigned flow fmax with the maximum number of interfaces still not covered in its path (Line 7) and removes it from UFs (Line 8). In case of a tie, the algorithm selects any of the flows with the maximum telemetry capacity. After finding fmax from F, it is assigned to monitor every interface still uncovered in its path following the ordering given by SIF(f) (Lines 10-13) and respecting its telemetry capacity (Lines 11). The remaining telemetry capacity is updated after each assignment (Line 14). For every assignment, the value of NIFs of all flows traversing the interface just covered is decreased by one (Lines 15-16), as the interface is no longer uncovered and new flows cannot be assigned to monitor it. The main loop is repeated until every flow has been considered or all interfaces have been covered by the solution. The worst-case computational complexity of this algorithm is given by $\mathcal {O}(n) + \mathcal {O}(m) + \mathcal {O}(m \cdot n \cdot \log n) + \mathcal {O}((n + m) \cdot (n\cdot m)) = \mathcal {O}(n^{2}\cdot m + n\cdot m^{2})$, where n is the number of interfaces in I and m is the number of flows in F. Therefore, the algorithm runs in polynomial time to the number of interfaces and flows in the network. Balance heuristic algorithm In this subsection, we formalize the Balance algorithm, which strives to minimize the maximum number of telemetry items to be transported by any single flow. Algorithm 2 shows the pseudo-code of Balance. Balance has the same input parameters and output data structures of Algorithm 1. Algorithm 2 also maintains the same κr and NIFs variables of Concentrate, which indicate the remaining telemetry capacity and the number of interfaces not yet covered in the path of each flow, respectively. Balance has two additional variables: NFs and NCIFs. NFs indicates, for every interface, the number of flows with available capacity passing through it. NCIFs is the set of all intefaces that are not yet covered by any flow. Lines 7-19 contain the main repeat loop of the algorithm. At each iteration of the outermost loop, the algorithm first selects the uncovered interface imm with the minimum number of flows with available capacity passing through it (Line 8) and removes it from NCIFs (Line 9). In case of a tie, any of the interfaces with maximum telemetry demand may be chosen. Next, from all flows traversing imm, the fmin flow collecting the least amount of telemetry items (i.e., κ(f)−κr(f)) out of those with available capacity is selected (Lines 10-11). In case of a tie, the flow with the minimum number of interfaces still not covered in its path is chosen. If the tie persists, the algorithm selects any one of the flows that tied in both of the steps. When imm and fmin have been found, flow fmin is assigned to monitor interface imm (Lines 12-13). After the assignment, some adjustments are made to variables κr, NIFs, and NFs. The remaining capacity κr of flow fmin is decreased by the demand δ of interface imm (Line 14). The number of uncovered interfaces NIFs is decreased by one for every flow passing through interface imm (Lines 15-16). If fmin has used all its capacity (Line 17) after been assigned to monitor imm, then it is necessary to update the NFs value for every interface through which fmin passes (Lines 18-19). This procedure is repeated until all active device interfaces in the network are covered, or there is not any flow with available capacity. The worst-case complexity of this algorithm is given by $\mathcal {O}(n + m) + \mathcal {O}((n + m)\cdot (n + m)) = \mathcal {O}(n^{2} + m^{2})$, where n is the number of interfaces in I and m is the number of flows in F. In this section, we present computational experiments with the models and algorithms introduced in the previous two sections of this paper. We start by describing the experimental setup and the dataset used in the experiments. Then, we detail two sets of experiments. The first set of experiments evaluates the proposed mathematical programming models and heuristic algorithms with regards to solution quality and processing time. We refer to the models of Section 3 as CMP (Concentrate) and BMP (Balance) and to the algorithms of Section 4 as CH (Concentrate Heuristic) and BH (Balance Heuristic). The second set of experiments compares the heuristics with regards to the performance factors introduced in Section 2. We also use the "full assignment" introduced in Section 2 as a baseline (and refer to it as FA). The experiments were carried out in a computer with an Intel Core i7-5557U CPU running at 3.10GHz, 16GB of DDR3 1867MHz RAM, and Apple macOS 10.12 operating system. The GLPK SolverFootnote 1 4.65 was used to solve the mathematical programs. The computation time limit to find a solution was set to 10 min. The proposed heuristic algorithms were implemented in C++ and compiled with the Apple LLVM version 9.0.0 (clang-900.0.39.2) compiler. The dataset used in the experiments is composed of 260 topologies of real wide area networks catalogued by the Internet Topology Zoo (ITZ) project [20] and traffic matrices made available in Repetita [21]. ITZ topologies range from 4 to 197 points-of-presence and from 16 to 880 interfaces. The maximum (minimum) network diameter is 37 (3) hops. To generate realistic traffic matrices, Gay et al. [21] followed the randomized gravity model proposed in [22]. We converted the available topologies to INTO problem instances. For every link in the topology, we considered there were two interfaces, one in each extremity. Interface telemetry demands were randomly chosen from the range from four to ten items following a uniform distribution. We choose this range since four can be considered the minimum amount of items to identify the source of a metadata field and its value (e.g., device ID + queue ID + queue ingress timestamp + queue delay) and ten is the number of common metadata fields that can be exported by devices according to [23]. For each pair of network endpoints with positive demands according to the traffic matrices, we considered there is a single aggregate network flow (i.e., we differentiate flows by the pair of network entry point and exit point). Flow telemetry capacities were randomly chosen following a normal distribution. Otherwise stated, the mean telemetry capacity is equal to 35 items, and the standard deviation is 5 items, which amounts for approximately 10% of the MTU being available for transporting metadata in each packet. Mathematical programming models and heuristic algorithms To work in practice, a procedure to solve any variation of the INTO problem should be able to provide high-quality solutions within short time intervals. This is necessary so that the monitoring campaign can quickly adapt to network policy changes and traffic fluctuation. In this first set of experiments, we evaluate the solution quality and processing time of the algorithms introduced in Section 4, namely Concentrate Heuristic (CH) and Balance Heuristic (BH), by comparing them to the mathematical programming models. We start by analyzing the processing times of the approaches. Figure 6 shows the time taken by the GLPK Solver to run each of the INTO problem instances for the mathematical programming models. As expected, it grows quickly with relation to instance size for both models. We note that the time to process an instance is also subject to other network characteristics besides size (e.g., diameter, degree of connectivity of nodes, heterogeneity of paths). Thus, in the graphs, we can expect that some networks, although smaller than other, take more time to be solved. Processing times for the mathematical programming models For the Concentrate Mathematical Program (CMP) model, the solver was not able to find an optimal solution and check optimality for networks with more than 90 interfaces (14 devices) within the 10-min time limit. The solver was able to find the optimal solution within the time limit for the INTO Balance instances with up to 252 interfaces (56 devices) using the Balance Mathematical Program (BMP) model. From these results, we conclude that solving CMP is generally harder than BMP. The difference in processing time between the two approaches can be attributed in part to the fact that the mathematical model CMP has more decision variables than BMP. Models with more variables tend to have larger solution spaces and, thus, take longer to explore their totality in order to check optimality. In summary, Fig. 6 shows that solving both versions of the INTO problem using the mathematical models takes considerable time, making their use impracticable in real, highly dynamic scenarios. Figure 7 shows the processing time of the heuristic algorithms CH and BH as a function of the network size. Both algorithms generate feasible solutions to all instances of their corresponding INTO variation in less than one second. These results are up to three orders of magnitude lower than the processing times required by the mathematical models. The short processing times achieved by both heuristic algorithms argues in favor of their adequacy to be applied in highly dynamic networks. Next, to confirm that they are adequate, we also evaluate the quality of the solutions given by them. Processing times for the heuristic algorithms. To evaluate the quality of the solutions provided by the heuristics, we compare their objective function values to lower bound models. We start by comparing the lower bound models and the mathematical programming models to estimate how close to the optimal values are the lower bounds. Then, we compare the lower bounds with the heuristic algorithms solutions considering the estimated gap. The lower bound for INTO Concentrate is computed by exchanging Eq. 3 of the CMP model by Eq. 12Footnote 2. The original equation had two purposes: (i) guarantee that no flow is assigned to collect and transport more items then its capacity allows and (ii) activate the variable yf (which is used by the objective function of CMP to count the number of telemetry-active flows) when any telemetry item is assigned to flow f∈F. With the new equation we assume a scenario where all flows would have unlimited telemetry capacity. The new, simpler constraint presented in Eq. 12 does not consider telemetry demands and capacities (first purpose), eliminating a summation and making it quicker to compute. Only the second purpose of the original equation is kept, i.e., all flows performing at least one telemetry action will be accounted for in the objective function. $$ x_{i,f} \leq y_{f}, \forall i \in I, \forall f \in F $$ In our experiments, the solver was able to find feasible solutions for the CMP model for 248 out of the 260 networks. Out of those 248 cases, the solver was able to certify optimality for only 28 instances. No feasible solution was found for 12 problem instances. The mean gap between the lower bound and CMP across all 248 feasible solutions found by the solver was 12.62 flows (with standard deviation equal to 11.68 flows). The minimum and maximum gap values were 0 and 50 flows, respectively. Compared to the lower bound, the mean gap for CH was 9.82, and the standard deviation was 7.93. The minimum and maximum gap values were 0 and 49 flows. Comparing the gaps, we conclude that the solutions generated by CH are slightly better than the feasible solutions provided by the CMP model within the 10-min time limit. Thus, the CH algorithm is not only able to generate solutions within one second but also provides high-quality solutions. To evaluate the quality of the solutions found to the INTO Balance variation, we compute a lower bound for each instance as the maximum value between (i) the maximum telemetry demand of a single interface and (ii) the sum of all demands divided by the total number of flows. Out of all 260 instances evaluated, for the BMP model, the solver was able to find feasible solutions within the time limit for 223. The solver was able to certify optimality for 174 out of these 223 cases. No feasible solution was found within 10 min for 37 instances. In our comparison, the optimal solution matched the lower bound in 171 out of the 174 optimal cases. Considering all 223 feasible solutions found, the mean lower bound to BMP gap was 0.84 items (with standard deviation equal to 2.37). The minimum and maximum gap values were 0 and 14 items, respectively. Concerning the BH algorithm, the mean gap to the INTO Balance lower bound was 0.09 items (the standard deviation was 0.63). The minimum and maximum gap values were 0 and 5 items. The BH algorithm was able to generate an optimal solution for all but 5 instances. Both BMP and BH have solutions with object function values very close to the lower bounds. From the experiments in this subsection we conclude that both of the proposed algorithms, CH and BH, generate high-quality solutions within short processing times, and, thus, are well suited to be applied in highly dynamic networks. Comparison of the INTO problem variations When optimizing the use of INT to perform monitoring, an operator may opt to configure the network according to one of the two variations of the INTO problem. In this remaining set of experiments, we compare the solutions generated by the proposed heuristic algorithms (CH and BH) and the baseline full assignment (FA) introduced in Section 2. To evaluate the algorithms, we consider the main INT constraints and performance influencing factors discussed in Section 2. Maximizing interface coverage As previously discussed in Section 2, the telemetry capacity of flow packets in a network may limit how many of the device interfaces can be monitored. In this subsection, we evaluate how sensitive the INT orchestration strategies are regarding interface coverage. For each of the assignment strategies, we set the initial mean packet telemetry capacity to 5 items (the standard deviation was kept at 5 items for the whole experiment). We then calculated the interface coverage – i.e., the percentage of device interfaces covered by at least one flow – for every network of the Internet Topology Zoo [20]. Finally, we increase the mean capacity in steps of 5 items until each assignment strategy was able to provide a solution with full (100%) coverage for all networks. Fig. 8 presents the results of this experiment as a CDF where the x-axis indicates coverage levels and the y-axis indicates percentages of the networks. For every pair of strategy and capacity level, we plot a curve in the graph. For the full assignment (FA curves in the plot), we report the real coverage levels that would be achieved without exceeding the packet MTU (i.e., telemetry capacity). Interface Coverage The main conclusion from the results presented in Fig. 8 is that the proposed heuristics (CH and BH) are more resilient to lower levels of telemetry capacity than the full assignment (FA). Even when the capacity is at its lowest level (5 items), they can achieve 100% interface coverage (full coverage) for about 25% of the networks. Furthermore, in the same scenario, about 80% of the networks have good coverage of at least 90% of interfaces. CH and BH present similar coverage for all capacity levels, with a slightly better, yet noticeable result observed for the latter. While both of the heuristics achieve full coverage when the mean telemetry capacity is 20 items, the full assignment only achieve it when that capacity is at least 35 items. In the following subsections, to avoid biasing or tainting the comparison, we will only present and consider the results where each strategy was able to achieve full coverage for all networks. That is, when the capacity is of at least 35 and 20 items for the full assignment and heurstic algorithms, respectively. Next, we continue the evaluation by considering quality and cost metrics related to the four performance factors introduced in Section 2. Minimizing flow packet load As introduced in Section 2 (Item (a)), one of the INT factors that may influence network performance is intrinsically related to the extent to which packets vary in size along their paths. The number of telemetry items flow packets collect from device interfaces (i.e., its telemetry load) determines this variation. The best approach to avoid causing significant jitter or drift in transmission times is to minimize the telemetry load of packets. Fig. 9 presents the cumulative distribution function of the mean flow packet load. For each orchestration strategy, the figure presents a curve representing the distribution of values when the mean telemetry capacity ($\bar {\kappa }$) is 35 items. The figure also presents 95% confidence intervals as filled areas in the graph. Mean and confidence interval for flow packet load when the mean telemetry capacity is 35 items The results in Fig. 9 show that BH achieves the best possible telemetry load per flow packet. The mean load is approximately seven items, which is also the mean telemetry demand of interfaces. This value indicates that in its solutions, BH tends to assign each telemetry-active flow to monitor one interface. The variability shown in the graph for BH is due to the variation of the interface telemetry demands. In all cases, CH and FA present higher load values than BH. CH presents higher values than BH because when minimizing the number of telemetry-active flows it tends to use as much as possible the capacity of (a small subset of) flows. CH also presents high variability for flow packet load, which is due to its greedy rationale to flow assignment. Its heuristic causes a group of flows to use most of their packet capacity while another group uses only a fraction to cover the remaining interfaces. Figure 10 illustrates the influence of the mean capacity of flow packets over the mean telemetry load. It reveals that BH is not influenced by the capacity. This phenomenon was expected since an increase in capacity has no impact in minimizing the maximum flow packet load (i.e., the optimization goal of BH). CH presents small increases in flow load as capacity increases. In turn, FA increases significantly the telemetry load imposed on flows when more capacity is available, which aligns with its objective of collecting as many items as possible with all flows. In a case where the telemetry capacity is assumed to be infinite, the mean flow packet load of FA would be an approximation of the mean telemetry demand of all flow paths in a network. Evaluation of flow load as telemetry capacity varies Minimizing flow usage The limitation on the processing capacity of forwarding devices and monitoring sinks (Section 2, Items (b) and (c)) prompts orchestration strategies to minimize the number of telemetry reports generated periodically. This minimization has the objective of alleviating the packet processing overhead on both forwarding devices and monitoring sinks/analyzers. In this subsection, we evaluate the flow usage (i.e., the number of telemetry-active flows) demanded by the strategies, as this number directly influences the number of reports generated. Figure 11 presents the flow usage as a function of the number of device interfaces in a network. For every combination of strategy, telemetry capacity and network we plot a point in the graph. We limit the y-axis to 1 800 flows to be able to compare the flow usage of the proposed heuristics. The total number of flows for the largest tested network (i.e., the one with 880 interfaces) is 38 612. Flow usage as a function of the number of interfaces in a network CH uses the minimum amount of flows across all strategies, which was expected since its main optimization objective is to minimize this value. CH typically assigns each telemetry-active flow to monitor about four interfaces, a 4:1 interface to flow ratio. BH presents a direct relationship between the number of active flows and of interfaces, i.e., each flow covers a single interface (1:1 ratio). Thus, BH uses, in the general case, four times more flows than CH. For a mean telemetry capacity of 35 items, CH uses 225 flows to cover the largest network in the dataset, which has 880 forwarding device interfaces, while BH uses 880 flows. For the same scenario, FA assigns all 38 612 flows (not shown in the graph) in the network to carry out telemetry. Thus, both of the heuristics use up to two orders of magnitude less flows then FA. CH is the most scalable of the strategies, followed by BH with a multiplicative increase by a constant factor of about four. Maximizing information correlation In addition to minimizing the number of telemetry-active flows, the limited processing capacity of monitoring sinks (Section 2, Item (c)) also motivates strategies to maximize the correlation of the information contained in each telemetry report received by the monitoring sinks, simplifying their analysis. In this evaluation, we consider the percentage of interfaces a flow covers from its path as a measure of this correlation. The results of the experiment are shown in Figs. 12 and 13. Figure 12 presents the CDF of the mean information correlation for the networks. The graph has a curve for each evaluated strategy showing the distribution of values when the mean telemetry capacity is 35 items. The figure also presents the 95% confidence intervals as filled areas in the graph. Figure 13 shows the effect of the telemetry capacity on the mean correlation. For clarity, we omit confidence intervals in this second figure. Mean and confidence interval for information correlation when the mean telemetry capacity is 35 items Evaluation of information correlation as the telemetry capacity of flows varies The results in Figs. 12 and 13 support the expected behavior of the heuristics. According to Fig 12 CH presents the best results among the heuristics, with (the top) da85% of networks having 50% or more information correlation. Note in the figure that the lower 15% of the networks (0%–15%) have an x-axis value below 50, while the remaining 85% (15%–100%) have a value equal or above 50. This means that a typical report covers at least half the path of a flow. We highlight that the results for FA in Fig. 13 show that reaching high correlation is very costly in terms of packet telemetry capacity. More specifically, to achieve 90% correlation for about 85% of the networks, the mean telemetry capacity must be about 50 items per packet. Observe (in Fig. 13) that the lower 15% of the networks have an x-axis value below 90 for curve FA ($\bar {\kappa } = 50$), while the remaining upper 85% have values above 90. Going back to Fig. 12, it also presents the significant variability in flow assignment (see filled area) regarding CH found previously in Fig. 9. This behavior confirms the previous conclusion that CH tends to assign a group of flows to cover (almost) their entire path, while another group covers only a few remaining interfaces each. BH is not influenced by telemetry capacity variation. This is concluded by the fact that all curves for BH in Fig. 13, representing different levels of telemetry capacity, superimpose each other. BH achieves at least 25% correlation for most of the networks in all scenarios, i.e., flows tend to cover about one-fourth of their paths. Optimizing information freshness As the last aspect of our comparison, the limitation on link bandwidth (Section 2, Item (d)) argues for (i) avoiding transporting telemetry data through too many links in a network and for (ii) distributing the origin of telemetry reports as much as possible among network devices. The mean information freshness – i.e., the mean number of hops the information collected at interfaces is transported in-band before being reported to a monitor sink – enables us to measure to which extent the strategies conform to this task. Figs. 14 and 15 present the freshness results. Figure 14 shows the CDF of the mean information freshness considering the three orchestration strategies. The filled areas in the graph represent the 95% confidence intervals. Figure 15 shows the freshness as a function of the network diameter (i.e., the length of the longest flow path). Mean and confidence interval for information freshness with mean telemetry capacity equal to 35 items Information freshness as a function of the network diameter BH keeps information freshness at the optimal value (zero) for most of the networks analyzed (Fig. 14). A value zero for freshness indicates that most information is reported to a monitoring sink immediately after being collected, which results in the best possible monitoring traffic distribution across a network. Figure 15 indicates that the network diameter has little to no effect on freshness for BH. FA typically causes flows to transport telemetry information for about two hops before reporting it. The freshness has slightly worse values for larger networks. CH presents the worst freshness values among strategies and is significantly influenced by the network diameter. CH comes to the point of making flows transport information up to 10 hops (in the mean case) for networks with a diameter of about 33 hops. Thus, CH tends to concentrate more the points where reports are generated, which may lead to link saturation. In this section, we review previous work that investigated the use of network and device mechanisms to monitor networks and services. NetSight [2] has packet mirroring as its fundamental monitoring piece, which is available in both OpenFlow [24] and traditional switches. In NetSight, every switch in the path of a packet creates a copy of it, called postcard, and sends it to a logically centralized control plane. The multiple postcards of a single packet passing through the network are combined in the control plane to form a packet history that tells the complete path the packet took inside the network and the modifications it underwent along the way. Depending on the size and level of activity of the network, NetSight may generate a considerable volume of monitoring data. To overcome this issue, Everflow [3] applies a match+action mechanism to filter packets and decide which ones should be mirrored, thus reducing the overheads at the cost of monitoring accuracy and level of detail. Stroboscope [4] also applies packet mirroring to monitor networks. It answers monitoring queries by scheduling the mirroring of millisecond-long slices of traffic while considering a budget to avoid network performance degradation. Payless [5] and AdaptiveSampling [6] followed a different direction of the previous work. They make use of two OpenFlow-enabled switch features to monitor a network: (i) the capability to store statistics related to table entries (which may represent flows) and (ii) the possibility of exporting these statistics via a polling mechanism. In these works, the polling frequency influences the quality (e.g., freshness) of the monitoring data. The higher the frequency, the more fine-grained the data. Payless and AdaptiveSampling dynamically and autonomously adjust the polling frequency to achieve a good trade-off between monitoring quality and cost. Another work in the context of software-defined measurement is DREAM [25]. DREAM is a system that dynamically adapts resources (i.e., TCAM entries) allocated to measurement tasks and partitions each of them among devices. DREAM supports multiple concurrent tasks and ensures that estimated values meet operator-specified levels of accuracy. Payless, AdaptiveSampling and DREAM have the goal of monitoring traffic characteristics and keeping costs low. Assessing the network state (e.g., switch queue occupancy) is outside their scope. The idea of orchestrating monitoring data collection across multiple devices to reduce costs is not new. Several investigations have been carried out with that objective. For example, Cormode et al. [26] proposed configuring devices to independently monitor their local variables and only report their values (to a centralized coordinator) when significant changes are observed. A-GAP [27] and H-GAP [28] organize measurement nodes into a logical tree graph. When a significant change is observed for a local variable, the node sends an update to its parent node. The latter node is responsible for aggregating the values from multiple devices and sending updates up the tree upon significant value change. The root node maintains network-wide aggregate values to be used for monitoring analysis. Tangari et al. [29] proposed decentralizing monitoring control. The monitoring control plane is composed of multiple distributed modules, each capable of performing measurement tasks independently. Their approach logically divides the network into multiple monitoring contexts, each with specific requirements. As a result, monitoring data tends to be aggregated and analyzed close to the source, reducing considerably the communication overhead. The rationale behind these works was conceived before the emergence of programmable data planes without considering the opportunity to programming it. As a consequence, in contrast to INTO, their solutions are based on traditional coarse-grained counters and aggregate statistics and their data exchange models operate at control plane timescales. More recently, with the emergence of programmable data planes and P4 [8], several works have explored programming forwarding devices to carry out custom, monitoring-oriented packet processing. For example, HashPipe [30] is an algorithm that implements a custom pipeline targeting programmable data planes [7, 31, 32] to detect heavy hitters. Snappy [33] and NCDA [34] focus on the use of in-switch memory and the visibility into device queue occupancy provided by P4 to detect congestion events, identify the offending flows, and execute congestion avoidance actions. These works contrast with ours in that they are focused on device-wise monitoring tasks, while INTO orchestrates network-wide monitoring telemetry. A work more related to our context is Sonata [35], a system that coordinates the collection and analysis of network traffic to answer operator-defined monitoring queries. These queries consist of a sequence of dataflow operators (e.g., filter, map, reduce) to be executed over a stream of packets. Sonata is based upon stream processing systems and programmable forwarding devices, partitioning queries across them. Similar to INTO, it has the goal of minimizing the amount of data that needs to be sent to and analyzed by the control plane (i.e., stream processors). Sonata leverages data plane programmability to offload as much as possible of each query to the forwarding devices, considerably reducing the packet stream before sending it to stream processors. Different from INTO – which targets monitoring network state, behavior and performance – Sonata focuses on the analysis of traffic characteristics. Furthermore, Sonata does not apply in-band network telemetry for metadata reporting. In our work, we revisit the challenge of monitoring networks effectively and efficiently. We identify the new opportunities for obtaining accurate and fine-grained information about forwarding device state, behavior and performance considering the recent advances in SDN and programmable networks. In a previous work [15], we have taken an initial step towards understanding the trade-offs involved in conducting network monitoring via a mechanism such as in-band network telemetry (INT) [10–12]. We identified the key factors that impact performance associated with it and proposed heuristic algorithms to orchestrate INT tasks to minimize overheads. In the current paper, we build upon our previous work [15] by formalizing in-band network telemetry orchestration as an optimization problem. We also prove that it is an NP-Complete problem, proposing integer linear programming models to solve it. And, finally, redesign the proposed heuristics to both better suit realistic network scenarios and produce high-quality solutions within strict computational time. This work introduced the In-band Network Telemetry Orchestration (INTO) problem. It consists in minimizing monitoring overheads in the data, control and management planes when using In-band Network Telemetry (INT) to collect the state and behavior of forwarding device interfaces. We formalized two variations of the INTO problem and proposed integer linear programming models to solve them. The first variation of the problem, INTO Concentrate, has the goal of minimizing the number of flows used for telemetry. The second variation, INTO Balance, seeks to minimize the maximum telemetry load (i.e., the number of telemetry items transported) among packets of distinct flows. We proved that both variations belong to the NP-Complete class of computational problems. Through our evaluation using real networks topologies, we found that both of the proposed models take a long time to solve the INTO problem. This result motivated us to design two heuristic algorithms to produce feasible solutions in polynomial computational time to the network size and number of flows. Experimental results show that the proposed heuristics produce high-quality solutions in under 1 second for all of the real networks evaluated. To assess the benefits and limitations of the proposed heuristics, we compared them against each other and with the baseline full assignment approach. We concluded that the heuristic to solve INTO Concentrate (CH) performs well in minimizing the overhead on forwarding devices and monitoring sinks. The number of telemetry reports that have to be generated periodically is minimal, and the information reported to sinks has a significant level of correlation to ease their analysis. As a consequence, CH is the most scalable of the strategies and may be particularly recommended for medium to large networks. The INTO Balance heuristic (BH) imposes the lowest telemetry load per monitoring-active flow, and results in the best distribution of the telemetry load among forwarding devices and links in a network. These results suggest that BH may be an adequate strategy for low latency networks or when monitoring traffic highly sensitive to packet size changes. Both of the heuristics also scale well with network size, which contrasts to the full assignment, as it causes considerable overhead on network traffic and devices. As future work, we intend to explore other assignment function options (e.g., interface demand partitioning, limited coverage redundancy). We also intend to investigate how to translate high-level monitoring policies to individual device interface-level demands. Finally, we plan to explore how in-band network telemetry orchestration can be used to help with tasks such as congestion avoidance and load balancing. Our data and material will be made available to any interested reader by sending a request for access to the corresponding author via e-mail. GNU Linear Programming Kit Linear Programming/Mixed-Integer Programming Solver (https://www.gnu.org/software/glpk/). The description of the variables can be found in Table 1. 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This work was partially funded by the Conselho Nacional de Desenvolvimento Científico e Tecnológico – Brasil (CNPq) project number 441892/2016-7, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) finance code 001, and the Rede Nacional de Ensino e Pesquisa – Brasil (RNP). Institute of Informatics, Federal University of Rio Grande do Sul, Porto Alegre, Brazil Jonatas Adilson Marques, Roberto Irajá Tavares da Costa Filho & Luciano Paschoal Gaspary Federal University of Pampa, Alegrete, Brazil Marcelo Caggiani Luizelli Jonatas Adilson Marques Roberto Irajá Tavares da Costa Filho Luciano Paschoal Gaspary JM collaborated in the formalization of the INTO problem, participated in the proposal of optimization models, participated in the formulation of the proofs of NP-completeness, participated in the design of the heuristic algorithms, coded proof-of-concept implementations, ran evaluation experiments, and participated in the analysis of results obtained from experimental evaluations. ML collaborated in the formalization of the INTO problem, participated in the proposal of optimization problems, and participated in the formulation of the proofs of NP-completeness. RT collaborated in the formalization of the INTO problem, and participated in the analysis of results obtained from experimental evaluations. LG collaborated in the formalization of the INTO problem, participated in the design of the heuristic algorithms, and analyzed results obtained from experimental evaluations. All authors wrote, read, and approved the final manuscript. Correspondence to Jonatas Adilson Marques. Marques, J., Luizelli, M., Tavares da Costa Filho, R. et al. An optimization-based approach for efficient network monitoring using in-band network telemetry. J Internet Serv Appl 10, 12 (2019). https://doi.org/10.1186/s13174-019-0112-0 Programmable Networks	CommonCrawl
Existence and uniqueness of global classical solutions to a two dimensional two species cancer invasion haptotaxis model A vicinal surface model for epitaxial growth with logarithmic free energy Yuan Gao , , Hangjie Ji ‡, , Jian-Guo Liu #,†, and Thomas P. Witelski #, Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong Department of Mathematics‡, University of California, Los Angeles, Los Angeles, CA 90095, USA Department of Mathematics#, Duke University, Durham, NC 27708, USA Department of Physics†, Duke University, Durham, NC 27708, USA * Corresponding author: Hangjie Ji ([email protected]) Received April 2017 Revised December 2017 Published June 2018 We study a continuum model for solid films that arises from the modeling of one-dimensional step flows on a vicinal surface in the attachment-detachment-limited regime. The resulting nonlinear partial differential equation, $u_t = -u^2(u^3+α u)_{hhhh}$, gives the evolution for the surface slope $u$ as a function of the local height $h$ in a monotone step train. Subject to periodic boundary conditions and positive initial conditions, we prove the existence, uniqueness and positivity of global strong solutions to this PDE using two Lyapunov energy functions. The long time behavior of $u$ converging to a constant that only depends on the initial data is also investigated both analytically and numerically. Keywords: Vicinal surface, attachment-detachment-limited case, step slope, nonlinear partial differential equations. Mathematics Subject Classification: Primary: 35K25, 35K55, 74A50. Citation: Yuan Gao, Hangjie Ji, Jian-Guo Liu, Thomas P. Witelski. A vicinal surface model for epitaxial growth with logarithmic free energy. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4433-4453. doi: 10.3934/dcdsb.2018170 H. Al Hajj Shehadeh, R. V. 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Xiang, Derivation of a continuum model for epitaxial growth with elasticity on vicinal surface, SIAM Journal on Applied Mathematics, 63 (2002), 241-258. doi: 10.1137/S003613990139828X. Google Scholar Figure 1. (Top) A typical PDE simulation for (1.10) with $\alpha = 1$ on $0\le x\le 1$ and (bottom) the corresponding plot of $u(t,h)$ with boundary conditions (1.15) and $H = 2$, clearly showing the convergence of $h$ to a straight line, with the slope $u$ approaching to a spatially-uniform profile $u = 2$. Figure 2. A numerical simulation of PDE (1.6) plotted in semi-log coordinates starting from the initial condition (5.1) (plotted with the dashed line): (top) early stage near-rupture is approached as the global minimum decreases from $0.07$ to $0.007$ for $0<t< 0.0032$; (bottom) later stage behavior for $t>0.0032$ as the solution approaches a constant $u^{\star} = 0.27$. Figure 3. (Top) A numerical simulation of PDE (1.13) starting from identical initial conditions used in Fig. 2 showing convergence to a spatially-uniform solution $u = u^{\star}$ as $t \to \infty$. (Bottom) A plot showing that $u_{m}(t) = \min_h u(t,h)$ is bounded below by $\mathcal{J}(E(t))$ given by (3.32) which is in line with the conclusion of Theorem 1, and that the asymptotic lower bound $\mathcal{J}(E(t)) \to {1}/{(2L)}$ for $t \to \infty$ as in (3.8). Figure 4. Plots of corresponding energy $E$ in (2.5) and (5.7) for PDE simulations in Fig. 2 and Fig. 3. The energy $E(t)$ decays exponentially to zero following (5.6) with $k = 2\pi$. Figure 5. Evolution of the surface height $h(t,x)$ and slope $h_x(t,x)$ following equation (6.2) with $\alpha = 0$ starting from initial condition $h_0(x) = \sin(2\pi x)$ on $0\le x\le 1$, showing convergence to spatially-uniform solution $h \equiv 0$ as $t \to \infty$. Figure 6. Evolution of the surface height $h(t,x)$ and slope $h_x(t,x)$ for equation (6.2) with $\alpha = 1$ starting from identical initial data used in Fig. 5, showing convergence to a piece-wise constant profile in $h$ and jump in $h_x$. Hua Qiu, Zheng-An Yao. The regularized Boussinesq equations with partial dissipations in dimension two. Electronic Research Archive, 2020, 28 (4) : 1375-1393. doi: 10.3934/era.2020073 Guido Cavallaro, Roberto Garra, Carlo Marchioro. Long time localization of modified surface quasi-geostrophic equations. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020336 Karoline Disser. Global existence and uniqueness for a volume-surface reaction-nonlinear-diffusion system. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 321-330. doi: 10.3934/dcdss.2020326 Maoding Zhen, Binlin Zhang, Vicenţiu D. Rădulescu. Normalized solutions for nonlinear coupled fractional systems: Low and high perturbations in the attractive case. 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Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 701-746. doi: 10.3934/dcds.2020298 Philippe G. Lefloch, Cristinel Mardare, Sorin Mardare. Isometric immersions into the Minkowski spacetime for Lorentzian manifolds with limited regularity. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 341-365. doi: 10.3934/dcds.2009.23.341 Yuan Gao Hangjie Ji Jian-Guo Liu Thomas P. Witelski	CommonCrawl
Volume 19 Supplement 9 Proceedings of the 2018 International Conference on Intelligent Computing (ICIC 2018) and Intelligent Computing and Biomedical Informatics (ICBI) 2018 conference: medical informatics and decision making A comparison between two semantic deep learning frameworks for the autosomal dominant polycystic kidney disease segmentation based on magnetic resonance images Vitoantonio Bevilacqua1, Antonio Brunetti1, Giacomo Donato Cascarano1, Andrea Guerriero1, Francesco Pesce2, Marco Moschetta2 & Loreto Gesualdo2 The automatic segmentation of kidneys in medical images is not a trivial task when the subjects undergoing the medical examination are affected by Autosomal Dominant Polycystic Kidney Disease (ADPKD). Several works dealing with the segmentation of Computed Tomography images from pathological subjects were proposed, showing high invasiveness of the examination or requiring interaction by the user for performing the segmentation of the images. In this work, we propose a fully-automated approach for the segmentation of Magnetic Resonance images, both reducing the invasiveness of the acquisition device and not requiring any interaction by the users for the segmentation of the images. Two different approaches are proposed based on Deep Learning architectures using Convolutional Neural Networks (CNN) for the semantic segmentation of images, without needing to extract any hand-crafted features. In details, the first approach performs the automatic segmentation of images without any procedure for pre-processing the input. Conversely, the second approach performs a two-steps classification strategy: a first CNN automatically detects Regions Of Interest (ROIs); a subsequent classifier performs the semantic segmentation on the ROIs previously extracted. Results show that even though the detection of ROIs shows an overall high number of false positives, the subsequent semantic segmentation on the extracted ROIs allows achieving high performance in terms of mean Accuracy. However, the segmentation of the entire images input to the network remains the most accurate and reliable approach showing better performance than the previous approach. The obtained results show that both the investigated approaches are reliable for the semantic segmentation of polycystic kidneys since both the strategies reach an Accuracy higher than 85%. Also, both the investigated methodologies show performances comparable and consistent with other approaches found in literature working on images from different sources, reducing both the invasiveness of the analyses and the interaction needed by the users for performing the segmentation task. Autosomal Dominant Polycystic Kidney Disease (ADPKD) is a hereditary disease characterised by the onset of renal cysts that lead to a progressive increase of the Total Kidney Volume (TKV) over time. Specifically, ADPKD is a genetic disorder in which the renal tubules become structurally abnormal, resulting in the development and growth of multiple cysts within the kidney parenchyma [1]. The mutation of two different genes characterises the disease. The ADPKD type I, which is caused by the PKD1 gene mutation, involves the 85 - 90% of the cases, usually affecting people older than 30 years. The mutation of the PKD2 gene, instead, leads to ADPKD type II (affecting the 10 - 15% of the cases), which mostly regards children developing cysts already when in the maternal uterus and die within a year. HConsidering the clinical characteristics of the patients with PKD1 or PKD2 mutations, they are the same, even though the latter mutation is associated with a milder clinical phenotype and a later onset of End-Stage Kidney Disease (ESKD). In all the cases, the size of cysts is extremely variable, ranging from some millimetres to 4 - 5 centimetres [2]. Currently, there is not a specific cure for ADPKD and the TKV estimation over time allows to monitor the disease progression. Tolvaptan has been reported to slow the rate of cysts enlargement and, consequently, the progressive kidney function decline towards ESKD [3, 4]. Since all the actual pharmacological treatments aimed at slowing the growth of the cysts, the design of a non-invasive and accurate assessment of the renal volume is of fundamental importance for the estimation and assessment of the ADPKD progression over time. There are several methods in the literature performing the TKV estimation; traditional methodologies, requiring imaging acquisitions, such as Computed Tomography (CT) and Magnetic Resonance (MR), include stereology and manual segmentation [5, 6]. Also, several studies tried to correlate this metric with body surface and area measurements in order to have a non-invasive estimation of TKV [7, 8]. Stereology consists in the superimposition of a square grid, with specific cell positions and spacing, on each slice of the volumetric acquisition (CT or MR). The bidimensional area obtained counting all the cells containing parts of the kidneys, interpolated with the other slices, considering the thickness of the acquisitions, allows obtaining the final three-dimensional volume. Manual segmentation, instead, requires the manual contouring of the kidney regions contained in every slice. Several tools supporting this task have been developed, introducing digital free-hand contouring tools or interactive segmentation systems to assist the clinicians while delineating the region of interest. Considering both the phenotyping of the disease and the introduced approaches, the segmentation of biomedical images of kidneys is a tricky and troublesome task, strictly dependent on the human operator performing the segmentation, also requiring expert training. In fact, co-morbidities and the presence of cysts in neighbouring organs or contact surfaces make challenging achieving an accurate and standardised assessment of the TKV. To reduce the limitations of the previous methodologies, both in time and performance, due to the manual interaction, several approaches for the semi-automatic segmentation of kidneys have been investigated such as the mid-slice or the ellipsoid methods, allowing to estimate the TKV starting from a reduced number of selected slices [9–11]. Although the reported methodologies are faster and more compliant than the previous ones, these are far from being accurate enough to be used in clinical protocols [12, 13]. In recent years, innovative approaches based on Deep Learning (DL) strategies have been introduced for the classification and segmentation of images. In details, deep architectures, such as Deep Neural Networks (DNNs) or Convolutional Neural Networks (CNNs), allowed to perform image classification tasks, detection of Regions Of Interest (ROIs) or semantic segmentation [14–17], reaching higher performance than traditional approaches [18]. The architecture of DL classifiers let avoiding the design of procedures for extracting hand-crafted features, as the classifier itself generally computes the most characteristic features automatically for each specific dataset. These peculiarities let DL approaches to be investigated in different fields, including medical imaging, signal processing or gene expression analysis [19–23]. Lastly, recent studies about imaging acquisitions for assessing kidneys growth suggested that MR should be preferred to other imaging techniques [24]. However, different research works allowed estimating TKV starting from CT images thanks to the higher availability of the acquisition devices and the more accurate and reliable measurement of TKV and the volume of cysts. On the other side, CT protocols for ADPKD are always contrast-enhanced using a contrast medium harmful for the health of the patient under examination; also, CT exposes the patients to ionising radiations. On these premises, the automatic, or semi-automatic, segmentation of images from MR acquisitions for improving the TKV estimation capabilities should be further investigated for improving the state-of-the-art performances. Starting from a preliminary work performed on a small set of patients [25], we present two different approaches based on DL architectures to perform the automatic segmentation of kidneys affected by ADPKD starting from MR acquisitions. Specifically, we designed and evaluated several Convolutional Neural Networks, for discriminating the class of each pixel of the images, in order to perform their segmentation; Fig. 1 represents the corresponding workflow. Subsequently, we investigated the object detection approach using the Regions with CNN (R-CNN) technique [26] to automatically detect ROIs containing parts of the kidneys, with the aim to subsequently perform the semantic segmentation only on the extracted regions; Fig. 2 shows a representation of the workflow implemented in this approach. Workflow for the semantic segmentation starting from the full image Workflow for the semantic segmentation of ROIs automatically detected with R-CNN Patients and acquisition protocol From February to July 2017, 18 patients affected by ADPKD (mean age 31.25 ± 15.52 years) underwent Magnetic Resonance examinations for assessing the TKV. The acquisition protocol was carried out by the physicians from the Department of Emergency and Organ Transplantations (DETO) of the Bari University Hospital. Examinations for the acquisition of the images were performed on a 1.5 Tesla MR device (Achieva, Philips Medical Systems, Best, The Netherlands) by using a four-channel breast coil. The protocol did not use contrast material intravenous injection and consisted of: Transverse and Coronal Short-TI Inversion Recovery (STIR) Turbo-Spin-Echo (TSE) sequences (TR/TE/TI = 3.800/60/165 ms, field of view (FOV) = 250 x 450 mm (AP x RL), matrix 168 x 300, 50 slices with 3 mm slice thickness and without gaps, 3 averages, turbo factor 23, resulting in a voxel size of 1.5 x 1.5 x 3.0 mm3; sequence duration of 4.03 min); Transverse and Coronal T2-weighted TSE (TR/TE = 6.300/130 ms, FOV = 250 x 450 mm (AP x RL), matrix 336 x 600, 50 slices with 3 mm slice thickness and without gaps, 3 averages, turbo factor 59, SENSE factor 1.7, resulting in a voxel size of 0.75 x 0.75 x 3.0 mm3; sequence duration of 3.09 min); Three-Dimensional (3D) T1-Weighted High Resolution Isotropic Volume Examination (THRIVE) sequence (TR/TE = 4.4/2.0 ms, FOV = 250 x 450 x 150 mm (AP x RL x FH), matrix 168 x 300, 100 slices with 1.5 mm slice thickness, turbo factor 50, SENSE factor 1.6, data acquisition time of 1 min 30 s). In this work, only the coronal T2-Weighted TSE sequence only was considered for the processing and classification strategies. In order to have the segmentation ground truth for all the acquired images, our framework included a preliminary step allowing the radiologists to manually contour all the ROIs using a digital tool specifically designed and implemented for this task. After the manual contouring of the kidneys, 526 images, with the corresponding labelled samples, constituted the working dataset; Fig. 3 represents an MR image with the corresponding labelled sample, where white pixels belong to the kidneys whereas the black ones include the remaining parts of the image. Example of an input image segmented manually; left: the representation of a DICOM image in greyscale; right: the mask obtained after the manual contouring of the selected slice Segmentation approaches Two different approaches based on DL techniques have been investigated to perform a fully-automated segmentation of polycystic kidneys without needing to design any procedure for the extraction of hand-crafted features. In details, the first approach allowed performing the semantic segmentation of the MR images, classifying each pixel belonging to the kidney or not; the second methodology, instead, allowed performing the detection of reduced areas containing the kidneys before their semantic segmentation. Semantic segmentation Semantic segmentation is a procedure allowing to perform the automatic classification of each pixel of images; thus, it is possible to classify each pixel of an image with a specific label. Although the segmentation of images is a well-established process in literature, counting a multitude of works and algorithms developed in several fields for different aims [27–29], the introduction and spread of DL architectures for performing this task, such as Convolutional Neural Networks, let image segmentation to regain interest in the scientific community [30, 31]. According to different architectures designed in previous works, such as SegNet [32] and Fully Convolutional Network (FCN) [33], the CNNs performing semantic segmentation tasks show an encoder-decoder design, as the architecture represented in Fig. 4. Traditionally, this kind of classifier includes several encoders interspersed with pooling layers for downsampling the input; each encoder includes sequences of Convolutional layers, Normalisation layers and Linear layers. Based on the encoding part, there are specular decoders with up-sampling layers for reconstructing the input size. Finally, there are fully-connected neural units before the final classification layer able to label each pixel of the input image. Encoder–Decoder architecture for SegNet [32] In this work, we designed and tested several CNNs architectures for the segmentation of the images. Since optimising the architecture of classifiers is still an open problem [34–36], often faced with evolutionary approaches, we decided to start from a well-known general CNN, the VGG-16 [37], and modify its structure varying several parameters. These included the number of encoders (and decoders), the number of layers for each encoder, the number of convolutional filters for each layer and the learner used during the training (i.e., SGDM - stochastic gradient descent with momentum, or ADAM [38]). All the investigated architectures included convolutional layers with kernels [3x3], stride [1 1] and padding [1 1 1 1] allowing to keep unchanged the dimensions of the input across each encoder; downsampling (and upsampling) was performed only in the max-pooling layers (upsampling layers for the decoder) having stride [2 2] and dimension [2x2]. The semantic segmentation of the input images took into account two classes: Kidney and Background. Considering the example reported in Fig. 3, the white pixels were labelled as Kidney, whereas the remaining pixels as Background. For training the classifiers, also the dataset augmentation was performed according to recent works demonstrating the effectiveness of this procedure for improving the classification performance [31, 39, 40]; the following image transformations were randomly performed: horizontal shift in the range [-200; 200] pixels; horizontal flip; scaling with factor ranging in [0.5; 4]. Table 1 reports the configurations designed and tested for performing this task in terms of number of layers per encoder, number of convolutional filters per layer and applied learner. The table reports only the three configurations showing the higher performance among all the investigated architectures. Table 1 Configurations designed and tested for the semantic segmentation of the full image Regions with convolutional neural networks Due to the presence of cysts in the organs near the kidneys and very similar structures located near the area of interest, which may affect the segmentation performance, we investigated a second approach based on the object detection strategy using R-CNN. In this approach, we designed a classifier for performing the automatic detection of smaller regions inside each input image to subsequently segment according to the procedure described in the previous section. Object detection is a technique for finding instances of specific classes in images or videos. Like the semantic segmentation, also the object detection is a well-established process in literature employed in different fields [41, 42]. According to the literature, the CNNs for object detection include a region proposal algorithm, often based on EdgeBoxes or Selective Search [43, 44], as a pre-processing step before running the classification algorithm. Traditional R-CNN and Fast R-CNN are the most employed techniques [26, 45]. Recently, Faster R-CNN was also introduced, addressing the region proposal mechanism using the CNN itself, thus making the region proposal a part of the CNN training and prediction steps [46]. FAs for the previous approach, we investigated several CNN architectures for detecting areas containing the kidney, considering the Fast R-CNN approach. For creating the ground truth, the manual contour of each kidney was enclosed in a rectangular bounding box and used for training the network. Differently for the CNN aimed at performing the semantic segmentation, these architectures have only the encoding part, where each encoder includes Convolutional layers and ReLu layers. Each encoder ends with a max-pooling layer to perform image sub-sampling (size [3x3] and stride [2 2]). At the end of the encoding part, there are two fully-connected layers before the final classification layer. Table 2 reports the configurations designed and tested for the detection purpose (in this case too, the table reports only the three configurations that reached the higher performance). Table 2 Configurations designed and tested for the CNN in the ROI detector After designing the classifier for the automatic detection of the ROIs, the same architectures designed for the segmentation of the whole images (reported in Table 1), were considered for performing the semantic segmentation of the ROIs. Furthermore, since the detected ROIs might have different sizes, a rescaling procedure was performed to adapt all the ROIs to the size required by the CNN for the segmentation task. Images augmentation was performed, as well, considering the following image transformations: horizontal shift in the range [-25; 25] pixels; vertical shift in the range [-25; 25] pixels; scaling with scale factor ranging in [0.5; 1.1]. This section reports the results for both the investigated approaches. In particular, we describe the performance obtained considering the R-CNN approach and subsequently, the results of the classifiers performing the semantic segmentation on both the full image and the ROIs automatically detected. The input dataset, which was constituted by MR images from 18 patients, was randomly split to create the training and test sets considering data from 15 and 3 patients, respectively. For improving the generalisation capabilities of the segmentation system, we performed a 5-fold cross-validation for the training the classifiers. The final segmentation on the images from the test set was obtained through the majority voting computed among the segmentation results from each trained classifier. We considered several metrics for evaluating the classifiers; all the reported results refer to the performance obtained evaluating the networks only on the test set. Accuracy (Eq. 1), Boundary F1 Score, or BF Score, (Eq. 2) and Jaccard Similarity Coefficient, or Intersection over Union - IoU, (Eq. 3)were computed considering the number of instances of True Positives (TP), True Negatives (TN), False Positives (FP) and False Negatives (FN), where the Positive label corresponds to a pixel belonging to the Kidney class for the semantic segmentation approach, or to a ROI correctly detected (confidence > 0.8), for the R-CNN approach. Regarding the semantic segmentation, the BF Score measures how close the predicted boundary of an object matches the corresponding ground truth; it is defined as the harmonic mean of the Precision (Eq. 5) and Recall (Eq. 6) values. The resulting score spreads in the range [0, 1], from a bad to a good match. The Jaccard Similarity Coefficient, instead, is the ratio between the number of pixels belonging to the Positive class classified correctly (TP) and the sum of the number of pixels belonging to the Positive class (P =TP+FN) and the Negative pixels wrongly predicted as Positive (FP). Regarding R-CNN performance, the Average Precision (Eq. 5) and the Log-Average Miss Rate were evaluated, considering the Miss Rate (MR) according to Eq. 4. $$ Accuracy \;=\; \frac{TP+TN}{TP+TN+FP+FN} $$ $$ Boundary\;F1\;Score \;=\; \frac{2PrecisionRecall}{Precision+Recall} $$ $$ Jaccard\;Similarity\;Coefficient \;=\; \frac{TP}{TP+FP+FN} $$ $$ Miss\;Rate \;=\; \frac{FN}{FN+TP} $$ $$ Precision \;=\; \frac{TP}{TP+FP} $$ $$ Recall \;=\; \frac{TP}{TP+FN} $$ R-CNN performance For each R-CNN architecture reported in Table 2, the Precision-Recall plot, showing the Precision obtained at different Recall values, and the Log-Average Miss Rate plot, reporting how varies the miss rate at different levels of FP per image are represented. Specifically, Figs. 5, 6 and 7 show the plots for R-CNN-1, R-CNN-2 and R-CNN-3 respectively. Figure 8, instead, shows the result obtained performing the detection of kidneys on an image sample. As represented in the plots, the average Precision for R-CNN-1 and R-CNN-3 is higher than 0.75, also maintaining low the Log-Average Miss Rate. Precision – Recall plot and log Average Miss rate for R-CNN-1 Results from R-CNN classifier. Input image is on the left; the image on the right contains squares on the detected ROIs, each one is associated with a score Since the aim of detecting ROIs was the identification of regions with fewer Background pixels, respect to the whole image, for the subsequent semantic segmentation step, R-CNN-1 revealed to be the best candidate among all the analysed architectures. In fact, it reached a Recall value of about 0.8 with the Precision higher than 0.65, meaning that the classifier was able to detect the 80% of the ROIs containing the kidneys, but with a high number of False Positives. However, this was not a problem since the subsequent step of semantic segmentation would detect all the pixels belonging to the Kidney class. Semantic segmentation performance Concerning the semantic segmentation, this section reports the performance obtained for the segmentation of both MR images and ROIs. Specifically, Table 3 shows the results obtained for each of the CNN architectures performing the semantic segmentation of the MR image, without performing any image processing procedure. As reported in the table, the architecture achieving the highest performance for the semantic segmentation of the full image is the S-CNN-1, showing an Accuracy higher than 88%. Table 3 Performance indices for the classifiers working on MR images The introduction of an additional layer into the first encoder of VGG-16 architecture allowed the network to create a set of features more significant and discriminative than those generated by the others, leading to more accurate classification performance. Conversely, increasing the number of convolutional filters in the first layer of the first encoder of S-CNN-1 did not improve the overall discrimination capabilities of the classifier. Table 4 reports the normalised confusion matrices obtained for the three considered cases in this approach, whereas Fig. 9 shows an example of the output generated by the implemented classifier performing the semantic segmentation of the MR images. Result of the semantic segmentation considering an image sample. Top left: the MR slice represented in greyscale; top right: the segmentation result; bottom left: the ground-truth mask; bottom right: superimposition of the segmentation result to the ground-truth mask Table 4 Normalized Confusion Matrix for VGG-16, S-CNN-1 and S-CNN-2 segmenting the MR images for the test set As for the segmentation of the whole MR images, Table 5 reports the performance indices for the semantic segmentation of the ROIs automatically detected by the R-CNN-1, which showed the optimal trade-off in detecting ROIs considering the miss rate. As for the previous case, the S-CNN-1 architecture allowed achieving the highest Accuracy in performing the semantic segmentation of the ROIs. Table 6 reports the normalised confusion matrices for all the classifiers investigated. Figure 10, instead, shows the results obtained for the semantic segmentation of ROI extracted from an image sample. Example result for ROI detection and semantic segmentation. Top left: the MR slice represented in greyscale; top right: the R-CNN detection result; middle left: one of the detected ROIs; middle right the segmentation result; bottom left: the ground-truth mask for the considered ROI; bottom right: superimposition of the classification result to the ground-truth mask Table 5 Performance indices for the classifiers working on the ROIs Table 6 Normalized Confusion Matrix for VGG-16, S-CNN-1 and S-CNN-2 segmenting the ROIs detected by the R-CNN-1 from the MR images of the test set In recent years, several works were proposed dealing with the segmentation of diagnostics images for assessing the ADPKD. Since the most used imaging procedure includes CT scans, most of the researches consider this kind of images in order to support the clinical assessment of the pathology. In some cases, the proposed approaches need minimum interaction by the user for the complete segmentation of the kidneys [47, 48]. Also, some procedures in literature dealt with the fully-automated segmentation of the images, some of them based on DL strategies [49, 50]. However, the proposed approaches for the automatic segmentation show several limitations, including the invasiveness from the contrast medium used for enhancing CT acquisitions [51], or rather the necessity of having an a-priori knowledge for the correct processing of the images [52]. In order to reduce the invasiveness of the imaging analysis, a preliminary investigation proposing a fully automated approach for the segmentation of non-contrast-enhanced CT images was proposed very recently, showing good performance on a reduced cohort of patients [53]. In this work, instead, the developed classification systems allowed to reach performances of about 80% of Accuracy in performing the segmentation of MR images, without using any procedure for contrast enhancement. However, the segmentation of the entire MR image revealed to be more reliable than those performed on the extracted ROIs. In fact, although the phase of extracting subregions from MR images showed an average Precision of 78%, it could still not find areas of interest, thus missing regions belonging to the kidneys. According to the analysed literature, the reported results are consistent with other precursory investigations dealing with MR images, including the preliminary results presented in [25] on a reduced cohort of patients. Also, the proposed approaches overcome the limitations shown by manual or semi-automatic procedures in segmenting kidneys affected by ADPKD for evaluating diagnostics and prognostics parameters. In addition, the proposed methodologies did not use any contrast medium, thus without any harmful or potentially lethal ionising radiation for the patients. In this work, we investigated two strategies performing the automatic segmentation of MR images from people affected by ADPKD based on DL architectures. Both the designed strategies considered several Convolutional Neural Networks for classifying, between Kidney or Backgroud, all the pixels in the images. In the first approach, we trained, validated and tested the classifiers considering the full MR image as input, without performing any procedure of image pre-processing. The second methodology, instead, investigated the object detection approach using the Regions with CNN (R-CNN) technique for firstly detecting ROIs containing parts of the kidneys. Subsequently, we employed (trained, validated and tested) the CNNs considered in the previous approach to perform the semantic segmentation on the ROIs automatically extracted by the R-CNN showing the most reliable performance. The obtained results show that both the approaches are comparable and consistent with other methodologies reported in the literature, but dealing with images from different sources, such as CT scans. Also, the proposed approaches may be considered reliable methods to perform a fully-automated segmentation of kidneys affected by ADPKD. In the future, the interaction among Deep Learning strategies and image processing techniques will be further investigated to improve the performance reached by the actual classifiers. Moreover, evolutionary approaches for optimising the topology of classifiers, or their hyper-parameters, will also be explored considering the acquired images in a three-dimensional way. The dataset employed for the current study is not publicly available due to restrictions associated with the anonymity of participants but could be made available from the corresponding author on reasonable request. 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Performance of an artificial multi-observer deep neural network for fully automated segmentation of polycystic kidneys. J Digit Imaging. 2017; 30(4):442–8. Kline TL, Korfiatis P, Edwards ME, Warner JD, Irazabal MV, King BF, Torres VE, Erickson BJ. Automatic total kidney volume measurement on follow-up magnetic resonance images to facilitate monitoring of autosomal dominant polycystic kidney disease progression. Nephrol Dial Transplant. 2015; 31(2):241–8. Sharma K, Rupprecht C, Caroli A, Aparicio MC, Remuzzi A, Baust M, Navab N. Automatic segmentation of kidneys using deep learning for total kidney volume quantification in autosomal dominant polycystic kidney disease. Sci Rep. 2017; 7(1):2049. Kim Y, Ge Y, Tao C, Zhu J, Chapman AB, Torres VE, Yu ASL, Mrug M, Bennett WM, Flessner MF, Landsittel DP, Bae KT, for the Consortium for Radiologic Imaging Studies of Polycystic Kidney Disease (CRISP). Automated segmentation of kidneys from mr images in patients with autosomal dominant polycystic kidney disease. Clin J Am Soc Nephrol. 2016; 11(4):576–84. https://doi.org/10.2215/CJN.08300815. Turco D, Valinoti M, Martin EM, Tagliaferri C, Scolari F, Corsi C. Fully automated segmentation of polycystic kidneys from noncontrast computed tomography: A feasibility study and preliminary results. Acad Radiol. 2018; 25(7):850–5. The authors wish to thanks the colleagues from University of Bari "Aldo Moro" who provided insight and expertise that greatly assisted the research. About this supplement This article has been published as part of BMC Medical Informatics and Decision Making Volume 19 Supplement 9, 2019: Proceedings of the 2018 International Conference on Intelligent Computing (ICIC 2018) and Intelligent Computing and Biomedical Informatics (ICBI) 2018 conference: medical informatics and decision making. The full contents of the supplement are available online at https://bmcmedinformdecismak.biomedcentral.com/articles/supplements/volume-19-supplement-9. Publication costs have been partially funded by the PON MISE 2014-2020 "HORIZON 2020" program, project PRE.MED.: Innovative and integrated platform for the predictive diagnosis of the risk of progression of chronic kidney disease, targeted therapy and proactive assistance for patients with autosomal dominant polycystic genetic disease. Department of Electrical and Information Engineering (DEI), Polytechnic University of Bari, Italy, Via Edoardo Orabona, 4, Bari, 70125, Italy Vitoantonio Bevilacqua , Antonio Brunetti , Giacomo Donato Cascarano & Andrea Guerriero D.E.T.O. University of Bari Medical School, Piazza Giulio Cesare, 11, Bari, 70124, Italy Francesco Pesce , Marco Moschetta & Loreto Gesualdo Search for Vitoantonio Bevilacqua in: Search for Antonio Brunetti in: Search for Giacomo Donato Cascarano in: Search for Andrea Guerriero in: Search for Francesco Pesce in: Search for Marco Moschetta in: Search for Loreto Gesualdo in: VB, LG and MM conceived the study and participated in its design and coordination. AB and GDC designed the classifiers and carried out the data classification and segmentation. MM and VB organized the enrolment of the patients and the acquisition of the data and then validated the final results. VB and AB drafted the manuscript and then all the authors read and approved the final manuscript. Correspondence to Vitoantonio Bevilacqua. The experimental procedures were conducted in accordance with the Declaration of Helsinki. All participants provided written informed consent. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver(http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Bevilacqua, V., Brunetti, A., Cascarano, G.D. et al. A comparison between two semantic deep learning frameworks for the autosomal dominant polycystic kidney disease segmentation based on magnetic resonance images. BMC Med Inform Decis Mak 19, 244 (2019) doi:10.1186/s12911-019-0988-4 R-CNN ADPKD	CommonCrawl
Full paper \| Open \| Published: 15 August 2017 Electrical conductivity of old oceanic mantle in the northwestern Pacific I: 1-D profiles suggesting differences in thermal structure not predictable from a plate cooling model Kiyoshi Baba ORCID: orcid.org/0000-0002-2963-24291, Noriko Tada1,2, Tetsuo Matsuno1,3, Pengfei Liang1, Ruibai Li1, Luolei Zhang4, Hisayoshi Shimizu1, Natsue Abe5, Naoto Hirano6, Masahiro Ichiki7 & Hisashi Utada1 Earth, Planets and Spacevolume 69, Article number: 111 (2017) \| Download Citation Seafloor magnetotelluric (MT) experiments were recently conducted in two areas of the northwestern Pacific to investigate the nature of the old oceanic upper mantle. The areas are far from any tectonic activity, and "normal" mantle structure is therefore expected. The data were carefully analyzed to reduce the effects of coastlines and seafloor topographic changes, which are significant boundaries in electrical conductivity and thus distort seafloor MT data. An isotropic, one-dimensional electrical conductivity profile was estimated for each area. The profiles were compared with those obtained from two previous study areas in the northwestern Pacific. Between the four profiles, significant differences were observed in the thickness of the resistive layer beyond expectations based on cooling of homogeneous oceanic lithosphere over time. This surprising feature is now further clarified from what was suggested in a previous study. To explain the observed spatial variation, dynamic processes must be introduced, such as influence of the plume associated with the formation of the Shatsky Rise, or spatially non-uniform, small-scale convection in the asthenosphere. There is significant room of further investigation to determine a reasonable and comprehensive interpretation of the lithosphere–asthenosphere system beneath the northwestern Pacific. The present results demonstrate that electrical conductivity provides key information for such investigation. The northwestern part of the Pacific Plate is composed of some of the oldest oceanic lithosphere on the planet. The history of its growth has been studied based on geomagnetic anomalies, which have indicated that the Pacific Plate began in a small triangular region at about 190 Ma; this oldest part of the plate is now located in the East Mariana Basin (Nakanishi et al. 1992). The seafloor off the Japanese islands formed 120–160 Ma through the spreading of the Pacific-Izanagi Ridge system, which has already been subducted into the mantle via the Kuril-Japan-Izu-Bonin Trenches. A large bathymetric high called the Shatsky Rise is thought to have formed through upwelling from deep in the mantle or decompression melting of chemically heterogeneous asthenosphere near the Pacific-Izanagi-Farallon triple junction between 149 and 124 Ma (e.g., Sager 2005). The seafloor surrounding the Shatsky Rise is relatively flat and is more than 5600 m deep, which is deeper than predicted by the model of Stein and Stein (1992) based on the cooling rate of a thermally conductive plate of finite thickness (Korenaga and Korenaga 2008). The structure of the mantle beneath such an old ocean basin can be investigated using geophysical approaches. Old oceanic lithosphere is generally believed to be thicker than younger oceanic lithosphere because of cooling over time. Many global surface wave tomography studies have demonstrated clear age-dependence of shear-wave velocity structure (e.g., Maggi et al. 2006; Nettless and Dziewonski 2008; Burgos et al. 2014), and the high-velocity lid, which is interpreted as cool lithosphere, is imaged to be as thick as 100–150 km in the northwestern Pacific, although the structure beneath the specific area of interest for this study has not been resolved in detail through such global studies. A local study using seismic receiver functions detected with a borehole seismometer in the northwestern Pacific revealed a sharp change (decreasing with depth) in seismic P- and S-wave velocities at ~82 km depth, which is thought to represent the lithosphere–asthenosphere boundary (LAB) (Kawakatsu et al. 2009). Note that LAB depth estimates are not consistent among different seismic proxies, such as changes in velocity based on tomography or receiver function, or changes in radial or azimuthal anisotropy (e.g., Burgos et al. 2014). The age-dependent evolution of both the lithosphere and the asthenosphere should be regarded as a part of a system (e.g., Kawakatsu and Utada 2017). From this perspective, the nature of the oceanic lithosphere–asthenosphere system (LAS), for example, the relation between the evolving thermal structure and mechanical properties, is not yet fully understood based on seismic imaging methods. Knowledge of the oceanic LAS from electrical images has been even more limited than those from seismic studies. Recently, we carried out the normal oceanic mantle (NOMan) project (http://www.eri.u-tokyo.ac.jp/yesman/), which aimed to investigate the state of the old Pacific mantle via marine seismic and electromagnetic (EM) observations. Baba et al. (2013a) analyzed magnetotelluric (MT) data obtained by the pilot survey and generated a preliminary one-dimensional (1-D) electrical conductivity profile for the upper mantle, which shows that the resistive lithospheric mantle is as thick as ~80 km. One important finding was that the resistive layer in this area of the lithosphere is unexpectedly different from that detected in the area off the Bonin Trench (Baba et al. 2010), although the lithospheric ages differ little between the two areas. This finding suggests a breakdown of the simple lithospheric cooling concept. The main phase of observation under the NOMan project began in 2011 and continued to 2015; a great deal of additional data are now available. In this paper, we present a comprehensive report on the EM part of the NOMan project. First, we introduce the datasets and 1-D conductivity profiles for the upper mantle, which are newly obtained for two areas: the northwest and the southeast of the Shatsky Rise. Compared with the dataset used by Baba et al. (2013a), (1) the number of observation sites was increased and the area covered is wider, (2) the data were collected from an additional area to examine the generality of structural features, and (3) the period range to be analyzed was extended to include both shorter and longer periods and thus yields more constraints for shallower and deeper structures. We discuss the features of the LAS beneath the northwestern Pacific by comparing the 1-D profiles from the NOMan project with those obtained with similar methods from the other two areas in the northwestern Pacific where data were acquired in past experiments (Baba et al. 2010, 2013b). Field experiments and data For the NOMan project, EM and seismic observations have been conducted since 2010. Here, we summarize the EM observations and data. Two survey areas were selected for this research: northwest (Area A) and southeast (Area B) of the Shatsky Rise (Fig. 1). Both areas have relatively flat seafloor as old as 130–145 Ma. Korenaga and Korenaga (2008) defined the normal seafloor as regions uncorrelated with anomalous crust. Our study areas have mostly normal seafloor according to this definition. Therefore, the mantle underneath is expected to be "normal" in the sense that the plate has cooled over time without effects from tectonic events since its formation at the spreading ridge. We originally intended to compare the two areas to examine the generality of the "normal" mantle state. Observations were initiated at five sites (NM01–NM05) in Area A as a pilot survey (Baba et al. 2013a), after which iterative deployments and retrievals of instruments in the two areas were performed each year through the main observation phase until 2015. A total of seven cruises were carried out for this experiment using the R/V KAIREI of the Japan Agency for Marine Science and Technology (JAMSTEC) and the W/V KAIYU of Offshore Operation Co., Ltd. The arrays consisted of 17 sites (labeled NM01–NM17) in Area A and eight sites (NM18–NM25) in Area B. A total of 39 EM instruments were deployed in the two areas, and most were successfully retrieved with usable data. The available time series length is at least 275 days (~9.2 months) at some sites, and, because of the iterative observation, the maximum duration of observation was 1348 days (~3.7 years) at NM01. Table 1 lists the coordinates of the sites and the status of the associated data. High-resolution bathymetry around each seafloor site, which is used for electrical conductivity modeling, was surveyed using the shipboard multi-narrow beam echo sounding (MBES) system during the KAIREI cruises. We compiled all available bathymetry data published by JAMSTEC in addition to those collected through the NOMan project cruises. The bathymetry map based on the MBES data is also shown in Fig. 1b. Bathymetry maps and site locations. a Regional bathymetry map based on ETOPO1 (Amante and Eakins 2009) with contour lines for seafloor age (Müller et al. 2008). b Bathymetry maps based on the available MBES data for Area A and Area B, respectively. Crosses and squares indicate the locations of sites where OBEMs and EFOSs were deployed. Yellow and red colors denote the sites of the NOMan experiment for which data are available and unavailable, respectively. Green and blue colors indicate the sites included in past experiments (Baba et al. 2010, 2013b). Stars represent the geomagnetic observatories at Kakioka (KAK) and seafloor of the North Western Pacific (NWP) (Toh et al. 2006) Table 1 Information on the OBEM and EFOS sites and data used in this study Two kinds of EM instruments were utilized in this experiment: ocean bottom electromagnetometers (OBEMs) and electric field observation systems (EFOSs). OBEMs measure the time variations of three components of the magnetic field, two horizontal components of the electric field, two components of instrumental tilt, and temperature. These instruments were deployed to the seafloor via free fall from the sea surface and were retrieved when they rose to the surface due to buoyancy after releasing an anchor. Most of the OBEMs recorded data with a sampling interval of 60 s. For some OBEMs, the sampling interval was first set at 10 s and then switched to 60 s, controlled by a timer. This function helps to optimize battery power consumption more efficiently because the magnetometer is powered on intermittently for only a few seconds around the time of sampling. The 10-s sampling recordings provide shorter-period data that are sensitive to shallower parts of the oceanic lithosphere. There were also sites where the OBEMs were deployed iteratively to collect longer time series data (Table 1). The positions between these sites on the seafloor were slightly different from each other (0.4–2.0 km) because they were settled via free fall. We therefore regarded the averages as the representative positions of the sites. As addressed later, these differences in position are not critical in the analysis for study of mantle structure and topographic effects. EFOSs measure just one component of the electric field, but with a much longer dipole (2–3 km for the NOMan experiment) than that of the OBEMs (~5.4 m), and therefore yield better signal-to-noise (S/N) ratios (Utada et al. 2013). An EFOS consists of a recorder and a cable drum attached to an anchor. The EFOS is deployed to the seafloor via free fall, and the cable drum is then caught and towed by a remotely operated underwater vehicle (ROV) KAIKO 7000II to extend the cable that generates the long electric dipole. An EFOS was deployed at NM03 in 2010 as the part of the pilot survey. In 2012, the recorder was replaced and the measurements were continued. Three additional EFOSs were deployed, at NM01, NM14, and NM16. The direction of the cable extension was restricted by the recorder side because of the instrumental design and a technical reason of the ROV operation (Utada et al. 2013). All of the EFOS recorders happened to settle facing between N40°E and N170°E after free fall deployment; therefore, the cables were extended approximately in the N110°E direction (Table 1), which is subparallel to the direction of Pacific Plate motion. The EFOS recorders at sites NM01, NM14, and NM16 were retrieved using the ROV KAIKO 7000II in 2014, and the recorder at NM03 was retrieved using ROV KAIKO Mk-IV in 2015. Further information about the EFOSs is listed in Table 1. The recovered time series data were first processed for quality control. Abnormal fluctuations, such as spikes and rectangular steps in raw time series data, were detected by eye through comparing different field components, and spikes were then linearly interpolated and steps were shifted to reduce discontinuity. The instrumental clock was compared with coordinated universal time (UTC) via global positioning system (GPS) just before deployment and after retrieval. The detected clock shift was corrected, based on the assumption that the shift accumulated linearly over time. For the OBEMs, the coordinate system was adjusted to a geographical one; the instrumental tilt was corrected using tilt angle data through Euler rotation, and the horizontal coordinate system was then rotated using the magnetic field declination predicted from the international geomagnetic reference field (IGRF) (IAGA Working Group V-MOD 2010). Coordinate system conversion was not applied to the EFOS data because the EFOSs measured only one component of the electric field. Magnetotelluric analysis The MT response Z(r, T) is defined as a 2 × 2 complex-valued tensor transfer function between the horizontal electric E(r, T) and magnetic B(r, T) fields, $${\mathbf{E}}\left( {{\mathbf{r}}, T} \right) = {\mathbf{Z}}\left( {{\mathbf{r}}, T} \right){\mathbf{B}}\left( {{\mathbf{r}}, T} \right),$$ where r is the observed position and T is the period. The responses were estimated for each OBEM site using a bounded influence algorithm (Chave and Thomson 2004). The magnetic field data from the Kakioka observatory (KAK) were employed as a remote reference to reduce the effects of site-dependent noise in the local (OBEM) magnetic field data. We also applied a generalized remote reference method based on two-stage processing (Chave and Thomson 2004). In the first stage, a transfer function between the local and remote horizontal magnetic fields was estimated, and in the second stage, the MT responses were estimated as a transfer function between the local observed electric field and the local horizontal magnetic field estimates predicted from the inter-site magnetic transfer function obtained in the first stage. The generalized remote reference method significantly improved the quality of the MT response estimation for periods shorter than ~500 s at the sites where 10-s sampling data were available. The final responses for each period were taken from those obtained using either the normal or generalized remote reference method with higher coherence. Finally, the MT responses were obtained for the period range between 53.3 and 163,840 s (the available range depends on the site). The longest available period is limited to 163,840 s, although data for more than 3 years were used, mainly because the S/N ratio of the electric field measured by the OBEMs becomes quite low with fluctuations over longer periods. We examined the influence of the different positions of the OBEMs deployed in the different observation phases by comparing the MT responses estimated from data for each observation phase and from all observation phases. For NM01, data are available from three observation phases (Table 1). The distances between pairs of OBEM positions are 0.4–2.0 km (Fig. 2a). The resulting MT responses all agree within the 95% confidence interval (Fig. 2b). These results suggest that, in the present study, relocation error is not critical in this analysis of mantle structure and topographic effects. Therefore, we used the MT responses estimated from all available observation phase data to represent the response at each site and used the average position for the MT response simulation in the following analysis. a OBEM locations and the average for NM01 plotted on a bathymetry map. b Comparison of the MT responses at NM01 obtained from all observation phase data (black crosses) and from data for each observation phase (colored symbols). From left to the right, different elements of the MT impedance tensor are plotted. The top and third panels show the log apparent resistivity and the impedance phase, and the second and bottom panels show the differences between those obtained from data for each observation phase and all data, respectively. The error bars indicate 95% confidence intervals The OBEM magnetic field data and EFOS data at the same sites were also processed jointly to yield a scalar MT response between the electric field along the EFOS dipole and the OBEM magnetic field component perpendicular to the EFOS dipole. In addition, the geomagnetic depth sounding (GDS) response, which is the transfer function between the vertical component and the horizontal component of the magnetic field, was estimated for each OBEM site and for the seafloor observatory at the North Western Pacific (NWP) (Toh et al. 2006). These responses were estimated for periods longer than ~105 s and are therefore useful to evaluate deeper structure. Matsuno et al. (2017) have provided a detailed analysis of the data and discussion of the structure of the mantle transition zone. Therefore, in this study, we focus on analysis of the MT responses obtained with the OBEM data and discussion of the upper mantle structure. Examples of the MT responses representative of each area (NM01 for Area A and NM24 for Area B) are plotted in the form of apparent resistivity and impedance phase sounding curves to reveal the variation as a function of period (Fig. 3). See Additional file 1: Figure S1 for the sounding curves of all sites. In Fig. 4, polar diagrams of the apparent resistivity (Swift 1967) are plotted, as well as phase tensor ellipses (Caldwell et al. 2004), on a bathymetric map for two selected periods (640 and 5120 s) to illustrate the lateral variations of the tensor MT responses. Examples of MT responses for Area A (left) and Area B (right) in terms of apparent resistivity (top) and impedance phase (bottom) sounding curves; x and y represent the geographical coordinate system. Symbols with error bars are the observed responses. The error bars indicate 95% confidence intervals. Solid lines are the responses predicted from a conductivity structure model that consists of the known 3-D topography over the estimated 1-D mantle structure Spatial variations of tensor MT responses in each area (left four panels Area A, right four panels Area B) at the periods of 640 s (upper panels) and 5120 s (lower panels). For each area and each period, polar diagrams of the log apparent resistivity colored according to the Swift's impedance skew (thin and thick lines are for diagonal and off-diagonal elements, respectively) are shown in the left column, and the phase tensor ellipses colored based on the phase tensor skew angle are shown in right columns. Background gray shading represents bathymetry. Blue crosses indicate the site locations We first show the overall features of the sounding curves. With periods shorter than about 500 s (Fig. 3), the apparent resistivity and phase in the major elements decrease with decreasing period, which suggests that the uppermost layer is relatively conductive, likely associated with the crust including a thick (~400 m) pelagic sediment layer (Shinohara et al. 2008). The apparent resistivities show a peak at around 500 s and then decrease with increasing period (Fig. 3). This feature is typical for oceanic mantle that consists of cool, resistive lithosphere and underlying hotter, more conductive asthenosphere (e.g., Filloux 1977). The peak of the apparent resistivity is higher for Area B than for Area A (Fig. 3). The responses look similar between sites within each area, but the spatial variation tends differ somewhat between Area A and Area B. For example, the phase tensors at 5120 s tend to elongate in the northeast–southwest direction in Area A, but form a more circular shape in Area B (Fig. 4). These observations suggest a difference in the upper mantle structure at a scale beyond the array size. Splitting between the off-diagonal elements suggests the effect/s of lateral heterogeneity and/or anisotropic structure. This phenomenon is smaller for Area B, which is more distant from the coastlines; therefore, the coast effect is likely a possible cause. In fact, our previous study showed that splitting in the responses for Area A is partly explained by the topography, including coastlines (Baba et al. 2013a). However, for Area A, the splitting tends to be slightly more significant at the western sites, NM01, NM02, and NM04 (Fig. 3; Additional file 1: Figure S1), and this feature is not reproduced well with the topographic effect alone (Baba et al. 2013a), which suggests the presence of lateral heterogeneity within the array or at a slightly larger scale. At periods of about 104 s, both the apparent resistivities and phases, especially for the xy and yy elements, abruptly change (Fig. 3). This feature is more significant for Area B, which is the most distant from the reference site (KAK). It is likely caused by imperfect reduction of Sq effects (Shimizu et al. 2011). Therefore, we have down-weighted the responses within the period range of 104–105 s, where the Sq effects dominate, in later analysis. Nevertheless, the splitting between the off-diagonal elements likely decreases with increasing periods, which suggests that the deeper part of the upper mantle tends to be more uniform laterally. Topographic effect correction and inversion We estimated one-dimensional (1-D) isotropic electrical conductivity profiles of the mantle for Area A and Area B separately, which fit the MT response averaged in each array, by applying an iterative topographic effect correction. The 1-D profile estimated by this procedure should be a representative of average 1-D structure of possibly laterally heterogeneous (and/or anisotropic) mantle beneath each array. We do not argue that the mantle structure is one-dimensional as we discuss possible lateral heterogeneity and anisotropy later. This procedure is critical to obtain a reliable subsurface structure model because the large contrast in conductivity between seawater and crustal rocks can severely distort the EM field at the seafloor. This procedure is based on our previous studies (Baba and Chave 2005; Baba et al. 2010, 2013a, c) and consists of four steps. The procedure of these steps is iterated until the results converge to obtain the final 1-D profile, as described below. In Step 1, we first calculate a scalar MT response from the tensor MT response at each site. We adopt the square root of the determinant of the tensor MT response, $Z_{ \det } = \sqrt {Z_{xx} Z_{yy} - Z_{xy} Z_{yx} }$, which is an invariant to rotation of the horizontal coordinate system, following the methods of our previous studies (Baba et al. 2010, 2013a). Rung-Arunwan et al. (2016) demonstrated that another rotational invariant based on the sum of squared elements, $Z_{\text{ssq}} = \sqrt {\left[ {Z_{xx}^{2} + Z_{xy}^{2} + Z_{yx}^{2} + Z_{yy}^{2} } \right]/2}$, is more robust to galvanic distortion. However, the distortion indicators, $\gamma = Z_{\text{ssq}}^{2} /Z_{ \det }^{2}$ (Rung-Arunwan et al. 2016), are real and nearly equal to unity independently of period for all sites, which indicates that $Z_{ \det }$ is almost identical to $Z_{\text{ssq}}$ (Fig. 5) and that the present dataset is affected little by galvanic distortion. This observation is consistent with the negligibly small relocation error mentioned above and can be attributed to the fact that oceanic crust generated at the mid-ocean ridge with thick sedimentary cover is generally much more homogeneous geologically than continental crust that has undergone tectonic processes and erosions. The estimates of $Z_{ \det } \left( {{\mathbf{r}}, T} \right)$ for all sites are then averaged in each array for each period. Local distortion indicators (Rung-Arunwan et al. 2016) for all sites in Area A and Area B. Red and blue symbols denote the real and imaginary parts, respectively. Error bars are 95% confidence limits In Step 2, Occam's inversion (Constable et al. 1987) is applied to the averaged response $\bar{Z}_{ \det } \left( T \right)$ to obtain a representative 1-D profile. The error floor of 2.5% of $\left\| {\bar{Z}_{det} } \right\|$ is applied, except for the periods between 104 and 105 s, to which an error floor five times larger (12.5%) is applied, because the responses in these periods are likely distorted by imperfect reduction of Sq effects, as described above. The conductivity at ~30 km depth is constrained to be 10−3.5 S m−1 in the inversion, following our previous studies (Baba et al. 2010, 2013a), because the inversion of $\bar{Z}_{ \det }$ with the smoothness constraint does not always reproduce such a resistive layer, although there is no doubt that the cold lithosphere exhibits very low conductivity (e.g., Baba et al. 2010, 2013a; Cox et al. 1986). The inversion did not converge if the target misfit was set to 1.0. Then, the target misfit was set to 1.24 and 1.25 for Area A and Area B, respectively, which correspond to the 99% confidence limit of χ 2 misfit. The uncertainty of the conductivity of each layer is estimated by evaluating the distribution of the acceptable models obtained through numerous inversion runs with different constraints, following our previous studies (Baba et al. 2010, 2013a). In Step 3, the topographic effect is simulated. A two-stage three-dimensional (3-D) forward modeling approach (Baba et al. 2013c) is applied to incorporate the effects of regional large-scale topography and local small-scale topography. The lateral dimensions of the regional model are 10,000 km × 10,000 km, and the horizontal mesh in the central area that includes the array is 50 km × 50 km. The local model is as large as 350 km × 350 km, with topography in the vicinity of each site based on MBES data and is also incorporated with a finer mesh (1 km × 1 km in the central area) in the second stage forward modeling (Baba et al. 2013c). Figure 6a shows the regional topography models for the two areas, and Fig. 6b shows examples of the local topography model at a particular site for each array. The regional model includes the East Asian coastlines and major topographic features such as abyssal rises and trenches. The local models incorporate finer-scale topographic changes, such as linear hills and valleys subparallel to the past seafloor spreading ridge. The conductivity values of seawater and land crust are set to 3.2 and 0.01 S m−1, respectively. The 1-D profile obtained in Step 2 is incorporated in the subsurface structure. a Regional topography models for Area A and Area B. b Example local topography models for NM01 in Area A and NM24 in Area B (only the central area of the model is plotted to show small-scale topography) In Step 4, the topographic distortion terms for each site, ${\mathbf{D}}\left( {{\mathbf{r}}, T} \right)$, are calculated from the 3-D and 1-D forward responses ${\mathbf{Z}}_{{3 - {\text{D}}}}^{\text{pre}} \left( {{\mathbf{r}}, T} \right)$ and ${\mathbf{Z}}_{{1 - {\text{D}}}}^{\text{pre}} \left( T \right)$, assuming that the 3-D response to be observed is expressed by multiplication of the surface 3-D topographic distortion and the response to the subsurface 1-D structure, $${\mathbf{D}} = {\mathbf{Z}}_{{3 - {\text{D}}}}^{\text{pre}} \left( {\varvec{Z}_{{1 - {\text{D}}}}^{\text{pre}} } \right)^{ - 1} .$$ Then, the observed responses ${\mathbf{Z}}^{\text{obs}} \left( {{\mathbf{r}}, T} \right)$ are corrected as, $$\varvec{Z}^{\text{cor}} = {\mathbf{D}}^{ - 1} {\mathbf{Z}}^{\text{obs}} .$$ We evaluate the root mean squared (RMS) misfit between the observed (non-corrected) and predicted responses in terms of log apparent resistivity log ρ and impedance phase ϕ, $${\text{RMS}} = \sqrt {\frac{1}{{2N_{\text{d}} }}\mathop \sum \limits_{i = 1}^{{N_{\text{d}} }} \left[ {\left( {\frac{{\log \rho_{i}^{\text{obs}} - \log \rho_{i}^{\text{pre}} }}{{\delta \log \rho_{i} }}} \right)^{2} + \left( {\frac{{\phi_{i}^{\text{obs}} - \phi_{i}^{\text{pre}} }}{{\delta \phi_{i} }}} \right)^{2} } \right]} ,$$ where N d is the total number of data points for Z involving four elements of the tensor, the number of available periods, which depends on the site, and the number of sites. The parameters $\delta \log \rho$ and $\delta \phi$ are the standard errors, to which the error floor is applied. Error floors are set to 2.5% for the off-diagonal elements of Z, for the diagonal elements, are set to the absolute value of 0.01 for periods shorter than 3000 s, and 5.0% for the longer periods. These criteria are based on our experience regarding the approximate accuracy of regional 3-D forward modeling. However, for periods between 104 and 105 s, the error floors are increased by a factor of five, i.e., to 12.5 and 25.0% for off-diagonal and diagonal elements, respectively, for the same reason as for the 1-D inversion in Step 2. Figure 7a presents $Z_{ \det } \left( {{\mathbf{r}}, T} \right)$ and $\bar{Z}_{ \det } \left( T \right)$ from Area A and Area B, as obtained in Step 1. The averaged responses differ significantly between the two areas, and this difference is beyond the dispersion between sites within each area. These features remain after topographic effect correction (Fig. 7c), which suggests that the subsurface structures differ significantly between the areas. The topographic effect correction increased the apparent resistivity at longer periods for both areas, but the change is larger for Area A than for Area B. Therefore, this change should mainly be attributed to relatively large-scale topographic effects, such as the coastlines west of the study areas. The dispersions in the responses within each array, which are larger with shorter periods, changed little with topographic effect correction. This result indicates that local topographic effects, which should affect the responses in shorter periods more strongly, are not as significant as the regional topographic effects and that the dispersions are caused by lateral heterogeneity in subsurface (but relatively shallow) structure. Because the dispersion is very small within Area B, the subsurface structure beneath Area B is inferred to be more uniform laterally. a Apparent resistivity and impedance phase sounding curves of $\bar{Z}_{ \det } \left( T \right)$ (red) and $Z_{ \det } \left( {{\mathbf{r}}, T} \right)$ for each site (pink) before topographic effect correction, i.e., the initial responses. Error bars indicate 95% confidence limits. Blue dashed lines are the model responses calculated from the 1-D profiles shown in (b). b Initial 1-D profiles obtained from $\bar{Z}_{ \det } \left( T \right)$ shown in (a). Dark and light shades indicate 70 and 95% uncertainty limits, respectively. Panels (c) and (d) are the same as (a) and (b), respectively, but after the topographic effect correction, i.e., the final responses and profiles The topographic effect correction and inversion procedure was iterated twice. Changes in RMS misfit against the iterations are listed in Table 2. Figure 8 shows the residuals between the responses observed and predicted from the final model, which were normalized based on the relative errors $\delta Z/\left\| Z \right\|$ after applying the error floors. The errors for each element are of a similar level for the two areas, such that the difference in the RMS misfit approximately reflects the difference in the absolute model fit. The RMS misfit decreased significantly at the first iteration and then slightly increased again at the second iteration; therefore, we took the result at the first iteration as the final model. The reduction of the misfit from the initial to the final model is as small as 14% for Area A and 2% for Area B. This small reduction indicates that the initial 1-D models were good enough compared to other choices for the initial model, such as a uniform half space, which is frequently used for inversion analyses (Baba et al. 2013a). For Area B, the RMS misfit is almost twice of that for Area A, and the reduction was smaller. This difference occurs because for Area B, the RMS misfit of the xx element is extremely high compared to that for the off-diagonal elements (Table 2; Fig. 8). The partial RMS misfits for the off-diagonal elements for Area B were smaller than those for Area A, and the reductions were as large as 9–38%. Table 2 The RMS misfit against the iteration Normalized residuals in four elements of the MT responses for Area A (left) and Area B (right). Colors indicate the different elements, as specified in the legend. Top and middle panels are those for the log apparent resistivity, (log ρ obs − log ρ pre)/δ log ρ, and phase, (ϕ obs − ϕ pre)/δϕ, respectively. The bottom panels show the relative errors (δZ/\|Z\|) The predicted responses explain the overall features of the observed responses, although there are some significant differences between them (Figs. 3, 8). Relatively large misfits are mainly seen with periods shorter than several thousand seconds. For Area A, the splitting between the xy and yx (off-diagonal) elements or the xx and yy (diagonal) elements of calculated responses is smaller than the observed splitting (Fig. 3; Additional file 1: Figure S1), as was pointed out in our previous study based on the pilot survey data (Baba et al. 2013a). For Area B, in contrast, the off-diagonal elements are very well reconstructed by the model. However, as shown in Fig. 3, the predicted apparent resistivities for the two diagonal elements are similar and much smaller than the observed values. They are largely depressed and accompanied by a large phase change at ~2000 s. In addition, the observed apparent resistivity for the xx element is higher, and its errors are smaller than those for the yy element. These values resulted in the high partial RMS misfit for the xx element (Fig. 8; Table 2). These features cannot be reproduced by the topographic effect alone and therefore must be attributed to lateral heterogeneity and/or anisotropy of the subsurface structure. We expect future studies to better explain these features. The 1-D profiles before and after the topographic effect correction for each area are shown in Fig. 7b, d. As anticipated from the observed sounding curves, the profiles were characterized by three layers, consisting of the uppermost conductive layer, the resistive lithospheric mantle, and the conductive asthenospheric mantle. As a result of topographic effect correction, the conductivity of the asthenospheric mantle decreased from the initial profile to the final profile. This reduction is more significant for Area A. Major differences in the final profiles between the two areas are: (1) the thickness of the resistive layer and (2) the conductivity values at the peak in the upper mantle. The definition of the thickness of the resistive layer is somewhat ambiguous because the profiles change smoothly with depth, and the gradient is controlled by the smoothness constraint in the inversion as well as by the data. If we define this thickness as the depth where the conductivity become greater than 0.01 S m−1, that thickness is ~90 km for Area A and ~100 km for Area B. It is quantitatively certain that the resistive layer in Area A is thinner than that in Area B. In the highly conductive zone below the resistive layer, the depth-dependent trend is much more gradual, with values of 0.02–0.03 S m−1 at depths of 100–150 km in Area A, and ~0.05 S m−1 at depths of 150–200 km in Area B. Update of the model for Area A The number of available sites for Area A was increased from four in the previous study (Baba et al. 2013a) to 16 in this study with completion of the main observation phase. The variation of observed MT responses in the array is of a similar level with that of the pilot survey array (four western sites). The obtained 1-D profile for mantle depth is also similar to the previous profile, which indicates that extension of the data to include shorter periods in this study did not affect the evaluation of the mantle, as is our main target. However, significant improvement is apparent in the uncertainty for the shallowest part of the profile (Fig. 9), which indicates that the conductive oceanic crust is better constrained by the new data and thus that the conductivity values are more reliable. We ran an inversion for a test with the present data but excluded some data points at periods shorter than 160 s, as in the previous study. The resulting profile is very similar to the previous one, but the uncertainty of the final profile in this study is much smaller. Shallower part of the 1-D profiles with uncertainties. Note that the depth in the vertical axis is given in log scale for clarity. Left the test profile for Area A; the data for the shorter three periods were excluded in the inversion. Middle and right the final profiles for Area A and Area B, respectively, which are identical to those in Fig. 7d. Green line represents the profile obtained from the pilot survey data in Area A in the previous study (Baba et al. 2013a) This improvement enables us to probe the uppermost mantle and crust (down to ~10 km below the seafloor) more reliably, even at the deep seafloor. The uppermost layer for Area A seems to be more conductive than those for Area B, although the uncertainty for Area B is larger than that for Area A (Fig. 9). Shinohara et al. (2008) conducted a seismic survey in the eastern end of our array in Area A and showed that the sediment layer is as thick as ~400 m. The seismic survey by Ohira et al. (2017) along a line 150 km southeast of our array in Area B showed that the thickness of the sediment layer is ~300 m. Both studies reported similar characters; the P-wave velocity structure in the crust below the sediment indicated typical oceanic crust, except for the transitional layer from the crust to the mantle. Although our models do not resolve the shallowest layer, which is thinner than 1 km, the thin but very conductive sediment layer can influence the mean conductivity in the uppermost layer in the inversion. Therefore, the difference between the shallower parts of the profiles from the two areas may be ascribed to the difference in the thickness of the sediment layer. Possibilities of lateral heterogeneity and anisotropy within each area The MT responses show some degree of spatial variations within each array (Figs. 4, 7a, c), which suggests the presence of lateral heterogeneity and/or anisotropy in conductivity. Although detailed 3-D and anisotropy analyses are now underway in subsequent studies, here we argue some implications regarding the lateral heterogeneity and anisotropy in the upper mantle for each area. Figure 10 shows the spatial distribution of the residuals between the apparent resistivity of $Z_{ \det } \left( {{\mathbf{r}}, T} \right)$ after the topographic effect correction and the forward response to the final 1-D profiles for each area. At three selected periods, 1280, 2560, and 5120 s, the apparent resistivity decreases with increasing period for both Area A and Area B, which suggests that the data for these periods may be responsible for the depths from the base of resistive layer to the underlying conductive zone. The radii of the colored circles in the figure are normalized for the standard error of the log apparent resistivity to demonstrate that the residuals with larger circles are more reliable than those with smaller circles. For Area A, the spatial trend is not very clear at 1280 s, but the eastern sites are more conductive at longer periods. For Area B, the northeastern region tends to be more conductive with all three periods, although the spatial variation is smaller than that in Area A. The overall difference in the data between Area A and Area B is significantly larger than the dispersion of the data within each array (Figs. 7, 10). Therefore, the major difference in the 1-D profiles between the two areas is a robust feature. Residuals between the log apparent resistivity of Z det after topographic effect correction and that calculated from the final 1-D profile at each site are plotted as colored circles on the bathymetry map (gray shading) for periods of 1280, 2560, and 5120 s. The dimensions of circles are inversely proportional to the error of Z det. Left and right panels are for Area A and Area B, respectively Anisotropy in the lithosphere and asthenosphere is an important property to assess mantle dynamics, although observational evidence is available only from relatively young oceanic mantle in the eastern Pacific region (Evans et al. 2005; Baba et al. 2006a, b; Naif et al. 2013). Recent experimental studies have also demonstrated that hydrous olivine and partially molten rock can be highly anisotropic under the temperature and pressure conditions of the asthenosphere (e.g., Dai and Karato 2014; Zhang et al. 2014; Pommier et al. 2015). Therefore, the possibility of anisotropy should not be ruled out for the old oceanic mantle in our study areas. Qualitatively, we can infer that the anisotropy in the study areas, if it exists, may be weaker than that observed in the southern East Pacific Rise (Evans et al. 2005; Baba et al. 2006a, b) because the major (off-diagonal) elements of the observed MT responses show only slight variation with rotation in horizontal coordinates (Fig. 4). Therefore, special care is necessary in examining the existence and degree of anisotropy more quantitatively, because the present MT data are affected by the 3-D topography, and mutual coupling between the topographic effect and the anisotropic mantle structure must be considered. Such a careful study is currently in progress to explore how the topography and possible anisotropy affect MT responses. Details of this analysis and its results will be reported elsewhere. Spatial dependence of electrical conductivity of the upper mantle in the northwestern Pacific and its implication for the lithosphere–asthenosphere system The electrical conductivity of the upper mantle differs between Area A and Area B, as demonstrated in the previous section. The major differences in the upper mantle are the thickness of the resistive layer and the high conductivity beneath the resistive layers. We confirmed that these differences are significant and not artifacts because of the high conductivity at the uppermost layers, through synthetic inversion tests (see Additional file 2: Figure S2). The seismological observations of the NOMan project have also revealed noticeable differences in shear-wave velocity structure between the two areas through surface wave tomography. The upper high-velocity layer tends to be thicker for Area B than for Area A, and the underlying low-velocity zone tends to show slower velocities for Area A than for Area B (Isse et al. 2017). The electrical conductivity and seismic slowness in the upper mantle can both be enhanced primarily by temperature increase. Therefore, the trends in the thickness of the upper resistive layer and the high-velocity layer between the two areas are qualitatively consistent, as the cool lithospheric mantle is thinner for Area A than for Area B. However, the conductivity and the velocity in the underlying conductive and low-velocity zone beneath the two areas appear to be opposite what would be explained by the thermal effect alone. This apparent inconsistency strongly suggests that other factors, such as volatile content and/or degrees of partial melting, differ in the mantle beneath the two areas. This observation also highlights the importance of further joint interpretation of seismic and EM results. We next evaluate the spatial dependence of electrical conductivity across a wider region by comparing the 1-D electrical conductivity profiles for four areas of the northwestern Pacific. Two additional areas, Area C and Area D, are in the Pacific basin off the Bonin Trench (the representative crustal age is ~147 Ma) and off the Japan Trench (~135 Ma), respectively (locations shown in Fig. 1), where seafloor MT data were collected in past experiments (Baba et al. 2010, 2013b). The representative 1-D profiles for Area C and Area D were previously obtained following a similar procedure to that used in the present study, but they were re-estimated in this study using the same up-to-date procedure as that applied for Area A and Area B to avoid potential artifacts due to slight differences in procedure. However, differences from the previous profiles are negligible. Figure 11 shows the 1-D profiles for the four areas, which further highlight the variation in resistive layer thickness (the profiles in machine-readable format are given in Additional file 3: Table and the sounding curves for $\bar{Z}_{ \det } \left( T \right)$ (red) and $Z_{ \det } \left( {{\mathbf{r}}, T} \right)$ for all sites in the four areas are shown in Additional file 4: Figure S3). Area C shows the thickest resistive layer, which was also confirmed to be a robust feature by 3-D inversion analysis (Tada et al. 2014), and that of Area D falls between those of Area B and Area C. All four models differ significantly from each other. The conductivity values of the underlying high conductive zones for Area C and Area D are around 0.04–0.05 S m−1, which is close to that of Area A. That of Area B is slightly more conductive than the others. Comparison of the 1-D electrical conductivity profiles for the mantle beneath four areas in the northwestern Pacific (Fig. 1). Solid lines are the profiles obtained through inversion. Dark and light shades indicate 70 and 95% uncertainty limits, respectively. Colored, dashed lines indicate the simulated profiles for the representative ages in each area, assuming different thicknesses of the thermally conductive plate, h (see text for details) The differences in resistive layer thickness between these four areas cannot be explained by the temperature differences of the corresponding lithospheric ages under a framework of the cooling of homogeneous mantle through thermal conduction. We have already argued this point based on the comparison of the earlier profiles for Area A and Area C (Baba et al. 2013a), and this comparison of four areas further strengthens this interpretation. Baba et al. (2013a) argued that if the mantle beneath Area A is "normal," as expected from the plate cooling model, the lithosphere beneath Area C is abnormally thick. However, adding Area B and Area D to this comparison demonstrates that the resistive layer beneath Area A is the thinnest, and therefore represents the opposite end-member rather than the average among the four areas explored thus far. It is now more doubtful that Area A represents "normal" mantle in the old northwestern Pacific. To demonstrate these inferences more clearly, we simulated the 1-D electrical conductivity profiles for several thermal structure models with the representative lithospheric age for each area and plotted these profiles in Fig. 11 (dashed lines). We applied simple 1-D cooling of a homogeneous, thermally conductive plate, assuming a potential temperature of 1350 °C and thermal diffusivity of 30 km2 Myr−1 (Turcotte and Schubert 2002). The plate thickness h is varied between 80 and 300 km. An adiabatic temperature gradient of 0.3 °C km−1 was superimposed onto this thermal profile. The mantle electrical conductivity was assumed to be represented by that of olivine. We applied the electrical conductivity model for olivine by Gardés et al. (2014), which was obtained by compiling published experimental results. The water content dissolved in olivine was assumed to be 0.01 wt.%, which is thought to be a typical value for mid-ocean ridge basalt (MORB) source mantle (Hirschmann 2010). Note that there are two competing groups that show significantly different results for the conductivity measurement of hydrous olivine, and therefore, selection of the laboratory model leads different impacts of water on the conductivity simulation. Olivine conductivity calculated using the model of Gardés et al. (2014) falls in a middle ground between values those calculated using the models of the two competing groups (Wang et al. 2006; Yoshino et al. 2009) in a case for water content of 0.01 wt.% at 1200 °C (see their Fig. 1). In the simulation, we considered only the solid-state mantle and the effects of temperature and water on that mantle. However, we do not rule out the possible contribution of partial melting due to the presence of water and carbon dioxide (e.g., Sifré et al. 2014). The calculated electrical conductivity profiles for any h are almost identical between the four different representative ages, because the thermal structure is almost identical in the range of ages compared here. However, the results for different values of h showed significantly different conductivity profiles. The inversion profile for Area A falls between the simulated profiles for h of 80 and 100 km. For Area B, the inversion profile is in between the profiles for h of 100 and 125 km. For Area D, it mostly corresponds to the simulated profiles for h of 200 and 300 km, which are almost the same. The resistive layer for Area C is much thicker than the simulated profile for h of 300 km, which suggests that it is more consistent with a cooling half space rather than a cooling plate, as discussed in previous studies (Baba et al. 2010, 2013a). This result suggests that the transition from the resistive to high-conductivity zones is mainly controlled by h. It is impossible to represent the 1-D profiles for all areas by a thermal model with a single value of h. In other words, it is likely that the thickness of the cool thermal lithosphere differs between these areas. If the appropriate values of h are chosen, the simulated profiles with the same value of potential temperature fit the high-conductivity zone well for all areas, although the inversion profile for Area B is slightly higher than the simulated profile at depths between 150 and 200 km. This observation suggests that the asthenospheric mantle in this region is rather homogeneous in potential temperature and chemical composition, except for Area B. Bathymetry subsidence and heat flow data seem to be consistent partly but not perfectly with the significant trend in the resistive layer thickness between the four areas. Residual bathymetry with respect to the plate cooling model of GDH1 (Stein and Stein 1992) estimated by Korenaga and Korenaga (2008) shows that the subsidence in Area A is the most comparable (~−200 m) with the model prediction and the other three areas are ~500 m deeper than the model prediction (Fig. 12). Abe et al. (2013) compared the bathymetry observed along a track crossing over Area B and Area D with the predictions by two plate cooling models, PSM (Parsons and Sclater 1977) and GDH1. Their result indicates that the seafloor in the two areas is more comparable with the prediction from PSM, which gives cooler (1350 °C) potential temperature and thicker (125 km) thermally conductive plate than that from GDH1 (1450 °C and 90 km, respectively). The bathymetry data support relatively thin thermal plate beneath Area A but do not show clear difference between the other three areas. Area C is not as deep as the prediction from a half space cooling model, which is ~1000 m deeper than the prediction from GDH1 (see Figure 1 of Stein and Stein 1992). Heat flow observations are limited in the northwestern Pacific basin. For Area A and Area B, although only a few data points are available, the heat flow values are 50–60 mW m−2. which are comparable with the prediction from GDH1, while, for Area C and Area D where more data points exist, the majority show 40–50 mW m−2, which are comparable with the prediction from PSM (Fig. 12). Note that the predictions of heat flow values from a half space cooling model and PSM are not significantly different and they both are about 10 mW m−2 lower than the prediction from GDH1 (see Figure 1 of Stein and Stein 1992). Thus, heat flow seems to support relatively thicker (may be as thick as the half space cooling model) thermal plate beneath Area C and Area D. In summary, both bathymetry and heat flow observations suggest that it is difficult to explain all data by a unique cooling model. Residual bathymetry with respect to the plate cooling model of Stein and Stein (1992) (Korenaga and Korenaga 2008) (gray shade with contour lines just for negative values) and heat flow (colored circles) in the northwestern Pacific. Crosses denote the EM observation sites. Red dashed line indicates the track that Abe et al. (2013) investigated the bathymetry It is therefore necessary to introduce more dynamic processes to explain the variation in the electrical structure beneath the northwestern Pacific, although it is still difficult to provide a reasonable and comprehensive interpretation involving all observed features. The concept of the thermally conductive plate with a finite thickness was originally introduced to explain the decrease in seafloor subsidence rate in regions older than ~70–80 Ma (e.g., Parsons and Sclater 1977; Stein and Stein 1992). However, there is no physical requirement that the temperature is constant at a certain depth over time. The concept, therefore, can be interpreted as an apparent feature of the actual thermal structure, with additional dynamic geophysical or geological processes, such as small-scale convection (e.g., Richter 1973) and/or rejuvenation by randomly distributed reheating events (e.g., Smith and Sandwell 1997), superimposed onto the cooling of a half space with thermal conduction. The difference in the electrical structures between the four areas may suggest that such a dynamic process developed with locality, or that different dynamic processes developed locally in each area. The electrical structures, their locations, and the major tectonic features in the northwestern Pacific are graphically summarized in Fig. 13. There is a major trend in the thickness of the resistive layer, with greater thickness to the southwest thinning to the northeast. In addition, the two western areas (C and D), which are both located close to subduction zones, have thicker resistive layers, and the two eastern areas (A and B), which are located farther offshore and closer to the Shatsky Rise, have thinner resistive layers. Graphical summary of the electrical structure of the upper mantle beneath the northwestern Pacific. The electrical conductivity beneath the four areas is depicted by colored columns. The color scale is provided as a bar in the right. Dashed lines in the column indicate depth intervals of 50 km, which are annotated in the left. In the bathymetric relief at the top, crosses indicate the observation sites with the same colors as in Fig. 1. The red circle and red dashed line indicate the locations of the seismic studies by Shinohara et al. (2008) and Ohira et al. (2017), respectively Area C is located at the southwestern edge of the present study region and has the thickest resistive layer. The possible thermal structure is more consistent with that expected based on a half space cooling model. This similarity may imply that the mantle beneath Area C is mostly static and therefore that it has cooled with age through conduction alone without additional dynamic processes. Baba et al. (2010) demonstrated that the temperature should be much lower than the peridotite solidus, even if the amount of water possibly dissolved in olivine is considered. Utada and Baba (2014) indicated that neither silicate melt nor carbonate melt, which can enhance bulk conductivity more than silicate melt, is required to explain the conductivity above ~170 km depth. Area D has a resistive layer that is slightly thinner than that of Area C, but thicker than that predicted from plate cooling models that fit bathymetric subsidence (Parsons and Sclater 1977). Therefore, the mantle here may also be rather static. However, in the central part of Area D, there is a petit-spot field (Hirano et al. 2006), which is thought to have formed as a result of melt leakage from the asthenosphere through fractures generated by plate bending before subduction. Preliminary results of 3-D inversion analysis of the MT data from Area D revealed a conductive anomaly in the lithospheric mantle beneath the petit-spot field, which suggested melt accumulation and migration to the surface (Baba et al. 2013b). Because carbon dioxide-rich melt is expected from the highly vesicular petit-spot basalt samples (Okumura and Hirano 2013), the mantle beneath the petit-spot field may be relatively enriched in carbon, which may be one of the causes of the difference in the electrical structure of Area D from that of Area C. For Area A and Area B, the plume associated with the formation of the Shatsky Rise may have affected the initial state of the temperature and/or composition of the mantle, although the two areas are located outside of the topographic anomaly of the Shatsky Rise itself. Ohira et al. (2017) found that along the spreading direction southeast of Area B, there are areas where the Moho is diffuse, weak, or absent, and are thus characterized by the presence of a gradual crust–mantle transition in seismic velocity. These authors suggested that the formation time of the crust–mantle transition layer is coincident with that of the Shatsky Rise and inferred a causal relationship. Shinohara et al. (2008) detected a similar crust–mantle transition layer at the eastern edge of Area A. Although they did not propose a geological interpretation of this feature, the same interpretation as that of Ohira et al. may be applicable in this case. The formation of the Shatsky Rise affects both areas, but additional factors are required to explain the differences between Area A and Area B. Note that the effect of the Shatsky Rise cannot be interpreted to represent the rejuvenation concept because it was formed on the ridge (Nakanishi et al. 1999). Instead, the plume may have promoted small-scale convection locally because of the low viscosity with excess heat and/or volatiles (Argusta et al. 2013). The difference between Area A and Area B may reflect the influence of different parts (i.e., upwelling and downwelling) of convection cells. The NOMan project completed EM array observations on the seafloor northwest (Area A) and southeast (Area B) of the Shatsky Rise in the northwestern Pacific. The collected data were analyzed based on MT methods, and 1-D electrical conductivity profiles that represent each array were then estimated after topographic effect correction. The newly acquired data from the NOMan project and the state-of-art analysis enabled us to extend the available period range of MT responses to shorter periods and to evaluate the implication to crustal structure in greater detail than achieved in previous deep ocean MT studies. The difference in the conductivity of the uppermost layers in Area A and Area B may reflect the difference in the thickness of the sedimentary layer. We compared the 1-D profiles of the NOMan arrays and two additional areas in the vicinity, off the Bonin Trench (Area C) and off the Japan Trench (Area D). The most remarkable finding is that the thickness of the resistive layer differs significantly for each area. Area A, which we assumed was "normal" in our previous study (Baba et al. 2013a), is not representative of the four areas because the resistive layer is thinnest in this area. The conductivity structure cannot be explained only by the age difference under a framework of the cooling of thermally conductive, homogeneous mantle. The thermal structure predicted for each area from the plate cooling model for the same plate thickness is almost identical because the lithospheric age is very old and differs only slightly between these areas (from ~130 to ~147 Ma). The significant differences in the thickness of the resistive layer suggest that the thickness of the cool thermal lithosphere is considerably different between these areas to a greater degree than predicted from the global datasets of heat flow and seafloor subsidence. The conductivity of the underlying highly conductive zone is fairly similar between areas, which suggests that the conductive (asthenospheric) mantle is rather uniform, although this zone beneath Area B seems slightly more conductive than those of the other areas. To explain the observed differences in the thickness of the resistive (lithospheric) layer, it is necessary to introduce dynamic processes. Possible processes may include local, small-scale convection in the asthenosphere and/or influence of the plume associated with the formation of the Shatsky Rise. There is a significant room for further discussion to reach a reasonable and comprehensive interpretation of the lithosphere–asthenosphere system beneath the northwestern Pacific. The present study shows that electrical conductivity information will make significant contributions to such investigation. 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The authors thank the captains, officers, crew, and ROV operation team of the R/V KAIREI of JAMSTEC (for cruises KR10-08, KR11-10, KR12-14, KR14-10, and KR15-14) and the W/V KAIYU of Offshore Operation Co., Ltd., for enabling the success of these cruises. Koji Miyakawa, Chikaaki Fujita, Atsushi Watanabe, Takeo Yagi, Toyonobu Ota, Tsukasa Yoshida, Hitoshi Okinaga, Takafumi Kasaya, Misumi Aoki, Kyoko Tanaka, Takeshi Takaesu, Satomi Minamizawa, and Toshikatsu Nasu are also thanked for technical assistance before, during, and after the cruises. The magnetic observatory data for KAK and NWP were provided by the Japan Meteorological Agency website (http://www.kakioka-jma.go.jp/metadata/) and the World Data Center for Geomagnetism, Kyoto (http://wdc.kugi.kyoto-u.ac.jp/), respectively. Bathymetry data based on MBES were provided by the JAMSTEC Data Site for Research Cruises (http://www.godac.jamstec.go.jp/darwin/). Jun Korenaga provided the residual bathymetry data. Heat flow data were acquired from the global heat flow database of the international heat flow commission (http://www.heatflow.und.edu/). Comments by two anonymous reviewers yielded improvements in the manuscript. All figures were produced using GMT software (Wessel et al. 2013). This study was partially supported by Grants-in-Aid for Scientific Research (KAKENHI) 22000003, 17340136, and 20340124 from the Japan Society for the Promotion of Science (JSPS). 1-D conductivity profiles supporting the conclusions of this article are included within the article and Additional file 3: Table. Grants-in-Aid for Scientific Research (KAKENHI) 22000003 from the Japan Society for the Promotion of Science (JSPS) supported the acquisition and analysis for the NOMan datasets. Grants-in-Aid for Scientific Research (KAKENHI) 17340136, and 20340124 from the Japan Society for the Promotion of Science (JSPS) supported the acquisition of the OBEM data in Area D. Earthquake Research Institute, The University of Tokyo, 1-1-1, Yayoi, Bunkyo-ku, Tokyo, 113-0032, Japan Kiyoshi Baba , Noriko Tada , Tetsuo Matsuno , Pengfei Liang , Ruibai Li , Hisayoshi Shimizu & Hisashi Utada Department of Deep Earth Structure and Dynamics Research, Japan Agency for Marine-Earth Science and Technology, 2-15, Natsushima, Yokosuka, Kanagawa, 237-0061, Japan Noriko Tada Kobe Ocean Bottom Exploration Center, Kobe University, 5-1-1, Fukaeminami, Higashinada-ku, Kobe, Hyogo, 658-0022, Japan Tetsuo Matsuno School of Ocean and Earth Science, Tongji University, 1239 Siping Road, Yangpu District, Shanghai, 200-092, China Luolei Zhang Center for Ocean Drilling Science, Japan Agency for Marine-Earth Science and Technology, 2-15 Natsushima, Yokosuka, Kanagawa, 237-0061, Japan Natsue Abe Center for Northeast Asian Studies, Tohoku University, 41 Kawauchi, Aoba-ku, Sendai, 980-8576, Japan Naoto Hirano Research Center for Prediction of Earthquakes and Volcanic Eruptions, Graduate School of Science, Tohoku University, 6-6, Aoba, Aramaki, Aoba-ku, Sendai, 980-8578, Japan Masahiro Ichiki Search for Kiyoshi Baba in: Search for Noriko Tada in: Search for Tetsuo Matsuno in: Search for Pengfei Liang in: Search for Ruibai Li in: Search for Luolei Zhang in: Search for Hisayoshi Shimizu in: Search for Natsue Abe in: Search for Naoto Hirano in: Search for Masahiro Ichiki in: Search for Hisashi Utada in: Correspondence to Kiyoshi Baba. Additional file 1: Figure S1. MT responses for all sites in Area A and Area B. Additional file 2: Figure S2. Synthetic inversion tests. Additional file 3: Table. 1-D electrical conductivity profiles shown in Fig. 11. Additional file 4: Figure S3. Sounding curves of the scalar MT responses (Z det) and their averages in the four study areas. Geomagnetic induction Marine magnetotellurics Electrical conductivity Oceanic lithosphere and asthenosphere Northwestern Pacific 1. Geomagnetism Studies on Electromagnetic Induction in the Earth: Recent advances	CommonCrawl
Determine from pKa if acid or base I'm studying medicine, not chemistry, but I hope you can help me anyway. I just had to solve a question where it is given that the drug Propranolol has a $\text{p}K_{\text{a}}$ of 9.5 and the un-ionized form is non-polar. Is there any way to say if propranolol is an acid or base just from the $\text{p}K_{\text{a}}$? Hope to hear from you, and sorry if it is a stupid question. acid-base drugs medicinal-chemistry Pritt says Reinstate Monica NannaNanna $\begingroup$ It's not a pKa of propranolol, but its pKbH+ - pKa of its conjugated acid. $\endgroup$ – Mithoron Jun 5 '17 at 14:43 $\begingroup$ Probably, but it only says "pka = 9,5". So if i don't have the information about propranolol being a base, how can i know? $\endgroup$ – Nanna Jun 5 '17 at 14:46 $\begingroup$ pKa of coniugated are often not properly distinguished, though luck kid... $\endgroup$ – Mithoron Jun 5 '17 at 14:54 $\begingroup$ Hi @Nanna, to answer your specific question, if all they tell you is 'Propranolol has a ${pKa}$ of 9.5 and the un-ionized form is non-polar', and you don't know anything else about it, then no, you can't tell if it's an acid or a base. Un-ionized molecules are generally non-polar, or at least less polar than ionized ones: for an acid the ionized form is an anion; for an amine, the ionized form is the protonated amine. Doesn't help, does it? I suspect what they actually meant to tell you was that in the acid-base reaction the loss of a proton produced a less polar species. Then it's a base. $\endgroup$ – user6376297 Jun 5 '17 at 16:36 $\begingroup$ You're welcome. And don't be afraid of asking questions, they are never stupid if you're someone who wants to learn. In fact, it's the exam/test question that is badly formulated, as it does not give you sufficient information to answer, or actually even misleads you. $\endgroup$ – user6376297 Jun 6 '17 at 17:24 Based on the structure, this drug is weakly basic. It has an amine moiety, which if protonated, would likely have a $\mathrm{p}K_{\mathrm{a}}$ value of around 9.5. ZheZhe $\begingroup$ I know you can say a lot about a drug based on the structure - but my exam is without any forms of 'aid' - I can't just look it up on the internet, so I have to use the information I am given. :-) $\endgroup$ – Nanna Jun 6 '17 at 9:05 $\begingroup$ At a pKa of 9.5 for a drug, you can probably assume an anime as a first guess. $\endgroup$ – Zhe Jun 6 '17 at 13:11 $\begingroup$ @Zhe That must be one hell of a drug to "assume" anime from:D $\endgroup$ – andselisk♦ Sep 5 '17 at 3:06 No, you cannot say because the terminology is, unfortunately, used interchangeably. For example, phenol has a pKa around 10. That means it is weakly acidic. However, amine pKa's are frequently referred to as being around 9-11, when in fact those numbers are the pKa of the conjugate acid. The pKa of secondary amines for example, is in the 20's as a very strong base is required to deprotonate them. So in your example, I would wager the pKa is of the salt form, not the neutral molecule. BeerhunterBeerhunter We are taught (assuming the $\ce{pK}$ values are about aqueous solutions) \begin{align} \mathrm{p}K_\mathrm{b} + \mathrm{p}K_\mathrm{a} &= 14& \text{so} && \mathrm{p}K_\mathrm{b} &\approx 14 - \mathrm{p}K_\mathrm{a}. \end{align} In this case, $\mathrm{p}K_\mathrm{b} \approx 3.5$, which is not a strong base ($\mathrm{p}K_\mathrm{b} < \approx 2-3$) but it's close. In medical literature a "drug" (i.e. a medicine) is a family of chemical compounds (or mixtures of compounds) where the exact chemical structure is often ignored. Propranolol may refer to the nonpolar compound, or one of several salts (such as Propranolol.HCl). There's no way to know without knowledge of how the drug is actually provided. Anyone studying medicine should also study $\mathrm{p}K$ values, you may have done that in high school. As far as identifying the organic chemical groups which may ionize, the good news is that there are only a few, so you can learn them. At least, only a few at physiological pH. Knowing that a group can ionize isn't as good as knowing it does ionize, but it's probably the best you can do from basic chemical knowledge. Experience will help some, but generally you'll have to rely on the literature since the exact electronic (and perhaps steric) effects that contribute are complex and difficult for the non-expert to analyze. Martin - マーチン♦ alphonsealphonse $\begingroup$ I have removed the unscientific banter at the beginning, which came off a bit rude. I invite you to review or be nice policy and act accordingly. $\endgroup$ – Martin - マーチン♦ Jun 6 '17 at 6:26 Not the answer you're looking for? Browse other questions tagged acid-base drugs medicinal-chemistry or ask your own question. How am I to interpret the phrase "a solution of acid"? Buffers calculating amounts of acid & base Is a metal hydroxide fully or partly oxidised in insufficient base? Ion concentration in acid and base How to calculate the concentration of conjugate acid from given pH and pKa values? Can Henderson-Hasselbalch equation be used to determine the pH of a solution when a strong base and a strong salt of that base stay together? NaHCO3 required to raise pH of weak HCl solution from 3.5 to 7.2 (doubting my calculations) Is there a terminology contradiction about whether the conjugate of a strong acid is a "weak base"? Why is a weak base more able to deprotonate a strong acid than a weak acid?	CommonCrawl
Misspecification of confounder-exposure and confounder-outcome associations leads to bias in effect estimates Noah A. Schuster1, Judith J. M. Rijnhart2, Lisa C. Bosman1, Jos W. R. Twisk1, Thomas Klausch1 & Martijn W. Heymans1 BMC Medical Research Methodology volume 23, Article number: 11 (2023) Cite this article Confounding is a common issue in epidemiological research. Commonly used confounder-adjustment methods include multivariable regression analysis and propensity score methods. Although it is common practice to assess the linearity assumption for the exposure-outcome effect, most researchers do not assess linearity of the relationship between the confounder and the exposure and between the confounder and the outcome before adjusting for the confounder in the analysis. Failing to take the true non-linear functional form of the confounder-exposure and confounder-outcome associations into account may result in an under- or overestimation of the true exposure effect. Therefore, this paper aims to demonstrate the importance of assessing the linearity assumption for confounder-exposure and confounder-outcome associations and the importance of correctly specifying these associations when the linearity assumption is violated. A Monte Carlo simulation study was used to assess and compare the performance of confounder-adjustment methods when the functional form of the confounder-exposure and confounder-outcome associations were misspecified (i.e., linearity was wrongly assumed) and correctly specified (i.e., linearity was rightly assumed) under multiple sample sizes. An empirical data example was used to illustrate that the misspecification of confounder-exposure and confounder-outcome associations leads to bias. The simulation study illustrated that the exposure effect estimate will be biased when for propensity score (PS) methods the confounder-exposure association is misspecified. For methods in which the outcome is regressed on the confounder or the PS, the exposure effect estimate will be biased if the confounder-outcome association is misspecified. In the empirical data example, correct specification of the confounder-exposure and confounder-outcome associations resulted in smaller exposure effect estimates. When attempting to remove bias by adjusting for confounding, misspecification of the confounder-exposure and confounder-outcome associations might actually introduce bias. It is therefore important that researchers not only assess the linearity of the exposure-outcome effect, but also of the confounder-exposure or confounder-outcome associations depending on the confounder-adjustment method used. Unlike in randomized controlled trials, the observed exposure values in observational studies are often influenced by the characteristics of the study subjects. As a result, there might be an unintended difference in baseline characteristics between exposed and unexposed individuals. If these characteristics are also associated with the outcome, then these covariates are confounders of the exposure-outcome effect. In other words, a confounder is a common cause of the exposure and the outcome [1]. A simple comparison of the outcome between exposure groups then results in a biased effect estimate [2, 3]. Therefore, in observational studies, to obtain an unbiased estimate of the exposure effect it is necessary to remove the spurious part of the exposure-outcome effect caused by the confounders. There are different methods to obtain confounder-adjusted exposure effect estimates, such as multivariable regression analysis and various propensity score (PS) methods. In multivariable regression analysis the confounders are added to the model in which the outcome is regressed on the exposure [4]. This way, the confounder-outcome association is controlled for when estimating the causal effect. In propensity score methods a balancing score is created which can subsequently be used to adjust, stratify, or weight the exposure-outcome effect [2, 5]. By creating this balancing score, the confounder-exposure association is removed and an unbiased exposure effect estimate can be obtained [6]. When multivariable regression analysis is used to adjust the relation between a continuous exposure and an outcome for a continuous confounder, both the exposure-outcome effect and the confounder-outcome association are assumed to be linear. It is common practice to assess the linearity assumption for the exposure-outcome effect and there is a substantial body of literature that covers this topic [4, 7]. However, various reviews found that the quality of the reporting of confounder adjustment methods is suboptimal [8,9,10,11] Often studies fail to explicitly report whether linearity was assessed [11]. When it is incorrectly assumed that the confounders are linearly related with the exposure and outcome (i.e., if the associations are misspecified), the exposure effect estimate might be over- or underestimated. Thus, in an attempt to remove bias, bias may actually be introduced. The bias that remains (or is introduced) after adjusting for confounding is also called residual confounding [7, 11, 12]. The aim of this paper is to demonstrate the importance of assessing the linearity assumption for confounder-exposure and confounder-outcome associations and the importance of correctly specifying these associations when the linearity assumption is violated. First, we describe how the linearity assumption can be assessed. Second, we provide an overview of methods that can be used to model non-linear effects. Third, we review four well-known confounder-adjustment methods and lay out their respective functional form assumptions. Fourth, we illustrate the importance of the correct specification of the confounder-exposure and confounder-outcome associations using a Monte Carlo simulation and an empirical data example. Fifth, we discuss methods that can be used to correctly specify the confounder-exposure and confounder-outcome associations. Examination of the linearity assumption Suppose that variable A represents a continuous independent variable, variable B represents a continuous dependent variable. There are several methods to assess the linearity of the association between variables A and B. A first method is visual inspection: a scatterplot with variable A on the X-axis and variable B on the Y-axis provides an indication of the nature of the relationship between A and B [13]. Figure 1 provides a hypothetical example of a linear relationship between variables A and B (panel A), and a non-linear relationship between those variables (panel B). In both panels, the circles represent the observed data and the dotted line represents the linear regression line, i.e., the line that describes a linear relationship between variables A and B. In panel A, the regression line fits the data well, because the circles in the scatterplot resemble a straight line. In panel B, however, the linear regression line is not a good representation of the non-linear relationship between A and B, because the circles in the scatterplot do not resemble a straight line. Then, failing to model the A-B association as non-linear results in a biased estimate of this association. Hypothetical example of the relationship between continuous variables A and B, where each point represents an observation. Panel a: linear relationship. Panel b: non-linear relationship. The dotted line represents the linear regression line for the relationship between variables A and B A second method to assess linearity is to categorize the continuous variable A into multiple groups of equal sizes, e.g., based on tertiles or quartiles of the distribution of variable A. Subsequently, variable B is modelled as a function of a categorized variable A. If the regression coefficients corresponding to the categories of variable A do not increase linearly, then this indicates that the A-B association is non-linear [7]. A third method to assess linearity is the addition of a non-linear term for variable A, e.g., a quadratic term, to the model. When adding a non-linear term to the model, variable B is modelled as a function of variable A and the non-linear term of variable A. If the A-B association is truly linear, then the coefficient corresponding to the non-linear term will be zero [4]. Often, statistical significance of the non-linear term is used as a threshold to determine whether the linearity assumption is violated. Although in this paper we focus on linear regression models, the linearity assumption is also applicable to continuous independent variables in generalized linear models, such as logistic regression models. In generalized linear models the linearity assumption can be checked using the two non-visual methods, i.e., categorization of the independent variable and by adding non-linear terms for the independent variable. Modelling non-linear associations There are several methods that can be used to model the non-linear associations, such as categorization, the use of non-linear terms and the use of spline functions. An overview of commonly used methods for modelling non-linear associations, their application and advantages and disadvantages can be found in Table 1. Table 1 Methods to approximate true non-linear effects A first method that is sometimes used to model non-linear associations is categorization [14,15,16,17]. Suppose that the confounder-outcome association is non-linear. With categorization the subjects in the dataset are being categorized based on their values on the continuous confounder variable. Groups can be created based on substantively meaningful cut-off points or statistical cut-off points (e.g., tertiles or quartiles). Subsequently, n-1 dummy variables are created based on the categorical confounder variable, where n represents the number of categories. For example, if the variable consists of four categories, then three dummy variables are created. The reference group is coded as 0 in each of these dummy variables, while in each dummy variable one of the other groups is coded as 1. Subsequently, the outcome is regressed on the dummy variables, where the regression coefficient for each dummy variable represents the difference in the outcome between the group coded as 1 and the reference group. A disadvantage of modelling a non-linear association by categorization is that the magnitude of the association is assumed to be the same for all subjects a within a specific group [14,15,16,17]. Therefore, a potential non-linear association within a category is not captured in the analysis. Another method that can be used to model the non-linear associations is the inclusion of non-linear terms, such as quadratic or cubic terms, in the regression model [18]. Suppose that the confounder-outcome association follows a quadratic shape, then this can be modelled by regressing the outcome on the original confounder variable and a quadratic term for the confounder. Adding non-linear terms increases the flexibility of the model, but also reduces the interpretability of the results [18]. However, using non-linear terms to approximate the non-linearity of the confounder-exposure or confounder-outcome association does not affect the interpretability of the exposure effect. Spline regression is another method that can be used to model non-linear associations. Two types of splines that are commonly used are linear splines and restricted cubic splines. With spline regression, the confounding variable is also categorized, but instead of assuming that the association is of the same magnitude for all subjects in a specific category, a regression line is estimated for each category [4, 13, 19]. Depending on whether linear or restricted cubic splines are used, the estimated regression line is linear or non-linear, respectively. The cut-off points in between categories are called knots. A 1-knot spline function is based on two categories, a 2-knot spline function on three categories, a 3-knot spline function on four categories, etcetera. Detailed information on the estimation of splines can be found elsewhere [20]. Like with non-linear terms, the interpretation of the coefficients can be complicated when spline functions are used [13]. However, because we are not necessarily interpreting the coefficients of the confounder-exposure or confounder-outcome associations, spline functions are a good and efficient way to approximate the non-linear shapes of those associations. Confounder-adjustment methods Studies are often interested in estimating the average effect of an exposure on an outcome. In terms of potential outcomes, the average effect of the exposure on the outcome is defined as the difference between two expected potential outcome values under two exposure values, i.e., E[Y(1) − Y(0)]. To obtain an unbiased estimate of this exposure effect it is necessary to adjust for any confounding. In this study we discuss four confounder-adjustment methods: multivariable regression analysis, covariate adjustment using the propensity score (PS), inverse probability weighting (IPW) and double robust (DR) estimation. As assessing the linearity assumption for the exposure-outcome effect is common practice, throughout this paper we assume that the exposure-outcome effect is always correctly specified as linear. However, we believe that the information in this paper also applies to models in which the exposure-outcome effect is (correctly specified as) non-linear. Table 2 shows which association (i.e., the confounder-exposure or the confounder-outcome association, or both) has to be correctly specified for each method in order to obtain unbiased exposure effect estimates. Table 2 Confounder-adjustment methods and the association(s) that need to be correctly specified to obtain an unbiased estimate of the exposure effect Multivariable regression analysis With multivariable regression analysis, the outcome is modelled as a function of the exposure and the confounders [4] (eq. 1): $$E\left(Y\|X,C\right)={i}_1+{\beta}_1X+{\beta}_2{C}_1+\dots +{\beta}_{n+1}{C}_n$$ where Y and X represent the continuous outcome and a dichotomous exposure, respectively, and i1 represents the intercept term. β1 is the multivariable confounder-adjusted exposure effect estimate and β2 to βn + 1 are the coefficients that correspond to the continuous confounding variables C1 to Cn. Multivariate regression analysis adjusts for confounding of the exposure-outcome effect by adding confounders C1 to Cn to the equation [4, 13]. If there are no unobserved confounders and the linear regression model in eq. 1 is correctly specified, then parameter β1 is equal to the average treatment effect E [Y(1)-Y(0)] [21]. In eq. 1, a linear association is assumed between the exposure and the outcome, and between each confounding variable and the outcome [13]. The confounder-exposure association is not modelled, therefore no assumptions are made about the functional form of that association. Propensity score adjustment The PS is the predicted probability of endorsing exposure (eq. 2): $$PS=P\left(X=1\|{C}_1,\dots, {C}_n\right)=\frac{1}{1+{e}^{-\left({i}_2+{\lambda}_1{C}_1+\dots +{\lambda}_n{C}_n\right)}}$$ where X represents the dichotomous exposure, i2 is the model intercept and λ1 to λn are regression coefficients corresponding to confounders C1 to Cn. The propensity score is estimated in two steps. First, the exposure is modelled as a function of the confounders C1 to Cn using a logistic regression model. Second, each individual's predicted probability of endorsing the exposure is estimated, which is the propensity score [2, 6, 22]. The PS can be used in different ways to adjust for confounding. In this paper we discuss three of these methods: covariate adjustment with the PS, inverse probability weighting and double robust estimation. All three methods assume that the propensity score is correctly specified, i.e., that the log odds of the exposure is linear in the confounders. Details on the computation of the PS in general and other PS methods such as matching and stratification can be found elsewhere [2, 6, 22,23,24,25,26,27,28,29]. Covariate adjustment using the propensity score Because the PS contains information on the confounders, it is possible to adjust for confounding by modelling the outcome as a function of the exposure and the PS [2, 22]. Thus, instead of conditioning on confounding variables C1 to Cn as in eq. 1, we now condition on the PS (eq. 3): $$E\left(Y\|X, PS\right)={i}_3+{\beta}_1^{\ast }X+{\beta}_2^{\ast } PS$$ where Y and X represent the continuous outcome and the dichotomous exposure, respectively, and i3 represents the intercept term. ${\beta}_1^{\ast }$ is the PS confounder-adjusted exposure effect estimate and ${\beta}_2^{\ast }$ is the coefficient that corresponds to the propensity score PS. Because in eq. 3 the outcome is regressed on the exposure and the propensity score, linearity assumptions apply both to the exposure-outcome effect and the PS-outcome association. Whereas all PS methods require the PS to be adequately specified, this is the only PS method that additionally makes assumptions about the linearity of the PS-outcome association [2, 4]. Inverse probability weighting Inverse probability weighting uses weights based on the PS to create a pseudo-population in which each confounder combination is balanced between the exposed and unexposed groups. When there is perfect confounder balance between the groups there is no longer an association between confounders C1 to Cn and the exposure [4]. With weighting, individuals who are underrepresented get larger weights assigned, whereas individuals who are overrepresented get smaller weights assigned. For exposed individuals the weight is calculated as $\frac{1}{PS}$, whereas for unexposed individuals the weight is calculated as $\frac{1}{1- PS}$ [2, 30]. A potential issue with IPW is that the weights can be unstable. This is because individuals with a PS close to 0 receive very large weights, whereas individuals with a PS close to 1 receive very small weights. Subjects with these large weights will then dominate the weighted analysis, resulting in a large variance of the IPW estimator [31]. As an alternative, stabilized weights have been proposed [2]. This reduces the weights of the treated individuals with a small PS and the untreated individuals with a large PS. For exposed individuals, these stabilized weights are calculated as $\frac{p}{PS}$ and for unexposed individuals stabilized weights are calculated as $\frac{1-p}{1- PS}$, with p being the probability of exposure without considering the confounders [2]. After calculating the weights for all individuals the IPW confounder-adjusted exposure effect is estimated by performing a weighted regression analysis with the exposure as the only independent variable. IPW does not make any linearity assumptions about the confounder-outcome or PS-outcome association [29]. Thus, IPW only assumes a correctly specified propensity model. If the propensity model is misspecified this results in inappropriate weights and possibly a biased IPW confounder-adjusted exposure effect estimate [32]. Double robust estimation Double robust estimation combines multivariable regression analysis and IPW and is done in two steps: first, a propensity model is specified and stabilized weights are calculated. Second, a weighted analysis is conducted in which the outcome is regressed on the exposure and the confounders. Because the model is weighted by the stabilized weights, an adequately specified propensity model is needed. In addition, because the confounders are included in the regression analysis, linearity assumptions about the confounder-outcome association are made. However, only one of these two associations (i.e., either the confounder-exposure associations in the propensity model or the confounder-outcome associations in the multivariable regression model) has to be correctly specified to obtain an unbiased exposure effect estimate [29, 32, 33]. However, if both effects are misspecified, the DR exposure effect estimate may be even more biased than the estimate of a less robust single confounder-adjustment method such as multivariable regression or IPW [34, 35]. Simulation study A simulation study was designed to assess and compare the performance of the four confounder-adjustment methods. Four different scenarios were considered based on the (mis)specification of the confounder-exposure and confounder-outcome association (see Table 3). The R programming language version 4.0.3 was used to generate and analyse the data [36]. Table 3 Overview of simulated scenarios To model both misspecified and correctly specified confounder-exposure and confounder-outcome associations, first two continuous confounders were generated. Confounder Z was generated from a standard normal distribution, and confounder C was its corresponding squared term. The dichotomous exposure was generated from a binomial distribution conditional on confounder Z and its squared term C (eq. 4), and the continuous outcome was a function of the exposure and confounders Z and C (eq. 5). $$P\left(X=1\|Z,C\right)=\frac{1}{1+{e}^{-\left({i}_4+{\theta}_1Z+{\theta}_2C\right)}}$$ $$E\left(Y\|X,Z,C\right)={i}_5+{\gamma}_1X+{\gamma}_2Z+{\gamma}_3C$$ This way, the exposure and the outcome had a quadratic relation with each of the confounders. Next, we estimated the confounder-adjusted exposure-outcome effect using the four confounder-adjustment methods. In the scenarios in which the non-linearity of the confounder-exposure and confounder-outcome association were correctly specified, the analysis was adjusted for confounders Z and C. This way, the underlying quadratic relation was modelled. In the scenarios in which the effects were misspecified, only confounder Z was included in the analysis. This way, only the incorrect linear relation was modelled. Sample sizes were 200, 500 and 1000. The parameter value for the exposure-outcome effect was set to 0.59 to mimic a large effect size. The parameter values for the confounder-exposure and confounder-outcome association were set to −0.14, −0.39, − 0.59 and 0.14, 0.39 and 0.59 to mimic negative and positive small, medium and large effect sizes, respectively [37]. In total, 72 conditions were simulated (4 scenarios; 3 sample sizes; 6 confounder-exposure and confounder-outcome effect sizes) with 1000 repetitions per condition, resulting in 72,000 observations. The performance of the confounder-adjustment methods was compared based on the absolute bias (AB) and the relative bias (RB) [38]. AB is the absolute difference between the estimated exposure effect and the true exposure-outcome effect of 0.59. RB is the ratio of AB to the true exposure-outcome effect [38, 39]. For both performance measures a lower score corresponds to a better performance. The simulation code is available in additional file 1. In additional file 2 we show an extra condition in which the direction of the exposure effect changes if the non-linearity of the confounder-exposure and confounder-outcome associations is not modelled correctly. Table 4 shows the mean estimated exposure effect, AB and RB for all models across the four simulated scenarios based on a sample size of 500 and positive confounder-exposure and confounder-outcome associations. Results for sample sizes 200 and 1000 can be found in additional files 3 and 4, respectively. Table 4 Model performance across all simulated scenarios, n = 500 In scenario 1, where both the confounder-exposure and confounder-outcome associations were correctly specified, multivariable regression analysis, PS adjustment and DR estimation all performed well. When the confounder-outcome association was misspecified (scenario 2), multivariable regression analysis and DR estimation resulted in biased exposure effect estimates. PS adjustment still performed well, but had the PS-outcome association been misspecified as well, then residual bias would also have been observed for that method. In both scenarios 1 and 2, bias was observed for IPW as IPW is a large sample technique [3]. Increasing the sample size resulted in exposure effect estimates closer to the true effect. In scenario 3, where the confounder-exposure association was misspecified but the confounder-outcome association was correctly specified, multivariable regression analysis and DR estimation performed well, whereas PS adjustment and IPW resulted in biased exposure effect estimates. When both associations were misspecified (scenario 4), all methods resulted in biased exposure effect estimates. In all scenarios, the amount of bias depended on the strength of the confounder-exposure and confounder-outcome associations: the weaker the associations were, the less biased was observed. The same patterns can be observed for negative confounder-exposure and confounder-outcome associations. For detailed results see additional file 5. Empirical data example To demonstrate the consequences of misspecification of the confounder-exposure and confounder-outcome association we used an illustrative example from the Amsterdam Growth and Health Longitudinal Study (AGHLS). The AGHLS is an ongoing cohort study that started in 1976 to examine growth and health among teenagers. In later measurement rounds, health and lifestyle measures, determinants of chronic diseases and parameters for the investigation of deterioration in health with age were measured [40]. For this demonstration we use data collected in 2000, when the participants were in their late 30s. Using data from the AGHLS, we estimated the effect of overweight (BMI ≥ 25) on systolic blood pressure. We adjusted this effect for confounding by alcohol consumption (measured in number of glasses per week) and cardiorespiratory fitness (VO2max). Only subjects with complete data on all variables were included in the analyses (n = 359). Note that this data example is included for illustrative purposes only and therefore represents a simplified scenario. In reality, it is likely that there will be additional confounders and time-varying confounders. As a result, substantive interpretations should be approached with caution. First, we examined the linearity of the confounder-exposure and the confounder-outcome associations. We did this by categorizing alcohol consumption and cardiorespiratory fitness, and separately regressing overweight and systolic blood pressure on the categorized confounders. In both cases, the regression coefficients corresponding to the categories of alcohol consumption and respiratory fitness did not increase linearly. Thus, both confounder-exposure and confounder-outcome associations were non-linear. There were no violations of the linearity assumption for the exposure-outcome effect, as systolic blood pressure was compared across only two groups (i.e., healthy weight and overweight). Second, to demonstrate the consequences of misspecification, we modelled systolic blood pressure as a function of overweight, adjusting for alcohol consumption and cardiorespiratory fitness. We did this first by (falsely) assuming a linear relation between the confounders and overweight and between the confounders and systolic blood pressure. Next, we took these non-linear associations into account by adjusting for alcohol consumption and cardiorespiratory fitness using 3-knot restricted cubic spline (RCS) regression, which has the ability to. fit non-linear shapes. A detailed explanation of RCS regression can be found elsewhere [4]. Although implementing RCS regression might still not equal perfect specification of both effects, it provides a better representation of the true non-linear relations than simply assuming linear confounder-exposure and confounder-outcome associations. The results of the analyses can be found in Table 5. Across all four methods, the exposure effects were smaller in magnitude when the confounder-exposure and confounder-outcome associations were modelled as non-linear. Given that in our example the confounder-exposure and confounder-outcome associations were non-linear, the exposure effects were overestimated when the confounder-exposure and confounder-outcome associations were incorrectly modelled as linear. Table 5 The effect of overweight on systolic blood pressure, adjusted for alcohol consumption. 2nd column: linear models in which the confounder-exposure and/or confounder-outcome associations are modelled as linear. 3rd column: spline models in which the confounder-exposure and/or confounder-outcome associations are modelled as non-linear This paper aimed to demonstrate the importance of assessing the linearity assumption for confounder-exposure and confounder-outcome associations and the importance of correctly specifying these associations when the linearity assumption is violated. If these associations are incorrectly specified as linear, then bias might be introduced in an attempt to remove bias. Our simulation study showed that bias is introduced if the confounder-exposure and/or the confounder-outcome association are misspecified. The amount of bias also depended on the confounder-adjustment method and the strength of the confounder-exposure and confounder-outcome association. We also illustrated how misspecification of the confounder-exposure and/or confounder-outcome associations biases exposure-outcome effect estimates our empirical data example. The simulation study and the empirical data example both showed that merely adjusting for confounding is not enough, but that correct specification of all effects in the model is crucial to obtain unbiased exposure effect estimates. Reporting of confounding The results in this paper demonstrate that misspecification of the confounder-exposure and confounder-outcome associations may lead to additional bias. However, in practice residual confounding may often go unnoticed, as inappropriate reporting makes it difficult to assess the reliability and validity of study results. In 2007 the STROBE (Strengthening the Reporting of Observational Studies in Epidemiology) initiative published a checklist of items that should be addressed in reports of observational studies, including two items that address confounding (9 'Bias' and 12 'Statistical methods') [41]. The explanatory and elaboration document of STROBE acknowledges that adjusting for confounding may involve additional assumptions about the functional form of the studied associations [42]. Despite the publication of the STROBE checklist, the overall quality of reporting of confounding remains suboptimal [9, 43]. To increase transparency on the risk of residual confounding, we advise researchers to report how the functional form of the confounder-exposure and confounder-outcome association was assessed and taken into account. The simulation study in this paper is a simplified representation of real world scenarios. We adjusted for one confounder, whereas in reality there might be multiple confounders. If there are multiple confounders, then the confounder-exposure and confounder-outcome association of each of the confounders needs to be assessed and non-linear effects need to be modelled for confounders that are not linearly related to either the exposure or the outcome. In the PS methods, the PS-outcome association was linear, so no additional bias was observed in scenarios in which the confounder-outcome association was misspecified. However, if the PS-outcome association is also misspecified, residual bias would be observed. Therefore, the linearity of the relation between the PS and the outcome should always be checked. IPW is known to perform less well in small samples, which was also confirmed in our simulation [3]. Last, in this paper we assume associations are either misspecified or correctly specified, whereas in reality, naturally, everything exists in shades of grey. In addition, there are other important contributors to bias in the exposure effect estimate that researchers should be aware of, such as omitted confounders, adjustment for colliders, and measurement error in the confounders. A limited theoretical understanding of factors that influence exposures and outcomes may cause researchers to overlook important confounders or to adjust for a collider (i.e., a variable that is influenced by both the exposure and outcome). In both situations the estimate of the exposure effect will be biased [44]. Finally, there may be residual confounding when the confounders are measured with error [45]. To summarize, in this study we showed the importance of correctly specifying the confounder-exposure and confounder-outcome associations to obtain unbiased exposure effect estimates. 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Using sensitivity analyses for unobserved confounding to address covariate measurement error in propensity score methods. Am J Epidemiol. 2018;187(3):604–13. The authors received no financial support for the research, authorship, and/or publication of this article. Department of Epidemiology and Data Science, Amsterdam Public Health Institute, Amsterdam UMC, Vrije Universiteit Amsterdam, De Boelelaan, 1117, Amsterdam, The Netherlands Noah A. Schuster, Lisa C. Bosman, Jos W. R. Twisk, Thomas Klausch & Martijn W. Heymans College of Public Health, University of South Florida, Tampa, FL, USA Judith J. M. Rijnhart Noah A. Schuster Lisa C. Bosman Jos W. R. Twisk Thomas Klausch Martijn W. Heymans NS, JR and LB designed the study. NS performed the statistical analyses and drafted the manuscript. All authors contributed to data interpretation, critically revised the manuscript and approved the final version of the manuscript. Correspondence to Noah A. Schuster. Informed consent for the Amsterdam Growth and Health Longitudinal Study was signed by the school authorities, parents and pupils at each follow-up round. Ethics approval was given by the VU Medical Center ethical committee at each follow-up round. All methods were carried out in accordance with relevant guidelines and regulations. Schuster, N.A., Rijnhart, J.J.M., Bosman, L.C. et al. Misspecification of confounder-exposure and confounder-outcome associations leads to bias in effect estimates. BMC Med Res Methodol 23, 11 (2023). https://doi.org/10.1186/s12874-022-01817-0 Accepted: 08 December 2022 Confounding Confounder-adjustment Linearity assumption Confounder-exposure association Confounder-outcome association Propensity score methods	CommonCrawl
Sat, 22 Jun 2019 21:23:08 GMT 3.2: Quadratic Functions [ "article:topic", "quadratic function", "license:ccbysa", "showtoc:no", "authorname:lippmanrasmussen" ] Precalculus & Trigonometry Book: Precalculus - An Investigation of Functions (Lippman & Rasmussen) 3: Polynomial and Rational Functions. Contributed by David Lippman & Melonie Rasmussen Professors (Mathematics) at Pierce College Sourced from The OpenTextBookStore Short run Behavior: Vertex Short run Behavior: Intercepts Important Topics of this Section In this section, we will explore the family of 2${}^{nd}$ degree polynomials, the quadratic functions. While they share many characteristics of polynomials in general, the calculations involved in working with quadratics is typically a little simpler, which makes them a good place to start our exploration of short run behavior. In addition, quadratics commonly arise from problems involving area and projectile motion, providing some interesting applications. A backyard farmer wants to enclose a rectangular space for a new garden. She has purchased 80 feet of wire fencing to enclose 3 sides, and will put the 4${}^{th}$ side against the backyard fence. Find a formula for the area enclosed by the fence if the sides of fencing perpendicular to the existing fence have length $L$. In a scenario like this involving geometry, it is often helpful to draw a picture. It might also be helpful to introduce a temporary variable, $W$, to represent the side of fencing parallel to the 4${}^{th}$ side or backyard fence. Since we know we only have 80 feet of fence available, we know that $L+W+L=80$, or more simply, $2L+W=80$. This allows us to represent the width, $W$, in terms of $L$: $W=80-2L$ Now we are ready to write an equation for the area the fence encloses. We know the area of a rectangle is length multiplied by width, so $A=LW=L(80-2L)$ $A(L)=80L-2L^{2}$ This formula represents the area of the fence in terms of the variable length $L$. We now explore the interesting features of the graphs of quadratics. In addition to intercepts, quadratics have an interesting feature where they change direction, called the vertex. You probably noticed that all quadratics are related to transformations of the basic quadratic function $f(x)=x^{2}$. Write an equation for the quadratic graphed below as a transformation of $f(x)=x^{2}$, then expand the formula and simplify terms to write the equation in standard polynomial form. We can see the graph is the basic quadratic shifted to the left 2 and down 3, giving a formula in the form $g(x)=a(x+2)^{2} -3$. By plugging in a point that falls on the grid, such as (0,-1), we can solve for the stretch factor: $\begin{array}{l} {-1=a(0+2)^{2} -3} \\ {2=4a} \\ {a=\dfrac{1}{2} } \end{array}$ Written as a transformation, the equation for this formula is $g(x)=\frac{1}{2} (x+2)^{2} -3$. To write this in standard polynomial form, we can expand the formula and simplify terms: $\begin{array}{l} {g(x)=\dfrac{1}{2} (x+2)^{2} -3} \\ {g(x)=\dfrac{1}{2} (x+2)(x+2)-3} \\ {g(x)=\dfrac{1}{2} (x^{2} +4x+4)-3} \\ {g(x)=\dfrac{1}{2} x^{2} +2x+2-3} \\ {g(x)=\dfrac{1}{2} x^{2} +2x-1} \end{array}$ Notice that the horizontal and vertical shifts of the basic quadratic determine the location of the vertex of the parabola; the vertex is unaffected by stretches and compressions. A coordinate grid has been superimposed over the quadratic path of a basketball(From http://blog.mrmeyer.com/?p=4778, © Dan Meyer, CC-BY). Find an equation for the path of the ball. Does he make the basket? The path passes through the origin with vertex at (-4, 7). $h(x) = -\dfrac{7}{16}(x + 4)^2 + 7$. To make the shot, $h(-7.5)$ would need to be about 4. $h(-7.5) \approx 1.64$; he doesn't make it. forms of quadratic function The standard form of a quadratic function is $f(x)=ax^{2} +bx+c$ The transformation form of a quadratic function is $f(x)=a(x-h)^{2} +k$ The vertex of the quadratic function is located at ($h$, $k$), where $h$ and $k$ are the numbers in the transformation form of the function. Because the vertex appears in the transformation form, it is often called the vertex form. In the previous example, we saw that it is possible to rewrite a quadratic function given in transformation form and rewrite it in standard form by expanding the formula. It would be useful to reverse this process, since the transformation form reveals the vertex. Expanding out the general transformation form of a quadratic gives: $\begin{array}{l} {f(x)=a(x-h)^{2} +k=a(x-h)(x-h)+k} \\ {f(x)=a(x^{2} -2xh+h^{2} )+k=ax^{2} -2ahx+ah^{2} +k} \end{array}$ This should be equal to the standard form of the quadratic: $ax^{2} -2ahx+ah^{2} +k=ax^{2} +bx+c$ The second degree terms are already equal. For the linear terms to be equal, the coefficients must be equal: $-2ah=b$, so $h=-\dfrac{b}{2a}$ This provides us a method to determine the horizontal shift of the quadratic from the standard form. We could likewise set the constant terms equal to find: $ah^{2} +k=c$, so $k=c-ah^{2} =c-a\left(-\dfrac{b}{2a} \right)^{2} =c-a\dfrac{b^{2} }{4a^{2} } =c-\dfrac{b^{2} }{4a}$ In practice, though, it is usually easier to remember that $k$ is the output value of the function when the input is $h$, so $k=f(h)$. finding the vertex of a quadratic For a quadratic given in standard form, the vertex ($h$, $k$) is located at: $h=-\dfrac{b}{2a} , k=f(h)=f\left(\dfrac{-b}{2a} \right)$ Find the vertex of the quadratic $f(x)=2x^{2} -6x+7$. Rewrite the quadratic into transformation form (vertex form). The horizontal coordinate of the vertex will be at $h=-\dfrac{b}{2a} =-\dfrac{-6}{2(2)} =\dfrac{6}{4} =\dfrac{3}{2}$ The vertical coordinate of the vertex will be at $f(\dfrac{3}{2} )=2(\dfrac{3}{2})^{2} -6(\dfrac{3}{2} )+7=\dfrac{5}{2}$ Rewriting into transformation form, the stretch factor will be the same as the $a$ in the original quadratic. Using the vertex to determine the shifts, $f(x)=2(x-\dfrac{3}{2} )^{2} +\dfrac{5}{2}$ Given the equation $g(x)=13+x^{2} -6x$ write the equation in standard form and then in transformation/vertex form. $g(x) = x^2 - 6x + 13$ in Standard form; Finding the vertex, $h = \dfrac{-(-6)}{2(1)} = 3$. $k = g(3) = 3^2 - 6(3) + 13 = 4$. $g(x) = (x - 3)^2 + 4$ in Transformation form As an alternative to using a formula for finding the vertex, the equation can also be written into vertex form by completing the square. This process is most easily explained through example. In most cases, using the formula for finding the vertex will be quicker and easier than completing the square, but completing the square is a useful technique when faced with some other algebraic problems. Rewrite $f(x)=2x^{2} -12x+14$ into vertex form by completing the square. We start by factoring the leading coefficient from the quadratic and linear terms. $2(x^{2} -6x)+14$ Next, we are going to add something inside the parentheses so that the quadratic inside the parentheses becomes a perfect square. In other words, we are looking for values $p$ and $q$ so that $(x^{2} -6x+p)=(x-q)^{2}$. Notice that if multiplied out on the right, the middle term would be -2q, so q must be half of the middle term on the left; $q = -3$. In that case, $p$ must be (-3)${}^{2}$ = 9. $(x^{2} -6x+9)=(x-3)^{2}$ Now, we can't just add 9 into the expression – that would change the value of the expression. In fact, adding 9 inside the parentheses actually adds 18 to the expression, since the 2 outside the parentheses will distribute. To keep the expression balanced, we can subtract 18. $2(x^{2} -6x+9)+14-18$ Simplifying, we are left with vertex form. $2(x-3)^{2} -4$ In addition to enabling us to more easily graph a quadratic written in standard form, finding the vertex serves another important purpose – it allows us to determine the maximum or minimum value of the function, depending on which way the graph opens. Returning to our backyard farmer from the beginning of the section, what dimensions should she make her garden to maximize the enclosed area? Earlier we determined the area she could enclose with 80 feet of fencing on three sides was given by the equation $A(L)=80L-2L^{2}$. Notice that quadratic has been vertically reflected, since the coefficient on the squared term is negative, so the graph will open downwards, and the vertex will be a maximum value for the area. In finding the vertex, we take care since the equation is not written in standard polynomial form with decreasing powers. But we know that $a$ is the coefficient on the squared term, so $a = -2$, $b = 80$, and $c = 0$. Finding the vertex: $h=-\dfrac{80}{2(-2)} =20, k=A(20)=80(20)-2(20)^{2} =800$ The maximum value of the function is an area of 800 square feet, which occurs when $L = 20$ feet. When the shorter sides are 20 feet, that leaves 40 feet of fencing for the longer side. To maximize the area, she should enclose the garden so the two shorter sides have length 20 feet, and the longer side parallel to the existing fence has length 40 feet. A local newspaper currently has 84,000 subscribers, at a quarterly charge of $30. Market research has suggested that if they raised the price to $32, they would lose 5,000 subscribers. Assuming that subscriptions are linearly related to the price, what price should the newspaper charge for a quarterly subscription to maximize their revenue? Revenue is the amount of money a company brings in. In this case, the revenue can be found by multiplying the charge per subscription times the number of subscribers. We can introduce variables, $C$ for charge per subscription and S for the number subscribers, giving us the equation Revenue = $CS$ Since the number of subscribers changes with the price, we need to find a relationship between the variables. We know that currently $S = 84,000$ and $C = 30$, and that if they raise the price to $32 they would lose 5,000 subscribers, giving a second pair of values, $C = 32$ and $S = 79,000$. From this we can find a linear equation relating the two quantities. Treating $C$ as the input and $S$ as the output, the equation will have form $S=mC+b$. The slope will be $m=\dfrac{79,000-84,000}{32-30} =\dfrac{-5,000}{2} =-2,500$ This tells us the paper will lose 2,500 subscribers for each dollar they raise the price. We can then solve for the vertical intercept $S=-2500C+b$ Plug in the point $S = 84,000$ and $C = 30$ $84,000=-2500(30)+b$ Solve for $b$ $b=159,000$ This gives us the linear equation $S=-2,500C+159,000$ relating cost and subscribers. We now return to our revenue equation. Revenue = $CS$ Substituting the equation for S from above Revenue = $C(-2,500C+159,000)$ Expanding Revenue = $-2,500C^{2} +159,000C$ We now have a quadratic equation for revenue as a function of the subscription charge. To find the price that will maximize revenue for the newspaper, we can find the vertex: $h=-\dfrac{159,000}{2(-2,500)} =31.8$ The model tells us that the maximum revenue will occur if the newspaper charges $31.80 for a subscription. To find what the maximum revenue is, we can evaluate the revenue equation: Maximum Revenue = $-2,500(31.8)^{2} +159,000(31.8) = $2,528,100$ As with any function, we can find the vertical intercepts of a quadratic by evaluating the function at an input of zero, and we can find the horizontal intercepts by solving for when the output will be zero. Notice that depending upon the location of the graph, we might have zero, one, or two horizontal intercepts. Find the vertical and horizontal intercepts of the quadratic $f(x)=3x^{2} +5x-2$ We can find the vertical intercept by evaluating the function at an input of zero: $f(0)=3(0)^{2} +5(0)-2=-2$ Vertical intercept at (0,-2) For the horizontal intercepts, we solve for when the output will be zero $0=3x^{2} +5x-2$ In this case, the quadratic can be factored easily, providing the simplest method for solution $0=(3x-1)(x+2)$ $\begin{array}{l} {0=3x-1} \\ {x=\frac{1}{3} } \end{array}$ or $\begin{array}{l} {0=x+2} \\ {x=-2} \end{array}$ Horizontal intercepts at $\left(\frac{1}{3} ,0\right)$ and (-2,0) Notice that in the standard form of a quadratic, the constant term c reveals the vertical intercept of the graph. Find the horizontal intercepts of the quadratic $f(x)=2x^{2} +4x-4$ Again we will solve for when the output will be zero Since the quadratic is not easily factorable in this case, we solve for the intercepts by first rewriting the quadratic into transformation form. $h=-\dfrac{b}{2a} =-\dfrac{4}{2(2)} =-1\ \ \ k=f(-1)=2(-1)^{2} +4(-1)-4=-6$ $f(x)=2(x+1)^{2} -6$ Now we can solve for when the output will be zero $\begin{array}{l} {0=2(x+1)^{2} -6} \\ {6=2(x+1)^{2} } \\ {3=(x+1)^{2} } \\ {x+1=\pm \sqrt{3} } \\ {x=-1\pm \sqrt{3} } \end{array}$ The graph has horizontal intercepts at $(-1-\sqrt{3} ,0)$and $(-1+\sqrt{3} ,0)$ In Try it Now problem 2 we found the standard & transformation form for the function $g(x)=13+x^{2} -6x$. Now find the Vertical & Horizontal intercepts (if any). Vertical intercept at (0, 13), No horizontal intercepts since the vertex is above the $x$-axis and the graph opens upwards. The process in the last example is done commonly enough that sometimes people find it easier to solve the problem once in general and remember the formula for the result, rather than repeating the process each time. Based on our previous work we showed that any quadratic in standard form can be written into transformation form as: $f(x)=a(x+\dfrac{b}{2a} )^{2} +c-\dfrac{b^{2} }{4a}$ Solving for the horizontal intercepts using this general equation gives: $0=a(x+\dfrac{b}{2a} )^{2} +c-\dfrac{b^{2} }{4a}$ start to solve for $x$ by moving the constants to the other side $\dfrac{b^{2} }{4a} -c=a(x+\dfrac{b}{2a} )^{2}$ divide both sides by $a$ $\dfrac{b^{2} }{4a^{2} } -\dfrac{c}{a} = (x+\dfrac{b}{2a})^{2}$ find a common denominator to combine fractions $\dfrac{b^{2} }{4a^{2} } -\dfrac{4ac}{4a^{2} } =\left(x+\dfrac{b}{2a} \right)^{2}$ combine the fractions on the left side of the equation $\dfrac{b^{2} -4ac}{4a^{2} } =\left(x+\dfrac{b}{2a} \right)^{2}$ take the square root of both sides $\pm \sqrt{\dfrac{b^{2} -4ac}{4a^{2} } } =x+\dfrac{b}{2a}$ subtract $b/2a$ from both sides $-\dfrac{b}{2a} \pm \frac{\sqrt{b^{2} -4ac} }{2a} =x$ combining the fractions $x=\dfrac{-b\pm \sqrt{b^{2} -4ac} }{2a}$ Notice that this can yield two different answers for $x$ Quadratic Formula For a quadratic function given in standard form $f(x)=ax^{2} +bx+c$, the quadratic formula gives the horizontal intercepts of the graph of this function. $x=\dfrac{-b\pm \sqrt{b^{2} -4ac} }{2a}$ A ball is thrown upwards from the top of a 40-foot-tall building at a speed of 80 feet per second. The ball's height above ground can be modeled by the equation $H(t)=-16t^{2} +80t+40$. What is the maximum height of the ball? When does the ball hit the ground? To find the maximum height of the ball, we would need to know the vertex of the quadratic. $h=-\dfrac{80}{2(-16)} =\dfrac{80}{32} =\dfrac{5}{2} , k=H\left(\dfrac{5}{2} \right)=-16\left(\dfrac{5}{2} \right)^{2} +80\left(\dfrac{5}{2} \right)+40=140$ The ball reaches a maximum height of 140 feet after 2.5 seconds. To find when the ball hits the ground, we need to determine when the height is zero – when $H(t) = 0$. While we could do this using the transformation form of the quadratic, we can also use the quadratic formula: $t=\dfrac{-80\pm \sqrt{80^{2} -4(-16)(40)} }{2(-16)} =\dfrac{-80\pm \sqrt{8960} }{-32}$ Since the square root does not simplify nicely, we can use a calculator to approximate the values of the solutions: $t=\dfrac{-80-\sqrt{8960} }{-32} \approx 5.458$ or $t=\dfrac{-80+\sqrt{8960} }{-32} \approx -0.458$ The second answer is outside the reasonable domain of our model, so we conclude the ball will hit the ground after about 5.458 seconds. For these two equations determine if the vertex will be a maximum value or a minimum value. $g(x)=-8x+x^{2} +7$ $g(x)=-3(3-x)^{2} +2$ a. Vertex is a minimum value, since $a > 0$ and the graph opens upwards b. Vertex is a maximum value, since $a < 0$ and the graph opens downwards Transformation form/Vertex form Vertex as a maximum / Vertex as a minimum Short run behavior Vertex / Horizontal & Vertical intercepts 3.1E: Power Functions (Exercises) 3.2E: Quadratic Functions (Exercises) David Lippman & Melonie Rasmussen quadratic function	CommonCrawl
Double and Half Angle Formulas Three formulas are usually referred to as "double angle formulas": $\begin{align} \sin 2\alpha &= 2\sin\alpha \cdot\cos \alpha ,\\ \cos 2\alpha &= \cos^{2}\alpha - \sin^{2}\alpha ,\\ \cos 2\alpha &= 2\cos^{2}\alpha - 1 ,\\ \cos 2\alpha &= 1 - 2\sin^{2}\alpha ,\\ \displaystyle\tan 2\alpha &= \frac{2\tan\alpha}{1-\tan^{2}\alpha}. \end{align}$ The first two formulas are a specialization of the corresponding addition formulas; the third and the fourth follow directly from the second with an application of the Pythagorean identity, $\cos^{2}\alpha + \sin^{2}\alpha = 1.$ The fourth follows from the first two and the definition of tangent. They can also be observed in a proof without words illustrated by the following diagram that depicts a semicircle and several associated right triangles [Nelsen]: For example, the area of $\Delta ABC$ can be computed in two ways so that $AC\cdot BC=AB\cdot CD$ which is the first formula. Further, since triangles $ACD$ and $ABC$ are similar, $\displaystyle\frac{AD}{AC}=\frac{AC}{AB},$ i.e., $\displaystyle\frac{1+\cos 2\alpha}{2\cos\alpha}=\frac{2\cos\alpha}{2},$ which is the third formula, $\cos 2\alpha = 2\cos^{2}\alpha - 1.$ From $\Delta BCD,$ $\displaystyle\tan\alpha=\frac{1-\cos 2\alpha}{\sin 2\alpha},$ and from $\Delta ACD,$ $\displaystyle\tan\alpha=\frac{\sin 2\alpha}{1+\cos 2\alpha},$ both of which are known under the moniker of "half-angle formulas" because they could be rewritten as $\displaystyle\tan\frac{\beta}{2}=\frac{1-\cos \beta}{\sin\beta}$ $\displaystyle\tan\frac{\beta}{2}=\frac{\sin\beta}{1+\cos\beta}.$ Other half-angle formulas are derived from the above. For example, $\displaystyle\cos\frac{\beta}{2}=\pm\sqrt{\frac{1+\cos \beta}{2}}$ $\displaystyle\sin\frac{\beta}{2}=\pm\sqrt{\frac{1-\cos \beta}{2}}.$ The latter formulas lead to other that I am sure many would find exciting if not beautiful. Taking $\displaystyle\beta=\frac{\pi}{2},$ and recollecting that $\displaystyle\cos\frac{\pi}{2}=0,$ the first of these gives (since cosine is positive in the first quadrant) $\displaystyle\cos\frac{\pi}{4}=\sqrt{\frac{1}{2}}=\frac{\sqrt{2}}{2},$ which just verifies a value of $\displaystyle\cos\frac{\pi}{4}.$ But the idea is to continue: let now $\displaystyle\beta=\frac{\alpha}{4}:$ $\displaystyle\cos\frac{\pi}{8}=\sqrt{ \frac{1+\cos\frac{\pi}{4}}{2} }=\frac{1}{2}\sqrt{2+\sqrt{2}}.$ The next term in the sequence is $\displaystyle\cos\frac{\pi}{16}=\frac{1}{2}\sqrt{2+\sqrt{2+\sqrt{2}}}$ and the one after $\displaystyle\cos\frac{\pi}{32}=\frac{1}{2}\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}.$ The general expression can be guessed (and if need be proved by induction): $\displaystyle\cos\frac{\pi}{2^n}=\frac{1}{2}\underbrace{\sqrt{2+\sqrt{2+\sqrt{2+\ldots+\sqrt{2}}}}}_{n-1\space\mbox{radicals}}.$ Since cosine is a continuous function and $\displaystyle\lim_{n\rightarrow\infty}\frac{\pi}{2^n}=0,$ $\displaystyle\lim_{n\rightarrow\infty}\frac{1}{2}\underbrace{\sqrt{2+\sqrt{2+\sqrt{2+\ldots+\sqrt{2}}}}}_{n\space\mbox{radicals}}=1.$ In a similar manner we can obtain $\displaystyle\sin\frac{\pi}{2^n}=\frac{1}{2}\underbrace{\sqrt{2-\sqrt{2+\sqrt{2+\ldots+\sqrt{2}}}}}_{n-1\space\mbox{radicals}}.$ But the limit it leads to is rather unexpected. It's a well known result that $\displaystyle\lim_{x\rightarrow 0}\frac{\sin x}{x}=1,$ from which $\displaystyle\lim_{n\rightarrow\infty}\frac{ \sin\frac{\pi}{2^n} }{\frac{\pi}{2^n}}=1,$ and, as a combination of the latest two equalities, $\displaystyle\pi=\lim_{n\rightarrow\infty}2^{n}\underbrace{\sqrt{2-\sqrt{2+\sqrt{2+\ldots+\sqrt{2}}}}}_{n\space\mbox{radicals}}.$ The double-angle formula for sine also leads to an engaging limit, first discovered by L. Euler. Note that $\begin{align} \sin x &= 2\sin\frac{x}{2}\cos\frac{x}{2}\\ &= 2^2\sin\frac{x}{4}\cos\frac{x}{4}\cos\frac{x}{2}\\ &= 2^3\sin\frac{x}{8}\cos\frac{x}{8}\cos\frac{x}{4}\cos\frac{x}{2}\\ &= 2^4\sin\frac{x}{16}\cos\frac{x}{16}\cos\frac{x}{8}\cos\frac{x}{4}\cos\frac{x}{2}\\ &\cdots\\ &= 2^n\sin\frac{x}{2^n}\cos\frac{x}{2^n}\ldots\cos\frac{x}{8}\cos\frac{x}{4}\cos\frac{x}{2}\\ &\cdots \end{align}$ Multiply and divide by $x$ to obtain a little different form: $\sin x=x\displaystyle\frac{\sin\frac{x}{2^n}}{\frac{x}{2^n}}\prod_{k=1}^{n}\cos\frac{x}{2^k},$ which, with $\displaystyle x=\frac{\pi}{2},$ gives $1=\displaystyle\frac{\pi}{2}\frac{\sin\frac{\pi}{2^{n+1}}}{\frac{\pi}{2^{n+1}}}\prod_{k=1}^{n}\cos\frac{\pi}{2^{k+1}},$ and, going to the limit: $\displaystyle\frac{2}{\pi}=\lim_{n\rightarrow\infty}\prod_{k=1}^{n}\cos\frac{\pi}{2^{k+1}}.$ Taking into account the radical expressions for $\displaystyle\cos\frac{\pi}{2^k}$ derived earlier, we arrive at Euler's formula [Maor]: $\displaystyle\frac{2}{\pi}=\frac{\sqrt{2}}{2} \frac{\sqrt{2+\sqrt{2}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2}}}}{2} \frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}{2}\ldots$ I. M. Gelfand, M. Saul, Trigonometry, Birkhäuser, 2001 (145-152, 163-167) E. Maor, Trigonometric Delights, Princeton University Press, 1998 (90, 140, 146,161) R. B. Nelsen, Proofs Without Words, MAA, 1993 (34-35) What Is Trigonometry? Addition and Subtraction Formulas for Sine and Cosine Sine of a Sum Formula Addition and Subtraction Formulas for Sine and Cosine II Addition and Subtraction Formulas for Sine and Cosine III Addition and Subtraction Formulas for Sine and Cosine IV Addition and Subtraction Formulas The Law of Cosines (Cosine Rule) Cosine of 36 degrees Tangent of 22.5o - Proof Wthout Words Sine and Cosine of 15 Degrees Angle Sine, Cosine, and Ptolemy's Theorem arctan(1) + arctan(2) + arctan(3) = π Trigonometry by Watching arctan(1/2) + arctan(1/3) = arctan(1) Morley's Miracle Napoleon's Theorem A Trigonometric Solution to a Difficult Sangaku Problem Trigonometric Form of Complex Numbers Derivatives of Sine and Cosine ΔABC is right iff sin²A + sin²B + sin²C = 2 Advanced Identities Hunting Right Angles Point on Bisector in Right Angle Trigonometric Identities with Arctangents The Concurrency of the Altitudes in a Triangle - Trigonometric Proof Butterfly Trigonometry Binet's Formula with Cosines Another Face and Proof of a Trigonometric Identity cos/sin inequality On the Intersection of kx and \|sin(x)\| Cevians And Semicircles A Nice Trig Formula Another Golden Ratio in Semicircle Leo Giugiuc's Trigonometric Lemma Another Property of Points on Incircle Much from Little The Law of Cosines and the Law of Sines Are Equivalent Wonderful Trigonometry In Equilateral Triangle A Trigonometric Observation in Right Triangle A Quick Proof of cos(pi/7)cos(2.pi/7)cos(3.pi/7)=1/8 \|Contact\| \|Front page\| \|Contents\| \|Algebra\|	CommonCrawl
Can you provide a basic and meaningful motivation for sigma-algebras/fields, measure theory, Lebsegue integration, and probability? My interest is more about getting back to Kansas than it is about following the Yellow Brick Road; I am trying to understand the ultimate logic, not the abstractions along the way. I have spent a great deal of my life dealing with probabilistic methods, though I was trained as an engineer, not a mathematician. When it comes to measurable functions and sigma algebras, I don't quite see the magic. One book gave an abstract example of the set of sets $\{\emptyset, \{a,b\},\{c,d\},\{a,b,c,d\}\}$meets the tests since the unions of any elements leads to another element, as does the intersections. But, I suppose, $\{\emptyset, \{a\}, \{a,b\},\{c,d\},\{a,b,c,d\}\}$does not, since $\{a\}\cup\{c,d\}$ is not a member, correct? Now, let's get away from finite sets and abstractions like this, and looking at the real number line in one dimension, what is accomplished by the fact that a countably infinite set of unions or intersections of open sets is also a member of the set of open sets on the real line? What would go wrong if they were closed sets? It seems intuitively that, on the real line, unions and intersections of closed sets are also closed sets. One could, for example, take the intersection of all closed sets of the form $[q,q+1]$ (q an integer) which would deliver up the set of integers, as all the intervals would have exactly one point in common with one other interval. Perhaps this is abusive notation, but all of these are closed sets if one can write the interval $[1,1]$ meaning the point at 1. Or is that exactly what is trying to be avoided? Is it simply that open sets that are non-empty have measure, and by narrowing ourselves to those it just makes measure theory work out, in part because the opposite of what would happened with closed sets occurs - i.e., the union of all open sets of the form $(q,q+1)$is the complement of the intersection of the closed sets: it is the real number line missing countably infinite entries (the integers) - but has well defined measure for a finite collection of such abutting sets? eSurfsnakeeSurfsnake $\begingroup$ Both the measure on $\Bbb R$ and its topology are defined by intervals. Actually, a closed interval can also be written as a countable intersection of open intervals and vica versa, so it doesn't matter which we start off. In measure theory we want to perform sum of countably infinitely many measurable sets. The need for introducing $\sigma$-algebras as a 'support' for measures is because it turns out (following e.g. by Banach-Tarski's sphere duplication theorem) it's not possible to measure all subsets of the Euclidean spaces. $\endgroup$ – Berci Sep 15 '18 at 23:36 $\begingroup$ Some passages in your question, like "the intersection of all closed sets of the form $[q,q+1]$ ($q$ an integer) which would deliver up the set of integers," suggest that you have not correctly understood what is meant by the intersection of a family of sets. $\endgroup$ – Andreas Blass Sep 15 '18 at 23:46 $\begingroup$ Interesting question, similar to this one in CrossValidate.SE. $\endgroup$ – Antoni Parellada Sep 16 '18 at 0:33 $\begingroup$ The reference to Cross-Validated is quite useful, but as noted in the comments it still does not explain quite what would "break" if countably infinite intersections and unions weren't required as part of the sigma algebra. $\endgroup$ – eSurfsnake Sep 16 '18 at 4:55 Browse other questions tagged measure-theory or ask your own question. A property of outer measure for bounded sets of real numbers. Constructively generating a sigma algebra Is there a null-set whose translations generate the set of all null-sets? Sigma algebra - motivation in measure theory How to show a subset of $\mathbb{R}^2$ is a Borel set? What motivated the use of $\sigma$-algebras in measure theory (or probability)? Does the sigma algebra over the real line contain the singleton sets? Borel sets as the countable intersection of open sets	CommonCrawl
Infectious Diseases of Poverty The rapid and efficient strategy for SARS-CoV-2 Omicron transmission control: analysis of outbreaks at the city level Jin-Xin Zheng1 na1, Shan Lv2 na1, Li-Guang Tian2, Zhao-Yu Guo2, Pei-Yong Zheng3, Yue-Lai Chen3, Shi-Yang Guan4, Wei-Ming Wang1 & Shun-Xian Zhang ORCID: orcid.org/0000-0002-8929-44333,5,6 Infectious Diseases of Poverty volume 11, Article number: 114 (2022) Cite this article Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) Omicron (B.1.1.529) variant is highly transmissible with potential immune escape. Hence, control measures are continuously being optimized to guard against large-scale coronavirus disease 2019 (COVID-19) outbreaks. This study aimed to explore the relationship between the intensity of control measures in response to different SARS-CoV-2 variants and the degree of outbreak control at city level. A retrospective study was conducted in 49 cities with COVID-19 outbreaks between January 2020 and June 2022. Epidemiological data on COVID-19 were extracted from the National Health Commission, People's Republic of China, and the population flow data were sourced from the Baidu migration data provided by the Baidu platform. Outbreak control was quantified by calculating the degree of infection growth and the time-varying reproduction number (${R}_{t}$). The intensity of the outbreak response was quantified by calculating the reduction in population mobility during the outbreak period. Correlation and regression analyses of the intensity of the control measures and the degree of outbreak control for the Omicron variant and non-Omicron mutants were conducted, respectively. Overall, 65 outbreaks occurred in 49 cities in China from January 2020 to June 2022. Of them, 66.2% were Omicron outbreaks and 33.8% were non-Omicron outbreaks. The intensity of the control measures was positively correlated with the degree of outbreak control (r = 0.351, P = 0.03). The degree of reduction in population mobility was negatively correlated with the Rt value (r = − 0.612, P < 0.01). Therefore, under the same control measure intensity, the number of new daily Omicron infections was 6.04 times higher than those attributed to non-Omicron variants, and the Rt value of Omicron outbreaks was 2.6 times higher than that of non-Omicron variants. In addition, the duration of non-Omicron variant outbreaks was shorter than that of the outbreaks caused by the Omicron variant (23.0 ± 10.7, 32.9 ± 16.3, t = 2.243, P = 0.031). Greater intensity of control measures was associated with more effective outbreak control. Thus, in response to the Omicron variant, the management to restrict population movement should be used to control its spread quickly, especially in the case of community transmission occurs widely. Faster than is needed for non-Omicron variants, and decisive control measures should be imposed and dynamically adjusted in accordance with the evolving epidemic situation. Infectious diseases tend to have unique features that are different from other diseases, and the most important characteristic is their unpredictability and the associated potentially explosive implications [1, 2]. Coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and is transmitted by respiratory droplets and contacts, it has posed an enormous threat to public health around the world [3, 4]. COVID-19 endangered human life and health and significantly impacted socio-economic development [1, 5]. SARS-CoV-2 has continuously evolved into novel variants, including Alpha (B.1.1.7), Beta (B.1.351), Gamma (P.1), Delta (B.1.617.2), and Omicron (B.1.1.529), and continuous mutation is expected [6, 7]. For the Delta variant, the basic reproduction number (R0) is close to 4, the median intergenerational interval is 3 days, and the incubation period is 4.4 days [8]. However, the R0 of the Omicron variant is close to 10 days, with an even shorter intergenerational interval [9]. The biological properties of the Omicron variant confer it with strong infectivity and rapid and surreptitious transmission, many infections are asymptomatic, and the virus is more likely to escape the immune response generated by previous infections or vaccines [10, 11]. The Omicron variant has a significantly higher breakthrough infection rate than that of the Delta variant, thereby greatly increasing the difficulty in implementing effective control measures [11]. The number of hospitalizations and deaths caused by the Omicron variant has been higher than that caused by the Delta variant and has seriously impacted healthcare systems [12, 13]. Therefore, effective prevention and control measures must be comprehensively applied to interrupt Omicron transmission. The control measures for the COVID-19 outbreak were based on the biological characteristics of SARS-CoV-2 and intended for long-term application [2, 14]. Previous expertise promoted the idea that herd immunity could be achieved as long as the vaccine coverage rate reached a critical value of over 80% [15, 16]. Thus, even if there were new COVID-19 infections, outbreaks and large-scale epidemics would not occur. However, the Omicron variant emerged and, with it, many more infections, indicating that the current vaccine was not able to prevent infections with the Omicron variant [2, 17]. Specific drugs for SARS-CoV-2 are being researched and developed [2, 18]. The emergence of new mutant variants, the imbalance of global vaccine distribution, and breakthrough infections in vaccinated populations have brought continuous challenges to the effectiveness of vaccinations, resulting in the inability to form a population-wide persistent immune barrier in the short-term [19, 20]. Non-drug interventions such as social distancing, mask-wearing, cleaning hands, and avoiding crowds remain the main prevention and control measures [14, 21]. Studies found that social distancing, including the cancellation of small gatherings and the closure of educational institutions, as well as travel and border restrictions, had the greatest impact on preventing and controlling COVID-19 outbreaks of all existing non-drug interventions [2, 18, 22]. In contrast, the least effective interventions were government-provided and international assistance actions, case tracking, and environmental disinfection and sterilization [18]. When the pandemic broke out on a large scale, implementing stricter measures effectively curbed the COVID-19 pandemic caused by the Omicron variant within a relatively short period and achieved the social management goal of dynamic zero-COVID-19. At the beginning of 2020, COVID-19 began to spread around the world [23, 24]. In the process of coping with the outbreak, beneficial knowledge was constantly accumulated from relevant experiences. The success of the response to COVID-19 threats came not just from the scientific recognition of the biological characteristics of SARS-CoV-2 variants but also from broad approaches [6, 25]. These approaches included the constant surveillance of SARS-CoV-2 variants, symptom-based surveillance, case isolation, the tracing of close contacts (requiring quarantine in separate facilities) and the contacts of contacts, occupation-based screening, the targeted screening of individuals at high risk of infection, the application of big data in epidemiological investigations, and a set of social distancing measures that included travel restrictions, stringent border control policies, and community confinement, all of which played a complementary role in fighting COVID-19 transmission [6, 25]. However, the Omicron variant began to spread in China in February 2022, and the effective prevention measures based on previous strategies were unsuccessful in preventing outbreaks promptly [26, 27]. Therefore, this study was conducted to explore the relationship between control measures and the transmission process of COVID-19 caused by Omicron and non-Omicron mutants across different cities in China. First, the intensity of the prevention measures and the degree of outbreak control were quantified. Second, the correlation between the intensity of the restriction measures and the degree of outbreak control caused by the Omicron variant and non-Omicron variants was analyzed. The conclusion from the study will provide a reference for formulating better control measures and strategies to effectively confront future COVID-19 outbreaks caused by new SARS-COV-2 variants with high infectivity. Data source and collection Epidemiological data on COVID-19 were extracted from the National Health Commission, People's Republic of China (http://www.nhc.gov.cn). The data included outbreak location (provincial level and city level), symptomatic status (including the clinical outcomes of initially asymptomatic infections), date and counts of official reporting (daily asymptomatic infected individuals, daily new cases, and daily death report cases), and other information between January 1, 2020, and June 30, 2022 (Fig. 1). Infectious individual (including asymptomatic person) were all considered to be counted cases in the study. Flow chart demonstrating the quantification of the strength of outbreak control and intensity of control measures The population flow data were sourced from the Baidu migration data provided by the Baidu platform (http://www.qianxi.baidu.com). The Baidu Migration Index indicates the scale of population flow between cities and covers 368 cities in China. Two types of population movement data (inflow intensity and outflow intensity) were extracted from the Baidu migration platform between January 1, 2020, and June 30, 2022. Study scenarios Since the large-scale outbreak in Wuhan, China, SARS-CoV-2 has continuously mutated, with concomitant changes in infectivity. Many cities in China experienced outbreaks caused by various SARS-CoV-2 variants (Delta, Omicron, and other major variants). However, the inclusion criteria need to be made to select cities for this study. The R0 value describes the potential transmission capacity of a pathogen. The R0 value of the Delta variant is between 3.2 and 8.0, and the R0 of the Omicron variant is 3.2 times that of Delta, with a doubling time of approximately 3 days [28], and 1–2 generations of SARS-CoV-2 in one city can cause an outbreak. Hence, we focused on the cities with more than 10 infected persons per day in an outbreak period. Cities with more than 10 new infected individuals daily for 3 consecutive days in normal social environments were included. In contrast, cities were excluded if a COVID-19 outbreak lasted fewer than 7 days or occurred on intermittent days. Cities with one to ten reported infected individuals with community transmission that covered a wide range of time and lasted for 3 months were also excluded, as were cities missing Baidu Migration Index data when the COVID-19 outbreak occurred. COVID-19 outbreak definition The Chinese Center for Disease Control and Prevention (China CDC) defines an outbreak as more occurrences of a particular infectious disease at a specific location and time than expected. However, the definition of a COVID-19 outbreak is usually local-context-related. In non-residential settings, the outbreak criteria were two or more test-confirmed COVID-19 infections among individuals associated with a specific non-residential setting with illness onset dates within 14 days. COVID-19 outbreak was expressed by the duration of the epidemic. If infected persons were reported in one city at time point T and the city had no infection individuals within 5 days from T-5 to T-1, point T was defined as the time of the onset of the outbreak (Fig. 1). Some cities may have had multiple outbreaks. If the time interval between the end of the first outbreak and the start of the second outbreak was greater than 14 days, it was considered to be a second outbreak. The time-varying reproduction number (${R}_{t}$) is an important index used to measure SARS-CoV-2 transmissibility during COVID-19 outbreaks. Estimating the increase or decrease in the rate using ${R}_{t}$ is critical for monitoring and adjusting outbreak control measures in the real world. One of the most common methods to estimate ${R}_{t}$ in real-time is through the renewal Eq. (1). This model assumes that the incidence of newly infected individuals on day t (It) can be represented by the following equation [29]: $${I}_{t}\sim \left({R}_{t}{\sum }_{s=1}^{t}{I}_{t-s}{w}_{s}\right)$$ where ${I}_{t}$ is the number of infections that are incident on day t, and ${w}_{s}$ is the serial interval distribution. In the renewal equation, the incidence at time t (${I}_{t}$) is expressed as a function of the serial interval distribution (${w}_{s}$), the time-varying reproduction number (${R}_{t}$), and the past incidence (${I}_{t-s}$). The ${R}_{t}$ of the model was quantified using the EpiNow2 package (https://cran.r-project.org/web/packages/EpiNow2) [30]. It estimates the time-varying reproduction number of infectors through the date of infection. The method uses the generation time, and the incidence is computed backward using distributions for the incubation period and reporting delays. In this study, for the non-Omicron variants, a gamma-distributed generation time with a mean of 3.6 days was used in the calculations [31]. For the incubation period, a log-normal incubation period with a mean of 5.2 days was fitted [32]. For the Omicron variant, we referenced the published estimated generation time of 2.7 days for the COVID-19 Omicron wave in Hong Kong [33]. The incubation period of the Omicron variant is set with 3.4 days [34]. Ultimately, ${R}_{t}$ was estimated using the EpiNow2 in R software (version 4.2.1, http://www.r-project.org). Quantification of outbreak control intensity Intervention measures were taken to control COVID-19 outbreaks. Thus, the intensity of the outbreak control was quantified based on the ratio of new cases to the extent of change in the Rt value. In the study, for an outbreak event in a specific city, the intensity of the outbreak control was defined as the ratio of the number of new cases on day T + 14, day T + 15, and day T + 16 to the number of new cases on day T + 4, day T + 5, and day T + 6 (Fig. 1), it was shown in formula (2). If the number of new infected persons each day after 2 weeks was less than the numbers of cases on days 4–6 of the outbreak, the outbreak was considered to be controlled. The lower the ratio, the more effective the outbreak control measures. $$Cases \;Control=\mathrm{log}\left(\frac{n}{m}\right)=\mathrm{log}\left(\frac{{Case}_{T14}+ {Case}_{T15}+{Case}_{T16}}{{Case}_{T4}+ {Case}_{T5}+{Case}_{T6}}\right)$$ An Rt of less than 1 suggests that the outbreak was controlled effectively. Therefore, the intensity of outbreak control was defined as the average of the Rt values on day T + 14, day T + 15, and day T + 16 in an outbreak event, as shown formula (3). $${R}_{t} Control=\frac{{R}_{t14}+{R}_{t15}+{R}_{t16}}{3}$$ Quantification of control measure intensity The intensity of the prevention and control measures was calculated based on the daily population flow. Baidu Migration Index values, which include inflow and outflow intensity, were used to comprehensively reflect the impact of control measures on population flow. The daily population flow intensity was the average of the inflow intensity and outflow intensity each day. Finally, the intensity of the restraining measures was defined as the ratio of the average population flow on day T + 4, day T + 5, and day T + 6 to that on day T − 1 (Fig. 1), shown in formula (4). Log transformation was additionally applied in the study. $$Strength \;Control = {\text{log}}\left( \frac{b}{a} \right) = {\text{log}}\left( {\frac{{(Flow_{T4} + Flow_{T5} + Flow_{T6} )/3}}{{Flow_{T - 1} }}} \right)$$ COVID-19 outbreak and SARS-CoV-2 variants in China A total of 65 outbreaks in 49 cities were collected across China from January 2020 to June 2022 in this study. The Omicron variant emerged in China in January 2022 and caused 66.2% of all COVID-19 outbreaks [43/65, 95% confidence interval (CI) 0.54–0.77], while the outbreak events caused by non-Omicron variants accounted for 33.8% (22/65, 95%CI 0.24–0.46). More than 24.4% (12/49, 95% CI 0.25–0.38) of the cities experienced two or more outbreaks. Relationship between infectious case number and population flow The relationship between population flow and the increase in cases caused by non-Omicron variants in 22 cities is shown in Fig. 2a, where a positive statistical association was observed (r = 0.173, P = 0.506). In Fig. 2a, values greater than 0 on the X-axis indicated that control measures were implemented against the pandemic outbreak. The larger the value, the lower the intensity of restraint management. Values less than 0 on the X-axis indicated that more stringent restraint measures were applied to address the outbreak. The smaller the value, the more rapid the reaction time to the COVID-19 outbreak, and the stricter the control measures. Larger values on the Y-axis indicate ineffective control of the COVID-19 outbreak. In contrast, smaller values on the Y-axis represent better effects of the measures used for handling one COVID-19 outbreak. The results showed that the cities where the outbreak was not effectively controlled included Shijiazhuang, Tonghua, Harbin, and Xi'an (Fig. 3). Cities with other COVID-19 outbreak events and dynamic changes in population flow are shown in the Additional file 1. Figure 2a shows that 81.8% (17/22, 95%CI 0.565–0.899) of the outbreaks were effectively controlled in China (Additional file 1), suggesting that cities had fewer newly cases after 2 weeks compared to the first 5 days. The results demonstrated that when the population flow decreased by 1%, the number of cases decreased by 2.06 (95%CI 0.25–16.54. Table 1). The relationship between intensity of outbreak with infection case control and the degree of population control in Omicron pandemic and non-Omicron pandemic. a The scatter plot of infection case control with log transform and population flow index control in non-Omicron pandemic. b The scatter plot of infection case control with log transform and population flow index control in Omicron pandemic The daily number of reported infection and the population flow index of the non-Omicron outbreak in Xi'an. a Simulations of daily cases in by time-varying reproduction number according to daily number of reported infection, the bar chart is the daily number of reported infected individuals. b Model estimating the effective reproductive numbers (Rt) in each day by EpiNow2 package. c The daily number of reported infections (bar plot) and population flow index (pink line) Table 1 Regression model of cases number, Rt value, and intensity of population flow The relationship between population flow and increases in the number of infections in COVID-19 outbreaks caused by the Omicron variant is shown in Fig. 2b. A positive statistical correlation was found (r = 0.351, P = 0.03), and 48.8% (21/43, 95%CI 0.346–0.653) of the urban outbreaks were found not to be effectively controlled timely, as reflected in cases numbers that continued to increase within 14 days after the COVID-19 outbreak caused by the Omicron variant. The cities with lower-intensity restrictions included Harbin and Wuhan (Additional file 1). The model showed that the number of infections decreased by 4.16 (95% CI 1.14–15.18. Table 1) when population flow increased by 1%. Association between COVID-19 transmission and population flow The association between the Rt value for COVID-19 prevalence caused by non-Omicron variants and the degree of reduction in population flow in 21 cities is shown in Fig. 4a. A negative correlation was identified (r = − 0.459, P = 0.06), where an Rt value of less than 1 indicated better control of the COVID-19 outbreak. Among all cities with outbreaks, those with non-Omicron variants were found to be effectively controlled after 2 weeks. The results showed that the Rt value decreased by 0.52 units when the intensity of restrictive measures increased by one unit (Table 1). The direct relationship between intensity of outbreak with time-varying reproduction number (Rt) and the degree of population control in Omicron pandemic and non-Omicron pandemic. a The scatter plot of time-varying reproduction number with population control intensity in non-Omicron pandemic. b The scatter plot of time-varying reproduction number with population control intensity in Omicron pandemic The relationship between the Rt value of a COVID-19 outbreak caused by the Omicron variant and the degree of reduction in population flow in the 43 cities is shown in Fig. 4b. A negative correlation was observed (r = − 0.612, P < 0.01). Of the urban outbreaks caused by the Omicron variant, 25.5% (11/43, 95% CI 0.149–0.402) were not effectively controlled in short time (Fig. 4b) using the restriction measures previously implemented in response to outbreaks caused by non-Omicron variants. That is, the Rt values remained greater than 1 for 14 days after the outbreak. Shanghai had the highest Rt value (Fig. 5). The results demonstrated that the Rt value decreased by 1.34 units as the intensity of the restriction measures increased by 1 unit. The daily number of reported infections and population flow index of the Omicron outbreak in Shanghai. a Simulations of daily infections in by time-varying reproduction number according to daily number of reported infections, the bar chart is the daily number of reported infections. b Model estimating the effective reproductive numbers (Rt) in each day by EpiNow2 package. c The daily number of reported infections (bar plot) and population flow index (pink line) Comparison of COVID-19 transmission between Omicron and non-Omicron variants The relationship between population flow and the growth rate of infection number was statistically significant in COVID-19 transmissions caused by the Omicron variant (r = − 0.323, P = 0.032), a negative correlation result was found in COVID-19 outbreaks caused by non-Omicron variants (r = − 0.341, P = 0.129). However, the intercept of the two regression models was different (Table 1). Under control measures of the same intensity, the log-transformation of increases in cases during the Omicron outbreak was 1.80 times higher than that of the non-Omicron variants (Table 1). These results showed that the number of new daily cases caused by the Omicron variant after 2 weeks was 6.04 times higher than the number of patients with non-Omicron variants in situations with the same initial outbreak conditions and the same intensity of restriction measures. In addition, the Rt value of COVID-19 outbreaks caused by the Omicron variant increased by 0.86 compared to COVID-19 outbreaks caused by non-Omicron variants under restriction measures of the same strength. The Rt value of the Omicron variant was 2.6 times higher than that of the non-Omicron variants (1.38/0.52). COVID-19 outbreak duration COVID-19 outbreaks caused by non-Omicron variants lasted an average of 23.0 days [standard deviation (SD) = 10.7], whereas Omicron outbreaks lasted an average of 32.9 days (SD = 16.3). In the presence of intervention and control measures, the mean duration of COVID-19 outbreaks caused by the Omicron variant was longer than that of outbreaks of non-Omicron variants (t = 2.243, P = 0.031). The study showed that if control measures were adopted at an early stage, the explosive growth of infection numbers rarely occurred in non-Omicron outbreaks even if the number of newly infected persons continued to rise. However, the same intensity of restriction measures provided invalid control for Omicron outbreak, and the potential risk of exponential growth of infected individuals and community transmission still existence. The findings from the study can help to render our response to COVID-19 more scientific-based and targeted measures, more targeted approaches must be adopted when it comes to quarantining and transporting patients and close contacts, conducting nucleic acid testing, managing personnel flows, administering vaccination, etc. Optimization of COVID-19 rules based on the nature of SARS-CoV-2 variant can help us to effective response to COVID-19 outbreak, specific measures include shortening quarantine periods for incoming travelers and close contacts of people with COVID-19 infection, cancel the circuit breaker for inbound flights, no longer determine secondary close contacts of confirmed cases, adjust the categories of COVID-19 risk areas to high and low, provide guidance for psychological counseling when necessary, modern material supply must be answered and handled properly. It is necessary to adjust to epidemic situation of infectious diseases and promote the construction of control capacity to coordinate anti-virus policies with social and economic development. It was pointed out that all individuals should adapt to the strong transmissibility of the virus, effectively implement the requirements of early detection, reporting, quarantine and treatment, and adopt swift measures, so as to prevent further expansion of infections or a prolonged prevention and control endeavor. The Omicron variant became the main pandemic strain worldwide at the end of 2021. There are no specific treatment drugs and preventive vaccine available. Although the fatality rate of Omicron is lower than that of the original strain, the absolute number of deaths in a certain population where the virus is left to spread unchecked would still be very high due to the virus's fast transmission and overextended medical systems. The conclusion of the study suggested that restriction measures reduce transmission and unknown contacts that can be difficult to trace, and the response stresses rapid and targeted action to bring new infections under control in regions with large elderly populations and limited healthcare resources, and it has enabled the country to keep infection and fatality rates very low. Also, similar to our findings, the scientists showed similar approach has been successfully adopted to rapidly subdue several waves of COVID-19 caused with Omicron BA.2 in China [35, 36]. In addition, a large number of established fact proved that effective measures are not taken to respond to Omicron, and the the epidemic will not stop even if the vaccination rate is high [37,38,39], it can cause massive infections, severe infections and many deaths, especially in a country with a large elderly population and a large number of people with chronic illnesses who are at high risk of severe morbidity and mortality [37,38,39]. Hence, adherence to positive control measures can also prevent most people from becoming infected and experiencing long-term COVID-19 symptoms (such as fatigue, breathing difficulties, and cognitive impairment) in the severe patients [40]. Thus, implementing positive control measures (dynamic zero-COVID strategy and restriction measures) can protect vulnerable populations and help to cope with the uncertainties associated with emerging variants and the lingering effects of COVID-19 in future. Although critical health services were exempt from the strict suppression strategy, widespread disruptions to routine and emergency non-COVID care due to transport and curfew barriers for patients and health workers, hospitals turning patients away, and supply chain disruptions that affected medicine access and costs [41]. It should be emphasized that life-saving services must be taken into account in the implementation of lockdown. It is necessary that making special arrangements by designating hospitals to receive COVID-19 risk groups and setting up green channels for their hospital visits. Blocking continuous community transmission can prevent large-scale epidemics, and a comprehensive strategy can promptly and precisely detect and control new outbreaks to halt the transmission of COVID-19 across communities, prevent large-scale viral flare-ups, and achieve a balance between virus control and socioeconomic development [42, 43]. Detecting and identifying the early infection is crucial for interrupting epidemic. Nucleic acid testing presents the opportunity to identify the number of infectious individuals in the early stages [43, 44], it was regularly performed for high-risk groups, including patients with COVID-19-related symptoms, the close contacts of someone with confirmed infection, as well as the contacts of close contacts, occupational-risk individuals, and personnel in key institutions [35, 44]. In addition, antigen detection could help to identify infected people and prevent community communication before nucleic acid testing were conducted in a large crowd. If transmission can be found within three generations, then an outbreak can be controlled in a small area through epidemiological investigations and targeted epidemic-control measures, and large-scale city lockdown measures will not be necessary [25]. By the time the outbreak spreads to more than the fifth generation, indicating a relatively large transmission scope, or community transmission has occurred in several independent communities, control measures must be strengthened to contain the outbreak [25]. The COVID-19 pandemic has created an unprecedented global crisis [2]. Many factors must be considered in making decisions to implement or terminate preventative measures [25, 45]. These factors mainly include government willingness, the COVID-19 transmission situation, public acceptance of the policies, public health capacity, and medical treatment resources and capabilities, as well as material security resources and capabilities [25]. During the early COVID-19 outbreak, many countries imposed restrictions on population movement, providing time to reduce the incidence, as well as to develop and apply sustained and robust transmission prevention measures [2, 46]. Strict suppression strategy were implemented to slow the spread of SARS-COV-2, prevent case spillovers, and prevent healthcare systems from being overwhelmed [2, 46]. Some cities and countries implemented either complete or partial lockdown. However, individuals affected by restraint measures may experience a loss of personal freedom and autonomy under lockdown, and lower production efficiency from working at home for a long period may result [47, 48]. Therefore, lockdown strategies and other extreme restrictions cannot be sustained for an extended period in one outbreak event. Governments around the world are now faced with the problems of when and how restrictions should be eased while balancing various health, social, and economic concerns, in certain circumstances that these is not specific therapeutic agents or an effective preventive vaccine, significant weakening of the pathogenicity of the COVID-19 virus has not been observed [2, 46]. The World Health Organization (WHO) warned that lifting lockdown restrictions may trigger a COVID-19 resurgence, but prolonged lockdown may lead to economic collapse in long term [2, 46]. Some studies reported the short-term and long-term effects of COVID-19 control strategies of different intensities on economic development from the perspective of supply chains [5, 36]. The losses incurred by the supply chain from strong restrictive measures were largely dependent upon the duration (primary significance) and severity (secondary significance) of the lockdown and other suppression strategies [5, 36]. However, longer-term lockdown measures were found to be less costly than short-term measures but high-frequency lockdown, and earlier, stricter, and shorter lockdown periods could minimize the overall losses. No matter what control measures are undertaken, the losses to the complex global supply chain will exceed the direct losses caused by the COVID-19 pandemic [5, 36]. Therefore, implementing a series of comprehensive measures that combine short-term intense restraint measures and other effective methods, such tenaciously pursue the general policy of "dynamic zero-COVID.", can coordinate COVID-19 prevention efforts with economic and social development, protect the people's safety and health to the utmost, so as to achieve safe development. Emerging pathogens with high transmissibility have the characteristic of biological invasion, where the pathogen can rapidly replicate and spread under the synergism of biological features and socioeconomic factors [25, 49]. An intelligent early warning platform for infectious diseases based on multi-point trigger mechanisms and multi-channel surveillance mechanisms can improve the monitoring capacity and control the outbreak of infectious diseases at the early stages [43], the optimised surveillance system have capable of providing early and robust data on a new pathogen. Infectious diseases caused by highly transmissible pathogens can be effectively intercepted by fast and accurate response actions by crossdisciplinary approach and multidisciplinary, multisectoral, and multiprofessional collaboration [50]. Once a highly transmissible pathogen colonizes a very small geographic region, and sporadic infections begin to appear across different regions in one city, a large-scale disease outbreak will soon follow [49]. In this case, precise and differentiated epidemic control strategies based on big data to quickly conduct epidemiological investigations, identify transmission chains, and trace close contacts have modest helpful for quickly controlling COVID-19 outbreaks. Delayed or inadequately prepared control measures are unable to successfully deal with biosecurity threats, resulting in devastating damages and costs. As long as the number of infected individuals increases rapidly, a great burden will be imposed on medical resources, causing medical limiting availability, and threatening the health of patients with underlying diseases, including elderly people, children, and pregnant women. At this stage, large-scale and powerful interventions need to be actively implemented at the beginning of community transmissions during an outbreak as they can successfully deal with highly transmissible infectious diseases within a short period. In addition, the COVID-19 crisis has exposed major weaknesses in health system and social management system [45, 51], a change in health-care framework is needed to improve pandemic prevention [51, 52]. Hence, One Health approach, it has been suggested to address complex global health problems at the human–animal–environment interface, coupled with inter- and trans-disciplinary involvement, that makes broader contributions to achieve optimal public health outcomes by monitoring and managing the interactions between humans, animals, and their environment, it can provide service for formulating policies to promote the prevention and control of emerging infectious diseases [45, 51]. There were several limitations to the study. Firstly, we used the daily number of new cases for each outbreak, and the actual infection time was earlier than the reported time, which may have led to some bias in calculating the effective reproductive number. Secondly, when estimating the Rt for each outbreak, we utilized the parameter for the distribution of delays between symptom onset in a primary and secondary case, and it was different between Omicron and non-Omicron variants. Hence, this may have affected the Rt results in the models. Thirdly, the strength of the governmental control policies was estimated using the Baidu Migration Index. However, mask-wearing, vaccinating, and the closing of public facilities in parks and schools were not considered in the study, which could have decreased the estimates of the strength of the control policies. Finally, real-world effectiveness of strict strategy was obtained from the perspective of preventing infection, it may not be appropriate from a full range of perspectives. Hence, information on outbreak and control policies will be collected systematically to conduct deep analyses. The COVID-19 transmission are complex and the intensity of the control measures are varied with different cities. However, the intensity of the control measures can be reflected by population movements. 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This work was supported by the fund of the fund of Three-year Action Plan for Promoting Clinical Skills and Innovation Ability of Municipal Hospitals (Grant No. SHDC2022CRS039) and Medical Innovation Research Special Project of the Shanghai "Science and Technology Innovation Action Plan" (Grant Nos. 21Y11922500, 21Y11922400), and the fund of talent fund of Longhua Hospital (Grant No. LH001.007). In addition, it was also supported by scientific research project on prevention and treatment of COVID-19 with traditional Chinese medicine (Grant No. XGYJKY2022-09) and the emergency study of traditional Chinese medicine on COVID-19 (Grant No. 2022ZYLCYJ05-10). Funding sources had no role in the design and conduct of the study, collection, management, analysis, and interpretation of the data; and preparation, review, or approval of the manuscript. Jin-Xin Zheng and Shan Lv have contributed equally to this work Department of Nephrology, Ruijin Hospital, Institute of Nephrology, Shanghai Jiao Tong University School of Medicine, Shanghai, 200025, People's Republic of China Jin-Xin Zheng & Wei-Ming Wang Chinese Center for Disease Control and Prevention (Chinese Center for Tropical Diseases Research), NHC Key Laboratory of Parasite and Vector Biology, WHO Collaborating Centre for Tropical Diseases, National Center for International Research On Tropical Diseases, National Institute of Parasitic Diseases, Shanghai, 200025, People's Republic of China Shan Lv, Li-Guang Tian & Zhao-Yu Guo Longhua Hospital, Shanghai University of Traditional Chinese Medicine, Shanghai, 200032, People's Republic of China Pei-Yong Zheng, Yue-Lai Chen & Shun-Xian Zhang Department of Epidemiology and Biostatistics, School of Public Health, Anhui Medical University, Hefei, 230032, People's Republic of China Shi-Yang Guan School of Global Health, Chinese Center for Tropical Diseases Research, Shanghai Jiao Tong University School of Medicine, Shanghai, 200025, People's Republic of China Shun-Xian Zhang One Health Center, Shanghai Jiao Tong University–The University of Edinburgh, Shanghai, 200025, People's Republic of China Jin-Xin Zheng Shan Lv Li-Guang Tian Zhao-Yu Guo Pei-Yong Zheng Yue-Lai Chen Wei-Ming Wang J-XZ, S-XZ and W-MW conceived and designed the research, J-XZ, Z-YG, S-YG, P-YZ and Y-LC collected and analyzed the data, S-XZ, J-XZ, Z-YG, SL and L-GT contributed to the draft writing-reviewing-editing. J-XZ and SL contributed equally to this work, W-MW and S-XZ are common correspondent authors. All authors read and approved the final manuscript. Correspondence to Wei-Ming Wang or Shun-Xian Zhang. The daily number of reported infections, population flow index and the estimated effective reproductive numbers of SARS-CoV-2 non-Omicron and Omicron outbreak in city levels. Zheng, JX., Lv, S., Tian, LG. et al. The rapid and efficient strategy for SARS-CoV-2 Omicron transmission control: analysis of outbreaks at the city level. Infect Dis Poverty 11, 114 (2022). https://doi.org/10.1186/s40249-022-01043-2 Population flow Community management and recovery from COVID-19 pandemic	CommonCrawl
Papers from the Theory of Computing Group Accepted to SODA 2020 Nine papers from CS researchers were accepted to the ACM-SIAM Symposium on Discrete Algorithms (SODA20), held in Salt Lake City, Utah. The conference focuses on algorithm design and discrete mathematics. Learning From Satisfying Assignments Under Continuous Distributions Clement Canonne Stanford University, Anindya De University of Pennsylvania, Rocco A. Servedio Columbia University A common type of problem studied in machine learning is learning an unknown classification rule from labeled data. In this problem paradigm, the learner receives a collection of data points, some of which are labeled "positive" and some of which are labeled "negative", and the goal is to come up with a rule which will have high accuracy in classifying future data points as either "positive" or "negative". In a SODA 2015 paper, De, Diakonikolas, and Servedio studied the possibilities and limitations of efficient machine learning algorithms when the learner is only given access to one type of data point, namely points that are labeled "positive". (These are also known as "satisfying assignments" of the unknown classification rule.) They showed that certain types of classification rules can be learned efficiently in this setting while others cannot. However, all of the settings considered in that earlier work were ones in which the data points themselves were defined in terms of "categorical" features also known as binary yes-no features (such as "hairy/hairless" "mammal/non-mammal" "aquatic/non-aquatic" and so on). In many natural settings, though, data points are defined in terms of continuous numerical features (such as "eight inches tall" "weighs seventeen pounds" "six years old" and so on). This paper extended the earlier SODA 2015 paper's results to handle classification rules defined in terms of continuous features as well. It shows that certain types of classification rules over continuous data are efficiently learnable from positive examples only while others are not. "Most learning algorithms in the literature crucially use both positive and negative examples," said Rocco Servedio. "So at first I thought that it is somewhat surprising that learning is possible at all in this kind of setting where you only have positive examples as opposed to both positive and negative examples." But learning from positive examples only is actually pretty similar to what humans do when they learn — teachers rarely show students approaches that fail to solve a problem, rarely have them carry out experiments that don't work, etc. Continued Servedio, "So maybe we should have expected this type of learning to be possible all along." Nearly Optimal Edge Estimation with Independent Set Queries Xi Chen Columbia University, Amit Levi University of Waterloo, Erik Waingarten Columbia University The researchers were interested in algorithms which are given access to a large undirected graph G on n vertices and estimate the number of edges of the graph up to a small multiplicative error. In other words, for a very small ϵ > 0 (think of this as 0.01) and a graph with m edges, they wanted to output a number m' satisfying (1-ε) m ≤ m' ≤ (1+ε) m with probability at least 2/3, and the goal is to perform this task without having to read the whole graph. For a simple example, suppose that the access to a graph allowed to check whether two vertices are connected by an edge. Then, an algorithm for counting the number of edges exactly would need to ask whether all pairs of vertices are connected, resulting in an (n choose 2)-query algorithm since these are all possible pairs of vertices. However, sampling Θ((n choose 2) / (m ε2)) random pairs of vertices one can estimate the edges up to (1± ε)-error with probability 2/3, which would result in a significantly faster algorithm! The question here is: how do different types of access to the graph result in algorithms with different complexities? Recent work by Beame, Har-Peled, Ramamoorthy, Rashtchian, and Sinha studied certain "independent set queries" and "bipartite independent set queries": in the first (most relevant to our work), an algorithm is allowed to ask whether a set of vertices of the graph forms an independent set, and in the second, the algorithm is allowed to ask whether two sets form a bipartite independent set. The researchers give nearly matching upper and lower bounds for estimating edges with an independent set queries. A Lower Bound on Cycle-Finding in Sparse Digraphs Xi Chen Columbia University, Tim Randolph Columbia University, Rocco A. Servedio Columbia University, Timothy Sun Columbia University The researchers imagined situations in which the graph is extremely large and wanted to determine whether or not the graph has cycles in a computationally efficient manner (by looking at as few of the nodes in the graph as possible). As yet, there's no known solution to this problem that does significantly better than looking at a constant fraction of the nodes, but they proved a new lower bound – that is, they found a new limit on how efficiently the problem can be solved. In particular, their proof of the lower bound uses a new technique to capture the best possible behavior of any algorithm for this problem. Suppose there is a large directed graph that describes the connections between neurons in a portion of the brain, and the number of neurons is very large, say, several billion. If the graph has many cycles, this might indicate that the portion of the brain contains recurrences and feedback loops, while if it has no cycles, this might indicate information flows through the graph in a linear manner. Knowing this fact might help deduce the function of this part of the brain. The paper's result is negative – it provides a lower bound on the number of neurons needed to determine this fact. (This might sound a little discouraging, but this research isn't really targeted at specific applications – rather, it takes a step toward better understanding the types of approaches we need to use to efficiently determine the properties of large directed graphs.) This is part of a subfield of theoretical computer science that has to do with finding things out about enormous data objects by asking just a few questions (relatively speaking). Said Tim Randolph, "Problems like these become increasingly important as we generate huge volumes of data, because without knowing how to solve them we can't take advantage of what we know." Lower Bounds for Oblivious Near-Neighbor Search Kasper Green Larsen Aarhus University, Tal Malkin Columbia University, Omri Weinstein Columbia University, Kevin Yeo Google The paper studies the problem of privacy-preserving (approximate) similarity search, which is the backbone of many industry-scale applications and machine learning algorithms. It obtains a quadratic improvement over the highest unconditional lower bound for oblivious (secure) near-neighbor search in dynamic settings. This shows that dynamic similarity search has a logarithmic price if one wishes to perform it in an (information theoretic) secure manner. A Face Cover Perspective to $\ell_1$ Embeddings of Planar Graphs Arnold Filtser Columbia University In this paper the researcher studied the case where there is a set K of terminals, and the goal is to embed only the terminals into `1 with low distortion. Given two metric spaces $(X,d_X),(Y,d_Y)$, an embedding is a function $f:X\to Y$. We say that an embedding $f$ has distortion $t$ if for every two points $u,v\in X$, it holds that $d_X(u,v)\le d_Y(f(u),f(v))\le t\cdot d_X(u,v)$. "Given a hard problem in a space $X$, it is often useful to embed it into a simpler space $Y$, solve the problem there, and then pull the solution back to the original space $X$," said Arnold Filtser, a postdoctoral fellow. "The quality of the received solution will usually depend on the quality of the embedding (distortion), and the simplicity of the host space. Metric embeddings have a fundamental place in the algorithmic toolbox." In $\ell_1$ distance, a.k.a. Manhattan distance, given two vectors $\vec{x},\vec{y}\in\mathbb{R}^d$ the distance defined as $\Vert \vec{x}-\vec{y}\Vert_1=\sum_i \|x_i-y_i\|$. A planar graph $G=(V,E,w)$, is a graph that can be drawn in the plane in such a way that its edges $E$ intersect only at their endpoints. This paper studies metric embeddings of planar graphs into $\ell_1$. It was conjectured by Gupta et al. that every planar graph can be embedded into $\ell_1$ with constant distortion. However, given an $n$-vertex weighted planar graph, the best upper bound on the distortion is only $O(\sqrt{\log n})$, by Rao. The only known lower bound is $2$' and the fundamental question of the right bound is quite eluding. The paper studies the case where there is a set $K$ of terminals, and the goal is to embed only the terminals into $\ell_1$ with low distortion and it's contribution is a further improvement on the upper bound to $O(\sqrt{\log\gamma})$. Since every planar graph has at most $O(n)$ faces, any further improvement on this result, will be a major breakthrough, directly improving upon Rao's long standing upper bound. It is well known that the flow-cut gap equals to the distortion of the best embedding into $\ell_1$. Therefore, our result provides a polynomial time $O(\sqrt{\log \gamma})$-approximation to the sparsest cut problem on planar graphs, for the case where all the demand pairs can be covered by $\gamma$ faces. Approximating the Distance to Monotonicity of Boolean Functions Ramesh Krishnan Pallavoor Boston University, Sofya Raskhodnikova Boston University, Erik Waingarten Columbia University A Boolean function f : {0,1}n → {0,1} is monotone if for every two points x, y ∈ {0,1}n where xi ≤ yi for every i∈[n], f(x) ≤ f(y). There has been a long and very fruitful line of research, starting with the work of Goldreich, Goldwasser, Lehman, Ron, and Samorodnitsky, exploring algorithms which can test whether a Boolean function is monotone. The core question studied in the first paper was: suppose a function f is ϵ-far from monotone, i.e., any monotone function must differ with f on at least an ϵ-fraction of the points, how many pairs of points x, y ∈ {0,1}n which differ in only one bit i∈[n] (an edge of the hypercube) must satisfy f(x) = 1 but f(y) = 0 but x ≤ y (a violation of monotonicity)? The paper focuses on the question of efficient algorithms which can estimate the distance to monotonicity of a function, i.e., the smallest possible ϵ where f is ϵ-far from monotone. It gives a non-adaptive algorithm making poly(n) queries which estimates ϵ up to a factor of Õ(√n). "The above approximation is not good since it degrades very badly as the number of variables of the function increases," said Erik Waingarten. "However, the surprising thing is that substantially better approximations require exponentially many non-adaptive queries." The Complexity of Contracts Paul Duetting London School of Economics, Tim Roughgarden Columbia University, Inbal Talgam-Cohen Technion, Israel Institute of Technology Contract theory is a major topic in economics (e.g., the 2016 Nobel Prize in Economics was awarded to Oliver Hart and Bengt Holmström for their work on the topic). A canonical problem in the area is how to structure compensation to employees (e.g. as a function of sales), when the effort exerted by employees is not directly observable. This paper provides both positive and negative results about when optimal or approximately optimal contracts can be computed efficiently by an algorithm. The researchers design such an efficient algorithm for settings with very large outcome spaces (such as all subsets of a set of products) and small agent action spaces (such as exerting low, medium, or high effort). How to Store a Random Walk Emanuele Viola Northeastern University, Omri Weinstein Columbia University, Huacheng Yu Harvard University Motivated by storage applications, the researchers studied the problem of "locally-decodable" data compression. For example, suppose an encoder wishes to store a collection of n correlated files using as little space as possible, such that each individual X_i can be recovered quickly with few (ideally constant) memory accesses. A natural example is a collection of similar images or DNA strands on a large sever, say, Dropbox. The researchers show that for file collections with "time-decaying" correlations (i.e., Markov chains), one can get the best of both worlds. This surprising result is achieved by proving that a random walk on any graph can be stored very close to its entropy, while still enabling constant time decoding on a word-RAM. The data structures generalize to dynamic (online) setting. Labelings vs. Embeddings: On Distributed Representations of Distances Arnold Filtser Columbia University, Lee-Ad Gottlieb Ariel University, Robert Krauthgamer Weizmann Institute of Science The paper investigates for which metric spaces the performance of distance labeling and of `∞- embeddings differ, and how significant can this difference be. A distance labeling is a distributed representation of distances in a metric space $(X,d)$, where each point $x\in X$ is assigned a succinct label, such that the distance between any two points $x,y \in X$ can be approximated given only their labels. A highly structured special case is an embedding into $\ell_\infty$, where each point $x\in X$ is assigned a vector $f(x)$ such that $\\|f(x)-f(y)\\|_\infty$ is approximately $d(x,y)$. The performance of a distance labeling, or an $\ell_\infty$-embedding, is measured by its distortion and its label-size/dimension. "As $\ell_\infty$ is a norm space, it posses a natural structure that can be exploited by various algorithms," said Arnold Filtser. "Thus it is more desirable to obtain embeddings rather than general labeling schemes." The researchers also studied the analogous question for the prioritized versions of these two measures. Here, a priority order $\pi=(x_1,\dots,x_n)$ of the point set $X$ is given, and higher-priority points should have shorter labels. Formally, a distance labeling has prioritized label-size $\alpha(.)$ if every $x_j$ has label size at most $\alpha(j)$. Similarly, an embedding $f: X \to \ell_\infty$ has prioritized dimension $\alpha(\cdot)$ if $f(x_j)$ is non-zero only in the first $\alpha(j)$ coordinates. In addition, they compare these prioritized measures to their classical (worst-case) versions. They answer these questions in several scenarios, uncovering a surprisingly diverse range of behaviors. First, in some cases labelings and embeddings have very similar worst-case performance, but in other cases there is a huge disparity. However in the prioritized setting, they found a strict separation between the performance of labelings and embeddings. And finally, when comparing the classical and prioritized settings, they found that the worst-case bound for label size often "translates" to a prioritized one, but also a surprising exception to this rule.	CommonCrawl
Determinants of livelihood diversification strategies in Borena pastoralist communities of Oromia regional state, Ethiopia Amare Molla Dinku1 Livelihood diversification strategies play a key role in development process. However, identification of the factors that determine households' choice of livelihood strategies of pastoralists has received little attention. This research was therefore proposed with the aim of generating location specific data on livelihood strategies and its determinants in Borena district of southern Oromia, Ethiopia. Multistage random sampling technique was employed to select 110 household heads from three kebeles of Borena district. Data were collected using both qualitative and quantitative methods. Descriptive statistics and multinomial logit model have been employed to analyze the data. Result and conclusion The income portfolio analysis revealed that pastoral production still plays a leading role by contributing higher share of the total household income. Different socioeconomic characteristics of the household significantly influence the level of livelihood diversification. Age of household head, farm input use, extension contact, market access, credit access and owned cattle size are the main factors. Therefore, household livelihoods are highly diverse and policy makers need to reflect on the most suitable ways of supporting this diversity and they should empower pastoralists to engage with policy formulation on more appropriate pastoral legislation that protect pastoral land rights and sustainable livelihoods options. Background and research problem Pastoralists represent approximately 10% percent of the Ethiopian population (over 72 million), and approximately 40% of the land area of Ethiopia is considered to be under pastoral production system. They live in much of the peripheral lowlands that surround the central highland plateaus dominated by rain-fed small-scale agriculture [1]. The pastoral system in Ethiopia is vulnerable to environmental degradation and food insecurity. Livelihood of pastoralist communities in Ethiopia is constrained by diverse natural, social and economic problems including recurrent drought, lack of basic infrastructure, conflict, and they have low resilient capacities to cope with and recover from such vulnerable situations. The large majorities' livelihoods in most seasons of the year are depending on food assistance of the government. About 15% of Borena pastoralists are food-insecure throughout the year [2]. Currently, as an emerging alternative of livestock destitute, pastoralists in Ethiopia are benign settled in and around urban centers to exploit the upcoming livelihood opportunities defined as nonpastoral livelihood options like petty trading and wage employment that would otherwise be unavailable in rural pastoral areas. The contribution of livelihood diversification to rural and pastoral livelihoods has often been ignored by policy makers, and there is a general perception among policy makers and technocrats that pastoral lands are underutilized and therefore should be brought under the plow. The pastoral mode of life based on mobility is perceived to be backward and needs to be transformed. Government development efforts focus on sedentarization of pastoralists in favor of cultivation instead of transhumant nomadism and for ease of provision of social services [3,4,5]. Annually, massive resources are invested by humanitarian aids and government for food security programs. However, food insecurity is becoming persistent, especially in pastoralist areas that do not have sufficient livelihood diversification option around them [6]. The Borana pastoralists have been hit hard by recurring droughts and consequent loss of livestock for the last three decades, the most recent one being in the period between 1999 and 2000. The study by [7] estimates that during the years 1980–1997 alone, monetary losses due to livestock deaths in the Borana plateau exceeded US $ 300 million. The study further argues that "cattle crashes", or widespread loss of cattle, occur in every 5–6 years, particularly during times of low rainfall and high stocking rates. The probability of drought occurrence remains high, and at the same time several factors are causing the decline of livelihood diversification. It is difficult to recover from such shocks and stresses. Problems like seasonal migration, alienation of traditional pastoral rights of accessing pastoral resources and restrictions of free movement in search of pasture and water are among triggering factors of this problem [8]. Thus, a thorough understanding of alternative livelihood strategies of pastoral households and communities is crucial in any attempt to bring the improvement of livelihood. It is important to commit a limited resource available for pastoral development based on new assumption about the rural poor and their livelihood strategies [9, 10]. This study, therefore, attempted to see the determinants of pastoral livelihood diversification choices of Borena pastoral communities of Ethiopia in their struggle to achieve food security goals. Conceptual framework and basic research questions The livelihoods framework provides comprehensive and complex approaches in understanding how people make a living. It can be used as a loose guide to a range of issues that are important for livelihoods, and it can be rigorously investigated in all its aspects [10]. Livelihood approaches emphasize the understanding of the context within which people live, the assets available for them, livelihood strategies they follow in the face of existing policies and institutions, and livelihood outcomes they intend to achieve [11, 12] (Fig. 1). Source: adopted from [13] Conceptual frame work of sustainable livelihood. The key question to be addressed in any analysis of livelihood is given a particular context (of policy setting, politics, history, agroecology and socioeconomic conditions), what combination of livelihood resources (different types of "capital") results in the ability to follow with what combination of livelihood strategies (agricultural intensification/extensification, "livelihood diversification" and migration) with what outcomes? [13]. The ultimate goal of livelihood diversification is therefore bringing sustainable livelihood outcome like securing more income, improved food security, reduced vulnerability and increased welfare. Based on this general assumption, the study formulates the following specific research question: What are the major determinant factors which affect the practice of livelihood diversification in Borena pastoralist community? Methods: sampling strategy, data collection and analysis Study area, data and sampling The study has been undertaken in Yabello Woreda of Borena Zone, Southern Oromia Ethiopia. It is located 570 km in south of Addis Ababa. It is the second largest Woreda in the zone with total landmass coverage of 5523 km2 [14]. The Woreda was selected as it was assumed to be the high concentration and attraction areas for pastoral livelihood dropouts. Both qualitative and quantitative approaches were employed for data collection. Multistage simple random sampling technique was undertaken for the selection of 110 household heads. First Yabello Woreda was selected from Borena Zone, and second three kebeles (the smallest administrative unit in Ethiopia), namely Hadi-Alle, HarWuyue and Dhirtu, were selected among 23 kebeles based on their agroecological location and its proximity to the Woreda urban center of Yabello town. Finally, 110 household heads were selected using Yemane, 1967, sampling formula (n = N/N (1 − e)2 using 95% confidence intervals. This was proportionally distributed among three kebeles. Finally, the individual households were selected randomly for conducting household interviews. The geographical map of study Woreda was delineated using geographical information system (GIS) data as shown in Fig. 2. Source: own field designing in 2015; develop by author, 2015 Topographical map of Borena Woreda. Model specification To identify the determinants of pastoral households' decision choices from various livelihood diversification options, multinomial regression model was preferred [15]. The assumption is that in a given period at the disposal of its asset endowment, a rational household head chooses among the four mutually exclusive livelihood strategy options that offer the maximum utility for a given household at a given circumstances. Following [15], for the ith respondent faced with J choices of pastoral livelihood diversification options, the utility choice j was specified as: $$U_{ij } = Z_{ij } \beta + \varepsilon_{ij}$$ If the respondent makes choice j in particular, then we assume that U ij is the maximum among the J utilities. So the statistical model is derived by the probability that choice j is made, which is: $${\text{Prop}}\; (U_{ij} > U_{ik} )\;{\text{for}}\;{\text{all}}\;{\text{other}}\;K \ne j$$ where U ij is the utility to the ith respondent from livelihood strategy j. U ik is the utility to the ith respondent from livelihood strategy k. If the household maximizes its utility defined over income realizations, then the household's choice is simply an optimal allocation of its asset endowment to choose livelihood that maximizes its utility [16]. Thus, the ith household decision can, therefore, be modeled as maximizing the expected utility by choosing the jth livelihood strategy among "J" discrete livelihood strategies, i.e., $$\max_{j} = E(U_{ij} ) = f_{j} (x_{i} ) + \varepsilon_{ij} ;\quad j = 0 \ldots J$$ In general, for an outcome variable with J categories, let the jth livelihood strategy that the ith household chooses to maximize its utility take the value 1 if the ith household chooses jth livelihood strategy and 0 otherwise. The probability that a household with characteristics "x" chooses livelihood strategy j, P ij is modeled as: $$P_{ij} = \frac{{\exp (X_{i}^{\prime } \beta_{j} )}}{{\sum\nolimits_{j = 0}^{J} {\exp (X_{i}^{\prime } \beta_{j} )} }},\quad J = (0 \ldots 3)$$ with the requirement that $\sum\nolimits_{j = 0}^{J} {P_{ij} = 1}$ for any i where P ij = probability representing the ith respondent's chance of falling into category j. X = predictors of response probabilities. β j = covariate effects specific to jth response category with the first category as the reference. Appropriate normalization that removes an indeterminacy in the model is to assume that $\beta_{1} = 0$ (this arises because probabilities sum to 1, so only J parameter vectors are needed to determine the J + 1 probabilities), [15] so that $\exp (X_{i} \beta_{1} ) = 1$, implying that the generalized Eq. (4) above is equivalent to $$\Pr (y_{i} = j /X_{i} ) = P_{ij} = \frac{{\exp (X_{i} \beta_{j} )}}{{1 + \sum\nolimits_{j = 1}^{J} {\exp (X_{i}^{\prime } \beta_{j} )} }},\quad {\text{For}}\; j = (0,2 \ldots J)\;{\text{and}}$$ $$\Pr (y_{i} = 1 /X_{i} ) = P_{i1} = \frac{1}{{1 + \sum\nolimits_{j = 1}^{J} {\exp (X_{i}^{\prime } \beta_{j} )} }},$$ where y = a polytomous outcome variable with categories coded from 0…J. Note: the probability of Pi1 is derived from the constraint that the J probabilities sum to 1. That is, $p_{i1} = 1 - \sum {p_{ij} }$. Similar to binary logit model, it implies that we can compute J log-odds ratios which are specified as: the dependent variable is the log of one alternative relative to the reference alternative. Then, coefficients in a multinomial logit model are difficult to interpret [15]. Therefore, the marginal effects of the explanatory variables on the choice of alternative livelihood diversification strategies are derived as follows: $$\ln \left[ {\tfrac{{p_{ij} }}{{p_{iJ} }}} \right] = x^{\prime } \left( {\beta_{j} - \beta_{J} } \right) = x^{\prime } \beta_{j} ,\quad {\text{if}}\;J = 0$$ According to [15], the marginal probabilities measure the expected change in the probability of a particular choice being selected with respect to a unit change in the independent variable. Definition of variables See Table 1. Table 1 Description of variables. Result and discussion Description of livelihood strategies Livelihood strategies are defined as those activities undertaken by households to provide a means of living. It is diverse and variable at micro–macro levels. As it has been reviewed from [17], there are several different methods of characterizing household livelihood strategies that are available in the real world. Most commonly, economists group households by shares of income earned from different sectors of the rural economy. Similarly, this study considered the income shares of each livelihood activity to conceptualize livelihood strategies. In addition, the local people have also their own wealth ranking criteria to say poor, less poor and better income. Accordingly, this study uses community wealth ranking criteria as bench mark to say poor, less poor and rich in the analysis of livelihood diversification. Income portfolio analysis has been done for each pastoral household to measure the share of income from different livelihood options (Table 2). Table 2 Income composition of sample households. From the income portfolio analysis, the percentage share of the broad livelihood activities indicates that the share of pastoral livelihood alone covers about 64.1%, nonfarm 22.8% and off-farm 13.1% in decreasing orders. Further observation of the study revealed that off-farm activities (daily wage, market brokering and environmental gathering) are survival mechanisms pursued mainly by the lower-income groups. This idea has been also reflected in focus group discussion sessions. The participants' opinion on off-farm livelihood opportunities indicates that engagement with such activity is mostly preferred by (poor pastoralist groups) individuals who do not have herds and those with limited option to construct sustainable (strategic) livelihood diversification. Nonfarm activities, such as rural craft, are also main choice of the poor than their counterparts. Thus, off-farm activities seem more of a coping mechanism for the poor pastoral community groups than as a means to accumulate wealth and reduce poverty by all pastoral community groups. According to the interviews, the poor tend to concentrate on off-farm activities characterized by low entry constraints (gathering, charcoal making and fire wood collection and wage). The finding indicates the need to understand the challenges faced by the poor and less poor that prevent them from engaging in pastoral production and more remunerative nonfarm activities (Table 2). Results of multinomial logit model Multinomial logistic regression model was used to identify determinants of farmers' decision choice on the use of livelihood diversification options. The result of logistic regression analysis is presented to identify determinants of livelihood diversification options by pastoral households. The maximum likelihood method of estimation was employed to estimate the parameter estimates of the multinomial logit model, and statistically significant variables were identified. In order to measure factors' relative importance on the farmers' choice of livelihood diversification options, STATA version 11 software was used to generate the parameter estimates. To identify the problem of multi co-linearity or association among the potential explanatory variables, variable inflation factors (VIF) (for continuous variables) and contingency coefficients (for the categorical) variables were checked and it shows good result. The result of the maximum likelihood estimates is presented in Table 3. Table 3 Determinants of livelihood diversification practices p value and RRR (marginal effects). The likelihood ratio test statistics is used to test the overall significance of the model [15]. The value of Pearson Chi-square indicated the goodness of fit for model fitting information. The overall likelihood test ratio statistics indicated by the Chi-square statistics is highly significant at 0.00001 point suggesting that strong explanatory power of the model. Parameter estimates of multinomial logit model provide only the directional effect of independent variables on dependent variables, and it represents neither actual magnitude of change nor probability levels [18]. However, the marginal effects or odds ratio (relative risk ratio) measures the expected change in probability of a particular choice being made with respect to a unit change in an independent variable [15]. Accordingly, it has been implemented for analyzing both direction and magnitude of changes. As indicated in Table 3, among 13 hypothesized explanatory variables 11 of them were significantly affecting the farmers' choice of decision to different livelihood options (pastoral and off-farm, pastoral and nonfarm and the combination of all) using pastoral livelihood alone as a base case scenario. Age structure of household heads was found to be negatively and significantly affecting pastoralists' decision choice of pastoral and off-farm combination and pastoral and nonfarm combination. This implies that in comparison with those who use only pastoral livelihood options as their livelihood means (base case), a year increase in age of household heads will likely shift choices of farmers' livelihood option to off-farm and nonfarm activities by the probability of 0.9 units than those who use pastoralism as their only sources of livelihoods. Therefore, keeping other factors constant, younger farmers' are motivated to engage more in nonfarm and off-farm activities than pastoral livelihood practices alone. This is also in proved by the research done [19]. He explained that younger pastoralist households do not have enough livestock herds and resources that support their livelihood compared to the older farm households (resource rich). Furthermore, researchers' inquiry on focus group discussion regarding sustainability of pastoral livelihood indicates that as the land in the pastoral community is fragile due to continuous communal grazing for longer time, it is less productive to continue pastoral livelihood practice as usual. As well, interview on farmers' perception on new livelihood options indicates that experienced farmers are more likely to stay in pastoralism. They also diversify their livelihood on other related livelihood options such as livestock market negotiator. Due to cultural and social realities, experienced pastoralists are also practicing livestock production for the sake of social recognition like getting appreciation in their societies. This is also in line with previous studies done by [18, 20,21,22]. In the pastoralist communities, agricultural inputs are supplied by the District agricultural office aiming to improve health and productivity of livestock. In this study, pastoralists who use agricultural inputs (veterinary services and animal feeds) are more likely and significantly employing off-farm and nonfarm activities in addition to their pastoralism practices. For example, those who practice all combination of livelihood options (pastoralism, nonfarm and off-farm) are more likely motivated to use agricultural input by 0.12 units better than those who practice pastoralism practices alone at 0.036 significant levels. This study indicates that application of multiple options of livelihood can increase earning incomes and enables pastoralists to purchase and use better livestock technologies or inputs. However, the study conducted by [23] in Yabello indicates that the percentage proportion of sum of expenditure for farm inputs (forage seed, farm tools and veterinary service) is decreasing when we see the status of rich, medium and poor income households (8.5, 6 and 0%). Thus, input suppliers have to consider the economic backgrounds of pastoralists and there must be credit schedule for resource-scarce farmers. The number of veterinary extension service providers contact dates has a positive and significant contribution for pastoralists to participate in off-farm and nonfarm livelihood activities at 0.04 and 0.03 significant level, respectively. The likelihood of choosing pastoral plus off-farm and pastoral plus nonfarm livelihood strategy by pastoralists is increasing as the number of veterinary extension contact dates increases as compared to pastoral practices alone. This implies that a day increase in pastoral extension contact with relevant extension message raises the likelihood of farmers' choice of pastoral plus off-farm and pastoral plus nonfarm activities by 1.4 and 1.5 units, respectively. Since the objective of government extension service is to enhance farmers' capabilities of solving their own difficulties by their own effort and resources; frequent extension contact with relevant messages has significant contribution in promoting pastoral livelihood diversification practices [24]. Thus, the information obtained and the knowledge and skill gained from veterinary extension service providers may influence farmers' skill and decision making on seeking and utilizing diversified livelihood options. Frequent extension contact with veterinary services provider personnel regarding their livestock health, production and productivity is likely to increase the engagement of households to other off-farm and nonfarm sectors. This is because timely and better agricultural (veterinary) extension services help to enhance productivity at household level. This can be also assured by the content of the message that farmers gain from extension agents that initiate them to use risk aversion strategies through the diversification of income within and out of pastoral livelihoods strategies. Remittance is another important income source for pastoralist communities. Remittance refers to money sent from inside and outside the country from families and relatives of household members. The system of supporting families is a continuous process. In this research, remittance has positive and significant contribution to households' entry to diversification of livelihood strategies toward pastoral and nonfarm combination at significance level of 0.019. Households' likelihood of diversifying nonfarm livelihood activities is increasing by 6.8% if they have access of remittance income in reference to those who employ pastoral practice alone as their livelihood means. The result is analogous with the findings of [17, 25]. In pastoralists, remittances constitute only a small part of total household income on average. However, it contributes positively in supporting rural households diversifying activities. It contributes about 10, 13 and 20 percents to the household income of the rich, medium and poor households, respectively. Livestock holding (cattle size in TLU) is positively influencing household's choice of combinations of pastoral, nonfarm and off-farm livelihood strategy at 0.01 significance level. This means that the probability of pastoralists who diversify their livelihood toward nonfarm and off-farm activity is increasing as it amplifies their opportunity to create other assets by exchanging and selling of their livestock herds. It is in contradiction with research finding conducted by [20]. His report indicates that pastoralists with lower livestock holding would be pressed to diversify livelihoods into off-farm and nonfarm activities as an "opportunistic" diversification activity in order to meet their household needs. However, the results of this study confirmed that livelihood diversification activity is capital intensive and requires assets and resources which can be mobilized to create and develop other livelihood options. Accordingly, households with higher livestock holdings are more capable of affording the cost of strategic livelihood diversification which aims at the accumulation of wealth. Therefore, to be able to bring about positive change in wellbeing, natural capitals (livestock) are exchanged to different assets. This is in line with the findings of [9, 10, 18] that are conducted at different pastoralist areas. As hypostasized, the market access of the residents had negative correlation with the decision of individuals to enter into livelihood diversification activities. Market facilitates individuals' involvement in all types of livelihood diversification options. This study implies the probability of individuals diversifying beyond the agricultural practice is likely to be reduced as the distance to market place increases from their villages. This is due to the fact that individuals who live near the market area had higher opportunity to engage in other livelihood option beyond their usual pastoral activities. It creates opportunities like wage laborer and petty trades, and market brokering. Market distance influences livestock marketing negatively. Chattel experiencing long distance travels to arrive at market places are usually exposed to weight losses that intern affecting their market price. Level of credit access and use is found to have significant (p < 0.1) and negative impact on the likelihood of choosing diversified livelihood strategies (pastoralism, off-farm and nonfarm). Households who have batter access and utilization of credit are 0.18 times more likely to withdraw from livelihood diversification activities than those whose livelihood is dependent on pastoral production practices alone. This negative impact may be attributed to the fact that credit use allows pastoralists to follow agricultural intensification by providing better access to farm inputs which in turn improves productivity. This implies that the formal and informal credit facilities that avail for rural farmers are a very important financial asset in rural livelihoods not only to finance agricultural inputs activities, but also to protect loss of crucial livelihood assets such as cattle due to seasonal food shortage, illness or death in bad seasons [10]. The result of the study, therefore, suggest that farmers' access and use of credit would play important role in promoting pastoral livelihood development and strategic livelihood diversifications processes. The result is also in line with that of [17, 18, 26] findings. This implies that the incentive for accessing credit accelerates pastoral production. Conclusion and recommendation The pastoral system in Ethiopia is vulnerability to environmental degradation and food insecurity. More specifically, livelihood insecurity has been characterized by the area where the large majority of pastoralists depend on food assistance (food aid). The vulnerability is due to the lack of livelihood diversification constrained by lack of basic infrastructure services, external shocks such as recurrent drought, flood, conflict and people's capacities to cope with the shocks, which depend on factors such as social networks, assets and political status [2]. Livelihood analysis using an assets framework could help to foster the appreciation of the way that combinations of assets are vital to secure livelihoods. Assets are not simply resources that people use in building livelihoods; they give people the capacity to be and to act. Clearer identification of livelihood strategies would provide an opportunity to focus on practical poverty reduction interventions and to assess outcomes. The sustainable livelihoods approach seeks to develop an understanding of the factors that lie behind people's choices of livelihood strategies and then reinforce factors which promote choice and flexibility, because the more choice and flexibility people have in their livelihood strategies through livelihood diversification, the greater their ability to withstand the external shocks and stresses. With the above-mentioned issues in mind, this study sought to identify the major determinants of farmers' decision choice on different livelihood diversification options and examine the extent to which different diversification options contribute for household income sources using a multinomial logit model, the study brings useful insights into policy formulation. From the income portfolio analysis, the share of agriculture (pastoral) accounts for about 64.1%, nonfarm (nonpastoral) for 22.8% and off-farm for 13.1% of the household income. Youth pastoralists show better performance for adopting available livelihood diversification options. Therefore, local government needs to design inclusive livelihood strategies that considered the demographic characteristics of pastoralists in general and age structure in particular. As well, frequent extension visit of pastoralists by development agents has shown an important motivation for utilizing the available livelihood diversification options. Hence, the contents of extension message (veterinary services) has to be revised as it can incorporate services of nonpastoral livelihood activities (off-farm activities). Infrastructure services (market access, credit access) were observed as motivating factor for expanding strategic livelihood diversification. Thus, deliveries of infrastructure services need to get special focus from government and nongovernment actors who work in the area. However, further research is still needed to gauge the challenges of livelihood diversification across different socioeconomic contexts of pastoralists. TLU: tropical livestock unit physical capital Fecadu G. Pastoral nomadism and rural development. In: Pauswang S, Cheru F, Brune S, Chole E, editors. Ethiopia: options for rural development. London: Zed Books; 1998. Beruk Y. Food insecurity in Pastoral Areas of Ethiopia unpublished document Harumaya University, Ethiopia; 2003. Barrett CB, Swallow BM. Dynamic poverty traps and rural livelihoods, Ch: 2. In: Ellis F, Freeman HA, editors. Rural livelihoods and poverty reduction policies. London: Routledge; 2005. p. 16–28. Carswell G. Livelihood diversification in southern Ethiopia IDS working paper 117. 2000. Roa J, Niehof A, Price L, Moerbeek H. Food security through the livelihoods lens: an integrative approach (the case of less favored areas in the Philippines) 2004. http://edepot.wur.nl/22061. Accessed 23 Dec 2015. Frankenberger TR, Sutter P, Amdissa T, Alemtsehay A, Mulugeta T, Moges T, Alemayehu S, Bernard T, Spangler T, Yeshewamebrat E. The path to self-reliancy, volume I: final report in Ethiopia; 2007. Desta S, Coppock DL. Cattle population dynamics in the southern Ethiopian rangelands, data from 1980-97. J Range Manag. 2002;55:439–51. Baxter PTW. Immediate problems: a view from a distance. In: Mohammed Salih MA, Dietz T, Ahmed AGM, editors. African pastoralism: conflict, institutions and government. London: Pluto Press; 2001. Beruk Y. The reality of pastoralism in Ethiopia. Paper presented at CRDA workshop on non-governmental organizations and sect oral development: pastoralism panel, Addis Ababa; 2001. Lemma Tesfaye. Diversity in livelihoods and farmers strategies in Hararghe highlands, Eastern Ethiopia. Pretoria: University of Pretoria; 2003. DFID. Sustainable rural livelihoods guidance sheet, London; 2000. Ellis F, Freeman HA. Rural livelihoods and poverty reduction policies. London: Routledge; 2005. Scoones I. Sustainable livelihoods, a framework for analysis, IDS working paper number 72, Brighton; 1998. CSA. Central statistical authority population estimates, unpublished document Ethiopia, Addis Ababa, Ethiopia; 2007. Green HW. Econometric analysis, 4th edn. New York University, Macmillan Publishing Company; 2003. Brown DR, Stephens EC, Okuro MJ, Murithi FM, Barrette CB. Livelihood strategies in the rural Kenyan highland; 2006. Berehanu E. Livelihood strategies of smallholder farmers and income poverty in draught prone areas: the case of Gena-Bosa woreda, SNNPRS. An M.Sc. thesis presented to the School of Graduate Studies of HarUmaya University; 2007. Edlam A. Pastoralists and development: the impact of development interventions on Borana pastoralists, Southern Ethiopia. Unpublished report M.Phil. Thesis, University of Cambridge; 2003. Adugna L. The dynamics of livelihood diversification in Ethiopia unpublished report: evidence from Panel Data. Boston: Department of Economics, University of Massachusetts; 2005. Barrett CB, Reardon T, Webb P. Non-farm income diversification and household livelihood strategies in rural Africa: concepts, dynamics, and policy implications. Food Policy. 2001;26:315–31. Destaw B. Non-farm employment and farm production of small holder farmers: a study in Edja District of Ethiopia. A thesis submitted to the School of Graduate Studies Harumaya University; 2003. Kanji N, MacGregor J, Tacoli C. Understanding market-based livelihoods in a globalizing world: combining approaches and methods. London: International Institute for Environment and Development (IIED); 2005. Samuel G-S. Summary report on recent economic and agricultural policy. Paper prepared for the Roles of agriculture international conference 20–22 October 2003, Rome, Italy. 2001. Bezemer DJ, Lerman Z. Rural livelihoods in Armenia. The Centre for Agricultural Economic Research, The Department of Agricultural Economics and Management Discussion Paper No. 4.03; 2002. Holden S, Bekele S, Pender J. Non-farm income, household welfare, and sustainable land management in a less favoured area in the Ethiopian highlands. Department of Economics and Resource Management Agricultural University of Norway; 2004. I would like to thank Yardstick International College and Wollo University for arrangement of such opportunity to travel to the area by securing vehicles. My gratitude also goes to Borena Zone Agricultural Office for giving us necessary information about the study area and for their unlimited support by providing informed consents. I also thank data collectors and supervisors for their unreserved effort for the successful completion of collection of the data. Finally, the author would like to acknowledge all other concerned bodies that have shared their support for the successful development and completion of this study. The author declares that there are no competing interests. The author wants to declare that he can submit the data at any time based on publisher's request. The datasets used and/or analyzed during the current study will be available from the author on reasonable request. Ethical approval and consent to participate Ethical clearance letters were collected from Wollo University research and community service directorate and Borena Zone administrative office to care for both the study participants and the researchers. Official letters were written for each kebele, informed verbal consent was obtained from each client, and confidentiality was maintained by giving codes for respondents rather than recording their name. Study participants were informed that clients have full right to discontinue or refuse to participate in the study. Therefore, all participants of the research including survey households, case studies, enumerators, the supervisors and key informants were fully informed about the objectives of the study. They were approached friendly in free moods. Collage of Agriculture, Wollo University, Dessie, Ethiopia Amare Molla Dinku Search for Amare Molla Dinku in: Correspondence to Amare Molla Dinku. Dinku, A.M. Determinants of livelihood diversification strategies in Borena pastoralist communities of Oromia regional state, Ethiopia. Agric & Food Secur 7, 41 (2018) doi:10.1186/s40066-018-0192-2 Livelihood diversification Pastoralist communities	CommonCrawl
Convergence of p-th mean in an averaging principle for stochastic partial differential equations driven by fractional Brownian motion DCDS-B Home The fast signal diffusion limit in nonlinear chemotaxis systems March 2020, 25(3): 1129-1139. doi: 10.3934/dcdsb.2019212 Global asymptotic stability of nonconvex sweeping processes Lakmi Niwanthi Wadippuli , Ivan Gudoshnikov and Oleg Makarenkov , Department of Mathematical Sciences, University of Texas at Dallas, 75080 Richardson, USA * Corresponding author: Oleg Makarenkov Received November 2018 Revised May 2019 Published September 2019 Figure(2) Building upon the technique that we developed earlier for perturbed sweeping processes with convex moving constraints and monotone vector fields (Kamenskii et al, Nonlinear Anal. Hybrid Syst. 30, 2018), the present paper establishes the conditions for global asymptotic stability of global and periodic solutions to perturbed sweeping processes with prox-regular moving constraints. Our conclusion can be formulated as follows: closer the constraint to a convex one, weaker monotonicity is required to keep the sweeping process globally asymptotically stable. We explain why the proposed technique is not capable to prove global asymptotic stability of a periodic regime in a crowd motion model (Cao-Mordukhovich, DCDS-B 22, 2017). We introduce and analyze a toy model which clarifies the extent of applicability of our result. Keywords: Sweeping process, prox–regular sets, monotone functions, periodic solutions, global asymptotic stability. Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35. Citation: Lakmi Niwanthi Wadippuli, Ivan Gudoshnikov, Oleg Makarenkov. Global asymptotic stability of nonconvex sweeping processes. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 1129-1139. doi: 10.3934/dcdsb.2019212 L. Adam and J. Outrata, On optimal control of a sweeping process coupled with an ordinary differential equation, Discrete Contin. 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Mordukhovich, Optimality conditions for a controlled sweeping process with applications to the crowd motion model, Discrete Cont. Dyn. Syst., Ser B., 22 (2017), 267-306. doi: 10.3934/dcdsb.2017014. Google Scholar T. H. Cao and B. Mordukhovich, Optimal control of a nonconvex perturbed sweeping process, Journal of Differential Equations, 266 (2019), 1003-1050. doi: 10.1016/j.jde.2018.07.066. Google Scholar C. Castaing and M. D. Monteiro Marques, BV periodic solutions of an evolution problem associated with continuous moving convex sets, Set-Valued Analysis, 3 (1995), 381-399. doi: 10.1007/BF01026248. Google Scholar G. Colombo and V. V. Goncharov, The sweeping processes without convexity, Set-Valued Analysis, 7 (1999), 357-374. doi: 10.1023/A:1008774529556. Google Scholar G. Colombo and M. D. Monteiro Marques, Sweeping by a continuous prox-regular set, Journal of Differential Equations, 187 (2003), 46-62. doi: 10.1016/S0022-0396(02)00021-9. Google Scholar J. F. Edmond and L. Thibault, BV solutions of nonconvex sweeping process differential inclusion with perturbation, Journal of Differential Equations, 226 (2006), 135-179. doi: 10.1016/j.jde.2005.12.005. Google Scholar J. F. Edmond and L. Thibault, Relaxation of an optimal control problem involving a perturbed sweeping process, Mathematical Programming, 104 (2005), 347-373. doi: 10.1007/s10107-005-0619-y. Google Scholar C. O. Frederick and P. J. Armstrong, Convergent internal stresses and steady cyclic states of stress, The Journal of Strain Analysis for Engineering Design, 1 (1966), 154-159. doi: 10.1243/03093247V012154. Google Scholar M. Kamenskii, O. Makarenkov, L. N. Wadippuli and P. R. de Fitte, Global stability of almost periodic solutions of monotone sweeping processes and their response to non-monotone perturbations, Nonlinear Analysis: Hybrid Systems, 30 (2018), 213-224. doi: 10.1016/j.nahs.2018.05.007. Google Scholar M. Kamenskii and O. Makarenkov, On the response of autonomous sweeping processes to periodic perturbations, Set-Valued and Variational Analysis, 24 (2016), 551-563. doi: 10.1007/s11228-015-0348-1. Google Scholar P. Krejci, Hysteresis, Convexity and Dissipation in Hyperbolic Equations, Gattotoscho, 1996. Google Scholar M. Kunze, Periodic solutions of non-linear kinematic hardening models, Math. Methods Appl. Sci., 22 (1999), 515-529. doi: 10.1002/(SICI)1099-1476(199904)22:6<515::AID-MMA48>3.0.CO;2-S. Google Scholar R. I. Leine and N. Van de Wouw, Stability and Convergence of Mechanical Systems with Unilateral Constraints, Lecture Notes in Applied and Computational Mechanics, 36. Springer-Verlag, Berlin, 2008. doi: 10.1007/978-3-540-76975-0. Google Scholar [19] E. H. Lockwood, A Book of Curves, Cambridge University Press, New York, 1961. Google Scholar B. Maury and J. Venel, A discrete contact model for crowd motion, ESAIM: Mathematical Modelling and Numerical Analysis, 45 (2011), 145-168. doi: 10.1051/m2an/2010035. Google Scholar B. S. Mordukhovich, Variational Analysis and Applications, Springer, 2018. doi: 10.1007/978-3-319-92775-6. Google Scholar R. A. Poliquin, R. T. Rockafellar and L. Thibault, Local differentiability of distance functions, Transactions of American Mathematical Society, 352 (2000), 5231-5249. doi: 10.1090/S0002-9947-00-02550-2. Google Scholar C. Polizzotto, Variational methods for the steady state response of elasticplastic solids subjected to cyclic loads, International Journal of Solids and Structures, 40 (2003), 2673-2697. doi: 10.1016/S0020-7683(03)00093-3. Google Scholar R. T. Rockafellar and R. J.-B. Wets, Variational Analysis, Springer, Berlin, 1998. doi: 10.1007/978-3-642-02431-3. Google Scholar W. Rudin, Principles of Mathematical Analysis, McGraw-hill New York, 1976. Google Scholar A. Tanwani, B. Brogliato and C. Prieur, Stability and observer design for Lur'e systems with multivalued, nonmonotone, time-varying nonlinearities and state jumps, SIAM Journal on Control and Optimization, 52 (2014), 3639-3672. doi: 10.1137/120902252. Google Scholar L. Thibault, Sweeping process with regular and nonregular sets, Journal of Differential Equations, 193 (2003), 1-26. doi: 10.1016/S0022-0396(03)00129-3. Google Scholar Y. V. Trubnikov and A. I. Perov, Differential Equations with Monotone Nonlinearities, "Nauka i Tekhnika", Minsk, 1986. Google Scholar V. A. Zorich, Mathematical Analysis. II, Translated from the 2002 fourth Russian edition by Roger Cooke, Universitext, Springer-Verlag, Berlin, 2004. Google Scholar Z. Zhu, H. Leung and Z. Ding, Optimal synchronization of chaotic systems in noise, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 46 (1999), 1320-1329. Google Scholar Figure 1. Illustrations of the notations of the example. The closed ball centered at $ (-1.5, 0) $ is $ \bar B_1 $ and the white ellipses are the graphs of $ S(t) $ for different values of the argument. The arrows is the vector field of $ \dot{x} = -\alpha x $ Figure Options Download as PowerPoint slide Figure 2. The parameters $ \phi_0 $ and $ \phi_*. $ Mengyu Cheng, Zhenxin Liu. Periodic, almost periodic and almost automorphic solutions for SPDEs with monotone coefficients. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021026 Yi Guan, Michal Fečkan, Jinrong Wang. Periodic solutions and Hyers-Ulam stability of atmospheric Ekman flows. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1157-1176. doi: 10.3934/dcds.2020313 Rong Chen, Shihang Pan, Baoshuai Zhang. Global conservative solutions for a modified periodic coupled Camassa-Holm system. Electronic Research Archive, 2021, 29 (1) : 1691-1708. doi: 10.3934/era.2020087 Tinghua Hu, Yang Yang, Zhengchun Zhou. 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Electronic Research Archive, , () : -. doi: 10.3934/era.2020119 2019 Impact Factor: 1.27 Lakmi Niwanthi Wadippuli Ivan Gudoshnikov Oleg Makarenkov	CommonCrawl
Types of naming errors in chronic post-stroke aphasia are dissociated by dual stream axonal loss Convergence of heteromodal lexical retrieval in the lateral prefrontal cortex Alexander A. Aabedi, Sofia Kakaizada, … Shawn L. Hervey-Jumper The neural and neurocomputational bases of recovery from post-stroke aphasia James D. Stefaniak, Ajay D. Halai & Matthew A. Lambon Ralph Specific disruption of the ventral anterior temporo-frontal network reveals key implications for language comprehension and cognition Evie Kourtidou, Dimitrios Kasselimis, … Michael Petrides High definition transcranial direct current stimulation modulates abnormal neurophysiological activity in post-stroke aphasia Priyanka P. Shah-Basak, Gayatri Sivaratnam, … Jed Meltzer Language in schizophrenia: relation with diagnosis, symptomatology and white matter tracts J. N. de Boer, M. van Hoogdalem, … I. E. C. 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Helpern1,2,3,7 & Leonardo Bonilha1,2,3 The types of errors during speech production can vary across individuals with chronic post-stroke aphasia, possibly due to the location and extent of brain damage. In this study, we evaluated the relationship between semantic vs. phonemic errors during confrontational naming, and their relationship with the degree of damage to ventral and dorsal white matter pathways extending beyond the necrotic stroke lesion. Based on the dual stream model of language processing, we tested the hypothesis that semantic errors would be associated with ventral stream damage, whereas phonemic errors would be associated with dorsal stream damage, but not vice-versa. Multi-shell diffusion MRI was used to obtain kurtosis-based white matter tractography from 32 chronic stroke survivors. Using diffusion microstructural tissue modeling, we estimated axonal loss along the length of the inferior and superior longitudinal fasciculi (ILF and SLF), representing the main pathways in the ventral and dorsal streams, respectively. The frequency of semantic paraphasias was strongly associated with ILF axonal loss, whereas phonemic paraphasias were strongly associated with SLF axonal loss, but not vice versa. This dissociation between semantic and phonological processing is in agreement with the dual stream model of language processing and corroborates the concept that, during speech production, knowledge association (semantics) depends on the integrity of ventral, whereas form encoding (phonological encoding) is more localized to dorsal pathways. These findings also demonstrate the importance of the residual integrity of specific white matter pathways beyond regional gray matter damage for speech production. Many stroke survivors experience language impairments (aphasia) beyond six months after a dominant hemisphere stroke1. One of the most common and debilitating impairments in individuals with chronic aphasia is the inability to accurately produce language, commonly represented by difficulties in naming objects or actions (anomia)2,3,4. Naming is often assessed in the clinical setting through confrontational naming tests, during which the individual with anomia is either unable to produce the correct name for a target item, or generates words that are related in sound or meaning with the target (paraphasias). Paraphasias are erroneous attempts that relate to the target, but are inaccurate regarding the chosen speech units (phonemic paraphasias), or are real words that relate in meaning to the intended word (semantic paraphasias). For example, when shown a picture of a "pencil", a phonemic paraphasia could be an utterance such as "wencil", whereas a semantic paraphasia could be "pen". Paraphasias offer a critical window into the mechanisms of speech production because they represent discrete deficits regarding (1) the spoken sound structure (phonemic) vs. (2) speech related knowledge association (semantic). They provide the opportunity to determine if these processes dissociate into different anatomic-functional pathways. Notably, they permit the assessment of a recent neurolinguistic theory, the dual stream model of speech processing, which suggests that distinct anatomical streams map phonological and lexical-semantic content retrieval during speech processing5. The model suggests the existence of two streams: a ventral, or "what" stream, which maps between lexical and semantic representations of knowledge associations, and a dorsal, or "how" stream, that maps between auditory and articulatory-motor representations for phonological production. In the context of a naming task, both networks are assumed to participate at integrated different levels of the naming process, lexical-semantic (ventral networks) and phonological encoding (dorsal networks). Paraphasias have been explored in the context of the dual stream model using computer simulations of speech data6, lesion symptom mapping7,8,9,10,11,12,13, and direct electrical cortical and subcortical stimulation in the intra-operative setting14. However, the relationship between residual white matter network integrity, subcortical networks (specifically in relationship to core tracts in the ventral and dorsal streams), and speech production errors is not yet fully defined. Diffusion MRI (dMRI) is ideally suited to study post-stroke residual white matter integrity non-invasively and to test the hypothesis that semantic and phonological processing dissociates between the ventral and dorsal white matter pathways. Specifically, dMRI permits the estimation of the remaining anatomical connections between brain regions through tractography, as well as an assessment of the microstructural integrity of these connections. The quantification of pathway-specific white matter integrity in stroke survivors with chronic aphasia allows for the evaluation of the relationship between regional white matter integrity and specific types of language deficits. This process is analogous to classical neuropsychological approaches which relate brain lesions to behavioral deficits, but it can leverage white matter tractography to identify residual pathways associated with language processing. Moreover, since dMRI also provides measures sensitive to axonal integrity, it can improve the sensitivity in determining which pathways are associated with phonological vs. semantic deficits and resolve the underlying neurobiological mechanisms of regional brain damage that contribute to speech production errors. In contrast with lesion-symptom mapping, which can provide information on damage to white matter regions, without directly testing the integrity of specific pair-wise connections, dMRI can provide information on the integrity and microstructural properties of residual regional connections. The axonal water fraction (AWF), i.e., the ratio of intra-axonal water to total MRI-visible water, reflects axonal density by assessing the portion of tissue water that resides inside axons. Multi-shell dMRI permits an estimation of AWF through the calculation of the diffusional kurtosis by fitting a second-order Taylor expansion to the decay of the logarithm of the dMRI signal as a function of diffusion weighting strength following the theory for diffusional kurtosis imaging (DKI)15,16. Fractional anisotropy (FA) is a dMRI measure more commonly used to investigate white matter microstructure17. However, FA is a generic indicator of diffusion anisotropy18. AWF can indicate brain damage through axonal loss19 and provides information complementary to FA that allows for a more comprehensive quantification of brain tissue properties. More microstructure specific diffusion metrics (e.g. AWF) should be used in conjunction with more traditional metrics (e.g. FA, MD) to enhance our understanding of the mechanisms underlying FA and MD changes, and ultimately brain pathology. In this study, we examined whether the degree of ventral vs. dorsal stream damage dissociates the proportion of phonemic and semantic paraphasias in a group of individuals with chronic aphasia. We employed multi-shell dMRI, DKI post-processing and the quantification of AWF and FA along stream-specific fiber pathways obtained from each individual with aphasia. Tract-specific measures were assessed in relation with paraphasias using multivariate statistical analyses. We hypothesized that in chronic stroke axonal loss, reflected by a decreased AWF in the ventral but not dorsal stream, would directly associate with semantic but not phonological paraphasias and vice versa. We studied 32 participants with chronic post-stroke aphasia (age: 57 ± 11 y, time post-stroke: 35 ± 30 mos, gender: 8 women). All subjects were recruited through local advertisement at the Medical University of South Carolina. They were right-handed native English speakers with a history of a single previous ischemic stroke in the left hemisphere at least 6 months before enrollment. Demographical and behavioral information is presented in Supplementary Table S1. Participants with a history of developmental language disorders, other neurological or psychiatric problems, brain surgery or with seizures during the previous 12 months were excluded. This study was approved by the Institutional Review Boards at the Medical University of South Carolina and the University of South Carolina. Written informed consent was obtained from all participants or their legal guardians. All methods were performed in accordance with guidelines and regulations from our institutions' IRB. Assessment of naming Participants were tested using the Western Aphasia Battery-Revised (WAB-R)20 to screen different language abilities and obtain a global measure of aphasia. The Pyramids and Palm Trees Test (PPT)21 was used to determine semantic knowledge, and the Philadelphia Naming Test (PNT)22 was used to test confrontational naming. The PNT was repeated within one week to determine intra-subject variability. During the PNT, participants had 10 seconds to produce a response. The last complete attempt was used for scoring. Semantic paraphasias were defined as all incorrect real word responses related to the target in meaning. Phonological paraphasias were defined as real word attempts with phonological similarities as well as non-word attempts with incorrect phonemes that preserved more than 50% of the target word. Circumlocutions were scored as no response; dysfluency as articulation errors, and partially phonologically related words were considered to be phonological errors (or, if it was more than 50% different than the target, a neologism). In the case of visual errors (e.g., person says "house" for the "garage"), we redirected the subjects and clarified so they knew which part of the picture to respond to. If the visual errors persisted they were coded as semantic paraphasias. Mixed paraphasias and articulation errors were not included in the analysis. The PNT results from both sessions were averaged, and semantic and phonemic paraphasias were expressed as a percentage of naming attempts excluding the number of no responses since we were interested in semantic and phonemic paraphasias when naming was attempted. All standardized speech and language tests were administered and scored by an experienced American Speech-Language-Hearing Association-certified speech-language pathologist. All participants were scanned on a Siemens 3 T TIM Trio MRI scanner (Siemens Healthcare, Erlangen, Germany) using a 12-channel head coil at the Medical University of South Carolina. Data were acquired in three series, with three degrees of diffusion weighting (b-value = 0, 1000, 2000 s/mm2), using 30 diffusion-encoding directions acquired twice for each b = 1000 and b = 2000, as well as eleven additional images without diffusion weighting (b = 0), for a total of 131 volumes. Additional acquisition parameters were: TE = 101 ms, TR = 6100 ms, 2.7 × 2.7 × 2.7 mm3 isotropic voxels, pixel bandwidth = 1355 Hz/px. All diffusion-weighted images (DWI) were acquired using a twice-refocused gradient scheme to minimize the contributions of eddy currents and without partial Fourier encoding. High resolution 1 mm3 isotropic T2-weighted images were acquired for lesion demarcation utilizing a 3D-TSE SPACE protocol (Field of view (FOV) = 256 × 256 mm2, 160 sagittal slices, TR = 3200 ms, TE = 212 ms, turbo factor = 129, echo trains per slice = 2, echo train duration = 432 ms) and, for anatomical reference, T1-weighted images were gathered using an isotropic 1 mm MPRAGE sequence: FOV = 256 × 256 mm, 9° flip angle, TI = 925 ms, TR = 2250 ms, TE = 4.15 ms. Image data processing The assessment of tract-specific microstructure included the calculation of scalar diffusion metrics along the length of the white matter fibers. The terms fiber or bundle are used here to indicate the deterministic paths identified by diffusion tractography, which are the biophysical representation of large collections of axonal projections in white matter. In this study, we employed three novel forms of structural white matter analyses: (a) patient specific white matter tractography was performed using DKI, a technique that requires a multi-shell diffusion acquisition and dedicated post-processing procedures to improve upon tractography through the delineation of fiber crossings23,24; (b) the integrity of individual fibers was described using microstructural modeling metrics (i.e. AWF) derived from DKI15, which provide a more specific description of the underlying microstructure than conventional dMRI metrics (i.e. FA); and (c) AWF and FA- were assessed in a fine grained pattern along specific tracts, enabling a detailed assessment of where and how post-stroke integrity can affect language. Figure 1 highlights these methodologies; all techniques are explained in further detail below. (A) DKI allows for voxel-wise estimation of the number of fiber directions through the calculation of a kurtosis diffusion orientation distribution function (dODF), while the dODF estimated from DTI provides only a single direction. (B) The AWF is the voxelwise ratio of intra-axonal water (orange) to the total water content (orange + blue). (C) (Left) The ILF estimated using kurtosis-based deterministic tractography with streamlines color-coded according to directionality. (Right) The ILF color-coded according to the underlying AWF values. Augmenting tractography with microstructural information paints a more complete picture of the underlying environment. DKI tractography DKI is an extension of the more conventional diffusion tensor imaging (DTI) method25 that provides a more thorough characterization of white matter microstructure, as well as more accurate fiber tractography16,23. In addition to the standard diffusion measures available with DTI, DKI also estimates the diffusional kurtosis, which quantifies the non-Gaussianity of the underlying water diffusion process16. The dMRI signal model for DTI can be expressed as $$\mathrm{ln}\,S(b)-\,\mathrm{ln}({S}_{0})\approx -\,bD,$$ while the signal model for DKI is $$\mathrm{ln}\,S(b)-\,\mathrm{ln}({S}_{0})\approx -\,bD+\frac{1}{6}{b}^{2}{D}^{2}K,$$ where $\,S(b)$ is the measured dMRI signal at diffusion weighting b,$\,{S}_{o}$ is the signal intensity for b = 0 s/mm2, $D$ is the apparent diffusion coefficient, and $K$ is the apparent diffusional kurtosis. Analogous to the diffusion tensor, a kurtosis tensor, which describes the kurtosis' dependence on direction, can be constructed with DKI16. The kurtosis tensor permits the assessment of the underlying microstructure through scalar metrics of kurtosis, which characterize the complexity of the brain cytoarchitecture, and it provides a voxel-wise description of fiber orientations and their crossings through the calculation of a kurtosis diffusion orientation distribution function (dODF) (Fig. 1)26. This is in contrast to other commonly used methods that more explicitly model fiber crossings (e.g. bedpostX)27. Previous work has demonstrated high sensitivity to pathology when using mean kurtosis as a measure of tissue microstructure28,29,30,31,32,33, as well as tractography that identifies intra-voxel fiber crossings that are not apparent with DTI24. Diffusion and kurtosis tensors were estimated using publicly available post-processing software known as Diffusion Kurtosis Estimator34 (DKE, Medical University of South Carolina, Charleston, USA, https://www.nitrc.org/projects/dke/). To improve the signal-to-noise ratio, raw dMRI images were first denoised using a principal components analysis approach35, and, Gibbs ringing artifacts were removed using the method of Kellner et al.36,37. All DWI acquisitions including the additional images with b = 0 were linearly coregistered between themselves using FSL (FMRIB Software Library v5.0)38 before averaging them into a final set of 61 image volumes which was used as the input for DKE. To localize ventral and dorsal stream white matter, we constructed tractography seed masks for two major components of the dual stream pathway: Inferior Longitudinal Fasciculus (ILF) (ventral stream) and Superior Longitudinal Fasciculus (SLF) (dorsal stream). For each participant, we located the core of each white matter bundle by calculating the intersection between the JHU atlas39 (SLF thresholded at 21% (20/97) and ILF at 25% (20/79)) and a white matter probability mask (thresholded at 50%) created using SPM12, while excluding any lesioned voxels that were drawn on the T2-weighted images. Lesion drawings included the entire post-stroke cavity as well as areas with laminar necrosis and gray and white matter gliosis. Enantiomorphic unified segmentation-normalization40 was employed to calculate the spatial transformation between MNI and native T1-space (Clinical Toolbox, SPM1241) taking into account lesions. This transformation was used to transfer the JHU atlas to native T1-weighted space, while the linear transformation from native T1-weighted to native diffusion space was calculated using FSL (FMRIB Software Library v5.0). The individual ILF and SLF seed masks were used for deterministic kurtosis-based white matter tractography using the FT-toolbox from DKE, which estimates fiber directions from both diffusion and kurtosis tensors. Streamlines were removed when the probability of belonging to a neighboring white matter bundle, defined by the overlap between the streamline coordinates and the JHU ROIs, was larger than the probability of belonging to the target bundle. Additional tractography parameters were FA-threshold = 0.1, angular threshold = 35°, minimum track length = 20 mm, step size = 1 mm and seed number = 1000. White matter lesion overlap was calculated as the cross-section between the manually delineated lesion mask and the third quartile of the JHU SLF and ILF ROIs. The third quartile was chosen to provide an inclusive representation of white matter lesion overlap, i.e., regions of the tract that were damaged. Crucially, all analyses were performed in native diffusion space, reducing interpolation artifacts. Microstructural modeling: Axonal Water Fraction From the kurtosis tensor, it is also possible to calculate information related to specific microstructural compartments (i.e., axonal vs. extra-axonal)15. AWF is a metric, obtained through the white matter tract integrity (WMTI) method, which estimates the relative amount of water inside axons to the total water content within one voxel (Fig. 1)15. Specifically, AWF is estimated by $$AWF=\frac{{K}_{max}}{{K}_{max}+3},$$ where ${K}_{max}$ is the maximal directional kurtosis calculated from the kurtosis tensor over all possible directions. Tissue modelling leverages neurobiological characteristics from tissue structure, which are translated into biophysical properties as follows: (1) axons can be approximated to long impermeable thin cylinders that are mostly coplanar, (2) diffusion in the extra-axonal water pool can be approximated as Gaussian, and 3) water exchange between compartments is negligible during the MRI sampled diffusion time (~50 ms). Except for the coplanarity condition, these are generally accepted properties of white matter that have been assumed in a variety of different tissue modeling approaches42. Because the model requires the axons to be coplanar, Eq. [3] may not be accurate in some white matter regions with complex patterns of fiber crossings15. In summary, we focused on the conventional metric FA, calculated from the diffusion tensor, and the tissue modeling metric AWF, determined from the kurtosis tensor (Eq. [3]). AWF was calculated from the kurtosis tensor using in-house scripts. FA was calculated using a DKI-based approach to improve its accuracy43. Along tract metrics Figure 2 demonstrates how FA and AWF were quantified along the length of two distinct white matter fiber bundles. To enable comparisons between individuals, we isolated the core of each bundle using a methodology based in part on AFQ44. While the AFQ pipeline performs whole brain seeding and uses the JHU atlas to assign each streamline to their respective fiber bundle, we created different seed masks to locate the specific bundles. The isolation of the core was performed based on the methods proposed in the original AFQ description with the exception that a straightforward averaging was used to identify the final values compared to a distance-weighted average in AFQ. Specifically, each subject's fiber bundle was cropped at similar locations employing the JHU-ROIs45, with each streamline being interpolated into 100 equidistant points using cubic B-splines46 (Fig. 2, middle). Cropping provides the streamlines with similar starting and ending points, which facilitates the identification of the core components of each tract. By assessing equivalent segments across patients, it is possible to relate their integrity with individualized naming performance through statistical analyses. AWF and FA values were quantified at each point, but to facilitate statistical analysis, we assigned the average metric to each point along the fiber bundle's geometric mean resulting in 100 values along the length of the ILF and SLF sections that were ultimately binned into 4 segments containing 25 nodes each (Fig. 2, right). In what follows, these midsections will be referred to as the SLF and ILF. Image processing pipeline used to construct the average SLF and ILF for a representative individual. Individual seedmasks (left) for the ILF (beige) and the SLF (pink) were constructed and used as starting points for deterministic tractography. Lesioned voxels (blue) were excluded from each seedmask. The tractography results were cropped (middle), averaged and divided into 4 different segments (right) in each of which we calculated the average AWF. Gray matter necrosis To investigate the interaction between dual stream gray matter necrosis and white matter integrity, we defined three gray matter ROIs: supra-Sylvian language-processing gray matter regions (dorsal stream) infra-Sylvian language-processing gray matter regions (ventral stream) identified using fMRI47 and the SMG. Gray matter necrosis was calculated as the percent overlap between the stroke lesion and the gray matter ROIs as defined by the JHU atlas48. Suprasylvian gray matter included the left posterior middle frontal gyrus (pMFG), the left inferior frontal gyrus (IFG) pars opercularis, the left IFG pars triangular, and the left angular gyrus (AG). Infrasylvian gray matter was composed by the superior temporal gyrus (STG), the pole of the STG, the middle temporal gyrus (MTG), the posterior superior temporal gyrus (pSTG) and the posterior middle temporal gyrus (pMTG). Damage to the SMG was also quantified since it has been implicated in phonological processing8. Lesion locations can be found in Supplementary Fig. 1. We created multiple linear regression models to assess the relationship between paraphasias and integrity of the ventral and the dorsal streams. Specifically, we used the percentage of semantic or phonemic paraphasias as dependent variables in two separate multiple linear regression models with SLF integrity (i.e., AWF and FA), as well as ILF integrity at four distinct tract locations as predictors controlling for white matter lesion overlap. We also assessed whether the inclusion of gray matter damage influenced the model. All reported correlation coefficients are Pearson r. P-values were adjusted using the Bonferroni correction. Fisher r-to-z transformations were performed to investigate if the dissociations between the dorsal and the ventral stream integrity and semantic and phonemic paraphasias were statistically significant. Language tests WAB aphasia quotient (WAB-AQ), aphasia types and average Philadelphia Naming Test results for all individuals are summarized in Supplementary Table S1. Aphasia ranged from severe to mild (WAB-AQ = [20.1–93.7]), with an average (±standard deviation) WAB-AQ of 54.1 (±22.5). During confrontational naming, participants elicited an average of 36.0% (±27.1) correct responses. Incorrect responses were identified as semantic paraphasias 14.7% (±12.5) and phonemic paraphasias 7.1% (±8.3) of the time. The Pyramids and Palm Trees Test [20] demonstrated that the semantic association pathway between pictures and their meaning was relatively preserved in the majority of subjects (45 ± 5). Tract-Based Integrity Analysis As explained in the methods, we used along tract quantification to assess AWF and FA along the longitudinal length of individual fiber bundles in order to provide a more detailed evaluation of tract integrity. Both the residual ILF and SLF were identified in 18 out of 32 subjects, while only the residual ILF was located in an additional 11 subjects. There were no cases where the SLF was not accompanied by the ILF. All subsequent tract-based analyses were performed on these residual connections. Tables 1 and 2 summarize the interactions between 1) the percentage of semantic and phonemic paraphasias and 2) the average AWF (Table 1) and FA (Table 2) at different parts along the ILF and SLF. As described in Table 1, semantic paraphasias had the highest relationship with the average AWF within the posterior portion of the ILF (segment 1: r = −0.67 and segment 2: r = −0.63, p < 0.05 corrected). Figure 3 shows the scatter plots (and their line of best fit with 95% confidence intervals) demonstrating the distribution of the percentage of semantic paraphasias and the AWF from each segment of the ILF. The FA of sections 1, 2 and 3 were also significantly correlated with semantic paraphasias (r = −0.66, r = −0.56 and r = −0.58, p < 0.05 corrected). However, neither AWF nor FA along the length of the SLF was associated with the percentage of semantic paraphasias. Table 1 Summary of all correlation coefficients between average AWF, calculated along the length of the ILF and the SLF, and both phonemic and semantic paraphasias. Table 2 Summary of all correlation coefficients between FA, calculated along the length of the ILF and the SLF, and both phonemic and semantic paraphasias. Scatterplots demonstrating the relationship between AWF and percent semantic paraphasias. Average AWF was calculated for different segments of equal size along the length of the ILF. A significant association was seen between the AWF and semantic paraphasias in the two most posterior segments (I & II; r = −0.67, r = −0.63) (after correction for multiple comparisons). The weak association between semantic paraphasias and the SLF diffusion measurements was not related to the smaller sample size of SLF compared to ILF (18 vs. 29). For a similar r-value (0.67), the statistical power from n = 29 to n = 18 drops from 0.98 to 0.88. We performed 1000 random sampling of the ILF with n = 18, the average r-value was 0.65, and r = 0.21 was below the 99th percentile of this sample. For this reason, the relationship between the SLF and semantic paraphasias was not significant taking into account the smaller sample size. In addition, Fisher r-to-z demonstrated that the AWF within the ILF (segment 1) related more strongly to semantic paraphasias than the AWF within the SLF (segment 1) (p < 0.05). Phonemic paraphasias had the most significant association with the average AWF within the most posterior part of the SLF (segment 1: r = −0.68, p < 0.05) (Table 1). The distribution of phonemic paraphasia prevalence and average AWF calculated from the different parts of the SLF is depicted in Fig. 4. The FA of segment 1 was weakly associated with phonemic paraphasias, albeit not surviving correction for multiple comparisons (r = −0.46, p > 0.05). The percentage of phonemic paraphasias was not related to any of the diffusion metrics calculated from the ILF. Fisher r-to-z transformations confirmed that phonemic paraphasias were more associated with AWF within segment 1 of the SLF than within segment 1 of the ILF (p < 0.05). Scatterplots demonstrating the relationship between AWF and percent phonemic paraphasias. Average AWF was calculated for different segments along the length of the SLF. A significant association was seen between the AWF and phonemic paraphasias in the two most posterior segments (I; r = −0.68) (after correction for multiple comparisons). It is important to highlight that ILF lesion burden was associated with the percentage of semantic paraphasias (r = 0.56, p < 0.05). Therefore, to exclude this potential confounder from the analyses relating paraphasias with tract-based microstructure, we recalculated the linear models described above (whose r and p values mentioned above did not control for lesion burden) now controlling for lesion overlap with the ILF and SLF. This stricter analysis resulted in two remaining significant correlations between 1) the average AWF in segment 1 of the ILF and the percentage of semantic paraphasias (r = −0.49, p < 0.05) and 2) the average AWF in segment 1 of the SLF and the percentage of phonemic paraphasias (r = −0.65; p < 0.05). AWF and FA were strongly correlated (ILF: r = 0.81, p < 0.05; SLF: r = 0.74, p < 0.05), but stepwise regression (based on an F-test of the change in the sum of squared error by adding a term) using AWF, FA, and lesion overlap as input variables resulted in a final linear model with AWF as the only variable. Impact of gray matter necrosis The degree of infra-Sylvian gray matter necrosis was associated with the frequency of semantic paraphasias made during confrontational naming (r = 0.42, p < 0.05). However, when correcting gray matter damage for the average AWF of the posterior ILF (segment 1), the relationship did not exceed statistical significance. Conversely, a statistically significant relationship between the AWF of the posterior ILF and semantic paraphasias (r = −0.67, p < 0.05) remained when adjusting for infra-Sylvian gray matter necrosis (r = −0.55 p < 0.05). Supra-Sylvian specific gray matter was not related to percent phonemic paraphasias and thus did not alter the relationship between the AWF of the SLF and phonemic paraphasias. Note that the AWF calculated from SLF's segment 1 was associated with supra-marginal gyrus (SMG) necrosis (−0.55, p < 0.05); however, SMG necrosis only weakly related to the percentage of phonemic paraphasias (r = 0.31, p = 0.21). In this study, we examined the importance of residual white matter pathways supporting semantic and phonological processing during confrontation naming in individuals with chronic post-stroke aphasia. We used advanced dMRI post-processing techniques to trace representative large pathways in the ventral and dorsal streams (ILF and SLF, respectively) and to measure a microstructural property of axonal integrity (AWF) along the fibers in each tract. Our results indicated a double dissociation between white matter axonal loss and semantic vs. phonemic naming impairments: AWF in the ILF (particularly in the posterior aspect of the tract) was associated with the number of semantic paraphasias, but not with the number of phonemic paraphasias. Conversely, AWF in the SLF (also more strongly in the posterior aspect of the tract) was related to the number of phonemic paraphasias, but not with the number of semantic paraphasias. These findings are in line with the dual stream model of language, which proposes the presence of functionally and anatomically distinct processing routes for lexical access (i.e., ventral stream) and phonological form encoding (i.e., dorsal stream). Importantly, they provide anatomical confirmation at the white matter network level and complement existing lesion based studies, which mostly focus on regional damage, not residual white matter connections. Moreover, these results also provide information on the relevance of the biological nature of damage, i.e., axonal loss, and their location within the white matter tracts. Multiple studies have demonstrated that regional post-stroke brain damage can be associated with naming errors, with damage to dorsal regions relating mostly to phonemic paraphasias, and damage to ventral regions predominantly associated with semantic paraphasias. Figure 5 demonstrates the positioning of the ILF and SLF relative to the gray matter regions most often implicated in naming impairments. Different studies have reported that semantic errors are related to lesion involvement of the temporal pole7,9, the inferior temporal gyrus49, as well as different portions (anterior, mid and posterior) of the MTG7,8,10,11,50. Taken together, it is possible that the intactness of these areas, in combination with the successful integration within the language network is required for unimpaired lexical access. The association between neuronal damage and word production errors has recently been further explored in relation to the Dell speech production model50. It is important to note that these studies did not focus on the residual integrity of the white matter as quantified by diffusion MRI, but instead focused on lesion location using structural MRI. We believe that our results complement their conclusions highlighting the importance of residual white matter integrity in concordance with cortical and white matter damage as shown on structural MRI. Left: Semantic paraphasias have been associated with damage to a multitude of temporal gray matter regions (e.g., TP, STG, ITG, and MTG)52,8,9,11,49,56. Here, we demonstrated that axon density of the ILF relates to the frequency of semantic paraphasias in individuals with post-stroke aphasia. The ILF interconnects these gray matter regions51 likely supporting parts of a semantic network12. Right: Damage to the PrCG, PoCG and the SMG has been shown to result in phonemic paraphasias7,8,12,13. These areas are interconnected primarily through the SLF and arcuate fasciculi, which bridge perisylvian frontal, parietal, and temporal cortices. A greater degree of axonal loss in the posterior SLF related to a larger number of phonemic paraphasias. TP = Temporal Pole, STG = Superior Temporal Gyrus, ITG = Inferior Temporal Gyrus, MTG = Middle Temporal Gyrus, PrCG = Precentral Gyrus, PoCG = Postcentral Gyrus, SMG = Supramarginal Gyrus. The ILF, whose fibers link the superior- middle- and inferior temporal gyri51, has been suggested by task-based functional MRI studies to support such a semantic network12,52. Phonology and articulatory representations are supported by the dorsal stream, and damage to the SMG and post-central gyrus has especially been related most frequently to impaired phonological encoding7,8,12,13. Schwartz et al. postulated in a structural voxel-based lesion-symptom mapping analysis that phonological paraphasias might also arise from damage to dorsal stream white matter pathways8. Here, we directly located the residual white matter pathways using dMRI, and demonstrated that the axon density of the residual SLF indeed relates to the frequency of phonemic paraphasias, confirming the hypothesis by Schwartz et al. In addition, we also demonstrated that the degree of axonal loss of the residual ILF relates with semantic paraphasias during confrontational naming, independent of the degree of damage to the MTG. Our results provide evidence that damage to the gray matter regions as well as the integrity of the remaining connections between them should be considered when studying naming impairments after stroke. More specifically, damage to the brain at the white matter network level can directly influence ventral and dorsal stream processing and lead to speech production errors. In comparison with the existing literature, this is the main novel finding from this study. It is important to note that the diffusion imaging methods used in this study are relatively different from conventional fiber tracing methods53. We employed an approach to best define the integrity of the residual white matter networks in stroke survivors and elucidate the nature and location of the white matter post-stroke damage. The specific innovations of the methods used here are threefold: 1) the use of DKI to track white matter fibers and ameliorate tracing inaccuracies in areas of fiber crossing or complex curvature; 2) the use of DKI tissue modeling (i.e., WMTI) to approximate axonal loss (AWF); and 3) the quantification of microstructural tissue properties along the main axis of each tract. This allows for the direct assessment of the local integrity of specific tracts since it entails the actual tracing of each tract in each individual. Since tracts can follow unusual paths in lesioned brains, scalar diffusion metrics obtained from ROI or skeletonized based analyses, without tracing connections, could miss important individual details. Studying changes along the main axis of the fibers was pioneered through a technique known as automated fiber quantification (AFQ)44, which is particularly useful when disease affects different parts of a fiber bundle to a different degree or when different segments of white matter pathways are composed of branches to different parts of gray matter. In a recent study, we used AFQ and demonstrated that aphasia recovery mediated plasticity varies along the length of a specific tract33. Here, we used the same principles of AFQ to determine AWF along the tracts, and we observed that damage to the posterior parts of the ILF and the SLF was more significantly associated with paraphasias highlighting the importance of local white matter integrity. While the explanation for these observations remains unclear, it may be related to the regional integration performed by these parts of the ILF, and SLF, with their posterior relationship to somatosensory processing areas in the temporal-parietal region, such as area Spt54. Alternatively, information transmission could preferably flow posteriorly to anteriorly where damage to segment 1 would impact the functioning of the downstream segments 2, 3, and 4. Lastly, it could be due to the posterior parts being more commonly lesioned after middle cerebral artery strokes and thereby strengthening the statistical association between damage and paraphasias in those areas. From our findings, we can conclude that posterior damage to either stream is a strong marker of paraphasias, but a more detailed dissection focusing on the regions connected by the specific streams is necessary. It is a limitation of this study that only the ILF and the SLF were studied in a small number of cases without the assessment of other tracts and other naming errors related to the multiple subnetworks that form the dual stream system. It is important to emphasize that the nomenclature of white matter fibers is inconsistent throughout the literature (e.g., arcuate fasciculus vs. SLF). In this paper, the names ILF and SLF were chosen in accordance with the John-Hopkins University (JHU) atlas labeling convention used to seed the tracks. The SLF, however, likely includes fibers from both the SLF and the arcuate fasciculus, since no filtering algorithm based on fiber curvature was implemented. Similarly, the posterior location of the ILF also highly overlaps with the location of the IFOF. A thorough dissection of the tracks is however beyond the scope of this paper, and future work should focus on studying white matter connections between specified gray matter regions. Another caveat would be that the AWF is based on assumptions and simplifications about the properties of axons. For example, the WMTI model assumes that in a voxel all axons lie in the same plane, which might be more or less accurate in different locations15. In lesioned brains, extra-cellular and glial changes could add confounders, but these are likely less pronounced in chronic strokes, where the brain parenchyma is more stable and inflammatory responses and edema are minimal. Regardless, the metric will always represent a specific property of the underlying water diffusion processes, albeit not necessarily the axon density. Finally, a decrease in AWF could also be related to an increase in water in the extra-axonal compartment. However, that seems unlikely to occur in isolation without the loss of any axons. Note that the same error types have been associated with more than one cause and revealing a one to one relationship between brain damage and paraphasias would be unrealistic55. Future work should focus on determining the integrity of the entire dual stream system and on studying the relationship between its residual structure and naming performance. Studying additional error types and further subcategorizing semantic and phonemic paraphasias might provide additional information about the origin of naming errors in post-stroke aphasia56,57. In summary, our results are in concordance with the dual stream model of language processing and further corroborates the notion that, during speech production, knowledge association (semantics) depends on the integrity of ventral, whereas form encoding (phonemics) is localized to dorsal pathways. 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This study was supported by research grants from the National Institutes of Health / National Institute on Deafness and Other Communication Disorders (NIDCD): DC014021 (PI: LB), DC011739 (PI: JF), DC014664 (PI: JF), R01 DC05375 (PI: AH); T32 DC0014435 (Trainees: EM, AB); The American Heart Association: SFDRN26030003 (PI: LB) and The Litwin Foundation (PI: JH). Department of Neurology, Medical University of South Carolina, 96 Jonathan Lucas St, Charleston, SC, 29425, USA Emilie T. McKinnon, Ezequiel Gleichgerrcht, Joseph A. Helpern & Leonardo Bonilha Center for Biomedical Imaging, Medical University of South Carolina, 96 Jonathan Lucas St, Charleston, SC, 29425, USA Emilie T. McKinnon, Jens H. Jensen, Joseph A. Helpern & Leonardo Bonilha Department of Neuroscience, Medical University of South Carolina, 173 Ashley Avenue, Charleston, SC, 29425, USA Department of Communication Sciences and Disorders, University of South Carolina, 921 Assembly Street, Columbia, SC, 29208, USA Julius Fridriksson & Alexandra Basilakos Department of Cognitive Sciences, Center for Language Science and Center for Cognitive Neuroscience, University of California, 2201 Social & Behavioral Sciences Gateway Building, Irvine, CA, 92697, USA Gregory Hickok Department of Neurology, Johns Hopkins University, 725 N Wolfe St, Baltimore, MD, 21205, USA Argye E. Hillis Department of Radiology and Radiological Science, Medical University of South Carolina, 96 Jonathan Lucas St, Charleston, SC, 29425, USA M. Vittoria Spampinato, Jens H. Jensen & Joseph A. Helpern Department of Psychology, University of South Carolina, 1512 Pendelton Street, Columbia, SC, 29208, USA Chris Rorden Emilie T. McKinnon Julius Fridriksson Alexandra Basilakos M. Vittoria Spampinato Ezequiel Gleichgerrcht Jens H. Jensen Joseph A. Helpern Leonardo Bonilha L.B., C.R., J.J., J.H. and J.F. designed the experiment E.M., L.B., E.G., A.B., A.H., G.H. and V.S. aided in data collection and analysis. L.B. and E.M. wrote the main manuscript text. E.M. prepared the figures. All authors reviewed the manuscript. Correspondence to Leonardo Bonilha. Drs Jensen and Helpern have patents related to diffusional kurtosis imaging and white matter tractography (US 8,811,706, US 9,478,026). However, all imaging and post-processing techniques used in this paper did not require proprietary software and are available to the research community. McKinnon, E.T., Fridriksson, J., Basilakos, A. et al. Types of naming errors in chronic post-stroke aphasia are dissociated by dual stream axonal loss. Sci Rep 8, 14352 (2018). https://doi.org/10.1038/s41598-018-32457-4 Chronic Post-stroke Aphasia Dual Stream Model Phonemic Paraphasia Semantic Paraphasia Dorsal Stream Evie Kourtidou Dimitrios Kasselimis Michael Petrides Communications Biology (2022) The Role of Cortico-Thalamo-Cortical Circuits in Language: Recurrent Circuits Revisited Bruce Crosson Neuropsychology Review (2021) The utility of lesion classification in predicting language and treatment outcomes in chronic stroke-induced aphasia Erin L. Meier Jeffrey P. Johnson Swathi Kiran Brain Imaging and Behavior (2019)	CommonCrawl
Analysis and modeling for illuminance and signal-to-noise of smart traffic information system Yaoting Chen1,2 & Huanting Chen3 The traffic lights using by light emitting diode (LED) are able to indicate and provide the information about the ambient. The signal transimission performance of traffic system is related to a variety of factors such as the signal-to-noise ratio (SNR), illuminance. Several factors are influence on illumiance and SNR, such as eatsink temperature and driver parameters. It has not been any substantial investigate on the operated effects of traffic light with sinusoidal waveform driver on illuminance and SNR. With the use of heatsink temperature and driver parameters of the LED source with sinusoidal waveform driver, prediction modeling for the illuminance and SNR of the mixed white LED sources with heatsink temperature, frequency, amplitude voltage, bias voltage and amplification factors are proposed in this paper to enhance the illuminance and SNR model of LED source inside smart traffic information system. The proposed model should carry out a series of calibration step for illuminance, heatsink temperature and driver parameters, which are easy for traffic designer and source system designers to follow in the traffic information system. The proposed model has been measured for the mixed white LED sources, with reasonably good agreements between theoretical and practical results. The main advantages of traffic lights with LED application are better luminous efficiency and reliability, compared to incandescent-based traffic lights. Traffic flow can be controlled using by traffic lights [1]. For a given location, the traffic lights are able to indicate and provide the information about the ambient. In existing traffic information systems, the signals of traffic light are used to transmit traffic message using by display traffic jam on a map. Flicker is dependent on operated parameters of LED source, such as spectrum, frequency, bias voltage, amplitude factor, voltage amplitude, and distance [2, 3]. The signal-to-noise ratio (SNR) is a key factor of the signal transmission of smart traffic information system. The signal transimission performance of traffic system is related to a variety of factors such as the SNR, illuminance and frequency [4]. The value of SNR is 15 dBs for minimum acceptable range of traffic information application [5]. However, it is incorrect to assume that the SNR is constant in smart traffic system applications. It should point out that both of the light output of traffic application are sensitive to the operated conditions of LED sources. The light output of LED source with forward voltages and frequency were compared to evaluate the effects of the electrical properties on the SNR [6]. Several factors are influence on signal transmission of traffic information system. These factors include heatsink temperature and driver parameters, which is not considered into the system modeling. SNR is a key parameter of smart traffic information applications; however, it has not been any substantial investigate on the operated effects of traffic light with sinusoidal waveform driver on illuminance and SNR. Flicker for traffic lights is highly dependent on the driver operation. A periodic waveform is dependent on seveal parameters, such as voltage amplitude, duty cycle, frequency etc. Therefore, the properties of a sinusoidal waveform can be determined as bias voltage, amplitude voltage, frequency and amplification factors. The properties of a sinuoidal waveform influences on human eye response. If frequencies is higher than 70 Hz, obvious detection of light flicker can cause uncomfortable symptoms of human beings [7]. Flicker also can be observed in signal transmission when the traffic light interacts with moving objects. It is important mentioned that many light sources inside smart traffic information system display obvious flicker. Reduction flicker of light sources inside traffic information system is using by electronic solutions, which is major cause of lower power efficiency [8]. Reduction flicker of light source can also acquire using by slow-decay phosphors [9]. The optical variation performance of LED source with sinusoidal waveform driver in smart traffic information system is not well understood. In practice, the electronic engineer or the signal designers are not familiar with optical controll for LED application with luminous efficiency, color characteristics, and reliability design. The practical performance of the mixed light output of the mixed white LED source with a warm white LED and a cool white LED under sinusoidal waveform driver is investigated. The proposed model includes the variations on the heatsink temperature, bias voltage, amplitude voltage, frequency and amplification factors. The proposed model can estimate the illuminance and SNR with different heatsink temperature and driver parameters that cannot be easily evaluated in practice. The proposed model cover extends the illuminance and SNR of LED source inside smart traffic information system to include the key parameters of sinusoidal waveform. It is pointed out that the proposed model can be used as a design tool for traffic designs. The work is important to signal transmission of smart traffic information system designers because the operating temperature and driver parameters of LED sources may change. Smart traffic information system transmits information from light source to detector. The most important ability of smart traffic information system is to detect signals including given information with background noise [10, 11]. Traffic light can be used for signal transmission based on vehicle infrastructure system. The network of smart traffic information includes left turn assistant, lane change warning, and pre-cash sensing [3, 12, 13], as shown in Fig. 1. Network of smart traffic information system The SNR is related to the acquired light power, which means that smart traffic information system perform high signal transmission mass with low signal loss. The noise sources of smart traffic information system are critical factors of signal distortion performance. The LED should be used as signal transmission and lighting application. The illuminance, heatsink temperature and driver parameters of LED systems are highly related to each other. Modelling of the photometric, electric, thermal and colorimetric aspects of white LED devices is proposed [14]. The photo-electro-thermal (PET) theory has provided a series studying for the white LED system. There are given technical specifications for LED systems based on Energy Star Program and IEC standards [15, 16]. The proposed new PC-LED model considered several factors, such as energy-storage and dynamic properties of the phosphor coating. This new model can accurately predict dynamic optical and energy loss in PC LED device [17, 18]. Normally, the illuminance is dependent on the heatsink temperature, voltage amplitude, and bias voltage. The relationship is reflected on the heatsink temperature and illuminance of LED with the constant voltage amplitude and bias voltage as shown in Fig. 2. LED sample is mounted on a temperature-controllable heatsink. The illuminance as a function of the heatsink temperature for constant LED voltage amplitude and bias voltage operation is fairly linear. Therefore, the illuminance of LED as a function of the heatsink temperature Ths for constant LED voltage amplitude Va,0 and bias voltage Vb,0 operation can be approximated as a linear relationship. $$E\left({T}_{\mathrm{hs}},{V}_{\mathrm{a},0},{V}_{\mathrm{b},0}\right)={a}_1{T}_{\mathrm{hs}}+{a}_2$$ Illuminance versus heatsink temperature of LED device under "constant voltage amplitude and constant bias voltage" operation Where α1 is a constant representing the slop and α2 is another constant. Both α1 and α2 can be obtained from the measurement in Fig. 2. Using the Everfine LFA-3000 light flicker analyzer system, the practical measurements of the illuminance as a function of the LED voltage amplitude under "constant heatsink temperature and constant bias voltage" operation are obtained and shown in Fig. 3. Therefore, it is can be given as $$E\left({V}_a,{T}_{\mathrm{hs},0},{V}_{b,0}\right)={\beta}_1{V_a}^2+{\beta}_2{V}_a+{\beta}_3$$ Illuminance versus voltage amplitude of LED device under "constant heatsink temperature and constant bias voltage" operation Where β1, β2, and β3 are coefficients that can be extracted from Fig 3 with constant heatsink temperature and bias voltage. Based on the above analysis, E can be obtained as heatsink temperature Ths and voltage amplitude Va with constant bias voltage using a two-dimensional mathematical function. Similar modeling method based on the 2D linear behavior has been proposed to [14]. Therefore, the illuminance E can be constructed as in the following $$E\left({V}_a,{T}_{\mathrm{hs}},{V}_{b,0}\right)=\frac{E\left({T}_{\mathrm{hs}},{V}_{\mathrm{a},0},{V}_{\mathrm{b},0}\right)E\left({V}_a,{T}_{\mathrm{hs},0},{V}_{b,0}\right)}{c_1}$$ Where c1 is intersection values of (1) and (2). It should be pointed out that the model can predict the illuminance of the LED at any heatsink temperature and voltage amplitude with constant bias voltage. Equation (3) links the illuminance to heatsink temperature and voltage amplitude together under constant bias voltage operation. The illuminance of the LED device is highly related to the bias voltage. To establish the dependence on illuminance E on the bias voltage, the LED device is operated in the bias voltage 1 to 5 V under constant heatsink temperature Ths,0 and constant voltage amplitude Va,0 operation. Generally, illuminance E obviously increases with bias voltage, as shown in Fig. 4. The theoretical model of the illuminance behavior as quadratic function of the bias voltage is indicated in Fig. 4, as shown in the following. $$E\left({V}_b,{A}_{a,0},{T}_{hs,0}\right)={\chi}_1{V_b}^2+{\chi}_2{V}_b+{\chi}_3$$ Illuminance versus bias voltage of LED device under "constant voltage amplitude and constant heatsink temperature" operation Where χ1, χ2, and χ3 are coefficients that can be extracted from the experimental results in Fig. 4. Combined with (3) and (4), the behavior of the illuminance of the LED is given by 3-D nonlinear function, as shown in (5), where c2 is the intersection value of function of (3) and (4). It is a model that combines the heatsink temperature Ths, amplitude voltage Va and bias voltage Vb aspects of an LED source. $$E\left({V}_a,{T}_{\mathrm{hs}},{V}_b\right)=\frac{E\left({T}_{\mathrm{hs}},{V}_{\mathrm{a},0},{V}_{\mathrm{b},0}\right)E\left({V}_a,{T}_{\mathrm{hs},0},{V}_{b,0}\right)E\left({V}_b,{A}_{a,0},{T}_{hs,0}\right)}{c_2}$$ The experimental results of the illuminance behavior of the LED are related to bias voltage with constant amplification factors and frequency. It can be seen that illuminance curve is similar with Fig. 4. In practice, the illuminance E is approximately nonlinearly proportional to the bias voltage Vb at constant amplification factors Af,0 and constant frequency f0, so it can be given as $$E\left({V}_b,{A}_{\mathrm{f},0},{f}_0\right)={\delta}_1{V_b}^2+{\delta}_2{V}_b+{\delta}_3$$ Where δ1, δ2, and δ3 are coefficients that can be extracted from experimental results of the illuminance as a function of the LED bias voltage with constant amplification factors and frequency. Figure 5 shows the practical measurements of the illuminance E as a function of the LED amplification factors Af, with constant bias voltage Vb,0 and constant frequency f0. Therefore, the illuminance can be expressed as $$E\left({A}_{\mathrm{f}},{V}_{b,0},{f}_0\right)={\varepsilon}_1{A}_{\mathrm{f}}+{\varepsilon}_2$$ Illuminance versus amplification factors of LED device under "constant bias voltage and constant frequency" operation Where ε1 and ε2 are coefficients that can be extracted from Fig. 5. Based on the above analysis, E can be related to amplification Af and bias voltage Vb using a two-dimensional function. Combined (6) and (7), illuminance of the LED device with bias voltage and amplification factors with constant frequency can be given as $$E\left({A}_{\mathrm{f}},{V}_b,{f}_0\right)=\frac{E\left({A}_{\mathrm{f}},{V}_{b,0},{f}_0\right)E\left({A}_{\mathrm{f},0},{V}_b,{f}_0\right)}{c_3}$$ Where c3 is intersection values of (6) and (7). It should be pointed out that this model can estimate the illuminance variation of the LED at any bias voltage and amplification factors with constant frequency. Equation (8) links the illuminance to bias voltage and amplification factors together. Figure 6 shows the practical measurements of the illuminance E as a function of the LED frequency f with constant bias voltage Vb,0 and constant amplification factors Af,0. Therefore, the illuminance can be expressed as $$E\left({A}_{\mathrm{f},0},{V}_{b,0},f\right)={\mu}_1{f}^2+{\mu}_2f+{\mu}_3$$ Illuminance versus frequency of LED device under "constant bias voltage and constant amplification factors" operation Where μ1, μ2, and μ3 are coefficients that can be extracted from the practical measurements of the illuminance as a function of the frequency with constant amplification factors and bias voltage, as shown in Fig. 6. Combined with (8) and (9), illuminance of the LED device with bias voltage, amplification factors and frequency can be given as $$E\left({A}_{\mathrm{f}},{V}_b,f\right)=\frac{E\left({A}_{\mathrm{f},0},{V}_{b,0},f\right)E\left({A}_{\mathrm{f}},{V}_{b,0},{f}_0\right)E\left({A}_{\mathrm{f},0},{V}_b,{f}_0\right)}{c_4}$$ Where c4 is intersection values of function of (8) and (9). It should be pointed out that this equation can estimate the illuminance of the LED at any bias voltage, amplification factors and frequency. Equation (10) links the illuminance to bias voltage, amplification factors and frequency together. Combined with (5) and (10), the illuminance as function of the LED device with five-dimensional parameters can be determined as $${\displaystyle \begin{array}{l}E\left({V}_a,{T}_{\mathrm{hs}},{V}_b,{A}_f,f\right)=\frac{\left[\frac{E\left({T}_{\mathrm{hs}},{V}_{\mathrm{a},0},{V}_{\mathrm{b},0}\right)E\left({V}_a,{T}_{\mathrm{hs},0},{V}_{b,0}\right)E\left({V}_b,{A}_{a,0},{T}_{hs,0}\right)}{c_2}\frac{E\left({A}_{\mathrm{f},0},{V}_{b,0},f\right)E\left({A}_{\mathrm{f}},{V}_{b,0},{f}_0\right)E\left({A}_{\mathrm{f},0},{V}_b,{f}_0\right)}{c_4}\right]}{c_5}\\ {}=\frac{\left[\frac{E\left({T}_{\mathrm{hs}},{V}_{\mathrm{a}},{V}_{\mathrm{b}}\right)}{c_2}\frac{E\left({A}_{\mathrm{f}},{V}_b,f\right)}{c_4}\right]}{c_5}\end{array}}$$ Therefore, the overall illuminance of a mixed white LED device Et(Va,t,Ths,t,Vb,t,Af,t, ft) with a cool white LED and a warm white LED is shown as Eq. (12) $${\displaystyle \begin{array}{l}{E}_t\left({V}_{a,t},{T}_{\mathrm{hs},\mathrm{t}},{V}_{b,t},{A}_{f,t},{f}_t\right)={E}_c\left({V}_{a,c},{T}_{\mathrm{hs},\mathrm{c}},{V}_{b,c},{A}_{f,c},{f}_c\right)+{E}_w\left({V}_{a,w},{T}_{\mathrm{hs},\mathrm{w}},{V}_{b,w},{A}_{f,w},{f}_w\right)\\ {}=\frac{\left[\frac{E_c\left({T}_{\mathrm{hs},\mathrm{c}},{V}_{\mathrm{a},\mathrm{c}},{V}_{\mathrm{b},\mathrm{c}}\right)}{c_{2,\mathrm{c}}}\frac{E\left({A}_{\mathrm{f},\mathrm{c}},{V}_{b,c},{f}_c\right)}{c_{4,\mathrm{c}}}\right]}{c_{5,c}}+\frac{\left[\frac{E_w\left({T}_{\mathrm{hs},\mathrm{w}},{V}_{\mathrm{a},\mathrm{w}},{V}_{\mathrm{b},\mathrm{w}}\right)}{c_{2,\mathrm{w}}}\frac{E\left({A}_{\mathrm{f},\mathrm{w}},{V}_{b,w},{f}_w\right)}{c_{4,\mathrm{w}}}\right]}{c_{5,w}}\end{array}}$$ Where Φc(Va,c,Ths,c,Vb,c,Af,c,fc) is individual illuminance of the cool white LED and Φw(Va,w,Ths,w,Vb,w,Af,w, fw) is individual illuminance of the warm white LED. Several important observations should be pointed out from Eq. (12): Equation (12) relates the illuminance to the heatsink temperature Ths, frequency f, amplitude voltage Va, bias voltage Vb and amplification factors Vf altogether. It is an equation that integrates the heatsink temperature and driver parameters of the LED device altogether. LED device manufactures can use heatsink temperature Ths, frequency f, amplitude voltage Va, bias voltage Vb and amplification factors Vf in Eq. (12) to quantify the overall illuminance of a mixed white LED device. This new equation quantitatively sums up the relationship of illuminance, heatsink temperature Ths, frequency f, amplitude voltage Va, bias voltage Vb and amplification factors Vf. The required parameters of the proposed model are calibrated from a series of measurement as shown in Figs. 2, 3, 4, 5, and 6. In the experiments, a cool white LED (CREE-XPE 1W) and a warm white LED (CREE-XPE 1W) making up the mixed white LED sources is mounted on a temperature-controllable heatsink. The rated CCT of the cool white and warm white LED are 5000 K and 2900 K respectively. The descriptions have been added above Fig. 7. Figure 7 shows the schematic of experimental setup. The light flicker analyzer (FA-3000) shows the waveform of the light output of the LED system with a sinusoidal wave of a given parameters (frequency: 100 Hz, heatsink temperature: 25 °C, amplitude voltage: 6 V, bias voltage: 2 V, amplification factors: 5 dB). A high power mixed white LED was electrically driven with different heatsink temperature. A wide band amplifier (Texas Instruments ATA-122D) adds the signal function (Gigol DG5071) to the DC component coming from DC power supply. The signal amplifying function with high speed is injected into the LED. The light output of the LED was captured from detector (FA-3000). The heatsink temperature is from 25 °C to 85 °C. The voltage amplitude is from 5 V to 9 V. The bias voltage is from 1 V to 5 V. The amplification factors are from 4.5 to 7.5. The frequency is from 100 Hz to 2000 Hz. Schematic of experimental setup The illuminances of LED source are measured through the dark-tube, as shown in Fig. 7. The LED source is connected to photodetector by the dark-tube. The distance between the source and photo detector is 20 cm. Therefore, the environments have not influence on measured results of photodetector. The measured optical performance of the mixed white LED source is dependent on the responsivity for the photodetector and the spectral power distribution of the LED source. Fig 8 shows responsivity of the photodetector and spectral power distribution of LED source with different current. It is clearly shows that the responsivity for the photodetector is different from wavelength distribution. The spectral power distribution of LED source exhibit variation due to thermal and electrical factors. As shown in Eqs. (1) and (12), the signal-to-noise ratio and illuminance of the LED source is highly related to spectral power distribution of LED source. Responsivity of photodetector and the spectral power distribution of the white LED sources with electrical-thermal effects The illuminance of cool white LED and warm white LED is measured at different heatsink temperature Ths, frequency f, amplitude voltage Va, bias voltage Vb and amplification factors Vf. The required coefficients of cool white LED and warm white LED in Eq. (12) can be extracted in Tables 1 and 2. Table 1 Required coefficients for proposed model of cool white LED Table 2 Required coefficients for proposed model of warm white LED Putting coefficients of Tables 1 and 2 into Eq. (12), the theoretical illuminance Et(Va,t,Ths,t,Vb,t,Af,t,ft) with different heatsink temperature Ths, frequency f, amplitude voltage Va, bias voltage Vb and amplification factors Vf can be determined. The illuminance is measured at different operation conditions. The theoretical and measured illuminance curves are measured and shown in Figs. 9, 10, and 11. The theoretical results have good agreement with experiment result in Fig. 9 for a set of heatsink temperature, voltage amplitude, and bias voltage. The average deviation between the calculations and the measurements are about 7.9%. The maximum deviation between the calculations and the measurements are 13.6%. For experiments, a temperature-controlled heatsink is adjusted to control heatsink temperature of LED sample. The LED sources consist of multiplicity conductor materials. The temperature-controlled heatsink could not provide high-precision control on the junction temperature. It means that the practical junction temperature may be lower than target value due to imperfect heat flow path. That is major cause of errors between the calculations and measurements of Fig 9. a Calculated illuminance of the mixed white LED source with heatsink temperature, bias voltage, and voltage amplitude. b Measured illuminance of the mixed white LED source with heatsink temperature, bias voltage, and voltage amplitude a Calculated illuminance of the mixed white LED source with amplification factor, bias voltage, and voltage amplitude. b Measured illuminance of the mixed white LED source with amplification factor, bias voltage, and voltage amplitude a Calculated illuminance of the mixed white LED source with frequency, bias voltage, and voltage amplitude. b Measured illuminance of the mixed white LED source with frequency, bias voltage, and voltage amplitude Based on coefficients in the Tables 1 and 2, the illuminance of the mixed white LED as a function of amplification factor, bias voltage and voltage amplitude is calculated using (12) and plotted in Fig. 10. In general, the calculated results are consistent with the practical measurements. The average deviation between the theoretical and experimental results is about 8.9%. The measured and calculated illuminance of the mixed white LED source with frequency, bias voltage and voltage amplitude are shown in Fig. 11. The theoretical curves of illuminance are in good agreement with the measured ones. Given a constant bias voltage 4 V and voltage amplitude 5 V, it is important to note that at a controlled frequency of 100 Hz, illuminance is about 985.5 lx. When the frequency is 1000 Hz, illuminance decreases to 860.5 lx. It is noted that illuminance decreases with increasing operating frequency under constant power. Figure 12 shows the calculated and measured SNR of the mixed white LED sources with frequency, bias voltage and voltage amplitude. The calculated values using the proposed model are generally consistent with the measurements. The average deviation between the theoretical and experimental results is about 13.5%. The variation SNR of the mixed white source with the bias voltage of 1V and voltage amplitude of 5 V is about 10.1% from frequency of 100 Hz to 2000 Hz. It is noted that the variation of SNR with frequency and voltage amplitude are kept within obvious ranges. a Calculated SNR of the mixed white LED source with frequency, bias voltage and voltage amplitude. b Measured SNR of the mixed white LED source with frequency, bias voltage and voltage amplitude Currently, the LED optical model is investigated with DC, PWM, bi-level, and n-level driver. Actually, the optical performance for traffic light is related to sinusoidal waveform driver. In other words, the optical performance and SNR of traffic source using by LED device can be affected by sinusoidal waveform driver. There is still a lack of understanding on such aspects, which are important for the optimization of the traffic light design. In this paper, we attempted to develop a five-dimensional model to study sinusoidal waveform driver and heatsink temperature effects on illuminance and SNR performance of traffic light with LED source. A prediction method for the illuminance and SNR of the mixed white LED source with a warm white LED source and a cool white LED source as function of heatsink temperature, frequency, amplitude voltage, bias voltage and amplification factors is proposed in this paper. The proposed model can estimate the illuminance and SNR with different heatsink temperature and driver parameters. The proposed model cover extends the illuminance and SNR of LED source inside smart traffic information system to include the key parameters of sinusoidal waveform. In general, the calculated results using by the proposed model are consistent with the practical measurements. The average deviation between the theoretical and experimental illuminance and SNR with different conditions is about 8.9% and 13.5% respectively. It is pointed out that the proposed model can be used as a design tool for traffic designs. LED manufacturers are encouraged to provide more results such as illuminance and SNR as a function of frequency, bias voltage, amplification factors and amplitude voltage in the datasheets as basic coefficients for LED system designs for traffic information system. It should be pointed out that required parameters of the proposed modeling are specific parameters for traffic light using by LED source. The re-calibration measurements should be carried out if the traffic light is used by the different type of LED. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to copyright considerations. α 1 : Constant representing the slop and α2 is another constant β 1, β 2 , and β 3 : Coefficients that can be extracted from Fig. 3 with constant heatsink temperature and bias voltage c 1 : is intersection values of (4) and (5) χ 1, χ 2 and χ 3 : Coefficients that can be extracted from the experimental results in Fig. 4 δ 1, δ 2 and δ 3 : Coefficients that can be extracted from experimental results of the illuminance as a function of the LED bias voltage with constant amplification factors and frequency ε 1 and ε 2 : Coefficients that can be extracted from Fig. 5 Intersection values of (9) and (10) μ 1, μ 2 , and μ 3 : Coefficients that can be extracted from the practical measurements of the illuminance as a function of the frequency with constant amplification factors and bias voltage Intersection values of function of (11) and (12) Φ c (V a,c ,T hs,c ,V b,c ,A f,c ,f c ) : Individual illuminance of the cool white LED Φ w (V a,w ,T hs,w ,V b,w ,A f,w , f w ) : Individual illuminance of the warm white LED Nian LX, Pei XM, Zhao ZL, Wang XZ (2019) Review of optical designs for light-emitting diode packaging. 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IEEE Trans Industral Electron 66:2785–2794 Chen HT, Hui SYR (2014) Dynamic prediction of correlated color temperature and color rendering index of phosphor-coated white light-emitting diodes. IEEE Trans Ind Electron 61:784–797 Hui SYR, Chen HT, Tao XH (2012) An extended photoelectrothermal theory for LED systems: a tutorial from device characteristic to system design for general lighting. IEEE Trans Power Electron 27:4571–4583 Lee ATL, Chen HT, Tan SC, Hui SYR (2016) Precise dimming and color control of LED systems based on color mixing. IEEE Trans Power Electron 31:65–80 Hui SYR, Lee ATL, Tan SC (2020) New dynamic photo-electro-thermal modeling of light-emitting diodes with phosphor coating as light converter part I: theory, analysis and modeling. IEEE J Em Sel Top P 20:777–779 Not Application. This research was funded by National Natural Science Foundation of China (Grant Number: 61975072, 62001200), Natural Science Foundation of Fujian Province (Grant Number: 2020J01820), Industry-University-Research Collaboration Foundation of the Fujian Province (Grant Number: 2020H6017), Social Science Foundation of the Fujian Province (Grant Number: FJ2019B143) and Natural Science Foundation of the Zhangzhou (Grant Number: ZZ2019J15). Program for Innovative Research Team in Science and Technology in Fujian Province University (Optoelectronic Materials and Device Application), Natural Science Foundation of the Fujian Higher Education Institutions (Grant Number: JAT200316), National College Students' innovation and entrepreneurship training program (202110402001, 202110402013, 202110402028X). School of Business, Minnan Normal University, Zhangzhou, 363000, China Yaoting Chen Analysis and Application for Business Big Data of Fujian Provincial Key Laboratory, Zhangzhou, 363000, China College of Physics and Information Engineering, Minnan Normal University, Zhangzhou, 363000, China Huanting Chen All authors contributed to the development and completion of this paper. YC did the conceptualization, preparation of manuscript, validation, formal analysis, data curation, and writing. HC performed the experiment and writing. All authors have read and agreed to the published version of the manuscript. Correspondence to Yaoting Chen. Chen, Y., Chen, H. Analysis and modeling for illuminance and signal-to-noise of smart traffic information system. J. Eng. Appl. Sci. 69, 24 (2022). https://doi.org/10.1186/s44147-022-00079-3 Mixed white LED source Sinusoidal waveform driver	CommonCrawl
Article \| Open \| Published: 16 May 2019 Stochastic simulations reveal few green wave surfing populations among spring migrating herbivorous waterfowl Xin Wang ORCID: orcid.org/0000-0002-4406-26711,2, Lei Cao1,3, Anthony D. Fox4, Richard Fuller ORCID: orcid.org/0000-0001-9468-96785, Larry Griffin6, Carl Mitchell6, Yunlin Zhao7, Oun-Kyong Moon8, David Cabot9, Zhenggang Xu7, Nyambayar Batbayar10, Andrea Kölzsch ORCID: orcid.org/0000-0003-0193-156311,12,13, Henk P. van der Jeugd14,15, Jesper Madsen4, Liding Chen1,3 & Ran Nathan2 Nature Communicationsvolume 10, Article number: 2187 (2019) \| Download Citation This article has been updated Tracking seasonally changing resources is regarded as a widespread proximate mechanism underpinning animal migration. Migrating herbivores, for example, are hypothesized to track seasonal foliage dynamics over large spatial scales. Previous investigations of this green wave hypothesis involved few species and limited geographical extent, and used conventional correlation that cannot disentangle alternative correlated effects. Here, we introduce stochastic simulations to test this hypothesis using 222 individual spring migration episodes of 14 populations of ten species of geese, swans and dabbling ducks throughout Europe, East Asia, and North America. We find that the green wave cannot be considered a ubiquitous driver of herbivorous waterfowl spring migration, as it explains observed migration patterns of only a few grazing populations in specific regions. We suggest that ecological barriers and particularly human disturbance likely constrain the capacity of herbivorous waterfowl to track the green wave in some regions, highlighting key challenges in conserving migratory birds. Long-distance migration reflects animal responses to large-scale spatial and temporal changes in environmental factors1. Tracking the seasonal availability of optimal food resources is generally considered as a widespread phenomenon2 and the main proximate driver of migration, as exemplified by the green wave hypothesis3,4 and the closely related forage maturation hypothesis5. Both hypothesise that spatial and temporal changes in foliage quality drive the progress of migration of herbivores and predict that the timing of migration links to foliage phenology. Field studies6,7,8,9 support these hypotheses. More extensively, empirical relationships between migration and vegetation indices derived from remote-sensing techniques, using migration data derived from remote telemetry devices10,11,12, citizen-science data13 or weather surveillance radar data14, as well as experimental approaches15, also support such hypotheses. These studies used various vegetation greening metrics, such as the normalised difference vegetation index (NDVI)16,17, green wave index (GWI, the scaled NDVI) and instantaneous rate of green-up (IRG, the acceleration of time-NDVI curve) calculated by fitting annual time-NDVI curves10,11,18. The application of migration–vegetation correlational studies to various species has prompted the widespread acceptance of the green wave as the proximate mechanism underpinning herbivore migration patterns11,12,19. Nevertheless, two major sources of doubt remain. First, because almost all studies draw conclusions based on correlations, it is impossible to determine whether the green wave is indeed the major determinant of migration patterns, or if such significant correlations arise coincidentally. Although the northward spring migration of northern hemisphere herbivores coincides with food availability (i.e., the green wave), avian spring migration could be associated with other environmental factors, such as day length and air temperature20, which correlate with latitude. Such multiple associations cannot be disentangled using correlations alone. Testing whether the green wave determines spring migration requires going beyond correlations, to estimate the probability of detecting a match against the corresponding random (null) expectations of directional northward movement irrespective of the progress of the green wave. Here, we derive such null models (sensu Gotelli and Graves21) using stochastic simulations (see Methods). Second, the generality of herbivores tracking the green wave, and evidence to support it, requires confirmation across multiple populations, species and geographical regions22. Previous studies focused on single species within restricted geographical ranges10,11,12, while comparative analyses across populations, species and regions are lacking. We therefore ask: does the green wave hypothesis represent a general mechanism pertinent to species belonging to various feeding guilds through indirect food web effects2, or, more simply, to all migratory avian herbivores? More specifically, while the hypothesis might explain grazing herbivore migration well, it might be expected to provide weak or no support for other herbivores or omnivores that tend to graze more facultatively23. Alternatively, the hypothesis might not apply robustly even to grazers, as they can occasionally exploit more diverse food items such as non-leaf and even non-plant material23,24, and migration timing can be affected by various other extrinsic (e.g., weather25 and competition26) and internal factors (e.g., fat deposits27). It is therefore important to examine whether the green wave represents a general mechanism that can explain spatio-temporal migration patterns of herbivorous waterfowl across species and geographical regions. To this end, one needs to test the conventional migration–green wave associations and compare empirical and simulated data, across multiple populations of several species. In this way, one can examine whether the green wave hypothesis explains spring migration of herbivorous waterfowl, or whether spring migration patterns simply reflect stochastic directional movement towards species' breeding grounds irrespective of the progress of the green wave. Specifically, we propose the following three predictions, arranged by decreasing level of support (i.e., from the ubiquitous to the particular) for the green wave hypothesis: Prediction 1: the green wave is the fundamental driver of spring migration of all studied herbivorous waterfowl, leading to significant migration–green wave associations for all populations of all study species; alternatively, Prediction 2: the green wave only holds for grazers, hence significant associations are expected for all populations of all known conventionally defined grazers, but not for other herbivores and omnivores; or finally, Prediction 3: the green wave might not explain migration patterns for all grazers, and migration–green wave associations are inconsistent among different populations of grazing species. To assess the level of support for these predictions, one can first evaluate the robustness of migration–green wave associations using three methods: the Simple Conventional Correlation12,20, the Correlation method evaluated by Stochastic Migrations18 and the Metric Selection approach based on Stochastic Migrations (MSSMs) introduced in this study. The Simple Conventional Correlation method12,28 uses linear models to test for significant correlations between observed and expected arrival dates (the latter is the day with peak green-up rate) at each stopover site. The Correlation method evaluated by Stochastic Migrations compares the observed-expected vs. simulated-expected correlation coefficients to validate the migration–green wave associations identified by Simple Conventional Correlation. The MSSM calculates the value of green wave metrics at the time observed/simulated birds arrive at each stopover site, and compares these values for observed vs. stochastic migrations (Supplementary Table 1). To build the null models of stochastic migration, one should consider the following three simulation types: (1) stochastic timing, (2) stochastic stopover site (when migration tracks are available) and (3) stochastic timing and stopover site modelling (when migration tracks are available) (Supplementary Table 2). If a population supports the green wave hypothesis, the observed migration should be different from all the three null models, reflecting a spatial-temporal migration–green wave association. Inherently, because the real association between migration and green wave is unknown, one cannot compare the three methods against known associations. Therefore, two general criteria—derived directly from the most basic argument of the green wave hypothesis (reliance on foliage quality)—were employed to evaluate the results obtained by these methods. The first criterion assumes that the tendency of avian migrants of different species to follow the green wave is determined by their reliance on foliage utilisation, based on conventional classification (grazers > other herbivores > omnivores). The second criterion is based on the same assumption, but the reliance on foliage consumption is based on more subtle differentiation in diet composition, found to correlate strongly with some measures of bill morphology, as demonstrated for grazing Anatidae in particular24. In this study, we focus on testing the green wave hypothesis rather than testing a range of alternative explanations, aiming to provide an unequivocal test of the ubiquity of the green wave as a main driver of avian herbivore migration. Our analyses show that among 222 individual spring migration episodes of 14 populations of 10 species of geese, swans and dabbling ducks throughout Europe, East Asia and North America, the green wave hypothesis is supported only for grazing species with a particular bill shape that optimises grazing performance, whereas all other observed migrants did not track the green wave better than simulated stochastic north-migrating ones. Furthermore, this support is inconsistent even among the grazing species and populations, exhibiting marked geographical variation, which leads us to suggest that ecological barriers and human disturbance likely constrain the capacity of herbivorous waterfowl to track the green wave in some regions more than in others. The dataset comprised 222 telemetry-tracked spring migrations from 193 individuals belonging to 14 populations (five grazers, seven facultative herbivores and two omnivores) of 10 species from Europe, East Asia and North America, from 1995 to 2016 (for details, see Supplementary Table 3 and Fig. 1). It contained 125 bird-years (108 birds, some containing multiple-year migrations) of grazing populations, including Greenland, Svalbard and Barents Sea barnacle goose Branta leucopsis, Barents Sea and East Asian greater white-fronted goose Anser albifrons, 82 bird-years (70 birds) of facultative herbivores including whooper swan Cygnus cygnus, tundra swan Cygnus columbianus, swan goose Anser cygnoides, Scandinavian taiga bean goose Anser fabalis, East Asian tundra bean goose Anser serrirostris, Svalbard pink-footed goose Anser brachyrhynchus, and Greenland greater white-fronted goose Anser albifrons flavirostris, and 15 bird-years (15 birds) from omnivores including East Asian mallard Anas platyrhynchos and North American northern pintail Anas acuta (see Supplementary Fig. 1, for example, stochastic migrations). All populations migrated north during spring in a fairly smooth manner in Europe and Siberia, and more heterogeneously in East Asia (Supplementary Fig. 2). Overview of spring migration and stopover site dataset for Anatidae. The dataset includes 222 spring migrations from 193 individuals belonging to 14 populations (five grazers, seven facultative herbivores and two omnivores) of 10 species covering Europe, East Asia and North America, from 1995 to 2016. Points are stopover site locations; point colour corresponds to background colour of species names; consecutive stopover sites during the individual migrations are connected by a line, as an indication of migration route. (Photo credits in order of appearance: J. Frade, M. Langthim, P. Ertl, Y. Muzika, O. Samwald, D. Cooper, B. Keen, S. Harvančík, S. Harvančík and M. Panchal) Method evaluation The Simple Conventional Correlation method yielded weak migration–green wave associations classified as weak surfers for three out of five grazers, for one out of seven facultative herbivores, and for one out of two omnivores. One facultative herbivore showed strong migration–green wave associations hence classified as surfer. The other populations were classified as non-surfers (Table 1, Fig. 2, Supplementary Fig. 2). Surfers, weak surfers and non-surfers were defined as cases of strong, weak or no significant migration–green wave regression, a terminology used only regarding the Simple Conventional Correlation method (for details, see the section on Simple Conventional Correlation of arrival time tests of migration–green wave of the Methods and Supplementary Table 1). The best models based on Simple Conventional Correlation did not include bill morphology as a predictor (Supplementary Table 4). Given its intrinsic variable multicollinearity problem, and according to the two criteria, the suitability of Simple Conventional Correlation for testing the green wave hypothesis is questionable. However, this method showed how the migration progress was associated with the green wave. The tracked birds migrated faster and arrived earlier than the green wave at stopover sites (Fig. 2, Supplementary Table 5), as all slopes were less than one and the data points mostly clustered within the lower-right part of the panel, below the expected 1:1 relationship. Most populations showed high between-individual variation in the migration–green wave correlation (Supplementary Table 5, Supplementary Fig. 3). Table 1 Comparison of three different methods for assessing the level of support for the green wave hypothesis Testing the green wave hypothesis for grazers by three different methods. We present the results of the Simple Conventional Correlation (a, upper row), Correlation method evaluated by stochastic migrations (b, second row) and the Metric Selection approach based on Stochastic Migrations (MSSMs) (c–e, three lower rows). Red, blue, turquoise and purple dots/boxes denote observed, stochastic timing, stochastic stopover site and stochastic timing and stopover site migrations, respectively. a The x and y axes denote the expected arrival day of the year at stopover sites (the day with peak instantaneous rate of green-up [IRG] value) and the observed arrival day of the year by birds, respectively. The grey pecked lines with slope = 1 and intercept = 0 indicate perfect match of migration and green wave. N.S. denotes insignificant slope; otherwise the p-value and coefficient of the slope, and marginal R2 are provided. Blue lines show the significant positive slope of the green wave in models of green wave surfers, and grey bands are the prediction intervals of the models. b Pearson's correlation coefficient r and 95% CI (y axis) of observed and stochastic migrations (x axis). For populations without available migration tracks, only stochastic timing simulations were performed, compared and plotted. Blank panels denote not applicable because this method only applies to green wave surfers or weak surfers identified by Simple Conventional Correlation. c–e Three metrics compared for observed versus stochastic migrations: IRG (instantaneous rate of green-up), day length and air temperature. Lower case letters indicate significantly different groups using Kruskal–Wallis test followed by Dunn's test of multiple comparisons. Boxplots show median, first and third quartiles with whiskers reaching to the last data point within 1.5 × interquartile range. For clear presentation, outliers out of 10 and 90% quantiles were excluded from the plots but kept in all analyses. All grey shaded plots in all panels denote significant migration–green wave associations. Source data are provided as a Source Data file The Correlation method evaluated by Stochastic Migrations suggested that all the surfers and weak surfers but one omnivore identified by Simple Conventional Correlation were indeed green wave surfers. However, this test failed to meet the two evaluation criteria (i.e., neither feeding guild nor bill morphology explain this pattern; Supplementary Table 4). Hence, despite its design to resolve the problem of multicollinearity, the Correlation method evaluated by Stochastic Migrations should be carefully considered in further tests of the green wave hypothesis. The MSSM method identified three grazing populations (Svalbard and Barents Sea barnacle goose and Barents Sea greater white-fronted goose) as green wave surfers. For these populations, both spatial (i.e., metrics of observed migrations differed from stochastic stopover site migrations) and temporal (i.e., metrics of observed migrations differed from stochastic timing migrations) simulations showed significant deviation from stochastic migration in the hypothesised direction using the metric instantaneous rate of green-up (IRG, Table 1, Figs. 2–4 and Supplementary Figs. 4–6). All other populations, including three populations (whooper swan, pink-footed goose and northern pintail) identified as green wave surfers or weak surfers by the Simple Conventional Correlation method showed no significant migration–green wave associations according to the MSSM method. The upper mandible depth-length ratio was found to play significant role in determining migration–green wave associations evaluated by MSSM (ΔAICc = 2.71, Supplementary Table 4). Overall, because the MSSM approach fulfilled both evaluation criteria, whereas both Simple Conventional Correlation and Correlation method evaluated by Stochastic Migrations did not, we focus on MSSM results in testing the green wave hypothesis and our three predictions. Testing the green wave hypothesis for facultative herbivores by three different methods. See Fig. 2 for definitions and details of panels, symbols, colours, acronyms and boxplots. For the population without available migration tracks (Whooper Swan from East Asia), only stochastic timing simulations were performed, compared and plotted. Source data are provided as a Source Data file Testing the green wave hypothesis for omnivores by three different methods. See Fig. 2 for definitions and details of panels, symbols, colours, acronyms and boxplots. For the population without available migration tracks (Northern Pintail from North America), only stochastic timing simulations were performed, compared and plotted. Source data are provided as a Source Data file Testing the green wave hypothesis The MSSM approach suggests that green wave surfers selected the peak value of the IRG, which approximately concurs with 50% GWI, rather than the peak values of other metrics. The approach also showed that both day length and air temperature were not significantly associated with the migration of any population (Fig. 2). This method rejects the hypotheses asserting that the green wave could explain spring migration of birds belonging to different feeding guilds (prediction 1) or all avian grazers (prediction 2). However, some grazers supported the green wave hypothesis (prediction 3). We used mixed-effect logistic models with the level of support for migration–green wave as the response variable, the bill morphology and biological family as fixed effects, and geographical range as random effects (for details, see Methods). Geographical region also emerged as a strong predictor of the tendency to follow the green wave (bill morphology explained 69.8% of total variance, and geographical explained 28.2%, leaving only 2.0% of total variance unexplained, Supplementary Table 4). This is in line with the marked geographical structure in the distribution of green wave surfers. Both of the two grazers in Western Europe—Barents Sea, the barnacle and greater white-fronted geese, were green wave surfers. In Western Europe—Svalbard, the barnacle goose, the only grazer, was a green wave surfer, whereas the pink-footed goose, a facultative herbivore, was not. In Western Europe—Greenland, neither the barnacle nor greater white-fronted geese surfed the green wave. In East Asia, the only grazer, the greater white-fronted goose, was not a green wave surfer. All populations but this one that did not surf the green wave showed the same IRG values by following alternative timing, i.e., the IRG values are nonsignificant between the observed and stochastic timing migrations. This suggests that these non-surfers cannot obtain improved green wave metrics within the overall constrained migration time window. The results also showed that the East Asian grazer and facultative herbivores modelled using stochastic stopover sites apparently followed the green wave better than the observed ones: the GWI values by stochastic migration was higher (Fig. 2 and Supplementary Figs. 4–6). A similar result held for the NVDI metric (excepting the bean goose) but was less clearly seen in the IRG. Using a large dataset of spring migrations of geese, swans and dabbling ducks, and a broad set of green wave metrics, we tested the green wave hypothesis using three methods, Simple Conventional Correlation, Correlation method evaluated by Stochastic Migrations and the introduced MSSM. Only the MSSM approach met the general expectations of the green wave hypothesis, and revealed that only a few of the grazer populations followed the green wave during spring migration. Hence, although the green wave hypothesis can explain migration patterns of some avian grazers, it does not represent the predominant proximate mechanism determining spring migration progress in the studied herbivorous waterfowl populations at large geographical scales. We therefore conclude that within the taxonomical and geographical range covered in this study, tracking the green wave is neither a global phenomenon nor a ubiquitous driver of spring migration of herbivorous waterfowl. Our study suggests that the variation in the associations between migration patterns and the green wave can, to some degree, be related to variation in bill shape of herbivorous waterfowl. Bill shape correlates with waterfowl diet composition24, specifically, with the level of dependence on grazing green leaves/shoots. Herbivorous bird species with higher bill depth-length ratios are more effective grazers, but less able to exploit other sources of plant food24. Therefore, species with large bill depth-length ratio are more likely than other species to migrate with the green wave during spring, to match closely the shift in the timing and location of suitable grazing sites along their routes. Our stochastic simulations supported the green wave hypothesis chiefly for the most exclusive grazer, the barnacle goose, with the highest depth-length ratio and the largest proportion (2/3 populations) of significant migration–green wave associations. The only other species for which stochastic simulations supported this hypothesis was the greater white-fronted goose (with the second largest bill depth-length ratio in our sample), whereas the East Asian population of that species (and all other populations of all other species) with smaller ratio showed no migration–green wave associations. The exception of the East Asian greater white-fronted goose from this otherwise general bill shape effect was notable. Furthermore, our analyses showed no support for the green wave hypothesis also for all other five populations of geese, swans and ducks in this region. We suggest that human disturbance, which plays an important role in determining the progress of bird migration29,30, could explain the geographical deviations from the green wave hypothesis, especially in East Asia. In this region, hunting pressure, land use change, poisoning and other human disturbance are intensive31,32. Five wintering goose species were almost entirely confined to natural wetlands in the Yangtze River Floodplain33, whereas geese elsewhere in the world commonly use energetically profitable farmland habitats34,35. This could explain our finding that for all East Asian species included in our analyses, simulated spatially stochastic migrants obtained higher green wave metric values than the observed tracks (Figs. 2–4 and Supplementary Figs. 4–6), indicating remarkably poor (worse than random) selection of stopover sites by the birds in relation to the green wave. Furthermore, tracked birds arrived consistently earlier than the green wave at stopover sites (Fig. 2, Supplementary Fig. 2, Supplementary Table 5). To explain these results, we propose the following scenario. Birds at initial (early spring) stopover sites departing northwards skip subsequent stopover sites along their migration route with high forage quality (i.e., green wave phenomenon) due to excessive human disturbance there (e.g., habitat loss or physical human activity), forcing the birds to undertake longer jumps to the next stopover sites. Consequently, the birds arrive to their next stopover sites prior to the date of optimum availability of local food resources at that latitude (i.e., ahead of the green wave) and stage longer in these sites. This proposed explanation is supported by the lack of stopover sites between the Yangtze wintering ground and northeast China, a huge area with potentially good green wave conditions rendered apparently inaccessible to migrating birds (Supplementary Fig. 2). This is also corroborated by the finding that waterbirds in this flyway progress northward in jumps double the length of those in the western Palearctic flyway36. Furthermore, early arrival to stopover sites ahead of the green wave would be expected to lengthen stopover duration, potentially explaining the ~25% longer stopover duration found for greater white-fronted geese in East Asia compared with the Barents Sea (mean ± SD 12.17 ± 11.37 vs. 9.79 ± 8.57 days, respectively; t-test, t = −2.0403, df = 183.31, p = 0.043). Hence, habitat loss, excessive human disturbance and hunting in East Asia and some other parts of the world might challenge the ability of migrating waterbirds to surf the green wave. In contrast to the greater white-fronted goose and five facultative herbivores of East Asia, two facultative herbivores outside this region—the bean goose from Scandinavia and pink-footed goose from Svalbard—would obtain lower (rather than higher) IRG values by spatially stochastic migrations. This suggests selection for stopover sites of high forage quality during migration, as leaf material comprises a considerable part of the diet of these two populations during migration37,38. However, birds of these two populations also feed on other food types such as grains during stopover37,38, so that their migrations were not constrained by the green wave. This explains the lack of difference in the green wave metrics between the observed and stochastic timing migrations, implying that observed birds did not tightly coordinate the timing of their migration with the green wave. Alternatively, the weak green wave surfing in these two populations might be attributed to other factors, such as ecological barriers and environmental predictability (discussed further below). However, such explanations seem unlikely because the Svalbard barnacle goose did surf the green wave within the same geographical range, obtaining a significantly higher IRG on observed migration compared with stochastic timing (and site, and timing and site) migration. Migratory herbivorous waterfowl might not follow the green wave for reasons other than human disturbance. First, birds may be limited in their ability to predict the progress of the green wave, especially when and where the next stopover lies beyond a large ecological barrier (e.g., open sea, desert, mountain ranges and ice sheets)39. This seems the case especially for north European geese migrating to breed in Greenland, as both the Greenland populations of barnacle and greater white-fronted geese, two species with high bill depth-length ratio, did not surf the green wave in the Western European–Greenland flyways, presumably due to the extended migration over stretches of ocean imposed on these populations. Second, even if birds are capable of perfectly predicting the green wave, unpredictable adverse weather conditions40,41,42 can alter migration progress and induce a mismatch with the green wave; migrating birds, for example, might delay departure from a stopover site due to storms or wait for sufficient tailwinds to assist with crossing migratory barriers25. Such effects, however, are more likely to delay than to advance arrival to stopover sites, hence contradict the finding that the likelihood of early arrival increases with distance to the next stopover site. Third, the advancement in peak food availability caused by climate change could exacerbate the mismatch between migration timing and phenology, because of the intrinsic time constraint on spring migrations43. Fourth, birds might progressively overtake the green wave to arrive well before the peak in food availability to produce a clutch of eggs that hatch to coincide with the peak in gosling food quality43,44. These factors in turn introduce further variation in migration timing, and potentially a larger mismatch between the green wave peak and migration timing (Supplementary Figs. 2 and 3). Such individual mismatches can be quantified using approaches such as the space-time-time matrix10. However, such between-individual variation seemed to be negated within populations, and some population-level migrations still showed predictable associations with the green wave. Comparing our results to those of previous studies requires a methodological comparison as the first step. In addition to the commonly applied Simple Conventional Correlation method and the more rarely used Correlation method evaluated by Stochastic Migrations method, we introduced the MSSMs. Overall, the MSSM approach was found to provide a much more conservative test to the green wave hypothesis compared with the other methods. Furthermore, the two other approaches tended to overestimate migration–green wave associations, as three populations—the whooper swan, the pink-footed goose and the northern pintail—were identified as green wave surfers or weak surfers by at least one of these methods, but showed no significant association according to the MSSM method. To our knowledge, no studies on avian migration have yet used stochastic spatio-temporal simulations to test the green wave hypothesis. Aikens et al.18 generated stochastic (null) migration models of ungulates using a coarse method (as they admitted), and tested their results using the Correlation method evaluated by Stochastic Migrations, which we found less suitable compared with MSSM in our study (Table 1). Bridge et al.45 constructed random migrations, without statistically comparing stochastic vs. observed metrics. Considering its reliable performance and ability to generate null expectations while controlling for confounding effects of potential driving factors common in animal movement studies, we advocate the use of the MSSM approach for investigating questions relating to environmental drivers of migration and other movement types for animals. Another important methodological comparison is among NDVI-derived metrics of vegetation phenology. Although each reflects certain features of vegetation, such as nutrition or quantity, no single index alone can capture the fine details of migrants' food availability in relation to requirements, which renders the a-priory use of any single index to test migration–green wave associations questionable. We therefore used a series of metrics, which highlighted the more reliable performance of the IRG compared with other indices. Using multiple green wave metrics in combination to test the green wave hypothesis may better represent vegetation features and animal demands on the vegetation, hence should be examined in future studies. In addition to the selection of different metrics, differences in spatial or temporal resolution and scale used to estimate these metrics might affect the study outcomes. For example, Kelly et al.14 attributed the lack of support for the green wave hypothesis to the lack of seasonal south-to-north greening derived from remotely sensed indices estimated in spatial resolution units of 80 km radius14. In our study, the typical spatial extent of a stopover site was 5–10 km radius across species and populations. This implies that an 80 km radius typically encompasses an area roughly 63–255 times larger than the relevant area for estimating stopover site characteristics of migratory ducks, geese and swans. Nevertheless, possible resolution and scale effects on the robustness of migration–green wave associations await further investigation. Methodological differences also occur in other dimensions of research practice and design. Both field manipulations aimed at testing the green wave hypothesis6,15, and meticulous empirical attempts to measure vegetation quality at each observed stopover site6 (rather than derive estimates from remote sensing), inherently remain limited practically in time and space. Furthermore, as discussed above, the spatio-temporal resolution of citizen-science data13 or weather surveillance radar data14 may not be sufficient to test the green wave hypothesis. The alternative approach, taken in this study—to couple data from advanced wildlife tracking technologies and remote sensing—has strong merits46,47 but important limitations as well48, including difficulties in trapping wild animals, adverse effects of trapping and tagging on animal behaviour and fitness, restricted sample sizes, bias to relatively large-bodied animals, and high costs. For these reasons, it is challenging to obtain sufficiently large sample sizes to achieve good taxonomical and geographical representativeness in wildlife tracking research. We have concentrated on long-distance migratory (mostly arctic nesting) herbivorous waterfowl and although the dataset of this study is by far larger than previous green-wave studies, the 10 study species are unlikely to adequately represent all 169 global species of Anatidae49, nor can one study population (northern pintail) represent all North America migratory waterfowl. Cost-effective use of wildlife tracking and other approaches should consider a broader coverage of the major migration flyways, though the paucity of datasets from North America might stem from restricted data availability rather than genuine data gaps. Furthermore, advances in wildlife bio-logging technologies offer complementary auxiliary data from accelerometers and other sensors might enable examining more direct links between the internal state (e.g., energy balance, behavioural context) and the external environment (e.g., meteorological conditions, land use) that individual migrating birds experience en route. In addition to bird movement and behaviour obtained by biotelemetry devices, an assessment of the human-induced changes in habitat use and bird distribution, site/food availability using multiple data source, is critical to evaluating the impact of human disturbance on migratory birds, most notably in East Asia. Overall, the results of our study, along with the various methodological issues we discussed, cast doubts on the ubiquity of the green wave as a main driver of (spring) migration of herbivorous birds, despite previous support from studies of single species12,28. Further broad multispecies comparisons using the MSSM or similar methods are needed to assess the generality of this conclusion in a broader taxonomical and geographical context. These will set the stage to test rigorously not only the green wave hypothesis, but alternative explanations (such as human disturbance, as proposed in this study) as well, to further elucidate the mechanisms driving bird migration and to better conserve migratory birds. Migration data We collected Anatidae migration data from two sources: published and our own movement information first presented in this study. We undertook the literature search on the Web of Science on 18 March 2016 with the terms: (GPS OR Argos OR PTT OR CTT OR (satellite* AND (track* OR transmitter* OR telemetr))) AND (screamer OR "magpie goose" OR "magpie geese" OR teal* OR shelduck* OR sheldgoose OR sheldgeese OR anas OR waterfowl OR wildfowl OR anseriformes OR waterbird* OR duck* OR goose OR geese OR swan*). We excluded migration data derived from geolocators or observations from banded individuals because of large spatial or temporal errors and biases involved in using these approaches. We used movement tracks derived from our tracking studies, involving birds caught in several places in East Asia from 2014 to 2016, and in Europe from 2008 to 2016, and tracked using different types of tracking devices (see Supplementary Data 1 for details of our tracked birds). We also searched and accessed published Anatidae movement tracks on the Movebank Data Repository (https://www.datarepository.movebank.org/). We excluded maritime populations from search results because their sub- and inter-tidal marine vegetation habitats are not always associated with land, so no specific vegetation metrics were relevant for these species. Because the simulated stochastic migrations required stopover duration for simulation, we excluded literature records, which only reported birds' arrival date. Paired adults and parent geese with their offspring frequently migrate and move together. To avoid pseudo-replication of stopovers caused by such associations, we removed all replicates except for one randomly selected movement tracks that were otherwise temporally and spatially identical. We classified feeding guilds using literature and observations of the corresponding populations (Supplementary Table 3). We classified populations according to the geographical range during migration. For biological and statistical representativeness, we excluded manipulated birds, such as translocated birds50, birds that performed incomplete migrations of <1000 km, or populations containing fewer than five individuals or fewer than 10 stopover sites to avoid type II error induced by small sample size. We also excluded tracks that contained gaps longer than 10 days within migration legs, which can cause a biased estimate of arrival date and problems in modelling the migration process using continuous-time correlated random walk (see below). We excluded migrations in 1994 because 16 out of 52 weekly NDVI images in this year were missing (due to unavailable satellite data), and therefore we could not generate reliable green wave values based on the double-logistic model (see below). Stopover/migration information We extracted stopover information from the literature that recorded both timing (arrival and departure date) and stopover site coordinates during a tracked individual's spring migration. Where stopover site locations were presented using maps rather than providing coordinates, we determined coordinates of stopover sites from maps in combination with the relevant literature descriptions. From individual movement tracks, we identified each stopover site and recorded arrival and departure dates. We followed the methods of van Wijk et al.20, Shariati-Najafabadi et al.12 and Kölzsch et al.51 to determine stopover sites, where birds stayed longer than 48 h. In this way, we excluded those stopover sites where birds probably only rested briefly or drank52. According to empirical migration observations22,53, we only included stopover locations after the 60th day of the year, to eliminate within-winter movements. In addition, full migration tracks from published sources such as Movebank Data Repository and tracking data held by the authors of this study were used for the use of stochastic stopover site modelling and stochastic timing and stopover site modelling (see below). We could not extract full migration tracks from the literature, and therefore the simulations of stochastic stopover site modelling and stochastic timing and stopover site modelling for the whooper swan from East Asia and the northern pintail from North America were not applicable in our analyses. Remote-sensing data and green wave metrics We used the Advanced Very High Resolution Radiometer Vegetation Health smoothed NDVI Product (AVHRR-VHP)54 for extraction of vegetation data and analyses. The critical advantage of this product is its larger temporal coverage (1989 onward) compared with MODIS-based products (2000 onward), permitting migration–green wave association analyses using migration data before 2000 extracted from the literature. Moreover, the AVHRR-VHP provides a higher temporal resolution (7 day) than MODIS-based products (8 day or 16 day), providing finer grained parameter estimates for annual NDVI models (see below for more details), which are critical for deriving green wave metrics. We included all stopover sites in the latitudinal range of AVHRR-VHP (55.152°S–75.024°N). The coarser spatial resolution unit of AVHRR-VHP (4 km, in comparison with 250 m to 8 km for MODIS) is unlikely to bias our analyses, because vegetation data at stopover sites were extracted from within a buffer (radius) of 5 to 30 km, conforming with the movement range at stopover sites (Supplementary Table 3), compared with 15 km12 or 50 km28 in previous studies. A sensitivity analysis showed that changing the buffer size from 5 to 30 km did not alter our conclusions (Supplementary Table 6). In this article, we reported results based on the 5-km buffer size, in accordance with the movement range within stopovers of the birds (Supplementary Table 3). We extracted the NDVI values from pixels occupying a 5-km radius buffer around each stopover site identified by a point location from the birds' positional data, accounting for any non-vegetated area within the buffer55. We excluded pixels within the buffer classified as forest, woodland, urban and built or bare ground by the AVHRR land cover product56. Overall, we obtained 9.8 ± 1.5 (SD) pixels per stopover site. Within each year, we fitted a time series model to the scaled NDVI values for each pixel within the buffer using a double-logistic model57, the method that performed best in a comparison of NDVI filtering approaches58 $${\mathrm{NDVI}}(t) = \alpha + (\beta - \alpha ) \cdot \left( {\frac{1}{{1 + {\mathrm{e}}^{ - \gamma \cdot (t - \delta )}}} + \frac{1}{{1 + {\mathrm{e}}^{\varepsilon \cdot (t - \theta )}}} - 1} \right)$$ where α and β are minimum and maximum NDVI values; γ and ε are the rates of increase/decrease of the curve at the inflection points; δ and θ are time of maximum/minimum green-up rate (Supplementary Fig. 7). We calculated the GWI at time t when a bird arrived at a stopover site using fitted values following the method by White et al.59 and Beck et al.60: $${\mathrm{GWI}}\left( t \right) = \frac{{{\mathrm{NDVI}}\left( t \right) - \alpha }}{{\beta - \alpha }} \times 100{\mathrm{\% }}$$ We calculated the predicted NDVI and IRG (the first derivative of NDVI time series rescaled from 0 to 1), based on Eq. (1). We also excluded pixels with anomalous spring phenology where the maximum green-up rate occurred (1) before the 50th day of the year, or (2) after the 240th day of the year, or (3) later than the time when the minimum green-up rate occurs, which often signifies essentially non-vegetated areas. We used the method of Teets61 to calculate the day length at specific locations and times. The air temperature data were obtained from the global land data assimilation system, on a fixed grid of 0.25° × 0.25° and at a 3-h temporal resolution62,63,64. We calculated daily mean temperature from pixels occupying a 5-km radius buffer around each stopover site, on the arrival day of the birds. Simple Conventional Correlation Using all the individual stopover data, we performed mixed-effect linear models using maximum likelihood estimates for each population to conduct Simple Conventional Correlation tests of migration and the green wave with the following structure $${\mathrm{Day}}_{{\mathrm{obs}}}\sim {\mathrm{ Day}}_{{\mathrm{pred}}} + \left( {1 + {\mathrm{Day}}_{{\mathrm{pred}}}\|{\mathrm{year}}/{\mathrm{bird}}} \right)$$ where Dayobs is the observed arrival day at a stopover site and Daypred is the predicted arrival day (the day with peak green-up rate, i.e., 50% GWI) at that site based on Eq. (1), (1 + Daypred\|year/bird) is the random effect of individual nested in year on both intercept and slope. If all individuals within a population contained only single-year stopover data, we conducted Simple Conventional Correlation tests using the following structure instead $${\mathrm{Day}}_{{\mathrm{obs}}}\sim {\mathrm{Day}}_{{\mathrm{pred}}} + \left( {1 + {\mathrm{Day}}_{{\mathrm{pred}}}\|{\mathrm{bird}}} \right)$$ A population is designated as green wave surfer when both of the two following conditions are met: (1) significant (p < 0.05) positive slope with 1 ≥ lower 95% CI > 0 and upper ≥1 and (2) nonsignificant (p > 0.05) intercept, and designated as weak surfer when either of the following two conditions is met: (1) significant slope with lower 95% CI > 0 and upper <1, or lower >1 and any intercept, or (2) intercept significantly different from zero (p < 0.05) and any significant positive slope12,18,20,28. Correlation method evaluated by Stochastic Migrations Correlation method evaluated by Stochastic Migrations compares Pearson correlation coefficients of green wave surfers/weak surfers identified by Simple Conventional Correlation with stochastic migrations. We used (1) stochastic timing modelling, (2) stochastic stopover site modelling and (3) stochastic timing and stopover site modelling to generate 1000 simulated migrations per individual bird to build null models (sensu Gotelli and Graves21) of the migration–green wave correlation and metric selection. The three null models were used as references for the observed migrations to examine the migration–green wave association for simulated migrations based on random timing, random sites and their combination, respectively (Supplementary Table 2). These null models were used to test whether a metric or an indicator links with migration temporally, spatially, or both, by determining the probability of obtaining the observed parameter values from the expected distributions based on the three stochastic migrations. Because migrations driven by the green wave should show spatial selectivity for sites with a green wave and temporal selectivity for peak time of green-up, observed migrations should differ from all of the three stochastic migrations in terms of the appropriate test metric. Hence, differences from some (but not all) stochastic migrations should not be considered as weak support for the green wave hypothesis. Under the simulation scheme of stochastic timing modelling, the number and locations of stopover sites and start day of migration for each individual were kept the same as in the individual's observed migration. The stopover duration at each stopover site was randomly drawn with replacement from the stopover duration pool of the population based on the observed stopover durations of the birds. Because of the considerable variation in stopover duration (Supplementary Table 3), the temporal component of migration was well shuffled in the simulations while adhering to the empirical range. The model repeats this process 1000 times to generate 1000 simulations. We rejected random migrations that generated arrival dates that were later than the 210th day of the year. Under the simulation scheme of stochastic stopover site modelling, the duration of the non-stopover period for migration and the number and duration of stopovers for each individual were kept the same as in the individual's observed migration, but stopover site locations and migration tracks were stochastically generated. Although stochastic movement track simulations have recently been used in several movement ecology studies65,66, they have never, to our knowledge, been applied to long-distance migration. Two challenges in using such simulations are (1) the contrasting movement pattern of migratory flights (long distance, short time, high speed) and stopover periods (short distance, long time, low speed), which renders successful simulation very difficult; (2) the often irregularly sampled and highly auto-correlated data, which make many movement models inapplicable67,68. To address these issues, we performed a four-step process to generate stochastic migration model outputs (Supplementary Fig. 8). First, for each individual's migration in each year, we clipped migration tracks from the last point on the wintering ground to the first point on the breeding grounds or the last stopover site. We removed movement tracks of stopover periods from the complete migration tracks, and fused adjacent segments by directly linking endpoints and set the time interval between the two endpoints the same as the interval between the first endpoint to its subsequent observed point. In this way, we constructed stopover-free migration tracks consisting of flights and short-time stopovers, which were more uniform in terms of movement pattern and easier to model and realistically simulate. For the sake of modelling validity, we excluded fused tracks consisting of fewer than 15 locations. Second, to preserve individual movement characteristics in random migrations, we applied a continuous-time correlated random walk model (CTCRW) for each individual on the fused migration tracks to estimate parameters for velocity and drift distributions69. This approach allows for unevenly sampled tracking data and can handle auto-correlated movement data. By including drift—a less variable movement type (the overall directional migration movement tendencies of larger spatio-temporal scales, i.e., from wintering to breeding ground), and velocity—a more variable movement type nested within drift (the variable movement patterns at finer spatio-temporal scales, such as the daily flight and roosting movements). For each single fused migration track, we fitted a CTCRW with the starting location of the track, mean migration speed (total displacement between the first and last points of the migration tracks divided by the time accounted for by the fused migration track) and zero as the initial location, drift and velocity, respectively. To obtain biologically meaningful models, we constrained model parameters to only allow decreasing autocorrelation of velocity and drift with increasing time lag (the time interval between any two considered locations), and less variability for drift than velocity, dropping models that were unsuccessful in estimating parameter confidence intervals (see Supplementary Data 2 for model parameters). Third, we generated 1000 stochastic migrations for each individual in each year based on the model parameters derived in the second step. We initialised the location, drift and velocity with the observed starting location, mean migration speed (as described in the second step) and the difference between observed speed of the first step and the mean migration speed. In the subsequent step, drift and velocity were drawn from distributions determined by the empirical model parameters and the current drift/velocity states (see Johnson et al.69 for more mathematical details of the model). We ended a simulation when the simulated track lasted the same time as the observed one and kept the simulation if the great-circle distance between the ends of stochastic and observed migration tracks was not >200 km. To make the simulations biologically meaningful, we constrained the maximum overall speed (the combination of drift and velocity) to 120 km per hour22. For the sake of speed of simulation and computation, we set the step interval to 2 h. To ensure the simulated migration tracks did not include unlikely migration routes, we estimated the regular migration range of each population based on literature sources70, eBird database71 and expert knowledge (Supplementary Fig. 9). We excluded simulated migration tracks if >5% of their locations were outside of the regular migration range. Finally, we randomly located stopover sites along each stochastic track with the same number of stopover and same durations as the observed tracks. We identified all available points for a stopover site as those which neither fell in the sea within the 5-km buffer zone based on the global shoreline database 2.3.6 at crude resolution72 nor were classified as forest, woodland, urban and built or bare ground by the AVHRR land cover product56. We then randomly chose the locations for stopover sites and designated the corresponding duration. In accordance with the identification of stopover sites, the distance between any stopover sites/wintering/breeding site was not <30 km. The flight distance of any migration leg was not allowed to exceed the maximum flight distance of observed migration legs of the corresponding species. Under the simulation scheme of stochastic timing and stopover site modelling, the total non-stopover period during the migration and the number of stopover sites for each individual were kept the same as the individual's observed migration, but stopover site locations, migration tracks, migration initiation starting dates and stopover durations were stochastically generated. This simulation scheme was the same as the four-step procedure of stochastic stopover site modelling in the initial three steps but differs in the fourth step where stochastic timing and stopover site modelling performed a stochastic process similar to stochastic timing modelling to generate stochastic stopover timing; that is, for each set of simulated tracks, we randomly located stopover sites along the tracks and then determined migration starting dates and stopover durations from the observed migration starting dates and stopover duration pools of that population, respectively. We only accepted migrations that generated arrival at breeding sites before the 210th day of the year (see Supplementary Table 2 for comparison of the three null models). We calculated and compared the Pearson's correlation coefficient of the observed arrival day vs. predicted arrival day for the observed migration and three types of stochastic migrations18. If (1) the observed migration was classified as a green wave surfer or weak surfer, by Simple Conventional Correlation, and (2) the Pearson's correlation coefficient of the observed migration was positive and significantly higher than those of all types of stochastic migrations, i.e., the observed migration surfed the green wave better than random, then the population was considered as green wave surfer. MSSM MSSM compares green wave metrics between observed and stochastic migrations generated by (1) stochastic timing modelling, (2) stochastic stopover site modelling and (3) stochastic timing and stopover site modelling, as described above. We calculated all GWIs (fitted NDVI, GWI and IRG), day length and air temperature, for simulated stopover in each simulation scheme and compared this with the observed migrations using Dunn's test of multiple comparisons with p-values using Benjamini–Hochberg's adjustment73. Because the non-normality of residuals, we could not use the mixed-effect linear model in this case, which can account for the multiple measurements per (observed and stochastic) migration track and year. For populations containing only observed and stochastic timing migrations, we performed Wilcoxon tests to identify differences in the two groups. A population was designated as surfer if the metric of observed migration was significantly higher than all stochastic ones, as suggested by the green wave hypothesis and other studies12,45. Variation in the migration–green wave associations We divided the migrations of birds into five geographical regions, based on their flyway and aggregation of stopover sites (Supplementary Fig. 10). Among several bill shape parameters that correlate with dietary composition24, mechanical advantage, calculated as the ratio of the in-lever (the distance from the bill axis of rotation to the upper mandible-jugal joint) to the out-lever (the distance from the bill axis of rotation to the tip of the upper mandible), correlates significantly with diet composition of individual species. Species with bills with a higher mechanical advantage have a higher proportion of leaves in the diet, and thus are more likely to be associated with the green wave during spring migration. Due to the lack of skeletal specimens for the measures for mechanical advantage calculation, we used the ratio of upper mandible depth-length ratio, which serves as a good approximation for mechanical advantage (adjusted R2 = 0.89, N = 5, linear modelling based on the study genus with available mechanical advantage data reconstructed from Olsen24). To obtain the upper mandible depth-length ratio, we obtained five lateral photos for each species and measured the bill depth-length ratio (Supplementary Table 7). We used the mixed-effect models, with the existence of migration–green wave associations as the response variable, the approximate mechanical advantage and biological family as fixed effects, and geographical range as a random effect. The three categories of the response variable (non-surfer, weak surfer and surfer) made a direct implementation of the mixed-effect logistic model difficult. We therefore applied three modelling schemes to represent models robust against type II error, with balanced robustness, and robust against type I error respectively: (1) mixed-effect logistic model, considering only surfer as 1 and others as 0; (2) mixed linear model, considering surfer as 1, weak surfer as 0.5, and non-surfer as 0; (3) mixed-effect logistic model, considering surfer and weak surfer as 1 and non-surfer as 0. We included biological family as a fixed factor in the model to account for the cross-family morphological difference, which may introduce systematic bias to the approximated mechanical advantage. We approximated variance partitioning of fixed and random effects using the methods of Nakagawa and Schielzeth74 and Johnson75. We did not use phylogenetic logistic models because our sample size (10 species) was too small to detect phylogenetic signal with sufficient statistical power76, or to induce type I error77, and because of the constant association between diet and bill shape irrespective of the use of non-phylogenetic or phylogenetic models24. The source data underlying Figs. 2–4 and Supplementary Figs. 4–6 are provided as a Source Data file in figshare (https://figshare.com/s/a65afee29225c6db51cd). The dataset generated and/or analysed during the current study are included in Supplementary Data and Source Data files. A reporting summary for this article is available as a Supplementary Information file. Code availability We conducted all analyses in R 3.3.278. We used the greenbrown package for double-logistic fitting79, lme4 package for generalised mixed modelling80 and crawl for continuous-time correlated random walk modelling69. 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Version 2.2, 2015-04-15, http://greenbrown.r-forge.r-project.org/ (2015). Bates, D., Mächler, M., Bolker, B. & Walker, S. Fitting linear mixed-effects models using lme4. J. Stat. Software 67, 1–48 (2015). We thank Lei Fang, Qin Zhu, Hui Yu, Yuzhan Yang and Zhujun Wang for fieldwork; Xianghuang Li, Hongbin Li and Shujuan Fan for collecting remote-sensing datasets; Stuart Pimm, Devin Johnson and Aaron Olsen for constructive comments. We appreciate assistance of the staff of the Poyang Lake National Nature Reserve, Nanjishan National Nature Reserve, East Dongting Lake National Nature Reserve, Shengjin Lake National Nature Reserve, U.S. Geological Survey Western Ecological Research Center, Wildlife Science and Conservation Center of Mongolia and Korea Institute of Environmental Ecology, during the field study. We thank Alyn Walsh, John Skilling, Ed Burrell, Mitch Weegman, Angus Maciver, Arthur Thirlwell and Maurice Cassidy for help with the catching and tagging of the geese in Scotland and Ireland. We thank K.-M. Exo and K. Oosterbeek for supporting obtaining the tracking data of barnacle geese (three populations). We thank David Cooper, Peter Ertl, José Frade, Stanislav Harvančík, Benjamin Keen, Marcel Langthim, Yann Muzika and Manish Panchal for kindly providing images. Bird capture and logger deployment in this study in the UK was carried out under license from the BTO, and elsewhere in accordance with the guidance and permission (no. rcees-ddll-001) of Research for Eco-Environmental Sciences, Chinese Academy of Sciences. The study was supported by the National Key Research and Development Program of China (grant no. 2016YFC0500406), the National Natural Science Foundation of China (grants no. 31661143027, 31670424, 31500315), China Biodiversity Observation Networks (Sino BON), Scottish Natural Heritage, FlySafe (http://iap.esa.int/flysafe)—a project of the European Space Agency Integrated Applications Promotion (IAP) programme (http://iap.esa.int/), the Israel Science Foundation (grant no. 2525/16), the Minerva Center for Movement Ecology, the Adelina and Massimo Della Pergola Chair of Life Sciences and China Scholarship Council—Hebrew University of Jerusalem Scholarship Program. State Key Laboratory of Urban and Regional Ecology, Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences, 100085, Beijing, China , Lei Cao & Liding Chen Movement Ecology Laboratory, Department of Ecology, Evolution and Behavior, Alexander Silberman Institute of Life Sciences, The Hebrew University of Jerusalem, 91904, Jerusalem, Israel & Ran Nathan University of Chinese Academy of Sciences, 100049, Beijing, China Lei Cao Department of Bioscience, Aarhus University, Kalø, Grenåvej 14, DK-8410, Rønde, Denmark Anthony D. Fox & Jesper Madsen School of Biological Sciences, University of Queensland, Brisbane, QLD, 4072, Australia Richard Fuller The Wildfowl & Wetlands Trust (WWT), Slimbridge, Gloucestershire, GL2 7BT, UK Larry Griffin & Carl Mitchell College of Life Science and Technology, Central South University of Forestry and Technology, 410004, Changsha, China Yunlin Zhao & Zhenggang Xu Animal and Plant Quarantine Agency, Gimcheon, 39660, Republic of Korea Oun-Kyong Moon School of Biological, Earth and Environmental Science, University College Cork, Distillery Fields, North Mall, Cork, T23 N73K, Ireland David Cabot Wildlife Science and Conservation Center, B-802 Union Building, Sukhbaatar District, Ulaanbaatar, 14210, Mongolia Nyambayar Batbayar Department of Migration and Immuno-Ecology, Max Planck Institute for Ornithology, Am Obstberg 1, 78315, Radolfzell, Germany Andrea Kölzsch Group of Mathematical Modelling, Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky University Oldenburg, Carl-von-Ossietzky-Straße 9-11, 26111, Oldenburg, Germany Institute for Wetlands and Waterbird Research e.V. (IWWR), Am Steigbügel 3, 27283, Verden(Aller), Germany Vogeltrekstation—Dutch Centre for Avian Migration and Demography (NIOO-KNAW), Wageningen, 6708 PB, The Netherlands Henk P. van der Jeugd Sovon Dutch Centre for Field Ornithology, PO Box 6521, 6503 GA, Nijmegen, The Netherlands Search for Xin Wang in: Search for Lei Cao in: Search for Anthony D. Fox in: Search for Richard Fuller in: Search for Larry Griffin in: Search for Carl Mitchell in: Search for Yunlin Zhao in: Search for Oun-Kyong Moon in: Search for David Cabot in: Search for Zhenggang Xu in: Search for Nyambayar Batbayar in: Search for Andrea Kölzsch in: Search for Henk P. van der Jeugd in: Search for Jesper Madsen in: Search for Liding Chen in: Search for Ran Nathan in: X.W., R.N. and L.C. conceived the study. X.W. and R.N. developed the methods, analysed the data, and wrote the paper. R.N. conceived the MSSM method. L.C. and R.N. obtained funding. X.W., L.C., L.G., C.M., D.C., Y.Z., O.M., Z.X., N.B., A.K., H.P.J. and J.M. acquired animal movement tracking data. A.D.F. and L.G. provided important input during manuscript preparation, and all other authors commented and contributed to the final version. Corresponding authors Correspondence to Lei Cao or Ran Nathan. Journal peer review information: Nature Communications thanks Sophie Bestley and other anonymous reviewers for their contribution to the peer review of this work. Peer reviewer reports are available. Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. peer review file Description of Additional Supplementary Files Source data Nature Communications menu Editors' Highlights Top 50 Read Articles of 2018	CommonCrawl
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up. How to interpret Bayesian (posterior predictive) p-value of 0.5? In the following paper found here and reference below, the author suggests that "if the model is true or close to true, the posterior predictive p-value will almost certainly be very close to 0.5" . This is found in the very beginning of Section 6 in the paper. I am trying to interpret what is meant when he says 'model is true'. My questions are: i) Statistically what is a "true model" as said in the quote above? ii) What does a value of 0.5 mean in simple words? Gelman, A. (2013). Two simple examples for understanding posterior p-values whose distributions are far from uniform. Electronic Journal of Statistics, 7, 2595-2602. probability bayesian posterior user121user121 $\begingroup$ Could you give a full reference to the paper just in case the link goes dead in the future (so as to make the thread comprehensible for future readers)? $\endgroup$ – Richard Hardy The model is true if the data are generated according to the model you are doing inference with. In other words, the unobserved parameter is generated by the prior, and then, using that parameter draw, your observed data are generated by the likelihood. This is not the setup where you consider multiple models $M_1, M_2, \ldots$ and have discrete probability distributions describing the model uncertainty. A posterior predictive "p-value" of .5 means your test statistic $T(y)$ will be exactly equal to the median of the posterior predictive distribution of $T(y^{\text{rep}})$. Generally, this distribution and its median are obtained by looking at simulated data. Roughly speaking, this tells us that predictions (i.e. $T(y^{\text{rep}})$) "look like" our real data $T(y)$. If our model's predictions are "biased" to be too high, then we will get a number greater than $.5$, and if they are generally on the low side, we will get a number less than $.5$. The posterior predictive distribution is \begin{align} p(y^{\text{rep}} \mid y) &= \int p(y^{\text{rep}},\theta \mid y) d\theta\\ &= \int p(y^{\text{rep}}\mid \theta, y)p(\theta \mid y) d\theta\\ &= \int \underbrace{p(y^{\text{rep}} \mid \theta)}_{\text{model}}\underbrace{p(\theta \mid y)}_{\text{posterior}} d\theta \\ &= E_{\theta \mid y}\left[p(y^{\text{rep}} \mid \theta) \right]. \end{align} Then you take this distribution and integrate over the region where $T(y^{\text{rep}})$ is greater than some calculated nonrandom statistic of the dataset $T(y)$. $$ P(T(y^{\text{rep}}) > T(y) \mid y) = \int_{\{T(y^{\text{rep}}) : T(y^{\text{rep}}) > T(y) \}} p(y^{\text{rep}} \mid y) dy^{\text{rep}}. $$ In practice, if computing the above integral is too difficult, this means drawing parameters from the posterior, and then, using these parameters, simulating many $y^{\text{rep}}$s. For each simulated data set (of the same size as your original/real data set), you calculate $T(y^{\text{rep}})$. Then you calculate what percent of these simulated values are above your single $T(y)$ coming from your real data set. For more information, see this thread: What are posterior predictive checks and what makes them useful? Because you are assuming there is no model uncertainty, $p(y^{\text{rep}} \mid y)$ is an integral over the parameter space; not the parameter space AND the model space. TaylorTaylor $\begingroup$ if I do a ppd check Pr(T(y_rep)> T(y)), and get 0.5,I know this means the simulated and observed data are similar and the model is a good fit. But my question is why? what does the 0.5 tell us as say opposed to 0.8? $\endgroup$ $\begingroup$ @user121 it might to help to think about the situation when it comes out to be .0001. This is bad because your model is predicting $T$s that are nowhere near the $T$ you calculated from the data. $\endgroup$ – Taylor $\begingroup$ what would .9999 imply? $\endgroup$ $\begingroup$ It's far away (as measured by your posterior) in the other direction. It means your model is predicting something not like the data you have, and it's impoetant to nderstand why it's overriding common sense/intuition. .5 is good because half of the simulations are above your one real T and half are below. $\endgroup$ $\begingroup$ appreciate the feedback. I dont think I am asking clearly what I'm looking for. If the p-val= 0.9999, what statement can we make versus a p-val =0.5214. I do not understand why 0.5 is the 'ideal' number for model fit. It is something fundamental I'm missing. Is there some physical meaning behind it? $\endgroup$ I would recommend reading the underlying papers that this paper is derived from as the terminology doesn't appear to have become standard in the field. The original paper is by Rubin, but Gelman is writing from Meng. Meng, X. (1994). Posterior Predictive p-Values. The Annals of Statistics, 22(3), 1142-1160. As to your questions: I am trying to interpret what is meant is meant when he says 'model is true'. My questions are: i) Statistically, what is a "true model" as said in the quote above? So there is some unfortunate language usage as p-values are a Frequentist idea and Bayesian methods do not have p-values. Nonetheless, within the context of the articles beginning with Rubin, we can discuss the idea of a Bayesian p-value in a narrow sense. As to question one, Bayesian models do not falsify a null hypothesis. In fact, except where some method is intending to mimic Frequentist methods, as in this paper, the phrasing "null hypothesis" is rarely used. Instead, Bayesian methods are generative methods and are usually constructed from a different set of axioms. The easiest way to approach your question is from Cox's axioms. Cox, R. T. (1961). The Algebra of Probable Inference. Baltimore, MD: Johns Hopkins University Press. Cox's first axiom is that plausibilities of a proposition are a real number that varies with the information related to the proposition. Notice the word probability wasn't used as this also allows us to think in terms of odds or other mechanisms. This varies very strongly from null hypothesis methods. To see an example, consider binary hypotheses $H_1,H_2$, which in Frequentist methods will be denoted $H_0,H_A$. What is the difference? $H_0$ is conditioned to be true and the p-value tests the probability of observing the sample, given the null is true. It does not test if the null is actually true or false and $H_A$ has no form of probability statement attached to it. So, if $p<.05$, this does not imply that $\Pr(H_A)>.95$. In the Bayesian framework, each proposition has a probability assigned to it so that if $H_1:\mu\le{k}$ and $H_2:\mu>k$, then it follows that if $\Pr(H_1)=.7327$ then $\Pr(H_2)=.2673$. The true model is the model that generated the data in nature. This varies from the Frequentist method which depends only on the sampling distribution of the statistic, generally. As to question two, Gelman is responding to Meng. He was pointing out that in a broad variety of circumstances if the null hypothesis is true, then $\Pr(y^{rep}\|y)$ will cluster around .5 if you average over the sample space. He provides a case where this is useful and one where it is a problem. However, the hint as to why comes from the examples, particularly the first. The first has been constructed so that there are great prior uncertainty and this use of a nearly uninformative prior propagates through to the predictive distribution in such a way that, almost regardless of your sample, Rubin and Ming's posterior predictive p-values will be near 50%. In this case, it would mean that it would tell you there is a 50% chance the null is true, which is highly undesirable since you would rather be either near 100% or in the case of falsehood, 0%. The idea of Bayesian posterior p-values is the observation that since you are now in the sample space as random, rather than the parameter space as random, the rough interpretation of a Bayesian posterior probability is remarkably close to the Frequentist p-value. It is problematic because the model is not considered a parameter, in itself, and has no prior probability as would be the case in a test of many different models. The model, $H_A$ versus $H_B$ is implicit. This article is a warning of something that should, in a sense, be obvious. Imagine you had fifty million data points and there was no ambiguity as to the location of the parameter, then you would be stunned if the resulting predictive distribution was a bad estimator over the sample space. Now consider a model where the results are ambiguous and the prior was at best weakly informative, then even if the model is true, it would be surprising to get a clear result from the posterior predictive distribution. He provides an example where data is drawn from a population that has a standard normal distribution. The required sample would have to be 28,000 to get a rejection of the model. In a standard normal population, that will never happen. The model is about the propagation of uncertainty and whether or not Rubin/Meng's idea generates a useful construct when it is needed most when the data is poor, small, weak or ambiguous as opposed to samples that are stunningly clear. As an out-of-sample test tool, its sampling properties are undesirable in some circumstances, but desirable in others. In this case, what Gelman is saying is that regardless of the true probability of the model, the out-of-sample validation score provided by the Bayesian posterior predictive p-value will be near 50% when the null is true when the data doesn't clearly point to a solution. This has lead to the criticism of the idea as uncalibrated with the true probabilities. See Bayarri, M. J. and Berger, J. (2000). P-values for composite null models. Journal of the American Statistical Association 95, 1127–1142. Dave HarrisDave Harris $\begingroup$ very good feedback $\endgroup$ On question (ii), there is much more to be said. Indeed, there are other kinds of "Bayesian" GOF p-values that have uniform distribution when the model used for inference was used to generate the data -which means that such p-values should not be compared to 0.5 but to 0 and 1. The simplest of these is the sampled posterio GOF p-value. See the following refernces: Robins JM, van der Vaart A, Ventura V (2000) Asymptotic distribution of P values in composite null models. J Am Stat Assoc 95: 1143–56. Johnson VE (2007) Bayesian Model Assessment Using Pivotal Quantities. Bayesian Anal 2: 719–34. Gosselin F. (2011) A New Calibrated Bayesian Internal Goodness-of-Fit Method: Sampled Posterior p-Values as Simple and General p-Values That Allow Double Use of the Data. Plos One. https://doi.org/10.1371/journal.pone.0014770 Frédéric GosselinFrédéric Gosselin Thanks for contributing an answer to Cross Validated! Not the answer you're looking for? Browse other questions tagged probability bayesian posterior or ask your own question. What are posterior predictive checks and what makes them useful? Calculate a Bayesian 'posterior predictive p-value' for a multinomial logistic regression Generate Posterior predictive distribution at every step in the MCMC chain for a hierarchical regression model Unexpected pattern in posterior predictive check with set.seed() Are predictive distributions supposed to be distributions of future data? The distribution of a posterior predictive p-value under certain assumptions Sampling distribution of the p-value	CommonCrawl
Write down the relation R on the Power-set of S = {1, 2, 3, 4}, … Write down the relation R on the Power-set of S = {1, 2, 3, 4}, defined by, R = {(A, B) \| A and B are subsets of S and they have the same cardinality} using any one of the methods: (i) set of ordered pairs, (ii) directed graphs, (iii) matrix notation. S = {1, 2, 3, 4} R = {(A, B) \| A and B are subsets of S and they have the same cardinality} Subsets of S = {\phiϕ,{1},{2},{3},{4},{1,2},{1,3},{1,4},{2,3},{2,4},{3,4},{1,2,3},{2,3,4},{1,3,4},{1,2,4},{1,2,3,4}} Now, we need those subsets whose cardinality are same/equal. n(\phiϕ)=0 n({1})=n({2})=n({3})=n({4})=1 n({1,2})=n({1,3})=n({1,4})=n({2,3})=n({3,4})=n({2,4})=2 n({1,2,3})=n({2,3,4})=n({1,3,4})=n({1,2,4})=3 n({1,2,3,4})=4 Thus, R = { ({1},{2}), ({1},{3}), ({1},{4}), ({2},{3}), ({2},{4}), ({3},{4}), ({1,2},{1,3}), ({1,2},{1,4}), ({1,2},{2,3}), ({1,2},{2,4}), ({1,2},{3,4}), ({1,3},{1,4}), ({1,3},{2,3}), ({1,3},{2,4}), ({1,3},{3,4}), ({1,4},{2,3}), ({1,4},{2,4}), ({1,4},{3,4}), ({2,3},{2,4}), ({2,3},{3,4}), ({2,4},{3,4}), ({1,2,3},{2,3,4}), ({1,2,3},{1,3,4}), ({1,2,3},{1,2,4}), ({2,3,4},{1,3,4}), ({2,3,4},{1,2,4}), ({1,3,4},{1,2,4}) } Describe the Hasse diagram formed by the Relation "x is a divisor of y" for the set A = {1, 3, 6, 12, 24, 48} Express each of these statement using quantifires : No one has climbed every mountain in the Himalayas Express each of these statement using quantifires : every movie actor has either been in a movie with Kevin Bacon or has been in a movie with someone who has been in. a movie with Kevin Bacon. 3.3 In a class of 100 learners, 80 do Mathematics and 35 do Physics. If x learners do Mathematics and Physics, and y learners do neither Mathematics nor Physics, find the greatest possible value of y. In the following Statement: " If the BIOS test runs fine, the CPU and motherboard must be OK. If the CPU and motherboard and memory are all OK, then there must be a flaw in the OS. The BIOS test runs fine and the memory is OK. … Express 2x+1 / x(x+1) in partial fractions and hence find the general solution of the differential equation x(x+1)dy/dx = y(2x+1) expressing y explicitly in terms of x. A Hasse diagram is a graphical rendering of a partially ordered set displayed via the cover relation of the partially ordered set with an implied upward orientation. A point is drawn for each element of the poset, and line segments ar… For the following relation on the set {1,2,3,4,5,6,7,8,9,10,11,12}. Find the number of distinct permutation of the word 'programmer ' Draw the Venn diagrams for each of these combinations of the sets A, B, and C. a) A ∩ (B − C) b) (A ∩ B) ∪ (A ∩ C) c) (A ∩ B) ∪ (A ∩ C) The number of elements in the Power set P(S) of the set S = { { Φ} , 1, { 2, 3 }} is? complete \space question \space is \space \\ Let \space f:R→R \space is \space defined \space by \space f(x)= \space \frac{x}{1+∣x∣}.\\ \space Then \space… Let f :R \to→ R be f (x) =x /(1+\|x\|) 2) Translate the given statements into propositional logic using the propositions provided You are eligible to be the President of the USA if and only if you are at least 35 years old, were born in the USA, or at the time of your … Suppose the city of MISSISSAUGA has a contest where they arrange the letters of their city name in a particular order. The city residents have to guess which order the city has chosen, and the winner gets $10 000. The rules allow peop… Determine whether the function f(x) = x^2 + 3x + 2 from Z to Z is a bijective function. Solve the recurrence by master's method. a) T(n) = 3T[n/4)+ cn^2 b) T(n)=T[2n/3)+1 Solve the recurrence by substitution method. T(n) = 2T (n/2)+n-1 and T (1) =1. Translate the following English sentences into Propositional Logic. Let: C A bird can fiy F A bird has wings a) If Bird has wings, then bird can fly. b) If bird has no wings, then it can't fly. Translate the following Propositional Logic to English sentences. Let: E-Lion is eating H=Lion is hungry a) E-H b) EA-H c)-(H-E) Is (p q) > I(p>q)> q] a tautology? Why or why not? Draw the Venn diagrams for each of these combinations of the sets A, B, C, and D. a) (A ∩ B) ∪ (C ∩ D) b) A c U B c U Cc U Dc c) A − (B ∩ C ∩ D) d) A ⊕ B How many strings of six lowercase letters from the English alphabet contain: i.The letter a? ii. The letters a and b? iii. The letters a and b in consecutive positions with a preceding b, with all the letters distinct? iv. The letters… Let A= {0, 1, 2, 3} and define relations R, S and T on A as follows: R= { (0,0),(0,1),(0,3),(1,0),(1,1),(2,2),(3,0),(3,3)} S= {(0, 0),(2,2),(1,1), (0, 2), (0, 3), (2, 3),(2,2)} T= {(0, 1), (2, 3),(0,0),(2,2),(1,0),(3,3),(3,2)} i. Is R… Determine whether the relation R on the set of all people is irreflexive, where (a, b) ∈ R if and only if : i) a and b were born on the same day. ii) a has the same first name as b. iii) a and b have a common grandparent Question No 05: [07 marks] Let f (x) = ax + b and g(x) = cx + d, where a, b, c, and d are constants. Determine necessary and sufficient conditions on the constants a, b, c, and d so that f ◦ g = g ◦ f Find the domain and range of these functions. i. The function that assigns to each pair of positive integers the first integer of the pair b) the function that assigns to each positive integer its largest decimal digit ii. The functio… Briefly answer the following short questions 1) Determine if the following argument is valid and explain why. Every CS major takes CMSC203. Mr. Ali is taking CMSC203, therefore he is a CS major. 2) What is the time complexity (in … Prove that for every positive integer n. 1.2.3+2.3.4++ n(n+1)(n+2) = n(n+1)(n+2)(n+3)/4. How many strings of six lowercase letters from the English alphabet contain: i.The letter a? ii. The letters a and b? iii. The letters a and b in consecutive positions with a preceding b, with all the letters distinct? iv. The lett… Determine whether the function f(x) = \|4x\| from Z to Z is a bijective function. A boy has 10 red balls, 20 blue balls,25 black balls ,and 30 pink balls .He select ball at random without looking at them .calculate the minimum number of balls he must select to be sure that at least 6 balls of the same color . 1) Draw the Hasse diagram for inclusion on the set P(S), where S = {a, b, c, d} 2) Let S = {1,2,3,4} with lexicographic order "<=" relation a. Find all pairs in S x S less than (2, 3) b. Find all pairs in S x S greater than… Determine how many bit strings of length 5 can be formed ,where three consecutive 0s are not allowed Determine whether the given relation is reflexive, symmetric, transitive, or none of these. R is the "greater than or equal to" relation on the set of real numbers: For all x, y ∈ R , xRy ⇐⇒ x ≥ y determine how many bit strings of length can be formed, where three consecutive 0s are not allowed Use a Venn diagram to illustrate the set of all months of the year whose names do not contain the letter R in the set of all months of the year. Let p and q be the propositions defined as below. p : It is below freezing. q : It is snowing. Show that a complete graph with n vertices has n(n -1) 2 edges Show that for any real number x, if x2 is odd, then x is odd. Let p, q and r be statements. Use the Laws of Logical Equivalence and the equivalence of → to a disjunction to show that: ∼ ((p ∨ (q →∼ r)) ∧ (r → (p∨ ∼ q))) ≡ (∼ p ∧ q) ∧ r. Let p, q and r be statements. Suppose you know that the statement form ((q → p) ∨ r) ∨ (∼ r ∧ p) is false. What can you conclude about the truth values of the three statement variables? Model two contextualized problems using binary trees both quantitatively and qualitatively Prove the following sentences using any prove method [ the most appropriate one]: a) If r is rational and s is irrational, prove that 2r+s is irrational. b) If t and s are integers and t × s is even, then t is even or s is even. Prove that (a ∧ (b → ¬a)) → ¬b is a tautology. Prove that the following argument is valid. Write all the necessary steps a)Rashid didn't perform well in the subject, but he was present in every class. b)Every student who completed all the assignments, performed well in the subje… Determine whether each of the following compound propositions is satisfiable. Justify your answer. 1. (a) (pv-g)^(-pVg)^(-p^ g) (b) ()^(-)^(-p)^(---) (c) (pvqv-r) ^ (pv-gv-8) ^ (pv-rv-8)^(-pv-gv-) A (pvqV-s) 2) Construct a circuit using NOT gates, OR gates and AND gates of the following proposition (P and -r)or(-q and r) 3) Using basic propositional equivalence (which we did in the class) show that (pr) ^ (4) and (pvg) → are logically equivalent. (Don't use truth table for this problem) O U 2.1 Differentiate f(x) = (2x3 + 3x2 )(x2 + 5x3 +5) using product rule. (5) 2.2 Differentiate f(x) = (8x 3 + 4x )(2x 2 +5) using product rule. (5) 2.3 Differentiate f(x) = 5𝑥³+7𝑥 2𝑥²−4𝑥+5 using quotient rule. (5) 2.4 Diffe… 2fn-f(n-2) = fn+1 for n>3 The trivial negation of a proposition is: "It is not the case that [proposition]." Write two negations of the following, one trivial and one not trivial. (a) It is snowing. (b) At least 3 inches of snow fell yesterday. (c) 1…	CommonCrawl
What is more fundamental: Fock space or Hilbert space? And why? In what sense do static field configurations enter into perturbative QFT? What really are superselection sectors and what are they used for? The role of representation theory in QM/QFT? May "Quantum tunneling" be wrong and an unnecessary term which should be deleted in later education of quantum mechanics? Are the possible momenta of a particle in an infinite square well on the interval [-½,½] countable or uncountable? One Particle State in Interacting QFT (4.88 4.89 in Peskin) Why does the divergence of perturbation theory in interacting QFT imply its Hilbert space to be non-Fock? What is an observer in QFT? + 10 like - 0 dislike In non-relativistic quantum mechanics, an observer can be roughly describe as a system with wavefunction $\vert \psi^O \rangle$ which, upon interaction with another system $\vert \psi^S\rangle$ (in some way that measures the observable $\hat A$) evolves into the following system $$\vert \psi^O \rangle \otimes\vert \psi^S \rangle \to \sum_\alpha a_\alpha \vert \psi^O_\alpha \rangle \otimes \vert \phi_\alpha \rangle $$ with $\hat A \vert \phi_\alpha \rangle = A_\alpha \vert \phi_\alpha \rangle$ and $a_\alpha = \langle \phi_\alpha\vert \psi^S \rangle$ the probability of measuring the system in the state $\alpha$. $\vert \psi^O_\alpha \rangle$ is the way the observer will be when it has interacted with the system in the state. From the "point of view" of the observing system, the state will be $$\vert \psi^O_\alpha \rangle \otimes \vert \phi_\alpha \rangle$$ for some $\alpha$. The basic example works fairly well because the two systems can be decomposed in two fairly distinct rays of the Hilbert space. But in the case of a quantum field theory, how does one define an observer? Any "realistic" object (especially for interactive QFTs) will likely be a sum of every state of the Fock space of the theory, hence I do not think it is trivial to separate the system and the observer into a product of two wavefunctionals. Is there a simple way of defining observers in QFT? Perhaps by only considering wavefunctionals on compact regions of space? I can't really think of anything that really delves into the matter so I don't have a clue. This post imported from StackExchange Physics at 2017-10-11 16:32 (UTC), posted by SE-user Slereah quantum-field-theory quantum-interpretations asked May 3, 2017 in Theoretical Physics by Slereah (540 points) [ no revision ] I like to think of "observer/system" separation in the context of boundary formalism, where quantum fields live on the compact bulk region of spacetime bounded by a 3-surface where boundary states live. These states describe the interaction with the outside "observer", though in this picture the term "observer" completely loses its original meaning. This post imported from StackExchange Physics at 2017-10-11 16:32 (UTC), posted by SE-user Solenodon Paradoxus commented May 4, 2017 by Solenodon Paradoxus (85 points) [ no revision ] Nima Arkani-Hamed speaks very eloquently on the general question of observers in quantum field theory and quantum gravity. See for example pirsa.org/displayFlash.php?id=10080010 This post imported from StackExchange Physics at 2017-10-11 16:32 (UTC), posted by SE-user Bruce Greetham commented May 9, 2017 by Bruce Greetham (0 points) [ no revision ] As long as only scattering experiments are involved, the observer prepares the in-state at time $-\infty$ and takes a measurement on the out-state at time $+\infty$. In this setting, the observer is completely outside the QFT formalism. A correct account of an observer in relativistic QFT would have to model it as a very massive (many-particle) part of the quantum field localized in some region, in the spirit of the nonrelativistic treatment by in the work by Allahverdyan et al. reviewed by me here. I haven't seen anything like this for the relativistic case. On the other hand, papers by Peres and Terno (e.g., https://arxiv.org/abs/quant-ph/0212023) discuss relativistic quantum mechanics (not QFT) for multiple observers in different Lorentz frames. answered Nov 27, 2017 by Arnold Neumaier (15,737 points) [ revision history ] I generally agree with Arnold's opinion and comments, and I would like just underline that "the observer" makes sure that the incident particles have the necessary energy/momentum and other properties, that the target is also has the necessary properties, that the collisions happen in a deep vacuum (no other obstacles), that the measuring devices detect the scattering products correctly, etc., etc. The observer makes a huge preparatory work, accompanying work, and result processing work. In other words, he makes a permanent work keeping the necessary and sufficient conditions for a given experiment. Only with all that we may be sure of the initial and final states, withing the experimental uncertainties established with the observer. As you can see, "observer" includes experimentalists, theorists, staff and stuff, all working to make sure that a (thus simplified) QFT is applicable to the studied processes. commented Nov 27, 2017 by Vladimir Kalitvianski (92 points) [ no revision ] In the book Bryce DeWitt, The Global Approach to Quantum Field Theory, Oxford 2003 the author amplifies two points (right at the beginning, first page of the preface on page "v" in volume 1): The relevance of the Peierls bracket for the spacetime-covariant formulation of QFT; its implication for a good theory of observers and measurement in QFT, which he attributes to Bohr-Rosenfeld 1933. There is no doubt about the relevance of the Peierls bracket: This is the covariant form of the Poisson bracket (explained in detail in "Mathematical QFT - 8. Phase space"); and the positive frequency part of its integral kernel is nothing but the vacuum 2-point function (explained in "Mathematical QFT - 9. Propagators"). Chapters 7 and 8 of DeWitt's book (volume 1) mean to lay out a theory of measurement and observers in QFT based on this. I don't feel quite qualified to review this here, but if you are interested, I would suggest to take a look. answered Nov 30, 2017 by Urs Schreiber (6,095 points) [ revision history ] edited Nov 30, 2017 by Urs Schreiber Does the Peierls bracket exist for interacting systems too? In particular, does the statement about 2-point functions still apply? It sounds very interesting. commented Dec 2, 2017 by Ryan Thorngren (1,925 points) [ no revision ] The positive frequency part of the Peierls bracket is the vacuum 2-point function of a free (linear) quantum field theory corresponding to the associated linear classical theory. Did you mean this? I don't know of any nonlinear version of this statement, and your PhysicsForums article is too big to see quickly the precise statement you intend here. commented Dec 2, 2017 by Arnold Neumaier (15,737 points) [ no revision ] The Peierls bracket exist generally, also for interacting field theories. I recommend Khavkine 14. Answering whether it's relation to the vacuum 2-point function goes beyond perturbation theory would seem to require non-perturbative theory which does not exist at this point. commented Dec 3, 2017 by Urs Schreiber (6,095 points) [ no revision ] Unfortunately, the book by deWitt has no significant contribution to the original question; no definition of a model observer is given. Chapters 7 and 8 of volume 1 are about classical measurement and heuristic quantum measurement of a primitive form. All problems are swept under the many-worlds carpet where no measurement is ever done - since there is no mechanism for splitting the worlds, and without splitting there are no definite measurement results. (See also my critique of Everett's many-worlds = relative state interpretation.) commented Dec 4, 2017 by Arnold Neumaier (15,737 points) [ revision history ] p$\hbar$ysic$\varnothing$Overflow	CommonCrawl
Activity and movement of free-living box turtles are largely independent of ambient and thermal conditions Adam F. Parlin1, Jessica A. Nardone1, John Kelly Dougherty1, Mimi Rebein1, Kamran Safi ORCID: orcid.org/0000-0002-8418-67592 & Paul J. Schaeffer1 Ectotherms are assumed to be strongly influenced by the surrounding ambient and environmental conditions for daily activity and movement. As such, ecological and physiological factors contribute to stimuli influencing navigation, extent of movement, and therefore habitat use. Our study focused on the intensity of activity (from acceleration data) and extent of movement (from GPS and thread trailing data) of Eastern box turtles (Terrapene carolina carolina) in a fragmented landscape near their northern population limit. First, we quantified the thermal performance curve of box turtles using activity as a measure of performance. Second, we investigated ecological factors that could influence activity and movement and characterized the movement as extensive (exploration) and intensive (foraging). In contrast to previous lab work investigating effects of temperature on activity, we found no relationship between box turtle activity and temperature in the field. Furthermore, box turtle activity was consistent over a wide range of temperatures. Cluster analysis categorized movement recorded with GPS more as intensive than as extensive, while thread trailing had more movement categorized as extensive than intensive. Box turtle activity was higher during the morning hours and began to decrease as the day progressed. Based on the microclimate conditions tested, we found that box turtle movement was influenced by precipitation and time of day, and activity was most influenced by absolute humidity, ambient temperature, cloud cover, and time of day. Our model ectotherm in this study, the Eastern box turtle, had activity patterns characteristic of a thermal generalist. Sampling resolution altered the characterization of movement as intensive or extensive movement, possibly altering interpretation. More information on the resolution needed to definitively identify foraging and exploratory behavior in turtles is needed. Activity and movement were nearly independent of environmental conditions, which supports the overall interpretation that turtle performance is that of a broad environmental generalist. Future studies of movement of other turtle and reptile species are needed to determine the generality of these findings. Animals move through their environment with a suite of inputs modified by ecological and physiological factors to determine navigation, migration, dispersal, foraging, and exploration. Furthermore, the environment needs to be navigable terrain and free of any major geographic barriers. The habitat occupied by a species, whether continuous or fragmented, is patchy and selection hierarchical [1], and as a result movement patterns depend on integration of numerous ecological, physiological, and behavioral variables [2]. Understanding animal navigation throughout their habitat thus requires high resolution measurements of activity, movement, and multiple aspects of ambient conditions [3], optimally with field-based studies of free-living animals. Free-living ectotherms are also dependent on microclimate conditions being within tolerable physiological limits [4]. Vegetative structure, topography, and geographic barriers are ecological factors that shape the landscape and influence the microclimate conditions available to ectotherms, thus impacting activity and movement. Additionally, the way in which an individual exploits its environment may be altered by extrinsic or intrinsic factors, potentially leading to alteration of the nature of movement in the available habitat [5]. Within these ecological factors, microclimate conditions including temperature, humidity, and rainfall can alter activity and movement [6, 7]. The relevance of microclimate on physiology depends on how each factor impacts performance. One of the most influential ambient conditions impacting ectotherms is temperature. Ambient temperature and environmental conditions must be within tolerable physiological limits for ectotherms, and laboratory observations strongly support a role for temperature on movement performance in many reptiles [8,9,10] including box turtles [11]. Prior work on box turtle movement and activity in the lab showed a strong thermal dependence of strides per minute, total time stopped and velocity through test temperatures between 10 and 32 °C [11]. However, laboratory studies may not always reflect patterns and processes observed in nature, and thus may not represent what animals are capable of, or choose to do, under natural conditions. For example, our recent work showed that in the field, box turtle movement was not correlated with body temperature [12]. Further, the physiologically optimal temperatures of an organism can be decoupled from ecologically relevant temperatures [13]. For instance, locomotor performance tends to decrease drastically when body temperatures rise even slightly above physiologically optimal levels [14]. As a result, body temperatures below the physiological optimum may be more ecologically relevant, especially in fluctuating environments to ensure that overheating is avoided. Active thermoregulation potentially permits activity in otherwise sub-optimal conditions. Thermoregulation relies on heat sources and sinks within a habitat to be able to maintain temperatures for physiological processes such as locomotion, assimilation, and growth [15]. Thermal sensitivity of performance permits us to categorize an organism as a thermal generalist or a thermal specialist. This thermal sensitivity ranges from a thermal generalist, which can perform over a broad range of temperatures, to a thermal specialist, whose performance is strongly dependent on temperature [10]. The interactions between thermal sensitivity and thermoregulation ultimately allow ectotherms to regulate their body temperature in concurrence with environmentally available temperatures to grow, survive, and reproduce [16]. Thus, changes in thermal conditions will potentially alter many aspects of activity and movement in ectotherms, including exploitation of available habitat [17], dispersal [18], and ultimately distribution [19]. The goal of the study was to analyze the ecological and physiological factors that influence daily activity and movement in box turtles throughout their active season using biologging devices carried by free-living animals. Overall dynamic body acceleration (ODBA) was used as a measure of box turtle activity, and the linear distance between consecutive GPS points or thread trailing were used as measures of movement. We analyzed the relationship between movement or accelerometer measurements with nearby weather-station data, determining the thermal sensitivity of activity, and analyzing domain and transition movement relative to activity. We hypothesized that (1) box turtle activity is thermally sensitive and thus temperature-dependent based on previous lab work, (2) box turtle movement and activity would be influenced by ambient conditions including precipitation and absolute humidity, and (3) fine-scale sampling methods will better reveal intensive movement while lower resolution sampling will be biased towards extensive movements. Study site We monitored Eastern box turtles (Terrapene carolina carolina) in Southwest Ohio at the Miami University Natural Areas (MUNA: 39.5° N, 84.7° W). For investigation of the environmental factors influencing activity and movement, box turtles are an ideal ectotherm to study because of their ability to tolerate heavy loads relative to their mass, allowing for multiple biologging devices to be attached. Our study sites are near the northern edge of their distribution east of the Mississippi river. Forest habitat in this landscape is highly fragmented due to the dominance of agriculture in the area, with forest fragments ranging in size from 5.5 ha to 400 ha. Climate in this region is characterized as humid continental with large seasonal temperature differences including warm to hot summers with high humidity and occasional severely cold winters, with precipitation distributed throughout the year [20]. Box turtles are listed as a species of special concern in Ohio with limited information on population demographics [21]. Movement and activity monitoring We monitored two groups of box turtles in 2014 and 2015 using a combination of thread trailing devices (group one) and GPS-Accelerometer tags (e-Obs, Grünwald, Germany; hereafter 'GPS-ACC', group two) which recorded both GPS locations and overall dynamic body acceleration (ODBA) data. Devices attached to the turtles were 83 × 26 × 20 mm (L x W x H) and were placed caudally on the shell such that the leading margin sloped upwards. Turtles monitored with GPS-ACC devices were all male (n = 12), and thread trailed turtles were both male (n = 7) and female (n = 4). We saw no difference between the sexes in our analyses and so data from thread trailing is presented as the combined data set. All box turtles were tracked with radio-telemetry using BD-52 transmitters (Holohil, Ontario, Canada) epoxied to the top of the shell for retrieval of devices. Turtles in group one were tracked from May to July in 2014 and from June to July in 2015 using a methodology for thread trailing similar to Claussen et al. (1998) [22]. We epoxied a small plastic cylinder (height = 1.5 cm, diameter = 3 cm) to the posterior portion of the carapace that held a spool of nylon thread (228 m). Each turtle was released where it was first located and allowed a one-day acclimation period before beginning the trailing process. Each morning, individual turtles were located, and the thread tied to an anchor at the start point. We recorded the starting GPS at the beginning of each day using a Garmin 62 s handheld GPS (3 - 10 m resolution). Turtles were then located every 24-h to generate maps of daily movement. Turns were determined when the thread was caught on an object and changed direction. Each turn had a flag placed at that location and the series of flags permitted us to determine the turn angle and distance between each turn to the nearest centimeter and compass bearing to the nearest degree. Each turtle was monitored for up to 5 days, and days were omitted if the thread was broken or if the turtle moved beyond the capacity of the spool (45 out of 55 days yielded usable data). We replaced the thread as needed. Thread trailing data was then converted to Universal Transverse Mercator (UTM) coordinates in Zone 16S (WGS84, Ohio, USA). We used the initial starting coordinate from each day and converted the polar coordinates (bearing and distance) measured in the field to Cartesian coordinates (x, y-coordinates) and plotted the results to verify paths. UTM coordinates were then converted back to decimal degrees for analyses as appropriate. Box turtles in group two were monitored during the 2015 field season from May until October. Turtles with the GPS-ACC devices also had temperature data loggers implanted internally (iButton DS1922L, see methods in Parlin et al. 2017 for details) which recorded body temperature at 5-min intervals throughout the study period. Box turtles in group two were monitored between 12 to 15 days. Loggers recorded GPS coordinates at 1-h intervals from 0700 to 1900, and accelerometer measurements recorded every 10 min (a 30-s burst) also between 0700 and 1900 h. All devices were calibrated prior to attachment and data was adjusted using device-specific calibrations. We had 1733 GPS observations for 12 turtles during the 2015 field season and 2337 thread trailing points converted to GPS coordinates for 11 turtles in 2014 and 2015 combined. All procedures followed approved MU Institutional Animal Care and Use Committee protocol (906) and complied with the Principles of Animal Care, publication no. 86–23, revised 1985, of the National Institutes of Health. All accelerometer measurements were converted into overall dynamic body acceleration (ODBA) prior to analysis. We used the average ODBA (± SE) at each degree Celsius of measured internal turtle body temperature to generate the data for testing non-linear splines to analyze intensity of activity as a function of body temperature. For later statistical analyses, we used the mean ODBA per hour to test across the units of measure of each relevant environmental variable. We characterized movement as extensive (larger mean turning angle and decreased step length) and intensive (smaller mean turning angle and increased step length) using three consecutive coordinates and two distances. Cluster analysis was used to characterize the turning angle and distance into each movement type for both GPS coordinates and thread trailing using the 'ade4' and 'adehabitatLT' package in R [23]. Movement was defined as the distance between two consecutive GPS coordinates and the turning angle was defined as the angle produced to reach the subsequent coordinate based on prior location. We also derived a binary classification for each 30 s burst of acceleration measurement as either active and inactive for each individual. This was achieved by power transforming ODBA (Eq. 1 $ x={ODBA}^{-\frac{1}{3}} $) and then fitting to a mixture distribution of two Gaussian distributions (Eq. 1). The assumption hereby is that the single ODBA measurements represent in their sum inactivity and activity resulting in a distribution consisting of two mixed Gaussian distributions each with an estimable mean (μa and μb) and variance (σa and σb in eq. 1) (for each individual). Based on a non-linear least-squares approach (using the package nlsr in R version 3.4.3) we fitted the probability distribution function estimating both means and variances for each individual [24]. $$ pdf(y)=\frac{1}{\sqrt{2\pi {\sigma}_a^2}}\dot{e^{\frac{-{\left(x-{\mu}_a\right)}^2}{2{\sigma}_a^2}}}+\frac{1}{\sqrt{2\pi {\sigma}_b^2}}\dot{e^{\frac{-{\left(x-{\mu}_b\right)}^2}{2{\sigma}_b^2}}} $$ Using the estimated means and variances of the two Gaussian distributions, we then estimated the probability for each burst belonging to either of the two distributions (active and inactive) based on a probability density function for single Gaussian distributions with the estimated means and variances. This classification is independent of sampling and individual differences, which allows cross comparability among all individuals in the study (for the complete R code used see Additional file 1). After defining ODBA values as active or inactive, we determined the proportion of activity (%) by counting the total number of active ODBA values per hour and dividing by the number of recordings taken during that hour. We analyzed the proportion of activity using a logistic regression test for differences between percentage groupings with turtle ID as a random effect, and analyzed comparisons using least-squares means. We then generated multiple non-linear splines and compared the equations using AIC to determine the best model fit. We then used the equation with the lowest AIC score for the thermal performance curves (TPC). We analyzed distance between GPS coordinates in relation to ecological factors from a nearby weather station (Butler County Regional Airport-Hogan Field weather station, Hamilton, OH, USA). We used stepwise regression (backward deletion) analysis to compare distance moved by box turtles and hourly ODBA with our predictor variables: ambient temperature (°C), absolute humidity (g/m3), precipitation, cloud cover, time of day, and their interactions. As interactions did not improve the model, they were not used in subsequent analyses. Predictor variables were based on previous natural history studies on box turtles and were consolidated to the most pertinent variables that could have an impact on box turtle activity and movement. Mixed-effect models of predictor variables as fixed effects and turtle ID as a random effect were tested against a null model using a likelihood ratio test [25]. We also compared the effect of slope on distance moved and intensity of activity with mixed effect models using turtle ID as a random effect and slope as a fixed effect. We did not use the distance between GPS coordinates from 1900 and 0700 h the next day as box turtles were sometimes active before our devices began recording. Distance data were natural log-transformed to meet assumptions of normality. Analysis of distance moved and percentage of activity, based on a gaussian distribution to define active and inactive ODBA values, was done using a least-squares regression analysis. For cluster analysis using GPS coordinates, we compared ODBA values associated with either extensive or intensive with a student's t-test. We also used student's t-test to compare distance moved and activity in the presence of precipitation. Data were analyzed in R version 3.0.2 [26], and in all cases α was set at 0.05. Thermal performance analysis We determined the relationship between the intensity of activity, measured as ODBA, as a function of the body temperatures experienced by the turtles in the field. Body temperature measurements for box turtles ranged between 11.0 and 36.0 °C, and very few temperatures were measured below 12 or above 30 °C. The thermal performance curve (TPC) based on field data showed a broad, nearly uniform, performance between 14 and 23 °C (Fig. 1). The wide relationship between intensity of activity and body temperature indicates that box turtles are thermal generalists, and thus the performance of free-living box turtles is not dependent on temperature. Thermal performance curve (TPC) of box turtle turtles (n = 12) monitored in 2015. Non-linear equation was fit to the mean overall dynamic body acceleration (ODBA) values. The black line represents the best fit regression. Box turtles had a relatively constant performance from 14 to 23 °C. Performance as a function of body temperature was not thermally dependent across this range giving box turtles a wide performance breadth Environment and activity analysis Linear mixed effect model analysis of microclimate variables including precipitation, ambient temperature, cloud cover, time of day, and humidity, indicated that precipitation (estimate = − 0.197; CI = − 0.279 – − 0.115) and time of day (estimate = 0.00293; CI = − 0.0266 – -0.0135) had the most influence on turtle movement (χ22 = 8.7552, p = 0.01256) with a marginal r2 of only 0.008 based on the fixed effects of precipitation and time of day and a conditional r2 of 0.076 when also incorporating the random effect of turtle ID. We found that box turtles move 13 m each hour after it rains compared to the average of 17 m each hour when not raining (Fig.2, t171 = 3.02, p = 0.002). We had previously reported that box turtles move more during the morning than in the evening [12], although the differences were small. As box turtles are influenced by geotaxis, we tested for an effect of slope on movement, but found no significant influence on distance moved (χ 21 = 2.63, p = 0.104). The regression analysis shows that more than 90% of the variation in the distance moved is unexplained by the model. Distance moved as a function of precipitation measured by a nearby weather station. Mixed-effect model indicated precipitation and time of day as the best predictors of distance moved with a marginal r2 of only 0.008 based on the fixed effects of precipitation and time of day and a conditional r2 of 0.076. Although including the turtle ID as a random effect increased the r2, more than 90% of the data remained unexplained by the mixed-effect model. Precipitation was only recorded during 135 of the hour-intervals where movement occurred in box turtles Box turtle activity was most influenced by ambient temperature (estimate = 0.000135; CI = 0.0009376–0.0017784), absolute humidity (estimate = 0.00291; CI = 0.00238–0.00345), cloud cover (estimate = 0.00229; CI = 0.00138–0.0032), and time of day (estimate = − 0.00373; CI = − 0.00419 – -0.00326) as significant (χ24 = 181.02, p = 2.2e-16) with a marginal r2 of 0.147 based on fixed effects and a conditional r2 of 0.198 when also incorporating the random effect of the turtle (Fig. 3). We also found no significant difference in turtle activity in the presence or absence of precipitation (t124 = − 0.76004, p = 0.44) or for an effect of slope (χ 21 = 2.63, p = 0.90). However, precipitation was only observed during 135 of the 1596 one-hour intervals when turtles were monitored. We additionally analyzed box turtle activity state as a percentage likelihood of activity during each hour interval and found that ambient temperature, absolute humidity, cloud cover, and time of day (χ24 = 48.962, p = 5.9e-10) had similar significant effects although the marginal r2 was 0.076 and the conditional r2 was 0.108. Thus, around 80% of the variation in the intensity of activity and about 90% of the variation in the likelihood for being active remains unexplained by either model. Climatic variables from the best model that had a significant influence on mean overall dynamic body acceleration (ODBA) including a absolute humidity, b weather condition, c temperature, and d time of day. Note that weather condition, classified by cloud cover, was split into five categories as follows: 0 = clear, 1 = scattered clouds, 2 = partly cloudy, 3 = mostly cloudy, 4 = overcast/haze, and 5 = light rain/thunderstorms. Intensity of activity as a function of climatic variable had a slight positive correlation with humidity and ambient temperature recorded. Mean ODBA decreased as time of day progressed from morning until the evening. The effect of clouds and rain did not follow a clear pattern Movement and activity analysis We categorized coordinates for GPS and thread trailing into extensive and intensive movement to compare continuous micro-scale and hour interval macro-scale resolution. Comparison of sampling resolutions using thread trailing (micro-scale) and GPS-coordinates (macro-scale) yielded opposite characterizations of extensive and intensive movement (Table 1). Cluster analysis using GPS locations assigned 36% of the movement as extensive, and 63% of the movement as intensive. For the thread trailing data, 79% of the values were characterized as extensive movement and 21% of the values as intensive. Mean turning angle for both movement modes were higher for the thread trailing data than the GPS coordinates (Table 1). Table 1 Total coordinates recorded for GPS and thread trailing monitoring techniques and subsequent classification of extensive and intensive movement counts using cluster analysis We then separated all the ODBA values into two distributions as active (0.0110–1.387 g) and inactive (0.0011–0.01085 g). Using this distribution, we analyzed the intensity of activity for each category of movement and found that intensity of activity for either movement mode had no correlation with the distance moved (Fig. 4). Although maximal values recorded for extensive and intensive movement were similar, we found the mean intensity of activity to be significantly higher for movements characterized as extensive (Fig. 4a, 0.046 g) than for those characterized as intensive (Fig. 4b, 0.026 g, t767 = 6.1192, p < 0.05), mainly due to a decreased likelihood of activity for intensive movement characterization. Although there was no relationship between the intensity of activity and movements, we found a significant relationship between the likelihood of activity in each hour and distance moved (F6 = 5.5994, p < 0.05, Additional file 2), such that the mean distance moved varied from 16.1 to 24.6 m as the likelihood of activity increased. Mean hourly distance moved as a function of mean overall dynamic body acceleration (ODBA) for a extensive movement and b intensive movement categorizations. There was no correlation between distance moved and activity for either extensive or intensive movements. However, mean ODBA was significantly higher during extensive movement (0.049 g) than intensive (0.026 g), mainly due to a decreased likelihood of activity in the latter category (see Additional file 2) Eastern box turtles are a species of special concern across most of their range with worrying population declines reported. One of the reasons for this decline is linked in part to habitat loss [21]. As habitats for box turtles are lost and other human impacts increase, we may expect turtle movement to decrease similarly to that of mammals as recently reported [27]. We had previously reported that the body temperature of box turtles was unrelated to the distances moved. We thus sought to expand this observation to determine what, if any, environmental factors may dictate turtle movement, based on prior work done on box turtles. Further, the determinants of the intensity of activity, as measured by 3-dimensional accelerometry, may also give insight into the movement ecology of free-living turtles as they interact with their environment. Previous work indicated that box turtles exist within a narrow range of microclimate variables [28], become more active if the temperature drops and rain begins to fall due to thunderstorms [29], and have their peak activity during the morning and become relatively inactive during the evening [30]. Our results did not support the hypothesis that movement is thermally sensitive. While there was a significant relationship between movement and several climatic variables, the strength of these were weak. Thus, other factors, such as feeding, hydration state, mate seeking or vegetation structure may prove to be more important determinants of turtle movement and activity. The recent advancement of biologging technology, allowing for continuous monitoring for extended periods of time, permits a more in depth understanding of box turtle life history. Our analysis based on these relevant environmental parameters showed no relationship between movement and ambient temperature, absolute humidity or cloud cover, while revealing significant impacts of both time of day and precipitation on movement. However, these only explained about 10% of the variation in distance moved. Thus, in several important ways, our data did not agree with these previous studies as we found that the factors measured did have an impact on box turtle movement but often in an opposite direction. For example, similar to our previous work [12], we found no effect of temperature, and we found that precipitation decreased movement in our population of box turtles, unlike Webb (1963) [29]. Intensity of activity, measured as ODBA, was best explained by ambient temperature, absolute humidity, cloud cover, and time of day, while precipitation was not significant. Similar to the extent of movement, these significant environmental factors only explained around 20% of the variation in activity. The environmental factors influencing the likelihood of activity, measured as a percentage of recording categorized as active per hour, also only explained around 10% of the variation in hourly activity. This fits well with our observation that the thermal reaction norm showed that the intensity of activity was nearly unchanged across a very broad range of body temperatures. As we previously showed that box turtles are thermal generalists, with body temperatures similar to ambient [12], it comes as no surprise that the ambient temperature also had little effect on activity. This work further supports the conclusion that box turtle movement and daily activity are highly resilient in response to climate conditions. Given that we used weather station data, it is possible that the differences between those data and micro-climates selected by turtles could alter these relationships. It is also plausible that activity is driven by prior exposure to the landscape. Box turtles have an incredible ability to navigate back towards their home range when displaced and are even capable of moving at night [31]. Further research monitoring the activity and movement of displaced turtles using biologging technology would provide added insight into the capability of these ectotherms to navigate their habitat, especially in fragmented landscapes. Unlike previous laboratory work of temperature-dependent movement on reptiles [8,9,10] including box turtles [11], we found that ambient and body temperature were generally irrelevant as determinants of both activity and movement. This suggests that laboratory measures of maximal locomotor capacity may be erroneous for most movement in nature, at least for turtles. Laboratory conditions may not represent patterns and processes observed in the field, thus our data point to the importance of studies of free-living animals to best delineate the factors that determine the realized performance. As box turtles were able to be active at all temperatures observed in the field, other factors presumably act to determine the extent moved. However, temperature is a driving force for ectotherms [10], dictating many physiological functions, one of which may supersede locomotion. To better understand the nature of box turtle movement within a habitat patch, we categorized each step as intensive (foraging) or extensive (exploratory). As resolution of the data collection method could influence this analysis [5, 32], we compared movement data collected with animal borne GPS loggers (with 1-h intervals) to data from continuous thread trailing. The outcomes from this analysis returned nearly opposite interpretations, suggesting that when data were sampled at low resolution that turtles are primarily foraging, while when sampled at high resolution that turtles are primarily engaged in exploratory movement. However, given that we did not simultaneously monitor GPS location and thread trailing, direct comparison between movement measurements in foraging sites remains unclear and caution must be taken with interpretation of data recorded at different scales. This data support and extend our earlier observation that Eastern box turtles are a thermoconforming ectotherm, with movement that is nearly identical across an impressively wide range of body temperatures [12]. Although the extent of movement and intensity of activity are significantly affected by several environmental factors, none do so with great explanatory power. Thus, we conclude that in addition to being thermal generalists, the movement ecology of Eastern box turtles is largely independent of the habitat characteristics examined. Movement patterns in Galapagos tortoises are driven by changes in vegetation [33] and similar constraints may be relevant for box turtles. Although we frequently observed turtles feeding and they tended to congregate in a region of the study area with a high density of mulberry trees (Morus spp.), we lack detailed data on feeding habits. Generally, box turtle movement appeared to be haphazard within each forest patch and we documented no box turtles traversing from one habitat fragment to another. Finally, given the marked difference between the categorization of movements as intensive (foraging) or extensive (exploratory) depending on the method used to record movements, further comparisons of fine-scale and coarse-scale movement, undertaken with a more uniform methodology, may be important for future studies. This study contributes to understanding the interaction between physiology and movement, and the effects of climate conditions on activity in the field. Our results also show the importance of difference in fine-scale sampling resolution compared to coarse-scale resolution for characterizing and analyzing movement. Although laboratory studies have shown a strong thermal dependence of physiological performance, field monitoring can decouple the ecologically relevant temperatures from the physiologically optimal. This provides further insight into the patterns and processes observed in the field for free-living individuals and can further our understanding of how changes in climate conditions can impact a species. Caldwell IR, Nams VO. A compass without a map: tortuosity and orientation of eastern painted turtles (Chrysemys picta picta) released in unfamiliar territory. Can J Zool. 2006;84:1129–37. Malishev M, Bull CM, Kearney MR. An individual-based model of ectotherm movement integrating metabolic and microclimatic constraints. Methods Ecol Evol. 2017; https://doi.org/10.1111/2041-210X.12909. Sears MW, Angilletta MJ Jr, Schuler MS, Borchert J, Dilliplane KF, Stegman M, Rusch TW, Mitchell WA. Configuration of the thermal landscape determines thermoregulatory performance of ectotherms. PNAS. 2016;113:10595–600. Gunderson AR, Leal M. Geographic variation in vulnerability to climate warming in tropical Caribbean lizard. Funct Ecol. 2012;26:783–93. Nams VO. Using animal movement paths to measure response to spatial scale. Oecologia. 2005;143:179–88. Stickel LF. Populations and home range relationships of the box turtle, Terrapene c. Carolina (Linnaeus). Ecol Monogr. 1950;20:351–78. Price-Rees SJ, Lindström T, Brown GP, Shine R. The effects of weather conditions on dispersal behaviour of free-ranging lizards (Tiliqua, Scincidae) in tropical Australia. Funct Ecol. 2014;28:440–9. Jayne BC, Bennett AF, Lauder GV. Effects of temperature on muscle-activity during lizard locomotion. Am Zool. 1988;28:A15. Rome LC, Bennett AF. Influence of temperature on muscle and locomotor performance – introduction. Am J Phys. 1990;259:R189–90. Angilletta MJ. Thermal adaptation: a theoretical and empirical synthesis. New York: Oxford University Press; 2009. Adams NA, Claussen DL, Skillings J. Effects of temperature on voluntary locomotion of the eastern box turtle, Terrapene carolina carolina. Copeia. 1989;1989:905–15. Parlin AF, do Amaral JPS, Kelly Dougherty J, Stevens MHH, Schaeffer PJ. 2017. Thermoregulatory performance and habitat selection of the eastern box turtle (Terrapene carolina carolina). Conserv Physiol. 2017;5:cox070. Huey RB, Hertz PE. Is a Jack-of-all temperatures a master of none? Evolution. 1984;38:441–4. Martin LT, Huey RB. Why "suboptimal" is optimal: Jensen's inequality and ectotherm thermal preferences. Am Nat. 2008;171:102–18. Huey RB. Physiological consequences of habitat selection. Am Nat. 1991;137:S91–S115. Huey RB, Stevenson RD. Integrating thermal physiology and ecology of ectotherms: a discussion of approaches. Am Zool. 1979;19:357–66. Kearney M. Activity restriction and the mechanistic basis for extinctions under climate warming. Ecol Lett. 2013;16:1470–9. Kearney M, Porter W. Mechanistic niche modelling: combining physiological and spatial data to predict species' ranges. Ecol Lett. 2009;12:334–50. Buckley LB, Tewksbury JJ, Deutsch CA. Can terrestrial ectotherms escape the heat of climate change by moving? Proc Roy Soc B. 2013;280(1765):20131149. https://doi.org/10.1098/rspb.2013.1149. Karl TR, Koss WJ. Regional and National Monthly, Seasonal, and Annual Temperature Weighted by Area, 1895–1983. Hist Climatol Ser. 1984;4:1–38. van Dijk PP. Terrapene carolina.(errata version published in 2016). The IUCN Red List of Threatened Species 2011. T21641A97428179. Accessed on 21 Mar 2018 Claussen DL, Finkler MS, Smith MM. Thread trailing of turtles: methods for evaluating spatial movements and pathway structure. Can J Zool. 1997;75:2120–8. Calenge C. The package "adehabitat" for the R software: a tool for the analysis of space and habitat use by animals. Ecol Model. 2006;197:516–9. Nash JC, Murdoch D. (2018). Nlsr: functions for nonlinear least squares solutions. R package version. 2018;1:28. https://cran.r-project.org/package=nlsr. Accessed 5 July 2018. Bates D, Maechler M, Bolker B, Walker S. Fitting linear mixed-effects models using lme4. J Stat Softw. 2015; https://doi.org/10.18637/jss.v067.i01. Accessed 5 July 2018. R Development Core Team. R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing; 2015. ISBN 3–900051–07-0, URL https://www.r-project.org. Accessed 5 July 2018. Tucker MA, Böhning-Gaese K, Fagan WF, Fryxell JM, Van Moorter B, Alberts SC, Ali AH, Allen AM, Attias N, Avgar T, Bartlam-Brooks H. Moving in the Anthropocene: global reductions in terrestrial mammalian movements. Science. 2018;359:466–9. Reagan DP. Habitat selection in the three-toed box turtle, Terrapene carolina triunguis. Copeia. 1974;1974:512–27. Webb RG, Minckley WL, Craddock JE. Remarks on the Coahuilan box turtle, Terrapene coahuila (Testudines, Emydidae). Southwest Nat. 1963;8:89–99. Dodd CK. North American box turtles: a natural history: University of Oklahoma Press; 2002. Metcalf E, Metcalf AL. Observations on ornate box turtles (Terrapene ornata ornata Agassiz). Trans Kans Acad Sci (1903-). 1970;73:96–117. Benhamou S. How to reliably estimate the tortuosity of an animal's path: straightness, sinuosity, or fractal dimension? J Theor Biol. 2004;229:209–20. Yackulic CB, Blake S, Bastille-Rousseau G. Benefits of the destinations, not costs of the journeys, shape partial migration patterns. J Anim Ecol. 2017;86:972–82. We thank R. Kolb and J. Fruth for their assistance at the ERC, and the laboratory animal research staff at Miami University for monitoring box turtles during recovery post-surgery. Research was conducted under permits 15-162 and 16-144 issued by the Ohio Department of Natural Resources, and permits 2014-23 and 2015-11 issued by the Ohio Department of Natural Resources State Nature Preserve for Hueston Woods. This work was supported by Sigma Xi, The Explorer's Club, Miami University and the National Science Foundation under grant numbers DBI-1156703 and DBI-1460518. Data used and analyzed during this study are available from the corresponding author upon request. Department of Biology, Miami University, Oxford, OH, 45056, USA Adam F. Parlin, Jessica A. Nardone, John Kelly Dougherty, Mimi Rebein & Paul J. Schaeffer Max Planck Institute for Ornithology, Vogelwarte Radolfzell, Am Obstberg 1, 78315, Radolfzell, Germany Adam F. Parlin Jessica A. Nardone John Kelly Dougherty Mimi Rebein Paul J. Schaeffer AFP and PJS conceived of the research idea and analyzed the data according, as well as wrote the manuscript. JAN, JKD, and MR aided in collection of thread trailing data and edits to the manuscript. KS developed the binary classification of activity, and assisted with writing and editing of the manuscript. All authors read and approved the final manuscript. Correspondence to Paul J. Schaeffer. All procedures were approved by the appropriate committees as mentioned in the methods. R Script for binary classification of ODBA values from accelerometer data. (R 6 kb) Additional figure of proportion of activity and distance moved. (DOCX 26 kb) Parlin, A.F., Nardone, J.A., Kelly Dougherty, J. et al. Activity and movement of free-living box turtles are largely independent of ambient and thermal conditions. Mov Ecol 6, 12 (2018). https://doi.org/10.1186/s40462-018-0130-8 Ecophysiology Overall dynamic body acceleration	CommonCrawl
Investigating circulating tumor cells and distant metastases in patient-derived orthotopic xenograft models of triple-negative breast cancer Vishnu C. Ramani1, Clementine A. Lemaire2, Melanie Triboulet1, Kerriann M. Casey3, Kyra Heirich1, Corinne Renier2, José G. Vilches-Moure3, Rakhi Gupta1, Aryana M. Razmara3, Haiyu Zhang1, George W. Sledge4, Elodie Sollier ORCID: orcid.org/0000-0001-5046-27892 & Stefanie S. Jeffrey1 Circulating tumor cells (CTCs) represent a temporal "snapshot" of a patient's cancer and changes that occur during disease evolution. There is an extensive literature studying CTCs in breast cancer patients, and particularly in those with metastatic disease. In parallel, there is an increasing use of patient-derived models in preclinical investigations of human cancers. Yet studies are still limited demonstrating CTC shedding and metastasis formation in patient-derived models of breast cancer. We used seven patient-derived orthotopic xenograft (PDOX) models generated from triple-negative breast cancer (TNBC) patients to study CTCs and distant metastases. Tumor fragments from PDOX tissue from each of the seven models were implanted into 57 NOD scid gamma (NSG) mice, and tumor growth and volume were monitored. Human CTC capture from mouse blood was first optimized on the marker-agnostic Vortex CTC isolation platform, and whole blood was processed from 37 PDOX tumor-bearing mice. Staining and imaging revealed the presence of CTCs in 32/37 (86%). The total number of CTCs varied between different PDOX tumor models and between individual mice bearing the same PDOX tumors. CTCs were heterogeneous and showed cytokeratin (CK) positive, vimentin (VIM) positive, and mixed CK/VIM phenotypes. Metastases were detected in the lung (20/57, 35%), liver (7/57, 12%), and brain (1/57, less than 2%). The seven different PDOX tumor models displayed varying degrees of metastatic potential, including one TNBC PDOX tumor model that failed to generate any detectable metastases (0/8 mice) despite having CTCs present in the blood of 5/5 tested, suggesting that CTCs from this particular PDOX tumor model may typify metastatic inefficiency. PDOX tumor models that shed CTCs and develop distant metastases represent an important tool for investigating TNBC. Despite the tremendous progress made in the diagnosis and treatment of breast cancer, tumors of the breast still remain one of the leading causes of cancer-related deaths in women [1]. The intertumoral and intratumoral molecular heterogeneity of breast cancer challenges its diagnosis and effective treatment [2,3,4,5,6,7,8,9]. Tailored therapies, such as hormone therapies (e.g., tamoxifen and inhibitors of the enzyme aromatase, involved in estrogen synthesis) for ER-positive disease and trastuzumab (Herceptin®) for HER2-overexpressing breast cancer have led to considerable success in treating some subtypes of breast cancer. However, drug resistance to these regimens can represent a major hurdle to successful treatment [10,11,12,13,14,15]. Most importantly, there is still no good targeted therapy for triple-negative breast cancer (TNBC), a very aggressive subtype that remains difficult to treat [16, 17]. Due to the very aggressive nature of TNBC and the lack of well-established molecular therapeutic targets, patients with TNBC tend to have a relatively poorer outcome compared to patients with other subtypes [18, 19]. In breast cancer, and especially in TNBC, dissemination and metastatic growth of tumors at distant sites is the major cause of patient mortality [20]. Despite chemotherapy, fewer than 30% of women diagnosed with metastatic TNBC will survive beyond 3 years, and, unfortunately, almost all women with metastatic TNBC will ultimately succumb to their metastatic disease [21,22,23]. Although newer therapies and combinations of therapies for TNBC are under active investigation and hold future promise, including the use of poly (ADP-ribose) polymerase (PARP) inhibitors for TNBC patients with homologous recombination DNA repair-deficient cancers associated with BRCA1 mutations, the use of immune checkpoint inhibitors, approaches that target other signaling pathways, or combination therapies, responses are still only observed in a small fraction of patients with advanced TNBC [24,25,26,27,28,29,30]. Factors that drive tumor metastasis have been a subject of intense scrutiny and research. As circulating tumor cells (CTCs) are considered contributory precursors that seed metastases in many cancers, including breast cancer, studying the biology of CTCs has provided vital clues regarding cancer metastasis [31]. Multiple mouse models may be used to study breast cancer biology, including syngeneic models (immunocompetent models generated from murine breast cancer cell lines, such as 4T1 cells), environmentally induced tumor models, transgenic models (models expressing mouse oncogenes, such as the polyomavirus middle T antigen controlled by the mouse mammary tumor virus long terminal repeat promoter, MMTV-PyMT model), genetically engineered mouse models (GEMMs), cell line-derived xenografts, and patient-derived xenografts [32,33,34,35,36,37,38,39]. However, the use of in vivo models to study the shedding and biology of human CTCs requires either human breast cancer cell line-derived xenografts [40] or patient-derived xenografts (PDXs). Generation of PDX models involves the transplantation of primary human cancer cells or pieces of tumor tissue into immunocompromised mice. Although most PDX models are generated in mice lacking a functional human immune system, they are still considered to be highly clinically relevant [41, 42], particularly when implanted orthotopically (e.g., human breast tumor tissue from the operating room implanted into the mammary fat pads of mice). Orthotopically implanted PDX models, called patient-derived orthotopic xenograft (PDOX) models, have been shown to recapitulate critical histological, genomic, transcriptomic, and proteomic features of the patients' tumors from which they were derived [43,44,45]; they are also better models of human metastatic disease [46] and of response to anti-cancer therapies [41, 45, 47] and, in the case of TNBC PDOX models, represent more aggressive phenotypes [48]. Currently, there is renewed interest in utilizing PDX models as evident in US National Cancer Institute's (NCI) plan to replace their NCI-60 cell line resource with PDX samples [49]. However, the background strain of mouse used for PDX studies is of key importance. NOD scid gamma (NSG) mice have been shown to be best at recapitulating the entire metastatic process in breast cancer from implantation in the mammary fat pad to distant metastatic spread, including development of metastases in cell line models that had not been previously associated with metastatic spread [50]. So while there has been an increasing interest in using PDOX models of breast cancer to study human CTCs captured from mouse blood and/or human disseminated tumor cells (DTCs) from mouse bone marrow [51,52,53,54,55,56,57], the studies from these other groups were performed in non-NSG mouse models. We had previously described the isolation of CTCs from two NSG mice from a single TNBC PDOX tumor [58]. In this study, we use NSG mice to examine the distribution of distant metastatic spread in 57 mice from seven PDOX models of TNBC and to analyze CTC shedding in 37 of these mice. Multiple technologies have been developed to enable CTC isolation from the peripheral blood of human patients with solid tumors. Approaches to capture and/or identify these rare cells rely on positive or negative cell selection, density gradient centrifugation, microfiltration, microfluidic or electrophoretic separation, direct imaging, or functional assays [59,60,61]. Here, we isolate human CTCs from mouse blood in PDOX models using the Vortex platform, a technology originally developed to allow fast and label-free isolation of human CTCs over a broad range of blood volumes (200 μL to 16 mL). CTCs are enriched from whole blood based on size and deformability, using inertial microfluidics combined with microscale vortices [62]. This technique had been successfully used to isolate human CTCs from blood samples from patients with metastatic breast, lung, colorectal, and prostate cancer [63,64,65,66,67]. In the present study, isolation of human CTCs from mouse blood was first optimized using a human breast cancer cell line-derived xenograft model of TNBC, generated from MDA-MB-231 cells, that we had previously shown to shed CTCs and metastasize to the lung [40]. Based on these experiments, a set of seven PDOX models of TNBC, including four that had previously undergone global genomic and transcriptomic analyses [44], were used for replicate isolation and characterization of human CTCs and for identification of sites of distant metastases. Vortex microfluidic chip design and operation Vortex chips are 70-μm-deep microfluidic chips comprising a parallelized array of 16 straight channels, 40 μm wide, with each channel leading to a series of 12 (Vortex HT chips) or 9 (Vortex VTX-1 chips) rectangular trapping reservoirs (480 μm × 720 μm). Vortex HT PDMS chips were fabricated following conventional poly (dimethylsiloxane) (PDMS) fabrication processes with a 1:10 PDMS mix [68]. Vortex VTX-1 chips were fabricated with poly (methyl methacrylate) (PMMA) (Vortex Biosciences) using a standard lithography process [58]. The blood samples were injected through the chip as previously described [58]. Briefly, two syringe pumps (Harvard Apparatus) were connected to the chip using a plastic manifold, connectors (Upchurch), and tubing (Tefzel® (ETFE) Tubing Natural 1/16″ OD × .040″ ID from IDEX). One syringe was used for the blood sample and one syringe for the phosphate-buffered saline (PBS) wash buffer. After a priming step to fill the microfluidic path, the diluted blood sample was injected at 8 mL/min to enable the CTC enrichment. A washing step with PBS was then injected at a similar flow rate to remove contaminating blood cells. Stopping the flow finally released the CTCs from the vortices to their collection downstream in a well plate. Cancer cell line culture and harvesting Cell lines used for characterization were grown aseptically to 30–60% confluence at 37 °C in a humidified atmosphere of 5% CO2. MDA-MB-231 (triple-negative breast carcinoma, ATCC® HTB-26™) cells were grown in DMEM medium supplemented with 10% inactivated FBS and 1% penicillin/streptomycin. Adherent cells were dissociated with TrypLE express cell dissociation reagent (Gibco) and resuspended in complete media. For experiments related to Fig. 2, the cell line used was MDA-MB-231 cells that stably expressed firefly luciferase-enhanced green fluorescent protein (FLuc-eGFP), a generous gift from the Paulmurugan lab at Stanford University [69]. Cell immunostaining and enumeration After Vortex processing of mice blood, cells were collected in a cell culture-treated 96-well plate (Nunc), fixed for 10 min with an equal volume of 4% paraformaldehyde (PFA; Electron Microscopy Sciences) for a final concentration of 2% PFA, permeabilized for 7 min with 0.4% Triton X-100 (Sigma Aldrich) volume/volume for a final concentration of 0.2%, blocked for 30 min with 10% goat serum (Invitrogen), and then stained for 1 h at room temperature (RT). The immunostains were 4,6-diamidino-2-phenylindole (DAPI) (Life Technologies), a rat anti-mouse CD45-PE antibody (CD45-PE, clone 30-F11, BD Pharmingen), and a cocktail of primary antibodies labeled with fluorescein isothiocyanate (FITC) to identify cytokeratin (CK)-positive cells (human anti-cytokeratin clone CK3-6H5, Miltenyi Biotec, and human anti-cytokeratin clone CAM5.2, BD Biosciences) [58]. For patient-derived orthotopic xenograft (PDOX) samples and MDA-MB-231 tumor xenograft samples, an anti-CK-AlexaFluor (AF) 488 antibody (human anti-pan cytokeratin clone AE1/AE3, eBioscience) and an anti-vimentin-AF647 antibody (clone V9, Abcam, reactive to human vimentin; non-reactive to mouse vimentin) were used in addition to the previously listed antibodies (Additional file 1: Figure S1). After staining, the cells were imaged using an Axio Observer Z1 microscope (Zeiss) and manually enumerated as described previously [58, 68]. Stitched images of stained cells were acquired, and cells enumerated by two different persons following a classification criterion developed at Vortex [58, 66, 68]. The cells were categorized into three large groups, namely CTCs (CK+/CD45−/DAPI+, VIM+/CD45−/DAPI+, and CK+/VIM+/CD45−/DAPI+), WBCs (CK−/CD45+/DAPI+, VIM−/CD45+/DAPI+, and VIM+/CD45+/DAPI+), or debris. CTC isolation from mouse blood Cell spiking in healthy mouse blood Two hundred to 500 MDA-MB-231 cells prepared as described above were spiked into 500 μL of blood isolated from healthy BALB/c mice via cardiac puncture and collected into EDTA-coated microtainer tubes. The spiked blood was diluted 10×, 20×, or 40× in filtered PBS and processed using the Vortex VTX-1 plastic chip. Once captured, the cells were released into a well plate, stained and enumerated. Capture performance can be described by cancer cell recovery and capture contamination using the following equations: $$ \mathrm{Cell}\ \mathrm{recovery}\ \left(\%\right)=\frac{\#\mathrm{of}\ \mathrm{target}\ \mathrm{cells}\ \mathrm{captured}}{\#\mathrm{of}\ \mathrm{target}\ \mathrm{cells}\ \mathrm{spiked}\ \mathrm{into}\ \mathrm{the}\ \mathrm{sample}} $$ $$ \mathrm{C}a\mathrm{pture}\ \mathrm{contamination}\ \left(\mathrm{WBCs}/\mathrm{mL}\right)=\frac{\#\mathrm{of}\ \mathrm{WBCs}\ \mathrm{captured}}{\mathrm{volume}\ \mathrm{of}\ \mathrm{blood}\ \mathrm{processed}} $$ PDOX samples At time of euthanasia and necropsy, blood (~ 750 μL) was collected via cardiac puncture from PDOX-bearing mice and diluted 40× with filtered PBS. The diluted samples were processed through Vortex VTX-1 plastic chips, and the isolated CTCs were immunostained and enumerated as described above. All studies were approved by the Stanford University Research Compliance Office's Human Subjects Research and IRB Panel and Stanford's Administrative Panel on Laboratory Animal Care (APLAC). All methods were performed in accordance with the relevant guidelines and regulations. All seven TNBC PDOX tumor models were generated from fresh-frozen live tumor tissue fragments from our bank of previously established patient-derived orthotopoic xenograft tumor models, including four models of different TNBC subtypes that were previously characterized using global genomic and transcriptomic analyses [44]. Tumor samples were collected from patients in accordance with the relevant IRB guidelines. Briefly, frozen fragments of tumor were thawed and washed once with RPMI-1640 media and transported under aseptic conditions to the Stanford animal facility. One to 2 mm fragments of individual PDOX tumors were then sterilely and orthotopically transplanted into the fourth mammary fat pads of at least 5 female NOD scid gamma (NSG) mice (NOD.Cg-Prkdcscid Il2rgtm1Wjl/SzJ (Jackson Laboratory West, Sacramento, CA, USA). These mice have deficiencies in innate immunity, and due to the severe combined immune deficiency mutation (scid) and an IL2 receptor gamma chain deficiency that disables cytokine signaling, they lack mature T cells, B cells, and functional NK cells and are deficient in cytokine signaling. In contrast to the more leaky NOD scid mice, NSG mice have a longer lifespan with more resistance to lymphoma. Animals were anesthetized using 1 to 3% isoflurane, hair at the implantation site was removed, and skin was sterilized with povidone-iodine and alcohol. A small skin incision was made, and the fourth mammary fat pad was identified. The fat pad was gently held with forceps while a small nick was made to create a pocket where tumor fragments were then placed. The skin incision was closed using interrupted monofilament sutures. Mice were maintained in pathogen-free animal housing. For MDA-MB-231 xenograft studies, a mixture of cell suspension and Matrigel (LDEV-free, Growth Factor Reduced, BD Biosciences) was injected into the fourth mammary fat pad. All the animals were monitored regularly, and tumor growth was measured at regular intervals. Tumor volume was calculated by the following formula: tumor volume = (l × w2)/2, where l was the longest diameter of the tumor and w was the shortest diameter of the tumor. Mean tumor volumes were calculated, and growth curves were established as a function of time. All animal care was performed in accordance with IACUC and Stanford University Administrative Panels on Laboratory Animal Care guidelines (APLAC Protocol #12809). For testing the impact of route of blood collection on CTC numbers, the TNBC xenograft models used were generated from MDA-MB-231 human breast cancer cells that stably expressed firefly luciferase-enhanced green fluorescent protein (FLuc-eGFP), as mentioned above, with tumor cells and CTCs showing green fluorescence. Briefly, 8 × 106 MDA-MB-231-FLuc-eGFP cells were injected orthotopically into the fourth mammary fat pads of NSG mice (n = 35). Tumor volumes were measured three times per week for all the animals. Starting from week 1 post injection, blood via cardiac puncture (500 μL) (n = 3 animals) or via lateral saphenous vein (100 μL) (n = 3 animals) was collected weekly, diluted to 40×, and processed on the Vortex platform to enrich for CTCs. After staining, CTCs were enumerated. For testing the retroorbital route of blood collection, blood from non-tumor-bearing NSG control mice was collected, processed on the Vortex platform, and stained for DAPI, cytokeratin, and CD45. H&E analyses for metastases Upon termination of the experiment, animals bearing PDOX tumors were humanely euthanized via CO2 asphyxiation. Blood, tumor tissue, and organs were collected immediately following euthanasia. Lungs from individual animals were inflated with 10% neutral buffered formalin (NBF) prior to submersion and storage in 10% NBF. All organs were immersion-fixed in 10% NBF for at least 48 h prior to transferring to 70% ethanol. Fixed sections of the lung, liver, and brain were routinely processed and embedded in paraffin, then serially sectioned at 5 μm and stained with hematoxylin and eosin (H&E; HISTO-TEC laboratories, Hayward, CA). Five serial H&E sections of each individual organ were then screened for tumor metastases at × 4 and × 40 magnification (Zeiss Axioskop 2 Plus) by board-certified veterinary pathologists (KMC and JGMV). Photomicrographs of metastases were captured and visualized using a Nikon DS-Ri1 camera and NIS-Elements Imaging Software (2011), respectively. Optimization of CTC isolation from mouse blood samples with spiking experiments Effect of blood dilution Mouse blood is less viscous than human blood [70] but of significantly smaller total volume, usually less than 2 mL per animal. Small volumes of collected blood pose a challenge for processing through fluidic tubing and microfluidic components because of the risk of loss of rare target cells in dead volume. To overcome this issue, diluting the blood sample becomes essential. In a previous study, different dilutions of human blood were tested on the Vortex technology, and the results demonstrated that a 10× dilution was optimal for cancer cell recovery and throughput [62]. To establish a dilution strategy for mouse blood, 200 MDA-MB-231 human breast cancer cells were spiked into 500 μL of healthy mouse blood, diluted with PBS (40×, 20×, and 10×) and processed on the Vortex platform (Fig. 1a). As illustrated in Fig. 1b, a similar cancer cell recovery was obtained for 40× and 20× dilutions (46.55% and 44.34% recovery) and 74 and 52 WBCs were also captured. With the 10× dilution, the recovery was poor (17.89%). Based on these results, a 40× dilution of mouse blood was used for all ensuing experiments. Workflow optimization for the isolation of human cancer cells spiked into healthy mouse blood using Vortex technology. a Workflow schematic, from blood collection to cell spiking into blood, cell isolation, and downstream immunostaining. b Effect of blood dilution on the performance of cancer cell isolation (n = 1). c Effect of blood efflux recycling on cancer cell recovery and WBC contamination (blood dilution factor of 40×) (n = 3) Effect of recycling the blood efflux To optimize CTC recovery from a small blood volume, we devised a strategy of recycling, wherein after processing once (first cycle), the efflux is collected and reinjected into the microfluidic chip for a second and third time (second and third cycles), to capture additional cancer cells that might have escaped capture in the first round of processing (Fig. 1c). For testing the efficiency of recycling, 500 MDA-MB-231 cells were spiked into 500 μL of mouse blood and processed through the microfluidic chip for up to three cycles. When processed in the High Purity Mode (one cycle), 34.38% of cells were collected on average. Cycling a sample twice captured 44.73% of the cancer cells. When the same sample was processed in the High Recovery Mode (three cycles), 47.96% of the cells were recovered. However, recycling also increased the number of co-isolated WBCs (447 WBCs with three cycles combined, compared to 171 with one cycle). For the following experiments, two cycles were selected as optimal. Effect of blood collection site on CTC capture Blood samples from mice bearing MDA-MB-231 tumor xenografts were collected at different time intervals from the saphenous vein or by cardiac puncture as tumor size increased (Fig. 2). CTCs were detected in blood collected via cardiac puncture as early as day 7. CTC counts ranged from 0.4 to 3649 CTCs/100 μL and increased over time, correlating with tumor burden (Fig. 2b). CTC clusters were also captured from day 7 (6 clusters/100 μL; frequency 1/3), with number and frequency increasing over time up to 147–485 clusters/100 μL by day 42 (Fig. 2c). In contrast, no CTCs were recovered from blood obtained from the lateral saphenous vein until day 28 post-implantation, and their number remained low (mean 2.15 ± 0.65 CTCs/100 μL) (Fig. 2d). Blood collected from the retroorbital sinus from healthy control animals without tumors had high numbers of contaminating epithelial (CK+/DAPI+/CD45−) cells making this route of blood collection unsuitable for CTC studies (Fig. 2e). Blood collection site for CTC isolation from mouse blood using a MDA-MB-231 TNBC xenograft model. a Workflow schematic. b, c Tumor growth and numbers of CTCs, including counts of single CTCs in panel b and CTC clusters in panel c; blood was obtained by cardiac puncture in sets of three mice weekly after implantation. d Saphenous vein collection provided less CTCs despite relatively similar tumor growth over time. e CK+ epithelial cells were identified in retroorbital blood collected from control mice without tumors Characterization of tumor growth, metastases, and CTCs in PDOX models of triple-negative breast cancer After implantation of fragments of TNBC PDOX tumor tissue into NSG mice, individual tumor volume was calculated and plotted as a function of time; after sacrifice, organs were examined and, in a subset of mice, blood was processed for CTCs (Fig. 3a). Different PDOX tumor models grew at different rates, and there were differences in tumor growth rates in individual mice bearing the same PDOX tumors (Fig. 3b). Growth rate and metastases in PDOX models of TNBC. a For individual animals, tumor fragments from previously derived and passaged PDOX tumors were implanted orthotopically in the fourth mammary fat pad and tumor volume was measured over time; at the end of the experiment, cardiac blood was collected for CTC isolation, and multiple organs were analyzed for metastases. b Representative growth curves for seven different PDOX tumor models grown in NSG mice. c Metastases were identified in the lung, liver, and rarely, brain of mice bearing the human TNBC tumors (H&E, × 20 and × 40 magnifications). Pulmonary metastases were found within alveolar septal capillaries or medium- to small-caliber vessels, where they were associated with peri-tumoral fibrin (black triangle) and/or desmoplasia (white arrow). Hepatic metastases were randomly distributed within hepatic sinusoids. Mitotic figures (black arrows) were frequently identified within metastatic foci To test for metastatic spread in our TNBC PDOX models, the lung, liver, and brain were screened for metastases by serial section and hematoxylin and eosin (H&E) staining (Fig. 3c). Metastases were detected in the lung (20/57, 35%), liver (7/57, 12%), and brain (1/57, 2%), with different TNBC PDOX models displaying varying sites and frequencies of metastases (Table 1). For example, PDOX tumor model SUTI151 displayed a high frequency of metastases with two thirds of the animals bearing this tumor showing metastases in at least one organ. Interestingly, this TNBC PDOX model was the most aggressive, derived from a patient's rapidly metastasizing breast cancer that was refractory to all standard therapies; the SUTI151 model also exhibited the highest number of CTCs per tumor-bearing mouse compared to other PDOX models in this study. We detected a brain metastasis in only one PDOX tumor model, SUBRTU2 (Fig. 3c and Table 1). Notably, one PDOX model in our cohort, SUTI368, showed no metastases at necropsy. Table 1 Tabulated results of metastases detected in 57 mice bearing seven different TNBC PDOX tumor models. Thirty-seven blood samples obtained by cardiac puncture from these seven TNBC tumor models were processed for CTC isolation Histologically, metastases were noted in association with vascular structures of the lung and liver (Fig. 3c). Within the lung, neoplastic thromboemboli were found in medium- to small-caliber pulmonary vessels (Fig. 3c, × 20 magnification), as well as within capillaries of the alveolar septa (Fig. 3c, × 40 magnification). Within medium- to small-caliber vessels, neoplastic thromboemboli partially to completely occluded vascular lumina and were segmentally adherent to the vascular endothelium. Occasionally, there was disruption of the vascular wall, and associated luminal and extraluminal fibrin deposition (Fig. 3c, black triangle). Within the lungs, neoplastic aggregates were occasionally associated with concentric bands of fibrous connective tissue (desmoplasia, Fig. 3c, white arrow). Within the liver, discrete neoplastic aggregates were randomly distributed within the sinusoids of the hepatic parenchyma. Concomitant desmoplasia was not noted within any of the examined sections of the liver. Neoplastic cells were polygonal with distinct cell borders and a low to moderate amount of eosinophilic cytoplasm. Nuclei were round to ovoid with finely stippled chromatin and up to one discrete nucleolus. Variation in cell size (anisocytosis) and nuclear size (anisokaryosis) were moderate, and mitotic figures were frequent (Fig. 3c, black arrows). Occasional bizarre mitotic figures were noted. Rarely, individual cell necrosis was characterized by contracted hypereosinophilic cytoplasm and karyorrhectic to pyknotic nuclei. CTCs in TNBC PDOX models To test for the presence of CTCs in our seven different TNBC PDOX models, we processed whole blood isolated via cardiac puncture from 37 of the PDOX tumor-bearing mice using the Vortex CTC isolation platform (Fig. 3a). Staining and imaging of captured cells revealed the presence of CTCs in all seven PDOX models tested, even in the SUTI368 model that showed no distant metastases (Fig. 4, Table 1). The total number of CTCs varied between different PDOX tumor models and between individual mice bearing the same PDOX tumor model (Table 1). Representative fluorescent images of CTCs isolated from different PDOX tumor-bearing mice. Live CTCs were isolated from individual PDOX tumor-bearing animals by label-free Vortex technology. Captured cells were then fixed, permeabilized, and stained for human cytokeratin (CK), human vimentin (VIM), and mouse CD45. Nuclei were highlighted with DAPI. CTCs were identified as DAPI-positive cells that were positive for cytokeratin and/or vimentin and negative for CD45 (to exclude mouse hematopoietic cells) Isolation of CTC clusters We found that both our MDA-MB-231 cell line-derived and PDOX models revealed the presence of CTC clusters (Fig. 2c and Fig. 5), and only one of our PDOX models, SUTI151, revealed the presence of CTC clusters. Importantly, some of the captured CTC clusters from this model displayed a clear heterogeneity in cytokeratin and vimentin staining among the individual cells present within the cluster. CTC clusters from mice bearing MDA-MB-231 xenograft tumors. CTC clusters were isolated using the Vortex platform and stained with DAPI, human cytokeratin (CK), human vimentin (VIM), and mouse CD45. CTCs within clusters were identified as cells positive for DAPI, cytokeratin, and/or vimentin and negative for CD45. Note the heterogeneous composition of cells within some clusters CTCs from TNBC PDOX models showed markers of epithelial, mesenchymal, and mixed phenotypes CTCs detected in our different PDOX tumor models of TNBC expressed basic epithelial (CK+) and/or mesenchymal (VIM+) markers, suggesting that individual CTCs may be in the process of undergoing epithelial-mesenchymal transition (EMT) (Figs. 4 and 6). Quantifying CTCs isolated from the TNBC PDOX model SUTI151 demonstrated that while some CTCs showed an epithelial phenotype (cytokeratin-positive, vimentin-negative) or a mesenchymal phenotype (cytokeratin-negative, vimentin-positive), the great majority of CTCs from this model expressed a mixed phenotype, positive for both cytokeratin and vimentin (Fig. 6a). Grouping the CTCs into distinct subsets based on the expression of these markers from two individual mice bearing SUTI151 tumors (as mentioned above, this model was derived from a particularly aggressive TNBC that metastasized rapidly) showed that the percentage of CTCs in each subset between the two animals were fairly similar (Fig. 6b). While such results highlight the utility of PDOX models for further investigations of EMT in CTCs, a strong correlation of EMT and the ability of CTCs to generate metastases would require further thorough investigation involving multiple PDOX models that display EMT changes. Here, it was only seen in one of our seven TNBC PDOX models. Epithelial, mesenchymal, and mixed phenotypes of CTCs isolated from a metastatic TNBC PDOX model. a Fluorescent images of CTCs isolated from a mouse bearing PDOX tumor SUTI151 captured using the Vortex platform and probed for the epithelial marker (cytokeratin, CK) and the mesenchymal marker (vimentin, VIM). Nuclei were highlighted with DAPI. CTCs were identified as DAPI positive, positive for CK and/or VIM, and negative for CD45. b Graph representing the percentage of CTCs staining positive for CK and/or VIM from two individual mouse models (#1, #2) bearing the same PDOX SUTI151 tumor, with the majority of CTCs showing a mixed epithelial and mesenchymal phenotype Circulating tumor cells, detected most often in metastatic cancer [71], are a key player in the metastatic cascade [31]. We have recently reported on label-free isolation and analysis of CTCs from two PDOX tumor-bearing mice as part of an evaluation of Vortex' fully automated VTX-1 Liquid Biopsy System [58]. Here, we investigated CTC shedding and metastases in TNBC PDOX models, examining 57 mice from a cohort of seven TNBC PDOX models for distant metastases in serially sectioned lung, liver, and brain, and using a marker-agnostic CTC isolation platform to isolate and analyze CTCs from 37 of these mice. As far as we are aware, seven previous studies have used breast cancer PDOX models to capture and analyze CTCs from mouse blood or DTCs from mouse bone marrow. One study [54] used a previous TP53 wildtype PDOX model of non-basal TNBC to generate cell lines that were transduced with lentivirus encoding CBR-luc and mCherry (FUW-CBR-luc-mCherry) and then infected with control retroviruses or retroviruses encoding p53-specific short hairpin RNAs (shRNAs) to knock down p53. They then implanted these wildtype and p53-deficient transduced cells into cleared mammary fat pads of NOD/SCID mice whose stroma was humanized using immortalized and irradiated human mammary stromal fibroblasts derived from a patient undergoing a reduction mammoplasty. Tumor growth; metastases to the lung, bone, liver, brain, and axillary lymph node; and CTC shedding (quantified using flow cytometry) were compared between wildtype and p53-deficient tumors. Although their PDOX models were generated very differently than ours, similar to our findings, metastatic tumor was identified at different sites in differing fractions of mice. Moreover, although CTC shedding increased with time, a finding more pronounced in mice whose tumors were p53-deficient, with numbers of CTCs in the less than 15 range at 9 weeks to the less than 220 range at 18 weeks, CTC shedding appeared more related to total primary and metastatic tumor burden. A different study [55] used PDOX models derived from five tumors of different breast cancer molecular subtypes that were implanted in humanized mammary fat pads (previously cleared and injected with GFP-labeled immortalized human fibroblasts) of NOD/SCID mice to investigate DTCs and distant metastases. Here, mouse bone marrow was analyzed by performing qRT-PCR for human transcripts as well as microarray analysis of gene expression in primary tumors, the bone marrow, and a metastatic lesion in one mouse. Only two PDOX tumor models developed metastases, both of which had human DTCs and which had variable sites of metastases. Global gene expression between diverse sources in the one mouse tested, a TNBC PDOX model, was also variable, but seemed to show patterns of human gene expression "reminiscent of a 'mesenchymal-like' phenotype in multiple animals across multiple passages," with the authors suggesting that DTCs from the bone marrow may have undergone a phenotypic transition that enabled migration to and survival in the bone marrow, similar to many of the CTCs we observed in our current study. Another study [52] measured CTCs from blood and DTCs from the bone marrow, detected using anti-human pan-cytokeratin immunohistochemistry (IHC), in 18 different breast cancer PDOX models, 13 of which were TNBC PDOX models, generated from human breast tumors implanted into the cleared mammary fat pads of SCID/beige mice. Again, differing fractions of individual mice in each model had detectable CTCs (overall, present in 83% of PDOX models) and/or DTCs (overall, present in 63% of PDOX models) and lung metastases (overall, present in 50% of PDOX models). Although no specific mesenchymal-like IHC marker was used, there was still a strong association between CTC and DTC detection. Importantly, all mice with lung metastases had detectable CTCs but not all mice with detectable CTCs had lung metastases, similar to our findings. A strong association between CTC clusters and the presence of lung metastases was also found. In a fourth study [51], single-cell suspensions of seven patient-derived breast tumors were orthotopically injected into SCID mice; two PDOX tumors developed CTCs as detected by an EpCAM-based platform, and no metastases were observed in any of the seven mice. An important study by the Werb group [53] using three PDOX models of TNBC in NOD/SCID mice showed that all models shed CTCs into blood, with variable CTC shedding (7/31 mice = 23% in one TNBC model had detectable cancer cells in their peripheral blood; 1/19 mice = 5% in another TNBC model had detectable cancer cells in their peripheral blood; and 3/22 mice = 14% in a third TNBC model had detectable cancer cells in their peripheral blood). All models developed metastases in different organs, but again, like our study, showed variability among individual mice within a TNBC model. Excitingly, single-cell gene expression signatures of cells from tissues with low and high metastatic burden and CTCs showed that a subpopulation of stem-like CTCs may potentially represent "metastatic seeder cells." A recent study of CTCs in non-NSG mice [56] used the same PDOX models described in their previous work [45, 52] but with CTCs isolated using a different CTC isolation platform that improved on CTC number and allowed identification of the PIK3CA T1035A mutation in single cells from CTCs, primary tumors, and lung metastases in one of their PDOX models. Finally, an interesting new study that analyzed human RNA transcripts in the blood (positive for CTCs), bone marrow (positive for DTCs), and tumor in severe combined immunodeficient (SCID) xenograft mouse models found that CTCs from an ER-positive PDOX model of lobular carcinoma expressed a possibly uncoupled epithelial-mesenchymal plasticity and lower expression of stem cell-like markers than CTCs from a cell line-derived TNBC xenograft [57]. A challenge when studying in vivo CTC models has been identifying an appropriate route of blood collection for maximal CTC yield for downstream analyses. We addressed this question first by using a metastatic, human TNBC cell line, MDA-MB-231, and discovered that blood collected via cardiac puncture yielded higher numbers of CTCs and CTC clusters, with some clusters heterotypic and containing both CTCs and WBCs. The importance of blood collection route for CTC analyses in mouse xenograft models was nicely addressed using cell line-derived xenografts and an EpCAM-based CTC isolation platform [51], concluding that cardiac puncture was the best route for obtaining CTCs compared to tail vein, retroorbital, and jugular vein aspiration. Similar to our findings, blood samples from the retroorbital venous plexus were uniformly contaminated by CTC-like normal murine epithelial cells in control mice without tumors. They also found that jugular vein aspiration yielded CTCs in only 15% of samples and also showed normal murine epithelial cell contamination from jugular vein aspiration in control mice. To our knowledge, our results are the first to address blood collection route using a marker-agnostic CTC isolation platform. While the cardiac route of blood collection is superior in its CTC yield, a major limitation of this route is that, as used here, it is a terminal method of blood collection, thereby limiting its application for serial CTC monitoring. Analyzing CTCs and distant metastases in different breast cancer PDOX models also depends on the genetic background of the mouse model selected. A recent study highlighted challenges and limitations of metastatic TNBC PDOX models using SCID mice [72]. The authors discussed several challenges that included low rate of metastases, long periods for metastases in the lungs to be detected, and development of thymic lymphomas of mouse origin, using their SCID mouse models. SCID mice may also develop spontaneous non-thymic tumors, including mammary adenocarcinomas [73]. Pertinently, while younger NSG models do not develop spontaneous tumors, a recent study of aging female NSG mice showed that tumors may indeed develop in mice of median age 52 weeks, when age was available, including 31% developing spontaneous mammary gland neoplasms [74], a recent finding for which the PDOX community should be made aware. In another study using NCr nude and SCID mice, only 2/7 PDOX models yielded CTCs and none had detectable distant metastases [51]. Addressing the issue of mouse model background, the Lippman group showed that NSG mice are superior for generating distant metastases in cell line- and patient-derived orthotopic xenograft models [50]. Using NSG mice for our study, most PDOX tumors grew aggressively and produced large tumors within 3 months of implantation, with detectable metastatic lesions in 6/7 of our TNBC PDOX tumor models. In our study, the percentage of PDOX tumor-bearing mice with metastases ranged from 78% for SUTI319 to 0 for SUTI368. It is interesting to note that although CTCs were detected in 5/5 of SUTI368 tumor-bearing mice, no distant metastases were detected in eight SUTI368 PDOX mice. While serial sectioning of organs was sufficient to detect metastases in the majority of our PDOX models, we may have missed micrometastases in un-sectioned portions of an organ that perhaps a more sensitive PCR-based approach, based on detecting human DNA in mouse whole organs, could have potentially detected, including PDOX model SUTI368 [75]. However, a more likely explanation for the presence of CTCs in 5/5 mice and lack of metastases in 0/8 mice from this model is that metastasis is an inefficient process [76]. In a classic murine melanoma model with intravital video-microscopy, metastatic inefficiency was found to be mainly due to (1) lack of initiation of growth (i.e., dormancy) of solitary cancer cells in a distant organ and (2) lack of growth of initial micrometastases into macroscopic tumors and vulnerability to early destruction [77]. This has also been confirmed in multiple other tumor models, including breast cancer [78], and additional mechanisms have been proposed as to why only a subset of circulating tumor cells may be associated with the development of metastases [79,80,81]. While the SUTI368 model is capable of generating CTCs, the tumor cells in circulation may not be capable of establishing metastatic growth because they may lack the ability to initiate the critical tumor-host interactions or may not possess intrinsic biomechanical or other molecular properties necessary for establishing metastases [82,83,84,85]. Moreover, it is interesting to note that even when all the individual animals were implanted with tumor tissue fragments from the same PDOX tumor, there were differences in tumor growth rates between the individual tumor-bearing animals as well as differences in the development of and site of metastases within the same PDOX tumor model. Heterogeneity in the amount of tumor tissue and associated stromal tissue in each fragment implanted, differences in the number of viable tumor cells, and the molecular heterogeneity of tumor cells in individual tumor fragments could trigger such different growth rates in vivo. To overcome such discrepancies, we are also using single-cell suspensions of tumor tissue for generating and passaging more uniform PDOX tumors (data not shown). CTCs can exist as single cells or clusters, and CTC clusters are predicted to have a greater potential to establish metastases than individual CTCs [86,87,88,89,90]. In mouse models of breast cancer, CTC clusters appear to be derived from oligoclonal groupings of primary tumor cells and have been shown to be a highly metastasis-competent subset of CTCs, compared to single circulating breast cancer cells [86, 87]. CTC clusters also may provide additional prognostic value in human breast cancer [91,92,93], and in patients with breast, prostate, and small cell lung cancer, the presence of single or increasing numbers of CTC clusters in sampled blood is found to correlate significantly with reduced progression-free survival rates [86, 91,92,93,94,95,96]. As a result, there has been an interest in isolating and understanding CTC clusters in different cancers and, in addition to filter and other technologies that identify clusters, some CTC isolation technologies have been specifically designed for isolating CTC clusters [97,98,99] or exploring their behavior [100]. In our studies, using the Vortex CTC isolation platform, we demonstrate rapid and efficient isolation of CTCs and CTC clusters from both cell line-derived xenograft and PDOX models of breast cancer. As this platform is marker-agnostic, we were able to capture heterogeneous clusters of CTCs that included individual cells that varied in the expression of CTC markers tested, demonstrating its utility for examining the biology and heterogeneity of CTC clusters in different cancer models. Another notable finding in our current study is the difference in the heterogeneous distribution of cytokeratin (epithelial), vimentin (mesenchymal), and mixed cytokeratin and vimentin markers in CTCs and CTC clusters within and between the TNBC PDOX tumors. For example, while some CTCs from these PDOX tumor models showed high expression of the epithelial marker cytokeratin or the mesenchymal marker vimentin, many CTCs stained strongly for both cytokeratin and vimentin. The distribution of epithelial-like, mesenchymal-like, and mixed epithelial and mesenchymal CTC phenotypes represents an important aspect of CTC heterogeneity. CTC heterogeneity, including differences in gene expression of vimentin and five other EMT markers, was previously highlighted by our group using high-dimensional single-cell transcriptional profiling of human CTCs from breast cancer patients, where cell-to-cell heterogeneity of CTCs was noted even within the same blood draw [101]. This was also demonstrated through the work of other groups that has shown mixtures of epithelial- and mesenchymal-like CTCs in human blood samples of breast and other cancers [102,103,104]. It has been postulated that hybrid EMT phenotypes may promote the development of cancer metastases [105,106,107], although how the role of EMT plasticity and the different EMT states precisely contribute to the metastatic process still remains under active investigation [108,109,110,111,112,113,114]. Heterogeneity among CTCs and resulting metastases may also be attributed to (i) differences in methylation patterns of specific genes [115], (ii) selective and differential expression of particular genes in a subset of CTCs [101, 116,117,118,119], and/or (iii) expression of certain genes at different stages of the disease [120,121,122,123]. Our data describes the heterogeneous distribution of lung, liver, and brain metastases in a group of seven TNBC PDOX models and confirms the shedding of CTCs captured by a marker-agnostic CTC isolation platform. It supports further use of PDOX models, generated in NSG mice, to study PDOX-derived CTCs, distant metastases, and for testing the impact and outcome of different anti-cancer agents on CTC shedding and metastasis in breast cancer. All data generated or analyzed during this study are included in this published article and can be shared by contacting the corresponding authors. Siegel RL, Miller KD, Jemal A. Cancer statistics, 2018. 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Expanded genomic profiling of circulating tumor cells in metastatic breast cancer patients to assess biomarker status and biology over time (CALGB 40502 and CALGB 40503, Alliance). Clin Cancer Res. 2018;24:1486–99. Lang JE, et al. RNA-Seq of circulating tumor cells in stage II-III breast cancer. Ann Surg Oncol. 2018;25:2261–70. Barbazán J, et al. Molecular characterization of circulating tumor cells in human metastatic colorectal cancer. PLoS One. 2012;7:e40476. Vishnoi M, et al. The isolation and characterization of CTC subsets related to breast cancer dormancy. Sci Rep. 2015;5:17533. Kwan TT, et al. A digital RNA signature of circulating tumor cells predicting early therapeutic response in localized and metastatic breast cancer. Cancer Discov. 2018;8(10):1286–99. Yeung C, et al. Estrogen, progesterone, and HER2/neu receptor discordance between primary and metastatic breast tumours-a review. Cancer Metastasis Rev. 2016;35:427–37. The authors thank Prof. R. Paulmurugan at Stanford University for sharing his MDA-MB-231-FLuc-eGFP cell line. This study was funded in part by Vortex Biosciences through a research contract with Stanford University (SSJ), the Susan G. Komen Foundation SAB1500003 (GWS, SSJ), the Breast Cancer Research Program of the Department of Defense W81XWH-14-1-0398 (SSJ), and the John and Marva Warnock Research Fund (SSJ). Department of Surgery, Stanford University School of Medicine, Stanford, CA, USA Vishnu C. Ramani , Melanie Triboulet , Kyra Heirich , Rakhi Gupta , Haiyu Zhang & Stefanie S. Jeffrey Vortex Biosciences Inc., Pleasanton, CA, USA Clementine A. Lemaire , Corinne Renier & Elodie Sollier Department of Comparative Medicine, Stanford University School of Medicine, Stanford, CA, USA Kerriann M. Casey , José G. Vilches-Moure & Aryana M. Razmara Department of Medicine, Stanford University School of Medicine, Stanford, CA, USA George W. Sledge Search for Vishnu C. Ramani in: Search for Clementine A. Lemaire in: Search for Melanie Triboulet in: Search for Kerriann M. Casey in: Search for Kyra Heirich in: Search for Corinne Renier in: Search for José G. Vilches-Moure in: Search for Rakhi Gupta in: Search for Aryana M. Razmara in: Search for Haiyu Zhang in: Search for George W. Sledge in: Search for Elodie Sollier in: Search for Stefanie S. Jeffrey in: VCR, CR, GWS, ES, and SSJ designed and planned the experiments. VCR, CAL, MT, KH, RG, and HZ performed the experiments; KMC and JGVM performed histologic studies. VCR, CAL, KMC, CR, AMR, GWS, ES, and SSJ analyzed the data. VCR, CAL, KMC, GWS, ES, and SSJ wrote the manuscript with assistance from the other authors. All authors have reviewed and approved this manuscript. Correspondence to Elodie Sollier or Stefanie S. Jeffrey. All studies were approved by the Stanford University Research Compliance Office's Human Subjects Research and IRB Panel and Stanford's Administrative Panel on Laboratory Animal Care (APLAC). All methods were performed in accordance with the relevant guidelines and regulations. Patient tumor samples were collected from patients in accordance with the relevant IRB guidelines. CAL, CR, and ES have financial interests in Vortex Biosciences and intellectual property described herein. The other authors declare that they have no competing interests. Figure S1. As a staining specificity control, human tumor cells from the MDA-MB-231 human TNBC cell line and mouse tumor cells from the 4T1 mouse TNBC cell line were both stained with the same set of antibodies used in the current study. The anti-pan cytokeratin antibody cocktail and the anti-vimentin antibody strongly stained human tumor cells; 4T1 mouse tumor cells showed minimal or absent staining with the same set of antibodies. (DOCX 234 kb) Ramani, V.C., Lemaire, C.A., Triboulet, M. et al. Investigating circulating tumor cells and distant metastases in patient-derived orthotopic xenograft models of triple-negative breast cancer. Breast Cancer Res 21, 98 (2019) doi:10.1186/s13058-019-1182-4 Circulating tumor cells (CTCs) Epithelial-mesenchymal transition (EMT) NOD scid gamma (NSG) Patient-derived orthotopic xenograft (PDOX) Triple-negative breast cancer (TNBC)	CommonCrawl
Sample records for rho-1670 resonances Petersen, Nils Holger A chapter in a book about terminology within the field of medievalism: the chapter discusses the resonance of medieval music and ritual in modern (classical) music culture and liturgical practice.......A chapter in a book about terminology within the field of medievalism: the chapter discusses the resonance of medieval music and ritual in modern (classical) music culture and liturgical practice.... Resonances an impetus or drive to that account: change, innovation, rupture, or discontinuity. Resonances: Historical Essays on Continuity and Change explores the historiographical question of the modes of interrelation between these motifs in historical narratives. The essays in the collection attempt to realize... Multiphoton resonances Shore, B.W. The long-time average of level populations in a coherently-excited anharmonic sequence of energy levels (e.g., an anharmonic oscillator) exhibits sharp resonances as a function of laser frequency. For simple linearly-increasing anharmonicity, each resonance is a superposition of various multiphoton resonances (e.g., a superposition of 3, 5, 7, . . . photon resonances), each having its own characteristic width predictable from perturbation theory Synchrobetatron resonances At the 1975 Particle Accelerator Conference it was reported that a class of resonances were observed in SPEAR II that had not appeared before in SPEAR I. While the existence of sideband resonances of the main betatron oscillation frequencies has been previously observed and analyzed, the resonances observed in SPEAR do not appear to be of the same variety. Experiments were performed at SPEAR to identify the mechanism believed to be the most likely explanation. Some of the current experimental knowledge and theoretical views on the source of these resonances are presented Snake resonances Tepikian, S. Siberian Snakes provide a practical means of obtaining polarized proton beams in large accelerators. The effect of snakes can be understood by studying the dynamics of spin precession in an accelerator with snakes and a single spin resonance. This leads to a new class of energy independent spin depolarizing resonances, called snake resonances. In designing a large accelerator with snakes to preserve the spin polarization, there is an added constraint on the choice of the vertical betatron tune due to the snake resonances. 11 refs., 4 figs Nonlinear resonances Rajasekar, Shanmuganathan This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo... Multiquark Resonances Esposito, A.; Polosa, A.D. Multiquark resonances are undoubtedly experimentally observed. The number of states and the amount of details on their properties has been growing over the years. It is very recent the discovery of two pentaquarks and the confirmation of four tetraquarks, two of which had not been observed before. We mainly review the theoretical understanding of this sector of particle physics phenomenology and present some considerations attempting a coherent description of the so called X and Z resonances. The prominent problems plaguing theoretical models, like the absence of selection rules limiting the number of states predicted, motivate new directions in model building. Data are reviewed going through all of the observed resonances with particular attention to their common features and the purpose of providing a starting point to further research. Neuroaesthetic Resonance Brooks, Anthony Lewis Neuroaesthetic Resonance emerged from a mature body of patient- centered gesture-control research investigating non-formal rehabilitation via ICT-enhanced-Art to question 'Aesthetic Resonance'. Motivating participation, ludic engagement, and augmenting physical motion in non-formal (fun) treatment...... sessions are achieved via adaptive action-analyzed activities. These interactive virtual environments are designed to empower patients' creative and/or playful expressions via digital feedback stimuli. Unconscious self- pushing of limits result from innate distractive mechanisms offered by the alternative...... the unencumbered motion-to-computer-generated activities - 'Music Making', 'Painting', 'Robotic' and 'Video Game' control. A focus of this position paper is to highlight how Aesthetic Resonance, in this context, relates to the growing body of research on Neuroaesthetics to evolve Neuroaesthetic Resonance.... Baryon Resonances Oset, E.; Sarkar, S.; Sun Baoxi; Vicente Vacas, M.J.; Ramos, A.; Gonzalez, P.; Vijande, J.; Martinez Torres, A.; Khemchandani, K. In this talk I show recent results on how many excited baryon resonances appear as systems of one meson and one baryon, or two mesons and one baryon, with the mesons being either pseudoscalar or vectors. Connection with experiment is made including a discussion on old predictions and recent results for the photoproduction of the Λ(1405) resonance, as well as the prediction of one 1/2 + baryon state around 1920 MeV which might have been seen in the γp→K + Λ reaction. 996 RESONANCE November 2013 Indian Academy of Sciences (India) IAS Admin 996. RESONANCE. November 2013. Page 2. 997. RESONANCE. November 2013. Page 3. 998. RESONANCE. November 2013. Page 4. 999. RESONANCE. November 2013. Page 5. 1000. RESONANCE. November 2013. Page 6. 1001. RESONANCE. November 2013. Page 7. 1002. RESONANCE. November 2013Â ... 817 RESONANCE September 2013 817. RESONANCE ⎜ September 2013. Page 2. 818. RESONANCE ⎜ September 2013. Page 3. 819. RESONANCE ⎜ September 2013. Page 4. 820. RESONANCE ⎜ September 2013. Page 5. 821. RESONANCE ⎜ September 2013. Page 6. 822. RESONANCE ⎜ September 2013. Page 7. 823. RESONANCE ⎜ September ... 369 RESONANCE April 2016 369. RESONANCE ⎜ April 2016. Page 2. 370. RESONANCE ⎜ April 2016. Page 3. 371. RESONANCE ⎜ April 2016. Page 4. 372. RESONANCE ⎜ April 2016. Page 5. 373. RESONANCE ⎜ April 2016. Page 6. 374. RESONANCE ⎜ April 2016. Page 7. 375. RESONANCE ⎜ April 2016. At the 1975 Particle Accelerator Conference it was reported that a class of resonances were observed in SPEAR II that had not appeared before in SPEAR I. These resonances occur when the betatron oscillation wave numbers ν/sub x/ or ν/sub y/ and the synchrotron wave number ν/sub s/ satisfy the relation (ν/sub x,y/ - mν/sub s/) = 5, with m an integer denoting the m/sup th/ satellite. The main difference between SPEAR II and SPEAR I is the value of ν/sub s/, which in SPEAR II is approximately 0.04, an order of magnitude larger than in SPEAR I. An ad hoc meeting was held at the 1975 Particle Accelerator Conference, where details of the SPEAR II results were presented and various possible mechanisms for producing these resonances were discussed. Later, experiments were performed at SPEAR to identify the mechanism believed to be the most likely explanation. Some of the current experimental knowledge and theoretical views on the source of these resonances are presented Autostereogram resonators Leavey, Sean; Rae, Katherine; Murray, Adam; Courtial, Johannes Autostereograms, or "Magic Eye" pictures, are repeating patterns designed to give the illusion of depth. Here we discuss optical resonators that create light patterns which, when viewed from a suitable position by a monocular observer, are autostereograms of the three-dimensional shape of one of the mirror surfaces. Resonating Statements Hjelholt, Morten; Jensen, Tina Blegind IT projects are often complex arrangements of technological components, social actions, and organizational transformation that are difficult to manage in practice. This paper takes an analytical discourse perspective to explore the process of legitimizing IT projects. We introduce the concept...... of resonating statements to highlight how central actors navigate in various discourses over time. Particularly, the statements and actions of an IT project manager are portrayed to show how individuals can legitimize actions by connecting statements to historically produced discourses. The case study...... as part of a feedback loop to re-attach the localized IT project to the broader national discourse. The paper concludes with reflections on how to actively build on resonating statements as a strategic resource for legitimizing IT projects... Gravitoelectromagnetic resonances Tsagas, Christos G. The interaction between gravitational and electromagnetic radiation has a rather long research history. It is well known, in particular, that gravity-wave distortions can drive propagating electromagnetic signals. Since forced oscillations provide the natural stage for resonances to occur, gravitoelectromagnetic resonances have been investigated as a means of more efficient gravity-wave detection methods. In this report, we consider the coupling between the Weyl and the Maxwell fields on a Minkowski background, which also applies to astrophysical environments where gravity is weak, at the second perturbative level. We use covariant methods that describe gravitational waves via the transverse component of the shear, instead of pure-tensor metric perturbations. The aim is to calculate the properties of the electromagnetic signal, which emerges from the interaction of its linear counterpart with an incoming gravitational wave. Our analysis shows how the wavelength and the amplitude of the gravitationally driven electromagnetic wave vary with the initial conditions. More specifically, for certain initial data, the amplitude of the induced electromagnetic signal is found to diverge. Analogous, diverging, gravitoelectromagnetic resonances were also reported in cosmology. Given that, we extend our Minkowski space study to cosmology and discuss analogies and differences in the physics and in the phenomenology of the Weyl-Maxwell coupling between the aforementioned two physical environments. Magnetic resonance annual 1986 Kressel, H.Y. This book contains papers written on magnetic resonance during 1986. Topics include: musculosketetal magnetic resonance imaging; imaging of the spine; magnetic resonance chemical shift imaging; magnetic resonance imaging in the central nervous system; comparison to computed tomography; high resolution magnetic resonance imaging using surface coils; magnetic resonance imaging of the chest; magnetic resonance imaging of the breast; magnetic resonance imaging of the liver; magnetic resonance spectroscopy of neoplasms; blood flow effects in magnetic resonance imaging; and current and potential applications of clinical sodium magnetic resonance imaging 1004 RESONANCE November 2013 1004. RESONANCE │ November 2013. Page 2. 1005. RESONANCE │ November 2013. Page 3. 1006. RESONANCE │ November 2013. Page 4. 1007. RESONANCE │ November 2013. Page 5. 1008. RESONANCE │ November 2013. Page 6. 1009. RESONANCE │ November 2013. Page 7. 1010. RESONANCE ... Even order snake resonances Lee, S.Y. We found that the perturbed spin tune due to the imperfection resonance plays an important role in beam depolarization at snake resonances. We also found that even order snake resonances exist in the overlapping intrinsic and imperfection resonances. Due to the perturbed spin tune shift of imperfection resonances, each snake resonance splits into two Applied neutron resonance theory Froehner, F.H. Utilisation of resonance theory in basic and applications-oriented neutron cross section work is reviewed. The technically important resonance formalisms, principal concepts and methods as well as representative computer programs for resonance parameter extraction from measured data, evaluation of resonance data, calculation of Doppler-broadened cross sections and estimation of level-statistical quantities from resonance parameters are described. (author) Utilisation of resonance theory in basic and applications-oriented neutron cross section work is reviewed. The technically important resonance formalisms, principal concepts and methods as well as representative computer programs for resonance parameter extraction from measured data, evaluation of resonance data, calculation of Doppler-broadened cross sections and estimation of level-statistical quantities from resonance parameters are described. (orig.) [de Narrow dibaryon resonances Kajdalov, A.B. Experimental data on np interactions indicating to existence of narrow resonances in pp-system are discussed. Possible theoretical interpretations of these resonances are given. Experimental characteristics of the dibaryon resonances with isospin I=2 are considered ... Procedures Medical Imaging MRI (Magnetic Resonance Imaging) MRI (Magnetic Resonance Imaging) Share Tweet Linkedin Pin it More sharing options Linkedin Pin it Email Print Magnetic Resonance Imaging (MRI) is a medical imaging procedure for ... Regenerative feedback resonant circuit Jones, A. Mark; Kelly, James F.; McCloy, John S.; McMakin, Douglas L. A regenerative feedback resonant circuit for measuring a transient response in a loop is disclosed. The circuit includes an amplifier for generating a signal in the loop. The circuit further includes a resonator having a resonant cavity and a material located within the cavity. The signal sent into the resonator produces a resonant frequency. A variation of the resonant frequency due to perturbations in electromagnetic properties of the material is measured. Resonances, resonance functions and spectral deformations Balslev, E. The present paper is aimed at an analysis of resonances and resonance states from a mathematical point of view. Resonances are characterized as singular points of the analytically continued Lippman-Schwinger equation, as complex eigenvalues of the Hamiltonian with a purely outgoing, exponentially growing eigenfunction, and as poles of the S-matrix. (orig./HSI) Stochastic resonance Wellens, Thomas; Shatokhin, Vyacheslav; Buchleitner, Andreas We are taught by conventional wisdom that the transmission and detection of signals is hindered by noise. However, during the last two decades, the paradigm of stochastic resonance (SR) proved this assertion wrong: indeed, addition of the appropriate amount of noise can boost a signal and hence facilitate its detection in a noisy environment. Due to its simplicity and robustness, SR has been implemented by mother nature on almost every scale, thus attracting interdisciplinary interest from physicists, geologists, engineers, biologists and medical doctors, who nowadays use it as an instrument for their specific purposes. At the present time, there exist a lot of diversified models of SR. Taking into account the progress achieved in both theoretical understanding and practical application of this phenomenon, we put the focus of the present review not on discussing in depth technical details of different models and approaches but rather on presenting a general and clear physical picture of SR on a pedagogical level. Particular emphasis will be given to the implementation of SR in generic quantum systems-an issue that has received limited attention in earlier review papers on the topic. The major part of our presentation relies on the two-state model of SR (or on simple variants thereof), which is general enough to exhibit the main features of SR and, in fact, covers many (if not most) of the examples of SR published so far. In order to highlight the diversity of the two-state model, we shall discuss several examples from such different fields as condensed matter, nonlinear and quantum optics and biophysics. Finally, we also discuss some situations that go beyond the generic SR scenario but are still characterized by a constructive role of noise Crossing simple resonances Collins, T. A simple criterion governs the beam distortion and/or loss of protons on a fast resonance crossing. Results from numerical integrations are illustrated for simple sextupole, octupole, and 10-pole resonances Acoustic Fano resonators KAUST Repository Amin, Muhammad; Farhat, Mohamed; Bagci, Hakan The resonances with asymmetric Fano line-shapes were originally discovered in the context of quantum mechanics (U. Fano, Phys. Rev., 124, 1866-1878, 1961). Quantum Fano resonances were generated from destructive interference of a discrete state Neutron resonance averaging Chrien, R.E. The principles of resonance averaging as applied to neutron capture reactions are described. Several illustrations of resonance averaging to problems of nuclear structure and the distribution of radiative strength in nuclei are provided. 30 refs., 12 figs A simple criterion governs the beam distortion and/or loss of protons on a fast resonance crossing. Results from numerical integrations are illustrated for simple sextupole, octupole, and 10-pole resonances. Pediatric magnetic resonance imaging Cohen, M.D. This book defines the current clinical potential of magnetic resonance imaging and focuses on direct clinical work with pediatric patients. A section dealing with the physics of magnetic resonance imaging provides an introduction to enable clinicians to utilize the machine and interpret the images. Magnetic resonance imaging is presented as an appropriate imaging modality for pediatric patients utilizing no radiation Resonant thermonuclear reaction rate Haubold, H.J.; Mathai, A.M. Basic physical principles for the resonant and nonresonant thermonuclear reaction rates are applied to find their standard representations for nuclear astrophysics. Closed-form representations for the resonant reaction rate are derived in terms of Meijer's G-function. Analytic representations of the resonant and nonresonant nuclear reaction rates are compared and the appearance of Meijer's G-function is discussed in physical terms Quantum mechanical resonances Cisneros S, A.; McIntosh, H.V. A discussion of the nature of quantum mechanical resonances is presented from the point of view of the spectral theory of operators. In the case of Bohr-Feshbach resonances, graphs are presented to illustrate the theory showing the decay of a doubly excited metastable state and the excitation of the resonance by an incident particle with proper energy. A characterization of resonances is given as well as a procedure to determine widths using the spectral density function. A sufficient condition is given for the validity of the Breit-Wigner formula for Bohr-Feshbach resonances. (author) Microstrip resonators for electron paramagnetic resonance experiments Torrezan, A. C.; Mayer Alegre, T. P.; Medeiros-Ribeiro, G. In this article we evaluate the performance of an electron paramagnetic resonance (EPR) setup using a microstrip resonator (MR). The design and characterization of the resonator are described and parameters of importance to EPR and spin manipulation are examined, including cavity quality factor, filling factor, and microwave magnetic field in the sample region. Simulated microwave electric and magnetic field distributions in the resonator are also presented and compared with qualitative measurements of the field distribution obtained by a perturbation technique. Based on EPR experiments carried out with a standard marker at room temperature and a MR resonating at 8.17 GHz, the minimum detectable number of spins was found to be 5×1010 spins/GHz1/2 despite the low MR unloaded quality factor Q0=60. The functionality of the EPR setup was further evaluated at low temperature, where the spin resonance of Cr dopants present in a GaAs wafer was detected at 2.3 K. The design and characterization of a more versatile MR targeting an improved EPR sensitivity and featuring an integrated biasing circuit for the study of samples that require an electrical contact are also discussed. Microstrip resonators for electron paramagnetic resonance experiments. Torrezan, A C; Mayer Alegre, T P; Medeiros-Ribeiro, G In this article we evaluate the performance of an electron paramagnetic resonance (EPR) setup using a microstrip resonator (MR). The design and characterization of the resonator are described and parameters of importance to EPR and spin manipulation are examined, including cavity quality factor, filling factor, and microwave magnetic field in the sample region. Simulated microwave electric and magnetic field distributions in the resonator are also presented and compared with qualitative measurements of the field distribution obtained by a perturbation technique. Based on EPR experiments carried out with a standard marker at room temperature and a MR resonating at 8.17 GHz, the minimum detectable number of spins was found to be 5 x 10(10) spins/GHz(1/2) despite the low MR unloaded quality factor Q0=60. The functionality of the EPR setup was further evaluated at low temperature, where the spin resonance of Cr dopants present in a GaAs wafer was detected at 2.3 K. The design and characterization of a more versatile MR targeting an improved EPR sensitivity and featuring an integrated biasing circuit for the study of samples that require an electrical contact are also discussed. Atlas of neutron resonances Mughabghab, Said Atlas of Neutron Resonances: Resonance Properties and Thermal Cross Sections Z= 1-60, Sixth Edition, contains an extensive list of detailed individual neutron resonance parameters for Z=1-60, as well as thermal cross sections, capture resonance integrals, average resonance parameters and a short survey of the physics of thermal and resonance neutrons. The long introduction contains: nuclear physics formulas aimed at neutron physicists; topics of special interest such as valence neutron capture, nuclear level density parameters, and s-, p-, and d-wave neutron strength functions; and various comparisons of measured quantities with the predictions of nuclear models, such as the optical model. As in the last edition, additional features have been added to appeal to a wider spectrum of users. These include: spin-dependent scattering lengths that are of interest to solid-state physicists, nuclear physicists and neutron evaluators; calculated and measured Maxwellian average 5-keV and 30-keV capture cross sections o... Magnetic resonance imaging apparatus Ehnholm, G.J. This patent describes an electron spin resonance enhanced magnetic resonance (MR) imaging (ESREMRI) apparatus able to generate a primary magnetic field during periods of nuclear spin transition excitation and magnetic resonance signal detection. This allows the generation of ESREMRI images of a subject. A primary magnetic field of a second and higher value generated during periods of nuclear spin transition excitation and magnetic resonance signal detection can be used to generate conventional MR images of a subject. The ESREMRI and native MR images so generated may be combined, (or superimposed). (author) Electron paramagnetic resonance Al'tshuler, S A Electron Paramagnetic Resonance is a comprehensive text on the field of electron paramagnetic resonance, covering both the theoretical background and the results of experiment. This book is composed of eight chapters that cover theoretical materials and experimental data on ionic crystals, since these are the materials that have been most extensively studied by the methods of paramagnetic resonance. The opening chapters provide an introduction to the basic principles of electron paramagnetic resonance and the methods of its measurement. The next chapters are devoted to the theory of spectra an Ramifide resonators for cyclotrons Smirnov, Yu.V. The resonators with the conductors ramified form for cyclotrons are systematized and separated into the self-contained class - the ramified resonators for cyclotrons (Carr). The ramified resonators are compared with the quarter-wave and half-wave nonramified resonators, accomplished from the transmitting lines fragments. The CRR are classified into two types: ones with the additional structural element, switched in parallel and in series. The CRR may include several additional structural elements. The CRR calculations may be concluded by analytical methods - the method of matrix calculation or the method of telegraph equations and numerical methods - by means of the ISFEL3D, MAFIA and other programs [ru Controlling Parametric Resonance Galeazzi, Roberto; Pettersen, Kristin Ytterstad the authors review the conditions for the onset of parametric resonance, and propose a nonlinear control strategy in order to both induce the resonant oscillations and to stabilize the unstable motion. Lagrange's theory is used to derive the dynamics of the system and input–output feedback linearization... Electron Paramagnetic Resonance Spectroscopy Home; Journals; Resonance – Journal of Science Education; Volume 20; Issue 11. Electron Paramagnetic Resonance Spectroscopy: Biological Applications. B G Hegde. General Article Volume 20 Issue 11 November 2015 pp 1017-1032. Fulltext. Click here to view fulltext PDF. Permanent link: Electromagnetic resonance waves Villaba, J.M.; Manjon, F.J.; Guirao, A.; Andres, M.V. We describe in this paper a set of experiments designed to make qualitative and quantitative measurements on electromagnetic resonances of several simple systems. The experiments are designed for the undergraduate laboratory of Electricity and Magnetism in Physics. These experiments can help the students understanding the concept of resonance, which appears in different fields of Physics. (Author) 8 refs Laser magnetic resonance spectroscopy Ferrari, C.A. The technique of laser resonance magnetic resonance allows one to study the high-resolution spectroscopy of transient paramagnetic species, viz, atoms, radicals, and molecular ions. This article is a brief exposition of the method, describing the principles, instrumentation and applicability of the IR and FIR-LMR and shows results of HF + . (Author) [pt Resonance and Fractal Geometry Broer, Henk W. The phenomenon of resonance will be dealt with from the viewpoint of dynamical systems depending on parameters and their bifurcations. Resonance phenomena are associated to open subsets in the parameter space, while their complement corresponds to quasi-periodicity and chaos. The latter phenomena Nuclear Magnetic Resonance Spectroscopy Home; Journals; Resonance – Journal of Science Education; Volume 9; Issue 1. Nuclear Magnetic Resonance Spectroscopy. Susanta Das. General Article Volume 9 Issue 1 January 2004 pp 34-49. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/009/01/0034-0049. Keywords. Cardiac magnetic resonance imaging Mar 6, 2011 ... Cardiac magnetic resonance imaging. Cardiovascular magnetic resonance imaging is becoming a routine diagnostic technique. BRUCE s sPOTTiswOOdE, PhD. MRC/UCT Medical Imaging Research Unit, University of Cape Town, and Division of Radiology, Stellenbosch University. Bruce Spottiswoode ... Fundamentals of nanomechanical resonators Schmid, Silvan; Roukes, Michael Lee This authoritative book introduces and summarizes the latest models and skills required to design and optimize nanomechanical resonators, taking a top-down approach that uses macroscopic formulas to model the devices. The authors cover the electrical and mechanical aspects of nano electromechanical system (NEMS) devices. The introduced mechanical models are also key to the understanding and optimization of nanomechanical resonators used e.g. in optomechanics. Five comprehensive chapters address: The eigenmodes derived for the most common continuum mechanical structures used as nanomechanical resonators; The main sources of energy loss in nanomechanical resonators; The responsiveness of micro and nanomechanical resonators to mass, forces, and temperature; The most common underlying physical transduction mechanisms; The measurement basics, including amplitude and frequency noise. The applied approach found in this book is appropriate for engineering students and researchers working with micro and nanomechanical... Resonant snubber inverter Lai, Jih-Sheng; Young, Sr., Robert W.; Chen, Daoshen; Scudiere, Matthew B.; Ott, Jr., George W.; White, Clifford P.; McKeever, John W. A resonant, snubber-based, soft switching, inverter circuit achieves lossless switching during dc-to-ac power conversion and power conditioning with minimum component count and size. Current is supplied to the resonant snubber branches solely by the main inverter switches. Component count and size are reduced by use of a single semiconductor switch in the resonant snubber branches. Component count is also reduced by maximizing the use of stray capacitances of the main switches as parallel resonant capacitors. Resonance charging and discharging of the parallel capacitances allows lossless, zero voltage switching. In one embodiment, circuit component size and count are minimized while achieving lossless, zero voltage switching within a three-phase inverter. Advances in magnetic resonance 10 Waugh, John S Advances in Magnetic Resonance, Volume 10, presents a variety of contributions to the theory and practice of magnetic resonance. The book contains three chapters that examine superoperators in magnetic resonance; ultrasonically modulated paramagnetic resonance; and the utility of electron paramagnetic resonance (EPR) and electron-nuclear double-resonance (ENDOR) techniques for studying low-frequency modes of atomic fluctuations and their significance for understanding the mechanism of structural phase transitions in solids. Multiple photon resonances Elliott, C.J.; Feldman, B.J. A detailed theoretical analysis is presented of the interaction of intense near-resonant monochromatic radiation with an N-level anharmonic oscillator. In particular, the phenomenon of multiple photon resonance, the process by which an N-level system resonantly absorbs two or more photons simultaneously, is investigated. Starting from the Schroedinger equation, diagrammatic techniques are developed that allow the resonant process to be analyzed quantitatively, in analogy with well-known two-level coherent phenomena. In addition, multiple photon Stark shifts of the resonances, shifts absent in two-level theory, are obtained from the diagrams. Insights into the nature of multiple photon resonances are gained by comparing the quantum mechanical system with classical coupled pendulums whose equations of motion possess identical eigenvalues and eigenvectors. In certain limiting cases, including that of the resonantly excited N-level harmonic oscillator and that of the equally spaced N-level system with equal matrix elements, analytic results are derived. The influence of population relaxation and phase-disrupting collisions on the multiple photon process are also analyzed, the latter by extension of the diagrammatic technique to the density matrix equations of motion. 11 figures Properties of spiral resonators Haeuser, J. The present thesis deals with the calculation and the study of the application possibilities of single and double spiral resonators. The main aim was the development and the construction of reliable and effective high-power spiral resonators for the UNILAC of the GSI in Darmstadt and the H - -injector for the storage ring HERA of DESY in Hamburg. After the presentation of the construction and the properties of spiral resonators and their description by oscillating-circuit models the theoretical foundations of the bunching are presented and some examples of a rebuncher and debuncher and their influence on the longitudinal particle dynamics are shown. After the description of the characteristic accelerator quantities by means of an oscillating-circuit model and the theory of an inhomogeneous λ/4 line it is shown, how the resonance frequency and the efficiency of single and double spiral resonators can be calculated from the geometrical quantities of the structure. In the following the dependence of the maximal reachable resonator voltage in dependence on the gap width and the surface of the drift tubes is studied. Furthermore the high-power resonators are presented, which were built for the different applications for the GSI in Darmstadt, DESY in Hamburg, and for the FOM Institute in Amsterdam. (orig./HSI) [de Magnetic Resonance Force Microscopy System Federal Laboratory Consortium — The Magnetic Resonance Force Microscopy (MRFM) system, developed by ARL, is the world's most sensitive nuclear magnetic resonance (NMR) spectroscopic analysis tool,... Resonant power converters Kazimierczuk, Marian K This book is devoted to resonant energy conversion in power electronics. It is a practical, systematic guide to the analysis and design of various dc-dc resonant inverters, high-frequency rectifiers, and dc-dc resonant converters that are building blocks of many of today's high-frequency energy processors. Designed to function as both a superior senior-to-graduate level textbook for electrical engineering courses and a valuable professional reference for practicing engineers, it provides students and engineers with a solid grasp of existing high-frequency technology, while acquainting them wit Excitation of Nucleon Resonances Burkert, Volker D. I discuss developments in the area of nucleon resonance excitation, both necessary and feasible, that would put our understanding of nucleon structure in the regime of strong QCD on a qualitatively new level. They involve the collection of high quality data in various channels, a more rigorous approach in the search for ''missing'' resonances, an effort to compute some critical quantities in nucleon resonance excitations from first principles, i.e. QCD, and a proposal focused to obtain an understanding of a fundamental quantity in nucleon structure Dihadronic and dileptonic resonances Gareev, F.A.; Barabanov, M.Yu.; Kazacha, G.S. Simple phenomenological rules are suggested for calculation of dihadron and dilepton resonance masses. A general interpretation is given for different exotic resonances in nuclear physics: Darmstadt-effect, dibaryon, dipion and other resonances. Information about the inner structure of e ± , proton, neutron, pions and so on can be obtained from the usual reactions of the type e + + e - =>γγ, e ± +γ=>e ± γ, e ± μ ± , e ± N... at low, intermediate and high energies using existing experimental devices Multiquark resonant states Shahbazian, B.A. The invariant mass spectra of forty nine hadronic systems with hypercharge, strangeness and baryon number, varied in wide limits have been studied. Resonance peaks have been found in the invariant mass spectra of Y 2 and #betta#pπ 2495 MeV/c 2 resonant states. Three more candidates for anti qq 4 states were found #bettaπ# + π + : 1705, 2072, 2605 MeV/c 2 . The masses of all these candidates are in good agreement with Bag Model predictions. A hypercharge selection rule is suggested: ''The hypercharge of hadronic resonances in weak gravitational fields cannot exceed one Y <= 1 Resonant halide perovskite nanoparticles Tiguntseva, Ekaterina Y.; Ishteev, Arthur R.; Komissarenko, Filipp E.; Zuev, Dmitry A.; Ushakova, Elena V.; Milichko, Valentin A.; Nesterov-Mueller, Alexander; Makarov, Sergey V.; Zakhidov, Anvar A. The hybrid halide perovskites is a prospective material for fabrication of cost-effective optical devices. Unique perovskites properties are used for solar cells and different photonic applications. Recently, perovskite-based nanophotonics has emerged. Here, we consider perovskite like a high-refractive index dielectric material, which can be considered to be a basis for nanoparticles fabrication with Mie resonances. As a result, we fabricate and study resonant perovskite nanoparticles with different sizes. We reveal, that spherical nanoparticles show enhanced photoluminescence signal. The achieved results lay a cornerstone in the field of novel types of organic-inorganic nanophotonics devices with optical properties improved by Mie resonances. Writing with resonance Meier, Ninna; Wegener, Charlotte In this article, we explore what organization and management scholars can do to write with resonance and to facilitate an emotional, bodily, or in other ways sensory connection between the text and the reader. We propose that resonance can be relevant for organization and management scholars in two......, and thus bring forward the field of research in question. We propose that writing with resonance may be a way to further the impact of academic work by extending the modalities with which our readers can relate to and experience our work.... Doubly resonant multiphoton ionization Crance, M. A particular case of doubly resonant multiphoton ionization is theoretically investigated. More precisely, two levels quasi-resonant with two successive harmonics of the field frequency are considered. The method used is based on the effective operator formalism first introduced for this problem by Armstrong, Beers and Feneuille. The main result is to show the possibility of observing large interference effects on the width of the resonances. Moreover this treatment allows us to make more precise the connection between effective operator formalism and standard perturbation theory Magnetic Resonance (MR) Defecography ... to a CD or uploaded to a digital cloud server. Magnetic resonance (MR) defecography is a special ... with you. top of page What are the benefits vs. risks? Benefits MR defecography helps assess pelvic ... Quantum Proximity Resonances Heller, E.J. It is well known that at long wavelengths λ an s-wave scatterer can have a scattering cross section σ on the order of λ 2 , much larger than its physical size, as measured by the range of its potential. Very interesting phenomena can arise when two or more identical scatterers are placed close together, well within one wavelength. We show that, for a pair of identical scatterers, an extremely narrow p-wave open-quote open-quote proximity close-quote close-quote resonance develops from a broader s-wave resonance of the individual scatterers. A new s-wave resonance of the pair also appears. The relation of these proximity resonances (so called because they appear when the scatterers are close together) to the Thomas and Efimov effects is discussed. copyright 1996 The American Physical Society Resonances in QCD Lutz, Matthias F.M., E-mail: [email protected] [GSI Helmholtzzentrum für Schwerionenforschung GmbH, D-64291 Darmstadt (Germany); Technische Universität Darmstadt, D-64289 Darmstadt (Germany); Lange, Jens Sören, E-mail: [email protected] [II. Physikalisches Institut, Justus-Liebig-Universität Giessen, D-35392 Giessen (Germany); Pennington, Michael, E-mail: [email protected] [Thomas Jefferson National Accelerator Facility, Newport News, VA 23606 (United States); Bettoni, Diego [Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, 44122 Ferrara (Italy); Brambilla, Nora [Physik Department, Technische Universität München, D-85747 Garching (Germany); Crede, Volker [Department of Physics, Florida State University, Tallahassee, FL 32306 (United States); Eidelman, Simon [Novosibirsk State University, Novosibirsk 630090 (Russian Federation); Budker Istitute of Nuclear Physics SB RAS, Novosibirsk 630090 (Russian Federation); Gillitzer, Albrecht [Institut für Kernphysik, Forschungszentrum Jülich GmbH, D-52425 Jülich (Germany); Gradl, Wolfgang [Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, D-55128 Mainz (Germany); Lang, Christian B. [Institut für Physik, Universität Graz, A-8010 Graz (Austria); Metag, Volker [II. Physikalisches Institut, Justus-Liebig-Universität Giessen, D-35392 Giessen (Germany); Nakano, Takashi [Research Center for Nuclear Physics, Osaka University, Osaka 567-0047 (Japan); and others We report on the EMMI Rapid Reaction Task Force meeting 'Resonances in QCD', which took place at GSI October 12–14, 2015. A group of 26 people met to discuss the physics of resonances in QCD. The aim of the meeting was defined by the following three key questions: • What is needed to understand the physics of resonances in QCD? • Where does QCD lead us to expect resonances with exotic quantum numbers? • What experimental efforts are required to arrive at a coherent picture? For light mesons and baryons only those with up, down and strange quark content were considered. For heavy–light and heavy–heavy meson systems, those with charm quarks were the focus. This document summarizes the discussions by the participants, which in turn led to the coherent conclusions we present here. Magnetic resonance angiography (MRA) Arlart, I.P.; Guhl, L. An account is given in this paper of the physical and technical principles underlying the 'time-of-flight' technique for imaging of vessels by magnetic resonance tomography. Major indications for the new procedure of magnetic resonance angiography at present are intracerebral and extracerebral vessels, with digital subtraction angiography quite often being required to cope with minor alterations (small aneurysms, small occlusions). Magnetic resonance angiography and digital subtraction angiography are compared to each other for advantages and disadvantages. Basically, replacement of radiological angiography by magnetic resonance angiography appears to be possible only within limits, since X-ray diagnostics primarily provides morphological information about vessels, whereas flow dynamics is visualized by the 'time-of-flight' technique. (orig.) [de Magnetic Resonance Cholangiopancreatography (MRCP) ... radio waves and a computer to evaluate the liver, gallbladder, bile ducts, pancreas and pancreatic duct for disease. It is ... of the hepatobiliary and pancreatic systems, including the liver, gallbladder, bile ducts, pancreas and pancreatic duct . Magnetic resonance imaging (MRI) ... Piezoelectric MEMS resonators Piazza, Gianluca This book introduces piezoelectric microelectromechanical (pMEMS) resonators to a broad audience by reviewing design techniques including use of finite element modeling, testing and qualification of resonators, and fabrication and large scale manufacturing techniques to help inspire future research and entrepreneurial activities in pMEMS. The authors discuss the most exciting developments in the area of materials and devices for the making of piezoelectric MEMS resonators, and offer direct examples of the technical challenges that need to be overcome in order to commercialize these types of devices. Some of the topics covered include: Widely-used piezoelectric materials, as well as materials in which there is emerging interest Principle of operation and design approaches for the making of flexural, contour-mode, thickness-mode, and shear-mode piezoelectric resonators, and examples of practical implementation of these devices Large scale manufacturing approaches, with a focus on the practical aspects associate... Lattices of dielectric resonators Trubin, Alexander This book provides the analytical theory of complex systems composed of a large number of high-Q dielectric resonators. Spherical and cylindrical dielectric resonators with inferior and also whispering gallery oscillations allocated in various lattices are considered. A new approach to S-matrix parameter calculations based on perturbation theory of Maxwell equations, developed for a number of high-Q dielectric bodies, is introduced. All physical relationships are obtained in analytical form and are suitable for further computations. Essential attention is given to a new unified formalism of the description of scattering processes. The general scattering task for coupled eigen oscillations of the whole system of dielectric resonators is described. The equations for the expansion coefficients are explained in an applicable way. The temporal Green functions for the dielectric resonator are presented. The scattering process of short pulses in dielectric filter structures, dielectric antennas and lattices of d... Lutz, Matthias F. M.; Lange, Jens Sören; Pennington, Michael; Bettoni, Diego; Brambilla, Nora; Crede, Volker; Eidelman, Simon; Gillitzer, Albrecht; Gradl, Wolfgang; Lang, Christian B.; Metag, Volker; Nakano, Takashi; Nieves, Juan; Neubert, Sebastian; Oka, Makoto; Olsen, Stephen L.; Pappagallo, Marco; Paul, Stephan; Pelizäus, Marc; Pilloni, Alessandro; Prencipe, Elisabetta; Ritman, Jim; Ryan, Sinead; Thoma, Ulrike; Uwer, Ulrich; Weise, Wolfram We report on the EMMI Rapid Reaction Task Force meeting 'Resonances in QCD', which took place at GSI October 12-14, 2015 (Fig.~1). A group of 26 people met to discuss the physics of resonances in QCD. The aim of the meeting was defined by the following three key questions; what is needed to understand the physics of resonances in QCD?; where does QCD lead us to expect resonances with exotic quantum numbers?; and what experimental efforts are required to arrive at a coherent picture? For light mesons and baryons only those with up, down and strange quark content were considered. For heavy-light and heavy-heavy meson systems, those with charm quarks were the focus.This document summarizes the discussions by the participants, which in turn led to the coherent conclusions we present here. Accidental degeneracy of resonances Hernandez, E.; Mondragon, A.; Jauregui, A. Full text: It will be shown that a degeneracy of resonances is associated with a second rank pole in the scattering matrix and a Jordan cycle of generalized eigenfunctions of the radial Schrodinger equation. The generalized Gamow-Jordan eigenfunctions are basis elements of an expansion in complex resonance energy eigenfunctions. In this orthonormal basis, the Hamiltonian is represented by a non-diagonal complex matrix with a Jordan block of rank two. Some general properties of the degeneracy of resonances will be exhibited and discussed in an explicit example of degeneracy of resonant states and double poles in the scattering matrix of a double barrier potential. The cross section, scattering wave functions and Jordan-Gamow eigenfunctions are computed at degeneracy and their properties as functions of the control parameters of the system are discussed. (Author) Resonant diphoton phenomenology simplified Panico, Giuliano; Vecchi, Luca; Wulzer, Andrea A framework is proposed to describe resonant diphoton phenomenology at hadron colliders in full generality. It can be employed for a comprehensive model-independent interpretation of the experimental data. Within the general framework, few benchmark scenarios are defined as representative of the various phenomenological options and/or of motivated new physics scenarios. Their usage is illustrated by performing a characterization of the 750 GeV excess, based on a recast of available experimental results. We also perform an assessment of which properties of the resonance could be inferred, after discovery, by a careful experimental study of the diphoton distributions. These include the spin J of the new particle and its dominant production mode. Partial information on its CP-parity can also be obtained, but only for J≥2. The complete determination of the resonance CP properties requires studying the pattern of the initial state radiation that accompanies the resonant diphoton production. Magnetic Resonance Sensors Robert H. Morris Full Text Available Magnetic Resonance finds countless applications, from spectroscopy to imaging, routinely in almost all research and medical institutions across the globe. It is also becoming more frequently used for specific applications in which the whole instrument and system is designed for a dedicated application. With beginnings in borehole logging for the petro-chemical industry Magnetic Resonance sensors have been applied to fields as varied as online process monitoring for food manufacture and medical point of care diagnostics. This great diversity is seeing exciting developments in magnetic resonance sensing technology published in application specific journals where they are often not seen by the wider sensor community. It is clear that there is enormous interest in magnetic resonance sensors which represents a significant growth area. The aim of this special edition of Sensors was to address the wide distribution of relevant articles by providing a forum to disseminate cutting edge research in this field in a single open source publication.[... Magnetic resonance angiography ... Saunders; 2015:chap 17. Litt H, Carpenter JP. Magnetic resonance imaging. In: Cronenwett JL, Johnston KW, eds. Rutherford's Vascular Surgery . 8th ed. Philadelphia, PA: Elsevier Saunders; 2014:chap ... Ethier, R.; Melanson, D.; Peters, T.M. Ten years following computerized tomography, a new technique called nuclear magnetic resonance revolutionizes the field of diagnostic imaging. A major advantage of nuclear magnetic resonance is that the danger of radiation is non-existent as compared to computerized tomography. When parts of the human body are subject to radio-frequencies while in a fixed magnetic field, its most detailed structures are revealed. The quality of images, the applications, as well as the indications are forever increasing. Images obtained at the level of the brain and spinal cord through nuclear magnetic resonance supercede those obtained through computerized tomography. Hence, it is most likely that myelography, along with pneumoencephalography will be eliminated as a diagnostic means. It is without a doubt that nuclear magnetic resonance is tomorrow's computerized tomography [fr Robertson, Angus An assessment is made of the clinical benefits of expensive diagnostic technology, such as the magnetic resonance imaging. It is concluded that to most radiologists, magnetic resonance imaging has a definite place in the diagnostic scenario, especially for demonstrating central nervous system lesions in multiple sclerosis. While it is recognized that medical and financial resources are limited, it is emphasised that the cost to society must be balanced against the patient benefit. 17 refs Comment on resonant absorption Hammerling, P. An average over angles of incidence of the usual resonant absorption function is presented. This form is appropriate under experimental conditions where the angles of incidence vary greatly and in an unknown manner. For comparison a lens-ellipsoidal mirror illumination system with a known longitudinal aberration is considered. In the latter example the angles of incidence are readily obtained and the resulting resonance absorption function evaluated. The associated fields are calculated in a similar fashion. (author) Nuclear magnetic resonance gyroscope Grover, B.C. A nuclear magnetic resonance gyro using two nuclear magnetic resonance gases, preferably xenon 129 and xenon 131, together with two alkaline metal vapors, preferably rubidium, potassium or cesium, one of the two alkaline metal vapors being pumped by light which has the wavelength of that alkaline metal vapor, and the other alkaline vapor being illuminated by light which has the wavelength of that other alkaline vapor Microwave Resonators and Filters 1 Microwave Resonators and Filters Daniel E. Oates MIT Lincoln Laboratory 244 Wood St. Lexington, MA 02478 USA Email: [email protected] in other chapters, the surface resistance of superconductors at microwave frequencies can be as much as three orders of magnitude lower than the...resonators and filters in the first edition of this handbook (Z.-Y. Shen 2003) discussed the then state of the art of microwave frequency applications Resonance phenomena near thresholds Persson, E.; Mueller, M.; Rotter, I.; Technische Univ. Dresden The trapping effect is investigated close to the elastic threshold. The nucleus is described as an open quantum mechanical many-body system embedded in the continuum of decay channels. An ensemble of compound nucleus states with both discrete and resonance states is investigated in an energy-dependent formalism. It is shown that the discrete states can trap the resonance ones and also that the discrete states can directly influence the scattering cross section. (orig.) Nuclear magnetic resonance imaging Young, I.R. In a method of imaging a body in which nuclear magnetic resonance is excited in a region including part of the body, and the free induction decay signal is measured, a known quantity of a material of known nuclear magnetic resonance properties, for example a bag of water, is included in the region so as to enhance the measured free induction decay signal. This then reduces the generation of noise during subsequent processing of the signal. (author) Resonance probe; La sonde a resonance Lepechinsky, D; Messiaen, A; Rolland, P [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires After a brief review of papers recently published on the resonance probe as a tool for plasma diagnostics, the main features of the theory proposed by one of us are recalled. In this theory the geometry of the resonator formed by the probe, the ion sheath and the plasma is explicitly taken into account with the quasi-static and cold plasma approximations. Some new results emerging from this theory are indicated and a comparison with experimental data obtained with a spherical probe placed in a quiescent mercury-vapour plasma is made. A good quantitative agreement has been observed, indicating that the theory is satisfactory and justifying the assumptions involved. Nevertheless it appears that in some cases experimental results can only be interpreted when non collisional damping phenomena are taken into consideration. (author) [French] Apres un apercu des etudes recemment publiees sur la sonde a resonance pour le diagnostic des plasmas, on rappelle l'essentiel de la theorie proposee par l'un de nous ou il est tenu compte explicitement de la geometrie du resonateur forme par le systeme sonde-gaine ionique-plasma dans l'approximation quasi-statique et du plasma froid. On indique quelques resultats nouveaux pouvant etre tires de cette theorie et on la confronte avec les donnees experimentales obtenues pour une sonde spherique placee dans un plasma de mercure en equilibre. Un tres bon accord quantitatif a ete constate, indiquant que la theorie est satisfaisante et justifiant les approximations faites dans celle-ci. Il apparait toutefois que certains resultats experimentaux ne peuvent etre interpretes qu'en tenant compte des phenomenes d'amortissement non collisionnels. (auteur) Resonant enhancement in leptogenesis Dev, P. S. B.; Garny, M.; Klaric, J.; Millington, P.; Teresi, D. Vanilla leptogenesis within the type I seesaw framework requires the mass scale of the right-handed neutrinos to be above 109 GeV. This lower bound can be avoided if at least two of the sterile states are almost mass degenerate, which leads to an enhancement of the decay asymmetry. Leptogenesis models that can be tested in current and upcoming experiments often rely on this resonant enhancement, and a systematic and consistent description is therefore necessary for phenomenological applications. In this paper, we give an overview of different methods that have been used to study the saturation of the resonant enhancement when the mass difference becomes comparable to the characteristic width of the Majorana neutrinos. In this limit, coherent flavor transitions start to play a decisive role, and off-diagonal correlations in flavor space have to be taken into account. We compare various formalisms that have been used to describe the resonant regime and discuss under which circumstances the resonant enhancement can be captured by simplified expressions for the CP asymmetry. Finally, we briefly review some of the phenomenological aspects of resonant leptogenesis. Resonant ultrasound spectrometer Migliori, Albert; Visscher, William M.; Fisk, Zachary An ultrasound resonant spectrometer determines the resonant frequency spectrum of a rectangular parallelepiped sample of a high dissipation material over an expected resonant response frequency range. A sample holder structure grips corners of the sample between piezoelectric drive and receive transducers. Each transducer is mounted on a membrane for only weakly coupling the transducer to the holder structure and operatively contacts a material effective to remove system resonant responses at the transducer from the expected response range. i.e., either a material such as diamond to move the response frequencies above the range or a damping powder to preclude response within the range. A square-law detector amplifier receives the response signal and retransmits the signal on an isolated shield of connecting cabling to remove cabling capacitive effects. The amplifier also provides a substantially frequency independently voltage divider with the receive transducer. The spectrometer is extremely sensitive to enable low amplitude resonance to be detected for use in calculating the elastic constants of the high dissipation sample. Electrothermally Tunable Arch Resonator Hajjaj, Amal Z. This paper demonstrates experimentally, theoretically, and numerically a wide-range tunability of electrothermally actuated microelectromechanical arch beams. The beams are made of silicon and are intentionally fabricated with some curvature as in-plane shallow arches. An electrothermal voltage is applied between the anchors of the beam generating a current that controls the axial stress caused by thermal expansion. When the electrothermal voltage increases, the compressive stress increases inside the arch beam. This leads to an increase in its curvature, thereby increasing its resonance frequencies. We show here that the first resonance frequency can increase monotonically up to twice its initial value. We show also that after some electrothermal voltage load, the third resonance frequency starts to become more sensitive to the axial thermal stress, while the first resonance frequency becomes less sensitive. These results can be used as guidelines to utilize arches as wide-range tunable resonators. Analytical results based on the nonlinear Euler Bernoulli beam theory are generated and compared with the experimental data and the results of a multi-physics finite-element model. A good agreement is found among all the results. [2016-0291 Josephson junctions array resonators Gargiulo, Oscar; Muppalla, Phani; Mirzaei, Iman; Kirchmair, Gerhard [Institute for Quantum Optics and Quantum Information, Innsbruck (Austria) We present an experimental analysis of the self- and cross-Kerr effect of extended plasma resonances in Josephson junction chains. The chain consists of 1600 individual junctions and we can measure quality factors in excess of 10000. The Kerr effect manifests itself as a frequency shift that depends linearly on the number of photons in a resonant mode. By changing the input power we are able to measure this frequency shift on a single mode (self-kerr). By changing the input power on another mode while measuring the same one, we are able to evaluate the cross-kerr effect. We can measure the cross-Kerr effect by probing the resonance frequency of one mode while exciting another mode of the array with a microwave drive. Electrothermally Tunable Bridge Resonator Hajjaj, Amal Z.; Alcheikh, Nouha; Ramini, Abdallah; Hafiz, Md Abdullah Al; Younis, Mohammad I. This paper demonstrates experimentally, theoretically, and numerically a wide-range tunability of an in-plane clamped-clamped microbeam, bridge, and resonator compressed by a force due to electrothermal actuation. We demonstrate that a single resonator can be operated at a wide range of frequencies. The microbeam is actuated electrothermally, by passing a DC current through it. We show that when increasing the electrothermal voltage, the compressive stress inside the microbeam increases, which leads eventually to its buckling. Before buckling, the fundamental frequency decreases until it drops to very low values, almost to zero. After buckling, the fundamental frequency increases, which is shown to be as high as twice the original resonance frequency. Analytical results based on the Galerkin discretization of the Euler Bernoulli beam theory are generated and compared to the experimental data and to simulation results of a multi-physics finite-element model. A good agreement is found among all the results. Higgs-photon resonances Dobrescu, Bogdan A.; Fox, Patrick J.; Kearney, John [Fermilab, Theoretical Physics Department, Batavia, IL (United States) We study models that produce a Higgs boson plus photon (h{sup 0}γ) resonance at the LHC. When the resonance is a Z{sup '} boson, decays to h{sup 0}γ occur at one loop. If the Z{sup '} boson couples at tree level to quarks, then the h{sup 0}γ branching fraction is typically of order 10{sup -5} or smaller. Nevertheless, there are models that would allow the observation of Z{sup '} → h{sup 0}γ at √(s) = 13 TeV with a cross section times branching fraction larger than 1 fb for a Z{sup '} mass in the 200-450 GeV range, and larger than 0.1 fb for a mass up to 800 GeV. The one-loop decay of the Z{sup '} into lepton pairs competes with h{sup 0}γ, even if the Z{sup '} couplings to leptons vanish at tree level. We also present a model in which a Z{sup '} boson decays into a Higgs boson and a pair of collimated photons, mimicking an h{sup 0}γ resonance. In this model, the h{sup 0}γ resonance search would be the discovery mode for a Z{sup '} as heavy as 2 TeV. When the resonance is a scalar, although decay to h{sup 0}γ is forbidden by angular momentum conservation, the h{sup 0} plus collimated photons channel is allowed. We comment on prospects of observing an h{sup 0}γ resonance through different Higgs decays, on constraints from related searches, and on models where h{sup 0} is replaced by a nonstandard Higgs boson. (orig.) Magnetic resonance annual, 1988 This book features reviews of high-resolution MRI of the knee, MRI of the normal and ischmeic hip, MRI of the heart, and temporomandibular joint imaging, as well as thorough discussion on artifacts in magnetic resonance imaging. Contributors consider the clinical applications of gadolinium-DTPA in magnetic resonance imaging and the clinical use of partial saturation and saturation recovery sequences. Timely reports assess the current status of rapid MRI and describe a new rapid gated cine MRI technique. Also included is an analysis of cerebrospinal fluid flow effects during MRI of the central nervous system Amin, Muhammad The resonances with asymmetric Fano line-shapes were originally discovered in the context of quantum mechanics (U. Fano, Phys. Rev., 124, 1866-1878, 1961). Quantum Fano resonances were generated from destructive interference of a discrete state with a continuum one. During the last decade this concept has been applied in plasmonics where the interference between a narrowband polariton and a broader one has been used to generate electromagnetically induced transparency (EIT) (M. Rahmani, et al., Laser Photon. Rev., 7, 329-349, 2013). Giant nuclear resonances Snover, K.A. Giant nuclear resonances are elementary mods of oscillation of the whole nucleus, closely related to the normal modes of oscillation of coupled mechanical systems. They occur systematically in most if not all nuclei, with oscillation energies typically in the range 10-30 MeV. One of the best - known examples is the giant electric dipole (El) resonance, in which all the protons and all the neutrons oscillate with opposite phase, producing a large time - varying electric dipole moment which acts as an effective antenna for radiating gamma ray. This paper discusses this mode as well as quadrupole and monopole modes Nanoantenna using mechanical resonance Chang Hwa Lee, Nanoantenna using mechanical resonance vibration is made from an indium tin oxide (ITO) coated vertically aligned nanorod array. Only this structure works as a radio with demodulator without any electrical circuit using field emission phenomenon. A top-down fabrication method of an ITO coated nanorod array is proposed using a modified UV lithography. The received radio frequency and the resonance frequency of nanoantenna can be controlled by the fabrication condition through the height of a nanorod array. The modulated signals are received successfully with the transmission carrier wave frequency (248MHz) and the proposed nanoantenna is expected to be used in communication system for ultra small scale sensor. ©2010 IEEE. Resonant freak microwaves Aguiar, F.M. de The Helmholtz equation describing transverse magnetic modes in a closed flat microwave resonator with 60 randomly distributed discs is numerically solved. At lower frequencies, the calculated wave intensity spatially distributed obeys the universal Porter-Thomas form if localized modes are excluded. A superposition of resonant modes is shown to lead to rare events of extreme intensities (freak waves) at localized 'hot spots'. The temporally distributed intensity of such a superposition at the center of a hot spot also follows the Porter-Thomas form. Branched modes are found at higher frequencies. The results bear resemblance to recent experiments reported in an open cavity. Physics of Sports: Resonances Browning, David When force is applied by an athlete to sports equipment resonances can occur. Just a few examples are: the ringing of a spiked volleyball, the strumming of a golf club shaft during a swing, and multiple modes induced in an aluminum baseball bat when striking a ball. Resonances produce acoustic waves which, if conditions are favorable, can be detected off the playing field. This can provide a means to evaluate athletic performance during game conditions. Results are given from the use of a simple hand-held acoustic detector - by a spectator sitting in the stands - to determine how hard volleyballs were spiked during college and high school games. Hadronic Resonances from STAR Wada Masayuki Full Text Available The results of resonance particle productions (�0, ω, K, ϕ, Σ, and Λ* measured by the STAR collaboration at RHIC from various colliding systems and energies are presented. Measured mass, width, 〈pT〉, and yield of those resonances are reviewed. No significant mass shifts or width broadening beyond the experiment uncertainties are observed. New measurements of ϕ and ω from leptonic decay channels are presented. The yields from leptonic decay channels are compared with the measurements from hadronic decay channels and the two results are consistent with each other. Uncertainty quantification in resonance absorption Williams, M.M.R. We assess the uncertainty in the resonance escape probability due to uncertainty in the neutron and radiation line widths for the first 21 resonances in 232 Th as given by . Simulation, quadrature and polynomial chaos methods are used and the resonance data are assumed to obey a beta distribution. We find the uncertainty in the total resonance escape probability to be the equivalent, in reactivity, of 75–130 pcm. Also shown are pdfs of the resonance escape probability for each resonance and the variation of the uncertainty with temperature. The viability of the polynomial chaos expansion method is clearly demonstrated. Magnetic resonance of phase transitions Owens, Frank J; Farach, Horacio A Magnetic Resonance of Phase Transitions shows how the effects of phase transitions are manifested in the magnetic resonance data. The book discusses the basic concepts of structural phase and magnetic resonance; various types of magnetic resonances and their underlying principles; and the radiofrequency methods of nuclear magnetic resonance. The text also describes quadrupole methods; the microwave technique of electron spin resonance; and the Mössbauer effect. Phase transitions in various systems such as fluids, liquid crystals, and crystals, including paramagnets and ferroelectrics, are also Imaging by magnetic resonance Duroure, J.F.; Serpolay, H.; Vallens, D. Here are described the advanced technology for nuclear magnetic resonance imaging: reduction of acquisition times, and rebuilding times, images quality improvement. The tendency is to open the machines at low and middle field, on a market being at 10% of NMR I sales, with economical, scientifical and ergonomic reasons broadly developed by constructors Neutron resonance spectroscopy Gunsing, F. The present document has been written in order to obtain the diploma 'Habilitation a Diriger des Recherches'. Since this diploma is indispensable to supervise thesis students, I had the intention to write a document that can be useful for someone starting in the field of neutron resonance spectroscopy. Although the here described topics are already described elsewhere, and often in more detail, it seemed useful to have most of the relevant information in a single document. A general introduction places the topic of neutron-nucleus interaction in a nuclear physics context. The large variations of several orders of magnitude in neutron-induced reaction cross sections are explained in terms of nuclear level excitations. The random character of the resonances make nuclear model calculation predictions impossible. Then several fields in physics where neutron-induced reactions are important and to which I have contributed in some way or another, are mentioned in a first synthetic chapter. They concern topics like parity nonconservation in certain neutron resonances, stellar nucleosynthesis by neutron capture, and data for nuclear energy applications. The latter item is especially important for the transmutation of nuclear waste and for alternative fuel cycles. Nuclear data libraries are also briefly mentioned. A second chapter details the R-matrix theory. This formalism is the foundation of the description of the neutron-nucleus interaction and is present in all fields of neutron resonance spectroscopy. (author) Gunsing, F Magnetic resonance fingerprinting. Ma, Dan; Gulani, Vikas; Seiberlich, Nicole; Liu, Kecheng; Sunshine, Jeffrey L; Duerk, Jeffrey L; Griswold, Mark A Magnetic resonance is an exceptionally powerful and versatile measurement technique. The basic structure of a magnetic resonance experiment has remained largely unchanged for almost 50 years, being mainly restricted to the qualitative probing of only a limited set of the properties that can in principle be accessed by this technique. Here we introduce an approach to data acquisition, post-processing and visualization--which we term 'magnetic resonance fingerprinting' (MRF)--that permits the simultaneous non-invasive quantification of multiple important properties of a material or tissue. MRF thus provides an alternative way to quantitatively detect and analyse complex changes that can represent physical alterations of a substance or early indicators of disease. MRF can also be used to identify the presence of a specific target material or tissue, which will increase the sensitivity, specificity and speed of a magnetic resonance study, and potentially lead to new diagnostic testing methodologies. When paired with an appropriate pattern-recognition algorithm, MRF inherently suppresses measurement errors and can thus improve measurement accuracy. Neutron resonance absorption theory Reuss, P. After some recalls on the physics of neutron resonance absorption during their slowing down, this paper presents the main features of the theoretical developments performed by the french school of reactor physics: the effective reaction rate method so called Livolant-Jeanpierre theory, the generalizations carried out by the author, and the probability table method [fr Resonance charge exchange processes Duman, E.L.; Evseev, A.V.; Eletskij, A.V.; Radtsig, A.A.; Smirnov, B.M. The calculation results for the resonance charge exchange cross sections for positive and negative atomic and molecular ions are given. The calculations are performed on the basis of the asymptotic theory. The factors affecting the calculation accuracy are analysed. The calculation data for 28 systems are compared with the experiment Voos, Avery; Pelphrey, Kevin Functional magnetic resonance imaging (fMRI), with its excellent spatial resolution and ability to visualize networks of neuroanatomical structures involved in complex information processing, has become the dominant technique for the study of brain function and its development. The accessibility of in-vivo pediatric brain-imaging techniques… Magnetic resonance imaging (MRI) is a new and innovative technique that affords anatomic images in multiple planes and that may provide information about tissue characterization. The magnetic resonance images are obtained by placing the patient or the area of interest within a powerful, highly uniform, static magnetic field. Magnetized protons (hydrogen nuclei) within the patient align like small magnets in this field. Radiofrequency pulses are then used to create an oscillating magnetic field perpendicular to the main field. Magnetic resonance images differ from those produced by x-rays: the latter are associated with absorption of x-ray energy while magnetic resonance images are based on proton density and proton relaxation dynamics. Proton characteristics vary according to the tissue under examination and reflect its physical and chemical properties. To resolve issues regarding safety and efficacy, the Warren Grant Magnuson Clinical Center and the Office of Medical Applications of Research of the National Institutes of Health (NIH) convened a consensus conference about MRI Oct 26 through 28, 1987. At the NIH, the Consensus Development Conference brings together investigators in the biomedical sciences, clinical investigators, practicing physicians, and consumer and special interest groups to make a scientific assessment of technologies, including drugs, devices, and procedures, and to seek agreement on their safety and effectiveness Baryon resonances in nuclei Arenhoevel, H. The field of baryon resonances in nuclei is reviewed. Theoretical developments and experimental evidence as well are discussed. Special emphasis is laid on electromagnetic processes for the two nucleon system. Some aspects of real isobars in nuclei are touched upon. (orig.) [de Resonant filtered fiber amplifiers Alkeskjold, Thomas Tanggaard; Laurila, Marko; Olausson, Christina Bjarnal Thulin In this paper we present our recent result on utilizing resonant/bandgap fiber designs to achieve high performance ytterbium doped fiber amplifers for achieving diffraction limited beam quality in large mode area fibers, robust bending performance and gain shaping for long wavelength operation... Rueterjans, H. Contributions by various authors who are working in the field of NMR imaging present the current status and the perspectives of in-vivo nuclear magnetic resonance spectroscopy, explaining not only the scientific and medical aspects, but also technical and physical principles as well as questions concerning practical organisation and training, and points of main interest for further research activities. (orig./TRV) [de Isotopic effect giant resonances Buenerd, M.; Lebrun, D.; Martin, P.; Perrin, G.; Saintignon, P. de; Chauvin, J.; Duhamel, G. The systematics of the excitation energy of the giant dipole, monopole, and quadrupole resonances are shown to exhibit an isotopic effect. For a given element, the excitation energy of the transition decreases faster with the increasing neutron number than the empirical laws fitting the overall data. This effect is discussed in terms of the available models Magnetostatic wave tunable resonators Castera, J.-P.; Hartemann, P. Theoretical principles and techniques for the implementation of magnetostatic surface wave and volume wave resonators in high frequency oscillators are discussed. Magnetostatic waves are magnetic waves that propagate in materials exposed to a polarized magnetic field. The propagation speed ranges from 3-300 km/sec for wavelengths between 1 micron and 10 mm, in the presence of lags from 10-1000 nsec/ cm. Tunable resonators in the 1-20 GHz frequency range have been manufactured with YIG using liquid phase epitaxy for deposition on gadolinium and gallium substrates. Distributed-mirror Fabry-Perot cavity resonators are described and performance tests results are reported, including losses of 8 dB, a quality coefficient under voltage of 450, and frequency rejection outside of resonance better than 10 dB. However, saturation occurs at low power levels at frequencies lower than 4.2 GHz, a feature overcome with forward volume magnetostatic wave generators, which have a quality factor of 500, an insertion loss of 22 dB, and rejection around 15 dB. Proton resonance spectroscopy Shriner, J.F. Jr. This report discusses the following topics: Complete Level Scheme for 30 P; A Search for Resonances Suitable for Tests of Detailed-Balance Violation; The Fourier Transform as a Tool for Detecting Chaos; Entrance Channel Correlations in p + 27 Al; The Parity Dependence of Level Densities in 49 V; and A Computer Program for the Calculation of Angular Momentum Coupling Screening Resonances In Plasmas Winkler, P. When it was suggested that a new recombination mechanism (Resonant Radiative Recombination (RRR)) which, based on very general physical arguments, should happen in dense plasmas and promises to provide useful information for the local temperature and density diagnostics of plasmas, they assumed the existence of screening resonances. For model potentials the existence of screening resonances has been demonstrated beyond reasonable doubt in a number of calculations. The key question, how well those potentials describe the dominant effects of a real plasma remains open. The relation of theoretical predictions to experimentally measurable effects is an important issue at the present stage of their research. In particular, RRR is expected to account for enhanced recombination rates of low energetic electrons with their ions, since the first stage is the resonant capture of a slow electron by an atom or ion. The mechanism that traps an electron is a combination of complicated many-body interactions of the ions and electrons. For clarity they start here, however, with a discussion in terms of local potential traps the shapes of which are determined predominantly and in an average way by two factors: the degree of screening present at the ionic site and the degree of short-range order in the immediate neighborhood of this ion Electron Paramagnetic Resonance Imaging Twentieth century bore witness to remarkable scientists whohave advanced our understanding of the brain. Among them,EPR (Electron Paramagnetic Resonance) imaging is particularlyuseful in monitoring hypoxic zones in tumors which arehighly resistant to radiation and chemotherapeutic treatment.This first part of the ... This report summarises the aspects of nuclear magnetic resonance imaging (NMRI) considered by the National Health Technology Advisory Panel and makes recommendations on its introduction in Australia with particular regard to the need for thorough evaluation of its cost effectiveness. Topics covered are: principles of the technique, equipment required, installation, costs, reliability, performance parameters, clinical indications, training and staff requirements, and safety considerations Isoscalar giant resonances Youngblood, D. H. [Texas A and M Univ., College Station (USA). Cyclotron Inst.; Ikegami, H.; Muraoka, M. [eds. The current status of the knowledges of giant quadrupole resonance (GQR), low energy octupole resonance (LEOR), and giant monopole resonance (GMR), is described. In the lowest order of multipole resonance, both isoscalar and isovector modes can occur. The characteristics of the GQR in light nuclei are apparent in the experimental result for Mg-24. All of the isoscalar E2 strength are known in Mg-24. The Goldhaber-Teller model is preferred over the Steinwedel-Jensen model for the giant dipole resonance (GDR) transition density. A few interesting and puzzling features have been seen in Pb-208. There is some conflict between inelastic alpha and electron scatterings. About LEOR, the RPA calculation of Liu and Brown was compared to the data for 3/sup -/ strength in Ca-40, Zr-90 and Pb-208. The calculation was employed the residual interaction of the Skyrme type. The agreement in Zr-90 was excellent. The effect of quadrupole deformation on the LEOR in Sm isotopes was large. The inelastic alpha scattering data on Al-27, Ca-40, Ti-48, Ni-58, Zn-64 and 66, Zr-90, Sn-116, 118, 120 and 124, Sm-144, 148 and 154, and Pb-208 were utilized in order to identify the GMR, and the GMR parameters were obtained. The GMR exhausting a large fraction of the sum rule was apparent in the nuclei with mass larger than 90. The splitting of the GDR and the broadening of the GQR in permanently deformed nuclei were established. The splitting of GMR was seen in Sm-154. The studies with heavy ions are also described. Magnetic Resonance Imaging (MRI) -- Head Full Text Available ... for Brain Tumors Radiation Therapy for Head and Neck Cancer Others : American Stroke Association National Stroke Association ... MRA) Magnetic Resonance, Functional (fMRI) - Brain Head and Neck Cancer Treatment Brain Tumor Treatment Magnetic Resonance Imaging ( ... Magnetic Resonance Imaging (MRI) Safety ... News Physician Resources Professions Site Index A-Z Magnetic Resonance Imaging (MRI) Safety What is MRI and how ... What is MRI and how does it work? Magnetic resonance imaging, or MRI, is a way of obtaining ... Nanoelectromechanical resonator for logic operations Kazmi, Syed N. R.; Hafiz, Md A. Al; Chappanda, Karumbaiah N.; Ilyas, Saad; Holguin, Jorge; Da Costa, Pedro M. F. J.; Younis, Mohammad I. We report an electro-thermally tunable in-plane doubly-clamped nanoelectromechanical resonator capable of dynamically performing NOR, NOT, XNOR, XOR, and AND logic operations. Toward this, a silicon based resonator is fabricated using standard e Magnetic Resonance Imaging of Stroke Bouts, Mark. J. R. J.; Wu, O.; Dijkhuizen, R. M. Magnetic resonance imaging (MRI) provides a powerful (neuro)imaging modality for the diagnosis and outcome prediction after (acute) stroke. Since MRI allows noninvasive, longitudinal, and three-dimensional assessment of vessel occlusion (with magnetic resonance angiography (MRA)), tissue injury Probabilistic interpretation of resonant states The present paper reviews the basic definition of the resonant state in quantum ... We show that particles leak from the central region in the resonant state. The ..... The basic idea is as follows (figure 4): Consider a resonant eigenstate. Φn(x ... Children's (Pediatric) Magnetic Resonance Imaging ... Physician Resources Professions Site Index A-Z Children's (Pediatric) Magnetic Resonance Imaging Children's magnetic resonance imaging (MRI) ... limitations of Children's (Pediatric) MRI? What is Children's (Pediatric) MRI? Magnetic resonance imaging (MRI) is a noninvasive ... Full Text Available ... Physician Resources Professions Site Index A-Z Children's (Pediatric) Magnetic Resonance Imaging Children's magnetic resonance imaging (MRI) ... limitations of Children's (Pediatric) MRI? What is Children's (Pediatric) MRI? Magnetic resonance imaging (MRI) is a noninvasive ... ... News Physician Resources Professions Site Index A-Z Magnetic Resonance Imaging (MRI) - Head Magnetic resonance imaging (MRI) of the head uses a powerful ... the Head? What is MRI of the Head? Magnetic resonance imaging (MRI) is a noninvasive medical test that ... Introduction lecture to magnetic resonance Conard, J. This lecture deals with all that is common either to electron paramagnetic resonance (E.P.R.) or to nuclear magnetic resonance (N.M.R.). It will present, in an as elementary form as possible, the main concepts used in magnetic resonance emphasizing some aspects, specific for interface science. (orig./BHO) Full Text Available ... News Physician Resources Professions Site Index A-Z Children's (Pediatric) Magnetic Resonance Imaging Children's magnetic resonance imaging ( ... the limitations of Children's (Pediatric) MRI? What is Children's (Pediatric) MRI? Magnetic resonance imaging (MRI) is a ... Full Text Available ... News Physician Resources Professions Site Index A-Z Magnetic Resonance Imaging (MRI) - Head Magnetic resonance imaging (MRI) of the head uses a powerful ... the Head? What is MRI of the Head? Magnetic resonance imaging (MRI) is a noninvasive medical test that ... Resonant SIMP dark matter Soo-Min Choi Full Text Available We consider a resonant SIMP dark matter in models with two singlet complex scalar fields charged under a local dark U(1D. After the U(1D is broken down to a Z5 discrete subgroup, the lighter scalar field becomes a SIMP dark matter which has the enhanced 3→2 annihilation cross section near the resonance of the heavier scalar field. Bounds on the SIMP self-scattering cross section and the relic density can be fulfilled at the same time for perturbative couplings of SIMP. A small gauge kinetic mixing between the SM hypercharge and dark gauge bosons can be used to make SIMP dark matter in kinetic equilibrium with the SM during freeze-out. Nuclear magnetic resonance apparatus Lambert, R. In order to include the effect of a magnetic object in a subject under investigation, Nuclear Magnetic Resonance (NMR) apparatus is operable at more than one radio frequency (RF) frequency. The apparatus allows normal practice as far as obtaining an NMR response or image from a given nuclear species is concerned, but, in addition, interrogates the nuclear spin system at a frequency which is different from the resonance frequency normally used for the given nuclear species, as determined from the applied magnetic field. The magnetic field close to a magnetised or magnetisable object is modified and the given nuclear species gives a response at the different frequency. Thus detection of a signal at the frequency indicates the presence of the chosen nuclei close to the magnetised or magnetisable object. Applications include validation of an object detection or automatic shape inspection system in the presence of magnetic impurities, and the detection of magnetic particles which affect measurement of liquid flow in a pipe. (author) A New Resonance Tube The measurement of the speed of sound in air with the resonance tube is a popular experiment that often yields accurate results. One approach is to hold a vibrating tuning fork over an air column that is partially immersed in water. The column is raised and lowered in the water until the generated standing wave produces resonance: this occurs at the point where sound is perceived to have maximum loudness, or at the point where the amplitude of the standing wave has maximum value, namely an antinode. An antinode coincides with the position of the tuning fork, beyond the end of the air column, which consequently introduces an end correction. One way to minimize this end correction is to measure the distance between consecutive antinodes. Resonance of curved nanowires Calabri, L [CNR-INFM-National Research Center on nanoStructures and bioSystems at Surfaces (S3), Via Campi 213/a, 41100 Modena (Italy); Pugno, N [Department of Structural Engineering and Geotechnics, Politecnico di Torino, Turin (Italy); Ding, W [Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208-3111 (United States); Ruoff, R S [Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208-3111 (United States) The effects of non-ideal experimental configuration on the mechanical resonance of boron (B) nanowires (NWs) were studied to obtain the corrected value for the Young's modulus. The following effects have been theoretically considered: (i) the presence of intrinsic curvature (ii) non-ideal clamps (iii) spurious masses (iv) coating layer, and (v) large displacements. An energy-based analytical analysis was developed to treat such effects and their interactions. Here, we focus on treating the effect of the intrinsic curvature on the mechanical resonance. The analytical approach has been confirmed by numerical FEM analysis. A parallax method was used to obtain the three-dimensional geometry of the NW. Sigal, R. This book is an introduction to magnetic resonance imaging (MRI). The basic principles for the interpretation of MR images are developed. The book is divided into five chapters: introduction, tissue, parameters, acquisition parameters, contribution to diagnosis, and practical management of an MR examination. Eight exercises allow the reader to test the knowledge he has acquired. Signal localization and MR artefacts are reviewed in an appendix Ultraminiature resonator accelerometer Koehler, D.R.; Kravitz, S.H.; Vianco, P.T. A new family of microminiature sensors and clocks is being developed with widespread application potential for missile and weapons applications, as biomedical sensors, as vehicle status monitors, and as high-volume animal identification and health sensors. To satisfy fundamental technology development needs, a micromachined clock and an accelerometer have initially been undertaken as development projects. A thickness-mode quartz resonator housed in a micromachined silicon package is used as the frequency-modulated basic component of the sensor family. Resonator design philosophy follows trapped energy principles and temperature compensation methodology through crystal orientation control, with operation in the 20--100 MHz range, corresponding to quartz wafer thicknesses in the 75--15 micron range. High-volume batch-processing manufacturing is utilized, with package and resonator assembly at the wafer level. Chemical etching of quartz, as well as micromachining of silicon, achieves the surface and volume mechanical features necessary to fashion the resonating element and the mating package. Integration of the associated oscillator and signal analysis circuitry into the silicon package is inherent to the realization of a size reduction requirement. A low temperature In and In/Sn bonding technology allows assembly of the dissimilar quartz and silicon materials, an otherwise challenging task. Unique design features include robust vibration and shock performance, capacitance sensing with micromachined diaphragms, circuit integration, capacitance-to-frequency transduction, and extremely small dimensioning. Accelerometer sensitivities were measured in the 1--3 ppm/g range for the milligram proof-mass structures employed in the prototypes evaluated to date. Magnetic resonance imaging (MRI Takavar A Full Text Available Basic physical principles of nuclear magnetic resonance imaging (N.M.R.I, a nonionizing medical imaging technique, are described. Principles of NMRI with other conventional imaging methods, ie, isotope scanning, ultrasonography and radiography have been compared. T1 and T2 and spin density (S.D. factors and different image construction techniques based on their different combinations is discussed and at the end physical properties of some N.M.R images is mentioned. Basic physical principles of nuclear magnetic resonance imaging (N.M.R.I), a nonionizing medical imaging technique, are described. Principles of NMRI with other conventional imaging methods, ie, isotope scanning, ultrasonography and radiography have been compared. T1 and T2 and spin density (S.D.) factors and different image construction techniques based on their different combinations is discussed and at the end physical properties of some N.M.R images is mentioned. Resonant state expansions Lind, P. The completeness properties of the discrete set of bound state, virtual states and resonances characterizing the system of a single nonrelativistic particle moving in a central cutoff potential is investigated. From a completeness relation in terms of these discrete states and complex scattering states one can derive several Resonant State Expansions (RSE). It is interesting to obtain purely discrete expansion which, if valid, would significantly simplify the treatment of the continuum. Such expansions can be derived using Mittag-Leffler (ML) theory for a cutoff potential and it would be nice to see if one can obtain the same expansions starting from an eigenfunction theory that is not restricted to a finite sphere. The RSE of Greens functions is especially important, e.g. in the continuum RPA (CRPA) method of treating giant resonances in nuclear physics. The convergence of RSE is studied in simple cases using square well wavefunctions in order to achieve high numerical accuracy. Several expansions can be derived from each other by using the theory of analytic functions and one can the see how to obtain a natural discretization of the continuum. Since the resonance wavefunctions are oscillating with an exponentially increasing amplitude, and therefore have to be interpreted through some regularization procedure, every statement made about quantities involving such states is checked by numerical calculations.Realistic nuclear wavefunctions, generated by a Wood-Saxon potential, are used to test also the usefulness of RSE in a realistic nuclear calculation. There are some fundamental differences between different symmetries of the integral contour that defines the continuum in RSE. One kind of symmetry is necessary to have an expansion of the unity operator that is idempotent. Another symmetry must be used if we want purely discrete expansions. These are found to be of the same form as given by ML. (29 refs.) Resonant Tunneling Spin Pump Ting, David Z. The resonant tunneling spin pump is a proposed semiconductor device that would generate spin-polarized electron currents. The resonant tunneling spin pump would be a purely electrical device in the sense that it would not contain any magnetic material and would not rely on an applied magnetic field. Also, unlike prior sources of spin-polarized electron currents, the proposed device would not depend on a source of circularly polarized light. The proposed semiconductor electron-spin filters would exploit the Rashba effect, which can induce energy splitting in what would otherwise be degenerate quantum states, caused by a spin-orbit interaction in conjunction with a structural-inversion asymmetry in the presence of interfacial electric fields in a semiconductor heterostructure. The magnitude of the energy split is proportional to the electron wave number. Theoretical studies have suggested the possibility of devices in which electron energy states would be split by the Rashba effect and spin-polarized currents would be extracted by resonant quantum-mechanical tunneling. Optical resonator theory Yoo, Jaeg Won; Cho, Sunh Oh; Jeong, Young Uk; Lee, Byung Cheol; Lee, Jong Min In this report we present a theoretical study of bare optical resonators having in mind to extend it to active resonators. To compute diffractional losses, phase shifts, intensity distributions and phases of radiation fields on mirrors, we coded a package of numerical procedures on bases of a pair of integral equations. Two numerical schemes, a matrix formalism and an iterative method, are programmed for finding numeric solutions to the pair of integral equations. The iterative method had been tried by Fox and Li, but it was not applicable to cases for high Fresnel numbers since the numerical errors involved propagate and accumulate uncontrollably. In this report, we implemented the matrix method to extend the computational limit further. A great deal of case studies are carried out with various configurations of stable and unstable resonators. Our results presented in this report show not only a good agreement with the results previously obtained by Fox and Li, but also a legitimacy of our numerical procedures in high Fresnel numbers. Injection-controlled laser resonator Chang, J.J. A new injection-controlled laser resonator incorporates self-filtering and self-imaging characteristics with an efficient injection scheme. A low-divergence laser signal is injected into the resonator, which enables the injection signal to be converted to the desired resonator modes before the main laser pulse starts. This injection technique and resonator design enable the laser cavity to improve the quality of the injection signal through self-filtering before the main laser pulse starts. The self-imaging property of the present resonator reduces the cavity induced diffraction effects and, in turn, improves the laser beam quality. 5 figs. Persistence, resistance, resonance Tsadka, Maayan Sound cannot travel in a vacuum, physically or socially. The ways in which sound operates are a result of acoustic properties, and the ways by which it is considered to be music are a result of social constructions. Therefore, music is always political, regardless of its content: the way it is performed and composed; the choice of instrumentation, notation, tuning; the medium of its distribution; its inherent hierarchy and power dynamics, and more. My compositional praxis makes me less interested in defining a relationship between music and politics than I am in erasing---or at least blurring---the borders between them. In this paper I discuss the aesthetics of resonance and echo in their metaphorical, physical, social, and musical manifestations. Also discussed is a political aesthetic of resonance, manifested through protest chants. I transcribe and analyze common protest chants from around the world, categorizing and unifying them as universal crowd-mobilizing rhythms. These ideas are explored musically in three pieces. Sumud: Rhetoric of Resistance in Three Movements, for two pianos and two percussion players, is a musical interpretation of the political/social concept of sumud, an Arabic word that literally means "steadfastness" and represents Palestinian non-violent resistance. The piece is based on common protest rhythms and uses the acoustic properties inherent to the instruments. The second piece, Three Piano Studies, extends some of the musical ideas and techniques used in Sumud, and explores the acoustic properties and resonance of the piano. The final set of pieces is part of my Critical Mess Music Project. These are site-specific musical works that attempt to blur the boundaries between audience, performers and composer, in part by including people without traditional musical training in the process of music making. These pieces use the natural structure and resonance of an environment, in this case, locations on the UCSC campus, and offer an active Parametric Resonance in Dynamical Systems Nijmeijer, Henk Parametric Resonance in Dynamical Systems discusses the phenomenon of parametric resonance and its occurrence in mechanical systems,vehicles, motorcycles, aircraft and marine craft, and micro-electro-mechanical systems. The contributors provide an introduction to the root causes of this phenomenon and its mathematical equivalent, the Mathieu-Hill equation. Also included is a discussion of how parametric resonance occurs on ships and offshore systems and its frequency in mechanical and electrical systems. This book also: Presents the theory and principles behind parametric resonance Provides a unique collection of the different fields where parametric resonance appears including ships and offshore structures, automotive vehicles and mechanical systems Discusses ways to combat, cope with and prevent parametric resonance including passive design measures and active control methods Parametric Resonance in Dynamical Systems is ideal for researchers and mechanical engineers working in application fields such as MEM... Resonance frequency analysis Rajiv K Gupta Full Text Available Initial stability at the placement and development of osseointegration are two major issues for implant survival. Implant stability is a mechanical phenomenon which is related to the local bone quality and quantity, type of implant, and placement technique used. The application of a simple, clinically applicable, non-invasive test to assess implant stability and osseointegration is considered highly desirable. Resonance frequency analysis (RFA is one of such techniques which is most frequently used now days. The aim of this paper was to review and analyze critically the current available literature in the field of RFA, and to also discuss based on scientific evidence, the prognostic value of RFA to detect implants at risk of failure. A search was made using the PubMed database to find all the literature published on "Resonance frequency analysis for implant stability" till date. Articles discussed in vivo or in vitro studies comparing RFA with other methods of implant stability measurement and articles discussing its reliability were thoroughly reviewed and discussed. A limited number of clinical reports were found. Various studies have demonstrated the feasibility and predictability of the technique. However, most of these articles are based on retrospective data or uncontrolled cases. Randomized, prospective, parallel-armed longitudinal human trials are based on short-term results and long-term follow up are still scarce in this field. Nonetheless, from available literature, it may be concluded that RFA technique evaluates implant stability as a function of stiffness of the implant bone interface and is influenced by factors such as bone type, exposed implant height above the alveolar crest. Resonance frequency analysis could serve as a non-invasive diagnostic tool for detecting the implant stability of dental implants during the healing stages and in subsequent routine follow up care after treatment. Future studies, preferably randomized Magnetic resonance instrumentation Bell, R.A. Magnetic resonance (MR), while opening new vistas to diagnostic medicine, utilizes equipment that is unfamiliar to most clinicians. Beyond learning to cope with new terms, such as spin-echo, T1, T2, and spin density, health care professionals are faced with the inclusion of magnetic and radiofrequency effects in their facilities produced by a complex array of devices. It is the purpose of this chapter to outline the components of an MR imaging system, to discuss their functions, and to note the variations in equipment commercially available General resonance mediation McGarrie, Moritz We extend the framework of general gauge mediation to cases where the mediating fields have a nontrivial spectral function, as might arise from strong dynamics. We demonstrate through examples that this setup describes a broad class of possible models of gauge mediated supersymmetry breaking. A main emphasis is to give general formulas for cross sections for σ(visible → hidden) in these resonance models. We will also give formulas for soft masses, A-terms and demonstrate the framework with a holographic setup. Advanced Nuclear Magnetic Resonance Alonso, Diego A. Transparencias en inglés de la asignatura "Resonancia Magnética Nuclear Avanzada" (Advanced Nuclear Magnetic Resonance) (36643) que se imparte en el Máster de Química Médica como asignatura optativa de 3 créditos ECTS. En esta asignatura se completa el estudio iniciado en la asignatura de quinto curso de la licenciatura en Química "Determinación estructural" (7448) y en la del Grado de Química de tercer curso "Determinación estructural de los compuestos orgánicos" (26030) en lo referente a té... Cranial magnetic resonance imaging Elster, A.D. Cranial Magnetic Resonance Imaging is comprehensive, well structured, and well written. The material is current and well referenced. The illustrations are good and complement the text well. The overall quality of publication is above average. The greatest attribute of the book is its readability. The author demonstrates ample skill in making complex subjects, such as MR physics and imaging of cerebral hemorrhage, easy to understand. The book closes with a detailed atlas on the anatomic appearance of the brain on MR images in the axial, coronal, and sagittal planes Dental magnetic resonance imaging Hilgenfeld, Tim; Bendszus, Martin; Haehnel, Stefan Growing distribution and utilization of digital volume tomography (DVT) extend the spectrum of clinical dental imaging. Additional diagnostic value, however, comes along with an increasing amount of radiation. In contrast, magnetic resonance imaging is a radiation free imaging technique. Furthermore, it offers a high soft tissue contrast. Morphological and numerical dental anomalies, differentiation of periapical lesions and exclusion of complications of dental diseases are field of applications for dental MRI. In addition, detection of caries and periodontal lesions and injury of inferior alveolar nerve are promising application areas in the future. We extend the framework of general gauge mediation to cases where the mediating fields have a nontrivial spectral function, as might arise from strong dynamics. We demonstrate through examples that this setup describes a broad class of possible models of gauge mediated supersymmetry breaking. A main emphasis is to give general formulas for cross sections for {sigma}(visible {yields} hidden) in these resonance models. We will also give formulas for soft masses, A-terms and demonstrate the framework with a holographic setup. Nuclear magnetic resonance scattering A nuclear magnetic resonance apparatus is described including a magnet system which is capable of providing a steady magnetic field along an axis, and is constructed so as to define a plurality of regions along the axis in each of which the field is substantially homogeneous so that in each region an imaging operation may be separately carried out. Iron shields increase the field homogeneity. In use, each patient lies on a wheeled trolley which is provided with magnetic field gradient coils and an RF coil system, some of the coils being movable to facilitate positioning of the patient, and there are terminals for connection to a common computing and control facility. (author) Resonant MEMS tunable VCSEL Ansbæk, Thor; Chung, Il-Sug; Semenova, Elizaveta We demonstrate how resonant excitation of a microelectro-mechanical system can be used to increase the tuning range of a vertical-cavity surface-emitting laser two-fold by enabling both blue- and red-shifting of the wavelength. In this way a short-cavity design enabling wide tuning range can...... be realized. A high-index-contrast subwavelength grating verticalcavity surface-emitting laser with a monolithically integrated anti-reflection coating is presented. By incorporating an antireflection coating into the air cavity, higher tuning efficiency can be achieved at low threshold current. The first... Resonance test system Musial, Walter [Boulder, CO; White, Darris [Superior, CO An apparatus (10) for applying at least one load to a specimen (12) according to one embodiment of the invention may comprise a mass (18). An actuator (20) mounted to the specimen (12) and operatively associated with the mass (18) moves the mass (18) along a linear displacement path (22) that is perpendicular to a longitudinal axis of the specimen (12). A control system (26) operatively associated with the actuator (20) operates the actuator (20) to reciprocate the mass (18) along the linear displacement path (22) at a reciprocating frequency, the reciprocating frequency being about equal to a resonance frequency of the specimen (12) in a test configuration. Electron spin resonance Wasson, J.R.; Salinas, J.E. Published literature concerning electron spin resonance (ESR) from July 1977 to July 1979 is reviewed. The 108 literature sources cited were chosen from literally thousands and are intended to serve as a guide to the current literature and to provide an eclectic selection of publications cited for their contributions to the advance and/or applications of ESR spectroscopy. 40 of the sources are reviews, and a table is included to indicate the topic(s) mainly covered in each review. Other divisions of the material reviewed are apparatus and spectral analysis, analytical applications, and selected paramagnetic materials Apodized coupled resonator waveguides. Capmany, J; Muñoz, P; Domenech, J D; Muriel, M A In this paper we propose analyse the apodisation or windowing of the coupling coefficients in the unit cells of coupled resonator waveguide devices (CROWs) as a means to reduce the level of secondary sidelobes in the bandpass characteristic of their transfer functions. This technique is regularly employed in the design of digital filters and has been applied as well in the design of other photonic devices such as corrugated waveguide filters and fiber Bragg gratings. The apodisation of both Type-I and Type-II structures is discussed for several windowing functions. Nanotube resonator devices Jensen, Kenneth J; Zettl, Alexander K; Weldon, Jeffrey A A fully-functional radio receiver fabricated from a single nanotube is being disclosed. Simultaneously, a single nanotube can perform the functions of all major components of a radio: antenna, tunable band-pass filter, amplifier, and demodulator. A DC voltage source, as supplied by a battery, can power the radio. Using carrier waves in the commercially relevant 40-400 MHz range and both frequency and amplitude modulation techniques, successful music and voice reception has been demonstrated. Also disclosed are a radio transmitter and a mass sensor using a nanotube resonator device. Proton capture resonance studies Mitchell, G.E. [North Carolina State University, Raleigh, North Carolina (United States) 27695]\|[Triangle Universities Nuclear Laboratory, Durham, North Carolina (United States) 27708; Bilpuch, E.G. [Duke University, Durham, North Carolina (United States) 27708]\|[Triangle Universities Nuclear Laboratory, Durham, North Carolina (United States) 27708; Bybee, C.R. [North Carolina State University, Raleigh, North Carolina (United States) 27695]\|[Triangle Universities Nuclear Laboratory, Durham, North Carolina (United States) 27708; Cox, J.M.; Fittje, L.M. [Tennessee Technological University, Cookeville, Tennessee (United States) 38505]\|[Triangle Universities Nuclear Laboratory, Durham, North Carolina (United States) 27708; Labonte, M.A.; Moore, E.F.; Shriner, J.D. [North Carolina State University, Raleigh, North Carolina (United States) 27695]\|[Triangle Universities Nuclear Laboratory, Durham, North Carolina (United States) 27708; Shriner, J.F. Jr. [Tennessee Technological University, Cookeville, Tennessee (United States) 38505]\|[Triangle Universities Nuclear Laboratory, Durham, North Carolina (United States) 27708; Vavrina, G.A. [North Carolina State University, Raleigh, North Carolina (United States) 27695]\|[Triangle Universities Nuclear Laboratory, Durham, North Carolina (United States) 27708; Wallace, P.M. [Duke University, Durham, North Carolina (United States) 27708]\|[Triangle Universities Nuclear Laboratory, Durham, North Carolina (United States) 27708 The fluctuation properties of quantum systems now are used as a signature of quantum chaos. The analyses require data of extremely high quality. The {sup 29}Si(p,{gamma}) reaction is being used to establish a complete level scheme of {sup 30}P to study chaos and isospin breaking in this nuclide. Determination of the angular momentum J, the parity {pi}, and the isospin T from resonance capture data is considered. Special emphasis is placed on the capture angular distributions and on a geometric description of these angular distributions. {copyright} {ital 1997 American Institute of Physics.} Resonantly scattering crystals and surfaces Gunn, J.M.F.; Mahon, P.J. We examine coherence effects from forming a crystal of resonant scatterers by generalising the Fano model for autoionising resonances in electron scattering from atoms to a lattice of such scatterers. (We have in mind the case of neutron scattering from nuclei.) We solve this problem to yield two branches to the dispersion relation for the neutron in general and three when the resonance coincides with a Brillouin Zone boundary. The 'width' of the resonance is enhanced over the isolated nucleus, the best candidate for observation being the 2eV 185 Re resonance near the Bragg condition. We use these results to calculate the reflection coefficient from a surface, revealing total external reflection near resonance. We discuss experimental feasibility in both the neutron and electron cases. (author) Rabenstein, D.L.; Guo, W. Nuclear magnetic resonance (NMR) spectroscopy is one of the most widely used instrumental methods, with applications ranging from the characterization of pure compounds by high-resolution NMR to the diagnosis of disease by magnetic resonance imaging (MRI). To give some idea of the wide-spread use of NMR, a computer search for the period 1985-1987 turned up over 500 books and review articles and over 7000 literature citations, not including papers in which NMR was used together with other spectroscopic methods for the routine identification of organic compounds. Consequently, they have by necessity been somewhat selective in the topics they have chosen to cover and in the articles they have cited. In this review, which covers the published literature for the approximate period Sept 1985-Aug 1987, they have focused on new developments and applications of interest to the chemist. First they review recent developments in instrumentation and techniques. Although there have not been any major break-throughs in NMR instrumentation during the past two years, significant refinements have been reported which optimize instrumentation for the demanding multiple pulse experiments in routine use today. Next they review new developments in methods for processing NMR data, followed by reviews of one-dimensional and two-dimensional NMR experiments Behavioral Stochastic Resonance Freund, Jan A.; Schimansky-Geier, Lutz; Beisner, Beatrix; Neiman, Alexander; Russell, David F.; Yakusheva, Tatyana; Moss, Frank Zooplankton emit weak electric fields into the surrounding water that originate from their own muscular activities associated with swimming and feeding. Juvenile paddlefish prey upon single zooplankton by detecting and tracking these weak electric signatures. The passive electric sense in the fish is provided by an elaborate array of electroreceptors, Ampullae Lorenzini, spread over the surface of an elongated rostrum. We have previously shown that the fish use stochastic resonance to enhance prey capture near the detection threshold of their sensory system. But stochastic resonance requires an external source of electrical noise in order to function. The required noise can be provided by a swarm of plankton, for example Daphnia. Thus juvenile paddlefish can detect and attack single Daphnia as outliers in the vicinity of the swarm by making use of noise from the swarm itself. From the power spectral density of the noise plus the weak signal from a single Daphnia we calculate the signal-to-noise ratio and the Fisher information at the surface of the paddlefish's rostrum. The results predict a specific attack pattern for the paddlefish that appears to be experimentally testable. Advances in Magnetic Resonance, Volume 11, presents a variety of contributions to the theory and practice of magnetic resonance. The book contains three chapters and begins with a discussion of the principles and applications of dynamic nuclear polarization, with emphasis on molecular motions and collisions, intermolecular couplings, and chemical interactions. Subsequent chapters focus on the assessment of a proposed broadband decoupling method and studies of time-domain (or Fourier transform) multiple-quantum nuclear magnetic resonance. Slowing down with resonance absorption Moura Neto, C. de; Nair, R.P.K. The presence of heavy nuclei in nuclear reactors, in significant concentrations, facilitates the appearance of absorption resonances. For the moderation in the presence of absorbers an exact solution of the integral equations is possible by numerical methods. Approximated solutions for separated resonances in function of the practical width, (NR and NRIM approximations) are discussed in this paper. The method is generalized, presenting the solution by an intermediate approximation, in the definition of the resonance integral. (Author) [pt Q-Boosted Optomechanical Resonators type a knob for optical Qo, where the inability to smooth etched nitride sidewall surfaces relegates OMO's using it to Qo's on the order of...6: Operation of an RP-OMO. As the ring resonator coupled to tapered fiber in (a) displaces by ∂r, the optical path length change produces the shift...frequency 0, B input pump laser field, tot the total optical resonator damping, ext the coupling between optical resonator and the tapered fiber Spectra of resonance surface photoionization Antsiferov, V.V.; Smirnov, G.I.; Telegin, G.G. [Budker Nuclear Physics Institute, Novosibirsk (Russian Federation) The theory of nonactivated electron transfer between atoms interacting reasonantly with coherent radiation and a metal surface is developed. The spectral resonances in photoabsorption and surface photoionization are found to be related to nonlinear interference effects in the interaction between discrete atomic levels and the continuum formed by the quasi-continuous electron spectrum of a normal metal. The asymmetry in the resonance surface photoionization spectrum is shown to have a shape typical of the Fano autoionization resonances. 18 refs. Resonance capture and Saturn's rings Patterson, C.W. We have assigned the resonances apparently responsible for the stabilization of the Saturn's shepherd satellites and for the substructure seen in the F-ring and the ringlets in the C-ring. We show that Saturn's narrow ringlets have a substructure determined by three-body resonances with Saturn's ringmoons and the sun. We believe such resonances have important implications to satellite formation. 17 refs., 1 fig., 1 tab Efficient primary and parametric resonance excitation of bistable resonators Ramini, Abdallah We experimentally demonstrate an efficient approach to excite primary and parametric (up to the 4th) resonance of Microelectromechanical system MEMS arch resonators with large vibrational amplitudes. A single crystal silicon in-plane arch microbeam is fabricated such that it can be excited axially from one of its ends by a parallel-plate electrode. Its micro/nano scale vibrations are transduced using a high speed camera. Through the parallel-plate electrode, a time varying electrostatic force is applied, which is converted into a time varying axial force that modulates dynamically the stiffness of the arch resonator. Due to the initial curvature of the structure, not only parametric excitation is induced, but also primary resonance. Experimental investigation is conducted comparing the response of the arch near primary resonance using the axial excitation to that of a classical parallel-plate actuation where the arch itself forms an electrode. The results show that the axial excitation can be more efficient and requires less power for primary resonance excitation. Moreover, unlike the classical method where the structure is vulnerable to the dynamic pull-in instability, the axial excitation technique can provide large amplitude motion while protecting the structure from pull-in. In addition to primary resonance, parametrical resonances are demonstrated at twice, one-half, and two-thirds the primary resonance frequency. The ability to actuate primary and/or parametric resonances can serve various applications, such as for resonator based logic and memory devices. (C) 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license Resonance phenomenon in classical cepheids Takeuti, Mine; Aikawa, Toshiki To investigate resonance phenomenon in classical cepheids, the non-linear radial oscillation of stars is studied based on the assumption that the non-adiabatic perturbation is expressed in terms of van der Pol's type damping. Two- and three-wave resonance in this system is applied to classical cepheids to describe their bump and double-mode behavior. The phase of bump and the depression of amplitude are explained for bump cepheids. The double-periodicity is shown by the enhancement of the third overtone in three-wave resonance. Non-linear effect on resonant period is also discussed briefly. (author) Transit time for resonant tunneling Garcia Calderon, G.; Rubio, A. This work considers properties of the partial widths in one dimensional elastic resonant tunneling in order to propose a transit-time τ tr = (h/2π)/Γ n T res ) where Γ n is the elastic width and T res the transmission coefficient at resonance energy. This time is interpreted as an average over the resonance energy width. It is shown that the tunneling current density integrated across a sharp resonance is inversely proportional to τ tr . This transit time may be much larger than the values predicted by other definitions. (author). 20 refs Advances in magnetic resonance 6 Advances in Magnetic Resonance, Volume 6 focuses on the theoretical and practical aspects of applying magnetic resonance methods to various problems in physical chemistry, emphasizing the different aspects of the exegesis of these problems. This book discusses the gas phase magnetic resonance of electronically excited molecules; techniques for observing excited electronic states; NMR studies in liquids at high pressure; and effect of pressure on self-diffusion in liquids. The nuclear magnetic resonance investigations of organic free radicals; measurement of proton coupling constants by NMR; an Orbital resonances around black holes. Brink, Jeandrew; Geyer, Marisa; Hinderer, Tanja We compute the length and time scales associated with resonant orbits around Kerr black holes for all orbital and spin parameters. Resonance-induced effects are potentially observable when the Event Horizon Telescope resolves the inner structure of Sgr A, when space-based gravitational wave detectors record phase shifts in the waveform during the resonant passage of a compact object spiraling into the black hole, or in the frequencies of quasiperiodic oscillations for accreting black holes. The onset of geodesic chaos for non-Kerr spacetimes should occur at the resonance locations quantified here. Properties of resonance wave functions. More, R. M.; Gerjuoy, E. Construction and study of resonance wave functions corresponding to poles of the Green's function for several illustrative models of theoretical interest. Resonance wave functions obtained from the Siegert and Kapur-Peierls definitions of the resonance energies are compared. The comparison especially clarifies the meaning of the normalization constant of the resonance wave functions. It is shown that the wave functions may be considered renormalized in a sense analogous to that of quantum field theory. However, this renormalization is entirely automatic, and the theory has neither ad hoc procedures nor infinite quantities. Advances in Magnetic Resonance, Volume 12, presents a variety of contributions to the theory and practice of magnetic resonance. The book contains six chapters and begins with a discussion of diffusion and self-diffusion measurements by nuclear magnetic resonance. This is followed by separate chapters on spin-lattice relaxation time in hydrogen isotope mixtures; the principles of optical detection of nuclear spin alignment and nuclear quadropole resonance; and the spin-1 behavior, including the relaxation of the quasi-invariants of the motion of a system of pairs of dipolar coupled spin-1/2 nu Amplitude saturation of MEMS resonators explained by autoparametric resonance Van der Avoort, C; Bontemps, J J M; Steeneken, P G; Le Phan, K; Van Beek, J T M; Van der Hout, R; Hulshof, J; Fey, R H B This paper describes a phenomenon that limits the power handling of MEMS resonators. It is observed that above a certain driving level, the resonance amplitude becomes independent of the driving level. In contrast to previous studies of power handling of MEMS resonators, it is found that this amplitude saturation cannot be explained by nonlinear terms in the spring constant or electrostatic force. Instead we show that the amplitude in our experiments is limited by nonlinear terms in the equation of motion which couple the in-plane length-extensional resonance mode to one or more out-of-plane (OOP) bending modes. We present experimental evidence for the autoparametric excitation of these OOP modes using a vibrometer. The measurements are compared to a model that can be used to predict a power-handling limit for MEMS resonators Van der Avoort, C; Bontemps, J J M; Steeneken, P G; Le Phan, K; Van Beek, J T M [NXP Research, Eindhoven (Netherlands); Van der Hout, R; Hulshof, J [Department of Mathematics, VU University—Faculty of Sciences, De Boelelaan 1081a, 1081 HV Amsterdam (Netherlands); Fey, R H B, E-mail: [email protected] [Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB, Eindhoven (Netherlands) This paper describes a phenomenon that limits the power handling of MEMS resonators. It is observed that above a certain driving level, the resonance amplitude becomes independent of the driving level. In contrast to previous studies of power handling of MEMS resonators, it is found that this amplitude saturation cannot be explained by nonlinear terms in the spring constant or electrostatic force. Instead we show that the amplitude in our experiments is limited by nonlinear terms in the equation of motion which couple the in-plane length-extensional resonance mode to one or more out-of-plane (OOP) bending modes. We present experimental evidence for the autoparametric excitation of these OOP modes using a vibrometer. The measurements are compared to a model that can be used to predict a power-handling limit for MEMS resonators. Cyclotron resonance for electrons over helium in resonator Shikin, V B The problem on the cyclotron resonance (CR) for electrons on the helium film, positioned in the resonator lower part, is solved. It is shown, that it relates to one of the examples of the known problem on the oscillations of the coupled oscillators system. The coupling constant between these oscillators constituting the variable function of the problem parameters. It is minimal in the zero magnetic field and reaches its maximum under the resonance conditions, when the cyclotron frequency coincides with one of the resonator modes. The CR details of the Uhf CR-energy absorption coupled by the electrons + resonator system, are calculated. The applications of the obtained results to the available CR experiments for electrons over helium Resonant High Power Combiners Langlois, Michel; Peillex-Delphe, Guy Particle accelerators need radio frequency sources. Above 300 MHz, the amplifiers mostly used high power klystrons developed for this sole purpose. As for military equipment, users are drawn to buy "off the shelf" components rather than dedicated devices. IOTs have replaced most klystrons in TV transmitters and find their way in particle accelerators. They are less bulky, easier to replace, more efficient at reduced power. They are also far less powerful. What is the benefit of very compact sources if huge 3 dB couplers are needed to combine the power? To alleviate this drawback, we investigated a resonant combiner, operating in TM010 mode, able to combine 3 to 5 IOTs. Our IOTs being able to deliver 80 kW C.W. apiece, combined power would reach 400 kW minus the minor insertion loss. Values for matching and insertion loss are given. The behavior of the system in case of IOT failure is analyzed. Laser cooling at resonance Yudkin, Yaakov; Khaykovich, Lev We show experimentally that three-dimensional laser cooling of lithium atoms on the D2 line is possible when the laser light is tuned exactly to resonance with the dominant atomic transition. Qualitatively, it can be understood by applying simple Doppler cooling arguments to the specific hyperfine structure of the excited state of lithium atoms, which is both dense and inverted. However, to build a quantitative theory, we must resolve to a full model which takes into account both the entire atomic structure of all 24 Zeeman sublevels and the laser light polarization. Moreover, by means of Monte Carlo simulations, we show that coherent processes play an important role in showing consistency between the theory and the experimental results. Cremin, B.J. Recent advances in diagnostic imaging, have been the medical application of nuclear magnetic resonance (NMR). It's been used to study the structure of various compounds in chemistry and physics, and in the mid-1970 to produce images of rabbits and eventually of the human hand and head. The images are produced by making use of the nuclear magnetization of the hydrogen ion, or proton, that is present in biological material to record the density distribution of protons in cellular water and lipids. An exploration of the end-results of complicated free induction decay signals, that have been digitized and frequency-analysed by mathematical computerized techniques to produce an image of tissue density, is given. At present NMR produces images comparable to those of early computed tomography Meyerhoff, D.J.; Weiner, M.W. A major function of the liver is regulation of carbohydrate, lipid, and nitrogen metabolism. Food is absorbed by the intestines and transported to the liver by the portal circulation. Substrates are metabolized and stored in the liver to maintain optimal blood concentrations of glucose and lipids. Ammonia generated in the gastrointestinal tract is converted to urea in the liver by the urea cycle. Various forms of liver disease are associated with disorders of carbohydrate, fat, and nitrogen metabolism. Therefore the ability to characterize liver metabolism noninvasively is of potential diagnostic value. Magnetic resonance spectroscopy (MRS) provides information about tissue metabolism by measuring concentrations of metabolites. However, to determine the anatomic location from which spectroscopic signals are derived, MRS could be performed in conjunction with MRI. This paper summarizes the current experience with spectroscopy ion animal models of human disease and reviews the clinical experience with hepatic MRS to date Magnetic resonance in neuroborreliosis Ustymowicz, A.; Zajkowska, J. Magnetic resonance (MR) is commonly used in diagnosing infections of the central nervous system. The aim of the study is to evaluate central nervous system changes in neuroborreliosis patients. MR examinations were performed in 44 patients with clinical symptoms, epidemiology and laboratory tests results of neuroborreliosis. Abnormalities were detected in 22 patients. Most of them presented cortico-subcortical atrophy (86%). In 9 cases foci of increased signal in T2-weighted and FLAIR images were observed in white matter. They were single or multiple, located subcorticaly and paraventriculary. In 2 subjects areas of increased signal were found in the brain stem. Central nervous system abnormalities detected with MR are not specific for Lyme disease. They can suggest demyelinating lesions and/or gliosis observed in many nervous system disorders (SM, ADEM, lacunar infarcts). (author) Cine magnetic resonance Higgins, C.B.; Sechtem, U.P.; Pflugfelder, P. Cine magnetic resonance (MR) is a fast MR imaging process with referencing of the imaging data to the electrocardiogram (ECG) so that images corresponding to 21-msec segments of the cardiac cycle are acquired. A series of such images, each corresponding to a 21-msec segment of the cardiac cycle, can be laced together for viewing in the cine format at a framing rate of 20 to 40 frames per second. Since cine angiograms of the heart are usually done at 30 frames per second, this technique achieves a temporal resolution adequate for the evluation of central cardiovascular function. The major application of this technique is to depict central cardiovascular function and blood flow Cascaded resonant bridge converters Stuart, Thomas A. (Inventor) A converter for converting a low voltage direct current power source to a higher voltage, high frequency alternating current output for use in an electrical system where it is desired to use low weight cables and other circuit elements. The converter has a first stage series resonant (Schwarz) converter which converts the direct current power source to an alternating current by means of switching elements that are operated by a variable frequency voltage regulator, a transformer to step up the voltage of the alternating current, and a rectifier bridge to convert the alternating current to a direct current first stage output. The converter further has a second stage series resonant (Schwarz) converter which is connected in series to the first stage converter to receive its direct current output and convert it to a second stage high frequency alternating current output by means of switching elements that are operated by a fixed frequency oscillator. The voltage of the second stage output is controlled at a relatively constant value by controlling the first stage output voltage, which is accomplished by controlling the frequency of the first stage variable frequency voltage controller in response to second stage voltage. Fault tolerance in the event of a load short circuit is provided by making the operation of the first stage variable frequency voltage controller responsive to first and second stage current limiting devices. The second stage output is connected to a rectifier bridge whose output is connected to the input of the second stage to provide good regulation of output voltage wave form at low system loads. Shape resonances in molecular fields Dehmer, J.L. A shape resonance is a quasibound state in which a particle is temporarily trapped by a potential barrier (i.e., the shape of the potential), through which it may eventually tunnel and escape. This simple mechanism plays a prominent role in a variety of excitation processes in molecules, ranging from vibrational excitation by slow electrons to ionization of deep core levels by x-rays. Moreover, their localized nature makes shape resonances a unifying link between otherwise dissimilar circumstances. One example is the close connection between shape resonances in electron-molecule scattering and in molecular photoionization. Another is the frequent persistence of free-molecule shape resonant behavior upon adsorption on a surface or condensation into a molecular solid. The main focus of this article is a discussion of the basic properties of shape resonances in molecular fields, illustrated by the more transparent examples studied over the last ten years. Other aspects to be discussed are vibrational effects of shape resonances, connections between shape resonances in different physical settings, and examples of shape resonant behavior in more complex cases, which form current challenges in this field Full Text Available ... Resources Professions Site Index A-Z Children's (Pediatric) Magnetic Resonance Imaging Children's magnetic resonance imaging (MRI) uses a powerful ... for an MRI exam contains a metal called gadolinium . Gadolinium can be used in patients with iodine ... Stark resonances in disordered systems Grecchi, V.; Maioli, M.; Modena Univ.; Sacchetti, A. By slightly restricting the conditions given by Herbst and Howland, we prove the existence of resonances in the Stark effect of disordered systems (and atomic crystals) for large atomic mean distance. In the crystal case the ladders of resonances have the Wannier behavior for small complex field. (orig.) Atomic and molecular resonance ionization Botter, R.; Petit, A. Published in summary form only the paper recalls the principle of resonance photoionization, transition probability, selectivity and critical parameters. Examples of applications are briefly treated: Trace analysis by resonance ionization mass spectroscopy for detection of Fe in Zr F 4 for fabrication of optical fibers and laser isotopic separation of U 235 and Gd 157 [fr Physics of optimal resonant tunneling Racec, P.N.; Stoica, T.; Popescu, C.; Lepsa, M.I.; Roer, van de T.G. The optimal resonant tunneling, or the complete tunneling transparence of a biased double-barrier resonant-tunneling (DBRT) structure, is discussed. It is shown that its physics does not rest on the departure from the constant potential within the barriers and well, due to the applied electric Full Text Available ... work? Unlike conventional x-ray examinations and computed tomography (CT) scans, MRI does not utilize ionizing radiation. Instead, ... Angiography Magnetic Resonance, Functional (fMRI) - Brain Children's (Pediatric) CT (Computed Tomography) Magnetic Resonance Imaging (MRI) Safety Contrast Materials Children ... Full Text Available ... Resources Professions Site Index A-Z Children's (Pediatric) Magnetic Resonance Imaging Children's magnetic resonance imaging (MRI) uses ... identify and accurately characterize diseases than other imaging methods. This detail makes MRI an invaluable tool in ... Resonance journal of science education RESONANCE \| May 2010. Resonance journal of science education. May 2010 Volume 15 Number 5. On the Measurement of Phase Difference using CROs b. SERIES ARTICLES. 400. Aerobasics – An Introduction to Aeronautics. Mini and Micro Airplanes. S P Govinda Raju. GENERAL ARTICLES. 411. Bird of Passage at ... Integrated unaligned resonant modulator tuning Zortman, William A.; Lentine, Anthony L. Methods and systems for tuning a resonant modulator are disclosed. One method includes receiving a carrier signal modulated by the resonant modulator with a stream of data having an approximately equal number of high and low bits, determining an average power of the modulated carrier signal, comparing the average power to a predetermined threshold, and operating a tuning device coupled to the resonant modulator based on the comparison of the average power and the predetermined threshold. One system includes an input structure, a plurality of processing elements, and a digital control element. The input structure is configured to receive, from the resonant modulator, a modulated carrier signal. The plurality of processing elements are configured to determine an average power of the modulated carrier signal. The digital control element is configured to operate a tuning device coupled to the resonant modulator based on the average power of the modulated carrier signal. Giant first-forbidden resonances Krmpotic, F.; Nakayama, K.; Sao Paulo Univ.; Pio Galeao, A.; Sao Paulo Univ. Recent experimental data on first-forbidden charge-exchange resonances are discussed in the framework of a schematic model. We also evaluate the screening of the weak coupling constants induced by both the giant resonances and the δ-isobar. It is shown that the last effect does not depend on the multipolarity of the one-particle moment. Due to the same reason, the fraction of the reaction strength pushed up into the δ-resonance region is always the same regardless of the quantum numbers carried by the excitation. Simple expressions are derived for the dependence of the excitation energies of the first-forbidden giant resonances on the mass number and isospin of the target. The model reproduces consistently both the Gamow-Teller and the first-forbidden resonances. (orig.) Nonlinear elasticity in resonance experiments Li, Xun; Sens-Schönfelder, Christoph; Snieder, Roel Resonant bar experiments have revealed that dynamic deformation induces nonlinearity in rocks. These experiments produce resonance curves that represent the response amplitude as a function of the driving frequency. We propose a model to reproduce the resonance curves with observed features that include (a) the log-time recovery of the resonant frequency after the deformation ends (slow dynamics), (b) the asymmetry in the direction of the driving frequency, (c) the difference between resonance curves with the driving frequency that is swept upward and downward, and (d) the presence of a "cliff" segment to the left of the resonant peak under the condition of strong nonlinearity. The model is based on a feedback cycle where the effect of softening (nonlinearity) feeds back to the deformation. This model provides a unified interpretation of both the nonlinearity and slow dynamics in resonance experiments. We further show that the asymmetry of the resonance curve is caused by the softening, which is documented by the decrease of the resonant frequency during the deformation; the cliff segment of the resonance curve is linked to a bifurcation that involves a steep change of the response amplitude when the driving frequency is changed. With weak nonlinearity, the difference between the upward- and downward-sweeping curves depends on slow dynamics; a sufficiently slow frequency sweep eliminates this up-down difference. With strong nonlinearity, the up-down difference results from both the slow dynamics and bifurcation; however, the presence of the bifurcation maintains the respective part of the up-down difference, regardless of the sweep rate. Auxiliary resonant DC tank converter Peng, Fang Z. An auxiliary resonant dc tank (ARDCT) converter is provided for achieving soft-switching in a power converter. An ARDCT circuit is coupled directly across a dc bus to the inverter to generate a resonant dc bus voltage, including upper and lower resonant capacitors connected in series as a resonant leg, first and second dc tank capacitors connected in series as a tank leg, and an auxiliary resonant circuit comprising a series combination of a resonant inductor and a pair of auxiliary switching devices. The ARDCT circuit further includes first clamping means for holding the resonant dc bus voltage to the dc tank voltage of the tank leg, and second clamping means for clamping the resonant dc bus voltage to zero during a resonant period. The ARDCT circuit resonantly brings the dc bus voltage to zero in order to provide a zero-voltage switching opportunity for the inverter, then quickly rebounds the dc bus voltage back to the dc tank voltage after the inverter changes state. The auxiliary switching devices are turned on and off under zero-current conditions. The ARDCT circuit only absorbs ripples of the inverter dc bus current, thus having less current stress. In addition, since the ARDCT circuit is coupled in parallel with the dc power supply and the inverter for merely assisting soft-switching of the inverter without participating in real dc power transmission and power conversion, malfunction and failure of the tank circuit will not affect the functional operation of the inverter; thus a highly reliable converter system is expected. Review on resonance cone fields Ohnuma, Toshiro. Resonance cone fields and lower hybrid heating are reviewed in this report. The resonance cone fields were reported by Fisher and Gould, and they proposed the use of the measurement of resonance cones and structure as a diagnostic tool to determine the plasma density and electron temperature in magnetoplasma. After the resonance cone, a wave-like disturbance persists. Ohnuma et al. have measured bending, reflection and ducting of resonance cones in detail. The thermal modes in inhomogeneous magnetoplasma were seen. The reflection of thermal mode near an electron plasma frequency layer and an insulating plate has been observed. The non-linear effects of resonance cones is reported. Monochromatic electron beam produces the noise of broad band whistler mode. Lower hybrid waves have been the subject of propagation from the edge of plasma to the lower hybrid layer. Linear lower hybrid waves were studied. The lower hybrid and ion acoustic waves radiated from a point source were observed. The parametric decay of finite-extent, cold electron plasma waves was studied. The lower hybrid cone radiated from a point source going along magnetic field lines was observed. Several experimental data on the lower hybrid heating in tokamak devices have been reported. The theories on resonance cones and lower hybrid waves are introduced in this report. (Kato, T.) Resonance ionization spectroscopy 1990 Parks, J.E.; Omenetto, N. The Fifth International Symposium on Resonance Ionization Spectroscopy (RIS) and its Applications was held in Varese, Italy, 16-21 September 1990. Interest in RIS and its applications continues to grow, and RIS is expanding into a more diverse and mature field of study. This maturity was evident in this meeting both in the basic science and understanding of RIS processes and in the number of new and improved applications and techniques. The application of RIS techniques to molecular detection problems made remarkable progress since the last meeting two years ago. Subtle effects pertaining to isotopic discrimination received more theoretical attention, and there now seems to be good understanding of these effects, which can lead to correction procedures and/or methods to avoid isotopic effects. RIS applications were presented in which significant, real world problems were addressed, demonstrating its capability to solve problems that previously could not be accurately solved by other more traditional techniques. The contributions to the conference are grouped under the following major topic headings: physics applications of rare atoms; laser ionization mechanisms - spectroscopy; atomic, molecular and ion sources; molecular RIS; atomic RIS - Rydberg states; environmental trace analysis; biological and medical applications; state selected chemistry; new laser sources and techniques; ultra-high resolution and isotopic selectivity; surface and bulk analysis. (Author) Transverse electron resonance accelerator Osonka, P.L. Transverse (to the velocity, v-bar, of the particles to be accelerated) electron oscillations are generated in high (e.g. solid) density plasms by either an electromagnetic wave or by the field of charged particles traveling parallel to v-bar. The generating field oscillates with frequency ω = ω/sub p/, where ω/sub p/ is the plasma frequency. The plasma is confined to a sequence of microstructures with typical dimensions of d≅2πc/ω/sub p/, allowing the generating fields to penetrate. Since ω/sub p/ is now high, the time scales, T, are correspondingly reduced. The microstructures are allowed to explode after t = T, until then they are confined by ion inertia. As a result of resonance, the electric field, E, inside the microstructures can exceed the generating field E/sub L/. The generating force is proportional to E/sub L/ (as opposed to E 2 /sub L/). Phase matching of particles is possible by appropriate spacing of the microstructures or by a gas medium. The generating beam travels outside the plasma, filamentation is not a problem. The mechanism is relatively insensitive to the exact shape and position of the microstructures. This device contains features of various earlier proposed acceleration mechanisms and may be considered as the limiting case of several of those for small d, T and high E Nucleon Resonance Physics Recent results of meson photo-production at the existing electron machines with polarized real photon beams and the measurement of polarization observables of the final state baryons have provided high precision data that led to the discovery of new excited nucleon and $\\Delta$ states using multi-channel partial wave analyses procedures. The internal structure of several prominent excited states has been revealed employing meson electroproduction processes. On the theoretical front, lattice QCD is now predicting the baryon spectrum with very similar characteristics as the constituent quark model, and continuum QCD, such as is represented in the Dyson-Schwinger Equations approach and in light front relativistic quark models, describes the non-perturbative behavior of resonance excitations at photon virtuality of $Q^2 > 1.5GeV^2$. In this talk I discuss the need to continue a vigorous program of nucleon spectroscopy and the study of the internal structure of excited states as a way to reveal the effective degrees of freedom underlying the excited states and their dependence on the distance scale probed. Csonka, P.L. Transverse (to the velocity, v, of the particles to be accelerated) electron oscillations are generated in high (e.g. solid) density plasmas by either an electromagnetic wave or by the field of charged particles traveling parallel to v. The generating field oscillates with frequency ω = ω/sub p/, where ω/sub p/ is the plasma frequency. The plasma is confined to a sequence of microstructures with typical dimensions of d approx. = 2πc/ω/sub p/, allowing the generating fields to penetrate. Since ω/sub p/ is now high, the time scales, T, are correspondingly reduced. The microstructures are allowed to explode after t = T, until then they are confined by ion inertia. As a result of resonance, the electric field, E, inside the microstructures can exceed the generating field E/sub L/. The generating force is proportional to E/sub L/ (as opposed to E/sub L/ 2 ). Phase matching of particles is possible by appropriate spacing of the microstructures or by a gas medium. The generating beam travels outside the plasma, filamentation is not a problem. The mechanism is relatively insensitive to the exact shape and position of the microstructures. This device contains features of various earlier proposed acceleration mechanisms and may be considered as the limiting case of several of those for small d, T and high E Parallel magnetic resonance imaging Larkman, David J; Nunes, Rita G Parallel imaging has been the single biggest innovation in magnetic resonance imaging in the last decade. The use of multiple receiver coils to augment the time consuming Fourier encoding has reduced acquisition times significantly. This increase in speed comes at a time when other approaches to acquisition time reduction were reaching engineering and human limits. A brief summary of spatial encoding in MRI is followed by an introduction to the problem parallel imaging is designed to solve. There are a large number of parallel reconstruction algorithms; this article reviews a cross-section, SENSE, SMASH, g-SMASH and GRAPPA, selected to demonstrate the different approaches. Theoretical (the g-factor) and practical (coil design) limits to acquisition speed are reviewed. The practical implementation of parallel imaging is also discussed, in particular coil calibration. How to recognize potential failure modes and their associated artefacts are shown. Well-established applications including angiography, cardiac imaging and applications using echo planar imaging are reviewed and we discuss what makes a good application for parallel imaging. Finally, active research areas where parallel imaging is being used to improve data quality by repairing artefacted images are also reviewed. (invited topical review) Magnetic resonance imaging methodology Moser, Ewald; Stadlbauer, Andreas; Windischberger, Christian; Quick, Harald H.; Ladd, Mark E. Magnetic resonance (MR) methods are non-invasive techniques to provide detailed, multi-parametric information on human anatomy, function and metabolism. Sensitivity, specificity, spatial and temporal resolution may, however, vary depending on hardware (e.g., field strength, gradient strength and speed) and software (optimised measurement protocols and parameters for the various techniques). Furthermore, multi-modality imaging may enhance specificity to better characterise complex disease patterns. Positron emission tomography (PET) is an interesting, largely complementary modality, which might be combined with MR. Despite obvious advantages, combining these rather different physical methods may also pose challenging problems. At this early stage, it seems that PET quality may be preserved in the magnetic field and, if an adequate detector material is used for the PET, MR sensitivity should not be significantly degraded. Again, this may vary for the different MR techniques, whereby functional and metabolic MR is more susceptible than standard anatomical imaging. Here we provide a short introduction to MR basics and MR techniques, also discussing advantages, artefacts and problems when MR hardware and PET detectors are combined. In addition to references for more detailed descriptions of MR fundamentals and applications, we provide an early outlook on this novel and exciting multi-modality approach to PET/MR. (orig.) Noncontrast Magnetic Resonance Lymphography. Arrivé, Lionel; Derhy, Sarah; El Mouhadi, Sanaâ; Monnier-Cholley, Laurence; Menu, Yves; Becker, Corinne Different imaging techniques have been used for the investigation of the lymphatic channels and lymph glands. Noncontrast magnetic resonance (MR) lymphography has significant advantages in comparison with other imaging modalities. Noncontrast MR lymphography uses very heavily T2-weighted fast spin echo sequences which obtain a nearly complete signal loss in tissue background and specific display of lymphatic vessels with a long T2 relaxation time. The raw data can be processed with different algorithms such as maximum intensity projection algorithm to obtain an anatomic representation. Standard T2-weighted MR images easily demonstrate the location of edema. It appears as subcutaneous infiltration of soft tissue with a classical honeycomb pattern. True collection around the muscular area may be demonstrated in case of severe lymphedema. Lymph nodes may be normal in size, number, and signal intensity; in other cases, lymph nodes may be smaller in size or number of lymph nodes may be restricted. MR lymphography allows a classification of lymphedema in aplasia (no collecting vessels demonstrated); hypoplasia (a small number of lymphatic vessels), and numerical hyperplasia or hyperplasia (with an increased number of lymphatic vessels of greater and abnormal diameter). Noncontrast MR lymphography is a unique noninvasive imaging modality for the diagnosis of lymphedema. It can be used for positive diagnosis, differential diagnosis, and specific evaluation of lymphedema severity. It may also be used for follow-up evaluation after treatment. Thieme Medical Publishers 333 Seventh Avenue, New York, NY 10001, USA. Magnetic resonance imaging. 1 Wall, E.E. van der; Roos, A.A. de; Doornbos, J.; Dijkman, P.R.M. van; Matheijssen, N.A.A.; Laarse, A. van der; Krauss, X.H.; Blokland, J.A.k.; Manger Cats, V.; Voorthuisen, A.E. van; Bruschke, A.V.G. The cardiovascular applications of MRI in coronary artery disease have considerably increased in recent years. Although many applications overlap those of other more cost-effective techniques, such as echocardiography, radionuclide angiography, and CT, MRI offers unique features not shared by the conventional techniques. Technical advantages are the excellent spatial resolution, the characterization of myocardial tissue, and the potential for three-dimensional imaging. This allows the accurate assessment of left ventricular mass and volume, the differentiation of infarcted tissue from normal myocardial tissue, and the determination of systolic wall thickening and regional wall motion abnormalities. Also inducible myocardial ischemia using pharmacological stress (dipyramidole or dobutamine) may be assessed by magnetic resonance imaging. Future technical developments include real-time imaging and noninvasive visualization of the coronary arteries. These advantages will have a major impact on the application of MRI in coronary artery disease, potentially unsurpassed by other techniques and certainly justifying the expenses. Consequently, the clinical use of MRI for the detection of coronary artery disease largely depends on the progress of technical developments. (author). 134 refs.; 10 figs.; 2 tabs Ramini, Abdallah; Alcheikh, Nouha; Ilyas, Saad; Younis, Mohammad I. efficient and requires less power for primary resonance excitation. Moreover, unlike the classical method where the structure is vulnerable to the dynamic pull-in instability, the axial excitation technique can provide large amplitude motion while protecting Superresolution Imaging Using Resonant Multiples Guo, Bowen A resonant multiple is defined as a multiple reflection that revisits the same subsurface location along coincident reflection raypaths. We show that resonant first-order multiples can be migrated with either Kirchhoff or wave-equation migration methods to give images with approximately twice the spatial resolution compared to post-stack primary-reflection images. A moveout-correction stacking method is proposed to enhance the signal-to-noise ratios (SNRs) of the resonant multiples before superresolution migration. The effectiveness of this procedure is validated by synthetic and field data tests. Advances in Magnetic Resonance, Volume 9 describes the magnetic resonance in split constants and dipolar relaxation. This book discusses the temperature-dependent splitting constants in the ESR spectra of organic free radicals; temperature-dependent splittings in ion pairs; and magnetic resonance induced by electrons. The electron impact excitation of atoms and molecules; intramolecular dipolar relaxation in multi-spin systems; and dipolar cross-correlation problem are also elaborated. This text likewise covers the NMR studies of molecules oriented in thermotropic liquid crystals and diffusion The Resonance Integral of Gold Jirlow, K; Johansson, E The resonance activation integral of gold has been determined, by means of cadmium ratio measurements of thin foils in a neutron beam. Comparison was made with a 1/v detector, and the neutron spectra were measured with a chopper. The resonance integral, RI, is defined as {integral}{sub 0.5}{sup {infinity}}{sigma}{sub r}(E)dE/E, where {sigma}{sub r}(E) is the differenc between the total absorption cross section and the 1/v part. An experimental value of 1490 {+-} 40 barns has been obtained. RI has also been computed from resonance parameter data with the result 1529 {+-} 70 barns. Advances in Magnetic Resonance, Volume 1, discusses developments in various areas of magnetic resonance. The subject matter ranges from original theoretical contributions through syntheses of points of view toward series of phenomena to critical and painstaking tabulations of experimental data. The book contains six chapters and begins with a discussion of the theory of relaxation processes. This is followed by separate chapters on the development of magnetic resonance techniques for studying rate processes in chemistry and the application of these techniques to various problems; the geometri Hadron excitation of giant resonances Morsch, H.-P. A review is given on giant resonance studies in heavy nuclei using scattering of different hadronic probes. Concerning isoscalar giant resonances compression modes are discussed with the possibility to obtain more detailed structure information. From detailed studies of α scattering the distribution of isoscalar strengths of multipolarity up to L=6 was obtained. Some recent aspects of heavy ion excitation of collective modes are mentioned. The possibility to study isovector giant resonances in hadron charge exchange reactions is discussed. Finally, a comparison is made between α and 200 MeV proton scattering from which isoscalar and spin-isospin continuum response are extracted. (orig.) Statistical decay of giant resonances Dias, H.; Teruya, N.; Wolynec, E. Statistical calculations to predict the neutron spectrum resulting from the decay of Giant Resonances are discussed. The dependence of the resutls on the optical potential parametrization and on the level density of the residual nucleus is assessed. A Hauser-Feshbach calculation is performed for the decay of the monople giant resonance in 208 Pb using the experimental levels of 207 Pb from a recent compilation. The calculated statistical decay is in excelent agreement with recent experimental data, showing that the decay of this resonance is dominantly statistical, as predicted by continuum RPA calculations. (Author) [pt Statistical calculations to predict the neutron spectrum resulting from the decay of Giant Resonances are discussed. The dependence of the results on the optical potential parametrization and on the level density of the residual nucleus is assessed. A Hauser-Feshbach calculation is performed for the decay of the monopole giant resonance in 208 Pb using the experimental levels of 207 Pb from a recent compilation. The calculated statistical decay is in excellent agreement with recent experimental data, showing that decay of this resonance is dominantly statistical, as predicted by continuum RPA calculations. (Author) [pt Guo, Bowen; Schuster, Gerard T. Surface Plasmon Resonance Biosensor Nina GRIDINA Full Text Available Performed in this paper is numerical modeling of the angular dependence for light reflectivity R(F in surface plasmon-polariton resonance (SPR realized in Kretschmann geometry when studying the interface gold/suspension of spherical particles (cells in the assumption that the dielectric permittivity of particles suspension is described by the theory of effective medium. It has been shown that availability of suspended particles in solution inevitably results in appearance of an intermediate layer with the ε gradient between gold surface and suspension bulk, as a result of which the SPR angle shifts to lower values. Near the critical angle, the first derivative dR/dF demonstrates a clearly pronounced peak, which allows determining the value for suspension bulk and the gradient in the intermediate layer. Obtained in our experiments were SPR curves for two suspensions of erythrocytes – the dense one (erythrocyte mass after centrifuging and loose solution (whole blood. In the case of erythrocyte mass, fitting the experimental and calculated curves enabled us to quantitatively determine the bulk value for this erythrocyte mass (εb =1.96, thickness of the intermediate layer dm (300…400 nm and gradient in the intermediate layer. On the contrary, the SPR curve for whole blood appeared to be close to that of pure plasma. This fact allows only estimation of the thickness dm~2000...3000 nm as well as minimum ε value in the intermediate layer, which is close to that of plasma (ε = 1.79. Also, discussed is the mechanism of influence of the cell shape near the gold surface on the SPR effect. Ion cyclotron resonance heating Tajima, T. Ion cyclotron resonance heating of plasmas in tokamak and EBT configurations has been studied using 1-2/2 and 2-1/2 dimensional fully self-consistent electromagnetic particle codes. We have tested two major antenna configurations; we have also compared heating efficiencies for one and two ion species plasmas. We model a tokamak plasma with a uniform poloidal field and 1/R toroidal field on a particular q surface. Ion cyclotron waves are excited on the low field side by antennas parallel either to the poloidal direction or to the toroidal direction with different phase velocities. In 2D, minority ion heating (vsub(perpendicular)) and electron heating (vsub(parallel),vsub(perpendicular)) are observed. The exponential electron heating seems due to the decay instability. The minority heating is consistent with mode conversion of fast Alfven waves and heating by electrostatic ion cyclotron modes. Minority heating is stronger with a poloidal antenna. The strong electron heating is accompanied by toroidal current generation. In 1D, no thermal instability was observed and only strong minority heating resulted. For an EBT plasma we model it by a multiple mirror. We have tested heating efficiency with various minority concentrations, temperatures, mirror ratios, and phase velocities. In this geometry we have beach or inverse beach heating associated with the mode conversion layer perpendicular to the toroidal field. No appreciable electron heating is observed. Heating of ions is linear in time. For both tokamak and EBT slight majority heating above the collisional rate is observed due to the second harmonic heating. (author) Nested trampoline resonators for optomechanics Weaver, M. J., E-mail: [email protected]; Pepper, B.; Luna, F.; Perock, B. [Department of Physics, University of California, Santa Barbara, California 93106 (United States); Buters, F. M.; Eerkens, H. J.; Welker, G.; Heeck, K.; Man, S. de [Huygens-Kamerlingh Onnes Laboratorium, Universiteit Leiden, 2333 CA Leiden (Netherlands); Bouwmeester, D. [Department of Physics, University of California, Santa Barbara, California 93106 (United States); Huygens-Kamerlingh Onnes Laboratorium, Universiteit Leiden, 2333 CA Leiden (Netherlands) Two major challenges in the development of optomechanical devices are achieving a low mechanical and optical loss rate and vibration isolation from the environment. We address both issues by fabricating trampoline resonators made from low pressure chemical vapor deposition Si{sub 3}N{sub 4} with a distributed Bragg reflector mirror. We design a nested double resonator structure with 80 dB of mechanical isolation from the mounting surface at the inner resonator frequency, and we demonstrate up to 45 dB of isolation at lower frequencies in agreement with the design. We reliably fabricate devices with mechanical quality factors of around 400 000 at room temperature. In addition, these devices were used to form optical cavities with finesse up to 181 000 ± 1000. These promising parameters will enable experiments in the quantum regime with macroscopic mechanical resonators. Full Text Available ... is not harmful, but it may cause some medical devices to malfunction. Most orthopedic implants pose no ... Head? Magnetic resonance imaging (MRI) is a noninvasive medical test that physicians use to diagnose medical conditions. ... Dipole Resonances of 76Ge Ilieva, R. S.; Cooper, N.; Werner, V.; Rusev, G.; Pietralla, N.; Kelly, J. H.; Tornow, W.; Yates, S. W.; Crider, B. P.; Peters, E. Dipole resonances in 76Ge have been studied using the method of Nuclear Resonance Fluorescence (NRF). The experiment was performed using the Free Electron Laser facility at HI γS/TUNL, which produced linearly polarised quasi-monoenergetic photons in the 4-9 MeV energy range. Photon strength, in particular dipole strength, is an important ingredient in nuclear reaction calculations, and recent interest in its study has been stimulated by observations of a pygmy dipole resonance near the neutron separation energy Sn of certain nuclei. Furthermore, 76Ge is a candidate for 0 ν 2 β -decay. The results are complimentary to a relevant experiment done at TU Darmstadt using Bremsstrahlung beams. Single-resonance parities and a preliminary estimate of the total photo-excitation cross section will be presented. This work was supported by the U.S. DOE under grant no. DE-FG02-91ER40609. Full Text Available ... are the limitations of MRI of the Head? What is MRI of the Head? Magnetic resonance imaging ( ... brain) in routine clinical practice. top of page What are some common uses of the procedure? MR ... Full Text Available ... As the hydrogen atoms return to their usual alignment, they emit different amounts of energy that vary ... story about radiology? Share your patient story here Images × Image Gallery Radiologist prepping patient for magnetic resonance ... Full Text Available ... As the hydrogen atoms return to their usual alignment, they emit different amounts of energy that vary ... story about radiology? Share your patient story here Images × Image Gallery Magnetic Resonance Imaging (MRI) procedure View ... Full Text Available ... bear denotes child-specific content. Related Articles and Media MR Angiography (MRA) Magnetic Resonance, Functional (fMRI) - Brain ... the web pages found at these links. About Us \| Contact Us \| FAQ \| Privacy \| Terms of Use \| Links \| ... Full Text Available ... bear denotes child-specific content. Related Articles and Media Catheter Angiography Magnetic Resonance, Functional (fMRI) - Brain Children's ( ... the web pages found at these links. About Us \| Contact Us \| FAQ \| Privacy \| Terms of Use \| Links \| ... Full Text Available ... immediately after the exam. A few patients experience side effects from the contrast material, including nausea and local ... Related Articles and Media Catheter Angiography Magnetic Resonance, Functional (fMRI) - Brain Children's (Pediatric) CT (Computed Tomography) Magnetic ... Full Text Available ... magnetic resonance imaging (MRI) uses a powerful magnetic field, radio waves and a computer to produce detailed ... problems, medications, recent surgeries and allergies. The magnetic field is not harmful, but it may cause some ... Full Text Available ... by the interpreting radiologist. Frequently, the differentiation of abnormal (diseased) tissue from normal tissues is better with ... Tumor Treatment Magnetic Resonance Imaging (MRI) Safety Alzheimer's Disease Head Injury Brain Tumors Images related to Magnetic ... Full Text Available ... or thyroid problems. Any of these conditions may influence the decision on whether contrast material will be ... bear denotes child-specific content. Related Articles and Media Catheter Angiography Magnetic Resonance, Functional (fMRI) - Brain Children's ( ... Full Text Available ... it is useful to bring that to the attention of the technologist or scheduler before the exam. ... patient for magnetic resonance imaging (MRI) exam. View full size with caption Pediatric Content Some imaging tests ... Full Text Available ... it is useful to bring that to the attention of the scheduler before the exam and bring ... Image Gallery Magnetic Resonance Imaging (MRI) procedure View full size with caption Pediatric Content Some imaging tests ... Full Text Available ... MRI) exam. View full size with caption Pediatric Content Some imaging tests and treatments have special pediatric considerations. The teddy bear denotes child-specific content. Related Articles and Media Catheter Angiography Magnetic Resonance, ... Full Text Available ... be necessary. Your doctor will explain the exact reason why another exam is requested. Sometimes a follow- ... necessary in trauma situations. Although there is no reason to believe that magnetic resonance imaging harms the ... Magnetic resonance imaging the basics Constantinides, Christakis Magnetic resonance imaging (MRI) is a rapidly developing field in basic applied science and clinical practice. Research efforts in this area have already been recognized with five Nobel prizes awarded to seven Nobel laureates in the past 70 years. Based on courses taught at The Johns Hopkins University, Magnetic Resonance Imaging: The Basics provides a solid introduction to this powerful technology. The book begins with a general description of the phenomenon of magnetic resonance and a brief summary of Fourier transformations in two dimensions. It examines the fundamental principles of physics for nuclear magnetic resonance (NMR) signal formation and image construction and provides a detailed explanation of the mathematical formulation of MRI. Numerous image quantitative indices are discussed, including (among others) signal, noise, signal-to-noise, contrast, and resolution. The second part of the book examines the hardware and electronics of an MRI scanner and the typical measurements and simulations of m... Ion Cyclotron Resonance Facility (ICR) Federal Laboratory Consortium — his facility is charged with developing and exploiting the unique capabilities of Fourier Transform Ion Cyclotron Resonance (FT-ICR) mass spectrometry, and leads the... Weaver, M. J.; Pepper, B.; Luna, F.; Perock, B.; Buters, F. M.; Eerkens, H. J.; Welker, G.; Heeck, K.; Man, S. de; Bouwmeester, D. Two major challenges in the development of optomechanical devices are achieving a low mechanical and optical loss rate and vibration isolation from the environment. We address both issues by fabricating trampoline resonators made from low pressure chemical vapor deposition Si 3 N 4 with a distributed Bragg reflector mirror. We design a nested double resonator structure with 80 dB of mechanical isolation from the mounting surface at the inner resonator frequency, and we demonstrate up to 45 dB of isolation at lower frequencies in agreement with the design. We reliably fabricate devices with mechanical quality factors of around 400 000 at room temperature. In addition, these devices were used to form optical cavities with finesse up to 181 000 ± 1000. These promising parameters will enable experiments in the quantum regime with macroscopic mechanical resonators Weaver, M. J.; Pepper, B.; Luna, F.; Buters, F. M.; Eerkens, H. J.; Welker, G.; Perock, B.; Heeck, K.; de Man, S.; Bouwmeester, D. Two major challenges in the development of optomechanical devices are achieving a low mechanical and optical loss rate and vibration isolation from the environment. We address both issues by fabricating trampoline resonators made from low pressure chemical vapor deposition Si3N4 with a distributed Bragg reflector mirror. We design a nested double resonator structure with 80 dB of mechanical isolation from the mounting surface at the inner resonator frequency, and we demonstrate up to 45 dB of isolation at lower frequencies in agreement with the design. We reliably fabricate devices with mechanical quality factors of around 400 000 at room temperature. In addition, these devices were used to form optical cavities with finesse up to 181 000 ± 1000. These promising parameters will enable experiments in the quantum regime with macroscopic mechanical resonators. Narrow n anti n resonances Bogdanova, L.N.; Dalkarov, O.D.; Kerbikov, B.O.; Shapiro, I.S. The present status of the problem of quasinuclear states in systems of nucleons and antinucleons is reviewed. The theoretical predictions are compared with experimental data on narrow meson resonances near N anti N threshold which appeared in 1971-74 Full Text Available ... Related Articles and Media Catheter Angiography Magnetic Resonance, Functional (fMRI) - Brain Children's (Pediatric) CT (Computed Tomography) Magnetic ... the possible charges you will incur. Web page review process: This Web page is reviewed regularly by ... Resonance detection of Moessbauer radiation Morozov, V.V. The resonance detection method as compared with the usual method of registering Moessbauer spectra has a number of advantages, one of which is the increase of resolution of the Moessbauer spectrum. The method is based on the modulation of a secondary radiation of a converter tuned in the resonance with the Moessbauer gamma-quantum source. The resonance detection method with account of supression, secondary radiation outgoing from the converter is investigated. The converter represents a substrate enriched by the Moessbauer isotope placed either inside the gas counter, or coupled with any other detecting device. Analytical expressions for Moessbauer spectrum parameters: effect, area and width of the spectral line are derived. It is shown that the joint application of usual and resonance detection methods for registering the Moessbauer spectrum allows one to determine parameters of the source, converter and the investigated absorber Triplet State Resonance Raman Spectroscopy Wilbrandt, Robert Walter; Jensen, N. H.; Pagsberg, Palle Bjørn Makes the first report on the resonance Raman spectrum of a molecule in its triplet state generated by pulse radiolysis. A solution of 0.01 mol dm-3 of p-terphenyl in benzene was studied......Makes the first report on the resonance Raman spectrum of a molecule in its triplet state generated by pulse radiolysis. A solution of 0.01 mol dm-3 of p-terphenyl in benzene was studied... Magnetic Resonance Imaging. Chapter 15 Leach, M. O. [The Institute of Cancer Research and The Royal Marsden Hospital, London (United Kingdom) In Chapter 14, the principles of nuclear magnetic resonance were presented, along with an introduction to image forming processes. In this chapter, magnetic resonance imaging (MRI) will be reviewed, beginning with the hardware needed and its impact on image quality. The acquisition processes and image reconstruction will be discussed, as well as the artefacts that are possible, with discussion of the important area of safety and bioeffects completing the chapter. The nuclear magnetic resonance spectroscopy Goyer, Ph. The spectroscopy of nuclear magnetic resonance constitutes a major analytical technique in biological and organic analysis. This technique appears now in the programme of preparatory classes and its teaching is developed in the second year of DEUG. The following article reviews on the nuclear magnetic resonance and on the possibilities it offers to bring to the fore the physico-chemical properties of molecules. (N.C.) Resonant Impulsive Stimulated Raman Scattering Mokhtari, A; Chesnoy, J Using a femtosecond dye laser, we observe in real-time vibrational oscillations excited by impulsive stimulated Raman scattering (ISRS) close to an electronic resonance. We perform single-beam Raman excitation and probe the driven coherence by a polarization-sensitive detection. We demonstrate for the first time impulsively Raman-induced dichroism, birefringence as well as frequency and time delay shifts. We analyse the characteristics of resonant ISRS on a vibrational mode of a dye molecule (malachite green) in solution. Hadronic resonances at FAIR energies Vogel, Sascha These proceedings cover the analysis of hadronic resonances in heavy ion collisions. The model used for these studies is the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model. The model will be briefly explained, resonance observables will be highlighted and various kinematical issues will be investigated. Special emphasis will be put on the FAIR energy regime, especially highlighting the Compressed Baryonic Matter (CBM) program. Mokhtari, A.; Chesnoy, J. Using a femtosecond dye laser, we observe in real-time vibrational oscillations excited by impulsive stimulated Raman scattering (ISRS) close to an electronic resonance. We perform single-beam Raman excitation and probe the driven coherence by a polarization-sensitive detection. We demonstrate for the first time impulsively Raman-induced dichroism, birefringence as well as frequency and time delay shifts. We analyse the characteristics of resonant ISRS on a vibrational mode of a dye molecule (malachite green) in solution Memory effects on stochastic resonance Neiman, Alexander; Sung, Wokyung We study the phenomenon of stochastic resonance (SR) in a bistable system with internal colored noise. In this situation the system possesses time-dependent memory friction connected with noise via the fluctuation-dissipation theorem, so that in the absence of periodic driving the system approaches the thermodynamic equilibrium state. For this non-Markovian case we find that memory usually suppresses stochastic resonance. However, for a large memory time SR can be enhanced by the memory. Advances in Magnetic Resonance, Volume 2, features a mixture of experimental and theoretical contributions. The book contains four chapters and begins with an ambitious and general treatment of the problem of signal-to-noise ratio in magnetic resonance. This is followed by separate chapters on the interpretation of nuclear relaxation in fluids, with special reference to hydrogen; and various aspects of molecular theory of importance in NMR. Micro-machined resonator oscillator Koehler, Dale R.; Sniegowski, Jeffry J.; Bivens, Hugh M.; Wessendorf, Kurt O. A micro-miniature resonator-oscillator is disclosed. Due to the miniaturization of the resonator-oscillator, oscillation frequencies of one MHz and higher are utilized. A thickness-mode quartz resonator housed in a micro-machined silicon package and operated as a "telemetered sensor beacon" that is, a digital, self-powered, remote, parameter measuring-transmitter in the FM-band. The resonator design uses trapped energy principles and temperature dependence methodology through crystal orientation control, with operation in the 20-100 MHz range. High volume batch-processing manufacturing is utilized, with package and resonator assembly at the wafer level. Unique design features include squeeze-film damping for robust vibration and shock performance, capacitive coupling through micro-machined diaphragms allowing resonator excitation at the package exterior, circuit integration and extremely small (0.1 in. square) dimensioning. A family of micro-miniature sensor beacons is also disclosed with widespread applications as bio-medical sensors, vehicle status monitors and high-volume animal identification and health sensors. The sensor family allows measurement of temperatures, chemicals, acceleration and pressure. A microphone and clock realization is also available. Fourier transform nuclear magnetic resonance Geick, R. This review starts with the basic principles of resonance phenomena in physical systems. Especially, the connection is shown between the properties of these systems and Fourier transforms. Next, we discuss the principles of nuclear magnetic resonance. Starting from the general properties of physical systems showing resonance phenomena and from the special properties of nuclear spin systems, the main part of this paper reviews pulse and Fourier methods in nuclear magnetic resonance. Among pulse methods, an introduction will be given to spin echoes, and, apart from the principle of Fourier transform nuclear magnetic resonance, an introduction to the technical problems of this method, e.g. resolution in the frequency domain, aliasing, phase and intensity errors, stationary state of the spin systems for repetitive measurements, proton decoupling, and application of Fourier methods to systems in a nonequilibrium state. The last section is devoted to special applications of Fourier methods and recent developments, e.g. measurement of relaxation times, solvent peak suppression, 'rapid scan'-method, methods for suppressing the effects of dipolar coupling in solids, two-dimensional Fourier transform nuclear magnetic resonance, and spin mapping or zeugmatography. (author) Symmetry and resonance in Hamiltonian systems Tuwankotta, J.M.; Verhulst, F. In this paper we study resonances in two degrees of freedom, autonomous, hamiltonian systems. Due to the presence of a symmetry condition on one of the degrees of freedom, we show that some of the resonances vanish as lower order resonances. After giving a sharp estimate of the resonance domain, we In this paper we study resonances in two degrees of freedom, autonomous, hamiltonian systems. Due to the presence of a symmetry condition on one of the degrees of freedom, we show that some of the resonances vanish as lower order resonances. After determining the size of the resonance domain, we Microelectromechanical resonator and method for fabrication Wittwer, Jonathan W [Albuquerque, NM; Olsson, Roy H [Albuquerque, NM A method is disclosed for the robust fabrication of a microelectromechanical (MEM) resonator. In this method, a pattern of holes is formed in the resonator mass with the position, size and number of holes in the pattern being optimized to minimize an uncertainty .DELTA.f in the resonant frequency f.sub.0 of the MEM resonator due to manufacturing process variations (e.g. edge bias). A number of different types of MEM resonators are disclosed which can be formed using this method, including capacitively transduced Lame, wineglass and extensional resonators, and piezoelectric length-extensional resonators. Transmission Line Resonator Segmented with Series Capacitors Zhurbenko, Vitaliy; Boer, Vincent; Petersen, Esben Thade Transmission line resonators are often used as coils in high field MRI. Due to distributed nature of such resonators, coils based on them produce inhomogeneous field. This work investigates application of series capacitors to improve field homogeneity along the resonator. The equations for optimal...... values of evenly distributed capacitors are presented. The performances of the segmented resonator and a regular transmission line resonator are compared.... Highly Tunable Electrostatic Nanomechanical Resonators Kazmi, Syed Naveed Riaz There has been significant interest towards highly tunable resonators for on-demand frequency selection in modern communication systems. Here, we report highly tunable electrostatically actuated silicon-based nanomechanical resonators. In-plane doubly-clamped bridges, slightly curved as shallow arches due to residual stresses, are fabricated using standard electron beam lithography and surface nanomachining. The resonators are designed such that the effect of mid-plane stretching dominates the softening effect of the electrostatic force. This is achieved by controlling the gap-to-thickness ratio and by exploiting the initial curvature of the structure from fabrication. We demonstrate considerable increase in the resonance frequency of nanoresonators with the dc bias voltages up to 108% for 180 nm thick structures with a transduction gap of 1 $mu$m separating them from the driving/sensing electrodes. The experimental results are found in good agreement with those of a nonlinear analytical model based on the Euler-Bernoulli beam theory. As a potential application, we demonstrate a tunable narrow band-pass filter using two electrically coupled nanomechanical arch resonators with varied dc bias voltages. Magnetic resonance and porous materials McDonald, P.; Strange, J. Mention the words magnetic resonance to your medical advisor and he or she will immediately think of a multi-million pound scanner that peers deep into the brain. A chemist, on the other hand, will imagine a machine that costs several hundred thousand pounds and produces high-resolution spectra for chemical analysis. Food technologists will probably think of a bench-top instrument for determining moisture content, while an oil prospector will envisage a device that can be operated several kilometres down an oil well. To a physicist the term is more likely to conjure up a mental picture of nuclear spins precessing in a magnetic field. These examples illustrate the diverse aspects of a phenomenon discovered by physicists over 50 years ago. Electron spin resonance was first discovered by Russian scientists, and nuclear magnetic resonance was discovered in the US shortly afterwards by Ed Purcell at Harvard University and Felix Bloch at Stanford University. Today, nuclear magnetic resonance (NMR) is the most widely used technique. Modern NMR machines are making it possible to probe microstructure and molecular movement in materials as diverse as polymers, cements, rocks, soil and foods. NMR allows the distribution of different components in a material to be determined with a resolution approaching 1μm, although the signal can be sensitive to even smaller lengthscales. In this article the authors describe how physicists are still developing magnetic resonance to exploit a range of new applications. (UK) Nonlinear Dynamics of Nanomechanical Resonators Ramakrishnan, Subramanian; Gulak, Yuiry; Sundaram, Bala; Benaroya, Haym Nanoelectromechanical systems (NEMS) offer great promise for many applications including motion and mass sensing. Recent experimental results suggest the importance of nonlinear effects in NEMS, an issue which has not been addressed fully in theory. We report on a nonlinear extension of a recent analytical model by Armour et al [1] for the dynamics of a single-electron transistor (SET) coupled to a nanomechanical resonator. We consider the nonlinear resonator motion in both (a) the Duffing and (b) nonlinear pendulum regimes. The corresponding master equations are derived and solved numerically and we consider moment approximations as well. In the Duffing case with hardening stiffness, we observe that the resonator is damped by the SET at a significantly higher rate. In the cases of softening stiffness and the pendulum, there exist regimes where the SET adds energy to the resonator. To our knowledge, this is the first instance of a single model displaying both negative and positive resonator damping in different dynamical regimes. The implications of the results for SET sensitivity as well as for, as yet unexplained, experimental results will be discussed. 1. Armour et al. Phys.Rev.B (69) 125313 (2004). Space charge in nanostructure resonances Price, Peter J. In quantum ballistic propagation of electrons through a variety of nanostructures, resonance in the energy-dependent transmission and reflection probabilities generically is associated with (1) a quasi-level with a decay lifetime, and (2) a bulge in electron density within the structure. It can be shown that, to a good approximation, a simple formula in all cases connects the density of states for the latter to the energy dependence of the phase angles of the eigen values of the S-matrix governing the propagation. For both the Lorentzian resonances (normal or inverted) and for the Fano-type resonances, as a consequence of this eigen value formula, the space charge due to filled states over the energy range of a resonance is just equal (for each spin state) to one electron charge. The Coulomb interaction within this space charge is known to 'distort' the electrical characteristics of resonant nanostructures. In these systems, however, the exchange effect should effectively cancel the interaction between states with parallel spins, leaving only the anti-parallel spin contribution. Kazmi, Syed Naveed Riaz; Hajjaj, Amal Z.; Hafiz, Md Abdullah Al; Da Costa, Pedro M. F. J.; Younis, Mohammad I. Pattern formation in optical resonators Weiss, C O; Larionova, Ye We review pattern formation in optical resonators. The emphasis is on 'particle-like' structures such as vortices or spatial solitons. On the one hand, similarities impose themselves with other fields of physics (condensed matter, phase transitions, particle physics, fluds/super fluids). On the other hand the feedback is led by the resonator mirrors to bi- and multi-stability of the spatial field structure, which is the basic ingredient for optical information processing. The spatial dimension or the 'parallelism' is the strength of optics compared to electronics (and will have to be employed to fully use the advantages optics offers in information processing). But even in the 'serial' processing tasks of telecoms (e.g. information buffering) spatial resonator solitons can do better than the schemes proposed so far-including 'slow light'. Pattern formation in optical resonators will likely be the key to brain-like information processing like cognition, learning and association; to complement the precise but limited algorithmic capabilities of electronic processing. But even in the short term it will be useful for solving serial optical processing problems. The prospects for technical uses of pattern formation in resonators are one motivation for this research. The fundamental similarities with other fields of physics, on the other hand, inspire transfer of concepts between fields; something that has always proven fruitful for gaining deeper insights or for solving technical problems Nuclear level mixing resonance spectroscopy Coussement, R.; Put, P.; Scheveneels, G.; Hardeman, F. The existent methods for measuring quadrupole interactions are not suited to nuclei with lifetimes in the micro-seconds to minutes region. AD/NQR, a possible candidate in this lifetime gap, has not yet succeeded in overcoming its predicted difficulties. A new resonant method, recently developed and based on the principles of level mixing (cfr atomic spectroscopy) covers this less accessible lifetime range. Many other kinds of resonances can be described according to the level mixing formalism. The particular example of NMR as a level mixing resonance (LMR) is discussed. The underlying theory of LMR and its important consequences, leading to some interesting features of the method, is briefly formulated. Two successfully performed measurements demonstrate the feasibility and the predicted characteristics of this new promising method. (orig.) Optical resonators and neural networks Anderson, Dana Z. It may be possible to implement neural network models using continuous field optical architectures. These devices offer the inherent parallelism of propagating waves and an information density in principle dictated by the wavelength of light and the quality of the bulk optical elements. Few components are needed to construct a relatively large equivalent network. Various associative memories based on optical resonators have been demonstrated in the literature, a ring resonator design is discussed in detail here. Information is stored in a holographic medium and recalled through a competitive processes in the gain medium supplying energy to the ring rsonator. The resonator memory is the first realized example of a neural network function implemented with this kind of architecture. Nuclear magnetic resonance diagnostic apparatus Sugimoto, H. Nuclear magnetic resonance diagnostic apparatus including a coil for generating a gradient field in a plane perpendicular to a static magnetic field, means for controlling the operation of the coil to rotationally shift in angular steps the gradient direction of the gradient field at an angle pitch of some multiple of the unit index angle through a plurality of rotations to assume all the shift positions of the gradient direction, a rough image reconstructor for reconstructing a rough tomographic image on the basis of nuclear magnetic resonance signals acquired during a rotation of the second gradient magnetic field, a rough image display for depicting the rough tomographic image, a final image reconstructor for reconstructing a final tomographic image on the basis of all nuclear magnetic resonance signals corresponding to all of the expected rotation shift positions acquired during a plurality of rotations and a final image display for depicting the final tomographic image Resonance Ionization Laser Ion Sources Marsh, B The application of the technique of laser resonance ionization to the production of singly charged ions at radioactive ion beam facilities is discussed. The ability to combine high efficiency and element selectivity makes a resonance ionization laser ion source (RILIS) an important component of many radioactive ion beam facilities. At CERN, for example, the RILIS is the most commonly used ion source of the ISOLDE facility, with a yearly operating time of up to 3000 hours. For some isotopes the RILIS can also be used as a fast and sensitive laser spectroscopy tool, provided that the spectral resolution is sufficiently high to reveal the influence of nuclear structure on the atomic spectra. This enables the study of nuclear properties of isotopes with production rates even lower than one ion per second and, in some cases, enables isomer selective ionization. The solutions available for the implementation of resonance laser ionization at radioactive ion beam facilities are summarized. Aspects such as the laser r... Kazmi, Syed N. R. We report an electro-thermally tunable in-plane doubly-clamped nanoelectromechanical resonator capable of dynamically performing NOR, NOT, XNOR, XOR, and AND logic operations. Toward this, a silicon based resonator is fabricated using standard e-beam lithography and surface nanomachining of a highly conductive device layer of a silicon-on-insulator (SOI) wafer. The performance of this logic device is examined at elevated temperatures, ranging from 25 °C to 85 °C, demonstrating its resilience for most of the logic operations; thereby paving the way towards nano-elements-based mechanical computing. The Resonance Integral of Niobium Hellstrand, E; Lundgren, G The resonance integral of niobium has been studied by both pile oscillator and activation techniques. A value of 8.15b {+-} 0.65 b was obtained for the infinitely dilute integral. In addition, the variation of the resonance integral with foil thickness has been measured for thicknesses in the range 0.06 mm to 1.36 mm. A separate study of the half-life of the isomeric state in {sup 94}Nb yielded a value T{sub 1/2} = 6.30 - 0.03 m which is about 5 % lower than the value given in literature. Recommendations concerning magnetic resonance spectroscopy In medicine the technique of nuclear magnetic resonance (NMR) is applied in the form of in vivo nuclear magnetic resonance spectroscopy (MRS). In vivo MRS can be carried out non-invasively. The committee of the Dutch Health Council briefly discusses the qualities and potentialities of the nuclei that will probably be used in future clinical spectroscopy: 31 P, 13 C, 1 H (and possibly 19 F and 23 Na). The committee discusses several possibilities of combining imaging and spectroscopy. The imaging of nuclei other than protons is also possible with MRS. Potential applications are considered in oncology, cardiology, neurology and hepatology. (Auth.) Inelastic scattering in resonant tunneling Wingreen, Ned S.; Jacobsen, Karsten Wedel; Wilkins, John W. The exact resonant-tunneling transmission probability for an electron interacting with phonons is presented in the limit that the elastic coupling to the leads is independent of energy. The phonons produce transmission sidebands but do not affect the integrated transmission probability or the esc......The exact resonant-tunneling transmission probability for an electron interacting with phonons is presented in the limit that the elastic coupling to the leads is independent of energy. The phonons produce transmission sidebands but do not affect the integrated transmission probability... Thermal resonance in signal transmission Reigada, Ramon; Sarmiento, Antonio; Lindenberg, Katja We use temperature tuning to control signal propagation in simple one-dimensional arrays of masses connected by hard anharmonic springs and with no local potentials. In our numerical model a sustained signal is applied at one site of a chain immersed in a thermal environment and the signal-to-noise ratio is measured at each oscillator. We show that raising the temperature can lead to enhanced signal propagation along the chain, resulting in thermal resonance effects akin to the resonance observed in arrays of bistable systems We use temperature tuning to control signal propagation in simple one-dimensional arrays of masses connected by hard anharmonic springs and with no local potentials. In our numerical model a sustained signal is applied at one site of a chain immersed in a thermal environment and the signal-to-noise ratio is measured at each oscillator. We show that raising the temperature can lead to enhanced signal propagation along the chain, resulting in thermal resonance effects akin to the resonance observed in arrays of bistable systems. Coupled-resonator optical waveguides Raza, Søren; Grgic, Jure; Pedersen, Jesper Goor Coupled-resonator optical waveguides hold potential for slow-light propagation of optical pulses. The dispersion properties may adequately be analyzed within the framework of coupled-mode theory. We extend the standard coupled-mode theory for such structures to also include complex-valued paramet......Coupled-resonator optical waveguides hold potential for slow-light propagation of optical pulses. The dispersion properties may adequately be analyzed within the framework of coupled-mode theory. We extend the standard coupled-mode theory for such structures to also include complex... Giant resonances: reaction theory approach Toledo Piza, A.F.R. de; Foglia, G.A. The study of giant resonances through the use of reaction theory approach is presented and discussed. Measurements of cross-sections to the many available decay channels following excitation of giant multipole resonances (GMR) led one to view these phenomena as complicated dynamical syndromes so that theoretical requirements for their study must be extended beyond the traditional bounds of nuclear structure models. The spectra of decay products following GMR excitation in heavy nuclei are well described by statistical model (Hauser-Feshback, HF) predictions indicated that spreading of the collective modes plays a major role in shaping exclusive cross-sections. (A.C.A.S.) [pt Nonlinear phenomena at cyclotron resonance Subbarao, D.; Uma, R. Finite amplitude electromagnetic waves in a magnetoplasma which typically occur in situations as in present day wave heating, current drives and other schemes in magnetically confined fusion systems, can show qualitatively different absorption and emission characteristics around resonant frequencies of the plasma because of anharmonicity. Linear wave plasma coupling as well as weak nonlinear effects such as parametric instabilities generally overlook this important effect even though the thresholds for the two phenomena as shown here are comparable. Though the effects described here are relevant to a host of nonlinear resonance effects in fusion plasmas, the authors mainly limit themselves to ECRH Classical resonances and quantum scarring Manderfeld, Christopher We study the correspondence between phase-space localization of quantum (quasi-)energy eigenstates and classical correlation decay, given by Ruelle-Pollicott resonances of the Frobenius-Perron operator. It will be shown that scarred (quasi-)energy eigenstates are correlated: pairs of eigenstates strongly overlap in phase space (scar in same phase-space regions) if the difference of their eigenenergies is close to the phase of a leading classical resonance. Phase-space localization of quantum states will be measured by L 2 norms of their Husimi functions Migraine and magnetic resonance spectroscopy Younis, Samaira; Hougaard, Anders; Vestergaard, Mark B. Purpose of review: To present an updated and streamlined overview of the metabolic and biochemical aspect of the migraine pathophysiology based on findings from phosphorous (31P) and hydrogen (1H) magnetic resonance spectroscopy (MRS) studies. Recent findings: Despite of the variation in the meth......Purpose of review: To present an updated and streamlined overview of the metabolic and biochemical aspect of the migraine pathophysiology based on findings from phosphorous (31P) and hydrogen (1H) magnetic resonance spectroscopy (MRS) studies. Recent findings: Despite of the variation... Algorithm of resonance orders for the objects Zhang, YongGang; Zhang, JianXue In mechanical engineering, the object resonance phenomena often occur when the external incident wave frequency is close to object of the natural frequency. Object resonance phenomena get the maximum value when the external incident frequency is equal to object the natural frequency. Experiments found that resonance intension of the object is changed, different objects resonance phenomena present different characteristics of ladders. Based on object orders resonance characteristics, the calculation method of object orders resonance is put forward in the paper, and the application for the light and sound waves on the seven order resonance characteristics by people feel, the result error is less than 1%.Visible in this paper, the method has high accuracy and usability. The calculation method reveals that some object resonance occur present order characteristic only four types, namely the first-orders resonance characteristics, third-orders characteristics, five orders characteristic, and seven orders characteristic. Miniaturised self-resonant split-ring resonator antenna Kim, Oleksiy S.; Breinbjerg, Olav at the resonance is governed by the arc length of the monopole. Numerical and experimental results are presented for an antenna configuration of 1/23.4 wavelength in diameter (ka~0.134). The antenna is tuned to 50 ohms without any matching network, and its efficiency is measured to be 17.5%.... Geometrical optics model of Mie resonances Roll; Schweiger The geometrical optics model of Mie resonances is presented. The ray path geometry is given and the resonance condition is discussed with special emphasis on the phase shift that the rays undergo at the surface of the dielectric sphere. On the basis of this model, approximate expressions for the positions of first-order resonances are given. Formulas for the cavity mode spacing are rederived in a simple manner. It is shown that the resonance linewidth can be calculated regarding the cavity losses. Formulas for the mode density of Mie resonances are given that account for the different width of resonances and thus may be adapted to specific experimental situations. Interface losses in multimaterial resonators Villanueva, L.G.; Amato, B.; Larsen, Tom We present an extensive study shedding light on the role of surface and bulk losses in micromechanical resonators. We fabricate thin silicon nitride membranes of different sizes and we coat them with different thicknesses of metal. We later characterize the 81 lowest out-of-plane flexural vibrati... Evanescent Waves Nuclear Magnetic Resonance Halidi, El Mohamed; Nativel, Eric; Akel, Mohamad Nuclear Magnetic Resonance spectroscopy and imaging can be classified as inductive techniques working in the near- to far-field regimes. We investigate an alternative capacitive detection with the use of micrometer sized probes positioned at sub wavelength distances of the sample in order... Jet-associated resonance spectroscopy Englert, Christoph [University of Glasgow, SUPA, School of Physics and Astronomy, Glasgow (United Kingdom); Ferretti, Gabriele [Chalmers University of Technology, Department of Physics, Goeteborg (Sweden); Spannowsky, Michael [Durham University, Department of Physics, Institute for Particle Physics Phenomenology, Durham (United Kingdom) We present a model-independent study aimed at characterising the nature of possible resonances in the jet-photon or jet-Z final state at hadron colliders. Such resonances are expected in many models of compositeness and would be a clear indication of new physics. At leading order, in the narrow width approximation, the matrix elements are parameterised by just a few constants describing the coupling of the various helicities to the resonance. We present the full structure of such amplitudes up to spin 2 and use them to simulate relevant kinematic distributions that could serve to constrain the coupling structure. This also generalises the signal generation strategy that is currently pursued by ATLAS and CMS to the most general case in the considered channels. While the determination of the P/CP properties of the interaction seems to be out of reach within this framework, there is a wealth of information to be gained about the spin of the resonance and the relative couplings of the helicities. (orig.) Trends in resonance ionization spectroscopy Hurst, G.S. The author reviews the history of resonance ionization spectroscopy and then comments on the delineations of RIS with reference to many related laser processes. The substance of the paper deals with the trends in RIS and especially how the needs for sensitive analytical methods have overshadowed the orginal plan to study excited species. 9 refs., 1 fig Full Text Available Toggle navigation Test/Treatment Patient Type Screening/Wellness Disease/Condition Safety En Español More Info Images/Videos About Us News Physician Resources Professions Site Index A-Z Children's (Pediatric) Magnetic Resonance ... Full Text Available Toggle navigation Test/Treatment Patient Type Screening/Wellness Disease/Condition Safety En Español More Info Images/Videos About Us News Physician Resources Professions Site Index A-Z Magnetic Resonance Imaging (MRI) - ... Low field magnetic resonance imaging Pines, Alexander; Sakellariou, Dimitrios; Meriles, Carlos A.; Trabesinger, Andreas H. A method and system of magnetic resonance imaging does not need a large homogenous field to truncate a gradient field. Spatial information is encoded into the spin magnetization by allowing the magnetization to evolve in a non-truncated gradient field and inducing a set of 180 degree rotations prior to signal acquisition. Charmed baryonic resonances in medium Tolos Laura Full Text Available We discuss the behavior of dynamically-generated charmed baryonic resonances in matter within a unitarized coupled-channel model consistent with heavy-quark spin symmetry. We analyze the implications for the formation of D-meson bound states in nuclei and the propagation of D mesons in heavy-ion collisions from RHIC to FAIR energies. Electro-Mechanical Resonance Curves Greenslade, Thomas B., Jr. Recently I have been investigating the frequency response of galvanometers. These are direct-current devices used to measure small currents. By using a low-frequency function generator to supply the alternating-current signal and a stopwatch smartphone app to measure the period, I was able to take data to allow a resonance curve to be drawn. This… Resonance journal of science education. May 2012 Volume 17 Number 5. SERIES ARTICLES. 436 Dawn of Science. The Quest for Power. T Padmanabhan. GENERAL ARTICLES. 441 Bernoulli Runs Using 'Book Cricket' to Evaluate. Cricketers. Anand Ramalingam. 454 Wilhelm Ostwald, the Father of Physical Chemistry. Full Text Available ... Magnetic Resonance Imaging Sponsored by Please note RadiologyInfo.org is not a medical facility. Please contact your ... links: For the convenience of our users, RadiologyInfo .org provides links to relevant websites. RadiologyInfo.org , ACR ... Giant resonances on excited states Besold, W.; Reinhard, P.G.; Toepffer, C. We derive modified RPA equations for small vibrations about excited states. The temperature dependence of collective excitations is examined. The formalism is applied to the ground state and the first excited state of 90 Zr in order to confirm a hypothesis which states that not only the ground state but every excited state of a nucleus has a giant resonance built upon it. (orig.) Biosensing by WGM Microspherical Resonators Giancarlo C. Righini Full Text Available Whispering gallery mode (WGM microresonators, thanks to their unique properties, have allowed researchers to achieve important results in both fundamental research and engineering applications. Among the various geometries, microspheres are the simplest 3D WGM resonators; the total optical loss in such resonators can be extremely low, and the resulting extraordinarily high Q values of 108–109 lead to high energy density, narrow resonant-wavelength lines and a lengthy cavity ringdown. They can also be coated in order to better control their properties or to increase their functionality. Their very high sensitivity to changes in the surrounding medium has been exploited for several sensing applications: protein adsorption, trace gas detection, impurity detection in liquids, structural health monitoring of composite materials, detection of electric fields, pressure sensing, and so on. In the present paper, after a general introduction to WGM resonators, attention is focused on spherical microresonators, either in bulk or in bubble format, to their fabrication, characterization and functionalization. The state of the art in the area of biosensing is presented, and the perspectives of further developments are discussed. RESONANCE--I-Ju-ne I read the above article in the Classroom Section of the March 2006 issue of Resonance with great interest, but was disappointed at the end. The problem investigated is an ... In our article, we have shown that the approach in solving of this problem is not correct. In a typical RC circuit, value of inductance is taken as zero, ... Full Text Available Toggle navigation Test/Treatment Patient Type Screening/Wellness Disease/Condition Safety En Español More Info Images/Videos About Us News Physician ... Magnetic resonance imaging (MRI) is a noninvasive medical test that physicians use to diagnose medical conditions. MRI ... Full Text Available ... structures of the brain and can also provide functional information (fMRI) in selected cases. MR images of ... Articles and Media MR Angiography (MRA) Magnetic Resonance, Functional (fMRI) - Brain Head and Neck Cancer Treatment Brain ... Model for resonant plasma probe. Warne, Larry Kevin; Johnson, William Arthur; Hebner, Gregory Albert; Jorgenson, Roy E.; Coats, Rebecca Sue This report constructs simple circuit models for a hairpin shaped resonant plasma probe. Effects of the plasma sheath region surrounding the wires making up the probe are determined. Electromagnetic simulations of the probe are compared to the circuit model results. The perturbing effects of the disc cavity in which the probe operates are also found. Resonance journal of science education. July 2007 Volume 12 Number 7. GENERAL ARTICLES. 04 Josiah Willard Gibbs. V Kumaran. 12 Josiah Willard ... IISc, Bangalore). Rapidity: The Physical Meaning of the Hyperbolic Angle in. Special Relativity. Giorgio Goldoni. Survival in Stationary Phase. S Mahadevan. Classroom. Full Text Available ... of which shows a thin slice of the body. The images can then be studied from different angles by ... about radiology? Share your patient story here Images ... Articles and Media Catheter Angiography Magnetic Resonance, Functional (fMRI) - Brain Children's ( ... Tuning Fano Resonances with Graphene Emani, Naresh K.; Chung, Ting-Fung; Prokopeva, Ludmila We demonstrate strong electrical control of plasmonic Fano resonances in dolmen structures using tunable interband transitions in graphene. Such graphene-plasmonic hybrid devices can have applications in light modulation and sensing. OCIS codes: (250.5403) Plasmonics; (160.4670) Optical materials... Resonance journal of science education. February 2012 Volume 17 Number 2. SERIES ARTICLES. 106 Dawn of Science. Calculus is Developed in Kerala. T Padmanabhan. GENERAL ARTICLES. 117 Willis H Carrier: Father of Air Conditioning. R V Simha. 139 Refrigerants For Vapour Compression Refrigeration. Systems. Englert, Christoph; Ferretti, Gabriele; Spannowsky, Michael We present a model-independent study aimed at characterising the nature of possible resonances in the jet-photon or jet- Z final state at hadron colliders. Such resonances are expected in many models of compositeness and would be a clear indication of new physics. At leading order, in the narrow width approximation, the matrix elements are parameterised by just a few constants describing the coupling of the various helicities to the resonance. We present the full structure of such amplitudes up to spin 2 and use them to simulate relevant kinematic distributions that could serve to constrain the coupling structure. This also generalises the signal generation strategy that is currently pursued by ATLAS and CMS to the most general case in the considered channels. While the determination of the P/CP properties of the interaction seems to be out of reach within this framework, there is a wealth of information to be gained about the spin of the resonance and the relative couplings of the helicities. Double Fano resonances in plasmon coupling nanorods Liu, Fei; Jin, Jie Fano resonances are investigated in nanorods with symmetric lengths and side-by-side assembly. Single Fano resonance can be obtained by a nanorod dimer, and double Fano resonances are shown in nanorod trimers with side-by-side assembly. With transverse plasmon excitation, Fano resonances are caused by the destructive interference between a bright superradiant mode and dark subradiant modes. The bright mode originates from the electric plasmon resonance, and the dark modes originate from the magnetic resonances induced by near-field inter-rod coupling. Double Fano resonances result from double dark modes at different wavelengths, which are induced and tuned by the asymmetric gaps between the adjacent nanorods. Fano resonances show a high figure of merit and large light extinction in the periodic array of assembled nanorods, which can potentially be used in multiwavelength sensing in the visible and near-infrared regions. (paper) Resonance – Journal of Science Education \| News Home; Journals; Resonance – Journal of Science Education. Website Reviews. Articles in Resonance – Journal of Science Education. Volume 4 Issue 8 August 1999 pp 91-93 Website Reviews. Website Review · Harini Nagendra · More Details Fulltext PDF ... Magnetic Resonance Imaging (MRI): Brain (For Parents) ... Staying Safe Videos for Educators Search English Español Magnetic Resonance Imaging (MRI): Brain KidsHealth / For Parents / Magnetic Resonance Imaging (MRI): Brain What's in this article? What ... High quality-factor optical resonators Henriet, Rémi; Salzenstein, Patrice; Coillet, Aurélien; Saleh, Khaldoun; Chembo, Yanne K; Ristic, Davor; Ferrari, Maurizio; Mortier, Michel; Rasoloniaina, Alphonse; Dumeige, Yannick; Féron, Patrice; Cibiel, Gilles; Llopis, Olivier Various resonators are investigated for microwave photonic applications. Micro-sphere, disk and fiber ring resonators were designed, realized and characterized. Obtained quality factors are as high as QÂ =Â 10 10 . (paper) Advances in magnetic and optical resonance Warren, Warren S Since 1965, Advances in Magnetic and Optical Resonance has provided researchers with timely expositions of fundamental new developments in the theory of, experimentation with, and application of magnetic and optical resonance. Highly Tunable Electrothermally Actuated Arch Resonator Hajjaj, Amal Z.; Ramini, Abdallah; Alcheikh, Nouha; Younis, Mohammad I. that after some electro-thermal voltage load, the third resonance frequency starts to become more sensitive to the axial thermal stress, while the first resonance frequency becomes less sensitive. These results can be used as guidelines to utilize arches Resonance formation in photon-photon collisions Gidal, G. Recent experimental progress on resonance formation in photon-photon collisions is reviewed with particular emphasis on the pseudoscalar and tensor nonents and on the γγ production of spin-one resonances. 37 refs., 17 figs., 5 tabs Electrically Tunable Plasmonic Resonances with Graphene Emani, Naresh K.; Chung, Ting-Fung; Ni, Xingjie Real time switching of a plasmonic resonance may find numerous applications in subwavelength optoelectronics, spectroscopy and sensing. We take advantage of electrically tunable interband transitions in graphene to control the strength of the plasmonic resonance.......Real time switching of a plasmonic resonance may find numerous applications in subwavelength optoelectronics, spectroscopy and sensing. We take advantage of electrically tunable interband transitions in graphene to control the strength of the plasmonic resonance.... Resonant acoustic radiation force optical coherence elastography Qi, Wenjuan; Li, Rui; Ma, Teng; Li, Jiawen; Kirk Shung, K.; Zhou, Qifa; Chen, Zhongping We report on a resonant acoustic radiation force optical coherence elastography (ARF-OCE) technique that uses mechanical resonant frequency to characterize and identify tissues of different types. The linear dependency of the resonant frequency on the square root of Young's modulus was validated on silicone phantoms. Both the frequency response spectrum and the 3D imaging results from the agar phantoms with hard inclusions confirmed the feasibility of deploying the resonant frequency as a mec... Resonance phenomena at high level density Sobeslavsky, E.; Dittes, F.M.; Rotter, I.; Technische Univ. Dresden We investigate the behaviour of resonances as a function of the coupling strength between bound and unbound states on the basis of a simple S-matrix model. Resonance energies and widths are calculated for well isolated, overlapping and strongly overlapping resonance states. The formation of shorter and longer time scales (trapping effect) is traced. We illustrate that the cross section results from an interference of all resonance states in spite of the fact that their lifetimes may be very different. (orig.) Magnetic resonance for wireless power transfer Hui, SYR Magnetic resonance has been a cornerstone of nonradiative wireless power transfer (WPT) since the late 19th century. However, some researchers have the misconception that magnetic resonance for WPT was developed recently. This article traces some early work of Tesla and other researchers related to the use of magnetic resonance in WPT. Included are some examples of magnetic resonance-based WPT projects conducted by researchers in the biomedical and power electronics communities over the last ... Noise in nonlinear nanoelectromechanical resonators Guerra Vidal, Diego N. Nano-Electro-Mechanical Systems (NEMS), due to their nanometer scale size, possess a number of desirable attributes: high sensitivity to applied forces, fast response times, high resonance frequencies and low power consumption. However, ultra small size and low power handling result in unwanted consequences: smaller signal size and higher dissipation, making the NEMS devices more susceptible to external and intrinsic noise. The simplest version of a NEMS, a suspended nanomechanical structure with two distinct excitation states, can be used as an archetypal two state system to study a plethora of fundamental phenomena such as Duffing nonlinearity, stochastic resonance, and macroscopic quantum tunneling at low temperatures. From a technical perspective, there are numerous applications such nanomechanical memory elements, microwave switches and nanomechanical computation. The control and manipulation of the mechanical response of these two state systems can be realized by exploiting a (seemingly) counterintuitive physical phenomenon, Stochastic Resonance: in a noisy nonlinear mechanical system, the presence of noise can enhance the system response to an external stimulus. This Thesis is mainly dedicated to study possible applications of Stochastic Resonance in two-state nanomechanical systems. First, on chip signal amplification by 1/falpha is observed. The effectiveness of the noise assisted amplification is observed to decrease with increasing a. Experimental evidence shows an increase in asymmetry between the two states with increasing noise color. Considering the prevalence of 1/f alpha noise in the materials in integrated circuits, the signal enhancement demonstrated here, suggests beneficial use of the otherwise detrimental noise. Finally, a nanomechanical device, operating as a reprogrammable logic gate, and performing fundamental logic functions such as AND/OR and NAND/NOR is presented. The logic function can be programmed (from AND to OR) dynamically, by Parametric resonance in neutrino oscillations in matter Neutrino oscillations in matter can exhibit a specific resonance enhancement - parametric resonance, which is different from the MSW resonance. Oscillations of atmospheric and solar neutrinos inside the earth can undergo parametric enhancement when neutrino trajectories cross the core of the earth. In this paper we ... Projection operator treatment of single particle resonances Lev, A.; Beres, W.P. A projection operator method is used to obtain the energy and width of a single particle resonance. The resonance energy is found without scanning. An example of the first g/sub 9/2/ neutron resonance in 40 Ca is given and compared with the traditional phase shift method. The results of both approaches are quite similar. 4 figures Interactions among resonances in the unresolved region Queiroz Bogado Leite, S. de. The theory on resonance absorption in the unresolved region is reviewed and a subroutine is presented, optional to UNRES in MC 2 code. Comparisons with the isolated resonance model suggest the necessity, in some cases, of considering interference and overlapping effects among resonances of the system. (Author) [pt Giant multipole resonances: perspectives after ten years Bertrand, F.E. Nearly ten years ago evidence was published for the first of the so-called giant multipole resonances, the giant quadrupole resonance. During the ensuing years research in this field has spread to many nuclear physics laboratories throughout the world. The present status of electric giant multipole resonances is reviewed. 24 figures, 1 table Review of 241 Pu resonance parameters Derrien, H. The status of 241 Pu resonance parameters is reviewed. The most important recent results are compared in some energy ranges, both from single level and multilevel point of view. It appears that an accurate set of resonance parameters is not still obtained for a general description of the cross-sections in the resonance region. Some recommendations are given for further experiments or evaluations Observation of pulsed neutron Ramsey resonance Masuda, Y. [High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba Ibaraki 305-0801 (Japan)]. E-mail: [email protected]; Skoy, V. [Joint Institute for Nuclear Reasearch, 141980 Dubna, Moscow Region (Russian Federation); Ino, T. [High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba Ibaraki 305-0801 (Japan); Jeong, S.C. [High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba Ibaraki 305-0801 (Japan); Watanabe, Y. [High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba Ibaraki 305-0801 (Japan) A Ramsey resonance for pulsed neutrons was observed. The separated oscillatory fields for nuclear magnetic resonance were synchronized with a neutron pulse, and then the Ramsey resonance was observed as a function of the neutron velocity. The phase of one of the oscillatory fields was modulated as a function of the neutron time of flight for a neutron velocity measurement. Depolarization due to the resonance tail during a fast resonance jump Ruth, R.D. The mechanism of depolarization due to a fast resonance jump is studied. The dominant effect for cases of interest is not dependent on the rate of passage through resonance, but rather on the size of the resonance jump as compared to the width, epsilon, of the resonance. The results are applied to a calculation of depolarization in the AGS at Brookhaven National Laboratory Numerical simulation of laser resonators Yoo, J. G.; Jeong, Y. U.; Lee, B. C.; Rhee, Y. J.; Cho, S. O. We developed numerical simulation packages for laser resonators on the bases of a pair of integral equations. Two numerical schemes, a matrix formalism and an iterative method, were programmed for finding numeric solutions to the pair of integral equations. The iterative method was tried by Fox and Li, but it was not applicable for high Fresnel numbers since the numerical errors involved propagate and accumulate uncontrollably. In this paper, we implement the matrix method to extend the computational limit further. A great number of case studies are carried out with various configurations of stable and unstable r;esonators to compute diffraction losses, phase shifts, intensity distributions and phases of the radiation fields on mirrors. Our results presented in this paper show not only a good agreement with the results previously obtained by Fox and Li, but also the legitimacy of our numerical procedures for high Fresnel numbers. A cyclotron resonance laser accelerator Sprangle, P.; Tang, C.M.; Vlahos, L. A laser acceleration mechanism which utilizes a strong static, almost uniform, magnetic field together with an intense laser pulse is analyzed. The interaction and acceleration mechanism relies on a self resonance effect. Since the laser field is assumed to be diffraction limited, the magnetic field must be spatially varied to maintain resonance. The effective accelerating gradient is shown to scale like 1/√E /SUB b/ , where E /SUB b/ is the electron energy. For a numerical illustration the authors consider a 1 x 10 13 W/cm 2 , CO 2 laser and show that electrons can be accelerated to more than 500 MeV in a distance of 15 m (approximately two Rayleigh lengths) Protein folding and wring resonances Bohr, Jakob; Bohr, Henrik; Brunak, Søren The polypeptide chain of a protein is shown to obey topological contraints which enable long range excitations in the form of wring modes of the protein backbone. Wring modes of proteins of specific lengths can therefore resonate with molecular modes present in the cell. It is suggested that prot......The polypeptide chain of a protein is shown to obey topological contraints which enable long range excitations in the form of wring modes of the protein backbone. Wring modes of proteins of specific lengths can therefore resonate with molecular modes present in the cell. It is suggested...... that protein folding takes place when the amplitude of a wring excitation becomes so large that it is energetically favorable to bend the protein backbone. The condition under which such structural transformations can occur is found, and it is shown that both cold and hot denaturation (the unfolding... Improving the wide resonance approximation Aboustta, Mohamed A.; Martinez, Aquilino S. A resonance is considered wide if its practical width, in energy, exceeds the average energy loss per collision, E(1-α A )/2, of the absorbing material. When the mass number, A, is taken infinite, the scattering produces only a change in the direction of motion of the neutron and not in its energy. Based on this assumption, the integral in the slowing-down equation describing the contribution of the resonant absorber is evaluated by taking its limit when α A →1. This work questions the necessity to take such a limit and shows that it is still possible to obtain a simple and more accurate expression for the integral without taking such limit Aboustta, Mohamed A.; Martinez, Aquilino S A resonance is considered wide if its practical width, in energy, exceeds the average energy loss per collision, E(1-{alpha}{sub A})/2, of the absorbing material. When the mass number, A, is taken infinite, the scattering produces only a change in the direction of motion of the neutron and not in its energy. Based on this assumption, the integral in the slowing-down equation describing the contribution of the resonant absorber is evaluated by taking its limit when {alpha}{sub A}{yields}1. This work questions the necessity to take such a limit and shows that it is still possible to obtain a simple and more accurate expression for the integral without taking such limit. Principles of magnetic resonance imaging Mlynarik, V.; Tkac, I.; Srbecky, M. The aim of this review is to describe and explain the basic principles of magnetic resonance imaging. The first part of the text is devoted to the phenomenon of magnetic resonance (the interaction of RF magnetic field with the set of magnetic moments in the homogeneous magnetic field) and to relaxation processes. Then, the creation of MR image is described (slice selection, phase and frequency encoding of spatial information). The basic and the most frequently used techniques are explained (spin echo, gradient echo). The way the repetition and echo times influence the image quality and contrast (T1 or T2 weighing) is described. The part with the technical description of the MR equipment is included in the review. The MR imagination examination are compared with X-ray computer tomography technique Resonant quasiparticles in plasma turbulence Mendonca, J.T.; Bingham, R.; Shukla, P.K. A general view is proposed on wave propagation in fluids and plasmas where the resonant interaction of monochromatic waves with quasiparticles is considered. A kinetic equation for quasiparticles is used to describe the broadband turbulence interacting with monochromatic waves. Resonant interactions occur when the phase velocity of the long wavelength monochromatic wave is nearly equal to the group velocity of short wavelength wave packets, or quasiparticles, associated with the turbulent spectrum. It is shown that quasiparticle Landau damping can take place, as well as quasiparticle beam instabilities, thus establishing a direct link between short and large wavelength perturbations of the medium. This link is distinct from the usual picture of direct and inverse energy cascades, and it can be used as a different paradigm for the fluid and plasma turbulence theories Limits to magnetic resonance microscopy Glover, Paul; Mansfield, Peter The last quarter of the twentieth century saw the development of magnetic resonance imaging (MRI) grow from a laboratory demonstration to a multi-billion dollar worldwide industry. There is a clinical body scanner in almost every hospital of the developed nations. The field of magnetic resonance microscopy (MRM), after mostly being abandoned by researchers in the first decade of MRI, has become an established branch of the science. This paper reviews the development of MRM over the last decade with an emphasis on the current state of the art. The fundamental principles of imaging and signal detection are examined to determine the physical principles which limit the available resolution. The limits are discussed with reference to liquid, solid and gas phase microscopy. In each area, the novel approaches employed by researchers to push back the limits of resolution are discussed. Although the limits to resolution are well known, the developments and applications of MRM have not reached their limit. (author) Simultaneous electrical and mechanical resonance drive for large signal amplification of micro resonators Hasan, M. H. Achieving large signal-noise ratio using low levels of excitation signal is key requirement for practical applications of micro and nano electromechanical resonators. In this work, we introduce the double electromechanical resonance drive concept to achieve an order-of-magnitude dynamic signal amplification in micro resonators. The concept relies on simultaneously activating the micro-resonator mechanical and electrical resonance frequencies. We report an input voltage amplification up to 15 times for a micro-resonator when its electrical resonance is tuned to match the mechanical resonance that leads to dynamic signal amplification in air (Quality factor enhancement). Furthermore, using a multi-frequency excitation technique, input voltage and vibrational amplification of up to 30 times were shown for the same micro-resonator while relaxing the need to match its mechanical and electrical resonances. Hasan, M. H.; Alsaleem, F. M.; Jaber, Nizar; Hafiz, Md Abdullah Al; Younis, Mohammad I. Dating by electron paramagnetic resonance Poupeau, G.; Rossi, A.M. Some natural materials behave like dosimeters in front of the ionizing particle flux coming from environmental radioactivity and the cosmic radiation. This property is used for the dating by Electron Paramagnetic Resonance (EPR). Before presenting the basic principles of the EPR analysis and the dating method which uses such a phenomenous, it is reviewed several types of application currently in course of development. (L.C.) [pt Pole counting and resonance classification Morgan, D. S-wave resonances occurring close to an inelastic threshold can be classified according to the number of nearby poles they possess. One then has a useful possibility of distinguishing dynamical alternatives by objective appeal to data. Making this quantitative entails developing suitable effective range expansions for various realizations of potential scattering. A key application is deciding the make-up of f 0 (976) (S). (author) Dynamic control of chaotic resonators Di Falco, A.; Bruck, R.; Liu, C.; Muskens, O.; Fratalocchi, Andrea We report on the all-optical control of chaotic optical resonators based on silicon on insulator (SOI) platform. We show that simple non-chaotic cavities can be tuned to exhibit chaotic behavior via intense optical pump- ing, inducing a local change of refractive index. To this extent we have fabricated a number of devices and demonstrated experimentally and theoretically that chaos can be triggered on demand on an optical chip. © 2016 SPIE. Nucleon Resonance Transition Form factors Burkert, Volker D. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Mokeev, Viktor I. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Aznauryan, Inna G. [Yerevan Physics Inst. (YerPhI) (Armenia) We discuss recent results from CLAS on electromagnetic resonance transition amplitudes and their dependence on the distance scale (Q2). From the comparison of these results with most advanced theoretical calculations within QCD-based approaches there is clear evidence that meson-baryon contributions are present and important at large distances, i.e. small Q2, and that quark core contributions dominate the short distance behavior. Nuclear quadrupole resonance of arsenolite Madarazo, R. A pulsed Nuclear Quadrupole Resonance (NQR) spectrometer was constructed using imported Matec units. Peripherical components were specially assembled and tested for the implantation of the spin-echo technique in the Laboratorio de Centros de Cor of IFUSP. The R.F. operation range is from 50 to 1 ) and spin-spin (T 2 ) relaxation times were carried out at room temperature in arsenolite. The 75 As NQR frequency measured at room temperature is 116.223 MHz. (author) [pt Parity violation in neutron resonances Mitchell, G.E.; Lowie, L.Y.; Bowman, J.D.; Knudson, J.; Crawford, B.E.; Delheij, P.P.J.; Haseyama, T.; Masaike, A.; Matsuda, Y.; Masuda, Y. The observation of very large parity violation in neutron resonances has led to a new approach to the study of symmetry breaking in nuclei. The origin of the enhancement of parity violation is discussed, as well as the new (statistical) analysis approach. The TRIPLE experimental system and analysis methods, their improvements are described. Sign correlation and results from recent parity violation experiments are presented and discussed. (author) Magnetic resonance and its applications Chizhik, Vladimir I; Donets, Alexey V; Frolov, Vyacheslav V; Komolkin, Andrei V; Shelyapina, Marina G The book provides a basic understanding of the underlying theory, fundamentals and applications of magnetic resonance The book implies a few levels of the consideration (from simple to complex) of phenomena, that can be useful for different groups of readers The introductory chapter provides the necessary underpinning knowledge for newcomers to the methods The exposition of theoretical materials goes from initial to final formulas through detailed intermediate expressions. Capacitance of circular patch resonator Miano, G.; Verolino, L.; Naples Univ.; Panariello, G.; Vaccaro, V.G.; Naples Univ. In this paper the capacitance of the circular microstrip patch resonator is computed. It is shown that the electrostatic problem can be formulated as a system of dual integral equations, and the most interesting techniques of solutions of these systems are reviewed. Some useful approximated formulas for the capacitance are derived and plots of the capacitance are finally given in a wide range of dielectric constants Radiative widths of resonances (experiments) After a hiatus of several years, this conference brings us considerable new data on resonance production in photon photon interactions. I will first discuss the contributions concerning the tensor, pseudoscalar and scalar mesons, then review the current status of the (c/ovr string/c /eta//sub c/) and finally summarize the exciting new results concerning the spin 1 mesons. 40 refs., 21 figs., 7 tabs Proton Resonance Spectroscopy -- Final Report Shriner, Jr., J. F. [Tennessee Technological Univ., Cookeville, TN (United States) This report summarizes work supported by the DOE Grant DE-FG02-96ER40990 during its duration from June 1996 to May 2009. Topics studied include (1) statistical descriptions of nuclear levels and measurements of proton resonances relevant to such descriptions, including measurements toward a complete level scheme for 30P, (2) the development of methods to estimate the missing fraction of levels in a given measurement, and (3) measurements at HRIBF relevant to nuclear astrophysics. Di Falco, A. Excitation of giant resonances in heavy ion collisions Kuehn, W. Introduction: What are Giant Resonances? General Features of Giant Resonances, Macroscopic Description and Classification, Basic Excitation Mechanisms, Decay Modes, Giant Resonances Built on Excited States, Relativistic Coulomb Excitation of Giant Resonances, Experimental Situation. (orig.) Determination of giant resonance strengths Serr, F.E. Using theoretical strength functions to describe the different giant resonances expected at excitation energies of the order of (60-85)/Asup(1/3) MeV, we calculate the double differential cross sections d 2 sigma/dΩ dE associated with the reactions 208 Pb(α, α') and 90 Zr(α, α') (Esub(α) = 152 MeV). The angular distributions for the giant quadrupole and giant monopole resonances obtained from fits to these spectra, making simple, commonly used assumptions for the peak shapes and background, are compared to the original angular distributions. The differences between them are an indication of some of the uncertainties affecting the giant resonance strengths extracted from hadron inelastic scattering data. Fits to limited angular regions lead to errors of up to 50% in the value of the energy-weighted sum rule, depending on the angles examined. While it seems possible to extract the correct EWSR for the GMR by carrying out the analyses at 0 0 , no single privileged angle seems to exist in the case of the GQR. (orig.) Electromagnetic decay of giant resonances Beene, J.R.; Bertrand, F.E.; Halbert, M.L.; Auble, R.L.; Hensley, D.C.; Horen, D.J.; Robinson, R.L.; Sayer, R.O.; Sjoreen, T.P. Coincidence experiments were done to investigate the photon and neutron emission from the giant resonance regions of 208 Pb and 90 Zr using the ORNL Spin Spectrometer, a 72-segment NaI detector system. We have determined the total gamma-decay probability, the ground-state gamma branching ratio, and the branching ratios to a number of low-lying states as a function of excitation energy in 208 Pb to approx.15 MeV. Similar data were also obtained on 90 Zr. The total yield of ground-state E2 gamma radiation in 208 Pb and the comparative absence of such radiation in 90 Zr can only be understood if decay of compound (damped) states is considered. Other observations in 208 Pb include the absence of a significant branch from the giant quadrupole resonance (GQR) to the 3 - state at 2.6 MeV, a strong branch to a 3 - state at 4.97 MeV from the same region, and transitions to various 1 - states between 5 to 7 MeV from the E approx. 14 MeV region (EO resonance) Giant multipole resonances: an experimental review During the past several years experimental evidence has been published for the existance of nondipole giant resonances. These giant multipole resonances, the so-called new giant resonances were first observed through inelastic hadron and electron scattering and such measurements have continued to provide most of the information in this field. A summary is provided of the experimental evidence for these new resonances. The discussion deals only with results from inelastic scattering and only with the electric multipoles. Emphasis is placed on the recent observations of the giant monopole resonance. Results from recent heavy-ion and pion inelastic scattering are discussed. 38 references Extraordinary acoustic transmission mediated by Helmholtz resonators Vijay Koju Full Text Available We demonstrate perfect transmission of sound through a rigid barrier embedded with Helmholtz resonators. The resonators are confined within a waveguide and they are oriented such that one neck protrudes onto each side of the barrier. Perfect sound transmission occurs even though the open area of the necks is less than 3% of the barrier area. Maximum transmission occurs at the resonant frequency of the Helmholtz resonator. Because the dimensions of the Helmholtz resonators are much smaller than the resonant wavelength, the transmission is independent of the direction of sound on the barrier and of the relative placement of the necks. Further, we show that the transmitted sound experiences a continuous phase transition of π radians as a function of frequency through resonance. In simulations of adjacent resonators with slightly offset resonance frequencies, the phase difference leads to destructive interference. By expanding the simulation to a linear array of tuned Helmholtz resonators we show that it is possible to create an acoustic lens. The ability of Helmholtz resonator arrays to manipulate the phase of a plane acoustic wave enables a new class of sonic beam-forming devices analogous to diffractive optics. Spin with two snakes and overlapping resonances Lee, S.Y.; Zhao, X.F. We study the effect of multiple spin depolarization resonances on the spin of the particles with two snakes. When two resonances are well separated, the polarization can be restored in passing through these resonances provided that the snake resonances are avoided. When two resonances are overlapping, the beam particles may be depolarized depending on the spacing between these two resonances. If the spacing between these two resonances is an odd number for two snakes, the beam particles may be depolarized depending on the strength of the resonance. When the spacing becomes an even number, the spin can tolerate a much larger resonance strength without depolarization. Numerical simulations can be shown to agree well with the analytic formula. However, the spin is susceptible to the combination of an intrinsic and an imperfection resonances even in the presence of the snakes. Numerical simulation indicates that the spin can be restored after the resonances provided that imperfection strength is less than 0.1 if intrinsic strength is fixed at 0.745 Resonance sensitivity of hydropower and pumping stations Popescu, M.; Halanay, A. Comparative analysis of resonance diagrams for several hydropower and pumping stations with surge tanks and air chambers shows large differences in the maximum resonance pressures. A strategy is advocated which consists of hydraulic resonance computations coupled with practical surveillance measures during the operation of resonance sensitive hydraulic systems. A fundamental hydraulic scheme is considered consisting of a reservoir, a pressure tunnel, a surge tank, a penstock and a turbine combined into a hydropower station. It is suggested that for each hydraulic surge system it is necessary to carry out special resonance analyses following the normal procedure to obtain the resonance sensitivity. For hydraulic systems which are resonance sensitive, mechanical electronic equipment should be used to measure non-stationary pressures of the water in the conduit as a way of continuous surveillance during functioning. 6 references, 6 figures. Quantum Graphs And Their Resonance Properties Lipovsky, J. In the current review, we study the model of quantum graphs. We focus mainly on the resonance properties of quantum graphs. We define resolvent and scattering resonances and show their equivalence. We present various results on the asymptotics of the number of resolvent resonances in both non-magnetic and magnetic quantum graphs and find bounds on the coefficient by the leading term of the asymptotics. We explain methods how to find the spectral and resonance condition. Most of the notions and theorems are illustrated in examples. We show how to find resonances numerically and, in a simple example, we find trajectories of resonances in the complex plane. We discuss Fermi's golden rule for quantum graphs and distribution of the mean intensity for the topological resonances. (author) Advances in mechanical detection of magnetic resonance Kuehn, Seppe; Hickman, Steven A.; Marohn, John A. The invention and initial demonstration of magnetic resonance force microscopy (MRFM) in the early 1990s launched a renaissance of mechanical approaches to detecting magnetic resonance. This article reviews progress made in MRFM in the last decade, including the demonstration of scanned probe detection of magnetic resonance (electron spin resonance, ferromagnetic resonance, and nuclear magnetic resonance) and the mechanical detection of electron spin resonance from a single spin. Force and force-gradient approaches to mechanical detection are reviewed and recent related work using attonewton sensitivity cantilevers to probe minute fluctuating electric fields near surfaces is discussed. Given recent progress, pushing MRFM to single proton sensitivity remains an exciting possibility. We will survey some practical and fundamental issues that must be resolved to meet this challenge. Optical Microspherical Resonators for Biomedical Sensing Full Text Available Optical resonators play an ubiquitous role in modern optics. A particular class of optical resonators is constituted by spherical dielectric structures, where optical rays are total internal reflected. Due to minimal reflection losses and to potentially very low material absorption, these guided modes, known as whispering gallery modes, can confer the resonator an exceptionally high quality factor Q, leading to high energy density, narrow resonant-wavelength lines and a lengthy cavity ringdown. These attractive characteristics make these miniaturized optical resonators especially suited as laser cavities and resonant filters, but also as very sensitive sensors. First, a brief analysis is presented of the characteristics of microspherical resonators, of their fabrication methods, and of the light coupling techniques. Then, we attempt to overview some of the recent advances in the development of microspherical biosensors, underlining a number of important applications in the biomedical field. Modeling of supermodes in coupled unstable resonators Townsend, S.S. A general formalism describing the supermodes of an array of N identical, circulantly coupled resonators is presented. The symmetry of the problem results in a reduction of the N coupled integral equations to N decoupled integral equations. Each independent integral equation defines a set of single-resonator modes derived for a hypothetical resonator whose geometry resembles a member of the real array with the exception that all coupling beams are replaced by feedback beams, each with a prescribed constant phase. A given array supermode consists of a single equivalent resonator mode appearing repetitively in each resonator with a prescribed relative phase between individual resonators. The specific array design chosen for example is that of N adjoint coupled confocal unstable resonators. The impact of coupling on the computer modeling of this system is discussed and computer results for the cases of two- and four-laser coupling are presented Forest fires have occurred across the globe at various times ... thought to have impacts on the ecology of plants and ... the soil and finally when it comes in contact with forest litter it .... UNDAC: United Nations Disaster Assessment Committee .... [2] Stephen J Pyne, America's Fire Management on Wildlands and Forests, ... Teaching and Learning 'Genetics with Drosophila. 3. Pattern of Inheritance of Autosome and Sex . Chromosome Linked Genes/Characters. Phenotypic characters or traits are determined by genes, and genes are physically located on different chromosomes. This is the basic tenet of the chromosomal theory of inheritance. Seymour Cray's idea was to build a 'balanced system', that is, a system whose ... operations per second in order to solve problems such as .... This is called a uniform address space and the time to access a .... CEs and managing message routing between CEs. .... which contains user callable routines for message passing,. To the extent that genes influence our behaviour it may well be that our ... other by a coefficient of genetic relatedness r of 0.75 but a female. Figure 1. ... cal and empirical work. ... rather famous one is called PSR, for paternally transmitted sex ... Life cycle of ... Genic balance sex determination (GBSD): According to this model ... one can ever be sure, of course, but it is possible that Einstein was as much hated as ... of thought, which is not to say one is better or worse than the other, of course. ... being passed over when assistantships at the University were offered to his ..... young men to refuse military service, provoking the hostility of nationalists in ... small bar magnets. NMR spectroscopy .... that the integrated area for the methylene .... in a network of spins. .... Schematic representation of the type of short (broken arrows) and medium-range .... we can define between cities and towns in the. born intoa mathematical family, (herfatherwasawell known mathematician), shehadto rebel ... ~mmy had to take special permission to be admitted as an auditor in ... She started working atthe Mathematical Institute at Erlangen without a formal ... Refresher Course in. Experimental Physics. Refresher Course on. Advanced in Biophysics. IISc Young Science. Fellowship Programme. Inside Back Cover. Flowering Trees. (Credit: K Sankara Rao,IISc,. Bangalore). 97. 83. Classics. REFLECTIONS. 71 Integrative Microbiology – The Third Golden Age. Moselio Schaechter. The Wright brothers were from a low middle class family and their formal education did not go beyond high school, and though each spent the time for a ... concealed is his hands, and before we ... sublime disregard for science, at once dubbed ... Magnetic resonance tomography in syringomyelia Koehler, D.; Treisch, J.; Hertel, G.; Schoerner, W.; Fiegler, W.; Staedtisches Rudolf-Virchow Krankenhaus, Berlin Thirteen patients with a clinical diagnosis of syringomyelia were examined by nuclear tomography (0.35 T magnet) in the spin-echo mode. In all thirteen patients, the T1 images (Se 400/35) showed a longitudinal cavity with a signal intensity of CSF. The shape and extent of the syrinx could be adequately demonstrated in 12 of the 13 examinations. Downward displacement of the cerebellar tonsils was seen in eight cases. The examination took between half and one hour. Advantages of magnetic resonance tomography (nuclear tomography) include the absence of artifacts, images in the line of the lesion and its non-invasiveness. (orig.) [de Multimachine subsynchronous resonance: Pt. 2 Lahoud, M.A.; Harley, R.G.; Levy, D.C. This paper describes a theoretical investigation into the subsynchronous resonance (SSR) behaviour of a power system containing synchronous generators, induction motors and series capacitors. By applying eigenvalue techniques, attention is paid to the effect of replacing the induction motor by an equivalent fixed resistor-inductor (R-L) load. Nonlinear transient simulations and their Fast Fourier Transforms (FFT's) are also used to investigate the effects of the complexity of the mechanical model of the generator on the SSR predictions. The results show that the model used for the induction motor has a significant effect on the SSR behaviour of a multimachine system Linear resonance acceleration of pellets Mills, R.G. A possible requirement for the acceleration of macroscopic pellets to velocities exceeding 10 4 meters per second implies the development of new apparatus. A satisfactory approach might be the linear resonance accelerator. Such apparatus would require the charging of pellets to very high values not yet demonstrated. The incompatibility of phase stability with radial stability in these machines may require abandoning phase stability and adopting feedback control of the accelerating voltage to accommodate statistical fluctuations in the charge to mass ratio of successive pellets Magnetic resonance imaging at Rikshospitalet Smith, H.J. During the first 18 months of operations of the nuclear magnetic resonance (NMR) unit at Rikshospitalet, 1453 NMR examinations have been performed on 1431 patients. 64% of the time has been devoted to examinations of the central nervous system and spine in children and adults, 9% of the time has been used on non-neuroradiology pediatric patients, while the rest of the time has been spent equally on ear, nose and throat, thoracic (including cardiac) and abdominal examinations in adult patients. The indications for doing NMR at Rikshospitalet are listed and discussed, and it is concluded that NMR has proved to be useful at several conditions in most organ systems. 15 refs Resonant primordial gravitational waves amplification Chunshan Lin Full Text Available We propose a mechanism to evade the Lyth bound in models of inflation. We minimally extend the conventional single-field inflation model in general relativity (GR to a theory with non-vanishing graviton mass in the very early universe. The modification primarily affects the tensor perturbation, while the scalar and vector perturbations are the same as the ones in GR with a single scalar field at least at the level of linear perturbation theory. During the reheating stage, the graviton mass oscillates coherently and leads to resonant amplification of the primordial tensor perturbation. After reheating the graviton mass vanishes and we recover GR. Magnetic resonance imaging in psychiatry Mann, K. Diagnosis and research in psychiatry are increasingly availing themselves of magnetic resonance imaging (MRI). In comparison to computed tomography (CT), this offers the combined benefits of no exposure to radiation, high resolution, artefact-free display of structures near bone, and a sharp contrast between the grey and white brain matter, with freedom to select the section. With the exception of very anxious patients, MRI will gradually replace CT scans for a wide range of differential diagnostic investigations. Its superiority in systematic studies of psychiatric patients with discrete cerebral parenchyma lesions is already considered proven. This is illustrated on the basis of research into schizophrenia and alcoholism. (orig.) [de Advances in Magnetic Resonance, Volume 3, describes a number of important developments which are finding increasing application by chemists. The book contains five chapters and begins with a discussion of how the properties of random molecular rotations reflect themselves in NMR and how they show up, often differently, in other kinds of experiments. This is followed by separate chapters on the Kubo method, showing its equivalence to the Redfield approach in the cases of most general interest; the current state of dynamic nuclear polarization measurements in solutions and what they tell us abou Micro-optomechanical trampoline resonators Pepper, Brian; Kleckner, Dustin; Sonin, Petro; Jeffrey, Evan; Bouwmeester, Dirk Recently, micro-optomechanical devices have been proposed for implementation of experiments ranging from non-demolition measurements of phonon number to creation of macroscopic quantum superpositions. All have strenuous requirements on optical finesse, mechanical quality factor, and temperature. We present a set of devices composed of dielectric mirrors on Si 3 N4 trampoline resonators. We describe the fabrication process and present data on finesse and quality factor. The authors gratefully acknowledge support from NSF PHY-0804177 and Marie Curie EXT-CT-2006-042580. Hadron scattering, resonances, and QCD Briceño, R. A. The non-perturbative nature of quantum chromodynamics (QCD) has historically left a gap in our understanding of the connection between the fundamental theory of the strong interactions and the rich structure of experimentally observed phenomena. For the simplest properties of stable hadrons, this is now circumvented with the use of lattice QCD (LQCD). In this talk I discuss a path towards a rigorous determination of few-hadron observables from LQCD. I illustrate the power of the methodology by presenting recently determined scattering amplitudes in the light-meson sector and their resonance content. Stochastic resonance for exploration geophysics Omerbashich, Mensur Stochastic resonance (SR) is a phenomenon in which signal to noise (SN) ratio gets improved by noise addition rather than removal as envisaged classically. SR was first claimed in climatology a few decades ago and then in other disciplines as well. The same as it is observed in natural systems, SR is used also for allowable SN enhancements at will. Here I report a proof of principle that SR can be useful in exploration geophysics. For this I perform high frequency GaussVanicek variance spectr... Electron Shell as a Resonator Karpeshin, F. F. Main principles of the resonance effect arising in the electron shells in interaction of the nuclei with electromagnetic radiation are analyzed and presented in the historical aspect. Principles of NEET are considered from a more general position, as compared to how this is usually presented. Characteristic features of NEET and its reverse, TEEN, as internal conversion processes are analyzed, and ways are offered of inducing them by laser radiation. The ambivalent role of the Pauli exclusion principles in NEET and TEEN processes is investigated. Fano resonances from gradient-index metamaterials. Xu, Yadong; Li, Sucheng; Hou, Bo; Chen, Huanyang Fano resonances - resonant scattering features with a characteristic asymmetric profile - have generated much interest, due to their extensive and valuable applications in chemical or biological sensors, new types of optical switches, lasers and nonlinear optics. They have been observed in a wide variety of resonant optical systems, including photonic crystals, metamaterials, metallic gratings and nanostructures. In this work, a waveguide structure is designed by employing gradient-index metamaterials, supporting strong Fano resonances with extremely sharp spectra. As the changes in the transmission spectrum originate from the interaction of guided modes from different channels, instead of resonance structures or metamolecules, the Fano resonances can be observed for both transverse electric and transverse magnetic polarizations. These findings are verified by fine agreement with analytical calculations and experimental results at microwave, as well as simulated results at near infrared frequencies. Magnetic resonance imaging of Parkinsonism Mukai, Eiichiro; Makino, Naoki; Fujishiro, Kenichiro. We have analyzed magnetic resonance images in 33 patients; 18 patients with Parkinson's disease, 1 patient with diurnally fluctuating progressive dystonia, 1 patient with pure akinesia, 6 patients with multiple system atrophy, 1 patient with flunarizine induced parkinsonism, and 4 patients with unclassified parkinsonism. The MR images were obtained using a 1.5-T GE MR System. A spin-echo pulse sequence was used with a TE of 30 msec and 80 msec and a TR of 2000 msec. No signal abnormalities were seen in any patient with Parkinson's disease but 3 showed slightly decreased signal intensity of the putamen on T2-weighted sequences. Patients with diurnally fluctuating progressive dystonia and pure akinesia evidensed no abnormal findings. All six patients with multiple system atrophy demonstrated decreased signal intensity of the putamen, particularly along their lateral and posterior portions, and an enlarged substantia nigra. Atrophy of the pons and cerebellum was detected in all cases with multiple system atrophy. One case of flunarizine induced parkinsonism showed slightly decreased signal intensity of the putamen. Four cases of unclassified parkinsonism showed decreased signal in the putamen on T2-weighted sequences. Magnetic resonance imaging has the potential to become a useful diagnostic tool in the management of parkinsonism. (author) Inductive measurements of ferromagnetic resonance Woodward, R.C.; Kennewell, K.; Crew, D.C.; Stamps, R.L. Full text: The rapid advance in magnetic data storage has driven groundbreaking work in the science that underpins the properties of ferromagnetic materials at high frequencies. Recent work in this area has included the use of precession in order to produce ultra-high speed switching of magnetic elements, the generation of excited dynamical structures by application of inhomogeneous field pulses, and examination of the propagation of localized spin waves. This paper describes explorations of ultra-fast magnetization dynamics being undertaken at The University of Western Australia. We have studied the differences in magnetization dynamics in simple permalloy films when a sample is excited with sharp pulse compared to the to the dynamics generated by the application of a small amplitude continuous wave signal. We have observed a difference in the resonant frequency determined from these two excitations and will propose reasons for the different resonance responses of the system. Using the ultra-fast techniques described above we have measured dynamical properties that are significantly different to the static properties. These results are explained by the dynamical measurements being made on time scales smaller than the characteristic relaxation time. Future applications of these devices will be to examine broadening of line widths and frequency shifts associated with the excitation of magnetostatic modes, factors limiting quasiballistic reversal and differences between the dynamic and static properties of magnetic materials Wave emission by resonance crossing Tracy, E.R.; Kaufman, A.N.; Liang, Y. The emission of collective waves by a moving charged particle in a nonuniform medium is discussed. Emission occurs in a nonuniform medium when the local dispersion relation of the collective wave is satisfied. This is a form of resonance crossing. Using the Weyl symbol calculus, a local expansion of the collective wave equation driven by the particle source is derived in the neighborhood of the crossing. The collective wave dispersion manifold and the gyroballistic wave dispersion manifold can be used as a pair of local coordinates in the neighborhood of the resonance crossing, which greatly simplifies the analysis. This change of representation is carried out using a metaplectic transform (a generalization of the fourier transform). The Wigner function of the emitted wave field is then computed in the new coordinates. The Wigner function is a phase space scalar, hence the numerical value is invariant under linear canonical transformations. This invariance is invoked to finally arrive at the Wigner function in the original (physical) coordinates. The wave-action and -energy emission rates are then computed from the Wigner function. copyright 1995 American Institute of Physics Resonance ionization spectroscopy in dysprosium Studer, D., E-mail: [email protected]; Dyrauf, P.; Naubereit, P.; Heinke, R.; Wendt, K. [Johannes Gutenberg-Universität Mainz, Institut für Physik (Germany) We report on resonance ionization spectroscopy (RIS) of high-lying energy levels in dysprosium. We developed efficient excitation schemes and re-determined the first ionization potential (IP) via analysis of Rydberg convergences. For this purpose both two- and three-step excitation ladders were investigated. An overall ionization efficiency of 25(4) % could be demonstrated in the RISIKO mass separator of Mainz University, using a three-step resonance ionization scheme. Moreover, an extensive analysis of the even-parity 6sns- and 6snd-Rydberg-series convergences, measured via two-step excitation was performed. To account for strong perturbations in the observed s-series, the approach of multichannel quantum defect theory (MQDT) was applied. Considering all individual series limits we extracted an IP-value of 47901.76(5) cm{sup −1}, which agrees with the current literature value of 47901.7(6) cm{sup −1}, but is one order of magnitude more precise. Mukai, Eiichiro [National Hospital of Nagoya (Japan); Makino, Naoki; Fujishiro, Kenichiro We have analyzed magnetic resonance images in 33 patients; 18 patients with Parkinson's disease, 1 patient with diurnally fluctuating progressive dystonia, 1 patient with pure akinesia, 6 patients with multiple system atrophy, 1 patient with flunarizine induced parkinsonism, and 4 patients with unclassified parkinsonism. The MR images were obtained using a 1.5-T GE MR System. A spin-echo pulse sequence was used with a TE of 30 msec and 80 msec and a TR of 2000 msec. No signal abnormalities were seen in any patient with Parkinson's disease but 3 showed slightly decreased signal intensity of the putamen on T2-weighted sequences. Patients with diurnally fluctuating progressive dystonia and pure akinesia evidensed no abnormal findings. All six patients with multiple system atrophy demonstrated decreased signal intensity of the putamen, particularly along their lateral and posterior portions, and an enlarged substantia nigra. Atrophy of the pons and cerebellum was detected in all cases with multiple system atrophy. One case of flunarizine induced parkinsonism showed slightly decreased signal intensity of the putamen. Four cases of unclassified parkinsonism showed decreased signal in the putamen on T2-weighted sequences. Magnetic resonance imaging has the potential to become a useful diagnostic tool in the management of parkinsonism. (author). Purpose of review: To present an updated and streamlined overview of the metabolic and biochemical aspect of the migraine pathophysiology based on findings from phosphorous (31P) and hydrogen (1H) magnetic resonance spectroscopy (MRS) studies. Recent findings: Despite of the variation in the meth......Purpose of review: To present an updated and streamlined overview of the metabolic and biochemical aspect of the migraine pathophysiology based on findings from phosphorous (31P) and hydrogen (1H) magnetic resonance spectroscopy (MRS) studies. Recent findings: Despite of the variation...... in the methodology and quality of the MRS migraine studies over time, some results were consistent and reproducible. 31P-MRS studies suggested reduced availability of neuronal energy and implied a mitochondrial dysfunction in the migraine brain. 1H-MRS studies reported interictal abnormalities in the excitatory...... and inhibitory neurotransmitters, glutamate and g-aminobutyric acid (GABA), suggesting persistent altered excitability in migraine patients. N-Acetylaspartate levels were decreased in migraine, probably due to a mitochondrial dysfunction and abnormal energy metabolism. The reported abnormalities may increase... Ponderomotive force near cyclotron resonance Kono, Mitsuo; Sanuki, Heiji The ponderomotive force, which is involved in the excitation of macroscopic behaviors of plasma caused by wave motion, plays an important role in various non-linear wave motion phenomena. In the present study, equations for the pondermotive force for plasma in a uniform magnetic field is derived using a renormalization theory which is based on the Vlasov equation. It is shown that the pondermotive force, which diverges at the cyclotron resonence point according to adiabatic approximation, can be expressed by a non-divergent equation by taking into account the instability of the cyclotron orbit due to high-order scattering caused by a wave. This is related with chaotic particle behaviors near cyclotron resonance, where the pondermotive force is small and the diffusion process prevails. It is assumed here that the amplitude of the high-frequency electric field is not large and that the broadening of cyclotron levels is smaller than the distance between the levels. A global chaos will be created if the amplitude of the electric field becomes greater to allow the broadening to exceed the distance between the levels. (Nogami, K.). Threshold enhancement of diphoton resonances Aoife Bharucha Full Text Available We revisit a mechanism to enhance the decay width of (pseudo-scalar resonances to photon pairs when the process is mediated by loops of charged fermions produced near threshold. Motivated by the recent LHC data, indicating the presence of an excess in the diphoton spectrum at approximately 750 GeV, we illustrate this threshold enhancement mechanism in the case of a 750 GeV pseudoscalar boson A with a two-photon decay mediated by a charged and uncolored fermion having a mass at the 12MA threshold and a small decay width, <1Â MeV. The implications of such a threshold enhancement are discussed in two explicit scenarios: i the Minimal Supersymmetric Standard Model in which the A state is produced via the top quark mediated gluon fusion process and decays into photons predominantly through loops of charginos with masses close to 12MA and ii a two Higgs doublet model in which A is again produced by gluon fusion but decays into photons through loops of vector-like charged heavy leptons. In both these scenarios, while the mass of the charged fermion has to be adjusted to be extremely close to half of the A resonance mass, the small total widths are naturally obtained if only suppressed three-body decay channels occur. Finally, the implications of some of these scenarios for dark matter are discussed. Bharucha, Aoife; Goudelis, Andreas The data collected by the LHC collaborations at an energy of 13 TeV indicates the presence of an excess in the diphoton spectrum that would correspond to a resonance of a 750 GeV mass. The apparently large production cross section is nevertheless very difficult to explain in minimal models. We consider the possibility that the resonance is a pseudoscalar boson $A$ with a two--photon decay mediated by a charged and uncolored fermion having a mass at the $\\frac12 M_A$ threshold and a very small decay width, $\\ll 1$ MeV; one can then generate a large enhancement of the $A\\gamma\\gamma$ amplitude which explains the excess without invoking a large multiplicity of particles propagating in the loop, large electric charges and/or very strong Yukawa couplings. The implications of such a threshold enhancement are discussed in two explicit scenarios: i) the Minimal Supersymmetric Standard Model in which the $A$ state is produced via the top quark mediated gluon fusion process and decays into photons predominantly through... Acoustic resonance spectroscopy intrinsic seals Olinger, C.T.; Burr, T.; Vnuk, D.R. We have begun to quantify the ability of acoustic resonance spectroscopy (ARS) to detect the removal and replacement of the lid of a simulated special nuclear materials drum. Conceptually, the acoustic spectrum of a container establishcs a baseline fingerprint, which we refer to as an intrinsic seal, for the container. Simply removing and replacing the lid changes some of the resonant frequencies because it is impossible to exactly duplicate all of the stress patterns between the lid and container. Preliminary qualitative results suggested that the ARS intrinsic seal could discriminate between cases where a lid has or has not been removed. The present work is directed at quantifying the utility of the ARS intrinsic seal technique, including the technique's sensitivity to ''nuisance'' effects, such as temperature swings, movement of the container, and placement of the transducers. These early quantitative tests support the potential of the ARS intrinsic seal application, but also reveal a possible sensitivity to nuisance effects that could limit environments or conditions under which the technique is effective Simulation of a quadrupole resonator Kleindienst, Raphael [Helmholtz Zentrum Berlin (Germany) Modern particle accelerators often rely on superconducting radio frequency (SRF) technology for accelerating cavities. In particular in CW operation, very high quality factors up into the high range are desirable, since one of the main cost drivers of such an accelerator, the cryogenic refrigeration plant, is inversely proportional to Q{sub 0}. Present day superconducting cavities are generally made of solid Niobium. A possibility to increase the quality factor as well as accelerating fields is to use thin film coated cavities. Apart from Niobium thin films, other superconducting materials, such as MgB{sub 2}, NbN and Nb{sub 3}Sn are promising candidates. Measuring and understanding the RF-properties of superconducting thin films, specifically the surface resistance, is needed to drive forward this development. Currently only few facilities exist capable of measuring the surface resistance of thin films samples with a resolution in the nano-ohm range at the operating frequency of typical cavities(e.g. L-band). A dedicated test stand consisting of a quadrupole resonator is therefore being constructed at the Helmholtz Zentrum Berlin. This system is based on the 400 MHz quadrupole resonator at CERN, with the design adapted to 433 MHz (making available the higher harmonic mode at 1.3 GHz) and optimized with respect to resolution and maximum achievable fields using simulation data obtained with CST Microwave Studio as well as ANSYS. The simulated design is being manufactured. An outlook for future physics runs is given. Single-Molecule Stochastic Resonance K. Hayashi Full Text Available Stochastic resonance (SR is a well-known phenomenon in dynamical systems. It consists of the amplification and optimization of the response of a system assisted by stochastic (random or probabilistic noise. Here we carry out the first experimental study of SR in single DNA hairpins which exhibit cooperatively transitions from folded to unfolded configurations under the action of an oscillating mechanical force applied with optical tweezers. By varying the frequency of the force oscillation, we investigate the folding and unfolding kinetics of DNA hairpins in a periodically driven bistable free-energy potential. We measure several SR quantifiers under varied conditions of the experimental setup such as trap stiffness and length of the molecular handles used for single-molecule manipulation. We find that a good quantifier of the SR is the signal-to-noise ratio (SNR of the spectral density of measured fluctuations in molecular extension of the DNA hairpins. The frequency dependence of the SNR exhibits a peak at a frequency value given by the resonance-matching condition. Finally, we carry out experiments on short hairpins that show how SR might be useful for enhancing the detection of conformational molecular transitions of low SNR. Magnetic resonance imaging of chemistry. Britton, Melanie M Magnetic resonance imaging (MRI) has long been recognized as one of the most important tools in medical diagnosis and research. However, MRI is also well placed to image chemical reactions and processes, determine the concentration of chemical species, and look at how chemistry couples with environmental factors, such as flow and heterogeneous media. This tutorial review will explain how magnetic resonance imaging works, reviewing its application in chemistry and its ability to directly visualise chemical processes. It will give information on what resolution and contrast are possible, and what chemical and physical parameters can be measured. It will provide examples of the use of MRI to study chemical systems, its application in chemical engineering and the identification of contrast agents for non-clinical applications. A number of studies are presented including investigation of chemical conversion and selectivity in fixed-bed reactors, temperature probes for catalyst pellets, ion mobility during tablet dissolution, solvent dynamics and ion transport in Nafion polymers and the formation of chemical waves and patterns. Niobium sputter deposition on quarter wave resonators Viswanadham, C; Jayaprakash, D; Mishra, R L Niobium sputter deposition on quarter wave copper R.F resonators, have been taken up in our laboratory, An ultra high vacuum system was made for this purpose. Niobium exhibits superconducting properties at liquid Helium temperature. A uniform coating of about 1.5 mu m of niobium on the internal surfaces of the copper resonant cavities is desired. Power dissipation in the resonators can be greatly reduced by making the internal surfaces of the R.F cavity super conducting. (author) Detection of gravitational waves with resonant antennas Ronga, Francesco The status of the 4 operating cylindrical gravitational waves resonant antenna detectors is summarized. A short review is given of the experimental results and of the next generation projects. Resonant detectors are now sensitive to the strongest potential sources of gravitational waves in our galaxy and in the local group. Recently interferometric detectors have achieved very good perfomances, but resonant detectors are still competitive particularly for what concern the very good live-time Quantum heat engine with coupled superconducting resonators Hardal, Ali Ãœmit Cemal; Aslan, Nur; Wilson, C. M. We propose a quantum heat engine composed of two superconducting transmission line resonators interacting with each other via an optomechanical-like coupling. One resonator is periodically excited by a thermal pump. The incoherently driven resonator induces coherent oscillations in the other one...... the signatures of quantum behavior in the statistical and thermodynamic properties of the system. We find evidence of a quantum enhancement in the power output of the engine at low temperatures.... Resonance ionization scheme development for europium Chrysalidis, K., E-mail: [email protected]; Goodacre, T. Day; Fedosseev, V. N.; Marsh, B. A. [CERN (Switzerland); Naubereit, P. [Johannes Gutenberg-Universität, Institiut für Physik (Germany); Rothe, S.; Seiffert, C. [CERN (Switzerland); Kron, T.; Wendt, K. [Johannes Gutenberg-Universität, Institiut für Physik (Germany) Odd-parity autoionizing states of europium have been investigated by resonance ionization spectroscopy via two-step, two-resonance excitations. The aim of this work was to establish ionization schemes specifically suited for europium ion beam production using the ISOLDE Resonance Ionization Laser Ion Source (RILIS). 13 new RILIS-compatible ionization schemes are proposed. The scheme development was the first application of the Photo Ionization Spectroscopy Apparatus (PISA) which has recently been integrated into the RILIS setup. Exit channels of autoionization resonances in atoms Krause, M.O. In many-electron atoms with open shells strong autoionization resonances occur when an electron from an inner, weakly bound subshell is excited. Usually, the resonance state lies above several ionization thresholds and, hence, will decay into more than one exit or continuum channel. Several cases are discussed in which the resonance state is induced by synchrotron radiation, and the exit channels are differentiated and characterized by the analysis of the ejected electrons Atomic resonances in nuclear fusion plasmas Clauser, C. F.; Barrachina, R. O. We present a study of zero energy resonances of photoionization and radiative recombination cross section for the different species in a fusion reactor. In this context, the interaction potential is screened and its typical length depends on the plasma density and temperature. Due to the nature of these resonances, we propose other atomic processes in which they can take place. Finally, we show the density and temperature conditions where these resonances occur and their probable consequence on the reactor performance. (author) A Family of Resonant Vibration Control Formats Krenk, Steen; Høgsberg, Jan Becker Resonant control makes use of a controller with a resonance frequency and an equivalent damping ratio.A simple explicit calibration procedure is presented for a family of resonant controllers in which the frequencyis tuned to the natural frequency of the targeted mode in such a way that the two resulting modes exhibit identicaldamping ratio. This tuning is independent of the imposed controller damping. The controller damping is thenselected as an optimal compromise between too small damping, ... Giant resonances in heavy-ion reactions Hussein, M.S. The several roles of multipole giant resonances in heavy-ion reactions are discussed. In particular, the modifications in the effective ion-ion potencial due to the virtual excitation of giant resonances at low energies, are considered and estimated for several systems. Real excitation of giant resonances in heavy-ion reactions at intermediate energies are then discussed and their importance in the approach phase of deeply inelastic processes in emphasized. Several demonstrative examples are given. (Author) [pt Determining properties of baryon resonances in nuclei Johnson, M.B.; Chen, C.M.; Ernst, D.J.; Jiang, M.F. Meson-nucleus and photon-nucleus interactions are important sources of information about the medium modifications of baryon resonances in nuclei. Indications of how large the medium effects are for resonances above the Δ 33 (1232) are provided by it combined analysis of photonuclear and pion cross sections in the GeV range of energies. Tile existing data indicate a possible 10-20% renormalization of the pion coupling to higher-lying resonances in nuclei The effect of asymmetry on resonant tunneling Garcia-Calderon, G. Resonant tunneling experiments on multibarrier coupled heterostructures probe the quasistationary nature of the states of the corresponding one dimensional potential. This work considers the effect of asymmetric one dimensional multibarrier potentials on resonant tunneling. It is shown, by using the properties of the propagator of the system, that this effect may lead to novel resonance phenomena and affects the lifetime of the quasistationary states of the system. The above considerations are illustrated by a simple analytical solvable model. (author) Radio frequency quadrupole resonator for linear accelerator Moretti, Alfred An RFQ resonator for a linear accelerator having a reduced level of interfering modes and producing a quadrupole mode for focusing, bunching and accelerating beams of heavy charged particles, with the construction being characterized by four elongated resonating rods within a cylinder with the rods being alternately shorted and open electrically to the shell at common ends of the rods to provide an LC parallel resonant circuit when activated by a magnetic field transverse to the longitudinal axis. Resonance gamma-transducer with thin converter Mirzababaev, R.M. A resonance detector with stainless steel foil (∼3000 A) is more efficient than conventional detectors as regards the recording Rayleigh scattering of Moessbauer effect. If the scatterer contains resonance nuclei (iron), the detector simultaneously records in the same spectrum both Zeeman lines and the line resulted to Rayleigh quanta scattering on electrons. Zeeman lines are formed due to photoabsorption in the converter. The central line is associated with resonance absorption in the converter Resonant power processors. I - State plane analysis Oruganti, R.; Lee, F. C. State-plane techniques in conjunction with piecewise-linear analysis is employed to study the steady-state and transient characteristics of a series resonant converter. With the direct viewing of the resonant tank energy and the device switching instants, the state portrayal provides unique insights into the complex behavior of the converter. Operation of the converter under both continuous and discontinuous current modes and at frequencies both below and above resonant frequency are discussed. Resonant power processors. II - Methods of control The nature of resonant converter control is discussed. Employing the state-portrait, different control methods for series resonant converter are identified and their performance evaluated based on their stability, response to control and load changes and range of operation. A new control method, optimal-trajectory control, is proposed which, by utilizing the state trajectories as control laws, continuously monitors the energy level of the resonant tank. The method is shown to have superior control properties especially under transient operation. An analytical approximation for resonance integral Magalhaes, C.G. de; Martinez, A.S. It is developed a method which allows to obtain an analytical solution for the resonance integral. The problem formulation is completely theoretical and based in concepts of physics of general character. The analytical expression for integral does not involve any empiric correlation or parameter. Results of approximation are compared with pattern values for each individual resonance and for sum of all resonances. (M.C.K.) [pt Measurement of global and local resonance terms Tomás, R; Calaga, R; Fischer, W; Franchi, A; Rumolo, Giovanni Recently, resonance driving terms were successfully measured in the CERN SPS and the BNL RHIC from the Fourier spectrum of beam position monitor (BPM) data. Based on these measurements a new analysis has been derived to extract truly local observables from BPM data. These local observables are called local resonance terms since they share some similarities with the global resonance terms. In this paper we derive these local terms analytically and present experimental measurements of sextupolar global and local resonance terms in RHIC. Nondestructive measurements of these terms using ac dipoles are also presented. On meson resonances and chiral symmetry Lutz, M.F.M. We study meson resonances with quantum numbers J P = 1 + in terms of the chiral SU(3) Lagrangian. At leading order a parameter-free prediction is obtained for the scattering of Goldstone bosons off vector mesons with J P = 1 - once we insist on approximate crossing symmetry of the unitarized scattering amplitude. A resonance spectrum arises that is remarkably close to the empirical pattern. In particular, we find that the strangeness-zero resonances h 1 (1380), f 1 (1285) and b 1 (1235) are formed due to strong K anti K μ and K K μ channels. This leads to large coupling constants of those resonances to the latter states. (orig.) Resonant tunneling of electrons in quantum wires Krive, I.V.; Shekhter, R.I.; Jonson, M.; Krive, I.V. We considered resonant electron tunneling in various nanostructures including single wall carbon nanotubes, molecular transistors and quantum wires formed in two-dimensional electron gas. The review starts with a textbook description of resonant tunneling of noninteracting electrons through a double-barrier structure. The effects of electron-electron interaction in sequential and resonant electron tunneling are studied by using Luttinger liquid model of electron transport in quantum wires. The experimental aspects of the problem (fabrication of quantum wires and transport measurements) are also considered. The influence of vibrational and electromechanical effects on resonant electron tunneling in molecular transistors is discussed. Fano resonances in bilayer phosphorene nanoring Zhang, Rui; Wu, Zhenhua; Li, X. J.; Li, L. L.; Chen, Qiao; Li, Yun-Mei; Peeters, F. M. Tunable transport properties and Fano resonances are predicted in a circular bilayer phosphorene nanoring. The conductance exhibits Fano resonances with varying incident energy and applied perpendicular magnetic field. These Fano resonance peaks can be accurately fitted with the well known Fano curves. When a magnetic field is applied to the nanoring, the conductance oscillates periodically with magnetic field which is reminiscent of the Aharonov–Bohm effect. Fano resonances are tightly related to the discrete states in the central nanoring, some of which are tunable by the magnetic field. Space charge effects: tune shifts and resonances Weng, W.T. The effects of space charge and beam-beam interactions on single particle motion in the transverse degree of freedom are considered. The space charge force and the resulting incoherent tune shift are described, and examples are given from the AGS and CERN's PSB. Equations of motion are given for resonances in the presence of the space charge force, and particle behavior is examined under resonance and space charge conditions. Resonance phase space structure is described with and without space charge. Uniform and bunched beams are compared. Beam-beam forces and resonances and beam-beam detuning are described. 18 refs., 15 figs Giant dipole resonance in hot nuclei Mau, N.V. Giant resonances built on an excited state of the nucleus at a finite temperature T are studied. The following questions are investigated: how long such collective effects occur in a nucleus when T increases. How the properties of the giant resonances vary when the temperature increases. How the study of giant resonances in hot nuclei can give information on the structure of the nucleus in a highly excited state. The special case of the giant dipole resonance is studied. Some of the experimental results are reviewed and in their theoretical interpretation is discussed. (K.A.). 56 refs., 20 figs., 4 tabs Resonance Raman Optical Activity and Surface Enhanced Resonance Raman Optical Activity analysis of Cytochrome C Johannessen, Christian; Abdali, Salim; White, Peter C. High quality Resonance Raman (RR) and resonance Raman Optical Activity (ROA) spectra of cytochrome c were obtained in order to perform full assignment of spectral features of the resonance ROA spectrum. The resonance ROA spectrum of cytochrome c revealed a distinct spectral signature pattern due...... to resonance enhanced skeletal porphyrin vibrations, more pronounced than any contribution from the protein back-bone. Combining the intrinsic resonance enhancement of cytochrome c with surface plasmon enhancement by colloidal silver particles, the Surface Enhanced Resonance Raman Scattering (SERRS) and Chiral...... Enhanced Raman Spectroscopy (ChERS) spectra of the protein were successfully obtained at very low concentration (as low as 1 µM). The assignment of spectral features was based on the information obtained from the RR and resonance ROA spectra. Excellent agreement between RR and SERRS spectra is reported... Quasi-resonant converter with divided resonant capacitor on primary and secondary side Shiroyama, Hironobu; Matsuo, Hirofumi; Ishizuka, Yoichi This paper presents a quasi-resonant converter with divided resonant capacitor on primary and secondary side of the isolation transformer. A conventional quasi-resonant converter using flyback topology can realize soft switching with simple circuit. However, relatively large surge voltage is generated in the switching device. To suppress such surge voltage, resonant capacitor is divided on primary side and secondary side in the proposed converter. In case of prototype 95W converter, the volta... One-loop renormalization of Resonance Chiral Theory: scalar and pseudoscalar resonances Rosell, Ignasi; Ruiz-FemenIa, Pedro; Portoles, Jorge We consider the Resonance Chiral Theory with one multiplet of scalar and pseudoscalar resonances, up to bilinear couplings in the resonance fields, and evaluate its β-function at one-loop with the use of the background field method. Thus we also provide the full set of operators that renormalize the theory at one loop and render it finite A New Look at an Old Activity: Resonance Tubes Used to Teach Resonance Nelson, Jim; Nelson, Jane There are several variations of resonance laboratory activities used to determine the speed of sound. This is "not" one of them. This activity uses the resonance tube idea to teach "resonance," not to verify the speed of sound. Prior to this activity, the speed of sound has already been measured using computer sound-sensors and… Relativistic effects in resonance absorption Drake, J.F.; Lee, Y.C. The role of the relativistic-electron-mass variation in the generation of plasma waves by the linear mode conversion of intense electromagnetic waves is investigated. The increase in the electron mass in high intensity regions of the mode-converted wave reduces the local plasma frequency and thereby strongly modifies the plasma-driver resonance. A spatial discontinuity in the structure of the mode-converted wave results and causes the wave to break. Under rather modest restrictions, the wave breaking resulting from these effects occurs before the wave amplitude is limited either by thermal convection or by breaking caused by previously investigated nonrelativistic effects. Consequently, the amplitude of the mode-converted plasma wave should saturate at a much lower level than previously predicted. For simplicity, the analysis is limited to the initial stages of mode conversion where the ion dynamics can be neglected. The validity of this approximation is discussed Electron cyclotron resonance plasma photos Racz, R.; Palinkas, J. [Institute of Nuclear Research (ATOMKI), H-4026 Debrecen, Bem ter 18/c (Hungary); University of Debrecen, H-4010 Debrecen, Egyetem ter 1 (Hungary); Biri, S. [Institute of Nuclear Research (ATOMKI), H-4026 Debrecen, Bem ter 18/c (Hungary) In order to observe and study systematically the plasma of electron cyclotron resonance (ECR) ion sources (ECRIS) we made a high number of high-resolution visible light plasma photos and movies in the ATOMKI ECRIS Laboratory. This required building the ECR ion source into an open ECR plasma device, temporarily. An 8MP digital camera was used to record photos of plasmas made from Ne, Ar, and Kr gases and from their mixtures. We studied and recorded the effect of ion source setting parameters (gas pressure, gas composition, magnetic field, and microwave power) to the shape, color, and structure of the plasma. The analysis of the photo series gave us many qualitative and numerous valuable physical information on the nature of ECR plasmas. Electron paramagnetic resonance (EPR) biodosimetry Desrosiers, Marc; Schauer, David A. Radiation-induced electron paramagnetic resonance (EPR) signals were first reported by Gordy et al. [Proc. Natl. Acad. Sci. USA 41 (1955) 983]. The application of EPR spectroscopy to ionizing radiation dosimetry was later proposed by Brady et al. [Health Phys. 15 (1968) 43]. Since that time EPR dosimetry has been applied to accident and epidemiologic dose reconstruction, radiation therapy, food irradiation, quality assurance programs and archaeological dating. Materials that have been studied include bone, tooth enamel, alanine and quartz. This review paper presents the fundamentals and applications of EPR biodosimetry. Detailed information regarding sample collection and preparation, EPR measurements, dose reconstruction, and data analysis and interpretation will be reviewed for tooth enamel. Examples of EPR biodosimetry application in accidental overexposures, radiopharmaceutical dose assessment and retrospective epidemiologic studies will also be presented Transition metal nuclear magnetic resonance Pregosin, P.S. Transition metal NMR spectroscopy has progressed enormously in recent years. New methods, and specifically solid-state methods and new pulse sequences, have allowed access to data from nuclei with relatively low receptivities with the result that chemists have begun to consider old and new problems, previously unapproachable. Moreover, theory, computational science in particular, now permits the calculation of not just 13 C, 15 N and other light nuclei chemical shifts, but heavy main-group element and transition metals as well. These two points, combined with increasing access to high field pulsed spectrometer has produced a wealth of new data on the NMR transition metals. A new series of articles concerned with measuring, understanding and using the nuclear magnetic resonance spectra of the metals of Group 3-12 is presented. (author) Gaucher's disease: Magnetic resonance findings Roca, M.; Gomez-Pereda, R.; Blasco, A.; Ros, L. The objective is to assess the role of magnetic resonance (MR) in determining the initial extension of Gaucher's disease and its complications. A retrospective study of eight patients diagnosed as having Gaucher's disease was carried out using MR. The study focused on pelvis, hip, femur, spine, liver parenchyma and splenic parenchyma. Infiltration of the cancellous portion of the vertebral bodies was observed in all but one of the patients. Three patients presented small hemangiomas in dorsal and lumbar vertebral bodies. Pelvic bone involvement was homogeneous in four cases and spotty in two, while the pelvic marrow was normal in the two patients with no vertebral infiltration. A vascular necrosis of the femoral head was detected in two cases. MR is very useful in determining the initial extension, in the early diagnosis of complications and in managing the posttreatment marrow response to assess the therapeutic efficacy. 16 refs Coincidence experiments are carried out to investigate the photon and neutron emission from the giant resonance regions of 208 Pb and 90 Zr using the ORNL Spin Spectrometer, a 72-segment NaI detector system. The authors determined the total gamma-decay probability, the ground-state gamma branching ratio, and the branching ratios to a number of low-lying states as a function of excitation energy in 208 Pb to ∼15 MeV. Similar data were also obtained on 90 Zr. The total yield of ground-state E2 gamma radiation in 208 Pb and the comparative absence of such radiation in 90 Zr can only be understood if decay of compound (damped) states is considered. (Auth.) Fetal abdominal magnetic resonance imaging Brugger, Peter C.; Prayer, Daniela This review deals with the in vivo magnetic resonance imaging (MRI) appearance of the human fetal abdomen. Imaging findings are correlated with current knowledge of human fetal anatomy and physiology, which are crucial to understand and interpret fetal abdominal MRI scans. As fetal MRI covers a period of more than 20 weeks, which is characterized not only by organ growth, but also by changes and maturation of organ function, a different MR appearance of the fetal abdomen results. This not only applies to the fetal intestines, but also to the fetal liver, spleen, and adrenal glands. Choosing the appropriate sequences, various aspects of age-related and organ-specific function can be visualized with fetal MRI, as these are mirrored by changes in signal intensities. Knowledge of normal development is essential to delineate normal from pathological findings in the respective developmental stages Olfactometer for functional resonance imaging Andrieu, Patrice The Magnetic Resonance Imaging (fMRI) has been developing for twenty years. Indeed, the marketing of high-resolution MRI (5 Tesla and 7 Tesla recently) allowed the study of brain mechanisms. The research work of this PHD was to develop instrumentation for objective studies of brain behavior during a sensory stimulation. We are interested in the study of olfaction. We have designed and built a six-channel olfactometer, synchronized with breathing and controlled by computer. The originality of our work lies in the modularity of our device, which makes it adaptable to a wide range of studies. We also propose a new method to change the intensity of stimulation delivered: the Pulse Width Modulation (PWM). This device has been used in several studies in fMRI. The effectiveness of the PWM is highlighted in a psychophysical study described in this manuscript. (author) Trapped atoms along nanophotonic resonators Fields, Brian; Kim, May; Chang, Tzu-Han; Hung, Chen-Lung Many-body systems subject to long-range interactions have remained a very challenging topic experimentally. Ultracold atoms trapped in extreme proximity to the surface of nanophotonic structures provides a dynamic system combining the strong atom-atom interactions mediated by guided mode photons with the exquisite control implemented with trapped atom systems. The hybrid system promises pair-wise tunability of long-range interactions between atomic pseudo spins, allowing studies of quantum magnetism extending far beyond nearest neighbor interactions. In this talk, we will discuss our current status developing high quality nanophotonic ring resonators, engineered on CMOS compatible optical chips with integrated nanostructures that, in combination with a side illuminating beam, can realize stable atom traps approximately 100nm above the surface. We will report on our progress towards loading arrays of cold atoms near the surface of these structures and studying atom-atom interaction mediated by photons with high cooperativity. Spin resonance with trapped ions Wunderlich, Ch; Balzer, Ch; Hannemann, T; Mintert, F; Neuhauser, W; Reiss, D; Toschek, P E [Institut fuer Laser-Physik, Universitaet Hamburg, Jungiusstrasse 9, 20355 Hamburg (Germany) A modified ion trap is described where experiments (in particular related to quantum information processing) that usually require optical radiation can be carried out using microwave or radio frequency electromagnetic fields. Instead of applying the usual methods for coherent manipulation of trapped ions, a string of ions in such a modified trap can be treated like a molecule in nuclear magnetic resonance experiments taking advantage of spin-spin coupling. The collection of trapped ions can be viewed as an N-qubit molecule with adjustable spin-spin coupling constants. Given N identically prepared quantum mechanical two-level systems (qubits), the optimal strategy to estimate their quantum state requires collective measurements. Using the ground state hyperfine levels of electrodynamically trapped {sup 171}Yb{sup +}, we have implemented an adaptive algorithm for state estimation involving sequential measurements on arbitrary qubit states. Wunderlich, Ch; Balzer, Ch; Hannemann, T; Mintert, F; Neuhauser, W; Reiss, D; Toschek, P E A modified ion trap is described where experiments (in particular related to quantum information processing) that usually require optical radiation can be carried out using microwave or radio frequency electromagnetic fields. Instead of applying the usual methods for coherent manipulation of trapped ions, a string of ions in such a modified trap can be treated like a molecule in nuclear magnetic resonance experiments taking advantage of spin-spin coupling. The collection of trapped ions can be viewed as an N-qubit molecule with adjustable spin-spin coupling constants. Given N identically prepared quantum mechanical two-level systems (qubits), the optimal strategy to estimate their quantum state requires collective measurements. Using the ground state hyperfine levels of electrodynamically trapped 171 Yb + , we have implemented an adaptive algorithm for state estimation involving sequential measurements on arbitrary qubit states Racz, R.; Palinkas, J.; Biri, S. Resonant ion transport in EBT Hastings, D.E.; Jaeger, E.F.; Hedrick, C.L.; Tolliver, J.S. We use a model for the ELMO Bumpy Torus as a bumpy cylinder with a toroidally induced vertical drift imposed on the plasma. With this model we obtain the neoclassical plasma-transport coefficients for ions in both the banana and plateau resonant regimes. The problem of solving the linearized bounce-averaged drift kinetic equation is formulated as a variational principle, which is shown to be valid for both the banana and plateau regimes. We use limiting forms of this principle to obtain a continuous collisionality approximation to the energy-dependent flux. We then use this approximation to obtain analytic formulae for the particle- and energy-diffusion coefficients. These are shown to give excellent agreement with numerical results Brugger, Peter C. [Center of Anatomy and Cell Biology, Integrative Morphology Group, Medical University of Vienna, Waehringerstrasse 13, 1090 Vienna (Austria)]. E-mail: [email protected]; Prayer, Daniela [Department of Radiology, Medical University of Vienna, Waehringerguertel 18-20, 1090 Vienna (Austria) This review deals with the in vivo magnetic resonance imaging (MRI) appearance of the human fetal abdomen. Imaging findings are correlated with current knowledge of human fetal anatomy and physiology, which are crucial to understand and interpret fetal abdominal MRI scans. As fetal MRI covers a period of more than 20 weeks, which is characterized not only by organ growth, but also by changes and maturation of organ function, a different MR appearance of the fetal abdomen results. This not only applies to the fetal intestines, but also to the fetal liver, spleen, and adrenal glands. Choosing the appropriate sequences, various aspects of age-related and organ-specific function can be visualized with fetal MRI, as these are mirrored by changes in signal intensities. Knowledge of normal development is essential to delineate normal from pathological findings in the respective developmental stages. Cyclotron resonance in bilayer graphene. Henriksen, E A; Jiang, Z; Tung, L-C; Schwartz, M E; Takita, M; Wang, Y-J; Kim, P; Stormer, H L We present the first measurements of cyclotron resonance of electrons and holes in bilayer graphene. In magnetic fields up to B=18 T, we observe four distinct intraband transitions in both the conduction and valence bands. The transition energies are roughly linear in B between the lowest Landau levels, whereas they follow square root[B] for the higher transitions. This highly unusual behavior represents a change from a parabolic to a linear energy dispersion. The density of states derived from our data generally agrees with the existing lowest order tight binding calculation for bilayer graphene. However, in comparing data to theory, a single set of fitting parameters fails to describe the experimental results. Magnetic resonance imaging in neuroradiology Voigt, K.; Lotx, J.W. Magnetic resonance imaging (MRI) is now accepted as an effective method of investigating a wide range of disorders, especially of the brain and spine. A short introduction on image contrast in MRI is given and the advantages and disadvantages for the different diseases of the brain is discussed. Excellent soft-tissue contrast, multiplanar imaging capabilities and lack of ionising radiation are conspicuous advantages, and it is now established as the investigation of choice in a large number of clinical conditions, especially when the central nervous system is involved. However, it remains only one of a series of imaging modalities. A confident provisional clinical diagnosis is essential for establishing an imaging protocol and the intention should always be to reach a definitive diagnosis in the least invasive and most cost-effective way. 7 figs., 19 refs Magnetic resonance imaging of the prostate Iversen, P; Kjaer, L; Thomsen, C Magnetic resonance imaging offers new possibilities in investigation of the prostate gland. Current results of imaging and tissue discrimination in the evaluation of prostatic disease are reviewed. Magnetic resonance imaging may be useful in the staging of carcinoma of the prostate.... Magnetic resonance imaging offers new possibilities in the investigation of the prostate. The current results of imaging and tissue discrimination in the evaluation of prostatic disease are reviewed. Magnetic resonance imaging may be of value in the staging of carcinoma of the prostate.... Resonant double photoionisation spectroscopy of strontium Sokell, E; Grimm, M; Sheridan, P, E-mail: [email protected], E-mail: [email protected] [School of Physics, University College Dublin, Belfield, Dublin 4 (Ireland) Resonant triple-differential cross-section (TDCS) measurements on atomic strontium on the 4p {yields} 4d resonance are presented. All of these TDCS measurements display unexpected lobes at a mutual emission angle for the two electrons of 180{sup o}. Possible explanations for these lobes are explored. Neutron resonance parameters for 238U Poortmans, F.; Mewissen, L.; Cornelis, E.; Vanpraet, G.; Rohr, G.; Shelley, R.; Veen, T. van der; Weigmann, H. A series of total, capture and scattering cross section measurements using the neutron time-of-flight facility at the CBNM linear electron accelerator were performed. The neutron widths have been obtained for more than 400 resonances below 4.3 keV and the total capture width for 73 resonances Random search for a dark resonance Kiilerich, Alexander Holm; Mølmer, Klaus A pair of resonant laser fields can drive a three-level system into a dark state where it ceases to absorb and emit radiation due to destructive interference. We propose a scheme to search for this resonance by randomly changing the frequency of one of the fields each time a fluorescence photon... Dynamic Resonance Sensitivity Analysis in Wind Farms Ebrahimzadeh, Esmaeil; Blaabjerg, Frede; Wang, Xiongfei (PFs) are calculated by critical eigenvalue sensitivity analysis versus the entries of the MIMO matrix. The PF analysis locates the most exciting bus of the resonances, where can be the best location to install the passive or active filters to reduce the harmonic resonance problems. Time... Vibrational resonance in the Morse oscillator In the damped and biharmonically driven classical Morse oscillator, by applying a theoretical approach, an analytical expression is obtained for the response amplitude at the low-frequency . Conditions are identified on the parameters for the occurrence of resonance. The system shows only one resonance and moreover ... Josephson plasma resonance in superconducting multilayers Pedersen, Niels Falsig We derive an analytical solution for the josephson plasma resonance of superconducting multilayers. This analytical solution is derived mainly for low T-c systems with magnetic coupling between the superconducting layers, but many features of our results are more general, and thus an application...... to the recently derived plasma resonance phenomena for high T-c superconductors of the BSCCO type is discussed.... Home; Journals; Resonance – Journal of Science Education. Face to Face. Articles in Resonance – Journal of Science Education. Volume 13 Issue 1 January 2008 pp 89-98 Face to Face. Viewing Life Through Numbers · C Ramakrishnan Sujata Varadarajan · More Details Fulltext PDF. Volume 13 Issue 3 March 2008 pp ... Home; Journals; Resonance – Journal of Science Education. Deepak Nandi. Articles written in Resonance – Journal of Science Education. Volume 23 Issue 2 February 2018 pp 197-217 General Article. Thymus: The site for Development of Cellular Immunity · Shamik Majumdar Sanomy Pathak Deepak Nandi · More Details ... Stark resonances: asymptotics and distributional Borel sum Caliceti, E.; Grecchi, V.; Maioli, M. We prove that the Stark effect perturbation theory of a class of bound states uniquely determines the position and the width of the resonances by Distributional Borel Sum. In particular the small field asymptotics of the width is uniquely related to the large order asymptotics of the perturbation coefficients. Similar results apply to all the ''resonances'' of the anharmonic and double well oscillators. (orig.) Looking inside giant resonance fine structure Ponomarev, V.Yu.; Voronov, V.V. Microscopic calculations of the fine structure of giant resonances for spherical nuclei are presented. Excited states are treated by wave function which takes into account coupling of simple one-phonon configurations with more complex ones. Nuclear structure calculations are applied to the description of the γ-decay of resonances into the ground and low-lying excited states. 16 refs.; 4 figs Systematic study on nuclear resonant scattering Suarez, A.A.; Freitas, M.L. New resonant scattering effect of thermal neutron capture gamma rays from Ti and Fe on Sb, Cu, Se and Ce target were observed. These results together with those published by other authors are summarized and discussed in terms of a possible systematic search for new resonant scattering effects Single voxel magnetic resonance spectroscopy in distinguishing ... Objective: Assess diagnostic utility of combined magnetic resonance imaging and magnetic resonance spectroscopy (MRI, MRS) in differentiating focal neoplastic lesions from focal non- neoplastic (infective or degenerative) brain lesions. Design: Descriptive, analytical - prospective study. Setting: The Aga Khan University ... Magnetic resonance imaging of radiation optic neuropathy Zimmerman, C.F.; Schatz, N.J.; Glaser, J.S. Three patients with delayed radiation optic neuropathy after radiation therapy for parasellar neoplasms underwent magnetic resonance imaging. The affected optic nerves and chiasms showed enlargement and focal gadopentetate dimeglumine enhancement. The magnetic resonance imaging technique effectively detected and defined anterior visual pathway changes of radionecrosis and excluded the clinical possibility of visual loss because of tumor recurrence Magnetic resonance: discovery, investigations, and applications Kessenikh, Aleksandr V The history of the development of the theoretical ideas and experimental methods of magnetic resonance, as well as the applications of these methods in modern natural science, technology, and medicine, are outlined, with allowance for the contribution of Russian researchers. An assessment of some promising trends of studies and applications of magnetic resonance is given. (from the history of physics) Contrast agents in magnetic resonance imaging Karadjian, V. The origine of nuclear magnetic resonance signal is reminded and different ways for contrast enhancement in magnetic resonance imaging are presented, especially, modifications of tissus relaxation times. Investigations have focused on development of agents incorporating either paramagnetic ions or stable free radicals. Pharmacological and toxicological aspects are developed. The diagnostic potential of these substances is illustrated by the example of gadolinium complexes [fr The nuclear magnetic resonance well logging Zhang Yumin; Shen Huitang In this paper, the characteristic of the nuclear magnetic resonance logging is described at first. Then its development and its principle is presented. Compared with the nuclear magnetic resonance spectrometer, the magnet techniques is the first question that we must solve in the manufacture of the NMR well logging Few-body system and particle resonances Mubarak, Ahmad. Techniques of few-body system in nuclear physics are exploited to analyze the spectrum of the T resonance and its family. Their relation to nuclear resonances are established so as to apply few-body dynamical techniques in the dynamical structure of particles carrying the truth quantum number. (author) Electromagnetic resonance waves. Resonancias de ondas electromagneticas We describe in this paper a set of experiments designed to make qualitative and quantitative measurements on electromagnetic resonances of several simple systems. The experiments are designed for the undergraduate laboratory of Electricity and Magnetism in Physics. These experiments can help the students understanding the concept of resonance, which appears in different fields of Physics. (Author) 8 refs. New applications of surface plasmon resonance technology Zhang Tianhao; Yin Meirong; Fang Zheyu; Yang Haidong; Yang Jia; Yang Huizhan; Kang Huizhen; Yang Dapeng; Lu Yanzhen Surface plasmon resonance technology is reviewed and its new applications in various fields are described. These fields include surface plasmon resonance sensors, near-field scanning optical microscopy, thin film optics and thickness measurement, holography, precise measurement of angles, and Q switching. (authors) Principles and theory of resonance power supplies Sreenivas, A.; Karady, G.G. The resonance power supply is widely used and proved to be an efficient method to supply accelerator magnets. The literature describes several power supply circuits but no comprehensive theory of operation is presented. This paper presents a mathematical method which describes the operation of the resonance power supply and it can be used for accurate design of components Resonance contribution to electromagnetic structure functions Bowling, A.L. Jr. The part of the pion and proton electromagnetic structure functions due to direct channel resonances in the virtual Compton amplitude is discussed. After a phenomenological discussion, based on the work of Bloom and Gilman, of resonance production in inelastic electroproduction, the single resonance contribution to the pion and proton structure functions is expressed in terms of transition form factors. Froissart-Gribov representations of the Compton amplitude partial waves are presented and are used to specify the spin dependence of the transition form factors. The dependence of the form factors on momentum transfer and resonance mass is assumed on the basis of the behavior of exclusive resonance electroproduction. The single resonance contributions are summed in the Bjorken limit, and the result exhibits Bjorken scaling. Transverse photons are found to dominate in the Bjorken limit, and the threshold behavior of the resonant part of the structure functions is related to the asymptotic behavior of exclusive form factors at large momentum transfer. The resonant parts of the annihilation structure functions are not in general given by simple analytic continuation in the scaling vari []ble ω' of the electroproduction structure functions. (Diss. Abstr. Int., B) Simple classical approach to spin resonance phenomena Gordon, R A A simple classical method of describing spin resonance in terms of the average power absorbed by a spin system is discussed. The method has several advantages over more conventional treatments, and a number of important spin resonance phenomena, not normally considered at the introductory level... Resonances in Electron Impact on Atomic Oxygen Yang, Wang; Ya-Jun, Zhou; Li-Guang, Jiao; Ratnavelu, Kuru The momentum-space coupled-channels-optical (CCO) method is used to study the resonances in electron-oxygen collision in the energy region of 9–12eV. Present results have shown agreement with the available experimental and theoretical results, and new positions of resonances are found by the comparison of total cross sections. (fundamental areas of phenomenology (including applications)) Resonances in η-light nucleus systems We locate resonances in -light nucleus elastic scattering using the time delay method. We solve few-body equations within the finite rank approximation in order to calculate the -matrices and hence the time delay for the - 3He and - 4He systems. We find a resonance very close to the threshold in - 3 He elastic ... Your Radiologist Explains Magnetic Resonance Angiography (MRA) Full Text Available ... Sponsored by Image/Video Gallery Your Radiologist Explains Magnetic Resonance Angiography (MRA) Transcript Welcome to Radiology Info dot ... I'd like to talk with you about magnetic resonance angiography, or as it's commonly known, MRA. MRA ... Neutron resonance parameters of CM isotopes Belanova, T.S.; Kolesov, A.G.; Poruchikov, V.A. The total neutron cross sections of isotopes 244, 245, 246, 248 Curium have been measured on reactor CM-2 using the time-of-flight method. Single-level Breit-Wigner resonance parameters: energy E 0 , neutron width 2g GITAn, total width GITA, total neutron cross section in resonance sigma 0 have been obtained by the shape and area methods Home; Journals; Resonance – Journal of Science Education. Film Review. Articles in Resonance – Journal of Science Education. Volume 22 Issue 3 March 2017 pp 317-318 Film Review. The Untold Story of NASA's Trailblazers: Hidden Figures sheds light on the contributions of black women to the US Space Race. Review of meson resonance radiative decays Thorndike, E.H. The radiative decays of meson resonances can be studied by three different approaches, it is noted. These are the meson-exchange, Primakoff effect, and the production of the desired resonance and subsequent observation of its decay. These approaches are criticized and examples of them are reviewed. Mass distributions are shown and branching ratios discussed. 21 references Thermally actuated resonant silicon crystal nanobalances Hajjam, Arash As the potential emerging technology for next generation integrated resonant sensors and frequency references as well as electronic filters, micro-electro-mechanical resonators have attracted a lot of attention over the past decade. As a result, a wide variety of high frequency micro/nanoscale electromechanical resonators have recently been presented. MEMS resonators, as low-cost highly integrated and ultra-sensitive mass sensors, can potentially provide new opportunities and unprecedented capabilities in the area of mass sensing. Such devices can provide orders of magnitude higher mass sensitivity and resolution compared to Film Bulk Acoustic resonators (FBAR) or the conventional quartz and Surface Acoustic Wave (SAW) resonators due to their much smaller sizes and can be batch-fabricated and utilized in highly integrated large arrays at a very low cost. In this research, comprehensive experimental studies on the performance and durability of thermally actuated micromechanical resonant sensors with frequencies up to tens of MHz have been performed. The suitability and robustness of the devices have been demonstrated for mass sensing applications related to air-borne particles and organic gases. In addition, due to the internal thermo-electro-mechanical interactions, the active resonators can turn some of the consumed electronic power back into the mechanical structure and compensate for the mechanical losses. Therefore, such resonators can provide self-sustained-oscillation without the need for any electronic circuitry. This unique property has been deployed to demonstrate a prototype self-sustained sensor for air-borne particle monitoring. I have managed to overcome one of the obstacles for MEMS resonators, which is their relatively poor temperature stability. This is a major drawback when compared with the conventional quartz crystals. A significant decrease of the large negative TCF for the resonators has been attained by doping the devices with a high Coherent and incoherent processes in resonant photoemission Magnuson, M.; Karis, O.; Weinelt, M. [Uppsala Univ. (Sweden)] [and others In this contribution the authors present the distinction between coherent and incoherent processes in resonant photoemission. As a first step they determine whether an autoionization process is photoemission-like or Auger-like. The discussion is based on measurements for a weakly bonded adsorption system, Ar/Pt(111). This type of system is well adapted to investigate these effects since it yields distinctly shifted spectral features depending on the nature of the process. After this, the question of resonance photoemission in metallic systems is addressed. This is done in connection with measurements at the 2p edges for Ni metal. Ni has been one of the prototype systems for resonant photoemission. The resonances have been discussed in connection with the strong correlation and d-band localization effects in this system. Based on the results some general comments about the appearance of resonant effects in metallic systems are made. Analytical approximations for wide and narrow resonances Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da This paper aims at developing analytical expressions for the adjoint neutron spectrum in the resonance energy region, taking into account both narrow and wide resonance approximations, in order to reduce the numerical computations involved. These analytical expressions, besides reducing computing time, are very simple from a mathematical point of view. The results obtained with this analytical formulation were compared to a reference solution obtained with a numerical method previously developed to solve the neutron balance adjoint equations. Narrow and wide resonances of U 238 were treated and the analytical procedure gave satisfactory results as compared with the reference solution, for the resonance energy range. The adjoint neutron spectrum is useful to determine the neutron resonance absorption, so that multigroup adjoint cross sections used by the adjoint diffusion equation can be obtained. (author) Suster, Luis Carlos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear]. E-mail: [email protected] This paper aims at developing analytical expressions for the adjoint neutron spectrum in the resonance energy region, taking into account both narrow and wide resonance approximations, in order to reduce the numerical computations involved. These analytical expressions, besides reducing computing time, are very simple from a mathematical point of view. The results obtained with this analytical formulation were compared to a reference solution obtained with a numerical method previously developed to solve the neutron balance adjoint equations. Narrow and wide resonances of U{sup 238} were treated and the analytical procedure gave satisfactory results as compared with the reference solution, for the resonance energy range. The adjoint neutron spectrum is useful to determine the neutron resonance absorption, so that multigroup adjoint cross sections used by the adjoint diffusion equation can be obtained. (author) Observations of Snake Resonance in RHIC Bai, Mei; Lee, Shyh-Yuan; Lin, Fanglei; MacKay, William; Ptitsyn, Vadim; Roser, Thomas; Tepikian, Steven Siberian snakes now become essential in the polarized proton acceleration. With proper configuration of Siberian snakes, the spin precession tune of the beam becomes $\\frac{1}{2}$ which avoids all the spin depolarizing resonance. However, the enhancement of the perturbations on the spin motion can still occur when the betatron tune is near some low order fractional numbers, called snake resonances, and the beam can be depolarized when passing through the resonance. The snake resonances have been confirmed in the spin tracking calculations, and observed in RHIC with polarized proton beam. Equipped with two full Siberian snakes in each ring, RHIC provides us a perfect facility for snake resonance studies. This paper presents latest experimental results. New insights are also discussed. Tunable Magnetic Resonance in Microwave Spintronics Devices Chen, Yunpeng; Fan, Xin; Xie, Yunsong; Zhou, Yang; Wang, Tao; Wilson, Jeffrey D.; Simons, Rainee N.; Chui, Sui-Tat; Xiao, John Q. Magnetic resonance is one of the key properties of magnetic materials for the application of microwave spintronics devices. The conventional method for tuning magnetic resonance is to use an electromagnet, which provides very limited tuning range. Hence, the quest for enhancing the magnetic resonance tuning range without using an electromagnet has attracted tremendous attention. In this paper, we exploit the huge exchange coupling field between magnetic interlayers, which is on the order of 4000 Oe and also the high frequency modes of coupled oscillators to enhance the tuning range. Furthermore, we demonstrate a new scheme to control the magnetic resonance frequency. Moreover, we report a shift in the magnetic resonance frequency as high as 20 GHz in CoFe based tunable microwave spintronics devices, which is 10X higher than conventional methods. Coherence Phenomena in Coupled Optical Resonators Smith, D. D.; Chang, H. We predict a variety of photonic coherence phenomena in passive and active coupled ring resonators. Specifically, the effective dispersive and absorptive steady-state response of coupled resonators is derived, and used to determine the conditions for coupled-resonator-induced transparency and absorption, lasing without gain, and cooperative cavity emission. These effects rely on coherent photon trapping, in direct analogy with coherent population trapping phenomena in atomic systems. We also demonstrate that the coupled-mode equations are formally identical to the two-level atom Schrodinger equation in the rotating-wave approximation, and use this result for the analysis of coupled-resonator photon dynamics. Notably, because these effects are predicted directly from coupled-mode theory, they are not unique to atoms, but rather are fundamental to systems of coherently coupled resonators. D-wave resonances in positronium hydride DiRienzi, Joseph; Drachman, Richard J. In a previous paper [Phys. Rev. A 65, 032721 (2002)] we reexamined a model describing the structure of the low-energy Ps-H resonances as being due to quasibound states of the positron in the perturbed Coulomb potential of the H - ion appearing in the closed, rearranged channel. In particular, we wished to understand why the lowest p-state resonance was so far away from the lowest quasibound (2p) state. We found that the lowest resonance actually corresponds to the first-excited [3p] state, while the lowest state is not recognizable as a resonance. In the present work we repeat our analysis, but this time for the lowest d state. We find that the lowest [3d] state does correspond to a resonance shifted moderately Hybrid simulation of electron cyclotron resonance heating Ropponen, T. [Department of Physics, University of Jyvaeskylae, P.O. Box 35, FI-40014 (Finland)], E-mail: [email protected]; Tarvainen, O. [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Suominen, P. [CERN Geneve 23, CH-1211 (Switzerland); Koponen, T.K. [Department of Physics, University of Jyvaeskylae, Nanoscience Center, P.O. Box 35, FI-40014 (Finland); Kalvas, T.; Koivisto, H. [Department of Physics, University of Jyvaeskylae, P.O. Box 35, FI-40014 (Finland) Electron Cyclotron Resonance (ECR) heating is a fundamentally important aspect in understanding the physics of Electron Cyclotron Resonance Ion Sources (ECRIS). Absorption of the radio frequency (RF) microwave power by electron heating in the resonance zone depends on many parameters including frequency and electric field strength of the microwave, magnetic field structure and electron and ion density profiles. ECR absorption has been studied in the past by e.g. modelling electric field behaviour in the resonance zone and its near proximity. This paper introduces a new ECR heating code that implements damping of the microwave power in the vicinity of the resonance zone, utilizes electron density profiles and uses right hand circularly polarized (RHCP) electromagnetic waves to simulate electron heating in ECRIS plasma. Integral data analysis for resonance parameters determination Larson, N.M.; Leal, L.C.; Derrien, H. Neutron time-of-flight experiments have long been used to determine resonance parameters. Those resonance parameters have then been used in calculations of integral quantities such as Maxwellian averages or resonance integrals, and results of those calculations in turn have been used as a criterion for acceptability of the resonance analysis. However, the calculations were inadequate because covariances on the parameter values were not included in the calculations. In this report an effort to correct for that deficiency is documented: (1) the R-matrix analysis code SAMMY has been modified to include integral quantities of importance, (2) directly within the resonance parameter analysis, and (3) to determine the best fit to both differential (microscopic) and integral (macroscopic) data simultaneously. This modification was implemented because it is expected to have an impact on the intermediate-energy range that is important for criticality safety applications Membrane metamaterial resonators with a sharp resonance: A comprehensive study towards practical terahertz filters and sensors Yongyao Chen Full Text Available We investigate the resonant properties of high quality-factor membrane-based metamaterial resonators functioning in the terahertz regime. A number of factors, including the resonator geometry, dielectric loss, and most importantly the membrane thickness are found to extensively influence the resonance strength and quality factor of the sharp resonance. Further studies on the membrane thickness-dependent-sensitivity for sensing applications reveal that high quality-factor membrane metamaterials with a moderate thickness ranging from 10 to 50 μm are the most promising option towards developing realistic integrated terahertz filters and sensors. Orbital Resonances in the Vinti Solution Zurita, L. D. As space becomes more congested, contested, and competitive, high-accuracy orbital predictions become critical for space operations. Current orbit propagators use the two-body solution with perturbations added, which have significant error growth when numerically integrated for long time periods. The Vinti Solution is a more accurate model than the two-body problem because it also accounts for the equatorial bulge of the Earth. Unfortunately, the Vinti solution contains small divisors near orbital resonances in the perturbative terms of the Hamiltonian, which lead to inaccurate orbital predictions. One approach to avoid the small divisors is to apply transformation theory, which is presented in this research. The methodology of this research is to identify the perturbative terms of the Vinti Solution, perform a coordinate transformation, and derive the new equations of motion for the Vinti system near orbital resonances. An analysis of these equations of motion offers insight into the dynamics found near orbital resonances. The analysis in this research focuses on the 2:1 resonance, which includes the Global Positioning System. The phase portrait of a nominal Global Positioning System satellite orbit is found to contain a libration region and a chaotic region. Further analysis shows that the dynamics of the 2:1 resonance affects orbits with semi-major axes ranging from -5.0 to +5.4 kilometers from an exactly 2:1 resonant orbit. Truth orbits of seven Global Positioning System satellites are produced for 10 years. Two of the satellites are found to be outside of the resonance region and three are found to be influenced by the libration dynamics of the resonance. The final satellite is found to be influenced by the chaotic dynamics of the resonance. This research provides a method of avoiding the small divisors found in the perturbative terms of the Vinti Solution near orbital resonances. 3C-SiC microdisk mechanical resonators with multimode resonances at radio frequencies Lee, Jaesung; Zamani, Hamidrera; Rajgopal, Srihari; Zorman, Christian A.; X-L Feng, Philip We report on the design, modeling, fabrication and measurement of single-crystal 3C-silicon carbide (SiC) microdisk mechanical resonators with multimode resonances operating at radio frequencies (RF). These microdisk resonators (center-clamped on a vertical stem pedestal) offer multiple flexural-mode resonances with frequencies dependent on both disk and anchor dimensions. The resonators are made using a novel fabrication method comprised of focused ion beam nanomachining and hydroflouic : nitric : acetic (HNA) acid etching. Resonance peaks (in the frequency spectrum) are detected through laser-interferometry measurements. Resonators with different dimensions are tested, and multimode resonances, mode splitting, energy dissipation (in the form of quality factor measurement) are investigated. Further, we demonstrate a feedback oscillator based on a passive 3C-SiC resonator. This investigation provides important guidelines for microdisk resonator development, ranging from an analytical prediction of frequency scaling law to fabrication, suggesting RF microdisk resonators can be good candidates for future sensing applications in harsh environments. Influence of resonance parameters' correlations on the resonance integral uncertainty; 55Mn case Zerovnik, Gasper; Trkov, Andrej; Capote, Roberto; Rochman, Dimitri For nuclides with a large number of resonances the covariance matrix of resonance parameters can become very large and expensive to process in terms of the computation time. By converting covariance matrix of resonance parameters into covariance matrices of background cross-section in a more or less coarse group structure a considerable amount of computer time and memory can be saved. The question is how important is the information that is discarded in the process. First, the uncertainty of the 55 Mn resonance integral was estimated in narrow resonance approximation for different levels of self-shielding using Bondarenko method by random sampling of resonance parameters according to their covariance matrices from two different 55 Mn evaluations: one from Nuclear Research and Consultancy Group NRG (with large uncertainties but no correlations between resonances), the other from Oak Ridge National Laboratory (with smaller uncertainties but full covariance matrix). We have found out that if all (or at least significant part of the) resonance parameters are correlated, the resonance integral uncertainty greatly depends on the level of self-shielding. Second, it was shown that the commonly used 640-group SAND-II representation cannot describe the increase of the resonance integral uncertainty. A much finer energy mesh for the background covariance matrix would have to be used to take the resonance structure into account explicitly, but then the objective of a more compact data representation is lost. Lateral acoustic wave resonator comprising a suspended membrane of low damping resonator material Olsson, Roy H.; El-Kady; , Ihab F.; Ziaei-Moayyed, Maryam; Branch; , Darren W.; Su; Mehmet F.,; Reinke; Charles M., A very high-Q, low insertion loss resonator can be achieved by storing many overtone cycles of a lateral acoustic wave (i.e., Lamb wave) in a lithographically defined suspended membrane comprising a low damping resonator material, such as silicon carbide. The high-Q resonator can sets up a Fabry-Perot cavity in a low-damping resonator material using high-reflectivity acoustic end mirrors, which can comprise phononic crystals. The lateral overtone acoustic wave resonator can be electrically transduced by piezoelectric couplers. The resonator Q can be increased without increasing the impedance or insertion loss by storing many cycles or wavelengths in the high-Q resonator material, with much lower damping than the piezoelectric transducer material. Iterative resonance self-shielding methods using resonance integral table in heterogeneous transport lattice calculations Hong, Ser Gi; Kim, Kang-Seog This paper describes the iteration methods using resonance integral tables to estimate the effective resonance cross sections in heterogeneous transport lattice calculations. Basically, these methods have been devised to reduce an effort to convert resonance integral table into subgroup data to be used in the physical subgroup method. Since these methods do not use subgroup data but only use resonance integral tables directly, these methods do not include an error in converting resonance integral into subgroup data. The effective resonance cross sections are estimated iteratively for each resonance nuclide through the heterogeneous fixed source calculations for the whole problem domain to obtain the background cross sections. These methods have been implemented in the transport lattice code KARMA which uses the method of characteristics (MOC) to solve the transport equation. The computational results show that these iteration methods are quite promising in the practical transport lattice calculations. Erbium-doped fiber ring resonator for resonant fiber optical gyro applications Li, Chunming; Zhao, Rui; Tang, Jun; Xia, Meijing; Guo, Huiting; Xie, Chengfeng; Wang, Lei; Liu, Jun This paper reports a fiber ring resonator with erbium-doped fiber (EDF) for resonant fiber optical gyro (RFOG). To analyze compensation mechanism of the EDF on resonator, a mathematical model of the erbium-doped fiber ring resonator (EDFRR) is established based on Jones matrix to be followed by the design and fabrication of a tunable EDFRR. The performances of the fabricated EDFRR were measured and the experimental Q-factor of 2 . 47 × 108 and resonant depth of 109% were acquired separately. Compared with the resonator without the EDF, the resonant depth and Q-factor of the proposed device are increased by 2.5 times and 14 times, respectively. A potential optimum shot noise limited resolution of 0 . 042∘ / h can be obtained for the RFOG, which is promising for low-cost and high precise detection. Magnetic resonance imaging of hypophysis Malla Huesh, I. V. Hypothalamic-pituitary diseases represent with wide variety of symptoms in regard with changes in the endocrine function. Magnetic resonance imaging has a crucial role in detecting the morphologic appearance in physiologic conditions, malformative diseases and acquired pathologies. The MR-imaging is established as the method of choice in assessing the changes in the hypothalamic-pituitary axis. The pituitary gland is a complex structure with an important role in the homeostasis of the organism even though it is so small? It is surrounded by bony structures, vessels, nerves and the brain parenchyma. It consists of three parts - anterior called - adenohypophysis, posterior - neurohypophysis and pituitary stalk. The anterior part comprises about 75% of the gland. Computed tomography (CT) has a limited role in detecting the pituitary gland. It is mainly used in cases of elevated intracranial pressure due to suspected apoplexy. The gland's small size, relation to other structures and its soft tissue characteristic make it an accessible region of interest for detecting with MR-imaging. The lack of ionizing energy and the technical advances in the MR-methods are responsible for the creating images with better spatial resolution and signal to noise ratio. The examination is carried out on a standard protocol. It is important that thin slices are executed in sagittal and coronal planes. Performing a sequence, regarding the brain parenchyma is essential, since many malformations of the pituitary gland are associated with other congenital conditions. The examination starts with a T1W sequence to assess the normal anatomic condition of the gland. The intensity of the adenohypophysis is compared to the one in the pons. It is hypointense, whereas the neurohypophysis is hyperintense, due to the lipid neurosecretory granules transported along the hypothalamic-pituitary axis. T2W-images in coronal plane are used to evaluate the hypothalamus, pituitary stalk, optic chiasm, olfactory Theory and Applications of Surface Plasmon Resonance, Resonant Mirror, Resonant Waveguide Grating, and Dual Polarization Interferometry Biosensors Billy W. Day Full Text Available Biosensors have been used extensively in the scientific community for several purposes, most notably to determine association and dissociation kinetics, protein-ligand, protein-protein, or nucleic acid hybridization interactions. A number of different types of biosensors are available in the field, each with real or perceived benefits over the others. This review discusses the basic theory and operational arrangements of four commercially available types of optical biosensors: surface plasmon resonance, resonant mirror, resonance waveguide grating, and dual polarization interferometry. The different applications these techniques offer are discussed from experiments and results reported in recently published literature. Additionally, recent advancements or modifications to the current techniques are also discussed. Ionization Cooling using Parametric Resonances Johnson, Rolland P. Ionization Cooling using Parametric Resonances was an SBIR project begun in July 2004 and ended in January 2008 with Muons, Inc., (Dr. Rolland Johnson, PI), and Thomas Jefferson National Accelerator Facility (JLab) (Dr. Yaroslav Derbenev, Subcontract PI). The project was to develop the theory and simulations of Parametric-resonance Ionization Cooling (PIC) so that it could be used to provide the extra transverse cooling needed for muon colliders in order to relax the requirements on the proton driver, reduce the site boundary radiation, and provide a better environment for experiments. During the course of the project, the theoretical understanding of PIC was developed and a final exposition is ready for publication. Workshops were sponsored by Muons, Inc. in May and September of 2007 that were devoted to the PIC technique. One outcome of the workshops was the interesting and somewhat unexpected realization that the beam emittances using the PIC technique can get small enough that space charge forces can be important. A parallel effort to develop our G4beamline simulation program to include space charge effects was initiated to address this problem. A method of compensating for chromatic aberrations by employing synchrotron motion was developed and simulated. A method of compensating for spherical aberrations using beamline symmetry was also developed and simulated. Different optics designs have been developed using the OptiM program in preparation for applying our G4beamline simulation program, which contains all the power of the Geant4 toolkit. However, no PIC channel design that has been developed has had the desired cooling performance when subjected to the complete G4beamline simulation program. This is believed to be the consequence of the difficulties of correcting the aberrations associated with the naturally large beam angles and beam sizes of the PIC method that are exacerbated by the fringe fields of the rather complicated channel designs that have been Wave energy extraction by coupled resonant absorbers. Evans, D V; Porter, R In this article, a range of problems and theories will be introduced that will build towards a new wave energy converter (WEC) concept, with the acronym 'ROTA' standing for resonant over-topping absorber. First, classical results for wave power absorption for WECs constrained to operate in a single degree of freedom will be reviewed and the role of resonance in their operation highlighted. Emphasis will then be placed on how the introduction of further resonances can improve power take-off characteristics by extending the range of frequencies over which the efficiency is close to a theoretical maximum. Methods for doing this in different types of WECs will be demonstrated. Coupled resonant absorbers achieve this by connecting a WEC device equipped with its own resonance (determined from a hydrodynamic analysis) to a new system having separate mass/spring/damper characteristics. It is shown that a coupled resonant effect can be realized by inserting a water tank into a WEC, and this idea forms the basis of the ROTA device. In essence, the idea is to exploit the coupling between the natural sloshing frequencies of the water in the internal tank and the natural resonance of a submerged buoyant circular cylinder device that is tethered to the sea floor, allowing a rotary motion about its axis of attachment. Acoustic Resonance between Ground and Thermosphere M Matsumura Full Text Available Ultra-low frequency acoustic waves called "acoustic gravity waves" or "infrasounds" are theoretically expected to resonate between the ground and the thermosphere. This resonance is a very important phenomenon causing the coupling of the solid Earth, neutral atmosphere, and ionospheric plasma. This acoustic resonance, however, has not been confirmed by direct observations. In this study, atmospheric perturbations on the ground and ionospheric disturbances were observed and compared with each other to confirm the existence of resonance. Atmospheric perturbations were observed with a barometer, and ionospheric disturbances were observed using the HF Doppler method. An end point of resonance is in the ionosphere, where conductivity is high and the dynamo effect occurs. Thus, geomagnetic observation is also useful, so the geomagnetic data were compared with other data. Power spectral density was calculated and averaged for each month. Peaks appeared at the theoretically expected resonance frequencies in the pressure and HF Doppler data. The frequencies of the peaks varied with the seasons. This is probably because the vertical temperature profile of the atmosphere varies with the seasons, as does the reflection height of infrasounds. These results indicate that acoustic resonance occurs frequently. Nakamura, Yusaku; Takahashi, Mitsuo; Kitaguchi, Masataka; Akaneya, Yukio; Mitui, Yoshiyuki; Tanaka, Hisashi We studied eighteen patients affected by Parkinsonism with symptoms of tremor, bradykinesia, or rigidity using magnetic resonance imaging (MRI). Patients ranged in age from 34 to 80 years (mean 62.8±11.6 years), and the duration of their disease had been 3.8±3.2 years. MRI examinations were performed with Shimazu and Siemens superconducting magnets, operating at 0.5 and 1.5 T magnetic fields, respectively. Both T 1 - and T 2 -weighted spin echo (SE) pulse sequences were used. In eight patients (44.4%), MRI demonstrated bilateral multiple lacunar infarction of the basal ganglia. The most common abnormality identified was multiple, bilateral lacunar infarcts in the lateral portion of the putamen. The average size of the lacunar infarction of the putamen was less than half that of the entire putamen. Patients with multiple lacunar infarction were significantly older than the other patients and had lower Yahr's scores. The clinical symptoms of patients with bilateral multiple lacunar infarction of the basal ganglia were compatible with the diagnosis of arteriosclerotic Parkinsonism of akinetic rigid type. It has been suggested that multiple lacunar infarction of the basal ganglia may have led to Parkinsonism in these patients. (author) String Resonances at Hadron Colliders Anchordoqui, Luis A; Dai, De-Chang; Feng, Wan-Zhe; Goldberg, Haim; Huang, Xing; Lust, Dieter; Stojkovic, Dejan; Taylor, Tomasz R [Abridged] We consider extensions of the standard model based on open strings ending on D-branes. Assuming that the fundamental string mass scale M_s is in the TeV range and that the theory is weakly coupled, we discuss possible signals of string physics at the upcoming HL-LHC run (3000 fb^{-1}) with \\sqrt{s} = 14 TeV, and at potential future pp colliders, HE-LHC and VLHC, operating at \\sqrt{s} = 33 and 100 TeV, respectively. In such D-brane constructions, the dominant contributions to full-fledged string amplitudes for all the common QCD parton subprocesses leading to dijets and \\gamma + jet are completely independent of the details of compactification, and can be evaluated in a parameter-free manner. We make use of these amplitudes evaluated near the first (n=1) and second (n=2) resonant poles to determine the discovery potential for Regge excitations of the quark, the gluon, and the color singlet living on the QCD stack. We show that for string scales as large as 7.1 TeV (6.1 TeV), lowest massive Regge exc... Magnetic resonance in obstructive jaundice Gupta, R.K.; Jena, A.; Khushu, S.; Kakar, A.K.; Mishra, P.K. Twelve cases of obstructive jaundice in whom ultrasound failed to demonstrate the site and/or the cause of obstruction of the biliary tract were examined with magnetic resonance imaging (MRI), correctly diagnosing the site and cause of obstruction in 10 of 12 surgically proven cases. In one case of cholangiocarcinoma, the site of obstruction was well shown on MR but a definite cause could not be ascertained. In another patient who developed intermittent jaundice following surgery for choledochal cyst, MR demonstrated a solitary stone in the common hepatic duct. Surgical confirmation could not be achieved as the patient was lost to follow up. There were 6 cases of choledocholithiasis, 3 cases of gall bladder carcinoma and one case each of pancreatic adenocarcinoma and cholangiocarcinoma. It is believed that MRI will provide obstructive jaundice and will be able to minimize the use of percutaneous transhepatic cholangiography (PTC) and endoscopic retrograde cholangiopancreatography (ERCP) in view of its ability to perform multiplanar imaging in multiple sequences. 11 refs., figs., 1 tab Low rank magnetic resonance fingerprinting. Mazor, Gal; Weizman, Lior; Tal, Assaf; Eldar, Yonina C Magnetic Resonance Fingerprinting (MRF) is a relatively new approach that provides quantitative MRI using randomized acquisition. Extraction of physical quantitative tissue values is preformed off-line, based on acquisition with varying parameters and a dictionary generated according to the Bloch equations. MRF uses hundreds of radio frequency (RF) excitation pulses for acquisition, and therefore high under-sampling ratio in the sampling domain (k-space) is required. This under-sampling causes spatial artifacts that hamper the ability to accurately estimate the quantitative tissue values. In this work, we introduce a new approach for quantitative MRI using MRF, called Low Rank MRF. We exploit the low rank property of the temporal domain, on top of the well-known sparsity of the MRF signal in the generated dictionary domain. We present an iterative scheme that consists of a gradient step followed by a low rank projection using the singular value decomposition. Experiments on real MRI data demonstrate superior results compared to conventional implementation of compressed sensing for MRF at 15% sampling ratio. Multidimensionally encoded magnetic resonance imaging. Lin, Fa-Hsuan Magnetic resonance imaging (MRI) typically achieves spatial encoding by measuring the projection of a q-dimensional object over q-dimensional spatial bases created by linear spatial encoding magnetic fields (SEMs). Recently, imaging strategies using nonlinear SEMs have demonstrated potential advantages for reconstructing images with higher spatiotemporal resolution and reducing peripheral nerve stimulation. In practice, nonlinear SEMs and linear SEMs can be used jointly to further improve the image reconstruction performance. Here, we propose the multidimensionally encoded (MDE) MRI to map a q-dimensional object onto a p-dimensional encoding space where p > q. MDE MRI is a theoretical framework linking imaging strategies using linear and nonlinear SEMs. Using a system of eight surface SEM coils with an eight-channel radiofrequency coil array, we demonstrate the five-dimensional MDE MRI for a two-dimensional object as a further generalization of PatLoc imaging and O-space imaging. We also present a method of optimizing spatial bases in MDE MRI. Results show that MDE MRI with a higher dimensional encoding space can reconstruct images more efficiently and with a smaller reconstruction error when the k-space sampling distribution and the number of samples are controlled. Copyright © 2012 Wiley Periodicals, Inc. Cyclotron-Resonance-Maser Arrays Kesar, A.; Lei, L.; Dikhtyar, V.; Korol, M.; Jerby, E. The cyclotron-resonance-maser (CRM) array [1] is a radiation source which consists of CRM elements coupled together under a common magnetic field. Each CRM-element employs a low-energy electron-beam which performs a cyclotron interaction with the local electromagnetic wave. These waves can be coupled together among the CRM elements, hence the interaction is coherently synchronized in the entire array. The implementation of the CRM-array approach may alleviate several technological difficulties which impede the development of single-beam gyro-devices. Furthermore, it proposes new features, such as the phased-array antenna incorporated in the CRM-array itself. The CRM-array studies may lead to the development of compact, high-power radiation sources operating at low-voltages. This paper introduces new conceptual schemes of CRM-arrays, and presents the progress in related theoretical and experimental studies in our laboratory. These include a multi-mode analysis of a CRM-array, and a first operation of this device with five carbon-fiber cathodes Presurgical functional magnetic resonance imaging Stippich, C. Functional magnetic resonance imaging (fMRI) is an important and novel neuroimaging modality for patients with brain tumors. By non-invasive measurement, localization and lateralization of brain activiation, most importantly of motor and speech function, fMRI facilitates the selection of the most appropriate and sparing treatment and function-preserving surgery. Prerequisites for the diagnostic use of fMRI are the application of dedicated clinical imaging protocols and standardization of the respective imaging procedures. The combination with diffusion tensor imaging (DTI) also enables tracking and visualization of important fiber bundles such as the pyramidal tract and the arcuate fascicle. These multimodal MR data can be implemented in computer systems for functional neuronavigation or radiation treatment. The practicability, accuracy and reliability of presurgical fMRI have been validated by large numbers of published data. However, fMRI cannot be considered as a fully established modality of diagnostic neuroimaging due to the lack of guidelines of the responsible medical associations as well as the lack of medical certification of important hardware and software components. This article reviews the current research in the field and provides practical information relevant for presurgical fMRI. (orig.) [de Endometrial cancer: magnetic resonance imaging. Manfredi, R; Gui, B; Maresca, G; Fanfani, F; Bonomo, L Carcinoma of the endometrium is the most common invasive gynecologic malignancy of the female genital tract. Clinically, patients with endometrial carcinoma present with abnormal uterine bleeding. The role of magnetic resonance imaging (MRI) in endometrial carcinoma is disease staging and treatment planning. MRI has been shown to be the most valuable imaging mod-ality in this task, compared with endovaginal ultrasound and computed tomography, because of its intrinsic contrast resolution and multiplanar capability. MRI protocol includes axial T1-weighted images; axial, sagittal, and coronal T2-weighted images; and dynamic gadolinium-enhanced T1-weighted imaging. MR examination is usually performed in the supine position with a phased array multicoil using a four-coil configuration. Endometrial carcinoma is isointense with the normal endometrium and myometrium on noncontrast T1-weighted images and has a variable appearance on T2-weighted images demonstrating heterogeneous signal intensity. The appearance of noninvasive endometrial carcinoma on MRI is characterized by a normal or thickened endometrium, with an intact junctional zone and a sharp tumor-myometrium interface. Invasive endometrial carcinoma is characterized disruption or irregularity of the junctional zone by intermediate signal intensity mass on T2-weighted images. Invasion of the cervical stroma is diagnosed when the low signal intensity cervical stroma is disrupted by the higher signal intensity endometrial carcinoma. MRI in endometrial carcinoma performs better than other imaging modalities in disease staging and treatment planning. Further, the accuracy and the cost of MRI are equivalent to those of surgical staging. Endovascular interventional magnetic resonance imaging Bartels, L W; Bakker, C J G Minimally invasive interventional radiological procedures, such as balloon angioplasty, stent placement or coiling of aneurysms, play an increasingly important role in the treatment of patients suffering from vascular disease. The non-destructive nature of magnetic resonance imaging (MRI), its ability to combine the acquisition of high quality anatomical images and functional information, such as blood flow velocities, perfusion and diffusion, together with its inherent three dimensionality and tomographic imaging capacities, have been advocated as advantages of using the MRI technique for guidance of endovascular radiological interventions. Within this light, endovascular interventional MRI has emerged as an interesting and promising new branch of interventional radiology. In this review article, the authors will give an overview of the most important issues related to this field. In this context, we will focus on the prerequisites for endovascular interventional MRI to come to maturity. In particular, the various approaches for device tracking that were proposed will be discussed and categorized. Furthermore, dedicated MRI systems, safety and compatibility issues and promising applications that could become clinical practice in the future will be discussed. (topical review) Magnetic resonance imaging and neurolupus Schott, A.M.; Colson, F.; Tebib, J.; Noel, E.; Bouvier, M. Magnetic resonance imaging (MRI) was assessed in the management of neuropsychiatric manifestations occurring in 6 SLE patients. The MRI scans were normal in 3 cases and was associated with remission of the symptoms except for a patient who experienced a chorea at the time of the examination. Abnormal MRI scans always revealed more lesions than CT scan. 2 different patterns of abnormalities seem to correspond to 2 specific disorders. In 2 patients with clinical presentation suggesting a cortical ischemia by vascular thrombosis, both MRI scans showed areas of abnormal high signal intensities located in the subcortical white matter. In one last patient, MRI scan revealed multiple focal areas of high signal intensities (on T 1 weighter scans) disseminated not only in the deep white matter but also in the gray one. These lesions could be depend upon demyelinisation which may occur by a local vascular process. This serie confirms the interest of MRI in the management of SLE brain involvement as well as it points out some problem of interpretation. This suggest further comparative studies especially at the real onset and during the course of neuro-psychiatric manifestations. At last, the coronal sections may be more informative for the diagnosis and patholophysiology than the horizontal ones [fr Strangeness photoproduction and hadronic resonances David, J.C. The purpose of this thesis is to study the kaon photoproduction off a proton (γp → K + Λ,γp → K + Σ 0 , γp → K 0 Σ + ), with a photon energy between 0.9 and 2.1 GeV. We use an isobaric model where the amplitudes are computed with Feynman diagrams. The insertion of nucleonic resonances with spin 3/2 and 5/2 is necessary to improve the existing models beyond 1.5 GeV. This step is also necessary to extend the elementary process of photoproduction to electroproduction where the data have been taken with photon energies above 2.0 GeV. The parameters of our models are the coupling constants which appear at each Feynman diagram vertex. They are determined by fitting our models to the experimental data (cross sections, polarization asymmetries). Before performing the minimization we drew some informations about coupling constants from mesonic and electromagnetic decays, and from SU(3) and SU(6) symmetries. In conclusion, the models developed here reproduce the experimental data (E γ ≤ 2.0 GeV) and the two main coupling constants are in good agreement with broken SU(3)-symmetry predictions. (author) Magnetic resonance in multiple sclerosis Scotti, G.; Caputo, D.; Cazzullo, C.L. Magnetic Resonance Imaging was performed in more than 200 patients with clinical suspicion or knowledge of Multiple Sclerosis. One hundred and forty-seven (60 males and 87 females) had MR evidence of multiple sclerosis lesions. The MR signal of demyelinating plaques characteristically has prolonged T1 and T2 relaxation times and the T2-weighted spin-echo sequences are generally superior to the T1-weighted images because the lesions are better visualized as areas of increased signal intensity. MR is also able to detect plaques in the brainstem, cerebellum and within the cervical spinal cord. MR appears to be an important, non-invasive method for the diagnosis of Multiple Sclerosis and has proven to be diagnostically superior to CT, evoked potentials (EP) and CSF examination. In a selected group of 30 patients, with the whole battery of the relevant MS studies, MR was positive in 100%, CT in 33,3%, EP in 56% and CSF examination in 60%. In patients clinically presenting only with signs of spinal cord involvement or optic neuritis or when the clinical presentation is uncertain MR has proven to be a very useful diagnostic tool for diagnosis of MS by demonstrating unsuspected lesions in the cerebral hemispheres. (orig.) Myositis ossificans: magnetic resonance images Dosda, R.; Marti-Bonmati, L.; Concepcion, L.; Galant, J. Myositis ossificans is characterized by a benign, self-limiting, ossifying mass of the white tissue. In the present report, we describe the magnetic resonance (MR) images in three cases of myositis ossificans in pediatric patients, correlating the MR findings with those obtained with other radiological studies. The lesions were detected in three patients, two boys and one girl, ranging in age between 10 and 14 years. The nature of the lesion was confirmed histologically in all three cases. The MR images were obtained using superconductive units at 0.5 Teslas, with T1 and T2-weighted spin-echo and STIR sequences. In two patients, gadolinium-enhanced T1-weighted images were also obtained. As in any process of maturation, the proliferation/maturation ratio depends on the moment in the course of the lesion, which affects its MR features,. In acute phases, the soft tissue mass with an intraosseous, perilesional adematous reaction predominates, while annular calcification and lesser edema are characteristic of subacute episode. Myositis ossificans is very rare in children. The inflammatory response may present a radiological pattern difficult to distinguish from that of aggressive tumor or infection, especially in the acute phase. (Author) 7 refs Nuclear magnetic resonance imaging method Johnson, G.; MacDonald, J.; Hutchison, S.; Eastwood, L.M.; Redpath, T.W.T.; Mallard, J.R. A method of deriving three dimensional image information from an object using nuclear magnetic resonance signals comprises subjecting the object to a continuous, static magnetic field and carrying out the following set of sequential steps: 1) exciting nuclear spins in a selected volume (90deg pulse); 2) applying non-aligned first, second and third gradients of the magnetic field; 3) causing the spins to rephase periodically by reversal of the first gradient to produce spin echoes, and applying pulses of the second gradient prior to every read-out of an echo signal from the object, to differently encode the spin in the second gradient direction for each read-out signal. The above steps 1-3 are then successively repeated with different values of gradient of the third gradient, there being a recovery interval between the repetition of successive sets of steps. Alternate echoes only are read out, the other echoes being time-reversed and ignored for convenience. The resulting signals are appropriately sampled, set out in an array and subjected to three dimensional Fourier transformation. (author) Voltage control of ferromagnetic resonance Ziyao Zhou Full Text Available Voltage control of magnetism in multiferroics, where the ferromagnetism and ferroelectricity are simultaneously exhibiting, is of great importance to achieve compact, fast and energy efficient voltage controllable magnetic/microwave devices. Particularly, these devices are widely used in radar, aircraft, cell phones and satellites, where volume, response time and energy consumption is critical. Researchers realized electric field tuning of magnetic properties like magnetization, magnetic anisotropy and permeability in varied multiferroic heterostructures such as bulk, thin films and nanostructure by different magnetoelectric (ME coupling mechanism: strain/stress, interfacial charge, spin–electromagnetic (EM coupling and exchange coupling, etc. In this review, we focus on voltage control of ferromagnetic resonance (FMR in multiferroics. ME coupling-induced FMR change is critical in microwave devices, where the electric field tuning of magnetic effective anisotropic field determines the tunability of the performance of microwave devices. Experimentally, FMR measurement technique is also an important method to determine the small effective magnetic field change in small amount of magnetic material precisely due to its high sensitivity and to reveal the deep science of multiferroics, especially, voltage control of magnetism in novel mechanisms like interfacial charge, spin–EM coupling and exchange coupling. Resonator quantum electrodynamics on a microtrap chip Steinmetz, Tilo In the present dissertation experiments on resonator quantum electrodynamics on a microtrap chip are described. Thereby for the first time single atoms catched in a chip trap could be detected. For this in the framework of this thesis a novel optical microresonator was developed, which can because of its miniaturization be combined with the microtrap technique introduced in our working group for the manipulation of ultracold atoms. For this resonator glass-fiber ends are used as mirror substrates, between which a standing light wave is formed. With such a fiber Fabry-Perot resonator we obtain a finess of up to ∼37,000. Because of the small mode volumina in spite of moderate resonator quality the coherent interaction between an atom and a photon can be made so large that the regime of the strong atom-resonator coupling is reached. For the one-atom-one-photon coupling rate and the one-atom-one-photon cooperativity thereby record values of g 0 =2π.300 MHz respectively C 0 =210 are reached. Just so for the first time the strong coupling regime between a Bose-Einstein condensate (BEC) and the field of a high-quality resonator could be reached. The BEC was thereby by means of the magnetic microtrap potentials deterministically brought to a position within the resonator and totally transformed in a well defined antinode of an additionally optical standing-wave trap. The spectrum of the coupled atom-resonator system was measured for different atomic numbers and atom-resonator detunings, whereby a collective vacuum Rabi splitting of more than 20 GHz could be reached. [de Electrical Characterization of Microelectromechanical Silicon Carbide Resonators Christian Zorman Full Text Available This manuscript describes the findings of a study to investigate the performance of SiC MEMS resonators with respect to resonant frequency and quality factor under a variety of testing conditions, including various ambient pressures, AC drive voltages, bias potentials and temperatures. The sample set included both single-crystal and polycrystalline 3C-SiC lateral resonators. The experimental results show that operation at reduced pressures increases the resonant frequency as damping due to the gas-rarefaction effect becomes significant. Both DC bias and AC drive voltages result in nonlinearities, but the AC drive voltage is more sensitive to noise. The AC voltage has a voltage coefficient of 1~4ppm/V at a DC bias of 40V. The coefficient of DC bias is about -11ppm/V to - 21ppm/V for poly-SiC, which is more than a factor of two better than a similarly designed polysilicon resonator (-54 ppm/V. The effective stiffness of the resonator decreases (softens as the bias potential is increased, but increases (hardens as drive voltage increase when scan is from low to high frequency. The resonant frequency decreases slightly with increasing temperature, exhibiting a temperature coefficient of -22 ppm/oC, between 22oC and 60oC. The thermal expansion mismatch between the SiC device and the Si substrate could be a reason that thermal coefficient for these SiC resonators is about twofold higher than similar polysilicon resonators. However, the Qs appear to exhibit no temperature dependence in this range. Resonance in a Cone-Topped Tube Angus Cheng-Huan Chia Full Text Available The relationship between ratio of the upper opening diameter of a cone-topped cylinder to the cylinder diameter,and the ratio of the length of the air column to resonant period was examined. Plastic cones with upper openings ranging from 1.3 cm to 3.6 cm and tuning forks with frequencies ranging from 261.6 Hz to 523.3 Hz were used. The transition from a standing wave in a cylindrical column to a Helmholtz-type resonance in a resonant cavity with a narrow opening was observed. Learning about nucleon resonances with pion photoproduction Walker, R.L. This chapter charts the discovery of nucleon resonances from pion-nucleon interactions. It was not until after the Albuquerque meeting in 1953 the experimentalists were able to persuade physicists about the existence of this phenomenon with the discovery of the P 33 resonance. The second and third resonances to be discovered, D 13 and F 15 , were seen as peaks in the total cross section for pion plus photoproduction, from 1956 onwards. Knowledge of pion-nucleon scattering has played an important role in the development of quark models. (UK) Cardiovascular magnetic resonance in congenital heart disease Cazacu, A.; Ciubotaru, A. The increasing prevalence of congenital heart disease can be attributed to major improvements in diagnosis and treatment. Cardiovascular magnetic resonance imaging plays an important role in the clinical management strategy of patients with congenital heart disease. The development of new cardiovascular magnetic resonance (CMR) techniques allows comprehensive assessment of complex cardiac anatomy and function and provides information about the long-term residual post-operative lesions and complications of surgery. It overcomes many of the limitations of echocardiography and cardiac catheterization. This review evaluates the role of cardiovascular magnetic resonance imaging modality in the management of subject with congenital heart disease (CHD). (authors) Functional magnetic resonance imaging by visual stimulation Nishimura, Yukiko; Negoro, Kiyoshi; Morimatsu, Mitsunori; Hashida, Masahiro We evaluated functional magnetic resonance images obtained in 8 healthy subjects in response to visual stimulation using a conventional clinical magnetic resonance imaging system with multi-slice spin-echo echo planar imaging. Activation in the visual cortex was clearly demonstrated by the multi-slice experiment with a task-related change in signal intensity. In addition to the primary visual cortex, other areas were also activated by a complicated visual task. Multi-slice spin-echo echo planar imaging offers high temporal resolution and allows the three-dimensional analysis of brain function. Functional magnetic resonance imaging provides a useful noninvasive method of mapping brain function. (author) Resonance Raman study of benzyl radical Langkilde, F.W.; Bajdor, K.; Wilbrandt, R. Time-resolved resonance Raman spectra are obtained of benzyl radicals created by laser flash photolysis of benzylchloride and diphenylacetone in solution. The spectra are obtained in resonance with the intense 2 2A2-1 B-2(2) transition of benzyl. The strong Raman bands are assigned to totally...... symmetric a1 modes. The remaining observed bands are tentatively assigned to fundamental modes of b1, a2, and b2 symmetry, and to overtones and combinations. The resonance Raman spectra are found to be quite different from previous fluorescence spectra of benzyl, and the origins of these differences... Neoclassical resonant transport of a mirror cell Ito, T.; Katanuma, I. The neoclassical resonant plateau transport in a mirror cell is studied theoretically. The analytical expression for a non-square-well magnetic field is obtained. The analytical result is applied to the GAMMA10 tandem mirror [T. Cho, M. Yoshida, J. Kohagura et al., Phys. Rev. Lett. 94, 085002-1 (2005)], which consists of several mirror cells in it, and the confinement time due to the neoclassical resonant plateau transport is determined in each mirror cell. It is found that the neoclassical resonant transport of ions trapped in the nonaxisymmetric anchor mirror cell and transition mirror cells is significantly smaller than those trapped in the central cell Resonant and nonresonant magnetic scattering (invited) McWhan, D.B.; Hastings, J.B.; Kao, C.; Siddons, D.P. The tunability and the polarization of synchrotron radiation open up new possibilities for the study of magnetism. Studies on magnetic materials performed at the National Synchrotron Light Source are reviewed, and they fall into four areas: structure, evolution of magnetic order, separation of L and S, and resonance effects. In the vicinity of atomic absorption edges, the Faraday effect, magnetic circular dichroism, and resonant magnetic scattering are all related resonance effects which measure the spin-polarized density of states. The production and analysis of polarized beams are discussed in the context of the study of magnetism with synchrotron radiation Resonant coupling applied to superconducting accelerator structures Potter, James M.; Krawczyk, Frank L. The concept of resonant coupling and the benefits that accrue from its application is well known in the world of room temperature coupled cavity linacs. Design studies show that it can be applied successfully between sections of conventional elliptical superconducting coupled cavity accelerator structures and internally to structures with spoked cavity resonators. The coupling mechanisms can be designed without creating problems with high field regions or multipactoring. The application of resonant coupling to superconducting accelerators eliminates the need for complex cryogenic mechanical tuners and reduces the time needed to bring a superconducting accelerator into operation. The discovery of resonances in multibaryon systems The properties of multibaryon resonances discovered in the collisions of fast neutrons and pions minus with the C 12 nuclei at 7.0 and 4.0 GeV/c momenta, respectively, in the JINR propane bubble chamber have been investigated. It has been shown that due to the hypercharge selection rule (Y<=1) found earlier multibaryon resonances are ultra-high density superstrange objects. The hypothesis has been brought up: the central regions of galaxies and quasars up to certain densities are huge multibaryon or even multihyperon resonances Multipole giant resonances in highly excited nuclei Xia Keding; Cai Yanhuang The isoscalar giant surface resonance and giant dipole resonance in highly excited nuclei are discussed. Excitation energies of the giant modes in 208 Pb are calculated in a simplified model, using the concept of energy wieghted sum rule (EWSR), and the extended Thomas-Fermi approximation at the finite temperature is employed to describe the finite temperature is employed to describe the finite temperature equilibrium state. It is shown that EWSR and the energy of the resonance depend only weakly on temperature in the system. This weak dependence is analysed Isovector resonances in pion charge exchange Bowman, J.D. The (π ± , π 0 ) reactions as probes of isovector resonances are discussed. Experimental observation of the isovector monopole resonance is reported. Experimental results are presented for L=0, 1, and 2 isovector resonances and are compared to random-phase approximation calculations. In the experiments 40 Ca, 60 Ni, 90 Zr, 120 Sn, 140 Ce, and 208 Pb, targets were bombarded with 165 MeV π ± beams. Neutral pions were detected and double differential cross sections were determined for angles between 0 and 33deg and for π 0 energies between 90, 180, and 230 MeV. (Auth.) Some links on this page may take you to non-federal websites. Their policies may differ from this site. Website Policies/Important Links	CommonCrawl
Does Science need Intersubjectivity? The Problem of Confirmation in Orthodox Interpretations of Quantum Mechanics. (arXiv:2203.16278v2 [quant-ph] UPDATED) Any successful interpretation of quantum mechanics must explain how our empirical evidence allows us to come to know about quantum mechanics. In this article, we argue that this vital criterion is not met by the class of 'orthodox interpretations,' which includes QBism, neo-Copenhagen interpretations, and some versions of relational quantum mechanics. We demonstrate that intersubjectivity fails in radical ways in these approaches, and we explain why intersubjectivity matters for empirical confirmation. We take a detailed look at the way in which belief-updating might work in the kind of universe postulated by an orthodox interpretation, and argue that observers in such a universe are unable to escape their own perspective in order to learn about the structure of the set of perspectives that is supposed to make up reality according to these interpretations. We also argue that in some versions of these interpretations it is not even possible to use one's own relative frequencies for empirical confirmation. Ultimately we conclude that it cannot be rational to believe these sorts of interpretations unless they are supplemented with some observer-independent structure which underwrites intersubjective agreement in at least certain sorts of cases. Strongly-interacting bosons at 2D-1D Dimensional Crossover. (arXiv:2204.02240v3 [cond-mat.quant-gas] UPDATED) We study a two dimensional (2D) system of interacting quantum bosons, subjected to a continuous periodic potential in one direction. The correlation of such system exhibits a dimensional crossover between a canonical 2D behavior with Berezinski-Kosterlitz-Thouless (BKT) properties and a one-dimensional (1D) behavior when the potential is large and splits the system in essentially independent tubes. The later is in the universality class of Tomonaga-Luttinger liquids (TLL). Using a continuous quantum Monte Carlo method, we investigate this dimensional crossover by computing longitudinal and transverse superfluid fraction as well as the superfluid correlation as a function of temperature, interactions and potential. Especially, we find the correlation function evolves from BKT to TLL type, with special intermediate behaviors appearing at the dimensional crossover. We discuss how the consequences of the dimensional crossover can be investigated in cold atomic gases experiments. Adaptive measurement filter: efficient strategy for optimal estimation of quantum Markov chains. (arXiv:2204.08964v3 [quant-ph] UPDATED) Continuous-time measurements are instrumental for a multitude of tasks in quantum engineering and quantum control, including the estimation of dynamical parameters of open quantum systems monitored through the environment. However, such measurements do not extract the maximum amount of information available in the output state, so finding alternative optimal measurement strategies is a major open problem. In this paper we solve this problem in the setting of discrete-time input-output quantum Markov chains. We present an efficient algorithm for optimal estimation of one-dimensional dynamical parameters which consists of an iterative procedure for updating a `measurement filter' operator and determining successive measurement bases for the output units. A key ingredient of the scheme is the use of a coherent quantum absorber as a way to post-process the output after the interaction with the system. This is designed adaptively such that the joint system and absorber stationary state is pure at a reference parameter value. The scheme offers an exciting prospect for optimal continuous-time adaptive measurements, but more work is needed to find realistic practical implementations. Modulating quantum evolution of moving-qubit by using classical driving. (arXiv:2204.10515v2 [quant-ph] UPDATED) In this work, we study quantum evolution of an open moving-qubit modulated by a classical driving field. We obtain the density operator of qubit at zero temperature and analyze its quantum evolution dynamics by using quantum speed limit time (QSLT) and a non-Markovianity measure introduced recently. The results show that both the non-Markovian environment and the classical driving can speed up the evolution process, this quantum speedup process is induced by the non-Markovianity and the critical points only depend on the qubit velocity. Moreover, the qubit motion will delay the evolution process, but this negative effect of the qubit velocity on the quantum speedup can be suppressed by the classical driving. Finally, we give the corresponding physical explanation by using the decoherence rates. Simulating key properties of lithium-ion batteries with a fault-tolerant quantum computer. (arXiv:2204.11890v2 [quant-ph] UPDATED) There is a pressing need to develop new rechargeable battery technologies that can offer higher energy storage, faster charging, and lower costs. Despite the success of existing methods for the simulation of battery materials, they can sometimes fall short of delivering accurate and reliable results. Quantum computing has been discussed as an avenue to overcome these issues, but only limited work has been done to outline how they may impact battery simulations. In this work, we provide a detailed answer to the following question: how can a quantum computer be used to simulate key properties of a lithium-ion battery? Based on recently-introduced first-quantization techniques, we lay out an end-to-end quantum algorithm for calculating equilibrium cell voltages, ionic mobility, and thermal stability. These can be obtained from ground-state energies of materials, which is the core calculation executed by the quantum computer using qubitization-based quantum phase estimation. The algorithm includes explicit methods for preparing approximate ground states of periodic materials in first quantization. We bring these insights together to perform the first estimation of the resources required to implement a quantum algorithm for simulating a realistic cathode material, dilithium iron silicate. Consistent circuits for indefinite causal order. (arXiv:2206.10042v2 [quant-ph] UPDATED) Over the past decade, a number of quantum processes have been proposed which are logically consistent, yet feature a cyclic causal structure. However, there is no general formal method to construct a process with an exotic causal structure in a way that ensures, and makes clear why, it is consistent. Here we provide such a method, given by an extended circuit formalism. This only requires directed graphs endowed with Boolean matrices, which encode basic constraints on operations. Our framework (a) defines a set of elementary rules for checking the validity of any such graph, (b) provides a way of constructing consistent processes as a circuit from valid graphs, and (c) yields an intuitive interpretation of the causal relations within a process and an explanation of why they do not lead to inconsistencies. We display how several standard examples of exotic processes, including ones that violate causal inequalities, are among the class of processes that can be generated in this way; we conjecture that this class in fact includes all unitarily extendible processes. Emergent s-wave interactions between identical fermions in quasi-one-dimensional geometries. (arXiv:2206.10415v2 [cond-mat.quant-gas] UPDATED) Orbital degrees of freedom play an essential role in metals, semiconductors, and strongly confined electronic systems. Experiments with ultracold atoms have used highly anisotropic confinement to explore low-dimensional physics, but typically eliminate orbital degrees of freedom by preparing motional ground states in strongly confined directions. Here we prepare multi-band systems of spin-polarized fermionic potassium ($^{40}$K) in the quasi-one-dimensional (q1D) regime and quantify the strength of atom-atom correlations using radio-frequency spectroscopy. The activation of orbital degrees of freedom leads to a new phenomenon: a low-energy scattering channel that has even particle-exchange parity along the q1D axis, as if the underlying interactions were s-wave. This emergent exchange symmetry is enabled by orbital singlet wave functions in the strongly confined directions, which also confer high-momentum components to low-energy q1D collisions. We measure both the q1D odd-wave and even-wave "contact" parameters for the first time, and compare them to theoretical predictions of one-dimensional many-body models. The strength and spatial symmetry of interactions are tuned by a p-wave Feshbach resonance and by transverse confinement strength. Near resonance, the even-wave contact approaches its theoretical unitary value, whereas the maximum observed odd-wave contact remains several orders of magnitude below its unitary limit. Low-energy scattering channels of multi-orbital systems, such as those found here, may provide new routes for the exploration of universal many-body phenomena. A Complete Equational Theory for Quantum Circuits. (arXiv:2206.10577v2 [quant-ph] UPDATED) We introduce the first complete equational theory for quantum circuits. More precisely, we introduce a set of circuit equations that we prove to be sound and complete: two circuits represent the same unitary map if and only if they can be transformed one into the other using the equations. The proof is based on the properties of multi-controlled gates -- that are defined using elementary gates -- together with an encoding of quantum circuits into linear optical circuits, which have been proved to have a complete axiomatisation. Experimental Realization of Two Qutrits Gate with Tunable Coupling in Superconducting Circuits. (arXiv:2206.11199v3 [quant-ph] UPDATED) Gate-based quantum computation has been extensively investigated using quantum circuits based on qubits. In many cases, such qubits are actually made out of multilevel systems but with only two states being used for computational purpose. While such a strategy has the advantage of being in line with the common binary logic, it in some sense wastes the ready-for-use resources in the large Hilbert space of these intrinsic multi-dimensional systems. Quantum computation beyond qubits (e.g., using qutrits or qudits) has thus been discussed and argued to be more efficient than its qubit counterpart in certain scenarios. However, one of the essential elements for qutrit-based quantum computation, two-qutrit quantum gate, remains a major challenge. In this work, we propose and demonstrate a highly efficient and scalable two-qutrit quantum gate in superconducting quantum circuits. Using a tunable coupler to control the cross-Kerr coupling between two qutrits, our scheme realizes a two-qutrit conditional phase gate with fidelity 89.3% by combining simple pulses applied to the coupler with single-qutrit operations. We further use such a two-qutrit gate to prepare an EPR state of two qutrits with a fidelity of 95.5%. Our scheme takes advantage of a tunable qutrit-qutrit coupling with a large on:off ratio. It therefore offers both high efficiency and low cross talk between qutrits, thus being friendly for scaling up. Our work constitutes an important step towards scalable qutrit-based quantum computation. Geometry of Degeneracy in Potential and Density Space. (arXiv:2206.12366v2 [quant-ph] UPDATED) In a previous work [J. Chem. Phys. 155, 244111 (2021)], we found counterexamples to the fundamental Hohenberg-Kohn theorem from density-functional theory in finite-lattice systems represented by graphs. Here, we demonstrate that this only occurs at very peculiar and rare densities, those where density sets arising from degenerate ground states, called degeneracy regions, touch each other or the boundary of the whole density domain. Degeneracy regions are shown to generally be in the shape of the convex hull of an algebraic variety, even in the continuum setting. The geometry arising between density regions and the potentials that create them is analyzed and explained with examples that, among other shapes, feature the Roman surface. Measurement driven quantum clock implemented with a superconducting qubit. (arXiv:2207.11043v2 [quant-ph] UPDATED) We demonstrate a quantum clock, near zero temperature, driven in part by entropy reduction through measurement, and necessarily subject to quantum noise. The experimental setup is a superconducting transmon qubit dispersively coupled to an open co-planar resonator. The cavity and qubit are driven by coherent fields and the cavity output is monitored with a quantum noise-limited amplifier. When the continuous measurement is weak, it induces sustained coherent oscillations (with fluctuating period) in the conditional moments. Strong continuous measurement leads to an incoherent cycle of quantum jumps. Both regimes constitute a clock with a signal extracted from the observed measurement current. This signal is analysed to demonstrate the relation between clock period noise and dissipated power for measurement driven quantum clocks. We show that a good clock requires high rates of energy dissipation and entropy generation. Electron subband degeneracy heat pump for cryogenic cooling. (arXiv:2207.14237v2 [cond-mat.mes-hall] UPDATED) An unconventional method of continuous solid-state cryogenic cooling utilizing the electron subband degeneracy of semiconductor heterostructures is proposed in this Letter. An electrostatic heat pump is modeled, which employs subband "expansion" and "compression" to reach sub-dilution refrigeration temperatures with the fundamental limit set by electron-phonon interaction. Using an ultra-wide GaAs quantum well as an example, the cooling power per unit volume is estimated to reach $4.5\ \rm mW/cm^3$ with a hot-side temperature of $300\ \rm mK$, suitable for applications such as quantum computers or infrared detectors. Unsupervised Interpretable Learning of Phases From Many-Qubit Systems. (arXiv:2208.08850v2 [quant-ph] UPDATED) Experimental progress in qubit manufacturing calls for the development of new theoretical tools to analyze quantum data. We show how an unsupervised machine-learning technique can be used to understand short-range entangled many-qubit systems using data of local measurements. 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Here, through custom co-design of opto-electronic integrated circuits and side-information reduction by digital filtering, we experimentally demonstrated an ultrafast generation rate of 100 Gbps, setting a new record for vacuum-based quantum random number generation by one order of magnitude. Furthermore, our experimental demonstrations are well supported by an upgraded device-dependent framework that is secure against both classical and quantum side-information and that also properly considers the non-linearity in the digitization process. This ultrafast secure random number generator in the chip-scale platform holds promise for next generation communication and cryptography applications. Testing of quantum nonlocal correlations under constrained free will and imperfect detectors. 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We also introduce a class of LRHV inequalities with constrained free will, and we discuss their implications in the testing of quantum nonlocal correlations. Parallel window decoding enables scalable fault tolerant quantum computation. (arXiv:2209.08552v2 [quant-ph] UPDATED) Large-scale quantum computers have the potential to hold computational capabilities beyond conventional computers for certain problems. However, the physical qubits within a quantum computer are prone to noise and decoherence, which must be corrected in order to perform reliable, fault-tolerant quantum computations. Quantum Error Correction (QEC) provides the path for realizing such computations. QEC continuously generates a continuous stream of data that decoders must process at the rate it is received, which can be as fast as 1 MHz in superconducting quantum computers. A little known fact of QEC is that if the decoder infrastructure cannot keep up, a data backlog problem is encountered and the quantum computer runs exponentially slower. Today's leading approaches to quantum error correction are not scalable as existing decoders typically run slower as the problem size is increased, inevitably hitting the backlog problem. That is: the current leading proposal for fault-tolerant quantum computation is not scalable. Here, we show how to parallelize decoding to achieve almost arbitrary speed, removing this roadblock to scalability. Our parallelization requires some classical feed forward decisions to be delayed, leading to a slow-down of the logical clock speed. However, the slow-down is now only polynomial in code size, averting the exponential slowdown. We numerically demonstrate our parallel decoder for the surface code, showing no noticeable reduction in logical fidelity compared to previous decoders and demonstrating the parallelization speedup. Mixedness timescale in non-Hermitian quantum systems. (arXiv:2209.11667v2 [quant-ph] UPDATED) We discuss the short-time perturbative expansion of the linear entropy for finite-dimensional quantum systems whose dynamics can be effectively described by a non-Hermitian Hamiltonian. We derive a timescale for the degree of mixedness for an input state undergoing non-Hermitian dynamics and specialize these results in the case of a driven-dissipative two-level system. Next, we derive a timescale for the growth of mixedness for bipartite quantum systems that depends on the effective non-Hermitian Hamiltonian. In the Hermitian limit, this result recovers the perturbative expansion for coherence loss in Hermitian systems, while it provides an entanglement timescale for initial pure and uncorrelated states. To illustrate these findings, we consider the many-body transverse-field $XY$ Hamiltonian coupled to an imaginary all-to-all Ising model. We find that the non-Hermitian Hamiltonian enhances the short-time dynamics of the linear entropy for the considered input states. Overall, each timescale depends on minimal ingredients such as the probe state and the non-Hermitian Hamiltonian of the system, and its evaluation requires low computational cost. Our results find applications to non-Hermitian quantum sensing, quantum thermodynamics of non-Hermitian systems, and $\mathcal{PT}$-symmetric quantum field theory. Dynamical many-body delocalization transition of a Tonks gas in a quasi-periodic driving potential. (arXiv:2209.12510v2 [cond-mat.quant-gas] UPDATED) The quantum kicked rotor is well-known for displaying dynamical (Anderson) localization. It has recently been shown that a periodically kicked Tonks gas will always localize and converge to a finite energy steady-state. This steady-state has been described as being effectively thermal with an effective temperature that depends on the parameters of the kick. Here we study a generalization to a quasi-periodic driving with three frequencies which, without interactions, has a metal-insulator Anderson transition. We show that a quasi-periodically kicked Tonks gas goes through a dynamical many-body delocalization transition when the kick strength is increased. The localized phase is still described by a low effective temperature, while the delocalized phase corresponds to an infinite-temperature phase, with the temperature increasing linearly in time. At the critical point, the momentum distribution of the Tonks gas displays different scaling at small and large momenta (contrary to the non-interacting case), signaling a breakdown of the one-parameter scaling theory of localization.	CommonCrawl
Full paper \| Open \| Published: 22 May 2019 Peak ground motions and characteristics of nonlinear site response during the 2018 Mw 6.6 Hokkaido eastern Iburi earthquake Yadab P. Dhakal ORCID: orcid.org/0000-0002-0399-48431, Takashi Kunugi1, Takeshi Kimura1, Wataru Suzuki1 & Shin Aoi1 Earth, Planets and Spacevolume 71, Article number: 56 (2019) \| Download Citation The observed peak ground accelerations and peak ground velocities (PGVs) of the 2018 Mw 6.6 Hokkaido eastern Iburi earthquake generally followed the median values from ground motion prediction equations with reasonable errors at fault distances ≥ 50 km. However, at smaller distances, the equations significantly underestimated the peak ground motions, and it was eminent for PGVs. A comparison of surface-to-borehole spectral ratios of S-waves during the mainshock and other events revealed that the sites at smaller distances experienced various degrees of nonlinear site response. The two most widely known characteristics of nonlinear site response are the weakening of higher-frequency components and shifting of predominant frequencies to lower ones in comparison with the linear site response. At one of the sites that recorded the largest intensity of 7 in JMA scale of 0–7, the latter nonlinear effect was so dominant that the ground motions around the new predominant frequency got intensified by one order of magnitude in comparison with that during the weak-motions. Two sites, which were closely located, recorded vertical peak ground accelerations exceeding 1 g for the up-going motions. The recordings showed asymmetric waveforms and amplitudes characteristics of the nonlinear site response in extreme vertical ground motions recorded during a few earthquakes in the past. Few sites having lower vertical peak ground accelerations were also suspected of being experienced nonlinear site response on vertical motions. These findings suggest taking a cautious approach to enumerate the reduction in amplification at higher frequencies using the single-station horizontal-to-vertical (H-to-V) spectral ratio technique. However, we found that the H-to-V technique was still useful to detect nonlinearity. Finally, an ad hoc equation was derived to correct the nonlinear site amplification in predicting horizontal PGVs with respect to one of the most widely used attenuation models in Japan. The results indicated that the effect was much stronger for a larger input motion than that for a proportional change in the Vs30 values. The 2018, Mw 6.6 Hokkaido eastern Iburi earthquake occurred on September 6, 03:08 JST (UTC + 9 h). The Mw value of 6.6 was determined by F-net NIED (Okada et al. 2004). The Mw values determined by USGS (2018) and GCMT (e.g., Ekström et al. 2012) were 6.6 and 6.7, respectively. The Japan Meteorological Agency (JMA) magnitude (Mj) was 6.7, and the focal depth was 37 km. The epicenter of the earthquake was located on the western foreland area of a collision zone known as Hidaka collision zone (e.g., Kimura 1996). Earthquakes of comparable magnitudes with similar focal depths have repeatedly occurred in the region (e.g., Kita et al. 2014). The 2018 earthquake caused loss of 42 lives, resulted into total collapse of 462 and partial collapse of 1570 residential buildings, and brought significant damage to lifelines (e.g., Cabinet Office Japan 2019; Takahashi and Kimura 2019). The casualties and damages were primarily related to geotechnical failures such as landslides and liquefaction (e.g., Yamagishi and Yamazaki 2018). The earthquake was followed by many aftershocks, which concentrated primarily on a steeply dipping fault plane. Based on the spatial and temporal distribution of hypocenters of the aftershocks, a fault plane of about 28 km in length and 20 km in width was estimated. The minimum depth to the top of the fault plane was assumed to be about 24 km. The coordinates of the fault plane are provided in Table 1. The horizontal vector peak ground accelerations (PGAs) and peak ground velocities (PGVs) recorded by K-NET, KiK-net, and JMA accelerometers are plotted in Fig. 1a, b, respectively, for the mainshock. The epicenters of aftershocks and numerical values of the PGAs and PGVs at small distances from the fault are shown in Fig. 1c for the mainshock. A vertical section of the subsurface velocity model (Koketsu et al. 2012) along an east–west direction passing through the epicenter of the mainshock is drawn in Fig. 1d, which also shows the plots of depths to hypocenters of the aftershocks and the mainshock. Figure 1d shows the epicenter area covered by low-velocity sedimentary layers above the basement rocks, and the thickness of sediments is larger in the western side of the epicenter. In this paper, mainshock is used to mean the 2018 Mw 6.6 Hokkaido eastern Iburi earthquake. Table 1 Coordinates of the four corners of the fault plane estimated in the present study and the hypocenter determined by JMA a, b Show the plots of observed horizontal vector PGAs and PGVs, respectively. A star denotes epicenter of the mainshock. Triangles and dashed red line denote active volcanoes and volcanic front line, respectively. c Enlarged view of the rectangular area drawn around the epicenter in a with additional information. Numbers in parentheses denote the values of horizontal vector PGAs (cm/s2) and PGVs (cm/s), respectively, at recording stations color-coded by PGAs. The magenta circles denote aftershocks of Mj ≥ 2 for the 9 days after the mainshock. The rectangle denotes the surface projection of an approximate fault plane. d Vertical section of JIVSM (Japan integrated velocity structure model) along the profile A–A′ shown in c. A red dashed line denotes the intersection line of the inferred fault plane with the vertical section The recorded maximum PGAs and PGVs for the eastern Iburi earthquake were comparable to those recorded during the 1995, Mw 6.9, Kobe earthquake (e.g., Kitagawa and Hiraishi 2004; Kawase 1996) and 2016, Mw 7.1 Kumamoto earthquake (e.g., Sakai 2016; Suzuki et al. 2017). The maximum horizontal vector PGA of 1429 cm/s2 was observed at the KiK-net site IBUH01 (Oiwake) (see Fig. 1c). The JMA instrumental intensity (e.g., JMA 2018a, b; Shabestari and Yamazaki 2001) of 6.7 was calculated at the site IBUH01. This value of 6.7 corresponds to the upper limit of JMA intensity on a discrete scale of 0–7 (JMA 2018b). The maximum horizontal vector PGV was 151 cm/s, which was recorded at two sites: K-NET site HKD126 (Mukawa) and KiK-net site IBUH03 (Atsuma). The JMA instrumental intensity of 6.4 and 6.2 was calculated at the HKD126 and IBUH03, respectively; these values correspond to the intensity of 6 Upper in a scale of 0–7. The JMA Atsuma station (47,004 in Fig. 1c) recorded JMA instrumental intensity of approximately 6.5 (which rounds to JMA intensity of 7, the largest in the scale of 0–7). Sawazaki et al. (2006) reported that the KIK-net Atsuma site (IBUH03, see Fig. 1c for site location) experienced a strong nonlinear site response during the 2003 Mw 8.3 Tokachi-oki earthquake. We found that the nonlinear site response was most probably one of the primary causes of the large JMA intensity at the site IBUH03 during the 2018 Mw 6.6 Hokkaido eastern Iburi earthquake. We discuss in some detail the characteristics of nonlinear site response at IBUH03 in later sections. Figure 1a, b shows that the large PGAs and PGVs were observed mostly in the northwest and southeast directions of the epicenter of the mainshock and also close to the southern coastal areas at small distances (Fig. 1c), where the thickness of sediments is substantial. These observations reflect the amplification of seismic waves by the thick sediments. Moreover, as the rupture initiated nearly midway of its bottom line at a deeper portion of the fault plane and propagated along strikes and up dips, some degrees of rupture propagation effects may also be stipulated at sites close to the fault plane. The typical characteristics of nonlinear site response are the diminution of high-frequency components of ground motions and shift of predominant frequency to lower one with respect to the linear site response (e.g., Wen et al. 1994; Satoh et al. 1995). These effects have been explained by the increase in damping and degradation of soil rigidity during strong-motions (e.g., Idriss and Seed 1968; Hardin and Drnevich 1972). Also known in the seismological and engineering communities are the atypical accelerograms, which contain large amplitude high-frequency acceleration spikes, as direct evidence of nonlinear site response during strong shakings (e.g., Holzer et al. 1989; Iai et al. 1995; Bonilla et al. 2005). These atypical accelerograms are explained as the effect of nonlinear soil response resulting from the pore water pressure changes in dilatant soils during strong shakings (e.g., Holzer et al. 1989; Iai et al. 1995). More recently, asymmetrical waveforms on vertical component accelerograms exceeding 1 g in upward direction have been described as direct evidence of nonlinear site response (e.g., Aoi et al. 2008). The asymmetric waveforms have been qualitatively explained by trampoline effect (Aoi et al. 2008) and as slap down phases (Yamada et al. 2009). During the 2018, Mw 6.6 Hokkaido eastern Iburi earthquake, we did not identify the atypical spiky accelerograms by visual inspection except a small indication on one of the horizontal components at site HKD125 (recordings not shown in this paper); however, the nonlinear site response associated with the decrease in shear modulus and increase in damping in soils was recognized at several sites, and also the asymmetrical waves on vertical components were identified at two sites. In this paper, we describe the above-mentioned nonlinear site responses during the mainshock based on observed recordings and discuss that the nonlinear site response was the most probable reason for the high-intensity ground motions at smaller distances. The surface-to-borehole (S-to-B) spectral ratio method has been proved to be an effective method to identify nonlinear site response during strong-motions (e.g., Wen et al. 1994; Satoh et al. 1995; Sato et al. 1996; Assimaki et al. 2008; Noguchi and Sasatani 2008; Régnier et al. 2013; Kaklamanos et al. 2015; Noguchi et al. 2016). Wen et al. (2006a) introduced the horizontal-to-vertical (H-to-V) spectral ratio method to detect nonlinear site response; the method also has been widely applied in detection of nonlinear site response during strong-motions, especially when downhole recordings or rock outcrops close to the site of interest are not available (e.g., Noguchi and Sasatani 2008; Wen et al. 2011; Dhakal et al. 2017; Ren et al. 2017). Below, we first describe the selection and processing of the data used in the present study. Then, we inquire into the general attenuation characteristics of the observed PGAs and PGVs with distance to examine whether the peak motions are compliant with the ground motion prediction equations (GMPEs). Thirdly, we compare the S-to-B spectral ratios of S-waves for the horizontal components, i.e., horizontal-to-horizontal (H-to-H) spectral ratios for the mainshock and weak-motions from earthquakes before the mainshock at selected KiK-net sites, and discuss the characteristics of nonlinear site response at the sites. We resume the aforementioned analysis for vertical components, i.e., vertical-to-vertical (V-to-V) spectral ratios at the same sites. Then, we discuss the characteristic vertical component waveforms featuring the direct evidence of nonlinear site response during the mainshock at two KiK-net and K-NET sites. After discussing the nonlinear site effects on horizontal and vertical component recordings, we present the H-to-V spectral ratios from surface recordings at the KiK-net sites where S-to-B spectral ratios are analyzed. We compare the results between the S-to-B and H-to-V spectral ratios at the KiK-net sites. We also analyze the H-to-V spectral ratios at selected K-NET sites. Finally, based on the analyses above and comparisons, we conclude by an ad hoc equation to take account of the nonlinear site amplification into an existing GMPE for PGVs. Data selection and processing Strong-motion seismometers of K-NET and KiK-net recorded ground motion data of mainshock at more than 475 stations and epicentral distances between about 10 and 900 km. Similarly, strong-motion data recorded by JMA intensity meters at 142 stations that spread for 700 km were made available by JMA. The PGAs and PGVs were calculated from the high-pass-filtered strong-motion seismograms with a cutoff frequency of 0.07 Hz. In this paper, the PGAs and PGVs refer to the maximum values of the vector sum (i.e., the square root of the sum of squares) of two horizontal component acceleration and velocity time histories, respectively, over the available time steps. We did not show PGAs and PGVs at large distances in Figs. 1 and 2 because of their small values. Attenuation relation by Si and Midorikawa (1999, 2000) has been the basis for seismic hazard evaluation in Japan (e.g., Fujiwara et al. 2009). They defined peak value in their equation as larger one of the two horizontal components. Therefore, when we compared the peak values with the attenuation relation by Si and Midorikawa (1999, 2000) in Fig. 2, we adhere to their definition. The fault distance to use in their equation was determined from the fault geometry model briefly mentioned in the previous section. The fault geometry model was estimated based on the automatically determined hypocenters provided by JMA (see Availability of data and materials). The geographical coordinates of the four corners of the fault model with depths at the corners are given in Table 1. The aftershocks of Mj ≥ 2 that occurred within 9 days were used. In Fig. 1c, d, 460 aftershocks of Mj between 2.0 and 2.9, 136 aftershocks of Mj between 3 and 3.9, 37 aftershocks of Mj between 4.0 and 4.9, and two aftershocks of Mj equal to 5.4 and 5.5 were plotted. a, b Plots of observed PGAs (larger of two horizontal components) and PGVs (larger of two horizontal components) after adjustment for site amplification, respectively. Only a subset of data shown in Fig. 1a were plotted where the values of Vs30 were known or estimated. The solid lines represent median prediction curves using equations in Si and Midorikawa (1999, 2000) for Mw = 6.6, depth = 37, and type of event = crust, and dashed lines denote plus–minus one standard deviation. In the legends, BA, FA, and NLA are the abbreviations for back-arc, fore-arc, and nonlinear site response analyzed sites. c, d Plots of residuals for the PGAs and PGVs plotted in a, b, respectively. Mean residuals with a plus–minus one standard deviation are shown by vertical bars for four different distance ranges 20–50 km, 50–100 km, 100–200 km, and 200–300 km The sites used for analysis of nonlinear characteristics are portrayed in Fig. 3; the total number of sites is 32. The KiK-net sites consist of a pair of surface and borehole sensors, and recordings from 16 KiK-net sites that recorded horizontal vector PGAs of about 70 cm/s2 or larger at the surface and 20 cm/s2 or larger at boreholes were analyzed. The K-NET sites consist of sensors at the surface only, and recordings from 16 K-NET sites that recorded horizontal vector PGAs of 200 cm/s2 or larger were analyzed. The Vs30 values (average S-wave velocities in the upper 30 m of the soil column) (e.g., BSSC 2003) are often used to define site condition. We obtained the Vs30 values at the KiK-net sites from NIED (see Availability of data and materials). Most of the K-NET sites have PS-loggings down to 10–20 m. We obtained the Vs30 values at the K-NET sites having PS-loggings down to 20 m by using the correlation formula between Vs30 and Vs20 derived by Kanno et al. (2006). At sites where Vs20 was not available, we obtained the Vs10 values for information. The PGAs, PGVs, and Vs10 or Vs30 values at the KiK-net and K-NET sites are listed in Tables 2 and 3, respectively. The shallow soil Vs values were not available at the JMA sites, and hence, the analysis of nonlinear site response was limited to the K-NET and KiK-net sites in this paper. Location of sites used in the evaluation of nonlinear site response. The K-NET and KiK-net sites are denoted by triangles and circles, respectively. The site codes are written next to the site symbols, which are color-coded by the JMA instrumental intensity. A star denotes epicenter of the mainshock, and rectangle denotes surface projection of the fault plane. A dashed red line denotes volcanic front (see also Fig. 1). See Tables 2 and 3 for various parameters at each site Table 2 List of KiK-net sites with site parameters, peak ground motions, and nonlinear site response indices Table 3 List of K-NET sites with site parameters, peak ground motions and nonlinear site response indices We selected recordings which contained both the P- and S-waves to assist in picking the onset of S-waves. The onset of S-waves was handpicked, and a time window of 10 s was used to compute Fourier spectral amplitudes. As a preliminary analysis, we also computed the Fourier spectral amplitudes from a time window of 15 s and compared them from the time window of 10 s. The two results were essentially identical at frequencies of our interest between 0.5 and 20 Hz. However, to avoid the possible effects of 3-D subsurface structure on computed spectra due to a long-time window (e.g., Dhakal and Yamanaka 2012), we limited the S-wave time window of 10 s in our analysis. The 10-s time window was also optimal to evaluate the signal-to-noise ratio considering the stability of the computed spectra as the recordings had pre-event noise time windows smaller than 15 s. In the actual calculation, the mean acceleration of the noise time window was subtracted from the whole recordings as a baseline correction. Then, cosine tapering of 1 s was applied just outside of the selected S-wave time window of 10 s at both ends, i.e., the 10-s time window becomes 12 s with the addition of 1-s time window for tapering at each end. Then, 20 s of zeroes was padded, so the length of the time window is 32 s. The Fourier spectral amplitudes were smoothed by applying a Parzen window of 0.4 Hz. The recordings were selected if the Fourier spectral ratios between the S-waves and noise window were greater than three at all frequencies between 0.5 and 20 Hz. The weak-motion recordings were obtained from events that occurred within 300 km of each site between 1996 and the day before the mainshock and were recorded by K-NET and KiK-net. The magnitudes of the events ranged mostly between Mj 4.0 and 6.5. In this paper, the weak-motion recordings mean those recordings having horizontal vector PGAs between 5 and 20 cm/s2 at the surface. A few recordings had PGAs lower than 5 cm/s2 or greater than 20 cm/s2 but lower than 30 cm/s2 to increase the number of recordings. The number of recordings varied from site to site and ranged between 10 and 130 (see Tables 2, 3). For the mainshock recordings, the beginning of S-wave time window for analysis was selected based on the dominant wave packet for S-waves. The Fourier spectral amplitudes for vertical components also were computed from the time windows same as horizontal component S-wave time windows for the both weak-motions and mainshock. The smoothing operation was also identically applied. An example of S-wave time windows for weak- and strong-motions is depicted for site IBUH01 in Fig. 4. The site IBUH01 is the site that recorded the largest PGA during the mainshock as described in the previous section. Example acceleration recordings and S-wave time windows (red portions) selected for evaluation of nonlinear site response at site IBUH01. a Recordings from an event that occurred on Nov 1, 2006, at 23:21 JST (Mj = 4.8, focal depth = 49 km, epicentral distance = 123 km, back azimuth = 120°). b Recordings from mainshock. The borehole and surface recordings are plotted in left and right panels, respectively. The north–south (NS), east–west (EW), and vertical (UD) components are indicated in each panel. Note that the scale of the vertical axis for surface recordings (right panels) is larger by a factor of 10 with respect to that for borehole recordings. The recordings for the mainshock are shifted to the right by 4 s to match with the S-wave arrivals on the weak-motion recordings in panel a Comparison of PGAs and PGVs Si and Midorikawa (1999) developed attenuation relations for PGAs on soil sites. They proposed a factor of 1.4 to convert the PGAs at rock sites to PGAs at soil sites. However, the objective definition of rock and soil was not available in their paper. They referred to the paper by Joyner and Boore (1981) for the definition of site condition. Joyner and Boore (1981) classified sites into two groups: rock and soil based on geological information. They described in another paper (Boore and Joyner 1997) Vs30 value of 620 m/s for generic rock sites in western North America. In the National Earthquake Hazards Reduction Program (NEHRP) recommendations (BSSC 2003; NEHRP 2019), sites having Vs30 value of 760–1500 m/s and higher than 1500 m/s are classified as rock and hard rock sites, respectively. In line with the literature mentioned above, we considered a site having Vs30 value of 760 m/s or larger as a rock site and a site having Vs30 value otherwise as a soil site. None of the sites at small fault distances have Vs30 values between 620 and 760 m/s in our data set. Therefore, selecting site class definition based on Joyner and Boore (1981) or NEHRP recommendations does not make a difference to our conclusions in this paper. We multiplied the PGAs at rock sites by 1.4 as aforementioned and plotted together with other soil sites in Fig. 2a; the prediction curves in Fig. 2a are for soil site condition. In the figure, the back-arc and fore-arc sites, separated by a volcanic front line, are denoted by triangles and circles, respectively. Red color symbols indicate the sites used in the nonlinear analysis. In the figure, it can be seen that the observed values are generally larger than the median predictions between 20 and about 50 km while the values do not show any visible trend at distances over about 50 km for a reasonable range of scattering. It can also be seen that the observed values at back-arc sites are systematically smaller than the values at the fore-arc sites at distances over about 100 km, which can be recognized in the plots of residuals in Fig. 2c. The mean residuals in base-10 log-scale are approximately 0.28, 0.01, − 0.10, and − 0.08 for binned data between 20 and 50 km, 50 and 100 km, 100 and 200 km, and 200 and 300 km, respectively. The above results suggest that despite the difference between the fore-arc and back-arc data, the absolute values of the mean residuals at the longer distances are smaller than those at smaller distances. A comparison of the observed PGVs with the empirical attenuation relation by Si and Midorikawa (1999) is shown in Fig. 2b. Unlike the PGAs, attenuation relation for PGVs was developed for a stiff site condition having Vs30 value of about 600 m/s. They adjusted the observed PGV at a site by a factor that is a function of Vs30 value at the site using the equation in Midorikawa et al. (1994). We followed the same procedure and adjusted the observed PGVs for site amplification effect. The adjusted observed values are plotted in Fig. 2b together with the prediction curves for stiff site condition having Vs30 value of 600 m/s. Similar to the PGAs discussed above, the observed PGVs are generally larger than the median predictions at distances smaller than about 40 km and are similar to the predictions at distances over about 40 km for a reasonable range of scattering. The distribution of residuals between the observed and predicted PGVs is plotted in Fig. 2d as a function of fault distance. The mean residuals in base-10 log-scale are approximately 0.42, -0.02, -0.06, and -0.04 for binned data between 20 and 50 km, 50 and 100 km, 100 and 200 km, and 200 and 300 km, respectively. The remarkably smaller mean residuals at distances beyond 50 km confirm that the observed PGVs at those distances are similar from the typical crustal earthquakes in Japan. On the other hand, the large positive mean residual at smaller distances point toward some specific causes or combination thereof not sufficiently addressed by the GMPEs. One notable difference between the plots for PGAs and PGVs is that the PGVs scatter less from the median predictions than the PGAs at longer distances, and the difference between the back-arc and fore-arc sites becomes smaller for PGVs. These results are generally desirable because the relatively long-period ground motions become less sensitive to very shallow earth structures compared to the short-period ground motions. Dhakal et al. (2010) reported that the distinction of fore-arc and back-arc data becomes less obvious at periods larger than about 0.5 s. In summary, the observed PGAs and PGVs were generally described very well by the attenuation relations in Si and Midorikawa (1999) at distances larger than about 50 km. In this paper, we are, therefore, primarily interested in sites of large residuals between the observed and predicted PGVs at smaller distances. We explore the observed characteristics of nonlinear site response at the selected KiK-net and K-NET sites mostly from the smaller distances in the next four sections. S-to-B spectral ratios of horizontal components In this study, we obtained S-to-B spectral ratios of horizontal components (H-to-H) in the following way. We calculated the Fourier spectral amplitudes for each horizontal component, smoothed them as explained in the data processing section, obtained the vector sum of two components at each frequency, and calculated the ratios between the surface and borehole spectra at each frequency. Wen et al. (2006b) proposed the following equation (Eq. 1) to express the deviation of H-to-V spectral ratios of the strong- and weak-motions quantitatively: $$ d\left( f \right) = \frac{s\left( f \right) - w\left( f \right)}{\sigma \left( f \right)}*100\% $$ where $ s\left( f \right) $ is the H-to-V spectral ratios of the strong-motions, $ w\left( f \right) $ is the mean H-to-V spectral ratios of the weak-motions, and $ \sigma \left( f \right) $ is the standard deviation of the H-to-V spectral ratios of the weak-motions at frequency $ f $. This method gives more than a single value of degree of nonlinearity (DNL) because it is calculated for each frequency. Wen et al. (2006b) suggested averaging the values at multiple frequency bands because the nonlinear effects may be stronger at certain frequencies than the others. In this study, we calculated the DNL value using Eq. 2, which was first employed by Noguchi and Sasatani (2008): $$ {\text{DNL}} = \sum \left\| {\log \left\{ {\frac{{R_{\text{strong}} }}{{R_{\text{weak}} }}} \right\}} \right\|\Delta f $$ where Rstrong and Rweak represent the spectral ratios for strong- and weak-motions, respectively, and ∆f is the frequency interval. The DNL value was obtained from spectral ratios between 0.5 and 20 Hz in Noguchi and Sasatani (2008, 2011). We also used the same frequency range for the computation of DNL values in this paper. One of the advantages of this DNL index is that it gives a single value that facilitates the comparison with other parameters like PGA. Equation 2 may be considered as a variant of Eq. 1 and was used in several previous studies. Interested readers can find further variants of Eq. 2 in Régnier et al. (2013) and Ren et al. (2017). Another important parameter that has been used to describe the effect of nonlinear site response is the amount of shift of predominant frequencies of site response during strong-motions as mentioned above. In this paper, we make use of both indices, DNL and shift of predominant frequencies, in the discussion of the characteristics of nonlinear site response during the mainshock. In this paper, predominant frequency means the frequency that corresponds to the peak spectral ratio between 0.5 and 20 Hz. The S-to-B spectral ratios at 16 KiK-net sites are plotted in Fig. 5 in the order of decreasing horizontal vector PGA from top-left to bottom-right panels a to p, respectively. The spectral ratios for the mainshock at the first five sites, panels a to e, namely IBUH01, IBUH02, HDKH01, IBUH03, and HDKH04, corroborated the two most well-known features of nonlinearity: the reduction in high-frequency components and shift of predominant frequency toward lower one during the strong-motions. The DNL values were between 4.7 (at HDKH01, Fig. 5c) and 11.7 (at IBUH03, Fig. 5d). The predominant frequencies of the sites were reduced by approximately 38% (at IBUH02, Fig. 5b) to 92% (at HDKH04, Fig. 5e). It can be seen that the site IBUH03 (Fig. 5d), which attained the largest DNL, was largely depleted in high-frequency components. We found that the reduction in peak frequency at the site IBUH03 was approximately 73% during the mainshock in comparison with the weak-motions (from 1.9 to ~ 0.5 Hz). This result at the site IBUH03 is commensurate with the reduction in peak frequency by 50% (from 1.2 to 0.6 Hz) reported in Sawazaki et al. (2006) during the 2003 Mw 8.3 Tokachi-oki earthquake. The smaller value of the peak frequency (~ 0.5 Hz) in this study may be due to the much stronger input motions at the site during the 2018 Mw 6.6 earthquake (surface PGA of ~ 651 cm/s2) compared to that during the 2003 Mw 8.3 Tokachi-oki earthquake (surface PGA of ~ 376 cm/s2). We note that the peak frequencies of weak-motions are slightly different between this study and Sawazaki et al. (2006); this may be due to the difference in the data set of weak-motions being used in the respective analyses. We obtained the peak frequency from S-wave portions of the small events while Sawazaki et al. (2006) obtained the values from coda waves. The next six sites, panels f to k in Fig. 5, namely IKRH02, IBUH05, IBUH06, IBUH07, HDKH06, and IKRH03, mostly showed the reduction in higher-frequency components; the DNL values ranged between 2.5 and 7.2. The spectral ratios at IKRH01 (Fig. 5l), SRCH07 (Fig. 5m), and OSMH02 (Fig. 5n) were very similar between the mainshock and weak-motions, suggesting for a little or no nonlinearity; the DNL values at the sites were between 1.5 and 2.7. The remaining two sites, namely SRCH08 (Fig. 5o) and HDKH05 (Fig. 5p), showed the reduction in higher-frequency components primarily; the DNL values were 5.1 and 3.8, respectively. The observed features of spectral ratios and the DNL values described above confirmed that the threshold DNL value of 2.5 suggested by Noguchi and Sasatani (2011) was generally robust to identify nonlinear site response using the S-to-B spectral ratios of S-waves. The results discussed above are summarized in Table 2. Comparison of surface-to-borehole spectral ratios of horizontal component recordings during weak-motions (gray lines) and those during the mainshock (red lines) at KiK-net sites. The plots are arranged in order of decreasing horizontal vector PGAs in panels a–p, respectively. Solid black lines denote mean spectral ratios for weak-motions, and dashed gray lines denote one standard deviation. The PGA in units of cm/s2, PGV in units of cm/s, Vs30 in units of m/s, DNL values, and fault-to-site distance (R) in units of km are also included for each site. See Fig. 3 for site locations It is often presumed that one of the reasons for the smaller variance of PGAs at short distances is due to soil nonlinearity because the nonlinearity averages out the amplifications at soft sites to that at stiff sites at high-frequency components (e.g., Midorikawa and Ohtake 2004). The observed spectral ratios at the site IBUH01 manifested the reduction in the spectral ratios at frequency components higher than about 3 Hz during the mainshock compared with those during the weak-motions (see Fig. 5a). At the same time, an increase in spectral ratios occurred between about 1 and 3 Hz. We compared the surface and borehole NS component recordings at two different passbands (0.5–3 Hz and 3–10 Hz) at the site IBUH01 in Fig. 6a for an event of Mj 4.8, an epicentral distance of 123 km, and focal depth of 49 km. It can be seen that the PGAs are larger for both the borehole and surface recordings in the passband of 3–10 Hz than the values in the passband of 0.5–3 Hz. The S-to-B ratio of PGAs in the passband of 0.5–3 Hz is approximately three while the ratio is approximately 11 in the passband of 3–10 Hz; the amplification of PGAs in the two passbands is in line with the spectral ratios for weak-motions. The borehole and surface NS component recordings during the mainshock are drawn in Fig. 6b. The borehole recording had the larger PGA in the passband of 3–10 Hz than that in the passband of 0.5–3 Hz; this feature was identical with the weak-motions shown in Fig. 6a. On the contrary, the observed PGA at the surface was much larger in the passband of 0.5–3 Hz than that in the passband of 3–10 Hz. The S-to-B PGA ratios were approximately 11 and 4 in the 0.5–3 Hz and 3–10 Hz passbands, respectively. The above results were very similar between the borehole and surface recordings for the EW components as well. In regions of high intensity, Midorikawa and Fukuoka (1988) found that the lower frequency motions with a frequency of around 2 Hz had a higher correlation with the JMA intensities. As shown in Fig. 4b, the vertical component recording had PGA larger than 1 g at the site IBUH01. However, we confirmed by calculation of the JMA intensity with and without the vertical component recording that the influence of vertical component recording was negligible on the reported intensity (6.74 vs 6.67). The above analysis confirmed that the large increase in amplification factors due to nonlinearity resulted in the largest JMA intensity at the site IBUH01. It is somewhat difficult to notice from only the spectral ratios that the nonlinear site response resulted in the large intensities at short distances such as at the sites IBUH03 and HKD126 because the sites are located up-dip and in the direction of rupture propagation (see Fig. 3). Indeed, the source-type effect that may be forward rupture directivity was recognized at the two sites. Because the site IBUH03 recorded horizontal components of ground motions both on the surface and at the borehole, we presented somewhat detail comparison of the amplification of the PGVs at different frequency bands for a small event and the mainshock in an Additional file 1. The analysis indicated that the nonlinear site amplification at the top of the large input motions caused one of the largest PGVs during the mainshock beyond the predominant frequency of linear site amplification. Examples of similar phenomena from the near field recordings may be found in Bray and Rodriguez-Marek (2004) and Garini et al. (2017). These observations suggested that the nonlinearity does a favor by reducing amplitudes of some frequency components but at the cost of increasing the strength of ground motions at other frequencies during strong-motions. We discuss the characteristics of nonlinear site response on the vertical components in the next two sections. Comparison of the borehole (left panel) and surface (right panel) NS component acceleration recordings for weak-motions (a) and mainshock (b) at site IBUH01 at different passband frequencies. The weak-motion recordings are from an event that occurred on November 1, 2006, at 23:21 JST (Mj = 4.8, focal depth = 49 km, epicentral distance = 123 km, back azimuth = 120°). In each panel, the uppermost recordings are unfiltered ones; the middle and lowermost recordings were bandpass filtered at 0.5–3 Hz and 3–10 Hz, respectively, as indicated in each plot. The maximum acceleration in the unit of cm/s2 is indicated above each trace. Note that the scale of the vertical axis in the right panels is larger by a factor of 10 with respect to that in left panels S-to-B spectral ratios of vertical components The S-to-B spectral ratios of vertical components (V-to-V) for the mainshock and weak-motions are plotted in Fig. 7 at all sites described in the previous section except at the site IBUH03, where the vertical component borehole sensor did not record the shakings correctly. The sites in Fig. 7 are arranged in the same order as those plotted in Fig. 5. The DNL values were obtained using Eq. 2. Our results described shortly indicated that the DNL value of 3.5 or larger may indicate nonlinear site response on vertical components. The threshold value is very similar to the threshold value of 4 suggested by Noguchi and Sasatani (2011) to identify nonlinear site response on horizontal components using the H-to-V spectral ratios. Comparison of surface-to-borehole spectral ratios of vertical component recordings during weak-motions (gray lines) and those during the mainshock (red lines) at KiK-net sites. The plots are arranged in order of the sites plotted in Fig. 5 (i.e., decreasing horizontal vector PGAs from top-left a to bottom-right p panels). Solid black lines denote mean spectral ratios for weak-motions and dashed gray lines one standard deviation. The vertical PGA in units of cm/s2, vertical PGV in units of cm/s, Vs30 in units of m/s, DNL values, and fault-to-site distance (R) in units of km are also included for each site. Note that the plot for site IBUH03 is not available due to malfunction of the vertical component instrument at underground. See Fig. 3 for site locations The site IBUH01 (Fig. 7a) exhibited a remarkable shift of peak spectral ratios and considerable amplifications at frequencies between about 3 and 6 Hz during the mainshock compared with those during the weak-motions. The DNL value was 5.5, and the reduction in peak frequency was approximately 76% (from 17.13 to 4.06 Hz). This site recorded vertical ground acceleration exceeding 1 g at the surface during the mainshock; the waveforms were asymmetric in shape and had different amplitudes for the down-going and up-going motions for a small duration (see the next section). The shift of peak frequency and relatively larger DNL value are indicative of a nonlinear site response at the site IBUH01. However, the evaluation of nonlinear site response at the site IBUH01 based on spectral ratios may not be suitable due to the presence of asymmetric waves on the surface recordings (e.g., Aoi et al. 2008), and hence, the results presented above are only for information. Similarly, the site HDKH01 (Fig. 7c) showed a possibility of nonlinear site response during the mainshock. The vertical PGA at the surface was approximately 317 cm/s2. The peak frequency was shifted toward lower one (from about 18–6 Hz) with larger amplification than that in the weak-motions. The DNL value was 3.8. At the site IBUH06 (Fig. 7h), the DNL value was 5, and a systematic decrease in spectral ratios was found at frequencies larger than about 10 Hz. This latter feature was not clear at the other sites. These results may indicate that the vertical component at IBUH06 experienced a small degree of nonlinear site response during the mainshock. Also, the site IBUH07 (Fig. 7i) may have experienced a small degree of nonlinearity as suggested by the small shift of the first peak frequency and the substantial decrease in spectral ratios at about 3–6 Hz. The DNL value for the site was 4.1. In fact, two comparable peaks can be seen in the spectral ratios at the IBUH07 site during the strong-motions at 2.1 and 12.3 Hz approximately. If the peak at higher frequency is neglected considering the range of scattering for weak-motions, a systematic decrease in spectral ratios between about 2- and 10-Hz points toward a nonlinear site response. Except for the four sites mentioned above, the other sites did not show clear signatures of nonlinearities in vertical component ground motions; the DNL values at the sites were between 2.2 and 3.3 (see also Table 2). The peak frequencies between S-to-B spectral ratios for horizontal components (H-to-H) (x axis) and vertical components (V-to-V) (y axis) during weak-motions are plotted in Fig. 8a. It can be seen in the figure that the peak frequencies are systematically higher for the V-to-V spectral ratios than those for the H-to-H spectral ratios except at one site, indicating that the two spectral ratios may represent the results for two different wave types: horizontal components mostly for S-waves and vertical components mostly for P-waves, at least for higher-frequency components. In the case of mainshock, the late-arriving P-waves might have also contaminated the S-waves in the vertical components and contributed to the higher predominant frequency. The peak frequencies for the V-to-V spectral ratios for the mainshock and weak-motions are plotted in Fig. 8b. They are similar at most sites. At two sites, namely IBUH01 and HDKH01 having relatively larger DNL values (the two data points near lower right corners in Fig. 8b), the peak frequencies during strong-motions are smaller than those for the weak-motions. However, a reverse trend for peak frequency can be seen at one site near 2.7 Hz along the horizontal axis; this is at the IBUH07 site due to the reason briefly mentioned in the previous paragraph. The spectral ratios at the site IBUH07 had two comparable peaks at about 2.1 and 12.3 Hz during strong-motions. The peak at 12.3 Hz was slightly larger than the peak at 2.1 Hz (see Fig. 7i). Therefore, the plot for IBUH07 is a purely mathematical one in Fig. 8b. a Comparison of peak frequencies between surface-to-borehole spectral ratios for horizontal components (H-to-H) (x axis) and vertical components (V-to-V) (y axis) during weak-motions. b Comparison of peak frequencies between surface-to-borehole spectral ratios for vertical components (V-to-V) during weak-motions (x axis) and strong-motions (y axis). The data points are color-coded by DNL values computed based on vertical component spectral ratios (V-to-V). Some data points that deviate largely from the diagonal line in b are provided with their site codes close to the data points Here we discuss the possible mechanisms qualitatively for the nonlinear site response on the vertical components. Sato and Kanatani (2006) suggested that the nonlinear site response can occur on the vertical motions (pressure waves) for unsaturated soils because the change of bulk modulus and damping for P-waves occur in response to strong input motions in addition to the changes in shear modulus and damping for S-waves. Meanwhile, they pointed out that the effect of change of shear modulus and damping for S-waves do not contribute significantly to induce nonlinear site response on the vertical motions for the saturated soil. Between the three sites, namely HDKH01, IBUH06, and IBUH07 which are suspected for nonlinear site response on the vertical components, available PS-logging data suggest that the sites HDKH01 and IBUH06 might be unsaturated in its top layers during the earthquake. At the site HDKH01, the measured P- and S-wave velocity in the top 4 m of soil is 860 and 120 m/s, respectively; the layer beneath the above layer has a thickness of 4 m and has P- and S-wave velocity of 1200 and 360 m/s, respectively. The recorded PGAs on the horizontal and vertical components were approximately 663 and 317 cm/s2, respectively, at the HDKH01 site (see Table 2). Indeed, the site experienced a significant nonlinear site response on the horizontal components as discussed in the previous section, which means that the nonlinear site response on the vertical component at the HDKH01 site is likely to be due to the changes in P-wave velocity and damping for the P-waves in addition to the corresponding changes for S-waves. At the site IBUH06, the top 5 m of soil has P- and S-wave velocity of 460 and 200 m/s, respectively; the second layer having a thickness of 5 m has P- and S-wave velocity of 850 and 340 m/s, respectively. The recorded PGAs on the horizontal and vertical components were approximately 260 and 203 cm/s2, respectively, at the IBUH06 site (see Table 2). The site also experienced nonlinear site response on the horizontal components (Fig. 5h). The smaller P-wave velocity and relatively large PGA on the vertical component suggest that the changes in both the P- and S-wave velocities and corresponding damping in response to strong input motions might have induced nonlinear site response on the vertical motions at the site IBUH06. At the site IBUH07, the P-wave velocity in the top 5 m and next 8 m of soil is 1600 m/s; the S-wave velocities in the layers are 400 and 200 m/s, respectively (velocity inversion is noted). The recorded PGAs on the horizontal and vertical components were approximately 222 and 82 cm/s2, respectively (see Table 2). The PS-logging velocity model and PGAs suggest that the change in P-wave velocity and damping for it may not be significant at the site, and the site might have experienced nonlinear site response on the vertical motions due to the changes in S-wave velocity and damping for S-wave. We defer the quantitative evaluation of nonlinear site response at the sites to future study. Direct evidence of nonlinear site response on vertical components In this section, we present the direct evidence that we think of nonlinear site response on vertical component waveforms at two sites (IBUH01 and HKD127) during the mainshock. See Fig. 3 for site location. The surface and borehole vertical component recordings at the sites are plotted in Fig. 9. The surface acceleration waveforms at both the IBUH01 and HKD127 showed some characteristic pulses barely reported in strong-motions: the larger amplitude of up-going acceleration pulses (often exceeding 1 g) than that for down-going ones (often lower than 1 g) and duration of up-going acceleration pulses smaller than that of the down-going ones. The borehole recordings at the site IBUH01 did not show the features above. The largest peak ground accelerations of up-going and down-going pulses at IBUH01 were approximately 1060 and − 745 cm/s2, respectively, at the surface, while the corresponding values at a depth of 101 m were approximately 75 and − 84 cm/s2, respectively. Similarly, the largest PGAs of up-going and down-going pulses at HKD127 were approximately 1590 and − 880 cm/s2, respectively. The ratio of the sums of duration for up-going and down-going pulses for a time window of 4 s plotted in Fig. 9b is 1.15 at IBUH01 and 1.07 at HKD127. The ratios become approximately 1.3 and 1.6 at the former and latter sites when the ratios are computed from the pertinent pulses only. These observations were similar to those observed during the 2008 Mw 6.8 Iwate-Miyagi crustal earthquake, Japan (Aoi et al. 2008). The asymmetric pulses were pertinent for longer durations at IWTH25 during the Iwate-Miyagi earthquake than those during the present earthquake. Yamada et al. (2009) summarized the characteristics of asymmetric waveforms in amplitude and duration on vertical component ground motions that had been recorded prior to the largest known vertical acceleration (Aoi et al. 2008), including the features at the site IWTH25 during the Iwate-Miyagi crustal earthquake. a Vertical component acceleration recordings at the surface (upper panel) and borehole (middle panel) at site IBUH01 and the surface at HKD127 (lower panel). The values for the borehole recordings are magnified by a factor of 10 to aid visual comparison. A black rectangle denotes the portion of the plot, which is enlarged in b. The ratio of total duration of negative pulses to the total duration of positive pulses is indicated above each trace for the time window from 26 to 30 s in b. See Fig. 3 for site location and text for further explanation The mechanisms, threshold motions, site geology, etc. to induce large amplitude asymmetric vertical ground motions are not well understood. Interested readers can find an intuitive explanation for asymmetric waves in extreme vertical component accelerations in Aoi et al. (2008), who explained the phenomena by trampoline effect. Some other explanations on mechanisms for the asymmetric waves can be found in Yamada et al. (2009), who explained the asymmetric waves as slap down phases. Tobita et al. (2010), based on numerical analysis, concluded that the asymmetrical waveforms might be related to the different behaviors of soils in compression and tension. The S-to-B spectral ratios of vertical components at IBUH01 for the mainshock, weak-motions, and an aftershock that occurred about 3 h later close to the mainshock hypocenter are plotted in Fig. 10 for the site IBUH01. The aftershock recordings at the surface had a horizontal vector PGA of approximately 124 cm/s2 and vertical PGA of approximately 51 cm/s2. In Fig. 10, it can be seen that the peak frequency of spectral ratios from the aftershock is more similar to that from the weak-motions than that from the mainshock recordings. The asymmetrical waveforms also were not present on the aftershock recordings. Thus, it is likely that the characteristic asymmetric waves for the down-going and up-going accelerations, which were recorded during the mainshock only, were due to the nonlinear soil response at the sites during the mainshock. Comparison of surface-to-borehole spectral ratios of vertical component acceleration recordings (V-to-V) at site IBUH01 during weak-motions (mean of the weak-motions, black line), mainshock (red line), and an aftershock (blue line). The gray lines denote the range of plus–minus one standard deviation from the mean of weak-motion spectral ratios. The aftershock (Mj = 5.4, focal depth = 40 km, epicentral distance = 24.3 km, back azimuth = 142.6°) occurred on September 6, 2018, at 06:11 JST, about 3 h later than the mainshock Here we explain the shallow soil velocity profiles briefly at the two sites mentioned above. The P- and S-wave velocity profiles based on PS-loggings are shown in Fig. 11. The velocity model based on PS-logging is available down to the depth of 10 m at the HKD127 site, while the model reaches to a depth of 101 m at the site IBUH01. Since the two sites are closely located, the deeper subsurface model beneath the sites may be considered similar. Based on the PS-logging data, the average S-wave velocities in the upper 10 m of the soil column beneath the sites IBUH01 and HKD127 are approximately 183 and 189 m/s, respectively. On the other hand, the P-wave velocities in the upper 10 m beneath the two sites are approximately 571 and 982 m/s, respectively. The maximum amplitude of the up-going pulses was relatively larger at the site HKD127 than that at the IBUH01 site. The maximum and minimum PGAs at the site IWTH25 were 3866 and 1703 cm/s2, respectively. We examined the PS-logging data at the site IWTH25 and found that the shallow soil layers are stiffer than those at the sites HKD127 and IBUH01; the average S-wave and P-wave velocities in the upper 10 m of the soil column beneath the site IWTH25 were approximately 465 and 1073 m/s, respectively. Yamada et al. (2009) noted that the sites that showed asymmetric waves were relatively stiff sites. These observations may suggest that the local site geology is one of the important factors to understand the mechanisms of asymmetric waves observed on vertical component recordings during strong-motions, and stiff sites may lead to stronger asymmetrical pulses with large vertical accelerations during strong-motions. We explore the characteristics of nonlinear site response using the single-station H-to-V spectral ratio technique at selected sites of the KiK-net and K-NET in the next section. P- and S-wave velocity profiles based on PS-loggings at sites IBUH01 (red lines) and HKD127 (blue lines). The P- and S-wave velocity profiles are drawn in dashed and solid lines, respectively. The vertical axis is drawn in log-scale to show the shallow layers clearly. The scale begins from 1 and corresponds to the free surface at the recording station H-to-V spectral ratios at surface KiK-net and K-NET sites In this paper, we obtained the H-to-V spectral ratios of surface recordings at the KiK-net and K-NET sites depicted in Fig. 3. The spectral ratios were obtained as the vector sum of two horizontal components Fourier spectral amplitudes divided by the corresponding Fourier spectral amplitudes of the vertical component. The H-to-V spectral ratios for the weak- and strong-motions at the KiK-net sites are plotted in Fig. 12 along with the S-to-B spectral ratios for horizontal components during the mainshock. The sites are arranged in the same order as that in Figs. 5 and 7. Figure 12 shows that the two types of mean spectral ratios for the weak-motions (H-to-V: black lines, and S-to-B: blue lines) are generally different. In the same way, the corresponding ratios during the mainshock (H-to-V: red lines, and S-to-B: green lines) are also different. These results are generally expected as the S-to-B spectral ratios are dependent on both site geology and depth of the downhole sensor (e.g., Steidl et al. 1996) while the H-to-V spectral ratios are mainly controlled by the site geology (e.g., Kawase et al. 2011). Plots of H-to-V spectral ratios of surface recordings during weak-motions (gray lines) and those during the mainshock (red lines) at KiK-net sites. The green and blue lines denote the S-to-B spectral ratios of horizontal components (H-to-H) for mainshock and weak-motions, respectively (see also Fig. 5). The plots are arranged in order of the sites depicted in Figs. 5 and 7. Solid black lines denote mean spectral ratios for weak-motions and dashed gray lines denote one standard deviation. The horizontal vector PGA in units of cm/s2, horizontal vector PGV in units of cm/s, Vs30 in units of m/s, DNL values, and fault-to-site distance (R) in units of km are also included for each site. See Fig. 3 for site location The peak frequencies for the two types of spectral ratios for weak-motions are plotted in Fig. 13a. It can be seen that the peak frequencies are comparable except at few sites, where the peak frequencies are higher for S-to-B spectral ratios. The site IBUH05 is exceptional; the weak-motions S-to-B spectral ratios had peak at frequency ~ 14.5 Hz while the weak-motions H-to-V had peak at frequency ~ 2.7 Hz. The S-to-B spectral ratios during the strong-motions suggested nonlinear site response, and the reasonable shift of peak frequency was recognized (from ~ 14.5 to 12 Hz) (see Fig. 5g). The H-to-V spectral ratios during the strong-motions also indicated a small degree of nonlinear site response, and the spectral ratios were smaller in relation to weak-motions at frequencies larger than about 10 Hz, but the shift of peak frequency was not evident (see Fig. 12g). The lack of clear peak for H-to-V spectral ratios for the weak-motions as well as the strong-motions may be one of the possible reasons for the large discrepancy of the peak frequencies between the two types of spectral ratios at the site IBUH05. The DNL values for the mainshock based on the two types of spectral ratios are plotted in Fig. 13b, and they may be considered similar considering the reasonable scattering of the spectral ratios. Similarly, the peak frequencies for the two types of spectral ratios during the mainshock are comparable at most sites as shown in Fig. 13c. Here, we note that the larger DNL value at the site IBUH01 based on the H-to-V spectral ratios is partially due to the effect of nonlinear amplification on the vertical component recording at the surface (see Fig. 7a). The above result suggests that the H-to-V spectral ratio method may not be suitable to reliably extract the degree of change in site response such as the reduction in spectral amplification factors at higher frequencies if the vertical components experienced nonlinear site response. However, as evident in Fig. 13b, c, the data points that deviate largely from equality are not systematic between the S-to-B and H-to-V methods for strong-motions. The H-to-V spectral ratio method is still able to detect the nonlinear site response in similar ways to that of S-to-B spectral ratio method of horizontal components, which was primarily due to the different ranges of frequencies that were affected on the horizontal and vertical component ground motions. The horizontal motions were affected up to relatively lower frequencies than those for vertical motions by the nonlinear site response (for example, see Figs. 5a, c, h and 7a, c, h for sites IBUH01, HDKH01, and IBUH06, respectively). a Comparison of peak frequencies between S-to-B spectral ratios for horizontal components (H-to-H) and horizontal-to-vertical (H-to-V) spectral ratios at the surface for weak-motions. b Comparison of DNL values based on S-to-B spectral ratios for horizontal components (H-to-H) and H-to-V spectral ratios at the surface. c Comparison of peak frequencies between S-to-B spectral ratios for horizontal components (H-to-H) and H-to-V spectral ratios at the surface for strong-motions. The data points are color-coded by DNL values based on the S-to-B spectral ratios. Some data points that deviate largely from the diagonal lines are provided with their site codes near the data points Here we discuss the nonlinear site response at the K-NET sites. The H-to-V spectral ratios at the selected 16 sites of K-NET are plotted in Fig. 14. All the sites recorded horizontal vector PGA of 200 cm/s2 or larger. The peak ground motions for the mainshock, predominant frequencies during the mainshock and weak-motions, and the DNL values at the K-NET sites are provided in Table 3. The sites, namely HKD127, HKD125, HKD128, HKD103, HKD126, HKD124, HKD129, HKD105, HKD184, HKD131 (Fig. 14a, b, c, d, e, f, h, i, j, l), showed the shift of predominant frequencies and reduction in higher-frequency spectral ratios in different amounts, suggesting that the sites experienced various degrees of nonlinear site response. The horizontal vector PGAs were between 387 cm/s2 and 1318 cm/s2, and the DNL values ranged between 3.3 (HKD125, Fig. 14b) and 13.4 (HKD126, Fig. 14e) at the sites. The site HKD126 with maximum DNL value of 13.4 showed a marked reduction in spectral ratios at frequencies higher than about 2 Hz during the mainshock, and the shift of predominant frequency was from 3.06 Hz to 0.53 Hz. The DNL value at the site HKD127 (Fig. 14a) was 13.1, and the shift of predominant frequency was from 7.78 to 2.06 Hz. As the site HKD127 experienced nonlinear site response on the vertical component as discussed in the previous section, the DNL value based on H-to-V spectral ratios may not be suitable to infer the degree of nonlinearity at the site. However, by analogy with the site IBUH01, the information on the shift of predominant frequency is useful for the identification of soil nonlinearity. The other six sites, namely HKD185, HKD104, HKD181, HKD130, HKD182, HKD106 (Fig. 14g, k, m–p), had DNL values between 2.6 (HKD182 and HKD106) and 3.8 (HKD182), and the sites did not show clear shift of predominant frequencies except an apparent shift of frequencies between about 1 and 10 Hz at the site HKD182. The horizontal vector PGAs ranged between 206 and 356 cm/s2 at the sites except at HKD185 that recorded 562 cm/s2. Despite the large PGA, the DNL value at HKD185 was 3.4. The spectral ratios as well as the DNL values at the sites HKD105 and HKD184 (Fig. 14i, j), for example where the PGAs were smaller than those at the site HKD185, indicated the nonlinear site response at the sites. Accordingly, the nonlinear site response is not related by simple relation with the PGAs at the surface, and rather, it signifies that the nonlinear site response is primarily controlled by soil stiffness and input ground motions at the bottom of the soil layers discussed briefly in the next section. Plots of H-to-V spectral ratios of surface recordings during weak-motions (gray lines) and those during the mainshock (red lines) at K-NET sites. See Fig. 3 for site location. The plots are arranged in order of decreasing horizontal vector PGAs in panels a–p, respectively. Solid black line denotes mean spectral ratios for weak-motions, and dashed gray lines denote one standard deviation. The horizontal vector PGA in units of cm/s2, horizontal vector PGV in units of cm/s, Vs30 in units of m/s, DNL values, and fault-to-site distance (R) in units of km are also included for each site The peak frequencies of S-to-B spectral ratios of horizontal components during strong-motions (mainshock) and weak-motions at the KiK-net sites and those of H-to-V spectral ratios at K-NET sites are plotted in Fig. 15. It is evident in the figure that the peak frequencies of the spectral ratios for the mainshock are mostly lower than those for the weak-motions except at a site (HKD129). The weak-motion spectral ratios at the HKD129 site are comparable to the spectral ratios during the mainshock at frequencies between about 0.5 and 10 Hz, and the ratios are almost flat between those frequencies as shown in Fig. 14h. Therefore, the difference between the weak-motion and strong-motion peak frequencies at the HKD129 site is mainly due to similar spectral ratios. Figure 15 suggests that the larger DNL values are related to larger PGAs and lower Vs30 values. However, the Vs30 values do not always indicate the plausibility of nonlinear site response sufficiently as discussed briefly in the next paragraph. Comparison of peak frequencies from strong-motions (mainshock) and weak-motions S-to-B spectral ratios for horizontal components at the KiK-net sites (circles) and H-to-V spectral ratios at the K-NET sites (triangles). The data points are color-coded by horizontal vector PGAs at the surface in a, Vs30 values in b, and DNL values based on the S-to-B spectral ratios in c, respectively. The sites where Vs30 values were not estimated are denoted by diamonds (see Table 3 for the Vs10 values at the sites). Some data points that might be of interest to readers are provided with their site codes near the data points Among the sites analyzed in this study, two KiK-net sites, namely IBUH02 and HDKH05, have Vs30 values exceeding 500 m/s (see Table 2). The IBUH02 site clearly showed signatures of nonlinear site response (see Fig. 5b); the Vs30 value at the site is 542 m/s, and horizontal vector PGA was 707 cm/s2. A site with such high Vs30 value is generally expected to undergo linear site amplification. However, a close examination of the PS-logging data at the site showed that the Vs30 is 130 m/s for the top 2 m of soil layer and 280 m/s for the next 5 m, which overlies the stiffer layers having Vs value of 810 m/s and larger. The above findings may suggest that the top layers having smaller Vs values overlying the more competent large impedance layers may experience significant nonlinear site response, and hence, the Vs30 values may not be a good indicator for nonlinear site response in every case. The HDKH05 site showed a small degree of nonlinear site response (see Fig. 5p) despite smaller input motions (the horizontal vector PGA was approximately 68 cm/s2 at the surface and 26 cm/s2 at a depth of 100 m) and large Vs30 value of 766 m/s. A close examination of the PS-logging data at the site showed that the Vs30 is 250 m/s for the top 2 m of soil layer, 470 m/s for the next 4 m, and larger than 1000 m/s for the underlying layers. These velocity models together with the above observations corroborate that the layers having S-wave velocities smaller than about 300 m/s are strongly susceptible to nonlinear site response during strong-motions. An ad hoc equation for nonlinear site amplification We found that the most sites at fault distances shorter than about 50 km experienced nonlinear site response during the mainshock, and it was confirmed that the sites gained the motions in the frequency bands that corresponded to the enhancement of amplification due to nonlinear site response. Even though both the PGA and PGV are affected by nonlinear site response, it is mostly the PGV that is amplified because the relatively longer-period ground motions get enhanced due to nonlinear site response. Kamiyama (1992) obtained a nonlinear site amplification model at a site statistically as a function of maximum particle velocity at a virtual rock site. Abrahamson and Silva (1997) obtained nonlinear site amplification terms in their GMPE as a function of rock site PGA. More recent studies (e.g., Walling et al. 2008; Kamai et al. 2014) proposed the rock site PGA as one of the input motion parameters as well as the Vs30 to address the unequal nonlinear site response at different site conditions. The studies mentioned above indicate that the strength of input motions at the base of a soil site may be represented in terms of the corresponding PGA or PGV for a virtual rock site at the site of interest. In this study, we followed the recent trend of using PGA as a reference motion to incorporate nonlinear site response in GMPEs. Over the last 40–50 years, an enormous amount of literature has been accumulated in the numerical simulation of nonlinear site response. For an overview of quantification of nonlinear site response by numerical simulations, we refer the paper by Régnier et al. (2016) and the references therein. Here we derived a correction formula for the PGVs with reference to the median values obtained from GMPEs. We first obtained the rock site PGAs at the selected sites using the GMPE by Si and Midorikawa (1999). These PGAs and Vs30 values at the sites were treated as independent variables, and the residuals for PGVs plotted in Fig. 2d were fitted against the two variables. Finally, we obtained the following relation (Eq. 3) between PGV residuals, input PGAs (rock site PGAs ≥ 50 cm/s2), and Vs30 values (between 110 and 540 m/s approximately) by linear regression: $$ \log _{{10}} \left( {\frac{{{\text{obsPGV}}}}{{{\text{prePGV}}}}} \right) = 0.0399 + 0.0028{\text{PGA}}_{{{\text{rock}}}} - 0.0002{\text{Vs}}_{{30}} $$ where $ {\text{obsPGV}} $ is the observed PGV (larger of two components), $ {\text{prePGV}} $ is the predicted PGV taking account of Vs30 in GMPE by Si and Midorikawa (1999), $ {\text{PGA}}_{\text{rock}} $ is the predicted PGA at a virtual rock site at the distance of site of interest using the GMPE for PGA in Si and Midorikawa (1999). To confine the equation within the range of nonlinear response, we obtained the equation using the data points at which the DNL values were 4 or larger at the both K-NET and KiK-net sites. This resulted in the rock site PGAs ≥ 50 cm/s2 and Vs30 values smaller than about 540 m/s in the above analysis. The standard deviation of the residuals for Eq. 3 is 0.1304 in base-10 log-scale. The obtained coefficients for PGA and Vs30 are generally in good agreement with the expected results that the PGV should decrease with the increase in Vs30 values and should increase with the increase in input motions. The PGV residuals are plotted against rock site PGAs in Fig. 16; a linear relationship can be easily seen between the two variables. The data points are color-coded by Vs30 and DNL values. The lines representing the correction values for PGVs in base-10 log-scale are also plotted in the figure for Vs30 values of 150 m/s (gray line) and 450 m/s (black line). It can be seen that the main contributor to the correction value is the input PGA, and this finding is similar to the previous results (e.g., Campbell and Bozorgnia 2008, 2014). The PGVs plotted in Fig. 2b were corrected by Eq. 3 at sites where input PGAs ≥ 50 cm/s2 were calculated, and these new values are plotted in Fig. 17. It can be seen that the same GMPE describes the data well after the corrections for the nonlinear site response. Plots of logarithmic residuals for PGVs as a function of rock site PGAs using the GMPEs in Si and Midorikawa (1999). The data are color-coded by Vs30 values in a and DNL values in b, respectively. The KiK-net and K-NET sites are indicated by circles and triangles, respectively. The gray and solid lines denote the correction values for PGVs as a function of PGAs at rock sites using Eq. 3 for Vs30 values of 150 and 450 m/s, respectively. Note that the data points having DNL values smaller than 4 were excluded in the derivation of Eq. 3; they are included in the above plots for reference only. Some data points are provided with their site codes for reference close to the data points Observed PGVs after corrections for nonlinear site effects plotted as a function of fault distance. The values were adjusted for nonlinear site effects if rock site PGAs exceeded 50 cm/s2, and Vs30 values were lower than about 550 m/s. For further explanation, see the text and figure captions in Fig. 2 Since Eq. 3 is derived for a specific data set for a single event and limited site conditions, we consider the correction coefficients an ad hoc result. We continue to investigate the relationships for other events as an effort toward our long-term goal of accomplishing the reliable prediction of ground motions for seismic hazard analysis and earthquake early warnings in our future studies. Discussions and conclusions We analyzed the strong-motion data of the 2018 Mw 6.6 Hokkaido eastern Iburi earthquake to understand the peak ground motions and characteristics of nonlinear site response during the earthquake. We compared the observed PGAs and PGVs with the values from the GMPEs by Si and Midorikawa (1999), which have been widely used for seismic hazard evaluation in Japan. We found that the data at fault distances larger than about 50 km were generally explained by the ground motion prediction equations very well. In contrast, in the regions of high seismic intensity at smaller distances and soft sites, the equations underestimated the data substantially. The underestimation was more evident to PGVs. We computed and analyzed the S-to-B spectral ratios of horizontal components, S-to-B spectral ratios of vertical components, and H-to-V spectral ratios of surface recordings for the mainshock and weak-motions at 16 KiK-net sites. Only the H-to-V spectral ratios were analyzed at the equal number of K-NET sites because the K-NET sites consisted of sensors only at the surface. We obtained DNL values following the method of Noguchi and Sasatani (2008) using the spectral ratios between 0.5 and 20 Hz. The threshold DNL value of 4 for H-to-V spectral ratio method and 2.5 for S-to-B spectral ratios of horizontal components as suggested by Noguchi and Sasatani (2011) generally served as a good criterion to identify nonlinear site response in this study. Furthermore, in the present study, we found that a DNL value of 3.5 or larger may indicate a nonlinear site response based on the S-to-B spectral ratios of vertical components for the time window that corresponds to S-waves on horizontal components. By comparing the weak-motions and strong-motions (mainshock) spectral ratios, we found that the sites having relatively smaller Vs30 values in regions of stronger input motions experienced a larger degree of nonlinear site response. These results were consistent with previous results regarding the commonly reported conditions for nonlinear site response. We found that a few sites might have experienced nonlinear site response on horizontal components having PGAs as low as about 70 cm/s2 depending on the site condition. In the earlier literature and the engineering community in general (e.g., Kramer 1996, p. 318), a decrease in PGAs at soil sites during strong-motions in comparison with weak-motions has been well accepted. More recent studies supported by many data (e.g., Campbell and Bozorgnia 2008, 2014) have emphasized the nonlinear amplification of ground motions at wide frequencies that depends on the input PGAs. We found that, during the 2018 Mw 6.6 Hokkaido eastern Iburi earthquake, the nonlinear amplification was larger by one order of magnitude at the IBUH01 site, and at the other several sites which experienced large intensities (e.g., IBUH03, HDKH01, HDKH04, HKD126, HKD128), the increase in amplification at lower frequencies in relation to the linear case was substantial. Indeed, amplifications decreased during strong-motions at the predominant frequencies of the linear case at the sites mentioned above, and at the site IBUH03, the horizontal vector PGA at the surface was somewhat smaller than that at the borehole at a depth of 153 m (651 cm/s2 vs 795 cm/s2 approximately). Contrarily, the horizontal vector PGV was significantly amplified at the site IBUH03 (surface 151 cm/s vs borehole 39 cm/s). We think that the nonlinear amplification was one of the main causes of high JMA intensities and underestimation of the observed PGVs at smaller fault distances. These observations suggest for greater attention to nonlinear site response in seismic hazard analyses. It is noteworthy to mention here that the sites IBUH01 and HKD127 experienced nonlinear site response on both the horizontal and vertical component ground motions at the surface. It is still not all out about the threshold motions and mechanisms that cause the generation of large amplitude asymmetric pulses, but the relatively stiffer site condition appears to be one of the factors in addition to the large vertical input motions at the base rock. Our analyses based on the S-to-B spectral ratios of vertical components suggested that most sites that showed nonlinear site response on horizontal components did not show nonlinear site response on vertical components. These findings suggested that the H-to-V spectral ratio method is equally useful as the S-to-B spectral ratio method to identify nonlinear site response at least in a statistical sense. However, we note that some sites might have experienced nonlinear site response on vertical components for vertical PGAs as low as approximately 80–200 cm/s2. This means that the DNL values obtained from the H-to-V method are not reliable if the site experienced nonlinear site response on vertical components. Larger DNL values as obtained in this study imply the larger reduction in higher-frequency components. Therefore, caution should be maintained to estimate the spectral amplifications at higher frequencies during strong-motions based on the H-to-V spectral ratio method. Interestingly, the shift of predominant frequency to lower one was quite similar between the S-to-B and H-to-V spectral ratio methods even at a site that experienced nonlinear site response on the vertical component. In our analysis, this was because the horizontal motions were affected up to lower frequencies than those for vertical motions by the nonlinear site response. By considering the PGAs at virtual rock sites as reference input motions, we obtained an ad hoc equation to account for nonlinear site amplification for PGVs with reference to the GMPEs in Si and Midorikawa (1999). We found that the input motions largely control the deviations from the median predictions given the identical site conditions. For a given input motion, the larger deviation was found for the softer site condition, but that deviation was relatively smaller for a proportional change in input motions. Since we did not investigate how much of the nonlinearity and other effects such as the rupture propagation effects had been already included in the GMPEs in Si and Midorikawa (1999) and the residuals analyzed in this study, the equation for correction of nonlinear site amplification should be taken as a general guide rather than the true estimate. The strong-motion (K-NET and KiK-net) recordings and PS-loggings used in this study were downloaded from the Web sites: http://www.kyoshin.bosai.go.jp/. The moment magnitude was taken from the Web site: http://www.fnet.bosai.go.jp/event/joho.php?LANG=en. The strong-motion recordings at the JMA sites were retrieved from https://www.data.jma.go.jp/svd/eew/data/ltpgm_explain/data/past/20180906030805/index.html, in Japanese. The hypocenter location and JMA magnitude of the mainshock were taken from the Web site: https://www.data.jma.go.jp/svd/eqev/data/bulletin/hypo_e.html. The hypocenter information of the aftershocks plotted in Fig. 1c, d was taken from https://hinetwww11.bosai.go.jp/auth/JMA/jmalist.php. For other specific information such as the list of recordings used in the study, contact author for data requests. 3-D: BA: back-arc DNL: degree of nonlinearity FA: fore-arc F-net: full-range seismograph network GCMT: global centroid moment tensor GMPE: ground motion prediction equation H-to-H: horizontal-to-horizontal H-to-V: horizontal-to-vertical JIVSM: Japan integrated velocity structure model JMA: JST: KiK-net: Kiban Kyoshin network K-NET: Kyoshin network Mj: JMA magnitude moment magnitude NEHRP: NIED: National Research Institute for Earth Science and Disaster Resilience P-wave: primary wave PGA: peak ground acceleration PGV: peak ground velocity S-to-B: surface-to-borehole S-wave: secondary wave/shear wave USGS: V-to-V: vertical-to-vertical Vs30: average S-wave velocity in the upper 30 m of the soil layer Abrahamson NA, Silva WJ (1997) Empirical response spectral attenuation relations for shallow crustal earthquakes. 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J Struct Constr Eng Trans AIJ 523:63–70. https://doi.org/10.3130/aijs.64.63_2 (in Japanese with English abstract) Si H, Midorikawa S (2000) New attenuation relations for peak ground acceleration and velocity considering effects of fault type and site condition. In: Proceedings of the 12th world conference on earthquake engineering, Auckland, New Zealand, Paper ID 0532 Steidl JH, Tumarkin AG, Archuleta RJ (1996) What is a reference site? Bull Seismol Soc Am 86:1733–1748 Suzuki W, Aoi S, Kunugi T, Kubo H, Morikawa N, Nakamura H (2017) Strong motions observed by K-NET and KiK-net during the 2016 Kumamoto earthquake sequence. Earth Planets Space 69:19. https://doi.org/10.1186/s40623-017-0604-8 Takahashi H, Kimura R (2019) The 2018 Hokkaido eastern Iburi earthquake and its aftermath. Disaster report: Sc20190112. Journal of Disaster Research 14: Scientific Communication Tobita T, Iai S, Iwata T (2010) Numerical analysis of near-field asymmetric vertical motion. Bull Seismol Soc Am 100:1456–1469. https://doi.org/10.1785/0120090301 USGS (United States geological Survey) (2018) M 6.6—27 km ENE of Tomakomai, Japan. https://earthquake.usgs.gov/earthquakes/eventpage/us2000h8ty/executive. Accessed on Feb 2019 Walling M, Silva W, Abrahamson N (2008) Nonlinear site amplification factors for constraining the NGA models. Earthq Spectra 24:243–255. https://doi.org/10.1193/1.2934350 Wen KL, Beresnev IA, Yeh YT (1994) Nonlinear soil amplification inferred from downhole strong seismic motion data. Geophys Res Lett 21(24):2625–2628. https://doi.org/10.1029/94GL02407 Wen KL, Chang TM, Lin CM, Chiang HJ (2006a) Identification of nonlinear site response using the H/V spectral ratio method. Terr Atmos Ocean Sci 17(3):533–546 Wen KL, Chang TM, Lin CM, Chiang HJ (2006b) Identification of nonlinear site response during the 1999, Chi–Chi, Taiwan earthquake from the H/V spectral ratio. In: Third international symposium on the effects of surface geology on seismic motion, Grenoble, France, Paper ID 012 Wen KL, Huang JY, Chen CT, Cheng YW (2011) Nonlinear site response of the 2010 Darfield, New Zealand earthquake sequence. In: Fourth international symposium on the effects of surface geology on seismic motion, University of California, Santa Barbara, pp 1–8 Wessel P, Smith WHF (1998) New, improved version of generic mapping tools released. EOS Trans AGU 79:579. https://doi.org/10.1029/98EO00426 Yamada M, Mori J, Heaton T (2009) The slapdown phase in high-acceleration records of large earthquakes. Seismol Res Lett 80:559–564. https://doi.org/10.1785/gssrl.80.4.559 Yamagishi H, Yamazaki F (2018) Landslides by the 2018 Hokkaido Iburi-Tobu earthquake on September 6. Landslides 15:2521–2524. https://doi.org/10.1007/s10346-018-1092-z We would like to thank the Japan Meteorological Agency for providing us with hypocenter information for the earthquakes used in this study and the strong-motion data. We would also like to thank Wessel and Smith (1998) for providing us with Generic Mapping Tools, which were used to make some figures in the manuscript. We would like to express our sincere thanks to the guest editor Dr. Nobuo Takai and three anonymous reviewers for their constructive comments which helped us to improve the manuscript significantly. National Research Institute for Earth Science and Disaster Resilience, Tsukuba, Japan Yadab P. Dhakal , Takashi Kunugi , Takeshi Kimura , Wataru Suzuki & Shin Aoi Search for Yadab P. Dhakal in: Search for Takashi Kunugi in: Search for Takeshi Kimura in: Search for Wataru Suzuki in: Search for Shin Aoi in: YPD analyzed the data and drafted the manuscript. TKs, WS, and SA provided helpful comments. All authors read and approved the manuscript. This study was supported by "Advanced Earthquake and Tsunami Forecasting Technologies Project" of NIED. Correspondence to Yadab P. Dhakal. Additional file 1. Comparison of the surface and borehole PGVs at the site IBUH03 for the mainshock and a small event. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Nonlinear site response Ground motion prediction equations Spectral ratios The 2018 Hokkaido eastern Iburi earthquake 4. Seismology The 2018 Hokkaido Eastern Iburi Earthquake and Hidaka arc-arc collision system	CommonCrawl
Sub-department: Of this and branch sub-departments Priority areas: Add a filter Research target Priority areas of development Of all publications in the section: 3 520 A Practical Comparison of the Bivariate Probit and Linear IV Estimators Lokshin M., Das J., C. Chiburis R. Policy Research Working Paper. WPS. World Bank Group, 2011. No. 5601. This paper presents asymptotic theory and Monte-Carlo simulations comparing maximum-likelihood bivariate probit and linear instrumental variables estimators of treatment effects in models with a binary endogenous treatment and binary outcome. The three main contributions of the paper are (a) clarifying the relationship between the Average Treatment Effect obtained in the bivariate probit model and the Local Average Treatment Effect estimated through linear IV; (b) comparing the mean-square error and the actual size and power of tests based on these estimators across a wide range of parameter values relative to the existing literature; and (c) assessing the performance of misspecification tests for bivariate probit models. The authors recommend two changes to common practices: bootstrapped confidence intervals for both estimators, and a score test to check goodness of fit for the bivariate probit model. A proof of the Gaudin Bethe Ansatz conjecture. Rybnikov L. G. arxiv.org. QA. Cornell University, 2016 Gaudin algebra is the commutative subalgebra in $U(\g)^{\otimes n}$ generated by higher integrals of the quantum Gaudin magnet chain attached to a semisimple Lie algebra $\g$. This algebra depends on a collection of pairwise distinct complex numbers $z_1,\ldots,z_n$. We prove that this subalgebra has a cyclic vector in the space of singular vectors of the tensor product of any finite-dimensional irreducible $\g$-modules, for all values of the parameters. The corollary of this result is the Bethe Ansatz conjecture in the Feigin-Frenkel form which states that the joint eigenvalues of the higher Gaudin Hamiltonians on the tensor product of irreducible finite-dimensional $\g$-modules are in 1-1 correspondence with monodromy-free opers on the projective line with regular singularities at the points $z_1,\ldots,z_n,\infty$ and prescribed residues at singular points. A Provocative Event, Media, and Religious Choice: The Pussy Riot Case as a Natural Experiment Skorobogatov A. Economics/EC. WP BRP. Высшая школа экономики, 2014. No. WP BRP 59/EC/2014. This paper uses the famous events related to Pussy Riot as a natural experiment to examine the effect of alternative media on church membership. A differences-in-differences strategy is used to explore the effect in question. The hypothesis is that, given a lack of religious background on the majority of the population and strong temporal interest in religious issues promoted by some provocative event, mass media can substantially affect religious choice. To check if this is the case, we compare the dynamics of religious choice of those exposed to alternative media reports on church topics and the rest of the people. As a proxy of familiarity with an alternative view, we use a dummy variable for using Internet. Our main result is that, during the experiment run over the year 2012, the growth of self-reported Orthodox and strict Orthodox believers was significantly lower in the treatment group than in the control group. Exposure to alternative media coverage turned out to heavily affect religious choice. A published answer to Petr Chaadaev's first "Philosophical letter": a comment on Russian political language of the 1830s Velizhev M. Literary Studies. WP BRP. Высшая школа экономики, 2017. No. WP BRP 19/LS/2017. This paper is aimed at exploring the rhetorical conventions of political polemics in 19th century Russia. We will compare two texts published in the 1830s – a classic "First Philosophical Letter" by Petr Chaadaev and a less known reply to it written by young Andrej Krayevsky – "Thoughts on Russia". First we plan to focus on their stated ideas, and then to consider the political language of the opponents. As we will see, if their ideas were completely different, Chaadaev and Krayevsky shared the same political idiom – the language of official national ideology. We will try to demonstrate that it was possible to use the language of the official ideology not only to establish that ideology but paradoxically also to start an open debate with it. A purity theorem for configuration spaces of smooth compact algebraic varieties Gorinov A. Working papers by Cornell University. Cornell University, 2017. No. 1702.08428 . B. Totaro showed \cite{totaro} that the rational cohomology of configuration spaces of smooth complex projective varieties is isomorphic as an algebra to the $E_\infty$ term of the Leray spectral sequence corresponding to the open embedding of the configuration space into the Cartesian power. In this note we show that the isomorphism can be chosen to be compatible with the mixed Hodge structures. In particular, we prove that the mixed Hodge structures on the configuration spaces of smooth complex projective varieties are direct sums of pure Hodge structures. A quasi-coherent description of the the category of D-mod(Gr_GL(n)) Finkelberg M. V., Braverman A. math. arxive. Cornell University, 2018 In arXiv:1807.09038 we formulated a conjecture describing the derived category D-mod(Gr_GL(n)) of (all) D-modules on the affine Grassmannian of the group GL(n) as the category of ind-coherent sheaves on a certain stack (it is explained in loc. cit. that this conjecture "follows" naturally from some heuristic arguments involving 3-dimensional quantum field theory). In this paper we prove a weaker version of this conjecture for the case n=2. A Quasi-Experimental Study of Contagion and Coordination in Urban Conflict: Evidence from The Syrian Civil War in Damascus Hassanpour N. Comparative Politics, Peace and Conflict Studies. PS. academia.edu, 2014 Motivated by dichotomous scholarly results on the conflict-communication nexus, I compare the predictions of two competing theories of urban conflict based on coordination and contagion. I exploit a quasi-experimental intervention in the Syrian nation-wide communications in November 2012 along with a geolocated dataset of daily conflict locations (n= 627) in Damascus to build a panel (n= 275 days x 252 spatial units = 69,300), to show that disruption of communications coincided with an unprecedented increase in the geographic dispersion of conflict. Furthermore, while compared to pro-regime atrocities rebel activity was more spread in space and time, lack of coordination meant more spatiotemporal clustering: a combination of global dispersion and local clustering defined the insurgency. On average, one additional prior incident in the spatiotemporal vicinity translated to 25% higher rates of recurrence. In addition to detecting significant spatiotemporal spillover of violence, I show that the contagion was effectively activated during the blackout. Are banks peer disciplined? Evidence from post-crisis Russia Semenova M., Andrievskaya I. K. Financial Economics. FE. Высшая школа экономики, 2012. No. 07. Market discipline is usually studied in the retail or the corporate deposit markets, while the interbank loan market is disregarded. Banks' abilities to exert market discipline are taken for granted, as they are expected to have the expertise to assess correctly the riskiness of other banks. However, the "crises of trust" (as one in 2004 in Russia) create some doubts as to whether efficient peer monitoring and peer discipline exist: the interbank loan market may be frozen in response to external information which is unrelated to the banks' current reliability. This seems to be one of the reasons for the interbank loan markets being extremely fragile during periods of financial instability, undermining the smooth functioning of the whole banking system, as banks are tightly interconnected. We provide some evidence for market discipline in the Russian interbank market. We show that the only disciplinary mechanism that functions is a price-based one: more reliable banks enjoy lower interest rates. The quantitative discipline functions only for the largest borrowers. In general, decisions on credit limits are based not on changes in another bank's riskiness but on other information like reputation, soft information or public announcements that may be even unrelated to a particular bank. Are books luxury goods in Russia or not? Nataliya Kochkina, Evgeniya Popova. ACEI Working Paper Series. AWP. Association for Cultural Economics International, 2017. No. AWP-06-2017. In the times of Soviet Union books were a luxury good. This paper examines whether books are still a luxury good in Russia. For this purpose data from one of the Russian book retail chains is used to empirically estimate a general book demand and separate demand models for genres. We focus on estimating income elasticity. For this reason we construct a covariate on the basis of monthly wages of working individuals that reveals consumer income. Moreover, this paper is one of the few which addresses in detail the influence of books content quality on book demand. The main result is that books on average are not luxury goods anymore in Russia. However two genres: foreign prose and poetry are exceptions and can be called luxury goods. We also conclude that quality control covariates (book rating and number of people who rated the book) are important determinants of book demand as they influence significantly the general book demand and the demand models for different genres as well. Are commodity price shocks important? A Bayesian estimation of a DSGE model for Russia Malakhovskaya O. A., Minabutdinov A. R. Economics/EC. WP BRP. Высшая школа экономики, 2013. No. WP BRP 48/EC/2013. This paper constructs a DSGE model for an economy with commodity exports. We estimate the model on Russian data, making a special focus on quantitative effects of commodity price dynamics. There is a widespread belief that economic activity in Russia crucially depends on oil prices, but quantitative estimates are scarce. We estimate an oil price effect on the Russian economy in the general equilibrium framework. Our framework is similar to those of Kollmann(2001) and Dam and Linaa (2005), but we extend their models by explicitly accounting for oil revenues. In addition to standard supply, demand, cost-push, and monetary policy shocks, we include the shock of commodity export revenues, which are supposed to be like a windfall. The main objective of the paper is to identify the contribution of structural shocks to business cycle fluctuations in the Russian economy. We estimate the parameters and stochastic processes that govern ten structural shocks using Bayesian techniques. The model yields plausible estimates, and the impulse response functions are in line with empirical evidence. We found that despite a strong impact on GDP from commodity export shocks, business cycles in Russia are mostly domestically based Are economic and political freedoms interrelated? Dabrowski M. Bruegel blog. Bruegel blog. Bruegel, 2018 Democracy has not always accompanied market economy. But in modern societies, economic and political freedoms are increasingly interconnected. Democracy and market economy can support each other. This is particularly true in post-communist economies of Central and Eastern Europe and the former Soviet Union. Thus, authoritarian tendencies observed in these and other regions can negatively affect quality of economic policy and governance. Are emotionally intelligent people more emotionally stable? An experience sampling study Lyusin D., Mohammed A. PSYCHOLOGY. WP BRP. Издательский дом НИУ ВШЭ, 2018 The temporal dynamic characteristics of mood play an important role in various aspects of our lives including our psychological health and well-being. It is assumed that the individuals with high emotional intelligence (EI) are characterized by more positive and stable moods. However, most studies analyze how EI is related to emotional traits or momentary assessments of mood; there are almost no findings on EI relationships with mood dynamics. The present study fills this gap. Two research questions were asked. How mood dynamics characteristics are related to each other and to what extent are they independent? Which aspects of EI are related to particular characteristics of mood dynamics? Method. To collect data on mood dynamics, an experience sampling procedure was implemented. Twenty-six female participants reported their mood for two weeks, three times a day, using the EmoS-18 questionnaire. Their emotional intelligence was measured with the EmIn questionnaire. Mean mood scores calculated across all measurement points were regarded as static characteristics showing a mood background typical for the participant. Also, three dynamic characteristics of mood were calculated, namely variability, instability, and inertia. Results. Mood variability and instability were found to be very closely related to each other, measuring essentially the same construct. Inertia is relatively independent. EI was not related to mean mood scores which contradicts the results of other studies and can be explained by the use of the experience sampling procedure. EI was positively related to the inertia of a positive mood with high arousal and a negative mood with low arousal. In addition, a negative relationship between EI and the instability of tension was found. Most of the correlations were low. Further studies with higher statistical power are needed for more decisive conclusions. However, the results show that experience sampling provides new important insights on the role of EI in mood Are Individual Value Orientations Related to Socio-Psychological Capital? A Comparative Analysis Data from Three Ethnic Groups in Russia Tatarko A. SEARCH Working Paper. WP5. Университет Барселоны, 2013. No. WP5/04. This study analyzes the phenomenology of socio-psychological capital viewed as a resource for psychological relations which constitutes the basis for the formation of social capital. A crosscultural analysis of the impact of value orientations on socio-psychological capital has been performed. Based on a sample of 3 ethnic groups (Russians, n = 103; Chechens, n = 100; Ingush, n = 109), it has been demonstrated that although the impact of individual values on socio-psychological capital obeys logic, it may be culture-specific. Values of Self-Transcendence (Benevolence and Universalism) have a positive impact on the socio-psychological capital of a multicultural society, whereas values of Self-Enhancement influence it negatively. Openness to Change values positively influence civic identity but have a negative effect on perceived social capital. Conservation values positively affect the civic (Russian) identity of the representatives of the Ingush ethnic group. Tatarko A. Psychology. PSY. Высшая школа экономики, 2012. No. 03. This study analyzes the phenomenology of socio-psychological capital viewed as a resource for psychological relations which constitutes the basis for the formation of social capital. A cross-cultural analysis of the impact of value orientations on socio-psychological capital has been performed. Based on a sample of 3 ethnic groups (Russians, n = 103; Chechens, n = 100; Ingush, n = 109), it has been demonstrated that although the impact of individual values on socio-psychological capital obeys logic, it may be culture-specific. Values of Self-Transcendence (Benevolence and Universalism) have a positive impact on the socio-psychological capital of a multicultural society, whereas values of Self-Enhancement influence it negatively. Openness to Change values positively influence civic identity but have a negative effect on perceived social capital. Conservation values positively affect the civic (Russian) identity of the representatives of the Ingush ethnic group. Are Interregional Wage Differentials in Russia Compensative? Oshchepkov A. Y. Discussion Papers of DIW Berlin. 750. DIW Berlin, German Institute for Economic Research, 2007. No. 750. A remark on Golod--Shafarevich algebras Piontkovski D. arxiv.org. math. Cornell University, 2014. No. arXiv:1412.8601. We show that a direct limit of surjections of (weak) Golod--Shafarevich algebras is a weak Golod--Shafarevich algebra as well. This holds both for graded and for filtered algebras provided that the filtrations are induced by the filtration of the first entry of the sequence. It follows that the limit is an algebra of exponential growth. An example shows that the assumptions of this theorem cannot be directly weakened. A report on locally conformally Kahler manifolds Liviu O., Verbitsky M. arxiv.org. math. Cornell University, 2010. No. 1002.3473. We present an overview of recent results in locally conformally K¨ahler geometry, with focus on the topological properties which obstruct the existence of such structures on compact manifolds. Are Public Sector Workers Underpaid in Russia? Estimating the Public-Private Wage Gap Gimpelson V. E., Lukyanova A. IZA Discussion Paper. IZA, 2009. No. 3941. The paper starts with discussing institutional framework for public sector wage setting in Russia. Given that individual choice of the sector is endogenous to wages, the authors recommend alternative econometric techniques for the public-private wage gap estimation. Applying switching regression that allows correcting for non-random sector selection, the paper provides wage gap estimates for various demographic, occupational, and territorial population subgroups. As it is shown, there is significant cross-group variation in the wage gap. The paper concludes that to eliminate the negative gap wages in the public sector should be linked to the private sector wages at the regional level. Arguments from natural law reevaluated through a dialogue between legal history and legal theory Poldnikov D. Law. LAW. Высшая школа экономики, 2013. No. 16/LAW/2013. The paper suggests several ways to rediscover the legacy of early modern and classical natural law of the 18th century in contemporary legal thought through the joint efforts of legal history and legal theory with particular reference to the domain of contract law. Additionally, the paper justifies the revival of the research in the domain of natural law in connection with legal argumentation. Arithmetic of 3-valent graphs and equidissections of flat surfaces Rudenko D. Cornell University Library, 2014 Our main object of study is a 3−valent graph with a vector function on its edges. The function assignes to an edge a pair of 2−adic integer numbers and satisfies additional condition: the sum of its values on three edges, terminating in the same vertex, is equal to 0. For each vertex of the graph three vectors corresponding to these edges generate a lattice over the ring of 2−adic integers. In this paper we study the restrictions, imposed on these lattices by the combinatorics of the graph. As an application we obtain the following fact: a rational balanced polygon cannot be cut into an odd number of triangles of equal areas. First result of this type was obtained by Paul Monsky in 1970. He proved that a square cannot be cut into an odd number of triangles of equal areas. In 2000 Sherman Stein conjectured that the same holds for any balanced polygon. We prove this conjecture in the case, when coordinates of all vertices of the cut are rational numbers. Arm's Length Method for Comparing Rating Scales Hainsworth R., Karminsky A. M., Solodkov V. M. Financial Economics. FE. Высшая школа экономики, 2012. No. 01. Investors are being encouraged after the global crisis to reduce their dependence on the largest credit rating agencies for risk assessments of companies and securities. Comparing risk assessments from different sources rapidly becomes non-trivial when more than three credit rating agencies are involved. We propose a method for comparing rating scales, and hence constructing correspondence diagrams and tables, thereby treating the rating scales used by different agencies as objects of study. Scales are compared by looking at sets of ratings assigned to similar entities (in this case banks) with the assumption that the risk being measured by each credit rating agency is the same for a given rated entity at a given point in time. Two ratings assigned by two credit rating agencies may differ for two reasons: the two agencies have different opinions about the relative positioning of the rated entity (e.g., issuer or security) with respect to the universe of other rated entities; both agencies position the rated entity with respect to the universe of other rated entities in the same way, but they use different symbols to represent this position. Type 1 differences should disappear when a large number of ratings are considered. The existence of type 2 differences will require a mapping from one rating scale to another. Studying international bank ratings for a five-year period shows that there are type 2 differences for the largest credit rating agencies. A mechanism for constructing mappings between scales could lead to more competition with new credit rating agencies. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ... 168	CommonCrawl
Factor Analysis Principal Component Analysis (PCA) 101 principal-component-analysis-101.xlsx (10 KB) principal-component-analysis-101.pdf (500 KB) This is the first entry in what will become an ongoing series on principal component analysis in Excel (PCA). In this tutorial, we will start with the general definition, motivation and applications of a PCA, and then use NumXL to carry on such analysis. Next, we will closely examine the different output elements in an attempt to develop a solid understanding of PCA, which will pave the way to a more advanced treatment in future issues. In this tutorial, we will use the socioeconomic data provided by Harman (1976). The five variables represent total population ("Population"), median school years ("School"), total employment ("Employment"), miscellaneous professional services ("Services"), and median house value ("House Value"). Each observation represents one of twelve census tracts in the Los Angeles Standard Metropolitan Statistical Area. First, let's organize our input data. First, we place the values of each variable in a separate column, and each observation (i.e. census tract in LA) on a separate row. Note that the scales (i.e. magnitude) of the variables vary significantly, so any analysis of raw data will be biased toward the variables with a larger scale, and downplay the effect of ones with a lower scale. To better understand the problem, let's compute the correlation matrix for the 5 variables: The five (5) variables are highly correlated, so one may wonder: If we were to use those variables to predict another variable, do we need the 5 variables? Are there hidden forces (drivers or other factors) that move those 5 variables? In practice, we often encounter correlated data series: commodity prices in different locations, future prices for different contracts, stock prices, interest rates, etc. In plain English, what is principal component analysis in Excel(PCA)? PCA is a technique that takes a set of correlated variables and linearly transforms those variables into a set of uncorrelated factors. To explain it further, you can think about PCA as an axis-system transformation. Let's examine this plot of two correlated variables: Simply put, from the (X, Y) Cartesian system, the data points are highly correlated. By transforming (rotating) the axis into (Z, W), the data points are no longer correlated. In theory, the PCA finds that those transformations (of the axis) of data points will look uncorrelated with their respect. OK, now where are the principal components? To transform the data points from the (X, Y) Cartesian system to (Z, W), we need to compute the z and w values of each data point: $$z_i=\alpha_1 x_i + \beta_1 y_i$$ $$w_i=\alpha_2 x_i + \beta_2 y_i$$ In effect, we are replacing the input variables ($x_i,y_i$) with those of ($z_i,w_i$). The values are ones we refer to as the principal components. Alright, how do we reduce the dimensions of the variables? When we transform the values of the data points ($x_i,y_i$) into the new axis system ($z_i,w_i$), we may find that a few axes capture more of the values' variation than others. For instance, in our example above, we may claim that all $w_i$ values are plain zero and don't really matter. $$ \left.\begin{matrix} x_i=\gamma_1 z_i + \phi_1 y_i \\\\ y_i=\gamma_2 z_i + \phi_2 y_i \end{matrix}\right\} \Rightarrow \left.\begin{matrix} x_i=\gamma_1 z_i \\\\ y_i=\gamma_2 z_i \end{matrix}\right\} $$ In effect, the two dimensional system ($z_i,w_i$) is reduced to a one-dimensional system ($z_i$). Of course, for this example, dropping the $W$ factor distorts our data, but for higher dimensions it may not be so bad. Which component should we drop? In practice, we order the components (aka factors) in terms of their variance (highest first) and examine the effect of removing the ones of lower variance (right most) in an effort to reduce the dimension of the data set with minimal loss of information. Why should we care about principal components? A risk manager can quantify their overall risk in terms of a portfolio aggregate exposure to a handful of drivers, instead of tens of hundreds of correlated securities prices. Furthermore, designing an effective hedging strategy is vastly simplified. For traders, quantifying trades in terms of their sensitivities (e.g. delta, gamma, etc.) to those drivers gives trader options to substitute (or trade) one security for another, construct a trading strategy, hedge, synthesize a security, etc. A data modeler can reduce the number of input variables with minimal loss of information. Now we are ready to conduct our principal component analysis in Excel. First, select an empty cell in your worksheet where you wish the output to be generated, then locate and click on the "PCA" icon in the NumXL tab (or toolbar). The principal component analysis Wizard pops up. Select the cells range for the five input variable values. The cells range includes (optional) the heading ("Label") cell, which would be used in the output tables where it references those variables. The input variables (i.e. X) are already grouped by columns (each column represents a variable), so we don't need to change that. Leave the "Variable Mask" field blank for now. We will revisit this field in later entries. By default, the output cells range is set to the current selected cell in your worksheet. Finally, once we select the Input data (X) cells range, the "Options" and "Missing Values" tabs become available (enabled). Next, select the "Options" tab. Initially, the tab is set to the following values: "Standardize Input" is checked. This option in effect replace the values of each variable with its standardized version (i.e. subtract the mean and divide by standard deviation). This option overcomes the bias issue when the values of the input variables have different magnitude scales. Leave this option checked. "Principal Component Output" is checked. This option instructs the wizard to generate PCA related tables. Leave it checked. Under "Principal Component," check the "Values" option to display the values for each principal component. The significance level (aka \alpha) is set to 5%. The "Input Variables" is unchecked. Leave it unchecked for now. Now, click on the "Missing Values" tab. In this tab, you can select an approach to handle missing values in the data set (X's). By default, any missing value found in any of input variables (X) in any observation would exclude the observation from the analysis. This treatment is a good approach for our analysis, so let's leave it unchanged. Now, click "OK" to generate the output tables. 1. PCA statistics The principal components are ordered (and named) according to their variance in a descending order, i.e. PC(1) has the highest variance. In the second row, the proportion statistics explain the percentage of variation in the original data set (5 variables combined) that each principal component captures or accounts for. The cumulative proportion is a measure of total variation explained by the principal components up to this current component. Note: In our example, the first three PC account for 94.3% of the variation of the 5 variables. Note that the sum of variances of the PC should yield the number of input variables, which in this case is five (5). 3. Loadings In the loading table, we outline the weights of a linear transformation from the input variable (standardized) coordinate system to the principal components. For example, the linear transformation for PC_1 is expressed as follows: $$PC_1=0.27X_1+0.503X_2+0.339X_3+0.56X_4+0.516X_5$$ The squared loadings (column) adds up to one. $\sum_{i=1}^5 \beta_i^2 = 1$ In the graph above, we plotted the loadings for our input variables in the first three components. The median school years, misc. professional services and median house value variables have comparable loadings in PC(1), next comes total employment loading and finally, population. One may propose this as a proxy for the wealth/income factor. Interpreting the loadings for the input variables in the remaining components prove to be more difficult, and require a deeper level of domain expertise. Finally, computing the input variables back from the PC can be easily done by applying the weights in the row instead of the column. For example, the population factor is expressed as follows: $$X_1=0.227 PC_1-0.657PC_2-0.64PC_3+0.308PC_4-0.109PC_5$$ We'll discuss the PC loading later in this tutorial. 3. Principal Component Values In the PC values table, we calculate the transformation output value for each dimension (i.e. component), so the 1st row corresponds to the 1st data point, and so on. The variance of each column matches the value in the PCA statistics table. Using Excel, compute the biased version of the variance function (VARA). By definition, the values in the PCs are uncorrelated. To verify, we can calculate the correlation matrix: In this tutorial, we converted a set of five correlated variables into five uncorrelated variables without any loss of information. Furthermore, we examined the proportion (and cumulative proportion) of each component as a measure of variance captured by each component, and we found that the first three factors (components) account for 94.3% of the five variables variation, and the first four components account for 98%. What do we do now? One of the applications of PCA is dimension reduction; as in, can we drop one or more components and yet retain the information in the original data set for modeling purposes? In our second entry, we will look at the variation of each input variable captured by principal components (micro-level) and compute the fitted values using a reduced set of PCs. We will cover this particular issue in a separate entry of our series. Principal Components Analysis (PCA) tutorial - Part 1 Statistical Summary Where can I download free trial of NumXL? Regression Analysis 102 - Influential Data	CommonCrawl
Journal Home About Issues in Progress Current Issue All Issues pp. 1237-1242 •https://doi.org/10.1364/OPTICA.435522 Laser-driven resonant magnetic soft-x-ray scattering for probing ultrafast antiferromagnetic and structural dynamics Daniel Schick, Martin Borchert, Julia Braenzel, Holger Stiel, Johannes Tümmler, Daniel E. Bürgler, Alexander Firsov, Clemens von Korff Schmising, Bastian Pfau, and Stefan Eisebitt Daniel Schick,1,†,* Martin Borchert,1,† Julia Braenzel,1 Holger Stiel,1 Johannes Tümmler,1 Daniel E. Bürgler,2 Alexander Firsov,3 Clemens von Korff Schmising,1 Bastian Pfau,1 and Stefan Eisebitt1,4 1Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie, Max-Born-Straße 2A, 12489 Berlin, Germany 2Peter Grünberg Institute, Forschungszentrum Jülich GmbH, Wilhelm-Johnen-Straße, 52428 Jülich, Germany 3Institute for Nanometre Optics and Technology, Helmholtz-Zentrum Berlin, Hahn-Meitner-Platz 1, 14109 Berlin, Germany 4Institut für Optik und Atomare Physik, Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany †These authors contributed equally to this paper. *Corresponding author: [email protected] Daniel Schick https://orcid.org/0000-0001-7988-6489 Martin Borchert https://orcid.org/0000-0001-9200-1198 Bastian Pfau https://orcid.org/0000-0001-9057-0346 D Schick M Borchert J Braenzel H Stiel J Tümmler D Bürgler A Firsov C von Korff Schmising B Pfau S Eisebitt Daniel Schick, Martin Borchert, Julia Braenzel, Holger Stiel, Johannes Tümmler, Daniel E. Bürgler, Alexander Firsov, Clemens von Korff Schmising, Bastian Pfau, and Stefan Eisebitt, "Laser-driven resonant magnetic soft-x-ray scattering for probing ultrafast antiferromagnetic and structural dynamics," Optica 8, 1237-1242 (2021) Check for updates Sub-15-fs X-ray pump and X-ray probe experiment for the study of ultrafast magnetization dynamics... Xuan Liu, et al. Soft x-ray imaging spectroscopy with micrometer resolution Jan O. Schunck, et al. Optica 8(2) 156-160 (2021) Disentangling x-ray dichroism and birefringence via high-purity polarimetry Annika T. Schmitt, et al. Optica 8(1) 56-61 (2021) Attosecond pulses Optical parametric chirped pulse amplification Thin disk lasers X ray lasers Original Manuscript: June 29, 2021 Revised Manuscript: August 13, 2021 Manuscript Accepted: August 15, 2021 Time-resolved resonant magnetic scattering in the soft-x-ray range is a powerful tool for accessing the spatially resolved and element-specific spin dynamics in magnetic materials. So far, the application of this photon-demanding technique was limited to large-scale facilities. However, upgrades to diffraction-limited storage rings supporting only x-ray pulses beyond 100 ps, and the shift of x-ray free-electron lasers toward attosecond pulses aggravate the competition for beamtime in the picosecond time window, which is of utmost relevance for magnetism research. Here we present the development of a lab-based instrument providing sufficient photon flux up to 1.5 keV photon energy covering the soft-x-ray resonances of transition and rare-earth metal atoms. Our setup features the mandatory tunability in energy and reciprocal space in combination with sub-10 ps temporal resolution, exploiting the broadband emission of a laser-driven plasma x-ray source, which is monochromatized to about 1 eV bandwidth by a reflection zone plate. We benchmark our approach against accelerator-based soft-x-ray sources by simultaneously probing the laser-induced magnetic and structural dynamics from an antiferromagnetically coupled Fe/Cr superlattice. Our development lays the foundation for laser-driven resonant scattering experiments to study ultrafast ordering phenomena of charges, spins, and orbitals. © 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement Throughout the last decades, the main focus of the ultrafast magnetism community has been predominantly on ferri- and ferromagnetic (FM) materials [1–3]. Today, the interest in antiferromagnetic (AFM) materials is growing because of their unique properties, such as their faster intrinsic time scales [4], their immunity to magnetic (stray) fields, and their advanced application in opto-spintronics [5]. Due to the absence of a net magnetization $M = \|{\vec M_1} + {\vec M_2}\| = 0$ in AFM materials with equivalent sublattice magnetizations ${\vec M_1} = - {\vec M_2}$, conventional pump-probe techniques, such as the time-resolved magneto-optical Kerr or Faraday effect, as well as x-ray magnetic circular dichroism (XMCD), fail to provide a measure of the magnetization, as they depend linearly on the magnetization $M$. More advanced techniques, such as magnetic second-harmonic generation (SHG) [6], the magnetic Voigt effect [7], or x-ray magnetic linear dichroism (XMLD) [8], can access the AFM order parameter ${\cal L} = \|{\vec M_1} - {\vec M_2}\|/2$, but they require distinct crystal symmetries and suffer from significant non-magnetic background contributions. Resonant magnetic soft-x-ray scattering (RMXS) overcomes the limitations of the former methods by combining spectroscopic sensitivity with access to reciprocal space [9]. The relevant resonances at the absorption edges of the transition metal (TM) $L$ edge and rare-earth (RE) $M$ edge enable element selectivity as well as large magnetic contrast. At the same time, the position of the magnetic scattering in reciprocal space is a direct measure of the AFM periodicity in real space, while the integrated magnetic scattering intensity is proportional to ${{\cal L}^2}$. This allows for probing AFM dynamics at its relevant time and length scale in a pump-probe manner utilizing ultrashort soft-x-ray pulses. Since time-resolved RMXS requires a bright, tunable, and pulsed soft-x-ray source, such experiments have so far been limited to large-scale facilities such as synchrotron-radiation sources [4,10,11] and free-electron lasers (FELs) [12,13]. While FELs are already approaching the attosecond regime [14,15], the ongoing upgrades of most storage rings toward the diffraction limit (DLSR) [16] will increase the default pulse length at most fourth generation synchrotrons above the 100 ps range. This will aggravate the competition at large-scale facilities for experiments with few picosecond temporal resolution, which are relevant for a plethora of phenomena in ultrafast magnetism, such as all-optical magnetic switching [17], remagnetization processes [18], spin precession dynamics [19,20], laser-driven phase transitions [21,22], as well as spin-lattice-related effects such as ultrafast magnetostriction [23,24], manipulation of the magneto-crystalline anisotropy [25], and heat diffusion in magnetic nanostructures [26], to name only a few. Fig. 1. High-energy laser pulses are focused onto a rotating and translating tungsten cylinder, emitting broadband soft-x-ray radiation into the full solid angle via laser-plasma generation. The inset shows the emitted spectral distribution as measured by a calibrated spectrometer at the source, and the gray area indicates the energy range around the Fe ${L_3}$ and ${L_2}$ edges from 695 to 735 eV. A reflection zone plate captures this part of the x-rays that are simultaneously focused and dispersed onto an adjustable slit for monochromatization. Part of the blocked x-rays are detected by an x-ray-sensitive SiC diode for normalization. Monochromatic soft x-rays pass the slit and resonantly scatter off the antiferromagnetic Fe/Cr superlattice, as depicted in the upper right scheme, in a $\vartheta$–$2\vartheta$-geometry onto a CCD. The pump beam is used to excite the sample at variable delays. To that end, a functional and reliable approach to carry out transient RMXS with a few picosecond temporal resolution is mandatory. Although laser-driven high-harmonic generation (HHG) sources [27–29] are steadily increasing in photon flux and now cover the water window up to 500 eV, their brightness in the relevant photon range from 500 to 1300 eV is still too low for RMXS experiments. Therefore, we developed a scattering instrument employing a laser-driven plasma x-ray source (PXS) [30] to generate ultrashort broadband soft-x-ray pulses from below 50 eV to above 1500 eV, covering the magnetically dichroic absorption $L$ and $M$ edges of most TM and RE elements, respectively. To maintain high photon flux, we collect, focus, and monochromatize the soft-x-ray pulses with a few-picosecond duration by a tailored reflection zone-plate (RZP) optic into an in-vacuum diffractometer for time-resolved laboratory RMXS experiments. In order to demonstrate the performance of the setup and to highlight the power of the RMXS technique, we investigate the photo-induced dynamics in an AFM-coupled Fe/Cr superlattice (SL) [31]. These artificial magnets typically provide sample structures of high structural quality with tailored functionality, leading to a high technological relevance, e.g., due to the giant magneto-resistance (GMR) effect [32,33]. By spectroscopically recording the reflectivity of the superlattice around the dichroic Fe ${L_3}$ resonance, we demonstrate the energy tunability and characterize the energy resolution of our instrument. We show static reciprocal space scans, which clearly evidence the resonant magnetic scattering off an AFM Bragg peak, which was, so far, inaccessible for lab-based instruments. In addition to the magnetic scattering, the large artificial unit cell of the Fe/Cr SL also leads to structural Bragg peaks, which we here exploit to provide access to the lattice dynamics [34] in one and the same experiment. By simultaneously probing the amplitude of the AFM Bragg peak and the shift of the structural Bragg peak after excitation, we are able to directly relate structural and magnetization dynamics, providing an ultimate understanding of the underlying coupling mechanisms of these two degrees of freedom on ultrafast time scales. Our instrumental approach enables a broad class of time-resolved experiments on ordering phenomena so far only feasible at large-scale facilities. In particular, it allows us to investigate the coupling of different degrees of freedom, such as spins and the lattice, on the relevant picosecond time and nanometer length scale. We produce pulses of monochromatized soft x-rays and tune them across the Fe $L$-absorption edges. The photons are scattered off the sample into a detector within a diffractometer setup as shown in Fig. 1. The driver for the PXS is an in-house-developed double-stage thin-disk amplified laser, producing pulses with a duration of 2 ps full width at half-maximum (FWHM) at a wavelength of 1030 nm with a sizable pulse energy of 150 mJ at 100 Hz repetition rate [35]. A pump beam for sample excitation is extracted from the same laser via a 3:97 beam splitter, where the larger part is focused into the vacuum chamber hosting the PXS. At the laser focus of ${\approx} 15\,\,\unicode{x00B5}{\rm m}$ diameter FWHM, a spinning tungsten cylinder is placed under an angle of 45°. Upon laser excitation of the tungsten target, a plasma is generated, which emits broadband x-ray radiation [30] in the range of 50–1500 eV into the full solid angle. The x-ray photon flux at the relevant Fe $L$ edges (695–735 eV) has been determined to be $5.6 \times {10^{11}}\; {\rm ph}\, {{\rm s}^{- 1}}{{\rm eV}^{- 1}}{{\rm sr}^{- 1}}$ by a calibrated spectrometer at the source. The full spectrum is shown as an inset in Fig. 1. The intrinsic time scales of the x-ray generation processes involved depend on the pulse duration of the driver laser and the lifetime of the electrons inside the plasma. Our results on probing sub-picosecond (ps) dynamics in the Fe/Cr superlattice allow for determining the actual x-ray pulse duration to be below 10 ps; see Section 3. We chose an RZP [36] as the single optical element to collect, disperse, and focus the x-rays from the point-like PXS with a diameter of $\approx 40\,\,\unicode{x00B5}{\rm m}$ FWHM toward the sample position. The RZP is placed 1000 mm away from the source point at a grazing incidence angle of 2.0°, operating at an exit angle of 3.6°. The calculated magnification of the RZP is 7.2 at its focus position 4000 mm downstream. The distances between source, RZP, and focus represent a compromise between obtaining a large collection angle and a sufficient resolving power of $E/\Delta E = 200$ with a focus of approximately 288 µm FWHM. We estimate the detectable photon flux at the sample position as $1.2 \times {10^6}\; {\rm ph}\,{{\rm s}^{- 1}} {{\rm eV}^{- 1}} $, which compares well with laser slicing facilities [37] or hard-x-ray PXS sources [38,39]. We increase the nominal energy resolution of the beamline to about 1.2 eV by closing a variable slit down to 100 µm at the focus position of the RZP. In order to scan the photon energy across the 40 eV range, including the Fe ${L_3}$ and ${L_2}$ absorption edges, we tilt the RZP pitch by only a few millidegrees [37]. For photon energies far away from the RZP's design energy of 705 eV, this procedure results in a decrease in energy resolution and an increase of the horizontal focus size as depicted by the RZP focus image at the slit position in Fig. 1. The latter issue can be addressed by horizontal slits in order to fix the x-ray spot size on the sample. Access to resonances of other magnetic elements is readily provided by additional RZPs mounted on the same manipulator [37]. The sample and a CCD detector are mounted onto an in-vacuum $\vartheta$–$2\vartheta$ diffractometer setup at room temperature. The previously split-off pump beam can be delayed by a mechanical stage and is coupled into the vacuum while being focused onto the sample. We use a pump focus diameter of approx. 500 µm FWHM with an incident fluence of $66 \;{{\rm mJ/cm}^2}$. The actual absorbed fluence in the sample can be estimated as only 7%–18% of the incident fluence due to reflectivity of the pump light at the sample surface and spot size broadening for the relevant range of incidence angles $\vartheta$. In order to account for the intensity fluctuations of the PXS due to the mechanical instabilities and material inhomogeneities of the rotating target, we use an IR-insensitive SiC photodiode, mounted onto the slit blades, monitoring part of the blocked x-ray intensity. The Fe/Cr SL sample was grown on a GaAs substrate by molecular beam epitaxy (MBE). Twenty repetitions of 0.9 nm thick Fe and 0.9 nm thick Cr layers were grown onto a 150 nm thick Ag buffer layer and capped by a single 0.9 nm thick Fe layer and a 2 nm thick MgO layer for oxidation protection. The individual Fe layers are aligned ferromagnetically in-plane as in standard thin-film samples, but the individual layers couple antiferromagnetically along the out-of-plane direction as seen in the sample sketch in Fig. 1 (top right). The artificial periodicity of the repeated Fe/Cr double-layer thickness ${D_{{\rm DL}}} = 1.8\;{\rm nm} $ enables us to access structural Bragg peaks even with soft x-rays of a few-nanometer wavelength [34]. We define the position of the first-order structural Bragg peak (SL1) as $L = 1$ in reciprocal lattice units (rlu). In addition to the structural periodicity, the AFM order causes a super-periodicity of two Fe/Cr double layers, containing two antiparallel aligned FM Fe layers [40]. Hence, the AFM order leads to purely magnetic half-order Bragg peaks at $L = n/2$ ($n \in {\mathbb N}$). For the special case of the symmetric 0.9 nm Fe and 0.9 nm Cr double layers, only odd diffraction orders are allowed, and no magnetic scattering contributes to the structural Bragg peaks. In order to probe the AFM Bragg peak, tuning of the photon energy to the magnetically relevant resonances is vital. We first determine the reflection spectrum of the Fe/Cr SL around the Fe ${L_3}$ and ${L_2}$ absorption edges. To that end, the sample and detector are aligned at $\vartheta = 10^ \circ$ ($2\vartheta = 20^ \circ$) to benefit from a high sample reflectivity and a rather small $L$-dependence of the reflectivity far away from the magnetic and structural Bragg peaks. By scanning the incident photon energy, we fully resolve the Fe ${L_3}$ and ${L_2}$ absorption edges as shown in Fig. 2. We use a linear conversion of the RZP pitch angle to the photon energy transmitted by the RZP monochromator by comparing the experimental data to a simulated spectrum [41]. The calculation relies on high-resolution atomic and magnetic form factors from synchrotron measurements and incorporates variations of the layer thickness, density, and Gaussian roughness [42]. Fig. 2. Reflectivity spectrum around the Fe ${L_3}$ and ${L_2}$ absorption edges of the Fe/Cr SL, measured at a grazing incidence angle $\vartheta = 10^ \circ$. The solid line represents a simulation including magnetic and charge scattering. The experimental data was scaled in intensity to fit the simulation. The experimental and simulated reflection spectra agree well and justify the working principle of the RZP-based monochromator. Moreover, we can determine the resolution of the spectrometer by convoluting the simulated spectrum with a Gaussian of variable width and fit it to the experimental data. This fit yields a resolution of $1.5 \pm 0.2\;{\rm eV} $ FWHM at the Fe ${L_3}$ absorption edge and is slightly larger than the estimated resolution of 1.2 eV for a 100 µm slit size. The broadening of the Fe ${L_2}$ peak in the experimental data can be explained by the decrease of spectral resolution of the RZP further away from its design energy of 705 eV. In order to achieve a simulation-independent energy calibration of the setup, a thin Fe foil can be placed in the polychromatic x-ray beam upstream of the RZP. This will lead to distinct absorption lines in the focus of the RZP, which can be used for calibration [43]. For the following experiments, we fix the x-ray photon energy to the maximum of the Fe ${L_3}$ absorption edge around 707 eV. We perform a static $\vartheta {-} 2\vartheta$ scan, also known as $L$-scan, and indeed detect the structural SL1 Bragg peak as well as the AFM SL0.5 superstructure diffraction peaks; see Fig. 3. To validate the resonant magnetic nature of the SL0.5 peak, we compare it to an off-resonant $L$-scan at $E = 680\;{\rm eV} $, which shows the presence of the structural Bragg peak with the AFM Bragg peak being absent due to the lack of magnetic contrast. Fig. 3. Static $L$-scan of the Fe/Cr SL at resonance ($E = 707\;{\rm eV} $, blue dots) and off resonance ($E = 680\;{\rm eV} $, orange dots). The blue solid line represents a scattering simulation of the sample structure including magnetic and charge scattering. At $L = 1$ the structural Bragg peak is present for both photon energies, while the AFM Bragg peak at $L = 0.5$ only appears on-resonance and is also reproduced by the simulations. The experimental data was scaled in intensity to fit the simulation. This data at the Fe ${L_3}$ edge undoubtedly proves resonant magnetic scattering from a laser-driven soft-x-ray source. In addition, we compare the on-resonant experimental data, (scaled in intensity) with a magnetic scattering simulation of the same sample structure [41] and again find a good agreement. This corroborates the use of our normalization scheme, covering more than two orders of scattering intensity variation. However, for reflectivities below ${10^{- 4}}$, a feasible signal-to-noise ratio of our current setup is reached. We want to highlight that although the magnetic scattering cross section depends on the x-ray polarization and magnetization direction of the sample [44], resonant magnetic scattering is still feasible with the unpolarized and temporally incoherent PXS. After determining the optimum x-ray photon energy and positions in reciprocal space, we probe the dynamics of the AFM order and lattice after photoexcitation. The temporal overlap of the pump pulses and the residual IR pulses in the probe beam is determined by sum-frequency generation in a beta-barium borate (BBO) crystal at the sample position. For probing the AFM order parameter, we record the scattered intensity of the AFM Bragg peak at $L = 0.5$ at the ${L_3}$ absorption edge as a function of pump-probe delay as shown in Fig. 4. Fig. 4. Average of multiple delay scans of the SL0.5 AFM Bragg peak intensity at the Fe ${L_3}$ absorption edge. The peak intensity decreases within a few ps and recovers over hundreds of ps upon photoexcitation, tracing the magnetic response of the sample. The solid line represents a double-exponential fit, and the error bars indicate a confidence interval of 67%. The delay scan shows a sharp drop of the magnetic SL0.5 peak intensity upon excitation at delay $t = 0$ ps within a few ps and a slow recovery over more than a nanosecond. These dynamics can be well explained by an ultrafast quenching of FM order in the individual Fe layers due to the excitation of electrons by the intense pump pulses and a subsequent loss of AFM order within the whole SL. The underlying processes of the demagnetization can include sub-ps effects such as direct field-driven transfer of spins [45,46], super-diffusive spin transport [2], and Elliot–Yafet-like spin-flip scattering [47]. As the demagnetization is at least an order of magnitude faster than the expected soft-x-ray pulse duration, we use the rapid signal drop to determine the upper bound of the temporal resolution of the RMXS experiment. We extract the temporal resolution from a fit with a double-exponential decay-recovery function convoluted by a Gaussian $g(t)$ with variable width $\sigma$ to the raw data of Fig. 4 as shown by the solid line. $${{\mathcal{L}}^{2}}(t)={{e}^{-{{t}^{2}}/2{{\sigma }^{2}}}}\circledast \left( A{{e}^{-t/{{\tau }_{1}}}}+B{{e}^{-t/{{\tau }_{2}}}} \right).$$ The decay constant ${\tau _1}$ is fixed to the 2 ps duration of the pump pulses, as the magnetization is guaranteed to be quenched within this time frame. The fit parameter $\sigma$ represents the temporal resolution, which is predominately governed by the duration of the x-ray pulses, which we find to be $\sigma = 9 \pm 3$ ps FWHM as an upper bound. The recovery of the AFM order takes up to 1.5 ns, again following an exponential dependency. The de- and remagnetization amplitudes have been determined as $A = - B = 0.16$. The photoexcited electrons also couple to the lattice degree of freedom by launching coherent and incoherent phonons. The temporal resolution of the PXS is ideally suited to follow the few-ps expansion of the Fe/Cr SL due to the excitation of coherent acoustic phonons (sound waves) [34,48], typically resulting in a pronounced shift of the structural Bragg peak. To demonstrate this capability, we plot the scattered intensity at the low-angle slope of the structural SL1 Bragg peak at $L = 0.95$, as seen in Fig. 5, to translate the peak shift into an intensity modulation of the detected x-ray signal. Fig. 5. Average of multiple delay scans on the low-angle side of structural SL1.0 peak at $L = 0.95$. The rapid rise of the signal is due to a Bragg peak shift toward smaller $L$ because of the photoinduced lattice expansion. The double-exponential fit is a guide to the eye and does not fully account for the complex phonon dynamics and the corresponding translation of peak shift and broadening into an intensity variation. The error bars indicate a confidence interval of 67%. The experimental data show a rise of the signal around delay $t = 0$ ps estimated to be within about 20 ps as the lattice expansion shifts the SL1 Bragg peak to lower $L$ and leads to significant peak broadening. The delay time for the maximum expansion of the SL after photoexcitation is determined by the time it takes coherent acoustic phonons to travel once across the SL with a thickness ${D_{{\rm SL}}} \approx 37\;{\rm nm} $. Assuming bulk longitudinal acoustic sound velocities, ${v_{{\rm Fe}}} = 4910 \;{\rm m/s}$ and ${v_{{\rm Cr}}} = 5940 \;{\rm m/s}$, results in a travel time of approximately 7.5 ps, which matches well with the observed rise time of the measured intensity. The recovery of the Bragg peak position happens again on a ns time scale (not shown) and provides important information about heat diffusion within the SL with its high density of interfaces. The two delay scans of the AFM SL0.5 and structural SL1 Bragg peaks provide direct access to the relevant time scales of the underlying spin and lattice dynamics. In the future, the full potential of transient RMXS will be exploited by time-resolved $L$-scans around both Bragg peaks, paving the way to a full spatiotemporal map of the correlated spin and lattice dynamics further complemented by comparison to simulations [41,48,49]. Such experiments will eventually provide access to layer systems containing non-collinear and incommensurate AFM spin structures as well as cases where non-equilibrium spin structures can appear transiently, e.g., during de- and remagnetization processes. We present the first resonant magnetic scattering results from a soft-x-ray scattering instrument that we have developed to realize time-resolved lab-based experiments with ps time resolution, in particular, on magnetic samples. In our instrument, an RZP monochromatizes and focuses the broadband emission from a laser-driven plasma x-ray source. Tuning the photon energy to the Fe ${L_3}$ resonance, we achieve a photon flux of $1.2 \times {10^6}\; {\rm ph}\,{{\rm s}^{- 1}} {{\rm eV}^{- 1}} $ at the sample position, which, so far, had remained unavailable in the laboratory context. We determine the pulse duration of the x-ray source to be $9 \pm 3\;{\rm ps}$, which allows for accessing the rich physics of spin–lattice interactions on a ps time scale, as well as magnon, phase-transition, and remagnetization/nucleation dynamics up to several ns delay. We demonstrate the performance of our setup by presenting a full set of static and transient resonant scattering data on an AFM-coupled Fe/Cr superlattice. Our instrument is able to fully resolve the Fe ${L_3}$ and ${L_2}$ absorption edges in a reflection spectrum. A resonant reciprocal-space scan proves the existence of a half-order Bragg peak due to the AFM coupling of consecutive layers. Realizing the simultaneous detection of the dynamics of the superlattice structure and the interlayer magnetic order in a time-resolved experiment, we achieve the first important milestone to comprehensively investigate correlated spin–lattice dynamics. The setup can be further improved by nonlinear optical up- or downconversion of the pump light, e.g., by pumping an additional optical parametric chirped pulse amplification (OPCPA) stage with part of the thin disk laser output [50]. This eventually enables the generation of photons in the mid-infrared range to resonantly excite phonon modes and to directly control magnetic order via spin–lattice interactions [51,52]. Our laboratory-based approach will further allow us to particularly study the influence of external parameters such as magnetic fields and temperature in great detail. Such experiments will significantly contribute to the field of picosecond dynamics in condensed matter, such as for charge, spin, and orbital ordering in correlated materials. We are convinced that our laboratory-based approach is not only an alternative but eventually a replacement for ps scattering experiments at synchrotron facilities, many of which will soon undergo a DLSR upgrade, making sub-100 ps pulses at these facilities hardly available. European Regional Development Fund (MOSFER #10168892); Deutsche Forschungsgemeinschaft (TRR227 project A02). We acknowledge the valuable discussions with Christian Schüßler-Langeheine, Niko Pontius, and Karsten Holldack about the beamline and diffractometer layout. M.B., C.v.K.S., and S.E. thank DFG for funding through TRR227 project A02. J.B. and H.S. thank EFRE for funding ProFit project MOSFER #10168892. The authors declare that they have no competing financial or non-financial interests. Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request. 1. E. Beaurepaire, J.-C. Merle, A. Daunois, and J.-Y. 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Schüler-Langeheine, "Ultrafast and energy-efficient quenching of spin order: antiferromagnetism beats ferromagnetism," Phys. Rev. Lett. 119, 197202 (2017). P. Němec, M. Fiebig, T. Kampfrath, and A. V. Kimel, "Antiferromagnetic opto-spintronics," Nature Physics 14, 229–241 (2018). M. Fiebig, V. V. Pavlov, and R. V. Pisarev, "Second-harmonic generation as a tool for studying electronic and magnetic structures of crystals: review," J. Opt. Soc. Am. B 22, 96 (2005). V. Saidl, P. Němec, P. Wadley, V. Hills, R. P. Campion, V. Novák, K. W. Edmonds, F. Maccherozzi, S. S. Dhesi, B. L. Gallagher, F. Trojánek, J. Kuneš, J. Železný, P. Malý, and T. Jungwirth, "Optical determination of the Néel vector in a CuMnAs thin-film antiferromagnet," Nat. Photonics 11, 91–96 (2017). T. Moriyama, K. Oda, T. Ohkochi, M. Kimata, and T. Ono, "Spin torque control of antiferromagnetic moments in NiO," Sci. Rep. 8, 14167 (2018). S. B. Wilkins, P. D. Hatton, M. D. Roper, D. Prabhakaran, and A. T. 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Scherwitzl, et al., "Spatially resolved ultrafast magnetic dynamics initiated at a complex oxide heterointerface," Nat. Mater. 14, 883–888 (2015). N. Hartmann, G. Hartmann, and R. Heider, et al., "Attosecond time-energy structure of x-ray free-electron laser pulses," Nat. Photonics 12, 215–220 (2018). S. Serkez, G. Geloni, S. Tomin, G. Feng, E. V. Gryzlova, A. N. Grum-Grzhimailo, and M. Meyer, "Overview of options for generating high-brightness attosecond x-ray pulses at free-electron lasers and applications at the European XFEL," J. Opt. 20, 024005 (2018). M. Yabashi and H. Tanaka, "The next ten years of x-ray science," Nat. Photonics 11, 12–14 (2017). L. Le Guyader, M. Savoini, S. El Moussaoui, M. Buzzi, A. Tsukamoto, A. Itoh, A. Kirilyuk, T. Rasing, A. V. Kimel, and F. Nolting, "Nanoscale sub-100 picosecond all-optical magnetization switching in GdFeCo microstructures," Nat. Commun. 6, 5839 (2015). L. Willig, A. von Reppert, M. Deb, F. Ganss, O. Hellwig, and M. Bargheer, "Finite-size effects in ultrafast remagnetization dynamics of FePt," Phys. Rev. B 100, 224408 (2019). R. R. Subkhangulov, A. B. Henriques, P. H. O. Rappl, E. Abramof, T. Rasing, and A. V. Kimel, "All-optical manipulation and probing of the d–f exchange interaction in EuTe," Sci. Rep. 4, 4368 (2014). T. Gerrits, H. A. M. van den Berg, J. Hohlfeld, L. Bär, and T. Rasing, "Ultrafast precessional magnetization reversal by picosecond magnetic field pulse shaping," Nature 418, 509–512 (2002). G. Ju, J. Hohlfeld, B. Bergman, R. J. Van Deveerdonk, O. N. Mryasov, J. Y. Kim, X. Wu, D. Weller, and B. Koopmans, "Ultrafast generation of ferromagnetic order via a laser-induced phase transformation in FeRh thin films," Phys. Rev. Lett. 93, 197403 (2004). F. Büttner, B. Pfau, and M. Böttcher, et al., "Observation of fluctuation-mediated picosecond nucleation of a topological phase," Nat. Mater. 20, 30–37 (2021). A. von Reppert, J. Pudell, A. Koc, M. Reinhardt, W. Leitenberger, K. Dumesnil, F. Zamponi, and M. Bargheer, "Persistent nonequilibrium dynamics of the thermal energies in the spin and phonon systems of an antiferromagnet," Struct. Dyn. 3, 054302 (2016). A. H. Reid, X. Shen, and P. Maldonado, et al., "Beyond a phenomenological description of magnetostriction," Nat. Commun. 9, 388 (2018). J. W. Kim, M. Vomir, and J. Y. Bigot, "Controlling the spins angular momentum in ferromagnets with sequences of picosecond acoustic pulses," Sci. Rep. 5, 8511 (2014). J. Pudell, A. A. Maznev, M. Herzog, M. Kronseder, C. H. Back, G. Malinowski, A. von Reppert, and M. Bargheer, "Layer specific observation of slow thermal equilibration in ultrathin metallic nanostructures by femtosecond x-ray diffraction," Nat. Commun. 9, 3335 (2018). S. M. Teichmann, F. Silva, S. L. Cousin, M. Hemmer, and J. Biegert, "0.5-keV soft x-ray attosecond continua," Nat. Commun. 7, 11493 (2016). C. Kleine, M. Ekimova, G. Goldsztejn, S. Raabe, C. Strüber, J. Ludwig, S. Yarlagadda, S. Eisebitt, M. J. J. Vrakking, T. Elsaesser, E. T. J. Nibbering, and A. Rouzée, "Soft x-ray absorption spectroscopy of aqueous solutions using a table-top femtosecond soft x-ray source," J. Phys. Chem. Lett. 10, 52–58 (2019). T. Feng, A. Heilmann, M. Bock, L. Ehrentraut, T. Witting, H. Yu, H. Stiel, S. Eisebitt, and M. Schnörer, "27 W 2.1 µm OPCPA system for coherent soft x-ray generation operating at 10 kHz," Opt. Express 28, 8724–8733 (2020). I. Mantouvalou, K. Witte, D. Grötzsch, M. Neitzel, S. Günther, J. Baumann, R. Jung, H. Stiel, B. Kanngießer, and W. Sandner, "High average power, highly brilliant laser-produced plasma source for soft x-ray spectroscopy," Rev. Sci. Instrum. 86, 035116 (2015). P. Grünberg, R. Schreiber, Y. Pang, M. B. Brodsky, and H. Sowers, "Layered magnetic structures: evidence for antiferromagnetic coupling of fe layers across Cr interlayers," Phys. Rev. Lett. 57, 2442–2445 (1986). M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroff, P. Etienne, G. Creuzet, A. Friederich, and J. Chazelas, "Giant magnetoresistance of (001)Fe/(001)Cr magnetic superlattices," Phys. Rev. Lett. 61, 2472–2475 (1988). G. Binasch, P. Grünberg, F. Saurenbach, and W. Zinn, "Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange," Phys. Rev. B 39, 4828–4830 (1989). D. Schick, S. Eckert, N. Pontius, R. Mitzner, A. Föhlisch, K. Holldack, and F. Sorgenfrei, "Versatile soft x-ray-optical cross-correlator for ultrafast applications," Struct. Dyn. 3, 054304 (2016). R. Jung, J. Tümmler, and I. Will, "Regenerative thin-disk amplifier for 300 mJ pulse energy," Opt. Express 24, 883–887 (2016). M. Brzhezinskaya, A. Firsov, K. Holldack, T. Kachel, R. Mitzner, N. Pontius, J. S. Schmidt, M. Sperling, C. Stamm, A. Föhlisch, and A. Erko, "A novel monochromator for experiments with ultrashort x-ray pulses," J. Synchrotron Radiat. 20, 522–530 (2013). K. Holldack, J. Bahrdt, A. Balzer, U. Bovensiepen, M. Brzhezinskaya, A. Erko, A. 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Ueberschaer, D. Vahaplar, K. Van Dau, F. N. van den Berg, H. A. M. Van Deveerdonk, R. J. Vodungbo, B. Vomir, M. von Grafenstein, L. von Korff Schmising, C. von Reppert, A. Vrakking, M. J. J. Wadley, P. Wall, S. Weller, D. Weschke, E. Wilkins, S. B. Will, I. Willems, F. Willig, L. Witte, K. Witting, T. Woerner, M. Yabashi, M. Yarlagadda, S. Yu, H. Zabel, H. Zamponi, F. Železný, J. Zinn, W. Anal. Chem. (1) Comput. Phys. Commun. (1) J. Magn. Reson. (1) J. Opt. Soc. Am. B (1) J. Phys. Chem. Lett. (1) J. Synchrotron Radiat. (1) J. Synchrotron. Radiat. (1) Nano Lett. (1) Nat. Commun. (5) Nat. Phys. (1) Nature Physics (1) Opt. Express (3) Phys. Rev. B (4) Phys. Rev. Lett. (8) Rev. Sci. Instrum. (2) Sci. Rep. (3) Struct. Dyn. (3) Fig. 1. High-energy laser pulses are focused onto a rotating and translating tungsten cylinder, emitting broadband soft-x-ray radiation into the full solid angle via laser-plasma generation. The inset shows the emitted spectral distribution as measured by a calibrated spectrometer at the source, and the gray area indicates the energy range around the Fe ${L_3}$ and ${L_2}$ edges from 695 to 735 eV. A reflection zone plate captures this part of the x-rays that are simultaneously focused and dispersed onto an adjustable slit for monochromatization. Part of the blocked x-rays are detected by an x-ray-sensitive SiC diode for normalization. Monochromatic soft x-rays pass the slit and resonantly scatter off the antiferromagnetic Fe/Cr superlattice, as depicted in the upper right scheme, in a $\vartheta$ – $2\vartheta$ -geometry onto a CCD. The pump beam is used to excite the sample at variable delays. Fig. 2. Reflectivity spectrum around the Fe ${L_3}$ and ${L_2}$ absorption edges of the Fe/Cr SL, measured at a grazing incidence angle $\vartheta = 10^ \circ$ . The solid line represents a simulation including magnetic and charge scattering. The experimental data was scaled in intensity to fit the simulation. Fig. 3. Static $L$ -scan of the Fe/Cr SL at resonance ( $E = 707\;{\rm eV} $ , blue dots) and off resonance ( $E = 680\;{\rm eV} $ , orange dots). The blue solid line represents a scattering simulation of the sample structure including magnetic and charge scattering. At $L = 1$ the structural Bragg peak is present for both photon energies, while the AFM Bragg peak at $L = 0.5$ only appears on-resonance and is also reproduced by the simulations. The experimental data was scaled in intensity to fit the simulation. Fig. 5. Average of multiple delay scans on the low-angle side of structural SL1.0 peak at $L = 0.95$ . The rapid rise of the signal is due to a Bragg peak shift toward smaller $L$ because of the photoinduced lattice expansion. The double-exponential fit is a guide to the eye and does not fully account for the complex phonon dynamics and the corresponding translation of peak shift and broadening into an intensity variation. The error bars indicate a confidence interval of 67%. Equations on this page are rendered with MathJax. Learn more. (1) L 2 ( t ) = e − t 2 / 2 σ 2 ⊛ ( A e − t / τ 1 + B e − t / τ 2 ) .	CommonCrawl
AMC Home Complete characterization of the first descent point distribution for the k-error linear complexity of 2n-periodic binary sequences August 2017, 11(3): 409-427. doi: 10.3934/amc.2017035 Parity check systems of nonlinear codes over finite commutative Frobenius rings Thomas Westerbäck Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland Received March 2012 Revised February 2016 Published August 2017 Fund Project: The author acknowledges support from the Knut and Alice Wallenberg Foundation under grant KAW 2005.0098. This support was given during the beginning of the work on this paper while the author was affiliated at the Department of Mathematics, KTH, S-10044 Stockholm, Sweden The concept of parity check matrices of linear binary codes has been extended by Heden [10] to parity check systems of nonlinear binary codes. In the present paper we extend this concept to parity check systems of nonlinear codes over finite commutative Frobenius rings. Using parity check systems, results on how to get some fundamental properties of the codes are given. Moreover, parity check systems and its connection to characters is investigated and a MacWilliams type theorem on the distance distribution is given. Keywords: Nonlinear codes, finite commutative Frobenius rings, parity check systems, characters, discrete Fourier analysis, MacWilliams type theorem. Mathematics Subject Classification: Primary: 94B25, 94B60; Secondary: 13M99. Citation: Thomas Westerbäck. Parity check systems of nonlinear codes over finite commutative Frobenius rings. Advances in Mathematics of Communications, 2017, 11 (3) : 409-427. doi: 10.3934/amc.2017035 T. Britz, MacWilliams identities and matroid polynomials, Electr. J. Combin., 9 (2002), R19, 16pp. Google Scholar P. 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Google Scholar M. Villanueva, Codis no lineals en Magma: construcció de codis perfectes Universitat Autónoma de Barcelona, 2009.Google Scholar M. Villanueva, F. Zeng and J. Pujol, Efficient representation of binary nonlinear codes: constructions and minimum distance computation, Des. Codes Crypt., 76 (2015), 3-21. doi: 10.1007/s10623-014-0028-4. Google Scholar J. A. Wood, Duality for modules over finite rings and applications to coding theory, Amer. J. Math., 121 (1999), 555-575. Google Scholar J. A. Wood, Code equivalence characterizes finite Frobenius rings, Proc. Amer. Math. Soc., 136 (2008), 699-706. doi: 10.1090/S0002-9939-07-09164-2. Google Scholar Steven T. Dougherty, Abidin Kaya, Esengül Saltürk. Cyclic codes over local Frobenius rings of order 16. Advances in Mathematics of Communications, 2017, 11 (1) : 99-114. doi: 10.3934/amc.2017005 Ferruh Özbudak, Patrick Solé. Gilbert-Varshamov type bounds for linear codes over finite chain rings. 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Communications on Pure & Applied Analysis, 2015, 14 (2) : 565-576. doi: 10.3934/cpaa.2015.14.565 Heide Gluesing-Luerssen. Partitions of Frobenius rings induced by the homogeneous weight. Advances in Mathematics of Communications, 2014, 8 (2) : 191-207. doi: 10.3934/amc.2014.8.191 David Grant, Mahesh K. Varanasi. The equivalence of space-time codes and codes defined over finite fields and Galois rings. Advances in Mathematics of Communications, 2008, 2 (2) : 131-145. doi: 10.3934/amc.2008.2.131 Hiroshi Isozaki, Hisashi Morioka. A Rellich type theorem for discrete Schrödinger operators. Inverse Problems & Imaging, 2014, 8 (2) : 475-489. doi: 10.3934/ipi.2014.8.475 Amina Amassad, Mircea Sofonea. Analysis of some nonlinear evolution systems arising in rate-type viscoplasticity. Conference Publications, 1998, 1998 (Special) : 58-71. doi: 10.3934/proc.1998.1998.58 Genady Ya. Grabarnik, Misha Guysinsky. Livšic theorem for banach rings. Discrete & Continuous Dynamical Systems - A, 2017, 37 (8) : 4379-4390. doi: 10.3934/dcds.2017187 Michael Ruzhansky, Jens Wirth. Dispersive type estimates for fourier integrals and applications to hyperbolic systems. Conference Publications, 2011, 2011 (Special) : 1263-1270. doi: 10.3934/proc.2011.2011.1263 Zilong Wang, Guang Gong. Correlation of binary sequence families derived from the multiplicative characters of finite fields. Advances in Mathematics of Communications, 2013, 7 (4) : 475-484. doi: 10.3934/amc.2013.7.475 Nabil Bennenni, Kenza Guenda, Sihem Mesnager. DNA cyclic codes over rings. Advances in Mathematics of Communications, 2017, 11 (1) : 83-98. doi: 10.3934/amc.2017004 Anh Tuan Duong, Quoc Hung Phan. A Liouville-type theorem for cooperative parabolic systems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (2) : 823-833. doi: 10.3934/dcds.2018035 Hilde De Ridder, Hennie De Schepper, Frank Sommen. The Cauchy-Kovalevskaya extension theorem in discrete Clifford analysis. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1097-1109. doi: 10.3934/cpaa.2011.10.1097 Konstantinos Drakakis, Rod Gow, Scott Rickard. Parity properties of Costas arrays defined via finite fields. Advances in Mathematics of Communications, 2007, 1 (3) : 321-330. doi: 10.3934/amc.2007.1.321 Nguyen Dinh Cong, Doan Thai Son, Stefan Siegmund, Hoang The Tuan. An instability theorem for nonlinear fractional differential systems. Discrete & Continuous Dynamical Systems - B, 2017, 22 (8) : 3079-3090. doi: 10.3934/dcdsb.2017164 David Keyes. $\mathbb F_p$-codes, theta functions and the Hamming weight MacWilliams identity. Advances in Mathematics of Communications, 2012, 6 (4) : 401-418. doi: 10.3934/amc.2012.6.401 HTML views (28)	CommonCrawl
Capital in the 21st Century - a model for Pareto distribution of income So I finally finished Thomas Piketty's book - Capital in the 21st Century, and I thought I'd write up an interesting result that Piketty mentions, but does not elaborate on. Given the book is already 700 pages, it's probably for the best that he drew the line somewhere. The result is specifically, that under basic models of the development of distribution of wealth in a society, it can be shown that when growth is equal to $g$, and return on capital is equal to $r$, then the distribution of wealth tends towards a Pareto distribution with parameter $r-g$. That sounds pretty interesting right? My notes below are largely based on following paper by Charles I. Jones of Stanford Business School, my addition is to derive the assumption of an exponential distribution of income from more basic assumptions about labour and capital income. Link to Jones's paper [1] Capital in the 21st Century - The Second Fundamental Law of Capital I'm really enjoying working my way through Thomas Piketty's Capital in the 21st Century, it's been sitting on my shelf unread for a few years now, and at 696 pages it looked like it's going to be a bit of a slog but it's actually been fairly easy and entertaining reading. The overall approach is the following; Piketty collected better data on wealth and income inequalities than anyone else before (going back to around 1700, across multiple countries, and correcting as many systematic biases and data issues as possible), he then analyses said data, drawing out interesting observations whilst writing everything in a fairly non-technical and entertaining. Piketty is able to weave a narrative that sheds light on economic history, predictions for future structural developments of the economy, the history of economic thought, and how the limited data available to past economists skewed their results and how our understanding is different now. Piketty also adds colour by tying his observations to the literature written at the time (Austen, Dumas, Balzac), and how the assumptions made by the authors around how money, income and capital work are also reflected in the economic data that Piketty obtained. Hopefully I've convinced you Piketty's programme is a worthwhile one, but that still leaves the fundamental question - is his analysis correct? That's a much harder question to answer, and to be honest I really don't feel qualified to pass judgement on the entirety of the book, other than to say it strikes me as pretty convincing from the limited amount of time I've spent on it. In an attempt to contribute in some small way to the larger conversation around Piketty's work, I thought I'd write about one specific argument that Piketty makes that I found less convincing than other parts of the book. Around 120 pages in, Piketty introduces what he calls the 'Second Fundamental Law of Capitalism', and this is where I started having difficulties in following his argument. The Second Fundamental Law of Capitalism The rule is defined as follows: $$ B = \frac{s} { g} $$ Where $B$ , as in Piketty's first fundamental rule, is defined as the ratio of Capital (the total stock of public and private wealth in the economy) to Income (NNP): $$B = \frac{ \text{Capital}}{\text{Income}}$$ And where $g$ is the growth rate, and $s$ is the saving rate. Unlike the first rule which is an accounting identity, and therefore true by definition, the second rule is only true 'in the long run'. It is an equilibrium that the market will move to over time, and the following argument is given by Piketty: "The argument is elementary. Let me illustrate it with an example. In concrete terms: if a country is saving 12 percent of its income every year, and if its initial capital stock is equal to six years of income, then the capital stock will grow at 2 percent a year, thus at exactly the same rate as national income, so that the capital/income ratio will remain stable. By contrast, if the capital stock is less than six years of income, then a savings rate of 12 percent will cause the capital stock to grow at a rate greater than 2 percent a year and therefore faster than income, so that the capital/income ratio will increase until it attains its equilibrium level. Conversely, if the capital stock is greater than six years of annual income, then a savings rate of 12 percent implies that capital is growing at less than 2 percent a year, so that the capital/income ratio cannot be maintained at that level and will therefore decrease until it reaches equilibrium." I've got to admit that this was the first part in the book where I really struggled to follow Piketty's reasoning – possibly this was obvious to other people, but it wasn't to me! Analysis – what does he mean? Before we get any further, let's unpick exactly what Piketty means by all the terms in his formulation of the law: Income = Net national product = Gross Net product 0.9 (where the factor of 0.9 is to account for depreciation of Capital) $g$ = growth rate, but growth of what? Here it is specifically growth in income, so while this is not exactly the same as GDP growth it's pretty close. If we assume net exports do not change, and the depreciation factor (0.9) is fixed, then the two will be equal. $s$ = saving rate – by definition this is the ratio of additional capital divided by income. Since income here is net of depreciation, we are already subtracting capital depreciation from income and not including this in our saving rate. Let's play around with a few values, splitting growth $g$, into per capita growth and demographic growth we get the following. Note that Total growth is simply the sum of demographic and per capita growth, and Beta is calculated from the other values using the law. So why does Piketty introduce this law? The argument that Piketty is intending to tease out from this equality is the following: Given per capita GDP is on average lower than many people realise (on the order of 1-2% pa in the long run) And given GDP growth is no longer offset by demographic GDP growth in many advanced economies, i.e. the demographic growth component is now very low GDP growth in the future is likely to only be on the order of 1.5% pa. Therefore for a fixed saving rate, and relatively low growth, we should expect much higher values of Beta than we have seen in the last 50 years. In fact using $g=1.5 \%$ as a long term average, we can expect Beta to crystallise around a Beta of $8$! Much higher than it has been for the past 100 years. Analysis - convergence As Piketty is quick to point out, this is a long run equilibrium towards which an economy will move. Moreover, it should be noted that the convergence of this process is incredibly slow. Here is a graph plotting the evolution of Beta, from a starting point of 5, under the assumption of $g=1.5 \%$, $s = 12 \%$: So we see that after 30 years ( i.e. approx. one generation), Beta has only increased from its starting point of $5$ to around $6$, it then takes another generation and a half to get to $7$, which is still short of its long run equilibrium of $8$. Analysis - Is this rule true? Piketty is of course going to want to use his formula to say interesting things about the historic evolution of the Capital/Income ratio, and also use it to help predict future movements in Beta. I think this is where we start to push the boundaries of what we can easily reason, without first slowing down and methodically examining our implicit assumptions. For example – is a fixed saving rate (independent of changes in both Beta, and Growth) reasonable? Remember that the saving rate here is a saving rate on net income. So that as Beta increases, we are already having to put more money into upkeep of our current level of capital, so that a fixed net saving rate is actually consistent with an increasing gross saving rate, not a fixed gross saving rate. An increasing gross saving rate might be a reasonable assumption or it might not – this then becomes an empirical question rather than something we can reason about a priori. Another question is how the law performs for very low rates of $g$, which is in fact how Piketty is intending to use the equation. By inspection, we can see that: As $g \rightarrow 0$, $B \rightarrow \infty $. What is the mechanism by which this occurs in practice? It's simply that if GDP does not grow from one year to the next, but the net saving rate is still positive, then the stock of capital will still increase, however income has not increased. This does however mean that an ever increasing share of the economy is going towards paying for capital depreciation. Piketty's law is still useful, and I do find it convincing to a first order of approximation. But I do think this section of the book could have benefited from more time spent highlighting some of the distortions potentially caused by using net income as our primary measure of income. There are multiple theoretical models used in macroeconomics, and it would have been useful for Piketty to help frame his law within the established paradigm. The great RPI swindle? Last week it was announced that UK Rail Fares were to increase once again at the maximum allowed rate - 3.4%, corresponding to the RPI increase in July 2017. News article: www.bbc.co.uk/news/business-42234488 When reading this it got me thinking - why is RPI even being used any more? Aren't we supposed to be using CPI now? In 2013 the ONS stated that: "Following a consultation on options for improving the Retail Prices Index (RPI), the National Statistician, Jil Matheson, has concluded that the formula used to produce the RPI does not meet international standards and recommended that a new index be published." So basically the ONS no longer endorses RPI as the best indicator of the level of inflation in the economy. The ONS instead supports the use of CPI. So why does it matter that some organisations are still using RPI? To see why, let's take a look at a chart showing the historic RPI and CPI increases in the UK: www.ons.gov.uk/economy/inflationandpriceindices RPI has been greater than CPI in every single month since 2010. In fact, in this time period, RPI has been an average of 0.8% higher than CPI. This fact might go some way to explain why the Government is so slow to move rail increases from RPI to CPI. This way the Government and Rail Companies can claim that they are only increasing their costs in line with inflation, which seems fair, yet the index they are using is actually higher than the usual inflation index used in the UK. The Government also indexes some of it's outgoings by an inflation index, for example the State Pension, so at least this is also being consistently overstated right? Well actually no! Wherever the government is using an inflation index to increase payments, it seems to have already transitioned to a CPI increase. Let's look at the list of items which use the inflation index which is more beneficial to the Government: (remember that CPI is almost always lower than RPI): There are some pretty hefty items on the list, including, the State Pension, Benefit Payments, Rail Fares, Utility bills, Student Loans. The ones that decrease government spending seem to have already transitioned over, and the ones that increase the amount of tax collected, or the cost of regulated items all seem to still be using the higher RPI index. Now let's look at the list of items which use the inflation index which is to the disadvantage of the Government. The list is certainly a lot shorter, and the items on it are less substantial. Indexed linked Government Bonds are however quite substantial. The reason that the Government is not able to move these to a CPI index is that it would be considered a default to downgrade the index once the bonds have been sold. The Government has no choice but to continue paying the bonds at RPI. Also, the yield on the bonds will be set with an eye towards the yield on a fixed bond, and the expected level of inflation. Therefore the actual index used is not necessarily that important. It's nice to see though that at least stamps are increased at a CPI rate! www.ons.gov.uk/economy/inflationandpriceindices/methodologies/usersandusesofconsumerpriceinflationstatistics Ogden Rates - Why have they gone up so much and why is everyone up in arms about it? What even are Ogden Rates anyway? The Ogden tables are tables of annuity factors, published by the Government's Actuary Department, which are used to calculate court awards for claimants who have had life changing injuries or a fatal accident and are eligible for a payout from their insurance policy. For example, consider a 50 year old, male, primary school teacher who suffers a car accident which means that they will not be able to work for the rest of their life. The Ogden Tables will be used to calculate how much they should be paid now to compensate them for their loss of earnings. Suppose the teacher is earning a salary of £33,000 when they have the accident, then under the Ogden Rates prior to March 2017, the teacher would be paid a lump sum of £33,000 20.53 = £677,490 where 20.53 is the factor from the tables. How did the Government's Actuary Department come up with these factors? The factors in the table are based on two main pieces of information, how long the person is expected to live, and how much money they can earn from the lump sum once they are given it (called the discount rate). It's this second part which has caused all the problems between the Ministry of Justice and the Insurance Industry. The discount rate should be selected to match the return generated on assets. For example, if the claimant puts all their money in shares then on average, they will generate much more income than if they put the lump sum in a savings account. So what should we assume our school teacher will invest their lump sum in? Since the school teacher will not be able to work again, and therefore will need to live off this money for the rest of their life, they will not want to risk losing all their money by investing in something too risky. In technical terms, we would say that the claimant is a risk adverse investor. In order to mimic the investment style of this risk adverse investor, when the Ogden tables were first set, it was decided to assume that the investor would put all their money in index-linked bonds. There are a couple of reasons to assume this, many risk adverse institutional investors do purchase a lot of index-linked bonds, and also, the average discount rate for these bonds is readily available as it is already published by the UK DMO. At the time the tables were set up, this seemed like a great idea, but recently it has made a lot of people very angry and been widely regarded as a bad move. What are Index-linked bonds again? In the 1981 the UK government started issuing a series of gilts which instead of paying a fixed coupon, paid a floating coupon which was a fixed percentage above the rate of inflation. The UK Debt Management Office is responsible for issuing these bonds, and the following website has details of the bonds that are currently in issue. It's quite interesting to see how it all works: www.dmo.gov.uk/reportView.aspx?rptCode=D1D&rptName=50545854&reportpage=D1D The basic principle is if you purchase a bond that pays 2% coupons, if inflation is 3%, they would pay 3%+2%, if inflation was 5%, then they would pay 5% + 2%. Due to the fact that these bonds always gave a fixed real return (2% in this case), institutional investors really like them. Because there is no inflation risk, on average index-linked bonds cost more than fixed coupon bonds once you account for the effects of inflation. Pension Schemes in particular purchase a lot of these bonds, Why do Pension Schemes like these bonds so much? Most pensions are increased annually in line with inflation, due to this Pension Schemes like to hold assets that also go up in line with inflation every year. In order to get real returns on their investments, Pension Schemes traditionally held a mix of shares and index-linked bonds, the shares gave better returns, but the bonds were more safe. This all started to go very wrong after the financial crisis . A huge drop in interest rates and investment returns, combined with soaring life expectancy lead to more and more pension schemes winding up and the remaining ones have funding issues. As the schemes started winding up they became more and more risk adverse and started to move away from the more volatile assets like shares and moved towards index-linked bonds instead. This table from the PPF's Purple Book shows the move away from shares into bonds. We can see that back in 2006, prior to the financial crisis, Pension Schemes were on average holding around 61% of their assets in equities. When we look again at 2014 this percentage has dropped to 33% and the slack has largely been taken up by bonds. Pension Schemes like these assets so much in fact that Schroders estimated that 80% of the long term index-linked gilts market is held by private sector pension schemes as the following chart shows. www.schroders.co.uk/en/SysGlobalAssets/schroders/sites/ukpensions/pdfs/2016-06-pension-schemes-and-index-linked-gilts.pdf Does it matter that Pension Schemes own such a high proportion of these gilts? The problem with the index-linked gilt market being dominated by Pension Schemes is one of supply and demand. The demand for these bonds from Pension Schemes far outweighs the supply of the bonds. Another chart from Schroder's estimates the demand for the bonds is almost 5 times the supply. www.schroders.co.uk/en/SysGlobalAssets/schroders/sites/ukpensions/pdfs/2016-06-pension-schemes-and-index-linked-gilts.pdf As you might expect with such a disparity between supply and demand, Pension funds have been chasing these assets so much that yields have actually become negative. This means that Pension Schemes on average are paying the government to hold their money for them, as long as it's protected against inflation. Here is a chart showing the yield over the last 5 years for a 1.25% 2032 index-linked gilt. www.fixedincomeinvestor.co.uk/x/bondchart.html?id=3473&stash=F67129F0&groupid=3530 So what does this have to do with Ogden Rates? So now we are in a position to link this back to the recent change in the Ogden Rate. Because the yield on index-linked bonds has traditionally been used as a proxy for a risk-free real return, the yield is still used to decide the discount rate that should be used to calculate court award payouts. Because Pension Schemes have been driving up the price of these bonds so much, we have the bizarre situation that the amount that insurance companies have to pay out to claimants has suddenly jumped up considerably. In the case of a 20 year old female for example, the amount that would be paid out has almost tripled. As these pay outs are already considerable, the financial impact of this change has been massive. So what should the Government do? There is no easy answer, if the Government doesn't use the yield on index-linked gilts to calculate the Ogden rate then there is no obvious alternative. I think the most reasonable alternative would be to use a weighted average of returns on the types of assets that an average claimant would hold. For example, we might assume the claimant is going to hold 50% of their lump sum in cash, 30% in shares, and 20% in bonds, and we would then calculate the weighted return from this portfolio. The issues with doing nothing is that the additional cost from these increased pay outs will inevitably be passed on to the policyholders through higher premiums. So ultimately there is an issue of fairness whereby people who are receiving payouts are being paid a disproportionate amount of money, and this is being subsidised by policyholders other policyholders. After Brexit, what about Engxit, or even Londonxit? Now that Brexit is looking like a reality, why stop there? Can we say anything sensible about the merits of seeking even further devolution? What about an English exit from the United Kingdom. One (slightly) tongue in cheek article I read even suggested that Londonxit should also be considered given the difference between how people in London voted in the Referendum, and how the rest of the country voted. So here is a tongue in cheek analysis of this suggestion. GVA, or Gross Value Added, is a measure of the value of the goods and services added to the economy. The ONS publishes figures for GVA split by region in the UK and the results are interesting: GVA per capita England 25,367 Wales 17,573 Scotland 23,102 Northern Ireland 18,682 So the first point to note is that the average person in England is contributing more to the economy as measured by GVA than the average person in Wales, Scotland or Northern Ireland, with Scotland being a close second. In graph form the results looks like this: One obvious candidate for why England is more efficient might be that England has higher levels of government investment. The ONS publishes figures on this as well and we can see that in fact the opposite is true: Public Spending per capita England 8,638 Wales 9,904 England in fact has the lowest level of public spending. So not only does England have the highest GVA, it is doing so with the lowest public spending per capita! It seems that England is being dragged down with it's fellow UK members. Lets not stop there though,.we can also look at GVA figures on a regional level. North East 18,216 Yorkshire and the Humber 19,863 West Midlands 20,086 East of England 20,524 North West 21,011 South West 22,324 East Midlands 23,063 South East 27,012 London 42,666 So we see that London is far ahead of the other regions in the UK when measured by GVA. If we once again add in public spending, (which according to the perception created by most media is heavily favoured towards London) we get the following chart: It turns out that public spending is actually pretty level through out England. Therefore on the face of it perhaps it's time for Londonxit after all?	CommonCrawl
Deep convolutional neural networks for image-based Convolvulus sepium detection in sugar beet fields Junfeng Gao1,2,3, Andrew P. French3,4, Michael P. Pound3, Yong He5, Tony P. Pridmore3 & Jan G. Pieters2 Convolvulus sepium (hedge bindweed) detection in sugar beet fields remains a challenging problem due to variation in appearance of plants, illumination changes, foliage occlusions, and different growth stages under field conditions. Current approaches for weed and crop recognition, segmentation and detection rely predominantly on conventional machine-learning techniques that require a large set of hand-crafted features for modelling. These might fail to generalize over different fields and environments. Here, we present an approach that develops a deep convolutional neural network (CNN) based on the tiny YOLOv3 architecture for C. sepium and sugar beet detection. We generated 2271 synthetic images, before combining these images with 452 field images to train the developed model. YOLO anchor box sizes were calculated from the training dataset using a k-means clustering approach. The resulting model was tested on 100 field images, showing that the combination of synthetic and original field images to train the developed model could improve the mean average precision (mAP) metric from 0.751 to 0.829 compared to using collected field images alone. We also compared the performance of the developed model with the YOLOv3 and Tiny YOLO models. The developed model achieved a better trade-off between accuracy and speed. Specifically, the average precisions ([email protected]) of C. sepium and sugar beet were 0.761 and 0.897 respectively with 6.48 ms inference time per image (800 × 1200) on a NVIDIA Titan X GPU environment. The developed model has the potential to be deployed on an embedded mobile platform like the Jetson TX for online weed detection and management due to its high-speed inference. It is recommendable to use synthetic images and empirical field images together in training stage to improve the performance of models. Sugar beet (Beta vulgaris ssp. vulgaris var. altissima) is very vulnerable to weed competition due to its slow growth and low competitive ability at the beginning of vegetation [1]. The yield loss caused by weed competition can be significant. Therefore, effective weed management in early stages is critical, and essential if a high yield is to be achieved. In modern agriculture, herbicide is widely used to control weeds in crop fields [2]. Weeds are typically controlled by spraying chemicals uniformly across the whole field. However, the overuse of chemicals in this approach has increased the cost of crop protection and promoted the evolution of herbicide-resistant weed populations in crop fields [3], which is a hindrance to sustainable agriculture development. Site-specific weed management (SSWM) refers to a spatially variable weed management strategy to minimize the use of herbicides [4]. However, the main technical challenge of SSWM implementation lies in developing a reliable and accurate weed detection system under field conditions [5]. As a result, various automated weed monitoring approaches are being developed based on unmanned aerial vehicle or on-ground platforms [6,7,8]. Among them, image-based methods integrating machine learning algorithms are considered a promising approach for crop/weed classification, detection and segmentation. Previous studies [7] utilized features like shape, texture and colour features with a random forest classifier for weed classification. Others, such as Ahmad el al [9] developed a real-time selective herbicide sprayer system to discriminate two weed species based on visual features and an AdaBoost classifier. Spectral features from multispectral or hyperspectral images could also be exploited for weed recognition [10, 11]. Although the works mentioned above show good results on weed/crop segmentation, classification and detection, challenges such as plant species variations, growth differences, foliage occlusions and interference from changing outdoor conditions still need to be further overcome in order to develop a real-time and robust model in agricultural fields. Deep learning, a subset of machine learning, enables learning of hierarchical representations and the discovery of potentially complex patterns from large data sets [12]. It has shown impressive advancements on various problems in natural language processing and computer vision, and the performance of deep convolutional neural networks (CNNs) on image classification, segmentation and detection are of particular note. Deep learning in the agriculture domain is also a promising technique with growing popularity. Kamilaris et al. [13] concluded that more than 40 studies have applied deep learning to various agricultural problems like plant disease and pest recognition [14, 15], crop planning [16] and plant stress phenotyping [17]. Pound et al. [18] demonstrated that using deep learning can achieve state-of-the-art results (> 97% accuracy) for plant root and shoot identification and localization. Polder et al. [19] adapted an fully convolutional neural network (FCN) for potato virus Y detection based on field hyperspectral images. Specifically, for crop/weed detection and segmentation, Sa et al. [20, 21] developed WeedNet and WeedMap architectures to analyse aerial images from an unmanned aerial vehicle (UAV) platform. Lottes et al. [8, 22] also did relevant studies on weed/crop segmentation in field images (RGB + NIR) obtained from the BoniRob, an autonomous field robot platform. All these studies have demonstrated the effectiveness of deep learning, with very good results provided. In practice, farmers usually plow fields before sowing to provide the best chance of germination and growth for crop seeds. Moreover, parts of pre-emergent weeds are buried under the ground and so killed through this procedure. However, Convolvulus sepium (hedge bindweed) can emerge from seeds and remaining rhizome segments left underground. This leads to different emergence times of C. sepium, resulting in multiple growth stages from first leaves unfolded to stem elongation being represented in a single field. The appearance of C. sepium at different growth stages varies. In the early growth stages, some C. sepium plants might have similar color features as sugar beet plants in their early growth stages. All these factors bring challenges to the development of a robust system for C. sepium detection under field conditions. To the best of our knowledge, no studies have attempted to detect them in a sugar beet field based on a deep learning approach. In our study, first we develop an image generation pipeline to generate synthetic images for model training. We then design a deep neural network to detect C. sepium and sugar beet based on field images. The major objectives of the present study are (i) to appraise the feasibility of using a deep neural network for C. sepium detection in sugar beet fields; (ii) to explore whether the use of synthetic images can improve the performance of the developed model; (iii) to discuss the possibility of our model to be implemented on mobile platforms for SSWM. A digital single-lens reflex (DSLR) camera (Nikon D7200) was used to manually collect field images from two sugar beet fields of West Flanders province in Belgium under different lighting conditions (from morning to afternoon in sunny and cloudy weather). Most sugar beet plants have 6 unfolded leaves, while the growth stages of C. sepium plants vary widely, from seedling to pre-flowering. The camera was held manually to capture images randomly in the sugar beet fields. The distance between camera and soil surface was around 1 m which is not strictly fixed in order to create more variations in the images. For camera settings, the ISO value is 1600 and the exposure times are 1 ms under sunny weather conditions and 1.25 ms under cloudy weather conditions. The resolution of raw images is 4000 × 6000 pixels. There are 652 images under different lighting conditions which were manually labelled with bounding boxes. Among them, 100 images are randomly selected as a test dataset and 100 images are randomly selected as a validation dataset. The remaining 452 images are used as a training dataset. All the images were resized to 800 × 1200 pixels. In this way, the resized images do not change their aspect ratio and are suitable for training based on our computation resources. Synthetic image generation Training a deep neural network with adequate performance generally requires a large amount of data. This is labour-intensive and time-consuming to collect and label. To overcome this problem, we generated synthetic images based on the training dataset from the formerly collected field images. The process of synthetic training image generation is depicted in Fig. 1. Seventy-seven images were selected as original source images. All these images contained either a sugar beet (51) or a C. sepium object (26). Their excess green (ExG) vegetation index [23] grayscale images were obtained using Eqs. (1) and (2). Equation (2) is used to normalize R, G and B channel. Next, we converted the ExG grayscale images into binary mask images with Otsu's algorithm [24]. Afterwards, the object images and their masks were transformed using a set of randomly chosen parameters. Rotation (from 0 to 360° with a 15° step), zoom (from 0.5 × to 1.5 × with 0.1 step), shift (from − 100 to 100 pixels with a 15-pixel step both in the horizontal and vertical directions) and flip (horizontal or vertical direction) operations were applied. The base image and their corresponding masks were subjected to flip (horizontal or vertical direction), limited rotation (0 or 180°) and limited zoom (from 1 × to 1.8 × with 0.1 step) operations to keep the soil background information. The object mask image (Boolean data type) was used as a logic control image. If the logic value in the object mask image is true, the pixel in the base image was replaced by the pixel from the object image. Otherwise, there is no replacement in the base image. After all the pixels from the object images were added to the base images, their brightness was adjusted using Gamma correction [25]. Gamma values varied from 0.5 to 1.5 with 0.2 step. In our study, we generated 2271 synthetic images in total. They are comprised of 1326 (51 × 26) images with sugar beet and C. sepium plants, 676 (26 × 26) images with C. sepium and C. sepium plants and 269 images with sugar beet and sugar beet plants. These synthetic images will be only used for training deep neural networks. The less images (269) with sugar beet and sugar beet plants were generated compared to the other two type images (1326 and 676), because the balance of different object numbers (sugar beet and C. sepium) is better to keep for the benefits of training deep neural network after considering most field images only contain sugar beet plants in the training dataset. The examples of real field images and synthetic images are shown in Fig. 2. There is no occlusion in base images and object images. However, the synthetic images could contain overlapped plants (see Fig. 2 bottom right image) as the object (sugar beet or C. sepium) was randomly placed in the base images in this pipeline, thus better representing the real scenario of field conditions. $${\text{ExG}} = 2*{\text{g}} - {\text{r}} - {\text{b}}$$ $${\text{r}} = \frac{R}{G + R + B},\;{\text{g}} = \frac{G}{G + R + B},\;{\text{b}} = \frac{B}{G + R + B}$$ The process of synthetic image generation The examples of real and synthetic images (top row: real images, bottom row: synthetic images) where R, G and B are the red, green and blue channel pixel values, respectively. Deep neural network architecture The deep neural network architecture used in this study is depicted in Fig. 3. It is similar to the tiny YOLOv3 (You Only Look Once) framework, a lighter and faster version of YOLOv3 [26]. In our case, there were only two object classes. The sugar beet objects generally had similar sizes in fields as they were sown in the same time. Thus, we reduced the number of detection scales to two scales instead of three scales in YOLOv3. This change speeded up inference time. Furthermore, we modified the route for feature concatenation and added two more convolutional layers for better feature fusion. Before feeding the image data into networks, all the images were resized to 608 × 608 spatial resolution to fit the network architecture. The network first comprised 5 convolution and max-pooling blocks. The number of convolutional filters in each block, starting with 16 filters, was doubled compared to the former block. The 5 max pooling layers resulted in a total down-sampling by a factor of 32. At the end of convolution and max pooling block, the dimension of the feature map was 19 × 19 × 256. A series of convolution operations were then carried out to obtain the final features (19 × 19 × 21), a 3-dimensional tensor encoding coordinate of the bounding box, object and class predictions, for initial object detection. One of the most notable features of YOLOv3 is to detect objects at different scales. In our network architecture, it detects objects at two different scales with 19 × 19 and 38 × 38 grids, respectively. In the tail of the network, we took the feature map from the previous 15th layer as input for a convolutional layer with 128 filters and then upsampled it by 2×. Subsequently, the upsampled features were concatenated with the earlier feature map resulting from a convolutional layer in the last convolution and max pooling block. Then two more convolutional layers were added to fuse this merged feature map, finally obtaining a similar tensor (38 × 38 × 21) for detection at the second scale. Compared to tiny YOLOv3, we adapted the order of the former layer to concatenate with the upsampled layers to keep the fine grained features and added more layers in decoder part for better fusion low-level features. In our network, instead of using the default anchor box sizes, we calculated our own anchor box sizes based on clustering of object bounding box sizes from the labelled training dataset. K-means clustering [26] approach was used to determine the 6 anchor box sizes for our detection at the two different scales, each scale with 3 anchor boxes. There are three parts, bounding box error for ${L}_{1}$, object confidence error for ${L}_{2}$, and classification error for ${L}_{3}$, in the loss function ${L}_{loss}$ [27]: $$\begin{aligned}{{L}_{1}} &= {\alpha}_{coord}\sum_{i=0}^{{S}^{2}}\sum_{j=0}^{B}{\omega}_{ij}^{obj}\left[{\left({x}_{i}-{\widehat{x}}_{i}\right)}^{2}+ {({y}_{i}-{\widehat{y}}_{i})}^{2}\right]+ {\alpha}_{coord}\sum_{i=0}^{{S}^{2}}\sum_{j=0}^{B}{\omega}_{ij}^{obj}\left[{\left({\sqrt{w}}_{i}-{\sqrt{\widehat{w}}}_{i}\right)}^{2}+ {({\sqrt{h}}_{i}-{\sqrt{\widehat{h}}}_{i})}^{2}\right] \\ {L}_{2}&=\sum_{i=0}^{{S}^{2}}\sum_{j=0}^{B}{\omega}_{ij}^{obj}{({C}_{i}-{\widehat{C}}_{i})}^{2} + {\alpha }_{noobj}\sum_{i=0}^{{S}^{2}}\sum_{j=0}^{B}{\omega}_{ij}^{noobj}{({C}_{i}-{\widehat{C}}_{i})}^{2}\\ {L}_{3}&=\sum_{i=0}^{{S}^{2}}{\omega }_{i}^{obj}\sum_{c\in classes}{({p}_{i}(c)-{\widehat{p}}_{i}(c))}^{2} \\ {L}_{loss}&= {L}_{1}+{L}_{2}+{L}_{3} \end{aligned}$$ where the weight constants ${\alpha }_{coord}$, ${\alpha }_{noobj}$ are 5 and 0.5, respectively. ${\alpha }_{coord}$ is ten times of ${\alpha }_{noobj}$ in order to focus more on detection. S is the number of the grid cell and B is the number of bounding box at each scale. ${\omega }_{ij}^{obj}$ denotes that the jth bounding box in the grid cell i is responsible for this prediction. The value is 1 if there is an object in cell and 0 otherwise. ${\omega }_{ij}^{noobj}$ is the opposite of ${\omega }_{ij}^{obj}$. c is the classes. ${\omega }_{i}^{obj}$ is 1 when the particular class is predicted, otherwise the value is 0.${x}_{i}$,${y}_{i}$, ${w}_{i}$ and ${h}_{i}$ are the centroid coordinate, width and height of the corresponding responsible anchor box. ${C}_{i}$ is the confidence score of object ${p}_{i}(c)$ is the classification loss. The parameters with hats are the corresponding estimated values. Transfer learning uses partial weights from a pre-trained model on a new problem to overcome any potential overfitting due to the lack of sufficient training data. It has been demonstrated that the first layer of deep neural networks extracts some generic features like edge and colour features [28] so that they are generally applicable to other computer vision tasks. Therefore, weights from these layers are expected to be more valuable when optimising the algorithm than randomly initialized weights in the networks [29]. In our study, we used the weights from the pre-trained model (darknet53), trained on the ImageNet dataset, a public dataset containing millions of natural images, to train the proposed, Tiny and YOLOv3 models. The Adam optimizer [30] with the initial learning rate 0.02, then dropping this value by 0.1 at every 20,000 iterations, was chosen to minimize the loss function. The batch size was set to 64. Data augmentation such as random scaling and cropping, and randomly adjusting exposure and saturation was also used during all the training process to reduce the risk of overfitting. For object detection applications, mean average precision (mAP) is a standard metric for evaluation of model performance. In our case, we calculated the average precision (AP) of sugar beet and C. sepium classes separately, and then averaged over APs of these two classes to calculate mAP value (Eq. 5) to check the overall performance of a model. Precision is a ratio of true object detections to the total number of objects that a model predicted. Recall is a ratio of true object detections to the total number of objects in the dataset. In our case, to be the true object detections, the area of the overlap, also called intersection over union (IoU, Eq. (3)), between the predicted bounding box and ground truth bounding box should exceed 0.5. The AP, calculated by Eq. 4, is precision averaged across all the values of recall between 0 and 1, namely the area under the PR curve [31]. An approximation of the area is calculated via Riemann summation. Note that both precision and recall metrics vary with IoU thresholds. In our case, we set the model threshold as 0.5 (at IoU = 0.5) and then combine all the detections from all the test images to draw a precision-recall (PR) curve. mAP50 and AP50 denote that the two values were achieved under the condition of IoU = 0.5. $${\text{IoU}} = \frac{{areaB_{p} \cap areaB_{gt} }}{{areaB_{p} \cup areaB_{gt} }}$$ where $area{B}_{p}$ is the area of the predicted bounding box, and $area{B}_{gt}$ is the area of ground truth bounding box. $${\text{AP}} = \sum\limits_{k = 1}^{N} {P(k)} \Delta recall(k)$$ $${\text{mAP}} = \frac{{\sum\limits_{m = 1}^{M} {AP(m)} }}{M}$$ where $N$ is the total number of images in the test dataset,$M$ is the number of classes, $P\left(k\right)$ is the precision value at $k$ images and $\Delta recall(k)$ is the change of the recall between $k$ and $k$ − 1 images. Model performance The training loss curve of the proposed deep neural network is shown in Fig. 4. As we can see, the training loss dropped sharply at the beginning of the training stage, and then the loss value slowly converged at around 0.18 after 22,000 batch iterations (527 epochs). We evaluated the performances of the developed model in the validation dataset at different batch iterations (Fig. 5). It is shown that the mAP50 obtained the highest value (0.839) in 26,000 iterations. After 26,000 iterations, the mAP50 started to slowly decrease as the model tends to be overfitting in the validation dataset, though the training loss still drops a little. We used the weights (26,000 iterations) to evaluate the developed model in the test dataset. Following the same procedure to other models, Table 1 sums up the performances of the other networks in the test dataset. In general, the proposed network achieved the highest average precision (AP50) of C. sepium detection (0.761). Although the YOLOv3 obtained the highest mAP50 (0.832) and the maximum AP50 value of sugar beet (0.938), it did not show good capability in C. sepium detection (0.726), which is the priority and most important consideration in SSWM. Loss curve of the proposed detection network mAP50 values of the developed model in the validation dataset at different batch iterations Table 1 Detection performances of the different models in the test dataset In terms of averaged inference time, all the trained networks were tested on a Linux server with an NVIDIA Titan X Pascal GPU (12G memory). The YOLOv3 model cost on average 40.75 ms to predict an 800 × 1200 image in test data. However, the tiny YOLOv3 and the proposed network performed much faster predictions, with detections in the same spatial resolution images at 6.39 ms and 6.48 ms, respectively. This can be attributed to the use of a less deep network architecture, thus the number of parameters needed to be tuned were far fewer than the YOLOv3 network. Figure 6 displays the precision-recall curves of sugar beet and C. sepium of the proposed network in the test dataset. The specific detection results of these three networks in 5 typical field images are provided in Fig. 7. Precision-recall curves of sugar beet and C. sepium (bindweed) in the proposed network Detection results comparison in the test dataset. From top to bottom, the first row is the input images. The second row is the ground truth of the input images, the third row is detection results from the YOLOv3, the forth row is detection results from the tiny YOLOv3 and the last row is the detection results from the proposed networks Synthetic images In this study, we used 2271 images for training the models and some examples are given in Fig. 8. Table 2 displays the effect of adding synthetic images. It can be seen that the overall mAP50 metric increased from 0.751 to 0.829 with the added synthetic images. The contributions come from the improvement of C. sepium detection increasing from 0.587 to 0.761. Examples of the synthetic images Table 2 Detection results with the different training dataset Anchor box The default anchor box sizes in the tiny YOLOv3 model were [10, 14], [23, 27], [51, 34], [81, 82], [135, 169] and [334, 272]. We used k-means clustering to calculate the 6 anchor box sizes based on our own training data set. The 6 anchor box sizes used for training are [14, 20], [32, 38], [56, 40], [75, 90], [185, 168] and [364, 222], respectively. The effect of anchor box for training is given in Table 3. We can see that the detection results (mAP50 = 0.829) with the own calculated anchor box sizes are slightly better than the results (mAP50 = 0.823) from the default anchor box sizes. Table 3 Detection results from different Anchor box size sets Transfer learning with adaptive learning rates was used to train our neural network, leading the training loss to sharply decrease at the beginning, before finally converging at a low loss value. In terms of weight initialization, the experiment [29] has shown that initializing the deep learning models with pre-trained weights from ImageNet leads to better accuracy in many cases. When training a deep neural network, data is a crucial component to reduce the risk of overfitting. We generated more than 2000 synthetic images for training based on conventional image processing techniques. Previous studies [32, 33] have presented other approaches to generate images for object detection and segmentation. Moreover, Generative Adversarial Networks (GANs) [34], inspired by game theory, is also a promising deep learning based approach to generate synthetic images for training neural networks [35]. Open source rendering software such as Blender [36] could be employed to generate synthetic images from 3D models [37]. Back to our approach for synthetic images generation, several ways can be done for improving the quality of synthetic images. For example, the selected base images and object images were taken under same view and lighting conditions. This could assure that the added objects fit well in the background of base images. Small object detections can be a very challenging problem, especially when using deep neural networks with pooling layers, due to the loss of spatial resolution. Increasing resolution of the input images is a direct way to alleviate that problem but it is usually constrained by the network architecture used and computation resources available. The proposed network detects objects at two different scales. The second scale is capable of detecting small objects because the feature maps are upsampled and then concatenated with the previous feature map, which contains fine-grained features for small object detections. Besides, Ren et al. [38] adapted Faster-RCNN for small object detection in remote sensing images. We also find that the detection results were improved by generating synthetic images based on conventional image processing techniques. Under field conditions, most sugar beets generally present relatively homogeneous appearances as their seeds were sown at the same time. However, C. sepium can present significant differences in colour, size, morphology and texture. Thus, the variations of C. sepium plants shown in Fig. 9 are far more than sugar beet crop. This is likely why all the networks in our study provide better sugar beet detection than C. sepium. For row crops like sugar beet, maize and potato, inter-row weeds can be detected after crop line detection [7]. These detected inter-row weeds have the potential to be used as training samples for intra-row weed detections. Kazmi et al. [39] used conventional image processing algorithms and explored hand-crafted features with traditional machine learning techniques for creeping thistle weed detection in sugar beet fields. Although good accuracy was achieved with only using colour information, the use of hand-crafted features makes it difficult to guarantee the robustness of the developed model under changing environmental conditions and variations in plant development. In contrast, deep learning methods can extract hierarchical features and learn very complex functions with a large amount of data provided [12]. Detecting weeds under different weather conditions is not the main challenge when using deep learning-based models because of the use of data augmentation such as random exposure and saturation adjustments or training with a large number of images collected in different weather conditions. It is more difficult to accurate detect weeds under heavy overlapping, and variable object size and shape scenarios. Suh et al. [40] discussed the classification of sugar beet and volunteer potato under field conditions using a VGG-19 modified neural network. A classification accuracy of 98.7% (inference time less than 0.1 s) was obtained, which exceeded previously reported accuracies by Nieuwenhuizen et al. [41] and Suh et al. [42] with hand-crafted features and conventional machine learning algorithms. However, the proposed approach [40] did not lead to the precise detection of volunteer potato in field images because it is a classification task without detecting individual plants in crop fields. The approach used in this study is capable of detecting C. sepium plants of various sizes. Compared to other studies [8, 19, 22] that used a hood or artificial lighting for image acquisition, our study targets weed detection under uncontrolled environments. It is difficult to directly compare the performance of the developed model as different datasets and metrics are used in different studies. To the best of our knowledge, this study is the first to detect C. sepium in sugar beet fields. Though a proper comparison is lacking, it seems fair to claim that deep learning-based C. sepium detection can be made under field conditions. C. sepium representations in the field The own-calculated anchor boxes do not show much improvement in mAP50 metric compared to the default bounding boxes which can be attributed to relatively small differences between calculated and default anchor boxes and only 2 object classes in our case. However, it is still highly recommended to use a k-mean clustering approach to calculate prior anchor box sizes for network. It would give networks the range of predicted bounding boxes for most objects, leading to a more accurate bounding box prediction. In practice, the choice of a network depends on a trade-off between accuracy and inference speed. The proposed network achieves a good balance with speed and accuracy. The proposed network shows a sizeable advantage in inference speed at only 6.48 ms per image. One of the reasons for this is the use of a shallower network architecture compared to the Darknet-53 based YOLOv3 [26] and VGG based Single Shot MultiBox Detector (SSD) architectures [43]. Another reason is the mechanism of employing anchor boxes, which does not require a computationally expensive region proposal step when selecting potential object candidates, as regional convolutional neural networks (R-CNN) [44] do. Although the test is performed on a desktop computer with an NVIDIA Titan X GPU, it is still possible to be implemented on real-time systems with a state-of-the-art mobile embedded device like NVIDIA Jetson TX [45]. The DSLR Nikon camera provides high spatial resolution raw images (4000 × 6000) for field data collection. In this study, the original images were resized twice to 608 × 608 pixels before feeding into networks. In this aspect, it is not necessary to use a very high resolution and costly imaging sensor when developing a vision-based site-specific spraying field robot with the trained deep neural network model. An affordable webcam is probably suitable for this prototype development as it also meets the resolution requirement and it is easy to use and low-cost. In this work, the synthetic images contain two objects (weeds or crop), which is still not complex enough compared to true field images, despite some overlapped plants images generated. More challenging synthetic images thus need to be introduced for training the networks in order to represent near-true harsh field conditions. Besides, we only investigated the effect of 2271 synthetic images for training networks without consideration of other number of synthetic images due to limited number of base and object images. It would be helpful to compare results among other number of synthetic images (e.g. 3000, 4000, 5000) to determine the optimal number of synthetic images for training neural networks. Barth et al. [46] discussed the effects of synthetic data size for model performances. Furthermore, it is interesting to investigate which crop growth stages result in the optimal prediction results. Our object detection results are denoted as bounding box formations. The coordinate information of bounding boxes in the image could be used to estimate actuator action time in the real world when developing a target spray platform with a machine vision system. Other than field vehicle platforms for weed management, drone-based platforms are also gaining popularity for weed mapping in precision farming [7, 21]. To put this study into perspective, the future works will be done on SSWM prototype development based on the deep learning algorithms. Besides, pixel-wise crop/weed segmentation based on fully convolutional networks (FCNs) is also worthwhile to be explored as it provides more precise predictions on decision boundary compared to object detections with bounding boxes. In terms of synthetic data, other ways like using GANs will be explored as well in the future. In this paper, we developed a pipeline to generate synthetic images from collected field images. There were 2271 synthetic images and 452 field images in total for training. Moreover, we designed a deep neural network based on the tiny YOLO architecture for C. sepium and sugar beet detection. We recommend calculating anchor box sizes based on an application-specific dataset instead of using the default values when employing YOLO-based neural networks. The added synthetic images in the training process improved the performance of the developed network in C. sepium detection. Comparing to other networks like YOLOv3, we conclude that our network achieved a better trade-off between speed and accuracy. Specifically, the average precisions (AP50) of C. sepium and sugar beet were 0.761, 0.897, respectively with 6.48 ms inference time per image (800 × 1200) on an NVIDIA Titian X GPU environment. The trained model could be deployed in a mobile platform (e.g., unmanned aerial vehicles and autonomous field robots) for weed detection and management. 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Comput Electron Agric. 2019; 161:291–304. The authors wish to express their gratitude to Joseph Best, technician at the computer vision laboratory of the University of Nottingham. This study is funded by the Special Research Fund (BOF) of the Ghent University (No. 01SC3616). We also would like to thank the mobility funding support from the doctoral school of Ghent University. Lincoln Institute for Agri-food Technology, University of Lincoln, Lincoln, Riseholme Park, LN2 2LG, UK Junfeng Gao Department of Biosystems Engineering, Ghent University, Coupure Links 653, 9000, Ghent, Belgium Junfeng Gao & Jan G. Pieters School of Computer Science, University of Nottingham, Jubilee Campus, Wollaton Road, Nottingham, NG8 1BB, UK Junfeng Gao, Andrew P. French, Michael P. Pound & Tony P. Pridmore School of Biosciences, University of Nottingham, Sutton Bonington Campus, Nr Loughborough, LE12 5RD, UK Andrew P. French College of Biosystems Engineering and Food Science, Zhejiang University, Yuhangtang Road 866, Hangzhou, 310058, Zhejiang, China Yong He Michael P. Pound Tony P. Pridmore Jan G. Pieters JG collected data and developed the codes. JG, APF and MPP analyzed data, YH, TPP and JGP supervised the project. JG wrote the paper with input from all authors. All authors read and approved the manuscript. Correspondence to Yong He. Gao, J., French, A.P., Pound, M.P. et al. Deep convolutional neural networks for image-based Convolvulus sepium detection in sugar beet fields. Plant Methods 16, 29 (2020). https://doi.org/10.1186/s13007-020-00570-z Weed detection	CommonCrawl
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Optimal investment and reinsurance to minimize the probability of drawdown with borrowing costs Effect of institutional deleveraging on option valuation problems Analysis of dynamic service system between regular and retrial queues with impatient customers Balasubramanian Krishna Kumar 1,, , Ramachandran Navaneetha Krishnan 1, , Rathinam Sankar 1, and Ramasamy Rukmani 2, Department of Mathematics, College of Engineering, Anna University, Chennai 600 025, India Department of Mathematics, Pachaiyappa's College, Chennai 600 030, India * Corresponding author: B. Krishna Kumar Received January 2020 Revised July 2020 Published October 2020 Fund Project: This research work is supported in part by Department of Science and Technology, New Delhi, India, under research grant INT/RUS/RFBR/377 Figure(17) In this article, we propose a dynamic operating of a single server service system between conventional and retrial queues with impatient customers. Necessary and sufficient conditions for the stability, and an explicit expression for the joint steady-state probability distribution are obtained. We have derived some interesting and important performance measures for the service system under consideration. The first-passage time problems are also investigated. Finally, we have presented extensive numerical examples to demonstrate the effects of the system parameters on the performance measures. Keywords: Oscillating system, retrial queue, impatience, ergodicity, steady-state performance, first-passage time, hypergeometric functions, sensitivity analysis. Mathematics Subject Classification: Primary: 60K25, 90B05; Secondary: 68M20, 90B22. Citation: Balasubramanian Krishna Kumar, Ramachandran Navaneetha Krishnan, Rathinam Sankar, Ramasamy Rukmani. Analysis of dynamic service system between regular and retrial queues with impatient customers. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020153 M. S. Aguir, O. Z. 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Dynamic oscillating queue with threshold and impatience Figure 2(a). $\pi(0, 0) ~\text { versus }~ \xi ~\text { for }~ \alpha = 3, \mu = 4, \mathrm{N} = 5$ Figure 2(b). $\text { E(L) versus }~ \xi~ \text { for } ~\alpha = 3, \mu = 4, N = 5$ Figure 2(c). $\mathrm{E}\left(\mathrm{W}_{\mathrm{S}}\right) ~~\text { versus } ~~\xi ~~\text { for }~~ \alpha = 3, \mu = 4, \mathrm{N} = 5$ Figure 2(d). $\mathrm{R}_{\mathrm{A}} ~~\text { versus } ~~\xi ~~\text { for }~~ \alpha = 3, \mu = 4, \mathrm{N} = 5$ Figure 2(e). $\mathrm{P}_{\mathrm{S}} ~~\text { versus } ~~\xi ~~\text { for }~~ \alpha = 3, \mu = 4, \mathrm{N} = 5$ Figure 3(a). $\pi(0, 0) \text { versus } \mu \text { for } \alpha = 3, \xi = 5, \mathrm{N} = 5$ Figure 3(b). $\mathrm{E}(\mathrm{L}) \text { versus } \mu \text { for } \xi = 5, \alpha = 3, \mathrm{N} = 5$ Figure 3(c). $\mathrm{E}\left(\mathrm{W}_{\mathrm{S}}\right) \text { versus } \mu \text { for } \xi = 5, \alpha = 3, \mathrm{N} = 5$ Figure 3(d). $\mathrm{R}_{\mathrm{A}} \text { versus } \mu \text { for } \xi = 5, \alpha = 3, \mathrm{N} = 5$ Figure 3(e). $\mathrm{P}_{\mathrm{S}} \text { versus } \mu \text { for } \xi = 5, \alpha = 3, \mathrm{N} = 5$ Figure 4(a). $\mathrm{E}\left(\tau_{\mathrm{j}}\right) ~~\text { versus } ~~\xi ~~\text { for }~~ \alpha = 3, \mu = 4, \mathrm{N} = 5, \mathrm{j} = 10$ Figure 4(b). $\mathrm{E}\left(\tau_{\mathrm{j}}\right) \text { versus } \mu \text { for } \xi = 5, \alpha = 3, \mathrm{N} = 5, \mathrm{j} = 10$ Figure 4(c). $\mathrm{E}\left(\tau_{\mathrm{j}}\right) ~~\text { versus } ~~\xi ~~\text { for }~~ \lambda = 18, \nu = 20, \alpha = 3, \mu = 4, \mathrm{N} = 5$ Figure 4(d). $\mathrm{E}\left(\tau_{\mathrm{i}}\right) \text { versus } \mu \text { for } \lambda = 18, \nu = 20, \xi = 5, \alpha = 3, \mathrm{N} = 5$ Figure 4(e). $\mathrm{E}\left(\tau_{\mathrm{j}}\right) \text { versus } \lambda \text { for } \xi = 5, \nu = 20, \mu = 4, \alpha = 3, \mathrm{N} = 5$ Figure 4(f). $\mathrm{E}\left(\tau_{\mathrm{j}}\right) \text { versus } \nu \text { for } \lambda = 18, \xi = 5, \alpha = 3, \mu = 4, \mathrm{N} = 5$ Manil T. 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A novel structured low-rank framework for ghost removal and denoising of EPSI data Ipshita Bhattacharya1, Ralph Noeske 2, Rolf F Schulte3, and Mathews Jacob1 1Electrical and Computer Engineering, The University of Iowa, Iowa City, IA, United States, 2GE Healthcare, Postdam, Germany, 3GE Global Research, Munich, Germany Spectral interleaving is often used in echoplanar spectroscopic imaging (EPSI) sequences to achieve high spatial and spectral resolution, especially on high field scanners with larger chemical shift dispersion. Unfortunately, a major roadblock is the spurious Nyquist ghost artifacts, resulting from phase errors between interleaves. We introduce a novel framework, that simultaneously capitalizes on annihilation relation between the interleaves introduced by phase relations, as well as a linear predicability of the spectra, to remove the phase errors and to provide spectral denoising of the spectra. In addition, we also exploit on the low-rank structure of the EPSI data to provide additional spatial denoising, which will further improve the signal to noise ratio of the datasets. Echo-planar spectroscopic imaging (EPSI) [1,2], which relies on echo-planar readouts to simultaneously encode one spectral and one spatial dimension, is a popular approach for rapid MRSI. Spectral interleaving is often used to simultaneously achieve high spectral and spatial resolution, which is an important need on high field systems that offer higher signal to noise ratio(SNR) and higher chemical shift dispersion. Specifically, multiple datasets are acquired with low temporal sampling rate, but with different temporal shifts between the readouts (see Fig. 1 for details); the interleaves are later interlaced to construct the final spectrum. A challenge in this approach is the phase inconsistencies between the interleaves, resulting from timing errors in the applied gradient trains, drifts in the magnetic field, and field inhomogeneity distortions. These errors manifest as spurious Nyquist ghost peaks in the spectral domain; associated line-shape variations and baseline fluctuations make the quantification of relatively weak metabolites rather challenging. We introduce a novel correction strategy, which exploits the annihilation relations resulting from phase relations between the interleaves and linear predictability of exponential signals. We consider the recovery of two MRSI datasets $$$\mathbf{P_o}$$$ and $$$\mathbf{P_e}$$$, corresponding to odd and even interleaves from their interleaved measurements $$$\mathcal{A_o}(\mathbf{P_o})=\mathbf{G_o}$$$ and $$$\mathcal{A_e}(\mathbf{P_e})=\mathbf{G_e}$$$, respectively, where $$$\mathcal{A}$$$ is the undersampling operator. We aim to recover the rows of the datasets, which are the FID signals. Note that $$$\mathbf{G_o}$$$ and $$$\mathbf{G_e}$$$ are uniformly undersampled in time. Our focus is to fill in the missing FID samples, while compensating for phase errors. The FID signal of a specific pixel $$$\rho^{(i)}[n]=\mathbf{P[i,n]}$$$ can be safely modeled as a multi-exponential: $$\rho[n]=\sum_{k=1}^K c_k \;\nu_k^n; ~~ n=0,..,N-1,~~~~~(1)$$ where $$$\nu_k=\exp\left\{-\left(1/T_{2,k}^* + j 2\pi f_k \right)T\right\}$$$ are the exponential parameters. Such exponential signals satisfy an annihilation relation $$$\rhoh=0$$$,[3,4] where $$$h$$$ is an finite impulse response(FIR) filter of the form $$$h(z)=\prod_{i=1}^{K}\left(1- \nu_k z^{-1}\right)$$$. This annihilation relation can be expressed as $$\mathcal{T}(\boldsymbol\rho)~\mathbf{h}=0,~~~~~(2)$$ where $$$\mathcal{T}(\boldsymbol{\rho})$$$ is a Toeplitz convolution matrix. We model the phase distortions in the odd and even interleaves as convolutions by FIR filters $$$g_{\rm{e}}$$$ and $$$g_{\rm{o}}$$$, respectively. Specifically, we assume that $$$\rho_{o}=\rhog_{o}$$$ and $$$\rho_{e}=\rhog_{e}$$$. In this case, there exists annihilation relations $$$\rho_{o}g_{e}-\rho_{e}g_{o}=0$$$. These relations, along with eq(2), can be compactly expressed in the matrix form as $$\underbrace{\begin{bmatrix}\mathcal{T}(\boldsymbol\rho_o)&\mathcal{T}(\boldsymbol\rho_e)\end{bmatrix}}_{\mathcal{H}(\boldsymbol \rho_o,\boldsymbol\rho_e)}\begin{bmatrix}\mathbf{h} & \mathbf{0} & \mathbf{g_e}\\ \mathbf{0} & \mathbf{h} &-\mathbf{g_o}\end{bmatrix}=0~~~~~(3)$$. The above relations imply that the matrix $$$\mathcal{H}(\boldsymbol{\rho_o},\boldsymbol{\rho_e})$$$ is low-rank. We use the above low-rank property to jointly recover the odd and even datasets: $$\{\mathbf{P_{o}},\mathbf{P_{e}}\}=\arg \min_{\mathbf{P_{o}},\mathbf{P_{e}}}\\|\mathcal{A_o}(\mathbf{P_{o}})-\mathbf{G_o}\\|^2+\\|\mathcal{A_e}(\mathbf{P_{e}})-\mathbf{G_e}\\|^2+\lambda_{1}\sum_{i=1}^{N_{\rm{pixels}}}\left\\|\mathcal{H}(\boldsymbol\rho_o^{(i)},\boldsymbol\rho_e^{(i)})\right\\|_{}+\lambda_{2}\left[\\|\underbrace{\mathbf{P_{o}}\\|_{}+\\|\mathbf{P_{e}}}_{\text{Casortai low-rank}}\\|_{}\right]~~~~~(4)$$. The third term synergistically uses the spectral & phase-induced annihilation relations, enables the removal of phase errors and provides spectral denoising. The combination of priors also eliminates the trivial solution introduced by structured sampling[5]. The last term is the sum of nuclear norms of the Casorati matrices $$$\mathbf{P_{o}}$$$ and $$$\mathbf{P_{e}}$$$, which facilitates in further spatial denoising high resolution MRSI data. We perform experiments on two datasets. The first dataset is a 13C hyperpolarized mouse kidney MRSI data, collected using a 9.4T small animal imaging scanner (Bruker BioSpin MRI GmbH, Germany)[6]. Axially oriented slice containing mouse kidney of 3 mm thickness was selected. EPSI data of matrix size 64×64 was collected using a bipolar gradient with 64 spectral points. Combination of odd and even echoes achieved a spectral bandwidth of 1562.5Hz. The second data was acquired from a volunteer on a GE MR750W 3T scanner at the University of Iowa using a 32-channel head coil. A press-box based EPSI acquisition scheme with flyback trajectory was used to collect a 64×64 sampled data with 8 averages for an axial slice of FOV=22×22×10cm3. The readout bandwidth is 600Hz and 256 spectral points was achieved using two interleaves. The scan time was about 8 mins and the residual water was removed in the post-processing stage. For Dataset 1, which had high signal only the annihilation relations are used by assigning $$$\lambda_{2}=0$$$ in eq(4). The pyruvate maps exhibit increased SNR as shown by the arrows in Fig. 2(f) whereas the spurious peak frame shows reduced intensity after reconstruction signifying removal of spurious peaks. The spectra in Fig.3 from three regions of the kidney (aorta, cortex & medulla) show complete removal of spurious peaks and also exhibits denoising. For dataset 2 we added the Casorati based denoising as the dataset had poor signal. The results(Fig.4) show increased Creatine and NAA signal where we can see the ventricles after reconstruction. The spurious peak frame shows removal of artifacts. The spectra(Fig.5) also exhibit improved SNR and is devoid of artifacts. We demonstrated a novel algorithm for denoising and deinterleaving of EPSI data without directly estimating phase or relying on theoretical k-space trajectory. The proposed scheme is highly beneficial for addressing this common problem for the MRSI community and especially useful for high field magnets. This work is supported by grants NIH 1R01EB019961-01A1 and ONR- N000141310202. The 13C Hyperolarized MRSI data used in the study was provided by Hansol Lee and Dong-Hyun Kim of Yonsei University College of Medicine, Seoul, Republicof Korea. 1 Stefan Posse, Gioacchino Tedeschi, Robert Risinger, Robert Ogg, and Denis Le Bihan, "High speed 1H spectroscopic imaging in human brain byecho planar spatial-spectral encoding," Magnetic resonance in medicine, vol. 33, no. 1, pp. 34–40, 1995. 2 Stefan Posse, Stephen R Dager, Todd L Richards, Chun Yuan, Robert Ogg, Alan A Artru, Hans-Wilhelm M¨uller-G¨artner, and Cecil Hayes, "In vivomeasurement of regional brain metabolic response to hyperventilation using magnetic resonance: proton echo planar spectroscopic imaging (pepsi),"Magnetic resonance in medicine, vol. 37, no. 6, pp. 858–865, 1997. 3 Arvind Balachandrasekaran, Vincent Magnotta, and Mathews Jacob, "Recovery of damped exponentials using structured low rank matrix completion,"arXiv preprint arXiv:1704.04511, 2017. 4 Petre Stoica and Randolph L Moses, Introduction to spectral analysis, vol. 1, Prentice hall Upper Saddle River, New Jersey, USA, 1997. 5 Rodrigo A Lobos, Tae Hyung Kim, W Scott Hoge, and Justin P Haldar, "Navigator-free epi ghost correction using low-rank matrix modeling:Theoretical insights and practical improvements," in Proc. ISMRM, 2017, p. 0449. 6 Hansol Lee, Jae E Song, Jaewook Shin, Eunhae Joe, Young-suk Choi, Ho-Taek Song, and Dong-Hyun Kim, "High resolution hyperpolarized 13cmrsi acquired by applying spice in mouse kidney," in Proc. ISMRM, 2017, p. 3698. Fig 1: Spectral interleaving using flyback EPSI: (a) For each excitation kx-t space is traversed simultaneously during readout time. This example shows kx dimension = 8. (b) By doubling the spatial resolution i.e. kx = 16, each interleave takes twice the time which results in half spectral bandwidth. Thus two interleaves are used (red and green) as on combining spectral bandwidth is preserved. Fig. 2: Metabolite maps for 13C Hyperpolarized MRSI experiments: (a) Reference image of mouse kidney with reference pixels marked in three regions. (b) & (c) Spurious peak (of pyruvate) frame for the uncorrected and reconstructed data respectively. After reconstruction reduced intensity implies removal of spurious peaks. (e) & (f) Pyruvate maps for uncorrected and reconstructed data respectively. The arrows show regions with increased signal intensity due to reconstruction. (d) Map showing percentage increase of signal intensity provided by proposed method compared to uncorrected data. Pixels showupto 70% increase. Fig. 3: Metabolite spectra for 13C Hyperpolarized MRSI experiments : First (a-c) and second (d-f) row show the spectra at aorta, renal cortex and renal medulla respectively (reference pixel location marked in Fig.2(a)) for the uncorrected data and the proposed method respectively. It can be observed that the reconstruction results in removal of spurious peaks. Also it improves the peak intensity of Pyruvate, especially in the renal cortex and renal medulla where the spurious peaks had high energy. Fig. 4: Metabolite maps for 1H in-vivo MRSI experiments: First (a-b) and second (d-e) row shows metabolite maps corresponding to NAA and Creatine for the uncorrected data and the proposed method respectively. For better visualization the image scale for the uncorrected data is 2 times higher than propsoed method for NAA and 4 times higher for Creatine. The proposed method clearly demonstrates denoising of highly noisy data while revealing high-resolution details like better visulaization of ventricles in the maps. (c) & (f) spurious peak frame (of water) for uncorrected and reconstructed data (on the same scale) shows complete removal of spurious peaks. Fig. 5: Metabolite spectra for 1H in-vivo MRSI experiments: First (a-c) row shows 3 pixels marked on the reference image (on left) for the uncorrected data. It can be observed it is highly noisy as it is a high-resolution EPSI dataset. The spurious peaks are marked by arrows. Second (d-f) row shows the same pixels from reconstructed data. The signal to noise ratio improves remarkably due to the 2 low-rank constraints and spurious peaks are removed.	CommonCrawl
The Health Risk Assessment of Essential Elemental Impurities (Cu, Mn and Zn) Through the Dermal Exposure of Herbal Ointment Extracted from Marjoram Herb (Majoranae herbae extractum) Kamil Jurowski ORCID: orcid.org/0000-0003-0310-28491, Maria Fołta2, Barbara Tatar2, Mehmet Berkoz3 & Mirosław Krośniak2 Biological Trace Element Research (2021)Cite this article Essential elements like Cu, Mn and Zn are extremely important for herbs' growth and physiological functions; however, from a toxicological point of view, the exposure of these elements (as essential elemental impurities) can exhibit potential harmful effects for patients. In Europe, very popular are ointments with Marjoram herb extract (Majoranae herbae extractum) as herbal medicinal products for adjunctively in rhinitis (runny nose). Based on posology of ointments with Marjoram herb extract, the exposure to these elemental impurities may be high during long-term use. Hence, the aim of this article is the health risk assessment of essential elemental impurities (Cu, Mn and Zn) through the dermal exposure of ointments with Marjoram herb extract (Majoranae herbae extractum) as herbal medicinal products applied adjunctively in rhinitis available in Polish pharmacies. The investigated essential elements were determined by well-validated methodology (R > 0.997, recoveries, LOD and LOQ values were acceptable) based on flame atomic absorption spectrometry (FAAS). Our results indicated that all analysed herbal medicinal products with Marjoram herb extract available in Polish pharmacies contain relatively low levels of essential element impurities, i.e. Cu (0.14–0.49 mg/kg), Mn (0.31–2.57 mg/kg) and Zn (0.73–3.19 mg/kg). The estimated exposure of the investigated elemental impurities confirms the safety of all products. To the best of our knowledge, the study about Cu, Mn and Zn contents in HMPs with Majoranae herbae extractum is described for the first time. The applied methodology and results are extremely important from regulatory toxicology point of view due to ICH Q3D elemental impurity guideline for pharmaceuticals. Origanum majorana L., herba (Marjoram) is an active pharmaceutical ingredient (API) in herbal medicinal products (HMPs)/phytotherapeutics used as a home remedy for adjunctively in rhinitis (runny nose). Usually, this kind of HMPs exists in semi-solid dosage forms for cutaneous use and are applied for relief of irritated skin around the nostrils [1]. The leaves of O. majorana L., herba has been traditionally used for the treatment of gastrointestinal disturbances, cough and bronchial diseases [2, 3]. However, the most important indication is rhinitis (runny nose). Based on posology, a small amount of the preparation should be spread around the nostrils, 2–4 times daily [1]. Hence, from toxicological point of view, there is a potential health risk related to dermal exposure. In this situation, potential health risks may be associated with elemental impurities (EIs). The appropriate control of EIs is currently required for quality assurance for the pharmaceutical industry. However, there is a lack of scientific original articles; there are only a few articles about this important issue [4,5,6,7]. Based on posology of ointments with Marjoram herb extract (Majoranae herbae extractum) mentioned earlier, exposure to EIs may be high during long-term use. From this point of view, essential EIs can be a very interesting problem and challenge. It is well-known that all herbs require essential elements for physiological functioning and growth [8]. It should be mentioned that essential elements cannot be synthesised by the plants itself; hence, uptake of these kind of elements is crucial [9]. These essential elements (especially Cu, Mn and Zn) are extremely important; however, from a toxicological point of view, the excess of these elements (as essential EIs) can exhibit potential harmful effects for patients [10]. For example, Cu has been recorded and shown to cause problems only under certain specific conditions, notably genetic disorders such as Wilson disease [5]. Additionally, the symptoms of Mn toxicity can result as manganism (a permanent neurological disorder) [5]. On the other hand, chronically high Zn intake can result in severe neurological diseases attributable to copper deficiency as the results of antagonism of both elements [5]. Hence, the aim of our work was the toxicological risk assessment of Cu, Mn and Zn as essential EIs in ointments with Marjoram herb extract (Majoranae herbae extractum) applied adjunctively in rhinitis. For this purpose, the levels of Cu, Mn and Zn in samples of HMPs available in Polish pharmacies were determined by atomic absorption spectrometry using flame atomisation (FAAS). To the best of our knowledge, the study about Cu, Mn and Zn contents in HMPs with Majoranae herbae extractum is described for the first time. All available in Poland (n = 5), ointments with Marjoram herb extract (Majoranae herbae extractum) as herbal medicinal products applied adjunctively in rhinitis (runny nose) were investigated. The choice of HMPs was justified by the fact that this kind of pharmaceutical products is very popular in Poland, especially among young children and seniors. It should be underlined that ointments with Marjoram herb extract are monocomponent herbal medicinal products; hence, there is exclusion of other sources of EIs. All traditional pharmaceutical products were collected from local pharmacies situated in the Lesser Poland Voivodeship (Kraków, Niepołomice, Bochnia, Wieliczka) in 2021. All the investigated samples were pharmaceutical product of individual manufacturers. To maintain the highest methodological standards, each sample was coded (A, B and so on). The short characteristics of the analysed samples was described in Table 1. Table 1 The short characterisation of investigated herbal medicinal products with Marjoram herb extract available in Polish pharmacies All applied reagents were of analytical grade. For the preparation of all solutions, demineralised water (Millipore) was applied. Ultrapure demineralised water had been obtained by Milli-Q water purification system (Millipore, Bedford, MA, USA). Concentrated nitric acid (HNO3, 65%) from Merck (SupraPur, Darmstadt, Germany) was applied. The purge gas was argon at purity 99.99%. The certified reference material (Corn Flour, INCT-CF-3) was purchased from the Institute of Nuclear Chemistry and Technology—Department of Analytical Chemistry (Warsaw, Poland). To minimise any potential impurities from other sources, all steps during the sampling procedure were carried out in plastic equipment. Laboratory glasswares (volumetric flasks, funnels etc.) were kept overnight in a 10% nitric acid (HNO3) solution and rinsed with deionised water and air dried before use. A CEM MDS-2000 microwave digestion system (CEM, Matthews, NC, USA) was applied for the digestion of ointments. All measurements for the determination of Cu, Mn and Zn were carried out using a Perkin-Elmer 5100 ZL spectrometer (Perkin-Elmer, Norwalk, CT, USA; FAAS). Cu, Mn and Zn hollow cathode lamps were used as the emission sources. Argon (99.999%) was applied as a purge gas. Background corrections were performed by Zeeman background correction. Further information about instrumentation and detailed parameters are described in Supplementary Material 1. Sample Preparations Before element determination, each ointment was homogenised. Because most of the ointments had an aluminium lid which could be a potential source of EIs, the first few centimetres of each ointment from the tube was discarded. Of each sample, 0.3 g was weighed, poured into Teflon vessels and digested with 5.0 mL of concentrated nitric acid (HNO3, 63%). The closed vessels were microwaved after 2 h. The detailed information about digestion procedure are described briefly in Supplementary Material 1. The samples were later cooled at room temperature (25 °C), and the final volume was made to 20 mL. The cooled samples were stored in plastic bottles as stock sample solutions until analysis. This methodology is based on our previously published articles [5, 11]. Five replications were kept and done for all samples to increase the precision of the result. The Essential Elemental Impurity Determination and Toxicological Risk Assessment Procedure All elemental impurities were determined in the digested ointment samples using FAAS (described earlier). All instrumentation and detailed parameters for this step are described briefly in Supplementary Material 1. The overview of our toxicological risk assessment has been schematically shown in Fig. 1. The summary of all health risk assessment steps applied in studies Analytical Calibration and Quality Control Approaches In all situations, very good linearity with good correlation coefficients (0.998 for Cu, 0.997 for Mn and 0.999 for Zn) were observed. The values of the correlation coefficients confirm the linearity of the AAS instrument for precision and accuracy of results. Five replications were performed for each sample. Additionally, the quality control and validation of applied methodology are confirmed by previously described studies using the same methodology and apparatus [5, 11]. The synthetic summary of analytical calibration parameters and quality control results are shown in Supplementary Material 1. The results of five independent replicates were expressed as the mean ± standard deviation. Additionally, the descriptive statistics were made (minimum, maximum, mean, skewness and kurtosis) using Origin 2021 Pro licenced by the Jagiellonian University in Krakow. All plots were made using Origin 2021 Pro licenced by the Jagiellonian University in Krakow. The Elemental Impurity Profiles of Cu, Mn and Zn in Ointments with Marjoram Herb Extract The elemental impurity profiles of analysed samples (n = 5; A–E) are presented in Fig. 2, as the graph for each element (mg/kg) determined in analysed HMPs available in Polish pharmacies. Additionally, the boxplot showing ranges of levels and violin plot showing log2 levels of all investigated elements are shown in Fig. 3A and B, respectively. The descriptive statistics of Cu, Mn and Zn contents in all samples is briefly described in Table 2. The elemental impurity profile for Cu, Mn and Zn in investigated herbal medicinal products with Marjoram herb extract (A, B, C, D and E) Concentrations of essential elemental impurities (Cu, Mn and Zn) in all investigated herbal medicinal products with Marjoram herb extract (A, B, C, D and E): A The boxplot (linear scale). B The violin plot showing log2 (logarithmic scale) values of concentration Table 2 The descriptive statistics of Cu, Mn and Zn levels in investigated herbal medicinal products with Marjoram herb extract available in Polish pharmacies In general, all investigated elemental impurities were present in all analysed samples below 3.5 mg/kg (in the range of 0.0142 to 3.19 mg/L). The level of copper is extremely lower than other metals. The violin plot (Fig. 3B) showing log2 (concentration) values of indicate that level of copper is similar in all investigated samples (in the range of 0.0142 to 0.0492 mg/kg). On the other hand, the Mn level was different (in the range of 0.309 to 2.579 mg/kg; Fig. 3A). Additionally, the Zn level was also different (in the range of 0.363 to 3.19 mg/kg; Fig. 3A). The descriptive analysis of the overall content (Table 2) shows that Cu levels (mean = 0.032 mg/kg) were approximately 31 times lower than Mn levels (mean = 1.0029 mg/kg), and Cu content was approximately 40 times lower than Zn levels (mean = 1.283 mg/kg). Additionally, the levels of Mn and Zn were quite similar. The values of skewness and kurtosis confirm the distribution of results and their consistency. Individual analysis of the content shows the lowest level of copper was in sample B (0.0142 ± 0.007 mg/kg) and the highest level was in sample C (approximately 0.0492 ± 0.006 mg/kg). The lowest level of manganese was in sample C (0.309 ± 0.06 mg/kg), and the highest content was in sample A (2.57 ± 0.06 mg/kg). Finally, the lowest level of Zn was in sample E (0.363 ± 0.07 mg/L), and the highest level was in sample A (3.19 ± 0.09 mg/L). Considering the levels of limits for Cu in pharmaceutical products via oral route recommended by ICH Q3D guideline (30.0 μg/g [12, 13]), all of the investigated herbal medicinal products with Marjoram herb extract meet the requirements in the guideline. Hence, our results confirm the safety of Cu contents in all samples. On the other hand, manganese and zinc are classified by ICH Q3D guideline as other metals, i.e. 'elemental impurities for which PDEs have not been established due to their low inherent toxicity and/or differences in regional regulations which are not addressed in this guideline' [12, 13]. Therefore, required sources of information about the acceptable levels of these elemental impurities should be other guidelines and/or reginal documents like regulations. However, based on literature review, there is a lack of guidelines and/or regional regulations or other related documents about copper and manganese impurities in pharmaceuticals. Therefore, it is not possible to compare obtained values with any existing regulatory documents. Based on scientific literature review, only Sazakli et al. [14] described Mn levels in O. majorana, L. leaves (46.48–77.32 µg/g); however, we analysed the final pharmaceutical product (diluted); hence, it is not possible to compare our results with these values. Notwithstanding, it can be summarised that the contents of all impurities are at a very low level (< 3.5 mg/kg). Estimation of Exposure of Elemental Impurities (Cu, Mn and Zn) in Ointments with Marjoram Herb Extract Available in Polish Pharmacies Appropriate toxicological risk assessment of the investigated essential elemental impurities in this kind of pharmaceuticals should include two steps (Fig. 1): Estimation of single exposure (single dose) (µg/kg) Estimation of daily exposure (µg/day) and comparison with cutaneous permitted daily exposure (μg/day) The required information in this situation is the actual level in the single dose of the product (approximately 0.25 g). The estimated levels of copper, manganese and zinc in the one-time administration of applied ointments are presented in Table 3. Table 3 The levels of Cu, Mn and Zn in analysed samples (ointment, ng/0.25 g) including single dose This step of calculation is necessary for the next step of toxicological risk assessment, i.e. the daily dermal exposure of investigated elements (the maximum daily dose of applied pharmaceuticals). For this purpose, the data about frequency of use is required. Based on information in the leaflet for each ointment and information from assessment report on O. majorana L. from EMA [1], small amount of the ointment should be spread around the nostrils, two to four times daily. Based on this information, the estimated daily exposures to Cu, Mn and Zn through applied ointments were calculated considering the maximum use during the day (Table 4). Table 4 The estimated daily exposure of investigated elemental impurities in analysed ointment (ng/day) Table 4 shows that the estimated exposure of Cu levels in five samples is quite similar (14.20–40.20 ng/day). Also, the estimated exposure for Zn is similar (1623.38–2579.69 ng/day). On the other hand, exposure to Mn has been estimated to be variable for these samples (661.10–2570.59 ng/day). The appropriate toxicological risk assessment is based on comparison of the obtained results with the cutaneous PDE. For this purpose, the generic and conservative approach has been applied for elemental impurities by ICH Q3D. This approach is based on a systematic adjustment of the parenteral PDE, which assumed 100% bioavailability, to derive a cutaneous permitted daily exposure by using a cutaneous modifying factor (in most cases, intact/irritated skin 10; 100%/10% = 10) (Eq. 1) [13]: $$\mathrm{CPDE}=\mathrm{Parenteral PDE}\times \mathrm{CMF}$$ CPDE is the cutaneous permitted daily exposure. Parenteral PDE is the parenteral permitted daily exposure. CMF is the cutaneous modifying factor. Hence, the calculations of CPDE are only possible for copper (manganese and zinc are classified by ICH Q3D guideline as other metals, see earlier section) (Table 5). Table 5 The calculations of cutaneous permitted daily exposure (CPDE) for copper impurities Acronyms: PDE, permitted daily exposure; CMF, cutaneous modifying factor; CPDE, cutaneous permitted daily exposure. The applied toxicological risk assessment approach confirms that the estimated dermal Cu daily exposure (μg/day) is below the CPDE value for this element (< 3000 μg/day) in all investigated herbal-based pharmaceutical products. Hence, the applied toxicological risk assessment confirms safety of investigated herbal medicinal product with Marjoram herb extract due to estimated daily exposure of this element. To the best of our knowledge, the study about Cu, Mn and Zn contents in herbal medicinal products with Majoranae herbae extractum is described for the first time. The contents of Cu, Mn and Zn as impurities in all ointments with Marjoram herb extract (Majoranae herbae extractum) available in Polish pharmacies are at a very low level (< 3.5 mg/kg). The toxicological risk assessment approach confirms that the estimated dermal daily exposure of investigated metals is very low. The estimated dermal daily exposure for Cu in comparison to the CPDE in all products is far below established the EMA requirements. It is not possible to obtain CPDE values for Mn and Zn, but based on estimated daily exposures (< 3.0 µg/day), this exposure is very low. Hence, the obtained results are in accordance with the standards of ICH Q3D guideline. It can be concluded that all analysed products with Marjoram herb extract do not represent a health hazard to the patients. The advantages of our research are the (1) practical methodology and (2) relevance of the obtained results from regulatory toxicology point of view (ICH Q3D elemental impurities guideline for pharmaceutical industry). The disadvantage is the applied technique (FAAS) which is slower and more demanding in comparison to ICP-MS. Based on the review of scientific literature, it would be important to carry out a broader toxicological risk assessment including other important metallic impurities and different herbal medicinal products [6, 15,16,17,18,19,20]. All data generated or analysed during this study are included in this published article and its Supplementary Information file. Educational Analysis Set SAS® 9 licenced by the Jagiellonian University in Krakow and Origin 2021 Pro licenced by the Jagiellonian University in Krakow. 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Reg Tox Phar. https://doi.org/10.1016/j.yrtph.2021.104945 (Online ahead of print) Jurowski K, Fołta M, Tatar B, Berkoz M, Krośniak M (2021) The toxicological risk assessment of dermal exposure of patients exposed to nickel and chromium due to application of ointments with Marjoram herb extract (Majoranae herbae extractum) available in Polish pharmacies. Biol Trace Elem Res. (Accepted manuscript) Institute of Medical Studies, Medical College, Rzeszów University, Aleja Majora Wacława Kopisto 2a, 35-959, Rzeszów, Poland Kamil Jurowski Department of Food Chemistry and Nutrition, Medical College, Jagiellonian University, Medyczna 9, 30-688, Kraków, Poland Maria Fołta, Barbara Tatar & Mirosław Krośniak Department of Biochemistry, Faculty of Pharmacy, Van Yuzuncu Yil University, 65080, Van, Turkey Mehmet Berkoz Maria Fołta Barbara Tatar Mirosław Krośniak KJ and MK wrote the manuscript; they took an active part in experimental research. MB checked the manuscript and made statistical adjustments. BT and MF determined the elements. Correspondence to Kamil Jurowski. All authors confirm ethical responsibilities. Not applicable. Our research includes available pharmaceuticals in Polish pharmacies. The authors declare no competing interests. Below is the link to the electronic supplementary material. Supplementary file1 (DOCX 21 kb) Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Jurowski, K., Fołta, M., Tatar, B. et al. The Health Risk Assessment of Essential Elemental Impurities (Cu, Mn and Zn) Through the Dermal Exposure of Herbal Ointment Extracted from Marjoram Herb (Majoranae herbae extractum). Biol Trace Elem Res (2021). https://doi.org/10.1007/s12011-021-02842-8 Marjoram herb extract Essential elemental impurities	CommonCrawl
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Tree parts (leaves, twigs) naturally falling into neighbor's yard Jokes about Monica's haircut more hot questions question feed about us tour help blog chat data legal privacy policy work here advertising The indices produced by an M {\displaystyle M} -level quantizer can be coded using a fixed-length code using R = ⌈ log 2 ⁡ M ⌉ {\displaystyle R=\lceil \log _{2}M\rceil } The additive noise model for quantization error[edit] A common assumption for the analysis of quantization error is that it affects a signal processing system in a similar manner to that of Generated Tue, 25 Oct 2016 02:42:45 GMT by s_wx1087 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.10/ Connection When the ramp starts, a timer starts counting. The value of the measured signal is Vm = Vs - e, where Vm is the measured value, Vs is the actual value, and e is the error. This line is often a best-fit line among the points in the plot but can also be a line that connects the highest and lowest data points, or endpoints. Digital signal processing[edit] People must use ADCs to process, store, or transport virtually any analog signal in digital form. maxim-ic.com (July 17, 2002). ^ "Jitter effects on Analog to Digital and Digital to Analog Converters" (PDF). The additive noise created by 6-bit quantization is 12 dB greater than the noise created by 8-bit quantization. Jay (1967), Modern Communication Principles, McGraw–Hill, ISBN978-0-07-061003-3 External links[edit] Quantization noise in Digital Computation, Signal Processing, and Control, Bernard Widrow and István Kollár, 2007. Electrical symbol[edit] Testing[edit] Testing an Analog to Digital Converter requires an analog input source and hardware to send control signals and capture digital data output. Note that dither can only increase the resolution of a sampler, it cannot improve the linearity, and thus accuracy does not necessarily improve. A quantizer designed for this purpose may be quite different and more elaborate in design than an ordinary rounding operation. Due to the complexity and the need for precisely matched components, all but the most specialized ADCs are implemented as integrated circuits (ICs). Generated Tue, 25 Oct 2016 02:42:45 GMT by s_wx1087 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.9/ Connection Dithering is also used in integrating systems such as electricity meters. doi:10.1109/49.761034. In the rounding case, the quantization error has a mean of zero and the RMS value is the standard deviation of this distribution, given by 1 12 L S B This can be observed as uneven spacing of the code "steps" or transition boundaries on the ADC's transfer-function plot. Such a plot is not continuous but is a plot of 2N codes, where N is the ADC's resolution in bits. The minimum change in voltage required to guarantee a change in the output code level is called the least significant bit (LSB) voltage. Norsworthy, Steven R.; Schreier, Richard; Temes, Gabor C. (1997). R. Sorry for my bad english, it isnt my native language. Kester, Walt, ed. (2005). It is therefore required to define the rate at which new digital values are sampled from the analog signal. The difference between the ideal voltage levels at which code transitions occur and the actual voltage is the INL error, expressed in LSBs. Your cache administrator is webmaster. An important consideration is the number of bits used for each codeword, denoted here by l e n g t h ( c k ) {\displaystyle \mathrm {length} (c_{k})} . Modestino, "Optimum Quantizer Performance for a Class of Non-Gaussian Memoryless Sources", IEEE Transactions on Information Theory, Vol. An ADC is defined by its bandwidth and its signal-to-noise ratio. The sliding scale principle uses an averaging effect to overcome this phenomenon. Focal Press. Dynamic performance An ADC's dynamic performance is specified using parameters obtained via frequency-domain analysis and is typically measured by performing a fast Fourier transform (FFT) on the output codes of the Berklee Press. ^ William Fleetwood Sheppard, "On the Calculation of the Most Probable Values of Frequency Constants for data arranged according to Equidistant Divisions of a Scale", Proceedings of the London The voltage resolution of an ADC is equal to its overall voltage measurement range divided by the number of intervals: Q = E F S R 2 M − 1 , Since the values are added together, the dithering produces results that are more exact than the LSB of the analog-to-digital converter. This negative feedback has the effect of noise shaping the error due to the Flash so that it does not appear in the desired signal frequencies. Bennett, "Spectra of Quantized Signals", Bell System Technical Journal, Vol. 27, pp. 446–472, July 1948. ^ a b B. For continuous capture of the signal, the frontend also divides the signal into multiple segments in addition to time-stretching. Comparison of quantizing a sinusoid to 64 levels (6 bits) and 256 levels (8 bits). Digital storage oscilloscopes need very fast analog-to-digital converters, also crucial for software defined radio and their new applications. For example, an ADC with a resolution of 8 bits can encode an analog input to one in 256 different levels, since 28=256. Both full-scale and gain errors are commonly used by ADC manufacturers. Full-scale error accounts for both gain and offset deviation from the ideal transfer function. Figure 2: 3-bit ADC transfer function with - 1/2 LSB offset The transfer function can be implemented with an offset of - 1/2 LSB, as shown in Figure 2. It's these deviations from the perfect transfer function that define the DC accuracy and are characterized by the specifications in a data sheet. You have a total 8 of quantizaton steps which would map to [-1 -.75 -.5 -25 0 .25 .5 .75]. Boca Raton, FL: CRC Press. The result is a sequence of digital values that have been converted from a continuous-time and continuous-amplitude analog signal to a discrete-time and discrete-amplitude digital signal. Iterative optimization approaches can be used to find solutions in other cases.[8][19][20] Note that the reconstruction values { y k } k = 1 M {\displaystyle \{y_{k}\}_{k=1}^{M}} affect only the distortion Retrieved 2016-10-18. ^ Lathi, B.P. (1998). Scientific instruments[edit] Digital imaging systems commonly use analog-to-digital converters in digitizing pixels. The Art of Digital Audio 3rd Edition. For this reason, such a quantizer has sometimes been called an 8-bit quantizer. Figure 7: Integral nonlinearity error Because nonlinearity in measurement will cause distortion, INL will also affect the dynamic performance of an ADC. Time-interleaved[edit] A time-interleaved ADC uses M parallel ADCs where each ADC samples data every M:th cycle of the effective sample clock. Lost password? For any ADC the mapping from input voltage to digital output value is not exactly a floor or ceiling function as it should be. How does a jet's throttle actually work? IT-6, pp. 7–12, March 1960. IEEE Transactions on Instrumentation and Measurement. 55 (1): 415–427. Though a typical number is not a guarantee, it should give the designer an idea of how the ADC will perform, since these numbers are generally derived from the manufacturer's characterization Staller has a bachelor's degree in electrical engineering from The University of Texas at Austin. W. (1974). Ind., Vol. 79, pp. 555–568, Jan. 1961. ^ Daniel Marco and David L. quantisation error pdf Gray and David L. Your cache administrator is webmaster. In order to make the quantization error independent of the input signal, noise with an amplitude of 2 least significant bits is added to the signal. However, it is common to assume that for many sources, the slope of a quantizer SQNR function can be approximated as 6dB/bit when operating at a sufficiently high bit rate. For example, vector quantization is the application of quantization to multi-dimensional (vector-valued) input ... quantisation error in adc Around the quantum limit, the distinction between analog and digital quantities vanishes.[citation needed] See also[edit] Analog-to-digital converter Beta encoder Data binning Discretization Discretization error Posterization Pulse code modulation Quantile Regression dilution Adapted from Franz, David (2004). Also see noise shaping.) For complex signals in high-resolution ADCs this is an accurate model. This slightly reduces signal to noise ratio, but, ideally, completely eliminates the disto... quantisation error How do I find out if there is an Esperanto club in my city? Sorry for my bad english, it isnt my native language. It is defined as: $$Q = \dfrac {\Delta x}{2^{N+1}}$$ where $N$ is the number of bits used for quantization in a analog to digital conversion, and $\Delta x$ is, in portuguese The use of this approximation can allow the entropy coding design problem to be separated from the design of the quantizer itself. For an otherwise-uniform quantizer, the dead-zone width can be set to ... quantisation error in pcm This results in affecting the peak-to-peak amplitude of sq(t) shown as Aq and has a value of (M-1)L.As shown in the figure, when the signal being quantized i.e. A device or algorithmic function that performs quantization is called a quantizer. ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.6/ Connection to 0.0.0.6 failed. For a fixed-length code using N {\displaystyle N} bits, M = 2 N {\displaystyle M=2^{N}} , ...	CommonCrawl
Diagram-chasing Posted 2020-09-27 Updated 2021-10-06 Algebra / Homological Algebra A long exact sequence of cohomology groups (zig-zag and diagram-chasing) Exterior differentiation (This section is intended to introduce the background. Feel free to skip if you already know exterior differentiation.) There are several useful tools for vector calculus on $\mathbb{R}^3,$ namely gradient, curl, and divergence. It is possible to treat the gradient of a differentiable function $f$ on $\mathbb{R}^3$ at a point $x_0$ as the Fréchet derivative at $x_0$. But it does not work for curl and divergence at all. Fortunately there is another abstraction that works for all of them. It comes from differential forms. Let $x_1,\cdots,x_n$ be the linear coordinates on $\mathbb{R}^n$ as usual. We define an algebra $\Omega^{\ast}$ over $\mathbb{R}$ generated by $dx_1,\cdots,dx_n$ with the following relations: \[ \begin{cases} dx_idx_i=0 \\ dx_idx_j = -dx_jdx_i \quad i \neq j \end{cases} \] This is a vector space as well, and it's easy to derive that it has a basis by \[ 1,dx_i,dx_idx_j,dx_idx_jdx_k,\cdots,dx_1\dots dx_n \] where $i<j<k$. The $C^{\infty}$ differential forms on $\mathbb{R}^n$ are defined to be the tensor product \[ \Omega^(\mathbb{R}^n)=\{C^{\infty}\text{ functions on }\mathbb{R}^n\} \otimes_\mathbb{R}\Omega^. \] As is can be shown, for $\omega \in \Omega^{\ast}(\mathbb{R}^n)$, we have a unique representation by \[ \omega=\sum f_{i_1\cdots i_k}dx_{i_1}\dots dx_{i_k}, \] and in this case we also say $\omega$ is a $C^{\infty}$ $k$-form on $\mathbb{R}^n$ (for simplicity we also write $\omega=\sum f_Idx_I$). The algebra of all $k$-forms will be denoted by $\Omega^k(\mathbb{R}^n)$. And naturally we have $\Omega^{\ast}(\mathbb{R}^n)$ to be graded since \[ \Omega^{}(\mathbb{R}^n)=\bigoplus_{k=0}^{n}\Omega^k(\mathbb{R}^n). \] The operator $d$ But if we have $\omega \in \Omega^0(\mathbb{R}^n)$, we see $\omega$ is merely a $C^{\infty}$ function. As taught in multivariable calculus course, for the differential of $\omega$ we have \[ d\omega=\sum_{i}\partial\omega/\partial x_idx_i \] and it turns out that $d\omega\in\Omega^{1}(\mathbb{R}^n)$. This inspires us to obtain a generalization onto the differential operator $d$: \[ \begin{aligned} d:\Omega^{k}(\mathbb{R}^n) &\to \Omega^{k+1}(\mathbb{R}^n) \\ \omega &\mapsto d\omega \end{aligned} \] and $d\omega$ is defined as follows. The case when $k=0$ is defined as usual (just the one above). For $k>0$ and $\omega=\sum f_I dx_I,$ $d\omega$ is defined 'inductively' by \[ d\omega=\sum df_I dx_I. \] This $d$ is the so-called exterior differentiation, which serves as the ultimate abstract extension of gradient, curl, divergence, etc. If we restrict ourself to $\mathbb{R}^3$, we see these vector calculus tools comes up in the nature of things. Functions \[ df=\frac{\partial f}{\partial x}dx+\frac{\partial f}{\partial y}dy+\frac{\partial f}{\partial z}dz. \] $1$-forms \[ d(f_1dx+f_2dy+f_3dz)=\left(\frac{\partial f_3}{\partial y}-\frac{\partial f_2}{\partial z}\right)dydz-\left(\frac{\partial f_1}{\partial z}-\frac{\partial f_3}{\partial x}\right)dxdz+\left(\frac{\partial f_2}{\partial x}-\frac{\partial f_1}{\partial y}\right)dxdy. \] $2$-forms \[ d(f_1dydz-f_2dxdz+f_3dxdy)=\left(\frac{\partial f_1}{\partial x}+\frac{\partial f_2}{\partial y}+ \frac{\partial f_3}{\partial z}\right)dxdydz. \] The calculation is tedious but a nice exercise to understand the definition of $d$ and $\Omega^{\ast}$. Conservative field - on the kernel and image of $d$ By elementary computation we are also able to show that $d^2\omega=0$ for all $\omega \in \Omega^{\ast}(\mathbb{R}^n)$ (Hint: $\frac{\partial^2 f}{\partial x_i \partial x_j}=\frac{\partial^2 f}{\partial x_j \partial x_i}$ but $dx_idx_j=-dx_idx_j$). Now we consider a vector field $\overrightarrow{v}=(v_1,v_2)$ of dimension $2$. If $C$ is an arbitrary simply closed smooth curve in $\mathbb{R}^2$, then we expect \[ \oint_C\overrightarrow{v}d\overrightarrow{r}=\oint_C v_1dx+v_2dy \] to be $0$. If this happens (note the arbitrary of $C$), we say $\overrightarrow{v}$ to be a conservative field (path independent). So when conservative? It happens when there is a function $f$ such that \[ \nabla f=\overrightarrow{v}=(v_1,v_2)=(\partial{f}/\partial{x},\partial{f}/\partial{y}). \] This is equivalent to say that \[ df=v_1dx+v_2dy. \] If we use $C^{\ast}$ to denote the area enclosed by $C$, by Green's theorem, we have \[ \begin{aligned} \oint_C v_1dx+v_2dy&=\iint_{C^}\left(\frac{\partial{v_2}}{\partial{x}}-\frac{\partial{v_1}}{\partial{y}}\right)dxdy \\ &=\iint_{C^}d(v_1dx+v_2dy) \\ &=\iint_{C^}d^2f \\ &=0 \end{aligned} \] If you translate what you've learned in multivariable calculus course (path independence) into the language of differential form, you will see that the set of all conservative fields is precisely the image of $d_0:\Omega^0(\mathbb{R}^2) \to \Omega^1(\mathbb{R}^2)$. Also, they are in the kernel of the next $d_1:\Omega^1(\mathbb{R}^2) \to \Omega^2(\mathbb{R}^2)$. These $d$'s are naturally homomorphism, so it's natural to discuss the factor group. But before that, we need some terminologies. de Rham complex and de Rham cohomology group The complex $\Omega^{\ast}(\mathbb{R}^n)$ together with $d$ is called the de Rham complex on $\mathbb{R}^n$. Now consider the sequence \[ \Omega^0(\mathbb{R}^n)\xrightarrow{d_0}\Omega^1(\mathbb{R}^n)\xrightarrow{d_1}\cdots\xrightarrow{d_{n-2}}\Omega^{n-1}(\mathbb{R}^n)\xrightarrow{d_{n-1}}\Omega^{n}(\mathbb{R^n}). \] We say $\omega \in \Omega^k(\mathbb{R}^n)$ is closed if $d_k\omega=0$, or equivalently, $\omega \in \ker d_k$. Dually, we say $\omega$ is exact if there exists some $\mu \in \Omega^{k-1}(\mathbb{R}^n)$ such that $d\mu=\omega$, that is, $\omega \in \operatorname{im}d_{k-1}$. Of course all $d_k$'s can be written as $d$ but the index makes it easier to understand. Instead of doing integration or differentiation, which is 'uninteresting', we are going to discuss the abstract structure of it. The $k$-th de Rham cohomology in $\mathbb{R}^n$ is defined to be the factor space \[ H_{DR}^{k}(\mathbb{R}^n)=\frac{\ker d_k}{\operatorname{im} d_{k-1}}. \] As an example, note that by the fundamental theorem of calculus, every $1$-form is exact, therefore $H_{DR}^1(\mathbb{R})=0$. Since de Rham complex is a special case of differential complex, and other restrictions of de Rham complex plays no critical role thereafter, we are going discuss the algebraic structure of differential complex directly. The long exact sequence of cohomology groups We are going to show that, there exists a long exact sequence of cohomology groups after a short exact sequence is defined. For the convenience let's recall here some basic definitions Exact sequence A sequence of vector spaces (or groups) \[ \cdots \rightarrow G_{k-1} \xrightarrow{f_{k-1}} G_k \xrightarrow{f_k} G_{k+1} \xrightarrow{f_{k+1}}\cdots \] is said to be exact if the image of $f_{k-1}$ is the kernel of $f_k$ for all $k$. Sometimes we need to discuss a extremely short one by \[ 0 \rightarrow A \xrightarrow{f} B \xrightarrow{g} C \rightarrow 0. \] As one can see, $f$ is injective and $g$ is surjective. Differential complex A direct sum of vector spaces $C=\oplus_{k \in \mathbb{Z}}C^k$ is called a differential complex if there are homomorphisms by \[ \cdots \rightarrow C^{k-1} \xrightarrow{d_{k-1}} C^k \xrightarrow{d_k} C^{k+1} \xrightarrow{d_{k+1}}\cdots \] such that $d_{k-1}d_k=0$. Sometimes we write $d$ instead of $d_{k}$ since this differential operator of $C$ is universal. Therefore we may also say that $d^2=0$. The cohomology of $C$ is the direct sum of vector spaces $H(C)=_{k }H^k(C) $ where \[ H^k(C)=\frac{\ker d_{k}}{\operatorname{im}d_{k-1}}. \] A map $f: A \to B$ where $A$ and $B$ are differential complexes, is called a chain map if we have $fd_A=d_Bf$. Now consider a short exact sequence of differential complexes \[ 0 \rightarrow A \xrightarrow{f} B \xrightarrow{g} C \rightarrow 0 \] where both $f$ and $g$ are chain maps (this is important). Then there exists a long exact sequence by \[ \cdots\rightarrow H^q(A) \xrightarrow{f^} H^{q}(B) \xrightarrow{g^} H^q(C)\xrightarrow{d^{}}H^{q+1}(A) \xrightarrow{f^}\cdots. \] Here, $f^{\ast}$ and $g^{\ast}$ are the naturally induced maps. For $c \in C^q$, $d^{\ast}[c]$ is defined to be the cohomology class $[a]$ where $a \in A^{q+1}$, and that $f(a)=db$, and that $g(b)=c$. The sequence can be described using the two-layer commutative diagram below. layer-000001 The long exact sequence is actually the purple one (you see why people may call this zig-zag lemma). This sequence is 'based on' the blue diagram, which can be considered naturally as an expansion of the short exact sequence. The method that will be used in the following proof is called diagram-chasing, whose importance has already been described by Professor James Munkres: master this. We will be abusing the properties of almost every homomorphism and group appeared in this commutative diagram to trace the elements. First, we give a precise definition of $d^{\ast}$. For a closed $c \in C^q$, by the surjectivity of $g$ (note this sequence is exact), there exists some $b \in B^q$ such that $g(b)=c$. But $g(db)=d(g(b))=dc=0$, we see for $db \in B^{q+1}$ we have $db \in \ker g$. By the exactness of the sequence, we see $db \in \operatorname{im}{f}$, that is, there exists some $a \in A^{q+1}$ such that $f(a)=db$. Further, $a$ is closed since \[ f(da)=d(f(a))=d^2b=0 \] and we already know that $f$ has trivial kernel (which contains $da$). $d^{\ast}$ is therefore defined by \[ d^[c]=[a], \] where $[\cdot]$ means "the homology class of". But it is expected that $d^{\ast}$ is a well-defined homomorphism. Let $c_q$ and $c_q'$ be two closed forms in $C^q$. To show $d^{\ast}$ is well-defined, we suppose $[c_q]=[c_q']$ (i.e. they are homologous). Choose $b_q$ and $b_q'$ so that $g(b_q)=c_q$ and $g(b_q')=c_q'$. Accordingly, we also pick $a_{q+1}$ and $a_{q+1}'$ such that $f(a_{q+1})=db_q$ and $f(a_{q+1}')=db_q'$. By definition of $d^{\ast}$, we need to show that $[a_{q+1}]=[a_{q+1}']$. Recall the properties of factor group. $[c_q]=[c_q']$ if and only if $c_q-c_q' \in \operatorname{im}d$. Therefore we can pick some $c_{q-1} \in C^{q-1}$ such that $c_q-c_q'=dc_{q-1}$. Again, by the surjectivity of $g$, there is some $b_{q-1}$ such that $g(b_{q-1})=c_{q-1}$. Note that \[ \begin{aligned} g(b_q-b_q'-db_{q-1})&=c_q-c_{q}'-g(db_{q-1}) \\ &=dc_{q-1}-d(g(b_{q-1})) \\ &=dc_{q-1}-dc_{q-1} \\ &= 0. \end{aligned} \] Therefore $b_q-b_q'-db_{q-1} \in \operatorname{im} f$. We are able to pick some $a_q \in A^{q}$ such that $f(a_q)=b_q-b_q'-db_{q-1}$. But now we have \[ \begin{aligned} f(da_q)=df(a_q)&=d(b_q-b_q'-db_{q-1}) \\ &=db_q-db_q'-d^2b_{q-1} \\ &=db_q-db_q' \\ &=f(a_{q+1}-a_{q+1}'). \end{aligned} \] Since $f$ is injective, we have $da_q=a_{q+1}-a_{q+1}'$, which implies that $a_{q+1}-a_{q+1}' \in \operatorname{im}d$. Hence $[a_{q+1}]=[a_{q+1}']$. To show that $d^{\ast}$ is a homomorphism, note that $g(b_q+b_q')=c_q+c_q'$ and $f(a_{q+1}+a_{q+1}')=d(b_q+b_q')$. Thus we have \[ d^[c_q+c_q']=[a_{q+1}+a_{q+1}']. \] The latter equals $[a_{q+1}]+[a_{q+1}']$ since the canonical map is a homomorphism. Therefore we have \[ d^[c_q+c_q']=d^[c_q]+d^[c_q']. \] Therefore the long sequence exists. It remains to prove exactness. Firstly we need to prove exactness at $H^q(B)$. Pick $[b] \in H^q(B)$. If there is some $a \in A^q$ such that $f(a)=b$, then $g(f(a))=0$. Therefore $g^{\ast}[b]=g^{\ast}[f(a)]=[g(f(a))]=[0]$; hence $\operatorname{im}f \subset \ker g$. Conversely, suppose now $g^{\ast}[b]=[0]$, we shall show that there exists some $[a] \in H^q(A)$ such that $f^{\ast}[a]=[b]$. Note $g^{\ast}[b]=\operatorname{im}d$ where $d$ is the differential operator of $C$ (why?). Therefore there exists some $c_{q-1} \in C^{q-1}$ such that $g(b)=dc_{q-1}$. Pick some $b_{q-1}$ such that $g(b_{q-1})=c_{q-1}$. Then we have \[ g(b-db_{q-1})=g(b)-d(g(b_{q-1}))=g(b)-dc_{q-1}=0. \] Therefore $f(a)=b-db_{q-1}$ for some $a \in A^q$. Note $a$ is closed since \[ f(da)=df(a)=d(b-db_{q-1})=db-d^2b_{q-1}=db=0 \] and $f$ is injective. $db=0$ since we have \[ g(db)=d(g(b))=d(dc_{q-1})=0. \] Furthermore, \[ f^[a]=[f(a)]=[b-dc_{q-1}]=[b]-[0]=[b]. \] Therefore $\ker g^{\ast} \subset \operatorname{im} f$ as desired. Now we prove exactness at $H^q(C)$. (Notation:) pick $[c_q] \in H^q(C)$, there exists some $b_q$ such that $g(b_q)=c_q$; choose $a_{q+1}$ such that $f(a_{q+1})=db_q$. Then $d^{\ast}[c_q]=[a_{q+1}]$ by definition. If $[c_q] \in \operatorname{im}g^{\ast}$, we see $[c_q]=[g(b_q)]=g^{\ast}[b_q]$. But $b_q$ is closed since $[b_q] \in H^q(B)$, we see $f(a_{q+1})=db_q=0$, therefore $d^{\ast}[c_q]=[a_{q+1}]=[0]$ since $f$ is injective. Therefore $\operatorname{im}g^{\ast} \subset \ker d^{\ast}$. Conversely, suppose $d^{\ast}[c^q]=[0]$. By definition of $H^{q+1}(A)$, there is some $a_q \in A$ such that $da_q = a_{q+1}$ (can you see why?). We claim that $b_q-f(a_q)$ is closed and we have $[c_q]=g^{\ast}[b_q-f(a_q)]$. By direct computation, \[ d(b_q-f(a_q))=db_q-d(f(a_q))=db_q-f(d(a_q))=db_q-f(a_{q+1})=0. \] Meanwhile \[ g^[b_q-f(a_q)]=[g(b_q)]-[g(f(a_q))]=[c_q]. \] Therefore $\ker d^{\ast} \subset \operatorname{im}g^{\ast}$. Note that $g(f(a_q))=0$ by exactness. Finally, we prove exactness at $H^{q+1}(A)$. Pick $\alpha \in H^{q+1}(A)$. If $\alpha \in \operatorname{im}d^{\ast}$, then $\alpha=[a_{q+1}]$ where $f(a_{q+1})=db_q$ by definition. Then \[ f^(\alpha)=[f(a_{q+1})]=[db_q]=[0]. \] Therefore $\alpha \in \ker f^{\ast}$. Conversely, if we have $f^{\ast}(\alpha)=[0]$, pick the representative element of $\alpha$, namely we write $\alpha=[a]$; then $[f(a)]=[0]$. But this implies that $f(a) \in \operatorname{im}d$ where $d$ denotes the differential operator of $B$. There exists some $b_{q+1} \in B^{q+1}$ and $b_q \in B^q$ such that $db_{q}=b_{q+1}$. Suppose now $c_q=g(b_q)$. $c_q$ is closed since $dc_q=g(db_q)=g(b_{q+1})=g(f(a))=0$. By definition, $\alpha=d^{\ast}[c_q]$. Therefore $\ker f^{\ast} \subset \operatorname{im}d^{\ast}$. As you may see, almost every property of the diagram has been used. The exactness at $B^q$ ensures that $g(f(a))=0$. The definition of $H^q(A)$ ensures that we can simplify the meaning of $[0]$. We even use the injectivity of $f$ and the surjectivity of $g$. This proof is also a demonstration of diagram-chasing technique. As you have seen, we keep running through the diagram to ensure that there is "someone waiting" at the destination. This long exact group is useful. Here is an example. Application: Mayer-Vietoris Sequence By differential forms on a open set $U \subset \mathbb{R}^n$, we mean \[ \Omega^(U)=\{C^{\infty}\text{ functions on }U\}\otimes_\mathbb{R}\Omega^. \] And the de Rham cohomology of $U$ comes up in the nature of things. We are able to compute the cohomology of the union of two open sets. Suppose $M=U \cup V$ is a manifold with $U$ and $V$ open, and $U \amalg V$ is the disjoint union of $U$ and $V$ (the coproduct in the category of sets). $\partial_0$ and $\partial_1$ are inclusions of $U \cap V$ in $U$ and $V$ respectively. We have a natural sequence of inclusions \[ M \leftarrow U\amalg V \leftleftarrows^{\partial_0}_{\partial_1}\leftleftarrows U \cap V. \] Since $\Omega^{}$ can also be treated as a contravariant functor from the category of Euclidean spaces with smooth maps to the category of commutative differential graded algebras and their homomorphisms, we have \[ \Omega^(M) \rightarrow \Omega^(U) \oplus \Omega^(V) \rightrightarrows^{\partial^_0}_{\partial^_1}\rightrightarrows\Omega^({U \cap V}). \] By taking the difference of the last two maps, we have \[ \begin{aligned} 0 \rightarrow \Omega^(M) \rightarrow \Omega^(U) \oplus \Omega^(V) &\rightarrow \Omega^(U \cap V) \rightarrow 0 \\ (\omega,\tau) &\mapsto \tau-\omega \end{aligned} \] The sequence above is a short exact sequence. Therefore we may use the zig-zag lemma to find a long exact sequence (which is also called the Mayer-Vietoris sequence) by \[ \cdots\to H^q(M) \to H^q(U) \oplus H^q(V) \to H^q(U \cap V) \xrightarrow{d^} H^{q+1}(M) \to \cdots \] This sequence allows one to compute the cohomology of two union of two open sets. For example, for $H^{*}_{DR}(\mathbb{R}^2-P-Q)$, where $P(x_p,y_p)$ and $Q(x_q,y_q)$ are two distinct points in $\mathbb{R}^2$, we may write \[ (\mathbb{R}^2-P)\cap(\mathbb{R}^2-Q)=\mathbb{R}^2-P-Q \] and \[ (\mathbb{R}^2-P)\cup(\mathbb{R}^2-Q)=\mathbb{R}^2. \] Therefore we may write $M=\mathbb{R}^2$, $U=\mathbb{R}^2-P$ and $V=\mathbb{R}^2-Q$. For $U$ and $V$, we have another decomposition by \[ \mathbb{R}^2-P=(\mathbb{R}^2-P_x)\cup(\mathbb{R}^2-P_y) \] where \[ P_x=\{(x,y_p):x \in \mathbb{R}\}. \] But \[ (\mathbb{R}^2-P_x)\cap(\mathbb{R}^2-P_y) \] is a four-time (homeomorphic) copy of $\mathbb{R}^2$. So things become clear after we compute $H^{\ast}_{DR}(\mathbb{R}^2)$. References / Further reading Raoul Bott, Loring W. Tu, Differential Forms in Algebraic Topology Munkres J. R., Elements of Algebraic Topology Micheal Spivak, Calculus on Manifolds Serge Lang, Algebra	CommonCrawl
On the incorporation of box-constraints for ensemble Kalman inversion FoDS Home Issues using logistic regression with class imbalance, with a case study from credit risk modelling December 2019, 1(4): 419-431. doi: 10.3934/fods.2019017 Quantum topological data analysis with continuous variables George Siopsis Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA Figure(5) I introduce a continuous-variable quantum topological data algorithm. The goal of the quantum algorithm is to calculate the Betti numbers in persistent homology which are the dimensions of the kernel of the combinatorial Laplacian. I accomplish this task with the use of qRAM to create an oracle which organizes sets of data. I then perform a continuous-variable phase estimation on a Dirac operator to get a probability distribution with eigenvalue peaks. The results also leverage an implementation of continuous-variable conditional swap gate. 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Zhang and S. L. Braunstein, Continuous-variable Gaussian analog of cluster states, Phys. Rev. A, 73 (2006), 032318. Google Scholar A. Zomorodian and G. Carlsson, Computing persistent homology, Discret. Comput. Geom., 33 (2005), 249–274. doi: 10.1007/s00454-004-1146-y. Google Scholar A. Zomorodian, Algorithms and Theory of Computation Handbook, 2nd edition, Ch. 3, section 2., Chapman and Hall/CRC, 2009. Google Scholar Figure 1. The Betti numbers $ \beta_{0,1,2} $ for four example shapes (point, cirlce, spherical shell, and torus). They are the number of connected components, one-dimensional holes (also called tunnels or handles), and two-dimensional voids, respectively Figure Options Download full-size image Download as PowerPoint slide Figure 2. (a) Given data represented by points. (b) For a given distance $ \varepsilon $, a circle is drawn around each point. (c) Between every two points with contacting circles a line is drawn. These connections are edges of $ n $-dimensional shapes (simplices), and the space of simplices in (c) is called a simplicial complex. For two different values of $ \varepsilon $, as in (b) i, ii, and (c) i, ii, one can get more or less connections between the data points resulting in different topologies. Therefore Betti numbers depend on the initial choice of $ \varepsilon $. It is useful to vary $ \varepsilon $ to find interesting structures Figure 3. The $ k $-simplices for $ k = 0,1,2,3 $. These are a vertex, an edge, a triangle, and a tetrahedron, respectively Figure 4. The action of the boundary operator is shown on a $ k = 2 $ simplex. A visual representation of a simplex being broken down into its boundary is depicted above. Its boundary consists of simplices of $ k-1 = 1 $. Below is the encoded representation of the boundary operator acting on the 2-simplex. In this encoding a 1 represents a vertex in the corresponding position in the string of bits. The boundary sum is represented by a clockwise rotation around the original simplex, and the negative sign in the result alternates as in Eq. (5) Figure 5. Consider the $ k = 2 $ complex on the left, for a given value of $ \varepsilon $. In order to show that the striped area is a void, it itself must be boundary-less, and not a boundary for any part of the complex. Fulfillment of these two properties is equivalent to the combinatorial Laplacian (11) applied to the stripped area returning zero. Therefore this area would be part of the kernel of the combinatorial Laplacian for $ k = 2 $ contributing to the $ \beta_{2} $ Betti number Pedro Branco. A post-quantum UC-commitment scheme in the global random oracle model from code-based assumptions. Advances in Mathematics of Communications, 2021, 15 (1) : 113-130. doi: 10.3934/amc.2020046 Felix Finster, Jürg Fröhlich, Marco Oppio, Claudio F. Paganini. Causal fermion systems and the ETH approach to quantum theory. 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Colonization rate of Streptococcus pneumoniae, its associated factors and antimicrobial susceptibility pattern among children attending kindergarten school in Hawassa, southern Ethiopia Aberash Assefa Haile1, Deresse Daka Gidebo1 & Musa Mohammed Ali1 BMC Research Notes volume 12, Article number: 344 (2019) Cite this article The aim of this study was to determine the colonization rate of Streptococcus pneumoniae, antimicrobial susceptibility pattern and associated risk factors among children attending kindergarten school in Hawassa, Ethiopia. Out of 317 study participants, 68 (21.5%) were colonized with S. pneumoniae. Colonization rate was significantly associated with factors such as age (3 to 4 years old) (P = 0.01), having a sibling whose age was less than 5 years (P = 0.011), sharing a bed with parents (P = 0.005), cooking within bedroom (P = 0.002), and previous hospitalization (P = 0.004). Forty-four (64.6%), 33 (48.5%), and 2942.6%) of S. pneumoniae isolated were resistant to cotrimoxazole, penicillin, and tetracycline respectively. Streptococcus pneumoniae (S. pneumoniae) is the major cause of childhood morbidity and mortality in the world [1, 2]. In Africa, S. pneumoniae caused 1–4 million episodes of disease among under-five children in 2007 [3]. In Ethiopia, 21.4% of invasive disease among children and adults were caused by S. pneumoniae [4, 5]. Even though pneumococcal conjugate vaccine (PCV-10) was introduced in Ethiopia since 2011 as part of childhood immunization, 43.3% of meningitis and sepsis were caused by S. pneumoniae among children in 2015 [6]. Nasopharyngeal colonization of S. pneumoniae always precedes disease and serves as a reservoir for the transmission of the pathogen within the community [1]. The colonization rate varies depending on age, vaccination status, and other factors [7]. The rate of S. pneumoniae colonization is particularly high among young children attending kindergarten schools [8, 9]. Vaccination status is assumed to reduce the colonization rate among children; however, its effect on colonization was not assessed in most low-income countries including Ethiopia. Factors such as environmental [10], socio-demographic [11] and previous health condition [8] can increase the prevalence of S. pneumoniae among school children. Moreover, nasopharyngeal colonization with antibiotic-resistant S. pneumoniae has been increasing in different parts of the world [10, 12, 13]. The rise of colonization rate with antibiotic-resistant S. pneumoniae creates a challenge to treat the disease caused by S. pneumoniae among carriers [10, 14]. Most of the studies focusing on S. pneumoniae in Ethiopia were conducted among sick children [4, 5]. Data on the S. pneumoniae colonization rate, associated risk factors, and antimicrobial susceptibility pattern among kindergarten school children were scarce in the study area. Therefore the present study was aimed to determine colonization rate, associated factors and antimicrobial susceptibility pattern of circulating S. pneumoniae among kindergarten school children in Hawassa, the southern part of Ethiopia. Study area and period Hawassa is the capital city of the Southern Nations, Nationalities and People Regional State. The city is located on the shores of Lake Hawassa in the Great Rift Valley and is located 275 km to the south of Addis Ababa, the capital of Ethiopia [15]. A community-based cross-sectional study was conducted from March 17, 2018, to May 20, 2018, at Tabor sub city, Hawassa, Ethiopia. All children who attended kindergarten schools found in Tabor sub city, Hawassa, Ethiopia during the study period. Sample size determination Sample size was calculated by using a single proportion formula. $$ n = \frac{{Z^{2} P\left( {1 - P} \right)}}{{d^{2} }} $$ where n: sample size; Z: reliability coefficient (confidence level) which is 95% = 1.96; P: anticipated population proportion; D: the margin of error, which is 5% = 0.05. By using the anticipated population proportion of 44.8% from a previous study [8], the sample size was calculated as follows: $$ n = \frac{{\left( {1.96} \right)^{2} 0.448\left( {1 - 0.448} \right)}}{{\left( {0.05} \right)^{2} }} = 380 $$ Since the source population was less than 10,000, the sample size was recalculated using the correction factor as follows: $$ {\text{nf }} = \frac{n}{{1 + \frac{n}{N}}} \to \frac{380}{{1 + \frac{380}{1302}}} = 294.6. $$ After adding 10% of non-respondent the final the sample size was 324. Sampling technique At Tabor sub city, there are seven primary schools with a total of 1302 children attending kindergarten. Out of the total children, 324 were selected randomly with an equal proportion from each school. From 324 selected children, seven refused to participate in the study. Children who attended kindergarten school during the study period, those whose age was less than or equal to 6 years, and children whose parents had accepted the consent to participate in the study were included. Children who were on an antibiotic for the last 3 weeks, those with any sign and symptoms of respiratory disease and those who were not brought to school by their parents or guardians were excluded from the study. At each selected school, the parents of the children were consented and interviewed for sociodemographic, the environmental and previous health condition of the children by the trained data collectors. Data was collected by using pre-structured and pre-tested questionnaire. Sample collection, handling, and transport The nasopharyngeal specimen was collected by passing sterile rayon-tipped swab gently back from one nostril along the floor of the nasal cavity until it touches the posterior wall of the nasopharynx. One nasopharyngeal specimen per child was collected by a trained nurse. Culture and identification of S. pneumoniae The specimens were inoculated onto sheep blood agar (Oxoid Ltd, CM0271) supplemented with 5 μg/ml gentamycin by rolling the swab over a small area of the plate and stretching the sample using a sterile loop within 3 h of collection. The inoculated media was incubated in 5% CO2 enriched atmosphere at 37 °C for 18 to 20 h. Suspected colonies, which appears as a greenish colony (alpha hemolytic), were subcultured on blood agar into which 5 μg Optochin disks (Mumbai, India) was placed, and then incubated within 5% CO2 enriched atmosphere at 37 °C for 24 h. After overnight incubation, the sensitivity of Optochin was checked by measuring the diameter of the inhibition zone. If the diameter was ≥ 14, it was assumed to be S. pneumoniae; if the diameter was < 14, bile solubility tests (tube method) was performed by using 2% sodium deoxycholate (Oxoid Ltd) [16]. Antimicrobial susceptibility testing Antimicrobial susceptibility pattern of all S. pneumoniae isolated was assessed by using the disk diffusion method. The antibiotics used were tetracycline (30 μg), cotrimoxazole (23.75 μg), oxacillin (1 μg), and chloramphenicol (30 μg), erythromycin (15 μg), clindamycin (2 μg), and rifampicin (5 μg). Data management and quality control Quality of the data was ensured by using a pre-structured questionnaire. For laboratory analysis, the sterility of the prepared media was checked by incubating 5% of prepared media within a 5% CO2 enriched atmosphere at 37 °C for 24 h before using it. A quality control strain of S. pneumoniae was used as a positive control for each test. Data processing and analysis Data were analyzed by using SPSS version 22. The frequency of variables, the prevalence of S. pneumoniae, and antibiotic susceptibility pattern was determined by using SPSS version 22. The association between risk factors and S. pneumoniae colonization was determined by using logistic regression. A P-value less than 0.05 at 95% confidence interval (CI) was considered statistically significant. Sociodemographic and health characteristics Out of 317 children who participated in the present study, 154 (48.6%) were males, 262 (82.6%) were within the age of 5 to 6 years, 17 (5.4%) were not vaccinated, and 13 (4.1%) lived with smoker families (Table 1). Table 1 Sociodemographic and health characteristics of children who attended kindergarten school owned by government at Tabor sub city, Hawassa from March 17, 2018 to May 20, 2018, (N = 317) Nasopharyngeal colonization rate of S. pneumoniae The colonization rate of S. pneumoniae among children who attended kindergarten was 68 (21.5%) 95% CI [17–26.2]. Colonization rate of S. pneumoniae among children who were 3 to 4 years old, 5 to 6 years old, those who were not vaccinated, and those who live with a smoker were 19 (34.5%), 49 (18.7%), 5 (29.4%), and 5 (38.5%) respectively (Table 2). Table 2 Factors that affect nasopharyngeal colonization rate of S. pneumoniae among children who attended kindergarten school owned by government at Tabor sub city, Hawassa from March 17, 2018 to May 20, 2018, (N = 317) Factors that affect the nasopharyngeal colonization rate of S. pneumoniae In this study variables which are listed below were significantly associated with colonization rate of S. pneumoniae among children who attended kindergarten: children within the age range of 3 to 4 years (Adjusted odds ratio (AOR) = 3.1; 95% CI [1.3–7.6]; P = 0.01), having sibling with age < 5 years old (AOR = 2.9; 95% [CI 1.3–6.8]; P = 0.011), sharing bed with parents (AOR = 3.5;95% CI [1.4–8.4]; P = 0.005), cooking within bedroom (AOR = 3.6; 95% CI [1.6–7.9]; P = 0.002) and previous hospitalization (AOR = 3.5; 95% CI [1.5–8.2]; P = 0.004) (Table 2). Out of 68 of S. pneumoniae isolated in this study, 67 (98.5%), 65 (95.6%), 62 (91.2%), and 58 (85.3%) were susceptible to rifampicin, clindamycin, chloramphenicol, and erythromycin respectively. Of all isolates, only three were sensitive to all of the seven antibiotics tested, 17 (25%) were resistant to only one antibiotic, 12 (17.6%) were resistant to two antibiotics and 2 (2.9%) were resistant for three antibiotics. Multidrug-resistant (resistant for three and more antibiotics) from this finding was 2 (2.9%). Majority of S. pneumoniae isolated in this study were resistant to cotrimoxazole 44 (64.6%), oxacillin 33 (48.5%) and tetracycline 29 (42.6%) (Table 3). Table 3 Antimicrobial susceptibility pattern of S. pneumoniae isolated from children who attended kindergarten school owned by government at Tabor sub city, Hawassa from March 17, 2018 to May 20, 2018, (N = 68) The S. pneumoniae colonization rate among children who attended kindergarten school in the present study was 21.5%. The finding of this study was higher than the study conducted in the northern part of Ethiopia (10.3%) [17], Gambia (7.6%) [18] and Tanzania (12.3%) [19]. S. pneumoniae colonization rate found in this study was low compared to report from Gondar, Ethiopia (41%) [10], Jimma, Ethiopia (43%) [14] and Kenya (35%) [20]. The possible explanation for the variation might be due to vaccination status and age differences. This indicates that children whose age is below 6 years old are more colonized compared with those who are above 6 years old. Additional explanations for the differences observed are sample size, seasonal variation and method used. Even though the nasopharyngeal colonization rate of S. pneumoniae among children varies throughout the world, the result of this study was in line with the colonization rate reported from Nigeria [21], Morocco [22] and Kenya [23]. In the present study, we assessed different factors that could possibly increase the colonization rate of S. pneumoniae. Children whose age was in between 3 and 4 years were 3.1 times at risk to be colonized with S. pneumoniae (P = 0.01). This finding was in line with studies conducted in Belgium, Spain, and Ethiopia [10, 24, 25]. The decline in S. pneumoniae colonization rate as age increases could be due to the gradual acquisition of mucosal immunity and reduction of exposure. This indicates children whose age was in between 3 and 4 year were at high risk of acquiring S. pneumoniae colonization than those whose age was in between 5 and 6 years. Children who lived together with a sibling(s) whose age was less than 5 years old had 2.9 times chance to be colonized with S. pneumoniae compared to children who did not have a sibling whose age was not less than 5 years old (P = 0.001). This finding was comparable with a report from other parts of Ethiopia [10, 14]. Unlike previous studies from Ethiopia [10, 14], children who did not have their own separate bed in the present study had 3.5 times chance to be colonized with S. pneumoniae (P = 0.005). Children who sleep in the cooking room had 3.6 times chance to be colonized with S. pneumoniae compared with children who sleep in a bedroom which was free from cooking (P = 0.002). This finding was comparable with a report from Kenya [26]. Children with a history of hospital admission had 3.5 times chance to be colonized with S. pneumoniae (P = 0.004). This finding was consistent with a study conducted in France and Uganda [27, 28]. Factors such as attending daycare centers and being passive smoker were not significantly associated with S. pneumoniae colonization during multivariable analysis. In contrast to the present study, a significant association of daycare attendance and passive smoking with S. pneumoniae colonization rate was reported from other countries [14, 29, 30]. In the current study, a high proportion (21%) of vaccinated children were colonized with S. pneumoniae even though it was not statistically significant (P < 0.05). Out of the total S. Pneumoniae strains collected in the present study, 64.6% and 42.6% were resistant to cotrimoxazole and tetracycline respectively. This finding was comparable with previous studies conducted in different parts of Ethiopia [8, 10, 14] and Morocco [31]. The prevalence of tetracycline resistant S. pneumoniae reported from Iran (22.6%) was low compared to our study [32]. Unlike the current study, the majority of S. pneumoniae isolated from Kenya (98.6%) were resistant to cotrimoxazole [33]. Wide usage of antibiotics could be one of the reasons for high resistance rate observed in different countries. The prevalence of penicillin (oxacillin) resistant S. pneumoniae we found (48.5%) was low compared to the report Kenya (82%) [33]. 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J Med Microbiol. 2008;57(3):185–9. https://doi.org/10.1099/jmm.0.47470-0. Petraitiene S, Alasevicius T, Staceviciene I, Vaiciunien D, Kacergius T, Usonis V. The influence of Streptococcus pneumoniae nasopharyngeal colonization on the clinical outcome of the respiratory tract infections in preschool children. BMC Infect Dis. 2015;15(403):1–9. https://doi.org/10.1186/s12879-015-1149-8. Warda K, Oufdou K, Zahlane K, Bouskraoui M. Antibiotic resistance and serotype distribution of nasopharyngeal isolates of Streptococcus pneumoniae from children in Marrakech region (Morocco). J Infect Public Health. 2013;6(6):473–81. Ghazi HM, Moniri R, Abbas SG, Rezaei M, Yasini M, Valipour M. Serotyping, antibiotic susceptibility and related risk factors aspects of nasopharyngeal carriage of Streptococcus pneumoniae in healthy school students. Iran J Publ Health. 2014;43(9):1284–90. Kobayashi M, Conklin LM, Bigogo G, Jagero G, Hampton L. Pneumococcal carriage and antibiotic susceptibility patterns from two crosssectional colonization surveys among children aged < 5 years prior to the introduction of 10-valent pneumococcal conjugate vaccine—Kenya, 2009–2010. BMC Infect Dis. 2017;17(25):1–12. https://doi.org/10.1186/s12879-016-2103-0. We would like to acknowledge data collector, all staff working at kindergarten school who facilitated data collection, Hawassa University College of Medicine and Health Sciences, college of Mizan Aman Health Sciences for their support during the study. We would also acknowledge parents who allowed their children to participate in this study. This study was supported by Hawassa University, College of Medicine and Health Sciences, and Mizan Aman College of Medicine and Health Sciences. The support included payment for data collectors and purchase of materials and supplies required for the study. The support did not include designing of the study, analysis, and interpretation of data, and manuscript preparation. Hawassa University College of Medicine and Health Sciences School of Medical Laboratory Science, P.O box 1560, Hawassa, Ethiopia Aberash Assefa Haile, Deresse Daka Gidebo & Musa Mohammed Ali Aberash Assefa Haile Deresse Daka Gidebo Musa Mohammed Ali AAH: Conceived and designed the study, performed the laboratory work, analyzed the data, involved in manuscript preparation. DDG: Involved in protocol development and manuscript write up. MMA: Conceived and designed the study, supervised the study, involved in analysis and manuscript preparation. All authors read and approved the final manuscript. Correspondence to Aberash Assefa Haile. This study was ethically cleared from the Institutional Review Board (IRB) of the College of Medicine and Health Sciences, Hawassa University (Reference number: IRB/160/10). Official permission was obtained from the study site and written informed consent was obtained from all parents/guardians of the children. Haile, A.A., Gidebo, D.D. & Ali, M.M. Colonization rate of Streptococcus pneumoniae, its associated factors and antimicrobial susceptibility pattern among children attending kindergarten school in Hawassa, southern Ethiopia. BMC Res Notes 12, 344 (2019). https://doi.org/10.1186/s13104-019-4376-z DOI: https://doi.org/10.1186/s13104-019-4376-z S. pneumoniae Nasopharyngeal colonization	CommonCrawl
The boundedness of multi-linear and multi-parameter pseudo-differential operators CPAA Home The degenerate Monge-Ampère equations with the Neumann condition doi: 10.3934/cpaa.2020290 The anisotropic fractional isoperimetric problem with respect to unconditional unit balls Andreas Kreuml Technische Universität Wien, Institut für Diskrete Mathematik und Geometrie, Wiedner Hauptstraße 8-10/1046, 1040 Vienna, Austria Received May 2020 Revised October 2020 Published December 2020 The minimizers of the anisotropic fractional isoperimetric inequality with respect to a convex body $ K $ in $ \mathbb{R}^n $ are shown to be equivalent to star bodies whenever $ K $ is strictly convex and unconditional. From this a Pólya-Szegő principle for anisotropic fractional seminorms is derived by using symmetrization with respect to star bodies. Keywords: Fractional perimeters, non-local functionals, isoperimetric inequalities, Pólya-Szegő principles, anisotropic symmetrization. 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Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020170	CommonCrawl
Arkiv för Matematik Ark. Mat. Volume 49, Number 1 (2011), 1-16. Density of the polynomials in Hardy and Bergman spaces of slit domains John R. Akeroyd More by John R. Akeroyd It is shown that for any t, 0< t<∞, there is a Jordan arc Γ with endpoints 0 and 1 such that $\Gamma\setminus\{1\}\subseteq\mathbb{D}:=\{z:\|z\|<1\}$ and with the property that the analytic polynomials are dense in the Bergman space $\mathbb{A}^{t}(\mathbb{D}\setminus\Gamma)$ . It is also shown that one can go further in the Hardy space setting and find such a Γ that is in fact the graph of a continuous real-valued function on [0,1], where the polynomials are dense in $H^{t}(\mathbb{D}\setminus\Gamma)$ ; improving upon a result in an earlier paper. Ark. Mat., Volume 49, Number 1 (2011), 1-16. First available in Project Euclid: 31 January 2017 https://projecteuclid.org/euclid.afm/1485907126 2009 © Institut Mittag-Leffler Akeroyd, John R. Density of the polynomials in Hardy and Bergman spaces of slit domains. Ark. Mat. 49 (2011), no. 1, 1--16. doi:10.1007/s11512-009-0110-8. https://projecteuclid.org/euclid.afm/1485907126 Akeroyd, J., Density of the polynomials in the Hardy space of certain slit domains, Proc. Amer. Math. Soc. 115 (1992), 1013–1021. Aleman, A., Richter, S. and Sundberg, C., Nontangential limits in Pt(μ)-spaces and the index of invariant subspaces, Ann. of Math. 169 (2009), 449–490. Digital Object Identifier: doi:10.4007/annals.2009.169.449 Brennan, J. E., Approximation in the mean by polynomials on non-Carathéodory domains, Ark. Mat. 15 (1977), 117–168. Mathematical Reviews (MathSciNet): MR450566 Digital Object Identifier: doi:10.1007/BF02386037 Conway, J. B., The Theory of Subnormal Operators, Math. Surveys Monogr. 36, Amer. Math. Soc., Providence, RI, 1991. Duren, P. L., Theory ofHpSpaces, Academic Press, New York, 1970. Garnett, J. B., Bounded Analytic Functions, Academic Press, Orlando, FL, 1981. Garnett, J. B. and Marshall, D. E., Harmonic Measure, Cambridge University Press, New York, 2005. Digital Object Identifier: doi:10.1017/CBO9780511546617 Gelbaum, B. R. and Olmstead, J. M. H., Counterexamples in Analysis, Dover, Mineola, NY, 2003. Hastings, W. W., A construction of Hilbert spaces of analytic functions, Proc. Amer. Math. Soc. 74 (1979), 295–298. Mergelyan, S. N., On the completeness of systems of analytic functions, Uspekhi Mat. Nauk 8 (1953), 3–63 (Russian). English transl.: Amer. Math. Soc. Transl. 19 (1962), 109–166. Mathematical Reviews (MathSciNet): MR58698 Shields, A. L., Weighted shift operators and analytic function theory, in Topics in Operator Theory, Math. Surveys 13, pp. 49–128, Amer. Math. Soc., Providence, RI, 1974. Thomson, J. E., Approximation in the mean by polynomials, Ann. of Math. 133 (1991), 477–507. Digital Object Identifier: doi:10.2307/2944317 Willard, S., General Topology, Addison-Wesley, Reading, MA, 1970. Institut Mittag-Leffler International Press Essential norms of Toeplitz operators on Bergman-Hardy spaces on the unit disk Michalak, Artur, Functiones et Approximatio Commentarii Mathematici, 2000 Optimal series representation of fractional Brownian sheets Kühn, Thomas and Linde, Werner, Bernoulli, 2002 Positive Toeplitz operators on the Bergman space Das, Namita and Sahoo, Madhusmita, Annals of Functional Analysis, 2013 Fredholmness and index of simplest weighted singular integral operators with two slowly oscillating shifts Karlovich, Alexei Yu., Banach Journal of Mathematical Analysis, 2015 Embedding of Hardy spaces into weighted Bergman spaces in bounded domains with {$C\sp 2$} boundary Cho, Hong Rae and Kwon, Ern Gun, Illinois Journal of Mathematics, 2004 Poly-Bergman Type Spaces on the Siegel Domain Ramírez Ortega, Josué and Sánchez Nungaray, Armando, Communications in Mathematical Analysis, 2013 On a Zero-Infinity Law of Olsen Zoli, Enrico, Real Analysis Exchange, 2009 On an integral-type operator between $H^2$ space and weighted Bergman spaces Zhu, Xiangling, Bulletin of the Belgian Mathematical Society - Simon Stevin, 2011 Isometries of weighted Bergman-Privalov spaces on the unit ball of Cn MATSUGU, Yasuo and UEKI, Sei-ichiro, Journal of the Mathematical Society of Japan, 2002 OPTIMALITY CONDITIONS FOR SEMI-PREINVEX PROGRAMMING Lai, Hang-Chin, Taiwanese Journal of Mathematics, 1997 euclid.afm/1485907126	CommonCrawl
[ "article:topic", "authorname:openstax", "polar coordinate system", "polar coordinates", "radial coordinate", "license:ccby", "showtoc:no", "transcluded:yes", "source-phys-3974" ] Polar Coordinates Vectors in Three Dimensions Takeoff of a Drone To describe locations of points or vectors in a plane, we need two orthogonal directions. In the Cartesian coordinate system these directions are given by unit vectors $\hat{i}$ and $\hat{j}$ along the x-axis and the y-axis, respectively. The Cartesian coordinate system is very convenient to use in describing displacements and velocities of objects and the forces acting on them. However, it becomes cumbersome when we need to describe the rotation of objects. When describing rotation, we usually work in the polar coordinate system. In the polar coordinate system, the location of point P in a plane is given by two polar coordinates (Figure 2.20). The first polar coordinate is the radial coordinate r, which is the distance of point P from the origin. The second polar coordinate is an angle $\varphi$ that the radial vector makes with some chosen direction, usually the positive x-direction. In polar coordinates, angles are measured in radians, or rads. The radial vector is attached at the origin and points away from the origin to point P. This radial direction is described by a unit radial vector $\hat{r}$. The second unit vector $\hat{t}$ is a vector orthogonal to the radial direction $\hat{r}$. The positive + $\hat{t}$ direction indicates how the angle $\varphi$ changes in the counterclockwise direction. In this way, a point P that has coordinates (x, y) in the rectangular system can be described equivalently in the polar coordinate system by the two polar coordinates (r, $\varphi$). Equation 2.17 is valid for any vector, so we can use it to express the x- and y-coordinates of vector $\vec{r}$. In this way, we obtain the connection between the polar coordinates and rectangular coordinates of point P: $$ \begin{cases} x = r \cos \varphi \\ r \sin \varphi \end{cases} \ldotp \tag{2.18}$$ Figure $\PageIndex{5}$: Using polar coordinates, the unit vector $\hat{r}$ defines the positive direction along the radius r (radial direction) and, orthogonal to it, the unit vector $\hat{t}$ defines the positive direction of rotation by the angle $\varphi$. A treasure hunter finds one silver coin at a location 20.0 m away from a dry well in the direction 20° north of east and finds one gold coin at a location 10.0 m away from the well in the direction 20° north of west. What are the polar and rectangular coordinates of these findings with respect to the well? The well marks the origin of the coordinate system and east is the +x-direction. We identify radial distances from the locations to the origin, which are rS = 20.0 m (for the silver coin) and rG = 10.0 m (for the gold coin). To find the angular coordinates, we convert 20° to radians: 20° = $\frac{\pi\; 20}{180}$ = $\frac{\pi}{9}$. We use Equation 2.18 to find the x- and y-coordinates of the coins. Solution The angular coordinate of the silver coin is $\varphi_{S}$ = $\frac{\pi}{9}$, whereas the angular coordinate of the gold coin is $\varphi_{G}$ = $\pi$ − $\frac{\pi}{9}$ = $\frac{8 \pi}{9}$. Hence, the polar coordinates of the silver coin are (rS, $\varphi_{S}$) = (20.0 m, $\frac{\pi}{9}$) and those of the gold coin are (rG, $\varphi_{G}$) = (10.0 m, \frac{8 \pi}{9}\)). We substitute these coordinates into Equation 2.18 to obtain rectangular coordinates. For the gold coin, the coordinates are $$ \begin{cases} x_{G} = r_{G} \cos \varphi_{G} = (10.0\; m) \cos \frac{8 \pi}{9} = -9.4\; m \\ y_{G} = r_{G} \sin \varphi_{G} = (10.0\; m) \sin \frac{8 \pi}{9} = 3.4\; m \end{cases} \Rightarrow (x_{G}, y_{G}) = (-9.4\; m, 3.4\; m) \ldotp$$ For the silver coin, the coordinates are $$ \begin{cases} x_{S} = r_{S} \cos \varphi_{S} = (20.0\; m) \cos \frac{\pi}{9} = 18.9\; m \\ y_{S} = r_{S} \sin \varphi_{S} = (20.0\; m) \sin \frac{\pi}{9} = 6.8\; m \end{cases} \Rightarrow (x_{S}, y_{S}) = (18.9\; m, 6.8\; m) \ldotp$$ To specify the location of a point in space, we need three coordinates (x, y, z), where coordinates x and y specify locations in a plane, and coordinate z gives a vertical positions above or below the plane. Three-dimensional space has three orthogonal directions, so we need not two but three unit vectors to define a three-dimensional coordinate system. In the Cartesian coordinate system, the first two unit vectors are the unit vector of the x-axis $\hat{i}$ and the unit vector of the y-axis $\hat{j}$. The third unit vector $\hat{k}$ is the direction of the z-axis (Figure 2.21). The order in which the axes are labeled, which is the order in which the three unit vectors appear, is important because it defines the orientation of the coordinate system. The order x-y-z, which is equivalent to the order $\hat{i}$ - $\hat{j}$ - $\hat{k}$, defines the standard right-handed coordinate system (positive orientation). Figure $\PageIndex{6}$: Three unit vectors define a Cartesian system in three-dimensional space. The order in which these unit vectors appear defines the orientation of the coordinate system. The order shown here defines the right-handed orientation. In three-dimensional space, vector $\vec{A}$ has three vector components: the x-component $\vec{A}_{x}$ = Ax $\hat{i}$, which is the part of vector $\vec{A}$ along the x-axis; the y-component $\vec{A}_{y}$ = Ay $\hat{j}$, which is the part of $\vec{A}$ along the y-axis; and the z-component $\vec{A}_{z}$ = Az $\hat{k}$, which is the part of the vector along the z-axis. A vector in three-dimensional space is the vector sum of its three vector components (Figure 2.22): $$\vec{A} = A_{x} \hat{i} + A_{y} \hat{j} + A_{z} \hat{k} \ldotp \tag{2.19}$$ If we know the coordinates of its origin b(xb, yb, zb) and of its end e(xe ye, ze), its scalar components are obtained by taking their differences: Ax and Ay are given by Equation 2.13 and the z-component is given by $$A_{z} = z_{e} - z_{b} \ldotp \tag{2.20}$$ Magnitude A is obtained by generalizing Equation 2.15 to three dimensions: $$A = \sqrt{A_{x}^{2} + A_{y}^{2} + A_{z}^{2}} \ldotp \tag{2.21}$$ This expression for the vector magnitude comes from applying the Pythagorean theorem twice. As seen in Figure 2.22, the diagonal in the xy-plane has length $\sqrt{A_{x}^{2} + A_{y}^{2}}$ and its square adds to the square Az2 to give A2. Note that when the z-component is zero, the vector lies entirely in the xy-plane and its description is reduced to two dimensions. Figure $\PageIndex{7}$: A vector in three-dimensional space is the vector sum of its three vector components. During a takeoff of IAI Heron (Figure 2.23), its position with respect to a control tower is 100 m above the ground, 300 m to the east, and 200 m to the north. One minute later, its position is 250 m above the ground, 1200 m to the east, and 2100 m to the north. What is the drone's displacement vector with respect to the control tower? What is the magnitude of its displacement vector? Figure $\PageIndex{8}$: The drone IAI Heron in flight. (credit: SSgt Reynaldo Ramon, USAF) We take the origin of the Cartesian coordinate system as the control tower. The direction of the +x-axis is given by unit vector $\hat{i}$ to the east, the direction of the +y-axis is given by unit vector $\hat{j}$ to the north, and the direction of the +z-axis is given by unit vector $\hat{k}$, which points up from the ground. The drone's first position is the origin (or, equivalently, the beginning) of the displacement vector and its second position is the end of the displacement vector. We identify b(300.0 m, 200.0 m, 100.0 m) and e(480.0 m, 370.0 m, 250.0m), and use Equation 2.13 and Equation 2.20 to find the scalar components of the drone's displacement vector: $$ \begin{cases} D_{x} = x_{e} - x_{b} = 1200.0\; m - 300.0\; m = 900.0\; m,\\ D_{y} =y_{e} - y_{b} = 2100.0\; m - 200.0\; m = 1900.0\; m, \\ D_{z} =z_{e} - z_{b} = 250.0\; m - 100.0\; m = 150\; m \ldotp \end{cases}$$ We substitute these components into Equation 2.19 to find the displacement vector: $$\vec{D} = D_{x}\; \hat{i} + D_{y}\; \hat{j} + D_{z}\; \hat{k} = 900.0\; \hat{i} + 1900.0\; \hat{j} + 150.0\; \hat{k} = (0.90\; \hat{i} + 1.90\; \hat{j} + 0.15\; \hat{k})\; km \ldotp$$ We substitute into Equation 2.21 to find the magnitude of the displacement: $$D = \sqrt{D_{x}^{2} + D_{y}^{2} + D_{z}^{2}} = \sqrt{(0.90\; km)^{2} + (1.90\; km)^{2} + (0.15\; km)^{2}} = 4.44\; km \ldotp$$ Exercise 2.7 If the average velocity vector of the drone in the displacement in Example 2.7 is $\vec{u}$ = (15.0 $\hat{i}$ + 31.7 $\hat{j}$ + 2.5 $\hat{k}$) m/s, what is the magnitude of the drone's velocity vector? polar coordinate system radial coordinate	CommonCrawl
Image steganography based on color palette transformation in color space Eugenijus Margalikas1 & Simona Ramanauskaitė ORCID: orcid.org/0000-0003-3195-42802 EURASIP Journal on Image and Video Processing volume 2019, Article number: 82 (2019) Cite this article In this paper, we present a novel image steganography method which is based on color palette transformation in color space. Most of the existing image steganography methods modify separate image pixels, and random noise appears in the image. By proposing a method, which changes the color palette of the image (all pixels of the same color will be changed to the same color), we achieve a higher user perception. Presented comparison of stegoimage quality metrics with other image steganography methods proved the new method is one of the best according to Structural Similarity Index (SSIM) and Peak Signal Noise Ratio (PSNR) values. The capability is average among other methods, but our method has a bigger capacity among methods with better SSIM and PSNR values. The color and pixel capability can be increased by using standard or adaptive color palette images with smoothing, but it will increase the embedding identification possibility. Nowadays, the phrase "Who owns the information, he owns the world" has a little bit different meaning, compared to the initial formulation. In 1815, information on Napoleon's defeat resulted in the Rothschilds in 1 day to earn 40 million pounds and became the owners of a large part of the British economy. Nowadays, information can lead to the defeat of information systems, organizations, and countries as well. Therefore, the data confidentiality is important as never before. Cryptography is used in most cases to ensure data confidentiality. However, encrypted data is not resistant to encryption identification. By encrypting only important, secret data, we can highlight it in the overall data flow and advanced search methods are capable to identify encrypted data. This leads to an increase in data camouflage technologies. Steganography is the science of hiding data. While digital steganography hides data into digital files and objects, image steganography is designed to hide the data into digital images and raster graphics. This type of steganography is one of the most popular as hardly anybody would think to look for secret information in image files. Image imperceptibility is the main feature to identify steganography method usage, and it is at odds with steganography capacity. The balance of these two characteristics is very important to assure the steganography method quality. This work aims to increase the imperceptibility of image steganography by changing the color palette rather than the color of separate pixels. The work involves the design of a new steganography method, suitable to hide data and to read it after the embedding into the cover images as well as ensure enough data can be embedded into the color image. Our contributions are as follows: We proposed a novel color palette transformation steganography method which is based on image color palette presentation and division into RGB cubes with one color only. This allows color change within the area of the RGB sub-cube and provided the possibility to embed stegomessage and ensure color similarity. Our approach has perception configuration possibility to ensure the acceptable modification level. In comparison to other steganography methods, our proposed method has a balance between user perception and embedding capability. To achieve the aim, a systematic literature review was executed to find existing steganography methods, their imperceptibility, and capability measurements. Based on existing solutions, we generated a new steganography method. This method uses color palette transformation, based on color location modification in divided RGB cube with one color only. The proposed method was validated by using the most commonly used images (Baboon, Barbara, Lena). Peak Signal Noise Ratio (PSNR) and Structural Similarity Index (SSIM) steganography measurements as well as capability calculations were calculated. This was the base for comparative analysis. An additional experiment was executed to identify the proposed steganography properties by using BSD-300 and Kodak datasets. Additionally, 108 randomly selected, different type images from the personal gallery were used to analyze the proposed method application. All experiments are summarized, and final conclusions are derived at the end of the paper. To secure data, cryptography algorithms are used. Cryptography allows data confidentiality assurance by encrypting data with a secret key. Encrypted data is not hard to be noticed. To provide the message secrecy, it can be sent over hidden channels or embedded into other objects to camouflage its existence. For this purpose, steganography is the best solution. It embeds a message into another object. Therefore, it is hard to identify where and how the message was hidden. Another steganography usage possibility is object watermarking. By embedding the owner's data into the image or another object, everybody can decode it and find the owner's data. At the same time, steganography usage for image watermarking is very limited, as no modifications are allowed after the message embedding. If the image is modified, the embedded data will be changed and we will not be able to retrieve the information. This applies to all steganography algorithms, despite the used method or application area. More advanced watermarking and tempering recovery methods exist [1,2,3] for image signing purpose. There is a variety of steganography methods, and they can be classified according to different properties. One of the properties, which can be used to classify steganography, is the need for shared data (except the methods and its parameters). For example, Chen et al. [4] propose a steganography method where the sender and the receiver own the cover image. By using this method, the receiver uses the cover image to get the embedded data from the stegoimage. The need for the original, cover image is not flexible in term of steganography usage. The biggest part of steganography methods does not require shared data. The least significant bit (LSB) steganography method embeds the secret message in the least significant bits of pixel values of the cover image [5]. Each pixel of the cover image is divided into RGB parts, and the least significant bits are replaced with the message bits. The change in color usually is far lesser than that perceivable by average human vision. The receiver needs to know the used steganography method and how many bits were used for the stegomessage, so there is no need for shared data for this method. The LSB steganography can be assigned to spatial domain category. This classification is based on image enhancement domain techniques and has two main categories [6]: Spatial domain—directly deals with the image pixels [7]. The manipulation with pixels leads to the fact it has high embedding capacity, has shorter computational time, and is vulnerable to geometric attacks. Transformation domain—deals with the image frequency content [8]. The need for transformations influences the higher computational time and limited embedding capacity, but it is more robust against geometric attacks and compression. LSB steganography is the most well-known spatial domain algorithm. Another example of spatial domain image steganography is pixel value differencing (PVD) [9]. This method is more imperceptible compared to LSB as the stegomessage is embedded by taking into account the difference between the colors of the pixel pair. The method does not embed a stegomessage where it might cause too big changes in the cover image. This reduces the capacity as not all pixels can be changed by embedding stegomessage. Another approach is based on pixel value ordering (PVO) when a digital image is sliced into blocks and each block is arranged according to the pixel value [10]. Usually, the differences between the two largest and two smallest values are analyzed while only the maximum and minimum values are changed to achieve the best results. Modifications of this method exist [11], where middle value is used too and leads to the increase of stegomessage length. Transformation domain steganography methods, first of all, execute some transformations. There are some examples of steganography methods, where different transformations are used: Thenmozhi and Chandrasekaran [12] use integer wavelet transform along with cropping. Senthooran and Ranathunga [13] apply DCT coefficients and modified quantization table values. Mazumder and Hemachandran [14] use DWT and change the stegomessage by optimizing message dispersion. Patel and Ragha [15] adopt binary image steganography and IWT. Dalvi and Kamathe [16] apply DWT and SWT. Huang and Zhou [17] extend the HUGO algorithm [18] by using a hybrid quantitative MINMAX feature. The idea of transformation domain steganography methods is to identify the edges between multiple regions [19] in the image where color changes would be less visible or to change the color for the plain region at once [20]. Image context understanding and captioning gaining enough accuracy just now [21] and the steganography does not take advantage of embedding messages to the background, unrecognized objects yet. The possibility to embed a message in text areas [22] is a consideration for the future steganography too. All techniques dedicated to identifying objects, edges, and the text are or can be used to optimize the user imperceptibility, when the user is not able to notice some color changes in the image. While most steganography methods rely on changing values of separate pixels, there are methods where the color palette is transformed. Color palette-based steganography is used by Seppanen et al. (SMK) [23]. These authors used a small color palette to conceal information within a color image. Brisbane et al. [24] proposed a pixel selection method and spherical coding structure method using shared color palette (SCP). The idea to change the color palette is used by Michiharu et al. [25] where image color space is decomposed into RBG components and changed to fit into the maximum number of colors after embedding data according to BPCS [26] algorithm. Raja et al. [27] also decompose the image color palette, cluster it, and provide indexes of shifted centroids. We believe there is space for another steganography method which uses color palette transformation. Therefore, we propose a method for color palette transformation in color space. Proposed method for color palette transformation in color space Requirements for the steganography method To increase the perception, we use color palette transformation rather than changing separate image pixels. As all pixels of the same color will be changed into one different color, areas of constant color will not be distorted. Illustration of color palette transformation advantages against separate pixel color changes is presented in Fig. 1. Figure 1a shows how changed pixels disturb the pattern of the original image (Fig. 1b), while the pattern remains the same in color palette transformation as shown in Fig. 1c. Original image (b), image with changed separate pixels (a), and image with changed color palette (c) To hide the message and later read the embedded message in a transformed image, we define some requirements for the color palette-based steganography algorithm: Each color from the original image has to be changed into a unique color as if multiple colors will be changed into the same color, later we will not be able to identify changes. The distance between similar colors has to be taken into account: The color change should "stay" in the same "color range" to make sure the image will contain the same pixel pattern. The number of the embedded bit should be selected according to the distance between similar colors as the user will be less perceptive to bigger color changes between two different colors compared to the same change in different shades of the same color. No reference models need to be used, but there should be a possibility to adjust the algorithms for a different level of color palette changes. Most of the presented requirements are the base for most steganography methods (for example LSB satisfies the second and third requirement, while the first requirement is different as changes pixel color, rather than color). Algorithm of the proposed steganography method A new steganography method was generated to fit all three earlier presented requirements. We propose to present the image color space as RGB cube, and no reference images will be needed; the stegomessage will be encoded in the new color palette. Each image color will be placed in the RGB cube according to its R, G, and B values in 3D space. It is not important to calculate the frequency of the color; only the existence of the color is used in the method. If the image has at least one pixel with color (x, y, z), then RGB cube (3D dimensional matrix) value in coordinates (x, y, z) will be equal to 1. While if color (x, y, z) does not exist in the image, the value will be equal to 0. 3D matrix can be used to store the RGB cube information. The matrix will be divided into sub-cubes, and all the sub-cubes should be stored in a list or other structure to ensure the same sequence of sub-cube processing. When all colors are stored in the RGB cube, we calculate where stegomessage bit can be stored the cube: If the RGB cube of sub-cube has more than one color in it, the cube has to be divided into sub-cubes. Each edge of the cube is divided into two parts, so we have eight sub-cubes and each color of the cube will belong to one of the sub-cubes. All eight sub-cubes will be processed recursively as the initial RGB cube till the sub-cube will have one or zero colors in it. If the RGB cube or sub-cube has one color, we analyze the size of the cube: If the sub-cube size is 1 × 1 × 1, it means there is only one possible color location in it and we cannot change it into another color within the range of the sub-cube. This cube is not suitable for stegomessage embedding. If the size of the RGB sub-cube is more than 1 × 1 × 1, it means we can change the location of the color. We use this cube or part of this cube to embed the stegomessage. The change is limited to be in the area of this RGB sub-cube only. This ensures that we will be able to decompose the changed RGB cube in the same sub-cubes after the embedding of stegomessage as well as the new color will not overlap with other colors in the RGB cube. If the RGB sub-cube has no colors, it will not be processed anymore as it means there are no colors that have to be changed (the area of the RGB cube is not used in the image). We are not using these cubes to embed stegomessage. The dividing fragment of the selected RGB cube into sub-cubes is presented in Fig. 2. The figure illustrates the processing of one sub-cube to eight smaller sub-cubes. Eight divided sub-cubes are further analyzed recursively. Only sub-cubes with at least one color in it and with cube edge length greater than 2 are analyzed for division further. "Empty" or too small sub-cubes are not divided anymore. Analyzed RGB cube (a) has more than one color; therefore, it is divided into eight sub-cubes (b-i), but only sub-cubes with at least one color (g–i) were analyzed further, while sub-cubes with no colors (b-f) are not analyzed anymore. Sub-cubes h and i are suitable to embed message as only one color exists. Sub-cube g has more than one color and it has to be divided, but the cube is too small for division and will not be used for message embedding in next iteration When RGB cube of size more than 1 × 1 × 1 and with one color in it is found, we can embed the stegomessage in it by changing the location of the color in the cube. How many bits N of stegomessage can be embedded in this cube depends on the length of the edge n of the cube or the number of possible color locations k in the cube (1). $$ N=3\bullet {\log}_2n={\log}_2k $$ Based on the example in Fig. 2, we will have only two sub-cubes where the message can be embedded (sub-cubes "h" and "i"). The length of the edge n of each of those sub-cubes is 2; therefore, we will be able to embed 6 bits (3·1 + 3·1). N bits of stegomessage are treated as a new location of the color in the RGB cube. We delete the existing color in the cube and replace it with a new color in the cube. As the color location stays in the same cube, we will be able to decompose the color space into the sub-cubes. The stegomessage will be read from RGB cubes of size more than 1 × 1 × 1 where only one color exists. This means we will be able to find the same RGB cubes, where stegomessage bits were stored and compose the stegomessage back with no complications. The stegomessage is expressed in binary code, and 3log2(n) bits are selected to be used as coordinates of the specific RGB sub-cube—log2(n) bits define the position in R-axis, log2(n) bits for G-axis, and log2(n) bits for B-axis. For example, we want to embed a message 111010 into the cube, presented in Fig. 2. Each sub-cube will use three bits of the stegomessage. Each axis will be presented by one bit as one bit has two possible values as well as the sub-cube axis has two possible values. The center of coordination system, coordinates (0, 0, 0) are in the bottom left corner, closest to us. Therefore the new location for sub-cube "h" in Fig. 2 will be in the same place, coordinates (1, 1, 1) in the sub-cube. The color of sub-cube "i" will be changed to coordinates (0, 1, 0) in the sub-cube. This will change the color, but the color will be in the range of the sub-cube and the color change will not be very contrast to the existing one. All the rest sub-cubes are not suitable for message embedding, but all sub-cubes will be combined into the initial RGB cube (see Fig. 3). Changed RGB cube (a), which was composed of all sub-cubes. Only sub-cubes h and i were suitable for embedding, while sub-cubes from b–g were left as it is, not changed Each axis in RGB cube has 256 values in 24-bit depth image, and by dividing the cube into the sub-cubes, the length of sub-cube length can be 256, 128, 64, 32, 16, 8, 4, or 2. According to the distribution of image colors in the color space, the size of RGB cubes with bits of stegomessage can vary a lot. To define the desired perception level of the stegoimage, the method applies an additional condition—if the size of RGB cube with one color is too big, we can treat it as a block with more than one color in it and divide it into sub-cubes. After dividing such a cube, only one sub-cube will have one color in it while the rest will have no colors in it. This will reduce the number of possible stegomessage bits N to be written and at the same time will impact smaller color palette changes. When all suitable RGB cubes were changed by embedding the stegomessage bits in it, we change the cover image by replacing the old color values with the new ones. As we are changing the color palette, all pixels of the same color will be changed to a new color. However, no compression or other transformations can be done after the color change and the image has to be stored as a new image (or a new version of the same image). For message decoding, the same actions should be executed to get sub-cubes with one color in it. As the algorithm is the same and message embedding changed the color, but left it in the same sub-cube, the list of sub-cubes will be identical as in the encoding algorithm. Therefore, only coordinates of the color have to be gathered and composed into one sequence to decode the embedded message. As an example in Fig. 3, we will get eight sub-cubes, but only sub-cubes "h" and "i" will be suitable for message reading (have only one color in it). By keeping the same sequence, we get the coordinates of the colors in those sub-cubes: (1, 1, 1) and (0, 1, 0). By converting each value into binary code and combining into one sequence of bits, we get the embedded message 111010. To identify the end of the stegomessage, it should end with some specific symbols (bit sequence). This will ensure the end of the stegomessage will be identified during the decoding and there will be no redundant information at the end of the message. A short bit sequence like two bytes of zeros will not be very noticeable for steganalysis as the bits might be embedded in different size and location sub-cubes. Therefore, it will not help to identify the method usage or message embedding fact. The algorithm of message embedding is presented in Fig. 4a and retrieving in Fig. 4b. Stegomessage embedding (a) and stegomessage retrieving (b) algorithms of the proposed method The palette changing might seem not enough for stegomessage storing. However, in an ideal situation, where image colors are distributed in the RGB cube to form all 2 × 2 × 2 cubes to have one color in it, the stegomessage length for 24-bit depth image can be 768 KB. This method does not depend on the size of the image directly (depends on the number of colors in the image) too and can excellence for lower resolution images with many colors. Results of proposed steganography method evaluation and discussion To prove the suitability of the proposed steganography method, its comparison to other steganography methods was executed and experiments on method application with different cover images were added. Comparison of stegoimage quality metrics The most used image quality metrics in steganography are Peak Signal Noise Ratio (PSNR) and Structural Similarity Index (SSIM) [26]. The PSNR (dB) is used to measure the visual quality of the stegoimage and evaluates the image quality between the input image f and the stegoimage g. For the image of size W × H, the PSNR between f and g is defined by: $$ \mathrm{PSNR}\left(f,g\right)=10{\log}_{10}\left(\frac{255^2}{\frac{1}{MN}{\sum}_{i=1}^M{\sum}_{j=1}^N{\left({f}_{ij}-{g}_{ij}\right)}^2}\right) $$ The SSIM is another image quality metric used to measure the similarity between images f and g and is considered to be correlated with the quality perception of the human visual system (HVS). The calculation of SSIM value includes three correlation loss factors l, s, and c: $$ \mathrm{SSIM}\left(f,g\right)=l\left(f,g\right)c\left(f,g\right)s\left(f,g\right) $$ $$ l\left(f,g\right)=\frac{2{\mu}_f{\mu}_g+{C}_1}{\mu_f^2+{\mu}_g^2+{C}_1} $$ $$ c\left(f,g\right)=\frac{2{\sigma}_f{\sigma}_g+{C}_2}{\sigma_f^2+{\sigma}_g^2+{C}_2} $$ $$ s\left(f,g\right)=\frac{\sigma_{fg}+{C}_3}{\sigma_f{\sigma}_g+{C}_3} $$ The l(f, g) (4) is the luminance comparison function which measures the closeness of the two images' mean luminance (μf and μg). The c(f, g) (5) is the contrast comparison function which measures the closeness of the contrast of the two images by using the standard deviation σf and σg. The s(f, g) (6) is the structure comparison function which measures the correlation coefficient between the two images f and g. The σfg is the covariance between f and g. The positive constants C1, C2, and C3 are used to avoid a null denominator [28]. We use well-known images (Baboon, Barbara, and Lena) of size 512 × 512 to compare the results of our method with the results of other existing steganography methods. We used three messages (zeros, ones, and randomly generated) and calculated the average of PSNR and SSIM values as well as capacity (number of bits, which can be embedded in the image). All the data is presented in Tables 1 and 2. Table 1 Quality comparison results of different steganography methods Table 2 Embedding capacity comparison results of different steganography methods Data for other methods were obtained from an analysis of other authors; therefore, some methods are not tested with the images and SSIM or capacity values are not provided. This complicated the comparison, and we were not able to implement the steganography methods. The results in Table 1 show our method is in the lead group in terms of SSIM value—none of the methods was able to get better value for all tested images. Sun's proposed method [19] leads according to the PSNR value, but our method goes just after it and shows similar results as Yu's method [19]. Despite the fact that there are other methods with better PSNR and SSIM values, results of our method are close to the leaders while the capacity of our method is up to three times bigger compared to Sun and Yu's methods (see Table 2). Our method is not a leader according to the capacity in the overall ranking. The method of Raja et al. claims to be the leader, but capacity cannot be accurately compared, as it achieved 6.2 bits per pixel capacity, but with 256 × 256 px image rather than 512 × 512 px. The fourth result is achieved with the 256 × 256 image too. The Brisbane et al. proposed method is possible to embed at up to 6 bits per pixel with a PSNR of 40 dB but up to 24 Kbit shared data is needed for it. The second and third results (EDSI and MPBDH methods) show similar results. Our proposed method does not fall very far from those four methods as the sixth results are three times smaller compared to ours. We were not able to find data on some steganography method capabilities for the analyzed images, but we believe our method can balance between the capacity and image quality and user perception. The experiment of the proposed method application on computer vision image datasets To analyze the message embedding possibilities of our proposed steganography method, two image datasets were selected—BSD-300 and Kodak Lossless True Color Image Suite. BSD-300 image dataset [29] is dedicated to image segmentation and boundary detection. This dataset includes 300 images (100 for testing and 200 for training). We do not use the segmentation and boundary detection data, just images. All images in the dataset are in JPG file format and 481 × 321 px dimensions. After embedding randomly generated stegomessages into all BSD-300 images, we calculated how many colors the image has, how many sub-cubes can be used for message embedding, how many bits can be embedded into the image, and what are the PSNR, SNR, and SSIM values after embedding randomly generated stegomessage into the cover image. The experiment data is presented in Table 3. The results of this experiment show the message embedding capacity for BSD-300 dataset is 0.45 bits for one pixel or 1.86 bits for one color. While the embedding capacity varies a lot for different images, the PSNR and SSIM values are stable. Table 3 Message embedding measurements for BSD-300 image dataset images As BSD-300 image dataset contains JPG files only, we used Kodak Lossless True Color Image Suite [30] too to get images of PNG format. Kodak image dataset was selected as it is the base of TID2013 image dataset [31], but the images have bigger dimensions. We used this dataset and generated additional variants of the images—all combinations of JPG and PNG file formats of 512 × 768, 341 × 512, 227 × 341, 151 × 227, 101 × 151, and 67 × 101 size were generated. This allowed having 288 cover images instead of the original 24 Kodak images. The purpose of having different size versions of the images was the desire to experiment how the number of colors depends on the embedding capacity and perception while similar color distribution should be kept by using the same content of the images. By reducing the size of the image, the number of colors is decreasing as well, while the color distribution should remain very similar. For extended Kodak Lossless True Color Image Suite, the average message embedding capacity is 55,803 bits and varies a lot (standard deviation is 43,727). The smallest capacity is for image kodim02.png of size 68 × 101 px. But this image has the smallest number of colors in the image too—3350 colors. The method was able to embed 0.83 bits/px or 1.67 bits/color for image kodim02.png of size 68 × 101 px. The smallest message embedding capacity per pixel is for image kodim16.jpg of size 512 × 768 px—0.09 bits/px. Image kodim16.png of size 341 × 512 has the smallest message embedding capacity per color—0.45 bits/color. The biggest relative capacities reach 6.58 bits/px and 7.16 bits/color. We were not able to inspect a strong correlation between image and stegomessage embedding capabilities (correlation coefficient is less than 0.1). The bigger message embedding capability can be noticed in images with more different colors (see Fig. 5). The embedded average number of bits for each image of extended Kodak image dataset The importance of color palette can be noticed in Fig. 6, where embedding capacity dependency on several colors in the image is presented (see Fig. 6). Linear dependency can be noted, but the value distribution is very high. It shows the importance of the color palette distribution in the image, not just the number of colors in the image. Stegomessage embedding capability (bits) dependency on file format and number of colors in the image Analysis on how the file format influences the embedding capability revealed some tendencies (correlation between file format and embedded bits per pixel is 0.184, correlation between file format and bits per color is 0.347)—in JPG file format images, 25% bigger stegomessage can be embedded (average embedded stegomessage size for PNG files is 49,632 bits and for JPG file 61,973bits) while the PSNR and SSIM values for both formats are the same (PSNR for PNG is 51.92 and for JPG 51.12, while SSIM values respectively are 0.9994 and 0.993). This is mostly explained by the fact that the number of colors in JPG files was bigger compared to PNG files. The experiments of the proposed method application on high-resolution images The efficiency of the proposed steganography method relies on the color distribution in the color space. Previously used image datasets had arbitrary low-resolution images, which reached 393,216 px only. Therefore, we executed an experiment where different photos taken with a recent camera from natural scenes were used as cover images and exploited to embed the stegomessages. We used 108 randomly selected images from personal photos: 48 high-resolution (4–24 million of pixels) 24 bit color depth images, 20 low-resolution (up to 1 million pixels) 24 bit color depth images, and 40 images with adaptive palette with up to 256 colors (20 images with smoothing and 20 images without smoothing). Randomly generated stegomessages were embedded into all 108 images. The message length was maximum possible for the cover image. We used the method with no limitations and by adding the limitation to use only 2 × 2 × 2 code blocks for message embedding. Analysis of experimental data with high-resolution images revealed there is a very weak correlation between the number of pixels in the image and the number of colors in the image (correlation coefficient is 0.04, while for previously used dataset images, the correlation coefficient between image resolution and color number was 0.57). The capacity of the image strongly correlates (correlation coefficient is 0.76) with the number of colors in the image. The average pixel capability for high-resolution images is 0.02 while for low-resolution images 0.47 bits per pixel. This confirms that the use of high-resolution cover images is not as optimal as low-resolution cover images. The color capability for low-resolution cover images is higher compared to higher resolution cover images too (averagely 1 bit for one color in high-resolution images can be embedded and 1.66 bits for one color in low-resolution images can be embedded). This can be explained by the fact that the lower resolution images have bigger distances between two colors (gradients in lower resolution images require less distinctive colors). The histograms of higher resolution images are smoother compared to lower resolution images. The bigger distance between colors allows a bigger number of bits to be embedded in our method. Experiments showed the image capacity increases 19% on average if there are no limitations for the color cube size for stegomessage embedding compared to the limitation to use 2 × 2 × 2 color blocks only. The experiments of the proposed method steganalysis Existing steganalysis tools (like Virtual Steganographic Laboratory for Digital Images, StegSecret, and others) are mostly based on brutal force decoding of existing steganography methods. It is difficult to resist to this kind of steganalysis without taking care of the stegomessage is prepared to be encrypted. Till our method is not publicly available and implemented in those tools, it makes no sense to use those tools for steganalysis of our method. Another group of steganalysis methods analyzes the image to detect some indicators if the image was modified. It does not decode the embedded message, just defines the probability the images has an additional message, embedded in it. In most cases, the analysis includes quality metrics [32] or noise analysis [33]. Our method took into account the most often used metrics for steganalysis and allowed limitation of sub-cube size. This makes sure the color changes will not be too big to identify the method, while the color palette change rather than pixel change allows resistance to analysis of adjacent pixel colors. Our method might not be resistant to steganalysis methods, which applies machine learning to analyze similar content images in order to find prevailing colors and other patterns. This kind of steganalysis method is presented by Zhao et al. [34]. These authors analyze unprocessed images of natural scenes and adapt the analysis for GIF image steganalysis. While the results are good for natural scene images with higher embedding rate, it still has limitations and is not adapted for our steganography method yet. For steganography of our method, color palette distribution should be analyzed rather than pixel color distribution in the image. In some cases, the machine learning can be not necessary if some type of cover images will be used—images with standard color palette. The standard color palette has its own specifics, and we present an experiment with images of the standard palette. This steganalysis experiment is a continuation of the experiment, described in Section 4.3. As colors in the standard palette are distributed evenly in all color space, it should make ideal conditions for our method to embed the biggest number of stegomessage bits. The analysis revealed that only 76 colors out of 256 are used in the image averagely and the method cannot reach the theoretical maximum. The increase of color capability increases because of the standard palette usage to 3 pixels per color if we use limitation to embed stegomessage to 2 × 2 × 2 size color cubes and 15.5 pixels per color if there are no limitations for cube size. The usage of the standard color palette has disadvantages as well. If there are no limitations for color cube size, most blocks for stegomessage embedding will be of size 32 × 32 × 32 and it might cause visual changes between the cover and stegoimage. The color palette is changed (see Fig. 7) and might indicate the use of steganography in the image as well. Color space distribution for an image of the standard palette (a) and how the palette looks after stegomessage embedding (b) If smoothing is used, the number of colors in the image with the standard palette increases by 28%. This increases the cover image quality as well as stegoimage uses smaller color sub-cubes to embed stegomessage bits; therefore, the stegoimage quality is better too. The presented steganography method proposes a new approach on how to change the color palette to keep the user perception as well as provide a reasonable capacity to embed a stegomessage. A comparison of the proposed method to existing methods revealed that the proposed method outperforms existing analogs in at least one of measured values (PSNR, SSIM, or embedding capacity). This method provides a better user perception compared to high capacity methods, while its embedding capacity is larger compared to methods with high PSNR and/or SSIM values. The proposed method is in the middle between user perception and capacity. It is worth to mention that the proposed method is transforming the color palette, rather than separate pixels. Its capacity is very dependent on a color palette (number of colors in the image and color palette distribution in color space) and is not influenced by image size (not directly). Therefore, the proposed method application area should be low-resolution images with a big number of colors (photos). This would allow highlighting the advantages of the proposed method. At the same time, the proposed method will be lacking capacity in several color paintings (not photos). Existing steganalysis methods are not adapted directly to the proposed method. Our analysis showed that the visual perception is good and the embedded message is not noticed in the image. However, the proposed methods are not resistant to color palette analysis and standard palette images should not be used to limit the steganography identification. The current version of the proposed method is not adapted to grayscale images as its usage without any limitation can cause color appearance after the stegomessage embedding. To minimize this kind of color space disturbance, the maximal cube dimension n should be minimized to 2. To adapt the method for grayscale image, the new color must be on the diagonal of the RGC cube. Therefore, log2(n) bits should be embedded in n × n × n size sub-cube by repeating the same bits for all three RGB color axes. Only one dimension will be used for grayscale images rather than three dimensions. Such a limitation would assure the smallest changes in the color palette or change into another gray color. The analysis of existing steganography methods revealed that the biggest number of methods is based on pixel modification rather than color palette changes to embed stegomessage. Existing color palette modification methods are not developed enough as one part of them requires some shared data, while the other part uses some complex calculations. We proposed a new steganography method, which is based on image color palette transformation by replacing the location of the color in RGB cube and does not require complex calculations, therefore can be used in mobile or embedded devices too. Comparison of stegoimage quality and capability metrics for different steganography methods revealed that our proposed method has a balance between user perception and capability to write as many data as possible—our method has the highest SSIM value among other methods, PSNR value is close to the leaders, and the capacity is average among all steganography methods. There is no method, which would outperform our method based on all embedding quality and capacity metrics. Experiments with different cover images revealed that the method does not require high-resolution cover images and the pixel, as well as embedding capacity, is higher when lower resolution images are used. If standard or adaptive color palette cover images are used, the average color capability can be increased up to 20 bits per color. This allows embedding averagely 2940 bits of data when adaptive palette with up to 256 colors is used, and it will not add random noise to the image (the color palette will be changed rather than separate pixels). Please contact the author for data (in the experiment used images or MatLab files with implemented method) requests. Contrast comparison function Image height (in pixels) The number of possible color location in the image RGB cube Luminance comparison function LSB: Least significant bit The edge length of the divided RGB cube, with one color inside of it The maximum number of bits, which can be embedded into stegoimage PSNR: Peak Signal Noise Ratio PVD: Pixel value differencing RGB: Red Green Blue Structure comparison function SCP: Shared color palette SMK: Seppanen, Makela, and Keskinarkaus SSIM: Structural Similarity Index Image width (in pixels) J. Li, C. Yu, B.B. Gupta, X. Ren, Color image watermarking scheme based on quaternion Hadamard transform and Schur decomposition. Multimed. Tools Appl. 77(4), 4545–4561 (2018) Z. Zhang, H. Sun, S. Gao, S. Jin, Self-recovery reversible image watermarking algorithm. PloS One 13(6), e0199143 (2018) C. Qin, P. Ji, C.-C. Chang, J. Dong, X. Sun, Non-uniform watermark sharing based on optimal iterative BTC for image tampering recovery. 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Sankur, Steganalysis using image quality metrics. IEEE Trans. Image Process. 12(2), 221–229 (2003) MathSciNet Article Google Scholar J. Fridrich, J. Kodovsky, Rich models for steganalysis of digital images. IEEE Trans. Inf. Forensics Secur 7(3), 868–882 (2012) H. Zhao, H. Wang, M.K. Khan, Steganalysis for palette-based images using generalized difference image and color correlogram. Signal Process. 91(11), 2595–2605 (2011) No other persons participated in the research. The research had no specific funding and was implemented as a master thesis in Šiauliai Univesity with the supervisor from Vilnius Gediminas Technical University. Šiauliai University, Šiauliai, Lithuania Eugenijus Margalikas Vilnius Gediminas Technical University, Vilnius, Lithuania Simona Ramanauskaitė EM was responsible for the method development and implementation. SR prepared the research methodology and wrote the paper. Joint work was used to execute the experiments and to compare the proposed method with other methods. Both authors read and approved the final manuscript. Eugenijus Margalikas was born in Siauliai, Lithuania, in 1983. He received the B.S. and M.S. degrees in Informatics Engineering from Siauliai University in 2006 and 2016. Since 2004, he applied his knowledge in several areas such as education and broadcasting. He is currently working as a CNC programmer at Nordisk Massivtre AS, Norway. Simona Ramanauskaitė is born on December 18, 1983. She received a PhD in Informatics Engineering in 2012 from Vilnius Gediminas Technical University, Lithuania. Currently, she is working as an assoc. prof. at Vilnius Gediminas Technical University. Her current research interests include different aspects of Information Security and Human-Computer Interaction. Correspondence to Simona Ramanauskaitė. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Margalikas, E., Ramanauskaitė, S. Image steganography based on color palette transformation in color space. J Image Video Proc. 2019, 82 (2019). https://doi.org/10.1186/s13640-019-0484-x Stegoimage	CommonCrawl
(Redirected from Protons) For other uses, see Proton (disambiguation). A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 e (elementary charge). Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ratio). Protons and neutrons, each with masses of approximately one atomic mass unit, are jointly referred to as "nucleons" (particles present in atomic nuclei). The quark content of a proton. The color assignment of individual quarks is arbitrary, but all three colors must be present. Forces between quarks are mediated by gluons. Baryon 2 up quarks (u), 1 down quark (d) Fermionic Gravity, electromagnetic, weak, strong p+ , 1 1H+ Antiparticle Antiproton Theorized William Prout (1815) Observed as H+ by Eugen Goldstein (1886). Identified in other nuclei (and named) by Ernest Rutherford (1917–1920). 1.67262192369(51)×10−27 kg[1] 1.007276466621(53) Da[2] 938.27208816(29) MeV/c2[3] Mean lifetime > 3.6×1029 years[4] (stable) +1 e Charge radius 0.8414(19) fm[5] Electric dipole moment < 2.1×10−25 e⋅cm[6] Electric polarizability 0.00112(4) fm3 Magnetic moment 1.41060679736(60)×10−26 J⋅T−1[7] 1.52103220230(46)×10−3 μB[5] 2.79284734463(82) μN[8] Magnetic polarizability 1.9(5)×10−4 fm3 Isospin I(JP) = 1/2(1/2+) One or more protons are present in the nucleus of every atom. They provide the attractive electrostatic central force that binds the atomic electrons. The number of protons in the nucleus is the defining property of an element, and is referred to as the atomic number (represented by the symbol Z). Since each element has a unique number of protons, each element has its own unique atomic number, which determines the number of atomic electrons and consequently the chemical characteristics of the element. The word proton is Greek for "first", and this name was given to the hydrogen nucleus by Ernest Rutherford in 1920. In previous years, Rutherford had discovered that the hydrogen nucleus (known to be the lightest nucleus) could be extracted from the nuclei of nitrogen by atomic collisions.[9] Protons were therefore a candidate to be a fundamental or elementary particle, and hence a building block of nitrogen and all other heavier atomic nuclei. Although protons were originally considered to be elementary particles, in the modern Standard Model of particle physics, protons are now known to be composite particles, containing three valence quarks, and together with neutrons are now classified as hadrons. Protons are composed of two up quarks of charge +2/3e and one down quark of charge −1/3e. The rest masses of quarks contribute only about 1% of a proton's mass.[10] The remainder of a proton's mass is due to quantum chromodynamics binding energy, which includes the kinetic energy of the quarks and the energy of the gluon fields that bind the quarks together. Because protons are not fundamental particles, they possess a measurable size; the root mean square charge radius of a proton is about 0.84–0.87 fm (1 fm = 10−15 m).[11][12] In 2019, two different studies, using different techniques, found this radius to be 0.833 fm, with an uncertainty of ±0.010 fm.[13][14] Free protons occur occasionally on Earth: thunderstorms can produce protons with energies of up to several tens of MeV.[15][16] At sufficiently low temperatures and kinetic energies, free protons will bind to electrons. However, the character of such bound protons does not change, and they remain protons. A fast proton moving through matter will slow by interactions with electrons and nuclei, until it is captured by the electron cloud of an atom. The result is a protonated atom, which is a chemical compound of hydrogen. In a vacuum, when free electrons are present, a sufficiently slow proton may pick up a single free electron, becoming a neutral hydrogen atom, which is chemically a free radical. Such "free hydrogen atoms" tend to react chemically with many other types of atoms at sufficiently low energies. When free hydrogen atoms react with each other, they form neutral hydrogen molecules (H2), which are the most common molecular component of molecular clouds in interstellar space. Free protons are routinely used for accelerators for proton therapy or various particle physics experiments, with the most powerful example being the Large Hadron Collider. 4 Quarks and the mass of a proton 5 Charge radius 5.1 Pressure inside the proton 5.2 Charge radius in solvated proton, hydronium 6 Interaction of free protons with ordinary matter 7 Proton in chemistry 7.1 Atomic number 7.2 Hydrogen ion 7.3 Proton nuclear magnetic resonance (NMR) 8 Human exposure 9 Antiproton DescriptionEdit Unsolved problem in physics: How do the quarks and gluons carry the spin of protons? (more unsolved problems in physics) Protons are spin-1/2 fermions and are composed of three valence quarks,[17] making them baryons (a sub-type of hadrons). The two up quarks and one down quark of a proton are held together by the strong force, mediated by gluons.[18]: 21–22 A modern perspective has a proton composed of the valence quarks (up, up, down), the gluons, and transitory pairs of sea quarks. Protons have a positive charge distribution, which decays approximately exponentially, with a root mean square charge radius of about 0.8 fm.[19] Protons and neutrons are both nucleons, which may be bound together by the nuclear force to form atomic nuclei. The nucleus of the most common isotope of the hydrogen atom (with the chemical symbol "H") is a lone proton. The nuclei of the heavy hydrogen isotopes deuterium and tritium contain one proton bound to one and two neutrons, respectively. All other types of atomic nuclei are composed of two or more protons and various numbers of neutrons. The concept of a hydrogen-like particle as a constituent of other atoms was developed over a long period. As early as 1815, William Prout proposed that all atoms are composed of hydrogen atoms (which he called "protyles"), based on a simplistic interpretation of early values of atomic weights (see Prout's hypothesis), which was disproved when more accurate values were measured.[20]: 39–42 Ernest Rutherford at the first Solvay Conference, 1911 Proton detected in an isopropanol cloud chamber In 1886, Eugen Goldstein discovered canal rays (also known as anode rays) and showed that they were positively charged particles (ions) produced from gases. However, since particles from different gases had different values of charge-to-mass ratio (q/m), they could not be identified with a single particle, unlike the negative electrons discovered by J. J. Thomson. Wilhelm Wien in 1898 identified the hydrogen ion as the particle with the highest charge-to-mass ratio in ionized gases.[21] Following the discovery of the atomic nucleus by Ernest Rutherford in 1911, Antonius van den Broek proposed that the place of each element in the periodic table (its atomic number) is equal to its nuclear charge. This was confirmed experimentally by Henry Moseley in 1913 using X-ray spectra. In 1917 (in experiments reported in 1919 and 1925), Rutherford proved that the hydrogen nucleus is present in other nuclei, a result usually described as the discovery of protons.[22] These experiments began after Rutherford had noticed that, when alpha particles were shot into air (mostly nitrogen), his scintillation detectors showed the signatures of typical hydrogen nuclei as a product. After experimentation Rutherford traced the reaction to the nitrogen in air and found that when alpha particles were introduced into pure nitrogen gas, the effect was larger. In 1919 Rutherford assumed that the alpha particle merely knocked a proton out of nitrogen, turning it into carbon. After observing Blackett's cloud chamber images in 1925, Rutherford realized that the alpha particle was absorbed. After capture of the alpha particle, a hydrogen nucleus is ejected, so that heavy oxygen, not carbon, is the result – i.e., the atomic number Z of the nucleus is increased rather than reduced. This was the first reported nuclear reaction, 14N + α → 17O + p. Rutherford at first thought of our modern "p" in this equation as a hydrogen ion, H+. Depending on one's perspective, either 1919 (when it was seen experimentally as derived from another source than hydrogen) or 1920 (when it was recognized and proposed as an elementary particle) may be regarded as the moment when the proton was 'discovered'. Rutherford knew hydrogen to be the simplest and lightest element and was influenced by Prout's hypothesis that hydrogen was the building block of all elements. Discovery that the hydrogen nucleus is present in other nuclei as an elementary particle led Rutherford to give the hydrogen nucleus H+ a special name as a particle, since he suspected that hydrogen, the lightest element, contained only one of these particles. He named this new fundamental building block of the nucleus the proton, after the neuter singular of the Greek word for "first", πρῶτον. However, Rutherford also had in mind the word protyle as used by Prout. Rutherford spoke at the British Association for the Advancement of Science at its Cardiff meeting beginning 24 August 1920.[23] At the meeting, he was asked by Oliver Lodge for a new name for the positive hydrogen nucleus to avoid confusion with the neutral hydrogen atom. He initially suggested both proton and prouton (after Prout).[24] Rutherford later reported that the meeting had accepted his suggestion that the hydrogen nucleus be named the "proton", following Prout's word "protyle".[25] The first use of the word "proton" in the scientific literature appeared in 1920.[26][27] StabilityEdit Main article: Proton decay Are protons fundamentally stable? Or do they decay with a finite lifetime as predicted by some extensions to the standard model? The free proton (a proton not bound to nucleons or electrons) is a stable particle that has not been observed to break down spontaneously to other particles. Free protons are found naturally in a number of situations in which energies or temperatures are high enough to separate them from electrons, for which they have some affinity. Free protons exist in plasmas in which temperatures are too high to allow them to combine with electrons. Free protons of high energy and velocity make up 90% of cosmic rays, which propagate in vacuum for interstellar distances. Free protons are emitted directly from atomic nuclei in some rare types of radioactive decay. Protons also result (along with electrons and antineutrinos) from the radioactive decay of free neutrons, which are unstable. The spontaneous decay of free protons has never been observed, and protons are therefore considered stable particles according to the Standard Model. However, some grand unified theories (GUTs) of particle physics predict that proton decay should take place with lifetimes between 1031 to 1036 years and experimental searches have established lower bounds on the mean lifetime of a proton for various assumed decay products.[28][29][30] Experiments at the Super-Kamiokande detector in Japan gave lower limits for proton mean lifetime of 6.6×1033 years for decay to an antimuon and a neutral pion, and 8.2×1033 years for decay to a positron and a neutral pion.[31] Another experiment at the Sudbury Neutrino Observatory in Canada searched for gamma rays resulting from residual nuclei resulting from the decay of a proton from oxygen-16. This experiment was designed to detect decay to any product, and established a lower limit to a proton lifetime of 2.1×1029 years.[32] However, protons are known to transform into neutrons through the process of electron capture (also called inverse beta decay). For free protons, this process does not occur spontaneously but only when energy is supplied. The equation is: e− The process is reversible; neutrons can convert back to protons through beta decay, a common form of radioactive decay. In fact, a free neutron decays this way, with a mean lifetime of about 15 minutes. A proton can also transform into neutrons through beta plus decay (β+ decay). According to quantum field theory, the mean proper lifetime of protons τ p {\displaystyle \tau _{\mathrm {p} }} becomes finite when they are accelerating with proper acceleration a {\displaystyle a} , and τ p {\displaystyle \tau _{\mathrm {p} }} decreases with increasing a {\displaystyle a} . Acceleration gives rise to a non-vanishing probability for the transition e. This was a matter of concern in the later 1990s because τ p {\displaystyle \tau _{\mathrm {p} }} is a scalar that can be measured by the inertial and coaccelerated observers. In the inertial frame, the accelerating proton should decay according to the formula above. However, according to the coaccelerated observer the proton is at rest and hence should not decay. This puzzle is solved by realizing that in the coaccelerated frame there is a thermal bath due to Fulling–Davies–Unruh effect, an intrinsic effect of quantum field theory. In this thermal bath, experienced by the proton, there are electrons and antineutrinos with which the proton may interact according to the processes: (i) , (ii) and (iii) . Adding the contributions of each of these processes, one should obtain τ p {\displaystyle \tau _{\mathrm {p} }} .[33][34][35][36] Quarks and the mass of a protonEdit In quantum chromodynamics, the modern theory of the nuclear force, most of the mass of protons and neutrons is explained by special relativity. The mass of a proton is about 80–100 times greater than the sum of the rest masses of its three valence quarks, while the gluons have zero rest mass. The extra energy of the quarks and gluons in a proton, as compared to the rest energy of the quarks alone in the QCD vacuum, accounts for almost 99% of the proton's mass. The rest mass of a proton is, thus, the invariant mass of the system of moving quarks and gluons that make up the particle, and, in such systems, even the energy of massless particles confined to a system is still measured as part of the rest mass of the system. Two terms are used in referring to the mass of the quarks that make up protons: current quark mass refers to the mass of a quark by itself, while constituent quark mass refers to the current quark mass plus the mass of the gluon particle field surrounding the quark.[37]: 285–286 [38]: 150–151 These masses typically have very different values. The kinetic energy of the quarks that is a consequence of confinement is a contribution (see Mass in special relativity). Using lattice QCD calculations, the contributions to the mass of the proton are the quark condensate (~9%, comprising the up and down quarks and a sea of virtual strange quarks), the quark kinetic energy (~32%), the gluon kinetic energy (~37%), and the anomalous gluonic contribution (~23%, comprising contributions from condensates of all quark flavors).[39] The constituent quark model wavefunction for the proton is \| p ↑ ⟩ = 1 18 ( 2 \| u ↑ d ↓ u ↑ ⟩ + 2 \| u ↑ u ↑ d ↓ ⟩ + 2 \| d ↓ u ↑ u ↑ ⟩ − \| u ↑ u ↓ d ↑ ⟩ − \| u ↑ d ↑ u ↓ ⟩ − \| u ↓ d ↑ u ↑ ⟩ − \| d ↑ u ↓ u ↑ ⟩ − \| d ↑ u ↑ u ↓ ⟩ − \| u ↓ u ↑ d ↑ ⟩ ) . {\displaystyle \mathrm {\|p_{\uparrow }\rangle ={\tfrac {1}{\sqrt {18}}}\left(2\|u_{\uparrow }d_{\downarrow }u_{\uparrow }\rangle +2\|u_{\uparrow }u_{\uparrow }d_{\downarrow }\rangle +2\|d_{\downarrow }u_{\uparrow }u_{\uparrow }\rangle -\|u_{\uparrow }u_{\downarrow }d_{\uparrow }\rangle -\|u_{\uparrow }d_{\uparrow }u_{\downarrow }\rangle -\|u_{\downarrow }d_{\uparrow }u_{\uparrow }\rangle -\|d_{\uparrow }u_{\downarrow }u_{\uparrow }\rangle -\|d_{\uparrow }u_{\uparrow }u_{\downarrow }\rangle -\|u_{\downarrow }u_{\uparrow }d_{\uparrow }\rangle \right)} .} The internal dynamics of protons are complicated, because they are determined by the quarks' exchanging gluons, and interacting with various vacuum condensates. Lattice QCD provides a way of calculating the mass of a proton directly from the theory to any accuracy, in principle. The most recent calculations[40][41] claim that the mass is determined to better than 4% accuracy, even to 1% accuracy (see Figure S5 in Dürr et al.[41]). These claims are still controversial, because the calculations cannot yet be done with quarks as light as they are in the real world. This means that the predictions are found by a process of extrapolation, which can introduce systematic errors.[42] It is hard to tell whether these errors are controlled properly, because the quantities that are compared to experiment are the masses of the hadrons, which are known in advance. These recent calculations are performed by massive supercomputers, and, as noted by Boffi and Pasquini: "a detailed description of the nucleon structure is still missing because ... long-distance behavior requires a nonperturbative and/or numerical treatment ..."[43] More conceptual approaches to the structure of protons are: the topological soliton approach originally due to Tony Skyrme and the more accurate AdS/QCD approach that extends it to include a string theory of gluons,[44] various QCD-inspired models like the bag model and the constituent quark model, which were popular in the 1980s, and the SVZ sum rules, which allow for rough approximate mass calculations.[45] These methods do not have the same accuracy as the more brute-force lattice QCD methods, at least not yet. Charge radiusEdit Main article: Proton radius puzzle The problem of defining a radius for an atomic nucleus (proton) is similar to the problem of atomic radius, in that neither atoms nor their nuclei have definite boundaries. However, the nucleus can be modeled as a sphere of positive charge for the interpretation of electron scattering experiments: because there is no definite boundary to the nucleus, the electrons "see" a range of cross-sections, for which a mean can be taken. The qualification of "rms" (for "root mean square") arises because it is the nuclear cross-section, proportional to the square of the radius, which is determining for electron scattering.[dubious – discuss] The internationally accepted value of a proton's charge radius is 0.8768 fm. This value is based on measurements involving a proton and an electron (namely, electron scattering measurements and complex calculation involving scattering cross section based on Rosenbluth equation for momentum-transfer cross section), and studies of the atomic energy levels of hydrogen and deuterium. However, in 2010 an international research team published a proton charge radius measurement via the Lamb shift in muonic hydrogen (an exotic atom made of a proton and a negatively charged muon). As a muon is 200 times heavier than an electron, its de Broglie wavelength is correspondingly shorter. This smaller atomic orbital is much more sensitive to the proton's charge radius, so allows more precise measurement. Their measurement of the root-mean-square charge radius of a proton is "0.84184(67) fm, which differs by 5.0 standard deviations from the CODATA value of 0.8768(69) fm".[46] In January 2013, an updated value for the charge radius of a proton—0.84087(39) fm—was published. The precision was improved by 1.7 times, increasing the significance of the discrepancy to 7σ.[12] The 2014 CODATA adjustment slightly reduced the recommended value for the proton radius (computed using electron measurements only) to 0.8751(61) fm, but this leaves the discrepancy at 5.6σ. If no errors were found in the measurements or calculations, it would have been necessary to re-examine the world's most precise and best-tested fundamental theory: quantum electrodynamics.[47] The proton radius was a puzzle as of 2017.[48][49] A resolution came in 2019, when two different studies, using different techniques involving the Lamb shift of the electron in hydrogen, and electron–proton scattering, found the radius of the proton to be 0.833 fm, with an uncertainty of ±0.010 fm, and 0.831 fm.[13][14] The radius of the proton is linked to the form factor and momentum-transfer cross section. The atomic form factor G modifies the cross section corresponding to point-like proton. R e 2 = − 6 d G e d q 2 \| q 2 = 0 d σ d Ω = d σ d Ω \| point G 2 ( q 2 ) {\displaystyle {\begin{aligned}R_{\text{e}}^{2}&=-6{{\frac {dG_{\text{e}}}{dq^{2}}}\,{\Bigg \vert }\,}_{q^{2}=0}\\{\frac {d\sigma }{d\Omega }}\ &={{\frac {d\sigma }{d\Omega }}\,{\Bigg \vert }\,}_{\text{point}}G^{2}(q^{2})\end{aligned}}} The atomic form factor is related to the wave function density of the target: G ( q 2 ) = ∫ e i q r ψ ( r ) 2 d r 3 {\displaystyle G(q^{2})=\int e^{iqr}\psi (r)^{2}\,dr^{3}} The form factor can be split in electric and magnetic form factors. These can be further written as linear combinations of Dirac and Pauli form factors.[49] G m = F D + F P G e = F D − τ F P d σ d Ω = d σ d Ω \| N S 1 1 + τ ( G e 2 ( q 2 ) + τ ϵ G m 2 ( q 2 ) ) {\displaystyle {\begin{aligned}G_{\text{m}}&=F_{\text{D}}+F_{\text{P}}\\G_{\text{e}}&=F_{\text{D}}-\tau F_{\text{P}}\\{\frac {d\sigma }{d\Omega }}&={{\frac {d\sigma }{d\Omega }}\,{\Bigg \vert }\,}_{NS}{\frac {1}{1+\tau }}\left(G_{\text{e}}^{2}\left(q^{2}\right)+{\frac {\tau }{\epsilon }}G_{\text{m}}^{2}\left(q^{2}\right)\right)\end{aligned}}} Pressure inside the protonEdit Since the proton is composed of quarks confined by gluons, an equivalent pressure that acts on the quarks can be defined. This allows calculation of their distribution as a function of distance from the centre using Compton scattering of high-energy electrons (DVCS, for deeply virtual Compton scattering). The pressure is maximum at the centre, about 1035 Pa, which is greater than the pressure inside a neutron star.[50] It is positive (repulsive) to a radial distance of about 0.6 fm, negative (attractive) at greater distances, and very weak beyond about 2 fm. Charge radius in solvated proton, hydroniumEdit The radius of the hydrated proton appears in the Born equation for calculating the hydration enthalpy of hydronium. Interaction of free protons with ordinary matterEdit Although protons have affinity for oppositely charged electrons, this is a relatively low-energy interaction and so free protons must lose sufficient velocity (and kinetic energy) in order to become closely associated and bound to electrons. High energy protons, in traversing ordinary matter, lose energy by collisions with atomic nuclei, and by ionization of atoms (removing electrons) until they are slowed sufficiently to be captured by the electron cloud in a normal atom. However, in such an association with an electron, the character of the bound proton is not changed, and it remains a proton. The attraction of low-energy free protons to any electrons present in normal matter (such as the electrons in normal atoms) causes free protons to stop and to form a new chemical bond with an atom. Such a bond happens at any sufficiently "cold" temperature (that is, comparable to temperatures at the surface of the Sun) and with any type of atom. Thus, in interaction with any type of normal (non-plasma) matter, low-velocity free protons do not remain free but are attracted to electrons in any atom or molecule with which they come into contact, causing the proton and molecule to combine. Such molecules are then said to be "protonated", and chemically they are simply compounds of hydrogen, often positively charged. Often, as a result, they become so-called Brønsted acids. For example, a proton captured by a water molecule in water becomes hydronium, the aqueous cation H3O+. Proton in chemistryEdit Atomic numberEdit In chemistry, the number of protons in the nucleus of an atom is known as the atomic number, which determines the chemical element to which the atom belongs. For example, the atomic number of chlorine is 17; this means that each chlorine atom has 17 protons and that all atoms with 17 protons are chlorine atoms. The chemical properties of each atom are determined by the number of (negatively charged) electrons, which for neutral atoms is equal to the number of (positive) protons so that the total charge is zero. For example, a neutral chlorine atom has 17 protons and 17 electrons, whereas a Cl− anion has 17 protons and 18 electrons for a total charge of −1. All atoms of a given element are not necessarily identical, however. The number of neutrons may vary to form different isotopes, and energy levels may differ, resulting in different nuclear isomers. For example, there are two stable isotopes of chlorine: 35 with 35 − 17 = 18 neutrons and 37 with 37 − 17 = 20 neutrons. Hydrogen ionEdit See also: Hydron (chemistry) Protium, the most common isotope of hydrogen, consists of one proton and one electron (it has no neutrons). The term "hydrogen ion" (H+ ) implies that that H-atom has lost its one electron, causing only a proton to remain. Thus, in chemistry, the terms "proton" and "hydrogen ion" (for the protium isotope) are used synonymously The proton is a unique chemical species, being a bare nucleus. As a consequence it has no independent existence in the condensed state and is invariably found bound by a pair of electrons to another atom. Ross Stewart, The Proton: Application to Organic Chemistry (1985, p. 1) In chemistry, the term proton refers to the hydrogen ion, H+ . Since the atomic number of hydrogen is 1, a hydrogen ion has no electrons and corresponds to a bare nucleus, consisting of a proton (and 0 neutrons for the most abundant isotope protium 1 ). The proton is a "bare charge" with only about 1/64,000 of the radius of a hydrogen atom, and so is extremely reactive chemically. The free proton, thus, has an extremely short lifetime in chemical systems such as liquids and it reacts immediately with the electron cloud of any available molecule. In aqueous solution, it forms the hydronium ion, H3O+, which in turn is further solvated by water molecules in clusters such as [H5O2]+ and [H9O4]+.[51] The transfer of H+ in an acid–base reaction is usually referred to as "proton transfer". The acid is referred to as a proton donor and the base as a proton acceptor. Likewise, biochemical terms such as proton pump and proton channel refer to the movement of hydrated H+ ions. The ion produced by removing the electron from a deuterium atom is known as a deuteron, not a proton. Likewise, removing an electron from a tritium atom produces a triton. Proton nuclear magnetic resonance (NMR)Edit Also in chemistry, the term "proton NMR" refers to the observation of hydrogen-1 nuclei in (mostly organic) molecules by nuclear magnetic resonance. This method uses the quantized spin magnetic moment of the proton, which is due to its angular momentum (or spin), which in turn has a magnitude of one-half the reduced Planck constant. ( ℏ / 2 {\displaystyle \hbar /2} ). The name refers to examination of protons as they occur in protium (hydrogen-1 atoms) in compounds, and does not imply that free protons exist in the compound being studied. Human exposureEdit Main article: Effect of spaceflight on the body See also: Proton therapy The Apollo Lunar Surface Experiments Packages (ALSEP) determined that more than 95% of the particles in the solar wind are electrons and protons, in approximately equal numbers.[52][53] Because the Solar Wind Spectrometer made continuous measurements, it was possible to measure how the Earth's magnetic field affects arriving solar wind particles. For about two-thirds of each orbit, the Moon is outside of the Earth's magnetic field. At these times, a typical proton density was 10 to 20 per cubic centimeter, with most protons having velocities between 400 and 650 kilometers per second. For about five days of each month, the Moon is inside the Earth's geomagnetic tail, and typically no solar wind particles were detectable. For the remainder of each lunar orbit, the Moon is in a transitional region known as the magnetosheath, where the Earth's magnetic field affects the solar wind, but does not completely exclude it. In this region, the particle flux is reduced, with typical proton velocities of 250 to 450 kilometers per second. During the lunar night, the spectrometer was shielded from the solar wind by the Moon and no solar wind particles were measured.[52] Protons also have extrasolar origin from galactic cosmic rays, where they make up about 90% of the total particle flux. These protons often have higher energy than solar wind protons, and their intensity is far more uniform and less variable than protons coming from the Sun, the production of which is heavily affected by solar proton events such as coronal mass ejections. Research has been performed on the dose-rate effects of protons, as typically found in space travel, on human health.[53][54] To be more specific, there are hopes to identify what specific chromosomes are damaged, and to define the damage, during cancer development from proton exposure.[53] Another study looks into determining "the effects of exposure to proton irradiation on neurochemical and behavioral endpoints, including dopaminergic functioning, amphetamine-induced conditioned taste aversion learning, and spatial learning and memory as measured by the Morris water maze.[54] Electrical charging of a spacecraft due to interplanetary proton bombardment has also been proposed for study.[55] There are many more studies that pertain to space travel, including galactic cosmic rays and their possible health effects, and solar proton event exposure. The American Biostack and Soviet Biorack space travel experiments have demonstrated the severity of molecular damage induced by heavy ions on microorganisms including Artemia cysts.[56] AntiprotonEdit Main article: Antiproton CPT-symmetry puts strong constraints on the relative properties of particles and antiparticles and, therefore, is open to stringent tests. For example, the charges of a proton and antiproton must sum to exactly zero. This equality has been tested to one part in 108. The equality of their masses has also been tested to better than one part in 108. By holding antiprotons in a Penning trap, the equality of the charge-to-mass ratio of protons and antiprotons has been tested to one part in 6×109.[57] The magnetic moment of antiprotons has been measured with error of 8×10−3 nuclear Bohr magnetons, and is found to be equal and opposite to that of a proton.[58] Physics portal Fermion field Hydron (chemistry) List of particles Proton–proton chain Quark model Proton spin crisis ^ "2018 CODATA Value: proton mass". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20. ^ "2018 CODATA Value: proton mass in u". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2022-09-11. ^ "2018 CODATA Value: proton mass energy equivalent in MeV". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2022-09-11. ^ The SNO+ Collaboration; Anderson, M.; Andringa, S.; Arushanova, E.; Asahi, S.; Askins, M.; Auty, D. J.; Back, A. 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Experimental test of the collapse time of a delocalized photon state Francesco Garrisi1, Micol Previde Massara1, Alberto Zambianchi2, Matteo Galli1, Daniele Bajoni ORCID: orcid.org/0000-0001-6506-84852, Alberto Rimini1 na1 & Oreste Nicrosini1,3 Scientific Reports volume 9, Article number: 11897 (2019) Cite this article Single photons and quantum effects We investigate whether the collapse of the quantum state of a single photon split between two space-like separated places takes a nonvanishing time. We realize this by using a source of heralded single photons, then splitting the resulting single photon state and letting it propagate over distances much larger than the experimental time resolution times the speed of light c. We find no additional delay within our accuracy and set a lower limit for the speed of collapse of the quantum state to 1550c. In the standard formulation of Quantum Mechanics two principles of evolution of the state vector of a given system are assumed. According to the first one, when the system is closed it evolves in time according to the Schrödinger equation. This evolution is deterministic and (complex) linear. This means that, once an initial state is given, the subsequent state is unambiguously determined for all future times. Moreover, if the time dependence of two states obeys the Schrödinger equation, any linear combination of them also satisfies that equation. The second principle of evolution, on the contrary, is stochastic. When the system is subject to a measurement process it happens that (i) the possible outcomes of such a measurement are the eigenvalues of the observable that is being measured and (ii) the state vector of the system, immediately after the measurement has been completed, becomes one of the eigenvectors of the observable measured, namely the one corresponding to the result actually observed, all the rest of the state vector being instantaneously annihilated (reduction postulate). Photon physics has historically provided the testing ground for several foundational issues (for a recent review see ref.1). In particular a lot of work has been dedicated to the study of the so called EPR-B correlations and non-localitity issues implied by entanglement and violations of Bell's inequalities. After the seminal work on entanglement and violation of Bell's inequalities by2 and 3 most recently violation of Bell's inequalities has been tested by T. Scheidl et al. in ref.4. Improving upon all existing experiments, the authors of ref.4 insure space-like separation of their measurement events in order to remove the possibility of transmitting any signal propagating at velocity ≤ c between the entangled particles. This Bell's test was, amazingly, performed between the two Canary Islands La Palma and Tenerife, separated by 144 km. As a corollary of their Bell's test one can argue that the collapse of the two-photon entangled state is instantaneous, as required by the second evolution postulate (see above) of the canonical formulation of quantum theory. More recently, the authors of ref.5 performed a Bell test using electrons separated by 1.3 km and obtained a loophole-free Bell inequality violation. In ref.6, a lower bound on the speed of nonlocal correlations in a Bell test has been set to be at least four orders of magnitude larger than the speed of light. Along the same line of research, the authors of ref.7 confirm the result of6 by also closing the locality and freedom-of choice lophooles over a distance of 16 km. All this as far as two-photon correlations are considered, i.e. when two (entangled) photons separately hit their respective detector. When it comes to considering single photons, the situation is different. Actually, experiments using light at the single photon level have historically given crucial contributions to test the foundations of Quantum Mechanics. In a recent review paper (see ref.1) the main achievements have been described, with emphasis on two foundational themes, namely wave-particle duality and Bell nonlocality. During the 5th Solvay Conference in 1927 (see8,9) Einstein considered a single particle that, after diffraction at a pin-hole, encounters a "detection plate" (a photographic plate in the case of photons). To simplify the discussion to the essence, one could consider a single photon impinging on a 50:50 beamsplitter (BS), followed by two Single Photon Detectors (SPD), positioned along the two arms of propagation of the wave. Einstein stressed that only one of them can detect the particle, otherwise energy would not be conserved. But he was deeply concerned about the situation in which the two detection events are space-like separated, since this prevents any possible coordination among the detectors. The fact that a photon can be found only in one among a set of places is a manifestation of its particle character, while diffraction undoubtedly indicates that a wave character is also there. The two aspects of the behaviour of photons (more generally of microsopic particles) are made compatible by the statistical interpretation of the quantum mechanical state. The fact that nothing remains in the places where the photon is not found is conveyed by the reduction postulate. In experiments performed by splitting each photon of a beam this behaviour is named antibunching. Actually, several experiments aimed at verifying antibunching have been devised and performed. Antibunching has been unambiguously proven by Clauser in ref.10: his experimental results, to a high degree of accuracy, contradict the predictions of any classical or semiclassical theory of light, confirming at the same time the prediction of Quantum Mechanics. A similar experiment was performed by Grangier et al. (see ref.11) who observed both antibunching and wave interference effects by a Mach-Zender interferometer with a visibility over 98%. More recently, heralded single photons have been used by Guerreiro et al. (see ref.12) to perform an antibunching experiment; the experimental set-up has been devised in such a way that the events consisting in the arrival of the photon wave packets at the detectors are space-like separated, and also in this case antibunching has been experimentally confirmed. Also, the experimental proof of nonlocal quantum state collapse for a single photon has been given in ref.13. The authors demonstrate the single particle nonlocal collapse by splitting a single photon between two laboratories and verifying that the choice of the measurement setup in one laboratory really causes the change of the local quantum state in the other laboratory by means of homodyne measurements. Moreover, experimental verification of antibunching was not limited to photons, but has been confirmed for other particles such as neutrons, as seen in ref.14. What is missing in all experiments of this kind is a thorough control of the time of flight of the single photon, leaving the possibility that the coordination about which detector clicks (the detector at which the photon is going to materialize) could take a time. The present paper concerns an experiment able to test whether the state vector collapse for a single particle, being not instantaneous, takes a time, in particular when the system is spatially delocalized. This is the first time that an experiment of this kind is performed using a single particle state instead of entangled EPR pairs: the use of single particle states is important to check whether the collapse process involving the actual displacement of the particle between the distant places requires a time, and could point out a possible difference with respect to EPR pairs, where only internal degrees of freedom are correlated like in EPR experiments. Conceptual Scheme Let us consider the setup of Fig. 1a, where a beam of light impinges on a 50:50 BS. If the input is a single photon Fock state15, it is easy to show (the full calculation can be found in15) that the output is $$\|{\phi }_{out}\rangle =\frac{1}{\sqrt{2}}{(\|1\rangle }_{f}+{\rm{i}}\|1{\rangle }_{b}),$$ representing a single photon de-localized between the propagation directions forward and backward. The same superposition is not found for other type of inputs, in particular in the case of classical sources. If we consider a coherent state, as would be the case for a laser beam, of complex amplitude α $$\|\alpha \rangle ={e}^{-\frac{\|\alpha {\|}^{2}}{2}}\mathop{\sum }\limits_{n=0}^{\infty }\frac{{\alpha }^{n}}{\sqrt{n!}}\|n\rangle ,$$ where \|n〉 are Fock states15, then for a 50:50 BS the output becomes $$\|{\phi }_{out}\rangle ={\|\frac{\alpha }{\sqrt{2}}\rangle }_{f}{\|\frac{\alpha }{\sqrt{2}}\rangle }_{b}.$$ (a) Single photons on a 50:50 beamsplitter; in the forward direction a single photon detector (SPD) is positioned; a mirror sends the wave packet to the backward direction. (b) When the compensation plate replaces the beamsplitter, no superposition is prepared. The output is therefore the factorized state of the coherent state ${\|\frac{\alpha }{\sqrt{2}}\rangle }_{f}$ propagating forward and the coherent state ${\|\frac{\alpha }{\sqrt{2}}\rangle }_{b}$ independently propagating backward. More in general, for a non-symmetrical BS the two states will be \|β〉f and \|γ〉b, with \|β\|2 + \|γ\|2 = \|α\|2. Should the input be a pulse of thermal light (as in the case of lamps or LEDs), then one has to take into account that a single mode of thermal light (see for instance ref.16) can be described by the statistical operator $$\rho =\int \,\frac{{d}^{2}\alpha }{\pi \langle n\rangle }\,\exp [-\frac{\|\alpha {\|}^{2}}{\langle n\rangle }]\|\alpha \rangle \langle \alpha \|,$$ where 〈n〉 is given by $$\langle n\rangle ={[\exp (\frac{\hslash \omega }{kT})-1]}^{-1}$$ and α are coherent states as in Eq. (2). Being the input state a mixture of coherent states, also the output is a mixture of factorized forward and backward states. According to Eq. (1), the quantum state of each single photon is coherently split as the superposition of "wave packet in the forward direction" and "wave packet in the backward direction". Notice that at the BS no reduction of the quantum state takes place; this is a well established experimental fact, for instance in Mach-Zender interferometry, delayed-choice experiments and homodyne measuments17,18 Let us suppose first that the second detector is not there and that the wave packet can propagate freely to the backward direction. The initial state of the system "photon + detector" is given by $$\|{{\rm{\Psi }}}_{in}\rangle =\frac{1}{\sqrt{2}}{(\|1\rangle }_{f}+{\rm{i}}\|1{\rangle }_{b})\|{D}_{0}\rangle ,$$ where \|D0〉 represents the SPD in the state "ready". With probability p = 1/2 the photon is detected by the SPD, and immediately after the measurement the quantum state of the system "photon + detector" is \|D+〉, where \|D+〉 represents the situation in which the photon has been absorbed and the detector fired; alternatively with probability p = 1/2, the photon is not detected by SPD and immediately after that the state of the system is \|1〉b\|D0〉. This is the description of what happens according to the reduction postulate. In formulae, taking into account Eq. (4): $$\|{\Psi }_{in}\rangle \to \{\begin{array}{ll}\|1{\rangle }_{f}\|{D}_{0}\rangle \to \|{D}_{+}\rangle & {p}_{f}=\frac{1}{2},\\ \|1{\rangle }_{b}\|{D}_{0}\rangle & {p}_{b}=\frac{1}{2}.\end{array}$$ It is worth noticing that, in the case of a single photon, the reduction of the quantum state as described by Eq. (5) is a non-local "process", the single photon being de-localized in both the forward and backward directions. One may ask what "immediately after" means. The answer of standard quantum mechanics is "immediately after the wave packet in the forward direction has reached SPD and SPD has completed, with positive or negative result, the measurement process", i.e. after the time of flight of the photon from the source to the detector, T, plus the reaction time of the detector, δ, that is of the order of nanoseconds or even picoseconds for nowadays devices. In a wide class of spontaneous collapse models, in which the quantum state collapse is a consequence of a modification of the Schrödinger equation effective at the macroscopic level (see for instance19,20,21,22), one must include in δ also the collapse time of the macroscopic pointer of SPD, a time that can be estimated to be of the order of a fraction of a picosecond. The times considered up to now include the time of flight of the wave packet in the forward direction and the time demanded by processes taking place inside the detector. One can imagine as a possible scenario that some sort of process takes place between the wave packets, and that this process takes a time (collapse time), in particular when the wave packets are far apart. The imagined process would consist of some kind of coordination of the forward and backward wave packets in order to ensure that the photon "appears" only in the forward/backward positions (otherwise antibunching is not guaranteed and energy is not conserved), possibly taking place at a finite speed c′. Then, if the two paths are opposite to one another as indicated in Fig. 1, the required time would be of the order of Δ = 2L/c′, L being the distance between the BS and the SPD. Note that a (would–be) finite value of Δ is described neither in standard quantum mechanics nor in the collapse models mentioned above. In the case in which a laser pulse is used instead of a single photon, taking into account eq. (2) the initial state of the system "photon + detector" can be written as $$\|{{\rm{\Psi }}}_{in}\rangle =\|\alpha \rangle \|{D}_{0}\rangle ={{\rm{e}}}^{-\frac{\|\alpha {\|}^{2}}{2}}\mathop{\sum }\limits_{n=0}^{\infty }\frac{{(\alpha {\hat{a}}_{in}^{\dagger })}^{n}}{n!}\|0\rangle \|{D}_{0}\rangle ,$$ and, by taking into account Eqs (3) and (6) $$\begin{array}{ll}\|\alpha \rangle \|{D}_{0}\rangle & \to \|\gamma {\rangle }_{b}\mathop{\underbrace{\|\beta {\rangle }_{f}\|{D}_{0}\rangle }}\limits_{\,}\\ & \to (\begin{array}{ll}\|\gamma {\rangle }_{b}\mathrm{\|0}{\rangle }_{f}\|{D}_{0}\rangle & {p}_{0}={{\rm{e}}}^{-\|{\beta }_{f}{\|}^{2}},\\ \|\gamma {\rangle }_{b}\|ph{\rangle }_{f}\|{D}_{0}\rangle \to \|\gamma {\rangle }_{b}\|{D}_{+}\rangle & {p}_{ph}=1-{p}_{0}\mathrm{.}\end{array}\end{array}$$ In Eq. (7) \|0〉f and \|ph〉f are the normalized vacuum and at least one photon states in the forward direction; p0 and pph are the probability of finding the vacuum or at least one photon in the forward direction, respectively, dependent on the parameter βf. It is worth noticing that in this case the collapse process involves the forward coherent state \|β〉f and the detector; hence the process is local and does not affect the distant coherent state \|γ〉b, that is left unchanged. This remains true even if the input of the beam splitter is a weak coherent state, for which the average number of photons \|α\|2 is close or even smaller than one: the output is still a factorized state and its effects are intrinsically different from the ones of the single photon Fock state. This in turn means that, in the assumption that the collapse of a non-local state requires a finite time in order to "coordinate" the distant parts of the quantum state, the finite collapse time is detectable only if a single photon state is used. Hence, if the initial state is a laser pulse the system is blind to a possible finite collapse time. The same is true for chaotic light, as thermal states can be expanded on the set of coherent states16, and would therefore result in a separable state after the BS. This is a very important point for this experiment: the fact that no additional delay would be observed using lasers implies that such an effect would be undetectable in time of flight measurements, in particular in LIDAR systems23 (even so called single-photon LIDAR systems work with Single Photon Detectors, but use laser pulses). Moreover, the delay due to the collapse would be undetectable by experiments that measure the time of flight of light produced by thermal sources, in particular distant astronomical sources24. If the collapse time Δ is non-vanishing, it can be revealed by comparing the emission-detection times T + δ + Δ and T + δ for the setup of Fig. 1a (without or with the second SPD) in the case of a single photon state or a laser pulse as initial states, respectively. As a cross check, one can also consider a setup like the one shown in Fig. 1b, where in place of the BS a Compensation Plate (CP) is inserted, in order to maintain the (small) delay the photon experiences when traveling through glass in both the experimental configurations. Experimental scheme In order to experimentally test the hypothesis, we use a source of heralded single photons (ref.25), as schematized in Fig. 2. Such configuration allows to test the various scenarios taken into account in the previous section. Experimental set-up. LD: Laser Diode; BBO: Beta-Barium Borate nonlinear crystal; BPF: 10 nm wide Band Pass Filter centered at 810 nm (fiber couplers) and 405 nm (laser diode); SPD: Single Photon Detector; BS: 50:50 beamsplitter; CP: Compensation Plate; the length L of the signal arm is varied between 2 and 20 m. A nonlinear BBO crystal is used as the medium for Spontaneous Parametric Downconversion. The crystal is cut so that, for normal incidence of the pump beam, the phase matching condition is met when the down-converted photons are emitted inside a cone with half-opening angle of 3 degrees. The crystal emits pairs at a wavelength of 810 nm. The downconverted photons are collected and separately focused on multi-mode fibres. Single Photon Detectors (SPD A and SPD B) are used for detection and have an efficiency of around 5% at 810 nm and a time resolution of 35 ps. The electronic pulses output from the detectors are however slightly degraded while traveling through the long electronic cables, and the time resolution in the experiment is measured to be about 60 ps. Time-tagging electronics is used for coincidence counting. The photon detected at SPD A heralds the single photon in the other arm and can be used as a time reference for the experiment; the time of click of SPD B can be compared when there is a BS, (i.e. the quantum state is split) or the CP (i.e. no choice of path). When using the BS, comparison can also be made between the single photon non-separable state (as in Eq. 1) and the coherent state separable state (as in Eq. 3). This is performed by launching, before the BBO, coherent light produced by a pulsed supercontinuum laser through the same path of the downconverted photons. The results obtained for the maximum length of the signal arm (20 m) are shown in Fig. 3, which shows the histogram of the coincidences between detectors A and B as a function of the time delay, both for quantum and coherent light. The histograms overlap perfectly and no relative delay is observed within the time resolution of the experiment. Coincidence histograms as a function of delay between the reaction times of the heralding and the distant SPDs when the 20 m fiber is connected (a) to a compensation plate or (b) to a beamsplitter. In both cases the lighter histogram is produced by coherent pulses while the dark one is produced by photon pairs. Integration time is 200 s in all cases. The mean delay times for multiple lengths of the signal fiber L were determined by taking the peaks of the corresponding histograms, as well as their full width at half maximum. For every distance, Fig. 4 shows the difference between the mean delays for coherent and quantum light; no appreciable delay difference can be observed at any length. Difference between the time of arrival of the single photons and the coherent pulses (Δ), with the BS inserted along the path, as a function of the length of the fiber connected to the distant SPD. The error bars are the sum of the FWHM of the coincidence peaks of the single photon and coherent pulse signal. The experimental data show clearly that the spatial collapse of the photon state takes a time shorter than the time resolution of our experiment, given the maximum available distance. This allows us to put an upper limit on the collapse time, and hence on its speed. If a nonzero collapse time is actually present, its duration Δ has to be shorter than 60 ps, which is the time resolution of the experiment. The maximum length for the detector arm in the experiment was L = 20.04 m (±1 cm) so the maximum investigated distance between the two ends of the arms was $\sqrt{2}L=28.4\,{\rm{m}}$. We can therefore put a lower bound to the collapse speed c′ of 1550 times c, since any other less direct path followed by the wavefunction would result in a higher collapse speed. This value is about one order of magnitude smaller than the best current results on the speed of the spooky action at a distance of refs6,7, but complementary to that, giving information on the behaviour of a single delocalized particle rather than the correlations of internal degrees of freedom as in entangled EPR pairs. In order to improve the present bound, an upgraded version of the experiment is being developed in which distances are increased up to the kilometric scale as done for EPR pairs4,7. To produce pairs by downconversion, we use a blue laser diode (Sanyo DL-LS5017) to pump the BBO crystal with 65 mW of continuous wave power at a wavelength of 405 nm. The beam is spectrally filtered by a 10 nm Band Pass Filter (BPF) centered at 405 nm. The BBO crystal is 1 mm thick and has a square 5 mm by 5 mm cross-section. The crystal is in sandwich configuration: two 0.5 mm crystals are stitched together rotated by 90 degrees. This configuration is useful to generate polarization entangled photon pairs, although in our experiment we are only interested in the generation of photon pairs and the subsequent heralding of single photons. Therefore, concerning conversion efficiency, the effective length of the crystal is 0.5 mm. The downconverted photons are spectrally shaped by BPF's with 10 nm bandwidth before they are focused to 60 μm core diameter multi-mode fibres. The BS (Thorlabs BSW29R) and the CP (Thorlabs BCP44R) are 1 mm thick, 25 × 36 mm UV fused silica plates. The BS is metal coated, while the CP is anti-reflection coated. The principal characteristics (quantum efficiency, response time, dead time) of the SPD's (ID Quantique id100-MMF50-STD) were certified by the manufacturer and also experimentally verified before the measurements. Time-tagging electronics (Picoquant HydraHarp-400) is used for coincidence counting. Note that the presented experimental scheme uses only information collected at SPD B. Indeed if the detector SPD B reacts to a single photon, a third detector on the other arm does not react; so the inclusion of a third detector does not convey any additional information on what is going on at SPD B, where all the observations used in the present experiment are performed. Hence the only experimental evidence that the collapse has truly ended is the reaction of SPD B. The dataset acquired during this work is available from the corresponding author on reasonable request. Shadbolt, P., Mathews, J. C. F., Laing, A. & O'Brien, J. L. 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Bassi, A., Lochan, K., Satin, S., Singh, T. P. & Ulbricht, H. Models of wave-function collapse, underlying theories and experimental tests. Rev. Mod. Phys. 85, 471–527 (2013). Ghirardi, G., Nicrosini, O. & Rimini, A. What really matters in Hilbert-space stochastic processes (Cambridge University Press 2018). Buller, G. S. et al. Multiple wavelength time-of-flight sensor based on time-correlated single-photon counting. Review of scientific instruments 76, 083112 (2005). Abbott, B. P. et al. Gw170817: observation of gravitational waves from a binary neutron star inspiral. Physical Review Letters 119, 161101 (2017). Kurtsiefer, C., Oberparleiter, M. & Weinfurter, H. High-efficiency entangled photon pair collection in type-ii parametric fluorescence. Physical Review A 64, 023802 (2001). Our colleague and friend Alberto Rimini sadly passed away before the completion of the present work; he lives in our hearts. Paolo Walter Cattaneo (Istituto Nazionale di Fisica Nucleare, Sezione di Pavia) is gratefully acknowledged for useful discussions. We thank Giancarlo Reali for fruitful discussions and for taking part in conceiving the experimental plan. We acknowledge also the University of Pavia Blue Sky Research Project Number BSR1732907. This research was also supported by the Italian Ministry of Education, University and Research (MIUR): "Dipartimenti di Eccellenza Program (2018–2022)", Department of Physics, University of Pavia. Alberto Rimini is deceased. Università degli Studi di Pavia, Dipartimento di Fisica, 27100, Pavia, via A. Bassi 6, Italy Francesco Garrisi , Micol Previde Massara , Matteo Galli , Alberto Rimini & Oreste Nicrosini Università degli Studi di Pavia, Dipartimento di Ingegneria Industriale e dell'Informazione, 27100, Pavia, via Ferrata 5, Italy Alberto Zambianchi & Daniele Bajoni Istituto Nazionale Fisica Nucleare - Sezione di Pavia, 27100, Pavia, via A. Bassi 6, Italy Oreste Nicrosini Search for Francesco Garrisi in: Search for Micol Previde Massara in: Search for Alberto Zambianchi in: Search for Matteo Galli in: Search for Daniele Bajoni in: Search for Alberto Rimini in: Search for Oreste Nicrosini in: This works stems from an idea of A.R. and O.N., D.B. and M.G. laid out the experimental apparatus; F.G., M.P.M. and A.Z. performed the experiments; D.B., M.G., F.G. and O.N. wrote the manuscript; all authors reviewed the manuscript. Correspondence to Francesco Garrisi. Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Garrisi, F., Massara, M.P., Zambianchi, A. et al. Experimental test of the collapse time of a delocalized photon state. 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It From Bit or Bit From It? It From Bit or Bit From It? pp 5-23 \| Cite as "It from Bit" and the Quantum Probability Rule M. S. Leifer First Online: 04 February 2015 Part of the The Frontiers Collection book series (FRONTCOLL) I argue that, on the subjective Bayesian interpretation of probability, "it from bit" requires a generalization of probability theory. This does not get us all the way to the quantum probability rule because an extra constraint, known as noncontextuality, is required. I outline the prospects for a derivation of noncontextuality within this approach and argue that it requires a realist approach to physics, or "bit from it". I then explain why this does not conflict with "it from bit". This version of the essay includes an addendum responding to the open discussion that occurred on the FQXi website. It is otherwise identical to the version submitted to the contest. Quantum Theory Boolean Algebra Wind Farm Fair Price Lottery Ticket Technical Endnotes In general, a betting context $\mathcal {B}$ is a Boolean algebra, which we take to be finite for simplicity. All such algebras are isomorphic to the algebra generated by the subsets of some finite set $\Omega _{\mathcal {B}}$, where AND is represented by set intersection, OR by union, and NOT by complement. In quantum theory, a betting context corresponds to a set of measurements that can be performed together that is as large as possible. A measurement is represented by a self-adjoint operator $M$ and all such operators have a spectral decomposition of the form $$\begin{aligned} M = \sum _j \lambda _j \Pi _j, \end{aligned}$$ with eigenvalues $\lambda _j$ and orthogonal projection operators $\Pi _j$ that sum to the identity $\sum _j \Pi _j = I$. The eigenvalues are the possible measurement outcomes and, when the system is assigned the density operator $\rho $, the Born rule states that the outcome $\lambda _j$ is obtained with probability $$\begin{aligned} p(\lambda _j) = \text {Tr} \left( \Pi _j \rho \right) . \end{aligned}$$ The eigenvalues just represent an arbitrary labelling of the measurement outcomes, so a measurement can alternatively be represented by a set of orthogonal projection operators $\{\Pi _j\}$ that sum to the identity $\sum _j \Pi _j = I$, which is sometimes known as a Projection Valued Measure (PVM).12 Two PVMs $A = \{\Pi _j\}$ and $B = \{\Pi '_j\}$ can be measured together if and only if each of the projectors commute, i.e. $\Pi _j \Pi '_k = \Pi '_k \Pi _j$ for all $j$ and $k$. If this is the case then $\Pi _j\Pi '_k$ is also a projector and $\sum _{jk}\Pi _j\Pi _k = I$. Therefore, one way of performing the joint measurement is to measure the PVM $C = \{\Pi ''_{jk}\}$ with projectors $\Pi ''_{jk} = \Pi _j\Pi '_k$ and, upon obtaining the outcome $(jk)$, report the outcome $j$ for $A$ and $k$ for $B$. This fine graining procedure can be iterated by adding further commuting PVMs and forming the product of their elements with those of $C$. The procedure terminates when the resulting PVM is as fine grained as possible and this will happen when it consists of rank-$1$ projectors onto the elements of an orthonormal basis. The outcome of any other commuting PVM is determined by coarse graining the projectors onto the orthonormal basis elements. Therefore, in quantum theory, we can take the sets $\Omega _{\mathcal {B}}$ that generate the betting contexts $\mathcal {B}$ to consist of the elements of orthonormal bases. An event $E \in \mathcal {B}$ is then a subset of the basis elements and corresponds to a projection operator $\Pi _E = \sum _{\vert \psi \rangle \in E} \vert \psi \rangle \langle \psi \vert $. The Boolean operations on $\mathcal {B}$ can be represented in terms of these projectors as Conjunction: $G = E \, {\text {AND}} \, F \,\, \Rightarrow \,\, \Pi _G = \Pi _E\Pi _F$. Disjunction: $G = E \, {\text {OR}} \, F \,\, \Rightarrow \,\, \Pi _G = \Pi _G + \Pi _F - \Pi _G\Pi _F$, which reduces to $\Pi _G = \Pi _G + \Pi _F$ when $E \cap F = \emptyset $. Negation: $G = {\text {NOT}} \, E \,\, \Rightarrow \,\, \Pi _G = I - \Pi _E$. From the Dutch book argument applied within a betting context, we have that our degrees of belief should be represented by a set of probability measures $p(E\|\mathcal {B})$ satisfying For any event $E \subseteq \Omega _{\mathcal {B}}$, $p(E\|\mathcal {B}) \ge 0$. For the certain events $\Omega _{\mathcal {B}}$, $p(\Omega _{\mathcal {B}}\|\mathcal {B}) = 1$. For disjoint events within the same betting context $E,F \subseteq \Omega _{\mathcal {B}}$, $E \cap F = \emptyset $, $p(E \cup F\|\mathcal {B}) = p(E\|\mathcal {B}) + p(F\|\mathcal {B})$. The Born rule is an example of such an assignment, and in this language it takes the form $$\begin{aligned} p(E\|\mathcal {B}) = \text {Tr} \left( \Pi _E \rho \right) . \end{aligned}$$ The Born rule also has the property that the probability only depends on the projector associated with an event, and not on the betting context that it occurs in. For example, in a three dimensional Hilbert space, consider the betting contexts $\Omega _{\mathcal {B}} = \{\vert 0 \rangle ,\vert 1 \rangle ,\vert 2 \rangle \}$ and $\Omega _{\mathcal {B}'} = \{\vert + \rangle ,\vert - \rangle ,\vert 2 \rangle \}$, where $\vert \pm \rangle = \frac{1}{\sqrt{2}} \left( \vert 0 \rangle \pm \vert 1 \rangle \right) $. The Born rule implies that $p(\{\vert 2 \rangle \}\|\mathcal {B}) = p(\{\vert 2 \rangle \}\|\mathcal {B}')$ and also that $p(\{\vert 0 \rangle ,\vert 1 \rangle \}\|\mathcal {B}) = p(\{\vert + \rangle ,\vert - \rangle \}\|\mathcal {B}')$ because, in each case, the events correspond to the same projectors. The Dutch book argument alone does not imply this because it does not impose any constraints across different betting contexts. A probability assignment is called noncontextual if $p(E\|\mathcal {B}) = p(F\|\mathcal {B}')$ whenever $\Pi _E = \Pi _F$. Gleason's theorem [34] says that, in Hilbert spaces of dimension $3$ or larger, noncontextual probability assignments are exactly those for which there exists a density operator $\rho $ such that $p(E\|\mathcal {B}) = \text {Tr} \left( \Pi _E \rho \right) $, i.e. they must take the form of the Born rule. 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Irish Veterinary Journal Prevalence and risk factors for hyperthyroidism in Irish cats from the greater Dublin area Laura Bree ORCID: orcid.org/0000-0001-5140-13551, Barbara A. Gallagher2, Robert E. Shiel1 & Carmel T. Mooney1 Irish Veterinary Journal volume 71, Article number: 2 (2018) Cite this article Hyperthyroidism is common in older cats. Prevalence varies geographically, but is anecdotally considered low in Ireland. The aim of this study was to document prevalence of hyperthyroidism in older cats in the greater Dublin area of Ireland and to assess environmental and clinical associations for development and identification of the disease. Primary-care veterinary practices were requested to select cats aged 10 years or older where blood sampling was being performed for health screening or clinical investigations. Surplus serum/plasma samples were submitted to University College Dublin Diagnostic Endocrine Laboratory for total thyroxine (T4) measurement. Cats were classified as hyperthyroid, equivocal or euthyroid based on a total T4 concentration (reference interval, 15–60 nmol/L), of >60 nmol/L, 30–60 nmol/L or <30 nmol/L, respectively. Simultaneous free T4 or repeat (after 4–6 weeks) total T4 measurement was recommended in all equivocal cases. Animals receiving treatment for hyperthyroidism were excluded. A questionnaire completed by the client and veterinarian detailing historical and physical information was also required. Associations between categorical variables were analysed by Chi-square or Fisher's exact test and odds ratio (OR) calculated. A P value of <0.05 was considered statistically significant. Samples were submitted from 507 cats including 107 (21.1%) hyperthyroid, 54 (10.6%) equivocal and 346 (68.2%) euthyroid. The presence of goitre (P < 0.0001), tachypnoea (P = 0.0378), tachycardia (P = 0.002), polyphagia (P = 0.0003) and weight loss (P < 0.0001) were significantly associated with hyperthyroidism. Cats with goitre were more likely to be diagnosed as hyperthyroid [OR 2.85, (95% CI 1.75–4.62] compared to those without. However, goitre was only palpated in 40 of 102 (39.2%) hyperthyroid cats. Increasing age was the only significant (P < 0.002) risk factor for development of hyperthyroidism. A relationship between hyperthyroidism and sex, breed, lifestyle, parasite control, vaccination status or feeding habits was not identified. Hyperthyroidism is not uncommon in Irish cats. Age was the only significant risk factor for its development. The high proportion of hyperthyroid cats without palpable goitre (> 60%) may reflect failure to detect goitre and account for the perceived low prevalence of this condition in Ireland. Hyperthyroidism is a disorder of older cats, resulting from excess circulating concentrations of triiodothyronine (T3) and, or thyroxine (T4) [1, 2] produced by an abnormally functioning thyroid gland. Histopathologically, most affected cats have benign adenomatous hyperplasia (adenoma) with only a small proportion having thyroid carcinoma [3, 4]. The median age at diagnosis is typically approximately 13 years and it is uncommonly diagnosed in cats less than 10 years of age [5]. Not only is hyperthyroidism recognized as the most common endocrinopathy in cats but also as one of the more frequently diagnosed disorders in small animal practice in the UK, USA, Australia, Japan and several other European countries. It was first definitively diagnosed in 1979 and has since been recognized with increasing frequency [3, 6, 7]. In the USA, a 20-fold increase in prevalence was reported from 0.1% in 1978–1980 to 2% in 1993–1997 [8]. Similarly, a 13-fold increase in prevalence has been reported in Germany from 0.2% between 1987 and 1994 to 2.6% in 1998 [9]. Other epidemiological studies have estimated prevalence in these and other countries and suggest a geographical variation. For instance, prevalence in older cats has been reported as 8.9% in 2002 for Japan [10], 11.4% in 2006 [11] and 12.3% in 2016 [12] for Germany, 3.9% in 2008 for Hong Kong [13], 20.1% in 2014 for Poland [14], 9.0% in 2014 for Portugal [15] and 7.0% in 2016 for South Africa [16]. A cumulative yearly incidence rate of 11.9% was reported in London, UK compared to 1.5% in Spain [17]) and in a similar UK study was suggested to be 7.4% [18]. Perhaps most relevant are the recent larger studies estimating prevalence of hyperthyroidism in primary-care veterinary practices in the UK. The prevalence in a population of 3584 cats unclassified by age was 3.0% [19]. In another study of 95,629 cats, the apparent prevalence was 2.4% but 8.7% in cats greater than 10 years of age [20]. Although direct comparisons between these studies is complicated by differing populations, varying age ranges and variable cut-offs for diagnosing hyperthyroidism and classification of equivocal cases, it appears that where hyperthyroidism is uncommon it has a prevalence of less than 4% and where more common, one of approximately 10% or more. Despite its close proximity to the UK and similar cultural and socio-economic status, the prevalence of feline hyperthyroidism in Ireland has anecdotally been considered as low. Undoubtedly cats are living longer today compared to decades ago and hyperthyroidism is a disease associated with ageing. However, an increase in the aged population alone does not explain the significant rise in prevalence over the last 30+ years as the prevalence of hyperthyroidism has increased at a rate exceeding that of diabetes mellitus and chronic kidney disease, both of which also occur in older cats [8]. Increased awareness and improved diagnostic capabilities have contributed to the increase in prevalence but again are unlikely to be solely responsible for the dramatic increase observed in the recent past. Although the clinical and pathological features of this disease have been well-described, the exact cause(s) remains elusive [2, 21, 22]. Many hypotheses have been explored such as immunological, infectious, nutritional, environmental and genetic factors, but a single dominant factor, other than advanced age, has not yet been identified. The most widely studied risk factors fall into the two broad categories of nutritional and environmental. The first large epidemiological study published in 1988 found an association between the development of hyperthyroidism and feeding canned food in the 5 years preceding diagnosis [23]. Such an association has been highlighted by almost all other studies where it has been addressed [3, 8, 12, 14, 16, 23,24,25,26] and in some instances, has been refined by certain flavours (e.g. fish, liver or giblet) [23, 25] and food specifically from ring pull (pop top) or aluminium cans [8, 12]. Other associations, variably reported in different studies have included exposure to fertilizers, herbicides, pesticides or flea products [3, 26], living indoors [3, 14], using cat litter [23, 24] and being female [8, 12, 26]. Undoubtedly, there are many potential thyroid disruptors that cats may be exposed to, either through their diet or from the environment. Several factors have since been implicated in the development of hyperthyroidism including dietary iodine intake [27], soy isoflavone excess [28, 29], exposure to bisphenol A from pop top or ring pull cans [8, 30] and polybrominated diphenyl ethers (PBDEs) from the environment [31,32,33]. Overall the association between diet and development of hyperthyroidism is controversial and exemplified by the presence of the same potential dietary risk factors in areas of low prevalence of the disease [13]. Numerous studies have also suggested that being purebred and particularly Siamese, Himalayan or Burmese is associated with lower odds of developing the disease [3, 19, 23, 24]. This suggests that whatever the cause of the disease, there is at least an underlying genetic predisposition for its development. The aims of this study were to determine the prevalence of hyperthyroidism in Irish cats in the greater Dublin area and to determine potential risk factors associated with the disease in this geographical location. A pilot questionnaire for veterinarians was first conducted at a national veterinary conference (University College Dublin (UCD) Veterinary Hospital Conference 2010) to more accurately estimate the perceived prevalence of hyperthyroidism in Ireland. Results of that pilot study confirmed the perceived low prevalence of the disorder. In order to calculate an appropriate sample size, in a population where a low prevalence was suspected, an estimated prevalence was calculated using the results of a similar study in Hong Kong [13], where a prevalence of 3.9% was identified using a test (total T4 estimation) with 98.5% sensitivity. This prevalence was utilized to calculate an appropriate sample size using the formula: $$ Sample size=\frac{Z^2P\ \left(P-1\right)}{d^2} $$ Where Z = confidence interval, P = estimated prevalence, d = precision. A precision of <5% of the estimated prevalence was advised where estimated prevalence was <5% [34]. A descriptive cross-sectional study was designed based on the results of the pilot study. Sample size was calculated to be approximately 500 cats, for a prevalence of 3.9% and 95% confidence interval (CI), with a predicted precision of 2.6%. Case selection A list of 45 first opinion veterinary practices in the greater Dublin area was compiled using the Veterinary Council of Ireland's Statutory Premises Accreditation Scheme (www.vci.ie) and veterinarians were invited to participate in the study between June 2011 and July 2012. Each practice received by mail a description of the study, questionnaires for completion by the owner and veterinarian and sample submission requests (Additional file 1). Two one-page questionnaires were designed for the owner and veterinarian, specifically based on previously reported risk factors (e.g. lifestyle, use of a litter box, exposure to ring pull cans). The information collected from the owner included age, breed, sex, length of time in possession, number of cats in the household, vaccination status, endo- and ectoparasiticide treatments and preparations, environmental surroundings, a detailed history of feeding habits including dry/wet proportion fed, type of container used (e.g. ring pull, regular or pouch) and preferred brand or flavouring. Information collected from the veterinarian included sample type, reason for veterinary attendance, and clinical features. Veterinarians were asked to describe the cat as 'sick' or 'healthy'. Cats were eligible for inclusion in the study if they were ≥ 10 years of age, both owner and veterinarian questionnaires were completed and blood sampling was being performed as part of their routine investigations. Exclusion criteria included cats already diagnosed as hyperthyroid or where they were receiving anti-thyroid medication. The study was approved by the UCD Academic Research and Ethics Committee (AREC-P-11-20-Mooney). Sample collection and analysis Blood samples were collected by jugular venipuncture, transferred into plain or lithium heparinized tubes and centrifuged prior to separating the serum or plasma. All samples were cooled to 4°C, transported to UCD Veterinary Diagnostic Endocrine Laboratory and stored at 4°C for a maximum of 4 days prior to total T4 measurement on site using an immunoassay previously validated for use in cats (Immulite 1000 canine total T4, Siemens) [35]. Where volume allowed, aliquots were stored at −20°C for future free T4 analysis, if required. The established laboratory reference interval for total T4 was 15–60 nmol/L. Cats were classified as hyperthyroid, equivocal or euthyroid based on a total T4 concentration of >60 nmol/L, 30–60 nmol/L or <30 nmol/L, respectively. For the purposes of the study, all cats with a total T4 concentration below the reference interval (<15 nmol/L) were included in the euthyroid group. For this assay, the limits of detection were 6.4 and 193.0 nmol/L and all values below or above were assigned as those values for the purposes of statistical analyses. Repeat measurement of total T4 after 4–6 weeks, or simultaneous free T4 measurement (reference interval 10–50 pmol/L) (Free T4 by equilibrium dialysis, Antech Diagnostics performed at Nationwide Diagnostic Laboratories, UK) was recommended in all equivocal cases. The prevalence of hyperthyroidism, with exact binomial 95% CI, was calculated for all cats combined, for cats classified as healthy and for cats classified as sick, using the Wilson interval test [36]. Data were examined for normality using the Shapiro Wilk test. Non-parametric data were reported as median (range) and parametric data were reported as mean ± standard deviation (SD). Breed was analysed by classification as crossbreed or purebred. To determine whether age should be treated as a continuous or categorical variable, it was examined for linearity (log odds of hyperthyroid cats) and as no linear trend was established, it was treated categorically. Age was therefore modeled with three categories (≥ 10 - < 12 years, ≥ 12 - < 14 years and ≥ 14 years). Equivocal cases were excluded from all association analysis. Univariate association analysis was performed using a two-tailed Fisher's exact test. Multivariate association analysis was performed using a Chi-square test for those variables with more than one category (e.g. indoor/outdoor/access to outdoor). Thereafter, any significant predictors resulting from these analyses were entered into a binary logistic regression model to further investigate their effects on the presence of hyperthyroidism. The Mann Whitney U test was used to compare the initial total T4 concentration between healthy and sick hyperthyroid cats and between healthy and sick euthyroid cats. This test was also used to compare total T4 concentrations in hyperthyroid cats with or without palpable goitre. In all cases a P value <0.05 was considered significant. The study population consisted of 507 cats, from 35 first opinion practices in the greater Dublin area. Each practice submitted a median of 5 (1–86) samples. There were 196 males, 271 females and 40 where gender was unspecified. Breeds included domestic shorthair (DSH) (n = 434), domestic longhair (DLH) (n = 27), British Blue (n = 4), Persian (n = 3), Siamese (n = 3), Burmese (n = 2), Birman (n = 1) and 33 where breed was not specified. The median age of the cats was 13 (range 10–21) years. Of the 507 cats, 395 presented for various illnesses, 70 for annual health check, 34 for routine vaccination and reasons were not recorded for 8 cats. Thus, the study comprised 395 (77.9%) cats classified as 'sick' and 104 (20.5%) classified as 'healthy'. Hyperthyroidism was definitively diagnosed after a single T4 measurement in 100 cats. Seven further cats were subsequently identified as hyperthyroid by repeat total T4 (n = 3) or free T4 (n = 4) measurement giving a total of 107 hyperthyroid cats and a prevalence for this disease of 21.1% (95% CI, 17.7–24.8). Of the remainder, 318 cats were considered euthyroid after a single T4 measurement. A further 28 cats were confirmed as euthyroid by repeat total T4 measurement (n = 2) or free T4 analysis (n = 26) resulting in 346 (68.2%) euthyroid cats. In total 89 cats initially had an equivocal total T4 concentration but 7 (7.9%) and 28 (31.5%) were subsequently diagnosed as hyperthyroid or euthyroid, respectively. Thus, 54 (10.7%) cats in total were considered equivocal including five cases where total T4 was repeat tested but remained within the equivocal range. Total T4 concentrations in the different groups of cat are presented in Fig. 1. The median initial total T4 concentration for hyperthyroid cats was 108.0 (43.7–193.0 nmol/L including the 7 (6.5%) equivocal cases on initial measurement. Within the hyperthyroid group 80 (74.8%) cats were classified as sick, 23 (21.5%) as healthy and 4 (3.7%) were not classified. Median initial total T4 concentration for healthy hyperthyroid cats (101.0 (43.7–193.0) nmol/L) was not significantly different (P = 0.153) from sick hyperthyroid cats (125.0 (44.5–193.0) nmol/L). Median initial total T4 concentration for euthyroid cats was 20.9 (6.4–46.0) nmol/L. For this group, 273 (78.9%) were classified as sick, 70 (20.2%) as healthy and 3 (0.9%) were not classified. Sixty-one (17.6%) of this group had initial total T4 concentration below the reference interval (< 15.0 nmol/L). Of these cats, 49 (80.3%) were classified as sick, 11 (18.0%) as healthy and one (1.7%) was not classified. There was a significant association (P < 0.0001) between a total T4 concentration < 15.0 nmol/L and being sick for all cats. There was no significant difference between the prevalence of hyperthyroidism in cats classified as sick (20.3%; 95% CI, 16.5–24.4) and healthy (22.1%; 95% CI, 15.2–31.0). Initial total thyroxine (T4) concentrations in cats classified as euthyroid, equivocal and hyperthyroid. The reference interval for total T4 (15–60 nmol/L) is indicated by the shaded area. Values above 193.0 and below 6.4 nmol/L are all assigned as those values, respectively There was a significant positive association between hyperthyroidism and increasing age (P < 0.002) but no association with sex, breed, lifestyle, parasite control, vaccination status or feeding habits (access to dry food or ring-pull canned food) (Table 1). When age was entered into the logistic regression model, cats between 10 and 12 years old were at reduced odds of hyperthyroidism compared to cats greater than 14 years of age (OR 0.47, 95% CI 0.26–0.84, P = 0.0094), while cats greater than 14 years of age were at significantly increased odds of hyperthyroidism compared to cats less than 12 years of age (OR 2.18, 95% 1.39–3.44, P = 0.0007). Of the euthyroid and hyperthyroid cats with breed information reported (n = 423), the majority (n = 411 (97.2%)) was DSH or DLH. Too few other breeds were included to allow meaningful statistical analyses but there was no significant association between hyperthyroidism and being crossbreed or purebred. The presence of goitre, increased respiration rate, tachycardia, polyphagia and weight loss were all significantly associated with a diagnosis of hyperthyroidism (Table 2). When heart rate was further examined using logistic regression, cats with heart rate > 240 bpm were at significantly increased odds of hyperthyroidism compared to cats with a heart rate < 200 bpm (OR 3.59, 95% CI 1.74–7.44,P = <0.0001). Diarrhoea, vomiting and presence of cardiac murmur were not significantly associated with disease. Table 1 Association of signalment and historical data with hyperthyroidism in 507 cats 10 years and older presented to primary care veterinary practices in the greater Dublin area Table 2 Association of clinical signs with hyperthyroidism (T4 > 60 nmol/L) in 507 cats 10 years and older presented to primary care veterinary practices in the greater Dublin area A total of 112 (23.1%) of 485 cats were reported as having goitre. Overall goitre was recorded in 40 of 102 (39.2%) hyperthyroid cats, 11 of 53 (20.8%) equivocal and 61 of 330 (18.4%) euthyroid cats. There was no significant difference (P = 0.645) between the initial total T4 concentration in hyperthyroid cats with palpable goitre (127.0 (range 44.5–193.0) nmol/L) compared to those with no palpable goitre (105.0 (range 43.7–193.0) nmol/L) (Fig. 2). Of the 40 hyperthyroid cats with goitre, 21 (52.2%) were unilateral, whilst 19 (47.5%) were bilateral. There was no significant difference (P = 0.469) between the detection of goitre and health status of the hyperthyroid cats. Serum total thyroxine (T4) concentration in 40 and 60 hyperthyroid cats with or without goitre. The reference interval for total T4 (15–60 nmol/L) is indicated by the shaded area. Values above 193.0 and below 6.4 nmol/L are all assigned as those values, respectively The prevalence of hyperthyroidism in cats older than 10 years of age presenting to primary-care veterinary practices was greater than 20% in the present study. This prevalence exceeds that of 3.9% in Hong Kong where the disease is considered uncommon [13]. It equates more to prevalences between 7 and 20.1% in older cats reported in Japan, Germany, Portugal, Poland, England and South Africa (10, 11, 12, 15, 14, 19, 20, 16], where the disease is considered relatively common. Although the prevalence may appear even higher than in some of these studies, direct comparisons are difficult because of differences in populations tested, inclusion and exclusion criteria used and thyroid hormone concentration cut-offs employed for diagnosing hyperthyroidism. It could be argued that the study design introduced inherent bias reflected by this high prevalence. Practitioners may have been more willing to enter into the study to obtain a diagnosis of hyperthyroidism free of charge in cats more likely to have the disease. Certainly, one practice only submitted a single sample from a cat later proven to be hyperthyroid. However, most practices submitted several samples from a range of both sick and healthy cats and those diagnosed as euthyroid and hyperthyroid. Overall the results of the study confirm that hyperthyroidism, contrary to anecdotal supposition, is frequently encountered in cats within the greater Dublin area of Ireland. Achieving an accurate diagnosis of hyperthyroidism was essential for this study. In the laboratory used, a cut-off of 60.0 nmol/L was employed to confirm a diagnosis. Although individual laboratory reference intervals vary, measurement of total T4 is considered to be highly specific for hyperthyroidism especially when, as in this study, higher cut-off values are used [37, 38]. On the other hand, total T4 concentrations may be within reference interval in between 5 and 10% of all hyperthyroid cats and in up to 40% of those considered mildly affected [37, 38]. In general, such values are within the mid to high end of the reference interval and may reflect the co-existence of hyperthyroidism and non-thyroidal illness (NTI) [39] or, more commonly, early or mild thyroid disease [37, 38]. Therefore, in the present study, hyperthyroidism could not be confidently eliminated with a total T4 concentration between 30 and 60 nmol/L. Initially approximately 18% of cats were classified as equivocal, comparable to 14% of 197 cats [15] and 15.6% of 302 cats [16] where an equivocal category was specifically reported. A recommendation for simultaneous free T4 analysis or repeat total T4 estimation was made to further elucidate thyroid status in these cats as has been recommended elsewhere [12, 15, 16]. However, the former was often not possible because of small sample volume or concerns over inappropriate sample handling that may have affected validity of free T4 analysis in the samples submitted. The possibility of prolonged storage during submission was a particular concern as it is known that free T4 concentrations increase by approximately 50% after 5 days at 37 °C, at least when assessed by equilibrium dialysis [38]. On the other hand, repeat testing was not always possible because of cats lost to further follow-up. How likely equivocal cases are to be ultimately classified as hyperthyroid is largely unknown but could significantly increase the prevalence of the disease if considered highly likely. In the present study, additional (free T4) or repeat (total T4) testing was only performed in approximately 45% of these equivocal cases and resulted most commonly (70.0%) in reclassification as euthyroid and less commonly as hyperthyroid (17.5%) or persistently equivocal (12.5%). In other studies, highlighting equivocal cases, only 1 of 47 (2.1%) overall [16] and 5 of 46 (10.9%) [12] cats with supportive clinical signs were reclassified as hyperthyroid. Measurement of canine thyroid stimulating hormone (cTSH) could have been used to support a diagnosis of hyperthyroidism in equivocal cases. However, it is neither wholly sensitive or specific for diagnosing hyperthyroidism [40] and was not routinely used at the time of the study. It has been used elsewhere when evaluating equivocal cases but was undetectable in 21 cases where free T4 concentration was only elevated in one [16], suggesting it should be interpreted cautiously in this group of cats. A possible advantage of measuring cTSH is that it provides some information on the likelihood of developing hyperthyroidism in the near future [18]. However, the current study was evaluating point prevalence and therefore future development of hyperthyroidism was not particularly relevant. Overall because there were so few equivocal cases and that most of those retested proved euthyroid, this group is unlikely to significantly impact the overall prevalence rate. Many euthyroid cats had a total T4 concentration below the reference interval. Further investigations to eliminate hypothyroidism were not performed, but such a diagnosis was considered unlikely and not truly relevant to the aims of the study. Naturally occurring adult-onset hypothyroidism is extremely rare with only four case reports in the literature [41,42,43,44]. On the other hand, non-thyroidal illness is a well-known cause of suppressed total T4 concentrations in cats [5]. The majority (approximately 80%) of cats with low total T4 concentrations were classified as sick in the current study, supporting a diagnosis of non-thyroidal illness as a potential cause. However, approximately 20% of these cats were reportedly healthy. It is possible that, given the limitations of a routine physical examination, these cats were incorrectly identified as healthy or that for some, the low values simply reflect normal variation. Hyperthyroidism is a disease of aged cats and it is therefore not surprising that cats older than 14 years were over twice as likely to have hyperthyroidism compared to the younger cats. This is consistent with all other studies where age has been evaluated [8, 12,13,14, 16, 18, 25]. However, whilst recognizing the importance of advancing age, it is also recognized that ageing alone is not responsible for the increasing prevalence of hyperthyroidism. Despite targeting similar risk factors for hyperthyroidism, the results of the current study did not always support other published reports. There were more female (61.4%) than male (38.6%) hyperthyroid cats in the current study, but there was no statistically significant difference in prevalence of hyperthyroidism between them. Most other previous studies where gender was examined also report no sex predilection [3, 13, 14, 16, 19, 24]. This is in contrast to three separate studies reporting a higher prevalence of hyperthyroidism in female cats [8, 12, 26] and one suggesting an increased association in male cats [11] In humans, toxic multinodular goitre, with which the feline condition is likened to, is many more times common in females, although the reasons remain unclear [45]. The variable and different sex predispositions in the reports of feline hyperthyroidism would question the true significance of this as a risk factor for the disorder in this species. Being purebred and particularly Siamese, Himalayan, Burmese or Persian has been associated with a decreased risk of hyperthyroidism suggesting a genetic predisposition to the disease [3, 19, 23, 24, 26]. In a study from Hong Kong, being non-DSH was significantly associated with being hyperthyroid but this might reflect a large percentage of DSH cats in that particular region being of oriental descent and could actually support the previously reported breed predispositions [13]. By contrast, in the current study, there was no significant association between hyperthyroidism and being purebred or crossbred. There were only eight cats of oriental origin, of which one was hyperthyroid. The small number of purebred cats (< 3%) prevented any meaningful analysis of a specific breed predilection but also may have influenced the lack of association found for breed overall. How the proportion of purebred cats presented during this study reflects the distribution of cats in the wider Irish cat population is largely unknown as reliable figures are not available. The association between different environmental factors and feline hyperthyroidism is variable in most studies and made no more well defined based on the results of the current study. Of the cats evaluated herein, the majority was indoor with access to outdoors, a minority was exclusively indoor with only a few being completely outdoors. There was no significant association between hyperthyroidism and lifestyle as assessed by living indoors and outdoors. This contrasts with a reported significant association between hyperthyroidism and living strictly indoors noted in two separate studies [3, 14] or presumably having indoor access as defined by use of cat litter [23, 24] or sleeping on the floor [26]. However, many other studies found no association between a mostly indoor lifestyle and hyperthyroidism [12, 13, 16, 25]. Undoubtedly, living strictly indoors could increase exposure to endocrine disruptors such as PBDEs that have been used as flame retardants. Their involvement in the aetiology of hyperthyroidism has recently been disputed, at least in Australian cats [46]. However, several other studies have suggested that PBDEs may be involved in the aetiopathogenesis of the disease, at least in Europe and California [31,32,33]. Alternatively, clients owning cats that are kept predominantly indoors may be more observant of clinical signs associated with hyperthyroidism and thus more likely to present for veterinary attention. This may be supported by the reported association between being insured and hyperthyroidism [19] as insured cats are more likely to attend for veterinary attention more regularly and to undergo more diagnostic investigation. Regular exposure to topical ectoparasiticides has also been associated with an increased risk of developing hyperthyroidism in some previous studies [3, 26]. However, in line with the current results, this association has not been identified in multiple other studies [12, 13, 16, 25]. Thus, the role of exposure to parasiticides and the development of feline hyperthyroidism is probably minimal. This presumably also applies to other environmental chemicals such as fertilizers and herbicides that have been associated with hyperthyroidism in only one previous study [3]. Multiple studies have identified an increased risk of hyperthyroidism associated with an increased proportion of canned or wet food in the diet [3, 8, 12, 14, 16, 23,24,25,26], particular flavours of canned food [23, 25] and types of packaging (easy open, ring pull or pop top tins) [8, 12]. Only one previous study failed to identify an association with feeding canned food [26] similar to the results of the current study. However, evaluating any association between types of food and hyperthyroidism was particularly difficult in the current study. There was a mixed response to this section of the questionnaire as the majority of respondents fed a combination of pouches, cans and dry food, and/or failed to specify the type of packaging. Thus, it was only possible to examine two groups considered large enough; cats that had access to ring pull cans versus those that did not, and cats that had dry food as part of their diet versus those fed exclusively wet food. There was no significant association in either case but this only included a proportion of the cats investigated. Thus, the role of diet in the development of hyperthyroidism cannot be dismissed from these results, be it, as suggested elsewhere, related to iodine content [27], soy isoflavone excess [28, 29], exposure to bisphenol A from pop top or ring pull cans [8, 30] or other as of yet unidentified factors. The variable risk factors identified in this and other studies suggests that a much larger multicenter study should be performed to truly identify those that are significant as recommended elsewhere [16, 47]. Within the current study, the clinical findings in hyperthyroid cats were not unexpected and have been reported extensively elsewhere [1,2,3, 18, 22]. Within this group, weight loss, tachypnoea, and polyphagia were noted in the majority of cases whilst goitre, cardiac murmur, increased heart rate and diarrhoea occurred in less than 50% of cases. There was a significant association between weight loss, tachypnoea, polyphagia, tachycardia and goitre and hyperthyroidism similar to previous reports [16] and suggesting that the presence of these signs should specifically prompt investigation for hyperthyroidism. Despite vomiting and diarrhoea described as relatively common clinical signs of hyperthyroidism [2], there was no association between these and thyroid dysfunction in the current study as reported elsewhere [26]. This presumably relates to the frequency (approximately 32%) with which vomiting was recorded in the cats overall and the fact that there are many wide-ranging differentials for such a presenting problem. On the other hand, a lack of association with diarrhoea may have reflected the low numbers of cases (just over 10%) with this complaint overall. Similarly, there was no association with the presence of a cardiac murmur. However, such was only identified in approximately one third of the hyperthyroid cats where it has been recognized in over half of affected cats in other studies [48]. This may reflect difficulties in auscultating cardiac murmurs during primary-care veterinary practice consultations and warrants further evaluation. Most notably in the present study, although there was an association between detection of goitre and hyperthyroidism, less than half of the hyperthyroid cats were reported as having the same. Additionally, just less than half of these were reported to have bilateral disease, there was no significant difference in total T4 concentration between hyperthyroid cats with or without goitre and no significant difference between the detection of goitre and the health status of these cats. There are numerous studies reporting that bilateral disease is more common in hyperthyroid cats and that increasing severity of hyperthyroidism correlates with the degree of thyroid gland enlargement. It has been reported elsewhere that in primary-care veterinary practice, goitre was accurately detected in over 90% of hyperthyroid cats, with the majority (87%) having bilateral disease [49]. In another study, all hyperthyroid cats had detectable goitre again with the majority being bilateral [50]. Both of these studies demonstrated increasing size of affected thyroid lobes with increasing total T4 concentration. Of particular note is that bilateral goitre was evident in over 60% of 2096 hyperthyroid cats as demonstrated by thyroid scintigraphy [51] confirming its preponderance in this disease. It appears most likely that the veterinarians contributing to the current study failed to detect goitre in hyperthyroid cats. This was not due to uncertainty as in only 14% of the hyperthyroid cats was the presence of goitre listed as 'unsure'. Undoubtedly, the low detection rates found in this study may account for the perceived low prevalence of feline hyperthyroidism in Ireland. Indeed, in South Africa where the prevalence of hyperthyroidism was also perceived as low before being specifically investigated, goitre was only detected in 2 of 12 hyperthyroid cats [16]. Goitre was also detected in between 20 and 25% of euthyroid and equivocal cases in the current study. Palpation of small cervical nodules, presuming a goitre, is not uncommon and has been previously reported in euthyroid cats [49, 50]. Such cervical nodules may represent other pathologies such as parathyroid enlargement. If truly representing goitre, it would be interesting to follow such cats to determine if hyperthyroidism develops with time. Certainly, in one study, half of the euthyroid cats with palpable goitre went on to develop increased total T4 concentrations, but only six cats were evaluated [49]. It would appear prudent to monitor these cases regularly over time. Hyperthyroidism is not uncommon in Irish cats and similar to other studies, advancing age is a significant risk factor. However, no associations between previously reported environmental and nutritional risk factors and feline hyperthyroidism were detected in the present study. 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BVSAVA manual of canine and feline endocrinology. 4th ed. Gloucester: British Small Animal Veterinary Association; 2012. p. 1–8. Rand JS, Levine J, Best SJ. Spontaneous adult-onset hypothyroidism in a cat. J Vet Intern Med. 1993;7:272–6. Blois SL, Abrams-Ogg ACG, Mitchell C. Use of thyroid scintigraphy and pituitary immunochemistry in the diagnosis of spontaneous hypothyroidism in a mature cat. J Feline Med Surg. 2010;12:156–60. Galgano M, Spalla I, Callegari C. Primary hypothyroidism and thyroid goiter in an adult cat. J Vet Intern Med. 2014;28:682–6. Kent A, Constantino-Casas F, Herrtage ME. Naturally occurring acquired primary hypothyroidism in a cat due to lymphocytic thyroiditis. Vet Rec Case Rep. 2016;4 Mandel SJ, Larsen PR, Davies TF. Thyrotoxicosis. In: Melmed S, Polonsky SK, Larsen PR, Kronenberg HM, editors. Williams textbook of endocrinology. Philadelphia: Elsevier; 2011. p. 362–406. Chow K, Hern LK, Zuber M, Beatty JA, Mueller JF, Barrs VR. Evaluation of polybrominated dipheyl ethers (PBDEs) in matched cat sera and house dust samples: investigation of a potential link between PBDEs and spontaneous feline hyperthyroidism. Environ Res. 2015;136:173–9. Van Hoek I, Hesta M, Biourge V. A critical review of food-associated factors proposed in the etiology of feline hyperthyroidism. J Feline Med Surg. 2014;17(10):837–47. Boussard JD, Peterson ME, Fox PR. Changes in clinical and laboratory findings in cats with hyperthyroidism from 1983 to 1993. J Am Anim Hosp Assoc. 1995;206(3):302–5. Norsworthy GD, Adams VJ, McElhaney MR, Milios JA. Palpable thyroid and parathyroid nodules in asymptomatic cats. J Feline Med Surg. 2016;4(3):145–51. Boretti FS, Sieber-Ruckstuhl NS, Gerber DD. Thyroid enlargement and its relationship to clinicopathological parameters and T4 status in suspected hyperthyroid cats. J Feline Med Surg. 2009;11(4):286–92. Peterson ME, Broome MR. Thyroid scintigraphy findings in 2096 cats with hyperthyroidism. Vet Radiol Ultrasound. 2014;56(1):84–95. The authors would like to thank Tracey Clegg for assisting with statistical analysis and Karolina Fawcett for assisting with total T4 analysis. We would also like to thank all participating veterinarians, owners and cats. This study was funded by MSD Animal Health. The datasets used and analysed in the current study are available on request and will be contained within the DVMS thesis of Laura Bree, Section of Veterinary Clinical Studies, School of Veterinary Medicine, University College Dublin. Section of Small Animal Clinical Studies, School of Veterinary Medicine, University College Dublin, Belfield, Dublin 4, Ireland Laura Bree, Robert E. Shiel & Carmel T. Mooney Present Address: Chestergates Veterinary Specialists, Telford Court Chestergates Roads Chester, Cheshire, CH1 6LT, UK Barbara A. Gallagher Laura Bree Robert E. Shiel Carmel T. Mooney BG and CTM were involved in the study design, questionnaire dispersal as well as recording of data and statistical analysis (LB, RS, CTM, BG). LB and CTM were involved with drafting the manuscript, while BG, RS and CTM gave final approval of the version to be published. All authors read and approved the final manuscript. Correspondence to Laura Bree. The study was approved by the University College Dublin (UCD) Academic Research and Ethics Committee (AREC-P-11-20-Mooney). Study Questionnaire Part 1 (veterinarian) & Part 2 (owner). (PDF 182 kb) Bree, L., Gallagher, B.A., Shiel, R.E. et al. Prevalence and risk factors for hyperthyroidism in Irish cats from the greater Dublin area. Ir Vet J 71, 2 (2018). https://doi.org/10.1186/s13620-017-0113-x DOI: https://doi.org/10.1186/s13620-017-0113-x	CommonCrawl
The spin rate of pre-collapse stellar cores: wave driven angular momentum transport i... Jim Fuller The core rotation rates of massive stars have a substantial impact on the nature of core collapse supernovae and their compact remnants. We demonstrate that internal gravity waves (IGW), excited via envelope convection during a red supergiant phase or during vigorous late time burning phases, can have a significant impact on the rotation rate of the pre-SN core. In typical (10 M⊙ ≲ M ≲ 20 M⊙) supernova progenitors, IGW may substantially spin down the core, leading to iron core rotation periods $P_{\rm min,Fe} \gtrsim 50 \, {\rm s}$. Angular momentum (AM) conservation during the supernova would entail minimum NS rotation periods of $P_{\rm min,NS} \gtrsim 3 \, {\rm ms}$. In most cases, the combined effects of magnetic torques and IGW AM transport likely lead to substantially longer rotation periods. However, the stochastic influx of AM delivered by IGW during shell burning phases inevitably spin up a slowly rotating stellar core, leading to a maximum possible core rotation period. We estimate maximum iron core rotation periods of $P_{\rm max,Fe} \lesssim 10^4 \, {\rm s}$ in typical core collapse supernova progenitors, and a corresponding spin period of $P_{\rm max, NS} \lesssim 400 \, {\rm ms}$ for newborn neutron stars. This is comparable to the typical birth spin periods of most radio pulsars. Stochastic spin-up via IGW during shell O/Si burning may thus determine the initial rotation rate of most neutron stars. For a given progenitor, this theory predicts a Maxwellian distribution in pre-collapse core rotation frequency that is uncorrelated with the spin of the overlying envelope. Software Use in Astronomy: An Informal Survey Ivelina Momcheva INTRODUCTION Much of modern Astronomy research depends on software. Digital images and numerical simulations are central to the work of most astronomers today, and anyone who is actively involved in astronomy research has a variety of software techniques in their toolbox. Furthermore, the sheer volume of data has increased dramatically in recent years. The efficient and effective use of large data sets increasingly requires more than rudimentary software skills. Finally, as astronomy moves towards the open code model, propelled by pressure from funding agencies and journals as well as the community itself, readability and reusability of code will become increasingly important (Figure [fig:xkcd]). Yet we know few details about the software practices of astronomers. In this work we aim to gain a greater understanding of the prevalence of software tools, the demographics of their users, and the level of software training in astronomy. The astronomical community has, in the past, provided funding and support for software tools intended for the wider community. Examples of this include the Goddard IDL library (funded by the NASA ADP), IRAF (supported and developed by AURA at NOAO), STSDAS (supported and developed by STScI), and the Starlink suite (funded by PPARC). As the field develops, new tools are required and we need to focus our efforts on ones that will have the widest user base and the lowest barrier to utilization. For example, as our work here shows, the much larger astronomy user base of Python relative to the language R suggests that tools in the former language are likely to get many more users and contributers than the latter. More recently, there has been a growing discussion of the importance of data analysis and software development training in astronomy (e.g., the special sessions at the 225th AAS "Astroinformatics and Astrostatistics in Astronomical Research Steps Towards Better Curricula" and "Licensing Astrophysics Codes", which were standing room only). Although astronomy and astrophysics went digital long ago, the formal training of astronomy and physics students rarely involves software development or data-intensive analysis techniques. Such skills are increasingly critical in the era of ubiquitous "Big Data" (e.g., , or the 2015 NOAO Big Data conference). Better information on the needs of researchers as well as the current availability of training opportunities (or lack thereof) can be used to inform, motivate and focus future efforts towards improving this aspect of the astronomy curriculum. In 2014 the Software Sustainability Institute carried out an inquiry into the software use of researchers in the UK (, see also the associated presentation). This survey provides useful context for software usage by researchers, as well as a useful definition of "research software": Software that is used to generate, process or analyze results that you intend to appear in a publication (either in a journal, conference paper, monograph, book or thesis). Research software can be anything from a few lines of code written by yourself, to a professionally developed software package. Software that does not generate, process or analyze results - such as word processing software, or the use of a web search - does not count as 'research software' for the purposes of this survey. However, this survey was limited to researchers at UK institutions. More importantly, it was not focused on astronomers, who may have quite different software practices from scientists in other fields. Motivated by these issues and related discussions during the .Astronomy 6 conference, we created a survey to explore software use in astronomy. In this paper, we discuss the methodology of the survey in §[sec:datamethods], the results from the multiple-choice sections in §[sec:res] and the free-form comments in §[sec:comments]. In §[sec:ssicompare] we compare our results to the aforementioned SSI survey and in §[sec:conc] we conclude. We have made the anonymized results of the survey and the code to generate the summary figures available at https://github.com/eteq/software_survey_analysis. This repository may be updated in the future if a significant number of new respondents fill out the survey[1]. [1] http://tinyurl.com/pvyqw59 A minimum standard for publishing computational results in the weather and climate sc... Weather and climate science has undergone a computational revolution in recent decades, to the point where all modern research relies heavily on software and code. Despite this profound change in the research methods employed by weather and climate scientists, the reporting of computational results has changed very little in relevant academic journals. This lag has led to something of a reproducibility crisis, whereby it is impossible to replicate and verify most of today's published computational results. While it is tempting to simply decry the slow response of journals and funding agencies in the face of this crisis, there are very few examples of reproducible weather and climate research upon which to base new communication standards. In an attempt to address this deficiency, this essay describes a procedure for reporting computational results that was employed in a recent _Journal of Climate_ paper. The procedure was developed to be consistent with recommended computational best practices and seeks to minimize the time burden on authors, which has been identified as the most important barrier to publishing code. It should provide a starting point for weather and climate scientists looking to publish reproducible research, and it is proposed that journals could adopt the procedure as a minimum standard. IEDA EarthChem: Supporting the sample-based geochemistry community with data resource... Leslie Hsu ABSTRACT Integrated sample-based geochemical measurements enable new scientific discoveries in the Earth sciences. However, integration of geochemical data is difficult because of the variety of sample types and measured properties, idiosyncratic analytical procedures, and the time commitment required for adequate documentation. To support geochemists in integrating and reusing geochemical data, EarthChem, part of IEDA (Integrated Earth Data Applications), develops and maintains a suite of data systems to serve the scientific community. The EarthChem Library focuses on dataset publication, accessibility, and linking with other sources. Topical synthesis databases (e.g., PetDB, SedDB, Geochron) integrate data from several sources and preserve metadata associated with analyzed samples. The EarthChem Portal optimizes data discovery and provides analysis tools. Contributing authors obtain citable DOI identifiers, usage reports of their data, and increased discoverability. The community benefits from open access to data leading to accelerated scientific discoveries. Growing citations of EarthChem systems demonstrate its success. Parameter estimation on gravitational waves from neutron-star binaries with spinning... Ben Farr INTRODUCTION As we enter the advanced-detector era of ground-based gravitational-wave (GW) astronomy, it is critical that we understand the abilities and limitations of the analyses we are prepared to conduct. Of the many predicted sources of GWs, binary neutron-star (BNS) coalescences are paramount; their progenitors have been directly observed , and the advanced detectors will be sensitive to their GW emission up to ∼400 Mpc away . When analyzing a GW signal from a circularized compact binary merger, strong degeneracies exist between parameters describing the binary (e.g., distance and inclination). To properly estimate any particular parameter(s) of interest, the marginal distribution is estimated by integrating the joint posterior probability density function (PDF) over all other parameters. In this work, we sample the posterior PDF using software implemented in the LALINFERENCE library . Specifically we use results from LALINFERNCE_NEST , a nest sampling algorithm , and LALINFERENCE_MCMC , a Markov-chain Monte Carlo algorithm \citep[chapter 12]{Gregory2005}. Previous studies of BNS signals have largely assessed parameter constraints assuming negligible neutron-star (NS) spin, restricting models to nine parameters. This simplification has largely been due to computational constraints, but the slow spin of NSs in short-period BNS systems observed to date \citep[e.g.,][]{Mandel_2010} has also been used as justification. However, proper characterization of compact binary sources _must_ account for the possibility of non-negligible spin; otherwise parameter estimates will be biased . This bias can potentially lead to incorrect conclusions about source properties and even misidentification of source classes. Numerous studies have looked at the BNS parameter estimation abilities of ground-based GW detectors such as the Advanced Laser Interferometer Gravitational-Wave Observatory \citep[aLIGO;][]{Aasi_2015} and Advanced Virgo \citep[AdV;][]{Acernese_2014} detectors. assessed localization abilities on a simulated non-spinning BNS population. looked at several potential advanced-detector networks and quantified the parameter-estimation abilities of each network for a signal from a fiducial BNS with non-spinning NSs. demonstrated the ability to characterize signals from non-spinning BNS sources with waveform models for spinning sources using Bayesian stochastic samplers in the LALINFERENCE library . used approximate methods to quantify the degeneracy between spin and mass estimates, assuming the compact objects' spins are aligned with the orbital angular momentum of the binary \citep[but see][]{Haster_2015}. simulated a collection of loud signals from non-spinning BNS sources in several mass bins and quantified parameter estimation capabilities in the advanced-detector era using non-spinning models. introduced precession from spin–orbit coupling and found that the additional richness encoded in the waveform could reduce the mass–spin degeneracy, helping BNSs to be distinguished from NS–black hole (BH) binaries. conducted a similar analysis of a large catalog of sources and found that it is difficult to infer the presence of a mass gap between NSs and BHs , although, this may still be possible using a population of a few tens of detections . Finally, and the follow-on represent an (almost) complete end-to-end simulation of BNS detection and characterization during the first 1–2 years of the advanced-detector era. These studies simulated GWs from an astrophysically motivated BNS population, then detected and characterized sources using the search and follow-up tools that are used for LIGO–Virgo data analysis . The final stage of the analysis missing from these studies is the computationally expensive characterization of sources while accounting for the compact objects' spins and their degeneracies with other parameters. The present work is the final step of BNS characterization for the simulations using waveforms that account for the effects of NS spin. We begin with a brief introduction to the source catalog used for this study and in section [sec:sources]. Then, in section [sec:spin] we describe the results of parameter estimation from a full analysis that includes spin. In section [sec:mass] we look at mass estimates in more detail and spin-magnitude estimates in section [sec:spin-magnitudes]. In section [sec:extrinsic] we consider the estimation of extrinsic parameters: sky position (section [sec:sky]) and distance (section [sec:distance]), which we do not expect to be significantly affected by the inclusion of spin in the analysis templates. We summarize our findings in section [sec:conclusions]. A comparison of computational costs for spinning and non-spinning parameter estimation is given in appendix [ap:CPU]. A search for R-parity violating Supersymmetric top decays at CMS with \(\sqrt{s} = 8\... Alec Aivazis A search for a supersymmetric top decay assuming a 100% branching ratio of $^* \rightarrow \mu^+ \mu ^- b $ is presented using a minimally supersymmetric model at an integrated luminosity of 19.5 fb−1. The datasets were recorded with the CMS detector at the LHC. Using Baysian marginalization, an upper limit on the cross section of this process is computed and a cut off point is calculated below which the data does not support the presence of the target decay. This cut off point was calculated to be around 780 GeV. Notes on Mixing Length Theory MLT These notes are mostly inspired from reading Cox & Giuli ("Principles of stellar structure"); some insights are from A.Maeder ("Physics, formation and evolution of rotating stars") and Kippenhahn & Weigert ("Stellar Structure and Evolution") Pressure Scale Height In hydrostatic equilibrium we can define the total pressure scale height, $\hp$, as -{\D r} \equiv {\hp} = {\p} where $\p$ is the total pressure ($ + $). The pressure scale height is a measure of the distance over which the pressure changes by an appreciable fraction of itself. A novel approach to diagnosing Southern Hemisphere planetary wave activity and its in... Southern Hemisphere mid-to-upper tropospheric planetary wave activity is characterized by the superposition of two zonally-oriented, quasi-stationary waveforms: zonal wavenumber one (ZW1) and zonal wavenumber three (ZW3). Previous studies have tended to consider these waveforms in isolation and with the exception of those studies relating to sea ice, little is known about their impact on regional climate variability. We take a novel approach to quantifying the combined influence of ZW1 and ZW3, using the strength of the hemispheric meridional flow as a proxy for zonal wave activity. Our methodology adapts the wave envelope construct routinely used in the identification of synoptic-scale Rossby wave packets and improves on existing approaches by allowing for variations in both wave phase and amplitude. While ZW1 and ZW3 are both prominent features of the climatological circulation, the defining feature of highly meridional hemispheric states is an enhancement of the ZW3 component. Composites of the mean surface conditions during these highly meridional, ZW3-like anomalous states (i.e. months of strong planetary wave activity) reveal large sea ice anomalies over the Amundsen and Bellingshausen Seas during autumn and along much of the East Antarctic coastline throughout the year. Large precipitation anomalies in regions of significant topography (e.g. New Zealand, Patagonia, coastal Antarctica) and anomalously warm temperatures over much of the Antarctic continent were also associated with strong planetary wave activity. The latter has potentially important implications for the interpretation of recent warming over West Antarctica and the Antarctic Peninsula. Satellite Dwarf Galaxies in a Hierarchical Universe: Infall Histories, Group Preproce... In the Local Group, almost all satellite dwarf galaxies that are within the virial radius of the Milky Way (MW) and M31 exhibit strong environmental influence. The orbital histories of these satellites provide the key to understanding the role of the MW/M31 halo, lower-mass groups, and cosmic reionization on the evolution of dwarf galaxies. We examine the virial-infall histories of satellites with $\mstar=10^{3-9} \msun$ using the ELVIS suite of cosmological zoom-in dissipationless simulations of 48 MW/M31-like halos. Satellites at z = 0 fell into the MW/M31 halos typically $5-8 \gyr$ ago at z = 0.5 − 1. However, they first fell into any host halo typically $7-10 \gyr$ ago at z = 0.7 − 1.5. This difference arises because many satellites experienced "group preprocessing" in another host halo, typically of $\mvir \sim 10^{10-12} \msun$, before falling into the MW/M31 halos. Satellites with lower-mass and/or those closer to the MW/M31 fell in earlier and are more likely to have experienced group preprocessing; half of all satellites with $\mstar < 10^6 \msun$ were preprocessed in a group. Infalling groups also drive most satellite-satellite mergers within the MW/M31 halos. Finally, _none_ of the surviving satellites at z = 0 were within the virial radius of their MW/M31 halo during reionization (z > 6), and only <4% were satellites of any other host halo during reionization. Thus, effects of cosmic reionization versus host-halo environment on the formation histories of surviving dwarf galaxies in the Local Group occurred at distinct epochs and are separable in time. The Victorian Earthquake Hazard Map Dan Sandiford SUMMARY This report summarises the development of a new Probabilistic Seismic Hazard Analysis (PSHA) for Victoria called the Victorian Earthquake Hazard Map (VEHM). PSHA provides forecasts of the strength of shaking in any given time (return period). The primary inputs are historical seismicity catalogues, paleoseismic (active fault) data, and ground-motion prediction equations. A key component in the development of the Victorian Earthquake Hazard Map was the integration of new geophysics data derived from deployments of Australian Geophysical Observing System seismometers in Victoria with a variety of publicly available datasets including seismicity catalogues, geophysical imagery and geological mapping. This has resulted in the development of a new dataset that constrains the models presented in the VEHM and is also is provided as a stand-alone resource for both reference and future analysis. The VEHM provides a Victorian-focussed earthquake hazard estimation tool that offers an alternative to the nationally focussed 2012 Australian Earthquake Hazard Map . The major difference between the two maps is the inclusion of active fault location and slip estimates in the VEHM. There is a significant difference in hazard estimation between the two maps (even without including fault-related seismicity) due primarily to differences in seismicity-analysis. These issues are described in the discussion section of this report, again resulting in a higher fidelity result in the VEHM. These differences make the VEHM a more conservative hazard model. The VEHM currently exists as a series of online resources to help assist those in engineering, planning, disaster management. This is a dynamic dataset and the inputs will continue to be refined as new constraints are included and the map is made compatible with the Global Earthquake Model (GEM) software, due for release in late 2014. The VEHM was funded through the Natural Disaster Resilience Grants Scheme. The NDRGS is a grant program funded by the Commonwealth Attorney-General's Department under the National Partnership Agreement on Natural Disaster Resilience signed by the Prime Minister and Premier. The purpose of the National Partnership Agreement is to contribute towards implementation of the National Strategy for Disaster Resilience, supporting projects leading to the following outcomes: 1. reduced risk from the impact of disasters and 2. appropriate emergency management, including volunteer, capability and capacity consistent with the State's risk profile. Distinguishing disorder from order in irreversible decay processes Jonathan Nichols Fluctuating rate coefficients are necessary when modeling disordered kinetic processes with mass-action rate equations. However, measuring the fluctuations of rate coefficients is a challenge, particularly for nonlinear rate equations. Here we present a measure of the total disorder in irreversible decay i A → products, i = 1, 2, 3, …n governed by (non)linear rate equations – the inequality between the time-integrated square of the rate coefficient (multiplied by the time interval of interest) and the square of the time-integrated rate coefficient. We apply the inequality to empirical models for statically and dynamically disordered kinetics with i ≥ 2. These models serve to demonstrate that the inequality quantifies the cumulative variations in a rate coefficient, and the equality is a bound only satisfied when the rate coefficients are constant in time. Real-space grids and the Octopus code as tools for the development of new simulation... Xavier Andrade Real-space grids are a powerful alternative for the simulation of electronic systems. One of the main advantages of the approach is the flexibility and simplicity of working directly in real space where the different fields are discretized on a grid, combined with competitive numerical performance and great potential for parallelization. These properties constitute a great advantage at the time of implementing and testing new physical models. Based on our experience with the Octopus code, in this article we discuss how the real-space approach has allowed for the recent development of new ideas for the simulation of electronic systems. Among these applications are approaches to calculate response properties, modeling of photoemission, optimal control of quantum systems, simulation of plasmonic systems, and the exact solution of the Schrödinger equation for low-dimensionality systems. The "Paper" of the Future Alyssa Goodman _A 5-minute video demonstration of this paper is available at this YouTube link._ PREAMBLE A variety of research on human cognition demonstrates that humans learn and communicate best when more than one processing system (e.g. visual, auditory, touch) is used. And, related research also shows that, no matter how technical the material, most humans also retain and process information best when they can put a narrative "story" to it. So, when considering the future of scholarly communication, we should be careful not to do blithely away with the linear narrative format that articles and books have followed for centuries: instead, we should enrich it. Much more than text is used to communicate in Science. Figures, which include images, diagrams, graphs, charts, and more, have enriched scholarly articles since the time of Galileo, and ever-growing volumes of data underpin most scientific papers. When scientists communicate face-to-face, as in talks or small discussions, these figures are often the focus of the conversation. In the best discussions, scientists have the ability to manipulate the figures, and to access underlying data, in real-time, so as to test out various what-if scenarios, and to explain findings more clearly. THIS SHORT ARTICLE EXPLAINS—AND SHOWS WITH DEMONSTRATIONS—HOW SCHOLARLY "PAPERS" CAN MORPH INTO LONG-LASTING RICH RECORDS OF SCIENTIFIC DISCOURSE, enriched with deep data and code linkages, interactive figures, audio, video, and commenting. Compressed Sensing for the Fast Computation of Matrices: Application to Molecular Vib... Jacob Sanders This article presents a new method to compute matrices from numerical simulations based on the ideas of sparse sampling and compressed sensing. The method is useful for problems where the determination of the entries of a matrix constitutes the computational bottleneck. We apply this new method to an important problem in computational chemistry: the determination of molecular vibrations from electronic structure calculations, where our results show that the overall scaling of the procedure can be improved in some cases. Moreover, our method provides a general framework for bootstrapping cheap low-accuracy calculations in order to reduce the required number of expensive high-accuracy calculations, resulting in a significant 3$\times$ speed-up in actual calculations. Large-Scale Microscopic Traffic Behaviour and Safety Analysis of Québec Roundabout De... Paul St-Aubin INTRODUCTION Roundabouts are a relatively new design for intersection traffic management in North America. With great promises from abroad in terms of safety, as well as capacity—roundabouts are a staple of European road design—roundabouts have only recently proliferated in parts of North America, including the province of Québec. However, questions still remain regarding the feasibility of introducing the roundabout to regions where driving culture and road design philosophy differ and where drivers are not habituated to their use. This aspect of road user behaviour integration is crucial for their implementation, for roundabouts manage traffic conflicts passively. In roundabouts, road user interactions and driving conflicts are handled entirely by way of driving etiquette between road users: lane merging, right-of-way, yielding behaviour, and eye contact in the case of vulnerable road users are all at play for successful passage negotiation at a roundabout. This is in contrast with typical North American intersections managed by computer-controlled traffic-light controllers (or on occasion police officers) and traffic circles of all kinds which are also signalized. And while roundabouts share much in common with 4 and 2-way stops, they are frequently used for high-capacity, even high-speed, intersections where 4 and 2-way stops would normally not be justified. Resistance to adoption in some areas is still important, notably on the part of vulnerable road users such as pedestrians and cyclists but also by some drivers too. While a number of European studies cite reductions in accident probability and accident severity, particularly for the Netherlands , Denmark , and Sweden , research on roundabouts in North America is still limited, and even fewer attempts at microscopic behaviour analysis exist anywhere in the world. The latter is important because it provides insight over the inner mechanics of driving behaviour which might be key to tailoring roundabout design for regional adoption and implementation efforts. Fortunately, more systematic and data-rich analysis techniques are being made available today. This paper proposes the application of a novel, video-based, semi-automated trajectory analysis approach for large-scale microscopic behavioural analysis of 20 of 100 available roundabouts in Québec, investigating 37 different roundabout weaving zones. The objectives of this paper are to explore the impact of Québec roundabout design characteristics, their geometry and built environment on driver behaviour and safety through microscopic, video-based trajectory analysis. Driver behaviour is characterized by merging speed and time-to-collision , a maturing indicator of surrogate safety and behaviour analysis in the field of transportation safety. In addition, this work represents one of the largest applications of surrogate safety analysis to date. Comparison of Various Time-to-Collision Prediction and Aggregation Methods for Surrog... INTRODUCTION Traditional methods of road safety analysis rely on direct road accident observations, data sources which are rare and expensive to collect and which also carry the social cost of placing citizens at risk of unknown danger. Surrogate safety analysis is a growing discipline in the field of road safety analysis that promises a more pro-active approach to road safety diagnosis. This methodology uses non-crash traffic events and measures thereof as predictors of collision probability and severity as they are significantly more frequent, cheaper to collect, and have no social impact. Time-to-collision (TTC) is an example of an indicator that indicates collision probability primarily: the smaller the TTC, the less likely drivers have time to perceive and react before a collision, and thus the higher the probability of a collision outcome. Relative positions and velocities between road users or between a user and obstacles can be characterised by a collision course and the corresponding TTC. Meanwhile, driving speed (absolute speed) is an example of an indicator that measures primarily collision severity. The higher the travelling speed, the more stored kinetic energy is dissipated during a collision impact . Similarly, large speed differentials between road users or with stationary obstacles may also contribute to collision severity, though the TTC depends on relative distance as well. Driving speed is used extensively in stopping-sight distance models , some even suggesting that drivers modulate their emergency braking in response to travel speed . Others content that there is little empirical evidence of a relationship between speed and collision probability . Many surrogate safety methods have been used in the literature, especially recently with the renewal of automated data collection methods, but consistency in the definitions of traffic events and indicators, in their interpretation, and in the transferability of results is still lacking. While a wide diversity of models demonstrates that research in the field is thriving, there remains a need of comparison of the methods and even a methodology for comparison in order to make surrogate safety practical for practitioners. For example, time-to-collision measures collision course events, but the definition of a collision course lacks rigour in the literature. Also lacking is some systematic validation of the different techniques. Some early attempts have been made with the Swedish Traffic Conflict Technique using trained observers, though more recent attempts across different methodologies, preferably automated and objectively-defined measures, are still needed. Ideally, this would be done with respect to crash data and crash-based safety diagnosis. The second best method is to compare the characteristics of all the methods and their results on the same data set, but public benchmark data is also very limited despite recent efforts . The objectives of this paper are to review the definition and interpretation of one of the most ubiquitous and least context-sensitive surrogate safety indicators, namely time-to-collision, for surrogate safety analysis using i) consistent, recent, and, most importantly, objective definitions of surrogate safety indicators, ii) a very large data set across numerous sites, and iii) the latest developments in automated analysis. This work examines the use of various motion prediction methods, constant velocity, normal adaptation and observed motion patterns, for the TTC safety indicator (for its properties of transferability), and space and time aggregation methods for continuous surrogate safety indicators. This represents an application of surrogate safety analysis to one of the largest data sets to date. The Fork Factor: an academic impact factor based on reuse. Ferdinando Pucci HOW IS ACADEMIC RESEARCH EVALUATED? There are many different ways to determine the impact of scientific research. One of the oldest and best established measures is to look at the Impact Factor (IF) of the academic journal where the research has been published. The IF is simply the average number of citations to recent articles published in such an academic journal. The IF is important because the reputation of a journal is also used as a proxy to evaluate the relevance of past research performed by a scientist when s/he is applying to a new position or for funding. So, if you are a scientist who publishes in high-impact journals (the big names) you are more likely to get tenure or a research grant. Several criticisms have been made to the use and misuse of the IF. One of these is the policies that academic journal editors adopt to boost the IF of their journal (and get more ads), to the detriment of readers, writers and science at large. Unfortunately, these policies promote the publication of sensational claims by researchers who are in turn rewarded by funding agencies for publishing in high IF journals. This effect is broadly recognized by the scientific community and represents a conflict of interests, that in the long run increases public distrust in published data and slows down scientific discoveries. Scientific discoveries should instead foster new findings through the sharing of high quality scientific data, which feeds back into increasing the pace of scientific breakthroughs. It is apparent that the IF is a crucially deviated player in this situation. To resolve the conflict of interest, it is thus fundamental that funding agents (a major driving force in science) start complementing the IF with a better proxy for the relevance of publishing venues and, in turn, scientists' work. RESEARCH IMPACT IN THE ERA OF FORKING. A number of alternative metrics for evaluating academic impact are emerging. These include metrics to give scholars credit for sharing of raw science (like datasets and code), semantic publishing, and social media contribution, based not solely on citation but also on usage, social bookmarking, conversations. We, at Authorea, strongly believe that these alternative metrics should and will be a fundamental ingredient of how scholars are evaluated for funding in the future. In fact, Authorea already welcomes data, code, and raw science materials alongside its articles, and is built on an infrastructure (Git) that naturally poses as a framework for distributing, versioning, and tracking those materials. Git is a versioning control platform currently employed by developers for collaborating on source code, and its features perfectly fit the needs of most scientists as well. A versioning system, such as Authorea and GitHub, empowers FORKING of peer-reviewed research data, allowing a colleague of yours to further develop it in a new direction. Forking inherits the history of the work and preserves the value chain of science (i.e., who did what). In other words, forking in science means _standing on the shoulder of giants_ (or soon to be giants) and is equivalent to citing someone else's work but in a functional manner. Whether it is a "negative" result (we like to call it non-confirmatory result) or not, publishing your peer reviewed research in Authorea will promote forking of your data. (To learn how we plan to implement peer review in the system, please stay tuned for future posts on this blog.) MORE FORKING, MORE IMPACT, HIGHER QUALITY SCIENCE. Obviously, the more of your research data are published, the higher are your chances that they will be forked and used as a basis for groundbreaking work, and in turn, the higher the interest in your work and your academic impact. Whether your projects are data-driven peer reviewed articles on Authorea discussing a new finding, raw datasets detailing some novel findings on Zenodo or Figshare, source code repositories hosted on Github presenting a new statistical package, every bit of your work that can be reused, will be forked and will give you credit. Do you want to do a favor to science? Publish also non-confirmatory results and help your scientific community to quickly spot bad science by publishing a dead end fork (Figure 1). The effect of carbon subsidies on marine planktonic niche partitioning and recruitmen... Charles Pepe-Ranney INTRODUCTION Biofilms are diverse and complex microbial consortia, and, the biofilm lifestyle is the rule rather than the exception for microbes in many environments. Large and small-scale biofilm architectural features play an important role in their ecology and influence their role in biogeochemical cycles . Fluid mechanics impact biofilm structure and assembly , but it is less clear how other abiotic factors such as resource availability affect biofilm assembly. Aquatic biofilms initiate with seed propagules from the planktonic community . Thus, resource amendments that influence planktonic communities may also influence the recruitment of microbial populations during biofilm community assembly. In a crude sense, biofilm and planktonic microbial communities divide into two key groups: oxygenic phototrophs including eukaryotes and cyanobacteria (hereafter "photoautotrophs"), and heterotrophic bacteria and archaea. This dichotomy, admittedly an abstraction (e.g. non-phototrophs can also be autotrophs), can be a powerful paradigm for understanding community shifts across ecosystems of varying trophic state . Heterotrophs meet some to all of their organic carbon (C) requirements from photoautotroph produced C while simultaneously competing with photoautotrophs for limiting nutrients such as phosphorous (P) . The presence of external C inputs, such as terrigenous C leaching from the watershed or C exudates derived from macrophytes , can alleviate heterotroph reliance on photoautotroph derived C and shift the heterotroph-photoautotroph relationship from commensal and competitive to strictly competitive . Therefore, increased C supply should increase the resource space available to heterotrophs and increase competition for mineral nutrients decreasing nutrients available for photoautotrophs (assuming that heterotrophs are superior competitors for limiting nutrients as has been observed ). These dynamics should result in the increase in heterotroph biomass relative to the photoautotroph biomass along a gradient of increasing labile C inputs. We refer to this differential allocation of limiting resources among components of the microbial community as niche partitioning. While these gross level dynamics have been discussed conceptually and to some extent demonstrated empirically , the effects of biomass dynamics on photoautotroph and heterotroph membership and structure has not been directly evaluated in plankton or biofilms. In addition, how changes in planktonic communities propagate to biofilms during community assembly is not well understood. We designed this study to test if C subsidies shift the biomass balance between autotrophs and heterotrophs within the biofilm or its seed pool (i.e. the plankton), and, to measure how changes in biomass pool size alter composition of the plankton and biofilm communities. Specifically, we amended marine mesocosms with varying levels of labile C input and evaluated differences in photoautotroph and heterotrophic bacterial biomass in plankton and biofilm samples along the C gradient. In each treatment we characterized plankton and biofilm community composition by PCR amplifying and DNA sequencing 16S rRNA genes and plastid 23S rRNA genes. Lattice polymers with two competing collapse interactions Andrea Bedini We study a generalised model of self-avoiding trails, containing two different types of interaction (nearest-neighbour contacts and multiply visited sites), using computer simulations. This model contains various previously-studied models as special cases. We find that the strong collapse transition induced by multiply-visited sites is a singular point in the phase diagram and corresponds to a higher order multi-critical point separating a line of weak second-order transitions from a line of first-order transitions. Non-cyanobacterial diazotrophs mediate dinitrogen fixation in biological soil crusts... ABSTRACT Biological soil crusts (BSC) are key components of ecosystem productivity in arid lands and they cover a substantial fraction of the terrestrial surface. In particular, BSC N₂-fixation contributes significantly to the nitrogen (N) budget of arid land ecosystems. In mature crusts, N₂-fixation is largely attributed to heterocystous cyanobacteria, however, early successional crusts possess few N₂-fixing cyanobacteria and this suggests that microorganisms other than cyanobacteria mediate N₂-fixation during the critical early stages of BSC development. DNA stable isotope probing (DNA-SIP) with ¹⁵N₂ revealed that _Clostridiaceae_ and _Proteobacteria_ are the most common microorganisms that assimilate ¹⁵N₂ in early successional crusts. The _Clostridiaceae_ identified are divergent from previously characterized isolates, though N₂-fixation has previously been observed in this family. The Proteobacteria identified share >98.5 %SSU rRNA gene sequence identity with isolates from genera known to possess diazotrophs (e.g. _Pseudomonas_, _Klebsiella_, _Shigella_, and _Ideonella_). The low abundance of these heterotrophic diazotrophs in BSC may explain why they have not been characterized previously. Diazotrophs play a critical role in BSC formation and characterization of these organisms represents a crucial step towards understanding how anthropogenic change will affect the formation and ecological function of BSC in arid ecosystems. KEYWORDS: microbial ecology / stable isotope probing / nitrogen fixation / biological soil crusts Ternary Ladder Operators Benedict Irwin ABSTRACT We develop a triplet operator system which encompasses the structure of quark combinations. Ladder operators are created. The constants β are currently being found. Counting the Cost: A Report on APC-supported Open Access Publishing in a Research Lib... At one-hundred twenty-two articles published, the open access journal _Tremor and other Hyperkinetic Movements_ (tremorjournal.org, ISSN: 2160-8288), is growing its readership and expanding its influence among patients, clinicians, researchers, and the general public interested in issues of non-Parkinsonian tremor disorders. Among the characteristics that set the journal apart from similar publications, _Tremor_ is published in partnership with the library-based publications program at Columbia University's Center for Digital Research and Scholarship (CDRS). The production of _Tremor_ in conjunction with its editor, a researching faculty member, clinician, and epidemiologist at the Columbia University Medical Center, has pioneered several new workflows at CDRS: article-charge processing, coordination of vendor services, integration into PubMed Central, administration of publication scholarships granted through a patient-advocacy organization, and open source platform development among them. Open access publishing ventures in libraries often strive for lean operations by attempting to capitalize on the scholarly impact available through the use of templated and turnkey publication systems. For CDRS, production on _Tremor_ has provided opportunity to build operational capacity for more involved publication needs. The following report introduces a framework and account of the costs of producing such a publication as a guide to library and other non-traditional publishing operations interested in gauging the necessary investments. Following a review of the literature published to date on the costs of open access publishing and of the practice of journal publishing in academic libraries, the authors present a brief history of the _Tremor_ and a tabulation of the costs and expenditure of effort by library staff in production. Although producing _Tremor_ has been more expensive than other partner publications in the center's portfolio, the experiences have improved the library's capacity for addressing more challenging projects, and developments for _Tremor_ have already begun to be applied to other journals. Large-Scale Automated Proactive Road Safety Analysis Using Video Data Due to the complexity and pervasiveness of transportation in daily life, the use and combination of larger data sets and data streams promises smarter roads and a better understanding of our transportation needs and environment. For this purpose, ITS systems are steadily being rolled out, providing a wealth of information, and transitionary technologies, such as computer vision applied to low-cost surveillance or consumer cameras, are already leading the way. This paper presents, in detail, a practical framework for implementation of an automated, high-resolution, video-based traffic-analysis system, particularly geared towards researchers for behavioural studies and road safety analysis, or practitioners for traffic flow model validation. This system collects large amounts of microscopic traffic flow data from ordinary traffic using CCTV and consumer-grade video cameras and provides the tools for conducting basic traffic flow analyses as well as more advanced, pro-active safety and behaviour studies. This paper demonstrates the process step-by-step, illustrated with examples, and applies the methodology to a case study of a large and detailed study of roundabouts (nearly 80,000 motor vehicles tracked up to 30 times per second driving through a roundabout). In addition to providing a rich set of behavioural data about Time-to-Collision and gap times at nearly 40 roundabout weaving zones, some data validation is performed using the standard Measure of Tracking Accuracy with results in the 85-95% range.	CommonCrawl
Minimizing fractional harmonic maps on the real line in the supercritical regime DCDS Home Quasi-periodic solution of quasi-linear fifth-order KdV equation December 2018, 38(12): 6215-6239. doi: 10.3934/dcds.2018267 Some questions looking for answers in dynamical systems Carles Simó Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Barcelona, Catalonia, Spain Dedicated to my friend, professor Rafael de la Llave Canosa, for his 60th birthday Received November 2017 Revised July 2018 Published September 2018 Dynamical systems appear in many models in all sciences and in technology. They can be either discrete or continuous, finite or infinite dimensional, deterministic or with random terms. Many theoretical results, the related algorithms and implementations for careful simulations and a wide range of applications have been obtained up to now. But still many key questions remain open. They are mainly related either to global aspects of the dynamics or to the lack of a sufficiently good agreement between qualitative and quantitative results. In these notes a sample of questions, for which the author is not aware of the existence of a good solution, are presented. Of course, it is easy to largely extend the list. Keywords: Breakdown of tori, relation with arithmetic properties, regularity of manifolds and of collisions, quantitative estimates of diffusion, effective stability, strange attractors, Gevrey class properties, open problems. Mathematics Subject Classification: Primary: 37C29, 37C45, 37C55, 37C70, 37D45, 37J30, 37J40, 37N05; Secondary: 70F10, 70F16. Citation: Carles Simó. Some questions looking for answers in dynamical systems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (12) : 6215-6239. doi: 10.3934/dcds.2018267 G. Arioli and H. Koch, The critical renormalization fixed point for commuting pairs of area-preserving maps, Comm. Math. 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Hydrodynamic loading in concomitance with exogenous cytokine stimulation modulates differentiation of bovine mesenchymal stem cells towards osteochondral lineages Stephen M. Goldman1,2 & Gilda A. Barabino1,3 Mesenchymal stem cells (MSCs) are viewed as a having significant potential for tissue engineering and regenerative medicine therapies. Clinical implementation of MSCs, however, demands that their preparation be stable and reproducible. Given that environmental and bioprocessing parameters such as substrate stiffness, seeding densities, culture medium composition, and mechanical loading can result in undirected differentiation of the MSC population, the objective of this study was to systematically investigate how hydrodynamic loading influences the differentiation of bone marrow-derived mesenchymal stem cells (MSCs) towards the osteochondral lineages both in the presence and absence of exogenous, inductive factors. Expanded bovine MSCs were suspended in 2.5 % agarose, cast in a custom mold, and placed into either static or one of two dynamic culture environments consisting of "high" and "low" magnitude shear conditions. Constructs were supplemented with varying concentrations (0, 1, 10, 100 ng/mL) of either TGF-β3 or BMP-2 throughout cultivation with tissue samples being collected following each week of culture. In the absence of exogenous supplementation, hydrodynamic loading had little effect on cell phenotype at either magnitude of stimulation. When cultures were supplemented with BMP-2 and TGF-β3, MSCs gene expression progressed towards the osteogenic and chondrogenic pathways, respectively. This progression was enhanced by the presence of hydrodynamic loading, particularly under high shear conditions, but may point the chondrogenic cultures down a hypertrophic path toward osteogenesis reminiscent of endochondral ossification if TGF-β3 supplementation is insufficient. Moving forward, these results suggest bioprocessing conditions which minimize exposure of chondrogenic cultures to fluid shear stress to avoid undesirable differentiation of the MSC population. Due to their limited supply and decreased proliferative capacity, the sole use of autologous chondrocytes and osteoblasts for regenerative medicines is likely unsustainable [1]. Subsequently, mesenchymal stem cells (MSCs) have emerged as a clinically relevant cell source for regenerative medicine, due to their ease of procurement, multipotentiality, high proliferation rate, and ability to be expanded in vitro while maintaining a stable phenotype [2–4]. Directed differentiation of MSCs along various mesenchymal pathways can be achieved by manipulation of the cell culture environment including supplementation of culture medium with soluble morphogens [5–9], modulation of culture substrate stiffness [10], and external forces [11, 12]. Of particular interest are environmental approaches which might increase differentiation efficiency while reducing upstream bioprocessing costs for the purpose of large scale commercial operations. A predominant challenge of the scaling operations required to process large numbers of cells and/or critically sized tissue constructs is the control of nutrient and waste transport from the cells/tissues during culture. To overcome these issues, a number of bioreactor concepts have been developed to provide the flow of culture media through [13], across [14], and around the constructs [15, 16]. As a result of the medium exchange, the constructs are concurrently nourished and exposed to hydrodynamic loading. Shear stress is known to cause varied effects on cell populations, including transmembrane ion leakage, as well as physiological and metabolic changes [17]. The presence of fluid shear stress, therefore, is an important environmental factor which may play an important role in the stability or instability of the MSC phenotype in culture. Furthermore, if the magnitude and spatiotemporal presentation of hydrodynamic loading can be controlled, it may represent a novel approach to modulating the efficiency of directed MSC differentiation. The primary objective of this study, therefore, was to determine the effect of uniform shear stress magnitude and duration on MSC gene expression through a panel of key differentiation markers along the osteochondral differentiation pathway. These genes were selected for their importance in orthopedic tissue engineering applications and potential to provide a window into the chondrogenic and osteogenic differentiation processes. Given the well-documented sensitivity of mature chondrocytes and osteoblasts to the TGF-β superfamily [8], a secondary objective of this study was to examine the response of MSCs to varying magnitudes of superficial hydrodynamic shear stress in cultures supplemented with varying concentrations of TGF-β3 and BMP-2. Drawing on evidence that both bone and cartilage are mechanosensitive [18, 19] and mechanical stimuli are anabolic [20, 21], we hypothesized that hydrodynamic loading would increase the efficiency of MSC differentiation down the desired pathways as revealed through systematic changes in phenotypic markers. The scope of the study was limited to a range of hydrodynamic conditions within the reported interstitial flow regime of bone [22] and cartilage [23] with a view to determining an optimum for lineage specific differentiation. Additionally, the cytokine concentrations were varied by one order of magnitude in either direction from the most ubiquitous supplementation protocols found in the literature concurrently, to determine how hydrodynamic culture might minimize their necessity. Unless specified otherwise, supplies and reagents were purchased from VWR International (West Chester, PA), Sigma (St. Louis, MO) or Invitrogen (Carlsbad, CA). Antibodies were from AbD Serotec (Raleigh, NC) or Abcam (Cambridge, MA). To elucidate the role of hydrodynamic loading in MSC differentiation towards the osteochondral lineages, we selected three magnitudes of fluid shear stress (0, 1, 10 dyn/cm2) to be applied in the presence of four levels of exogenous stimulation (0, 1, 10, 100 ng/mL) for two different cytokines (BMP-2, TGF-β3) resulting in 12 experimental groups which received some level of both hydrodynamic and exogenous stimuli, three groups which received only TGF-β3 stimulation of varying degrees, three groups which received only BMP-2 stimulation of varying degrees, and three unsupplemented groups which received only hydrodynamic stimulation of varying degrees (Additional file 1: Table S1). Samples from each experimental group were collected on a weekly basis for 2 weeks. Additional samples for each group were generated at the start of tissue culture (Week 0), but never subjected to any of the stated experimental conditions in order to generate a baseline for downstream analysis. MSCs isolated and characterized from the limbs three different animals post-mortem (see Additional file 2 Supplemental Methods, Additional file 3: Figure S1, Additional file 4: Figure S2) were mixed with sterile agarose solution such that the final concentration of MSCs in 2.5 % w/w agarose solution was 25 million cells/mL. Constructs were then cast into a polydimethylsiloxane [PDMS] mold and cultured either statically (0 dyn/cm2) or loaded in a custom flow chamber (Fig. 1) for dynamic culture at one of two wall shear stress (WSS) conditions: low shear (1 dyn/cm2) or high shear (10 dyn/cm2). To achieve the variation in shear stress at the wall (τ wall ), the channel height (h) was varied between two different chamber designs while the kinematic viscosity (μ), Volumetric Flow Rate, and the channel width (b) were held constant. This approach allowed multiple flow loops from different experimental groups to be driven simultaneously by a single, multi-channel peristaltic pump (Masterflex, Cole Parmer, Vernon Hills, IL). Unsupplemented culture groups received a serum free basal media (high glucose DMEM, 1× PSF, 0.1 μM dexamethasone, 50 μg/mL ascorbate 2-phosphate, 40 μg/mL l-proline, 100 μg/mL sodium pyruvate, 1× insulin–transferrin–selenium [ITS]). All other experimental groups received the serum free basal media supplemented with a prescribed concentration (1, 10, or 100 ng/mL) or either TGF-β3 or BMP-2. Tissue constructs were cultivated utilizing a custom built laminar flow chamber (left). Two separate devices with varying channel heights were produced such that parallel cultures of different hydrodynamic loading magnitudes could be simultaneously driven by a single peristaltic pump according to the relationship depicted (right) mRNA expression Real-time polymerase chain reaction (qRT-PCR) was used to quantify region specific gene expression within the constructs. Constructs were fixed in TRIzol, and RNA was isolated from the homogenized cell lysate through a series of rinse, elution, and centrifugation processes. The RNA samples were then reverse transcribed into cDNA using a QuantiTech Rev Transcription kit (Qiagen, Hilden, German) according to the manufacturer's protocol. Gene expression for target mesenchymal lineage markers using custom-designed primers (Additional file 1: Table S2) with quantitative PCR amplification performed on a StepOnePlus™ Real-Time PCR System (Applied Biosystems) in the presence of SYBR Green/ROX master mix (Applied Biosystems). To determine fold regulation over Day 0 controls, the raw fluorescence data was processed using LinRegPCR (v12.11; http://www.hartfaalcentrum.nl) with glyceraldehyde-3-phosphate dehydrogenase (GAPDH) and β-Actin (ACTB) serving as the endogenous controls through geometric averaging [24]. Relative expression (n = 3 per condition and time point) of each target gene was calculated according to Eqs. 1–2, where N 0,i represents the initial concentration of the target gene, N q,i represents the concentration of the target gene at the threshold, E i represents the amplification efficiency of the polymerase chain reaction, and C q is the selected threshold value. $$ {N}_{0,i}={N}_{q,i}/{E}_i^{C_q} $$ $$ Fold\ Change={\left(\frac{N_{0,i}}{\sqrt{N_{0, GAPDH}{N}_{0, ACTB}}}\right)}_{sample}/{\left(\frac{N_{0,i}}{\sqrt{N_{0, GAPDH}{N}_{0, ACTB}}}\right)}_{control} $$ Endogenous controls were evaluated for each experimental group to ensure that their expression levels were not significantly altered across time or culture conditions. Histological analysis For histological analysis, constructs were fixed in 10 % buffered formalin, embedded in paraffin and sectioned into 8 μm thick sections for the midsubstance of the construct. Sectioned samples were stained with Toluidine blue and Alizarin Red per established protocols. For immunofluorescence, sections were incubated with a citrate buffer heated to 99 °C for 30 min to retrieve antigens, and allowed to cool to room temperature. The samples were then incubated in blocking buffer for 30 min and primary rabbit anti-bovine antibodies (1:100, Abcam, Cambridge, MA) for Collagen types I, II, and X at 4 °C overnight. Sections were then washed three times in PBS and with DyLight®594 goat anti-rabbit secondary antibodies (1:200, Abcam, Cambridge, MA) for one hour at room temperature. Finally, samples were washed and mounted with Vectashield with DAPI and visualized on a Nikon Ti Eclipse inverted fluorescence microscope (Nikon Instruments, Inc., Melville, NY), with representative images captured using a CoolSNAP HQ2 CCD camera (Photometrics, Tucson, AZ). Independent experiments produced construct samples for RT-qPCR and immunohistochemistry (N = 3 per group). Gene expression is presented as the mean fold change ± SEM with statistically significant differences defined as p <0.05 using two-way ANOVA with Bonferroni post-hoc tests for multiple comparisons. Stability of gene expression in unsupplemented cultures In order to control for the effect of hydrodynamic loading on the gene expression profile of MSCs, a round of control experiments was performed to assess the stability of the MSC transcriptome in unsupplemented, static, three dimensional culture over the course of 2 weeks of cultivation (Fig. 2). None of the genes measured exhibited significant regulation over the time course of the experiment with respect to the initial expression profile, indicating three dimensional culture in isolation of other factors was not a significant contributor to differentiation of the MSCs toward the desired lineages and that this culture format represents a suitable control for differentiation studies. This was an important realization, as there is evidence in the literature that subtle changes in culture conditions, such as the transition from monolayer to three-dimensional culture represented here can induce phenotypic changes in stem cell populations [10, 11, 25], particularly as a significant contributor to chondrogenesis [26]. It is important to note, however, that many of the protocols from the prior art depend on pellet culture whereas this study is dependent on the encapsulation of the MSCs in a three dimensional agarose hydrogel. The introduction of the hydrogel material provides additional barriers to communication by cell to cell contact, a factor known to play a role in chondrogenesis [27], and the deviation of the observations produced between these different systems may exist due to the relative differences in cell density between the two culture types. It is also noteworthy that the seeding density of the constructs was not varied in this study. It is possible seeding density may also play a role in this observation, as prior literature indicates seeding density can have an impact on ECM deposition in MSC-based tissue constructs [28, 29]. While regulation of the chondrogenic markers herein was not found to be significant these factors may play a role in the weak upward trend of COL2A1 with time in culture. Nevertheless, this effect was small and our observations confirmed the utility of this culture condition as a suitable control for our subsequent hydrodynamic culture studies aiming to determine the effect of exogenous cytokine supplementation on the mRNA expression profiles of this MSC population. Gene Expression profiles were determined for unsupplemented, static cultures via RT-qPCR. No statistically significant regulation of the genes in the panel was observed Effect of hydrodynamic loading on unsupplemented cultures With a suitable control group established, the first step in addressing the potential of hydrodynamic loading as a differentiation tool was to culture MSC based tissue constructs under laminar flow profiles with nominal shear stress magnitudes of 1 and 10 dyn/cm2 and to compare the expression of a panel of genes spanning the phenotypic diversity of cells along the endochondral ossification pathway to the previously discussed static controls. When hydrodynamic culture was introduced as a variable to the three-dimensional, serum-free cultures (Fig. 3), no significant regulation of the chondrogenic gene panel was observed, significant upregulation of the osteogenic transcription factor (RUNX2), and two of the three collagens investigated (COL1Α1 and COLXΑ1) occurred under high shear conditions. RUNX2 and COLXA1 were both upregulated early in cultivation (1-week) and remained elevated relative to both the time matched static controls and the low shear treatment. At the 2-week time point, upregulation of COL1A1 was considered significant relative to the static cultures. Interestingly, no significant difference in gene expression was observed with lower magnitude hydrodynamic loading, indicating that magnitude of shear in the absence of exogenous cytokine supplementation is not inconsequential. While these changes are considered statistically significant, the nominal change in expression of these genes was of less than one order of magnitude from the expression profile measured in the cell source population. When compared to the magnitude of impact of cytokine supplementation on gene expression when controlled for culture duration (>2 orders of magnitude difference), this effect is not likely to be useful as a tool for directed differentiation. At the same time, however, this finding suggests that great care should be taken to minimize the hydrodynamic loading applied to MSC expansion cultures in upstream bioprocessing procedures to prevent non-specific induction of undesirable phenotypes. Hydrodynamic loading induced changes in gene expression of several osteochondral markers even in the absence of exogenous cytokine supplementation. Genes with statistically significant regulation are highlighted with a red box. Statistically significance is indicated by asterisks Effect of cytokine supplementation on differentiation markers While hydrodynamic loading in isolation of exogenous supplementation is not sufficiently potent to control differentiation in a selective manner, the results of our initial studies in unsupplemented, serum-free cultures suggested that hydrodynamic loading may be useful as when presented in concert with morphogens with a known inductive capacity. To investigate this possibility, we analyzed the expression profiles of statically cultured constructs which received either TGF-β3 or BMP-2 supplementation at a concentration of 1, 10 ng/mL, or 100 ng/mL for the purpose of inducing a chondrogenic or osteogenic phenotype, respectively. The resident MSCs tend towards expression of chondrogenic markers as function of time in culture and concentration of exogenous cytokine supplementation for both BMP-2 and TGF-β3 supplementation. For TGF-β3 supplemented cultures, the expression of all three chondrogenic markers increased significantly relative to the unsupplemented control group for culture durations of at least 2 weeks provided the culture medium was supplemented with TGF-β3 at a concentration of at least 10 ng/mL while differences in expression of the chondrogenic markers for cultures supplemented at concentrations lower than 10 ng/mL were not considered significant (Fig. 4). After two weeks of culture, SOX9 was expressed in a concentration dependent manner as the greatest change in expression relative to the source cell population occurred in the 100 ng/mL supplementation group (667 fold) which was significantly higher than the 10 ng/mL supplementation group (145 fold), which in turn was significantly greater than the 1 ng/mL supplementation group (12.7 fold). A similar trend in AGGRECAN and COL2A1 expression was observed as increases in AGGRECAN expression relative to the source cell population was highest in the 100 ng/mL supplementation group (181 fold), which was statistically indeterminate from the 10 ng/mL supplementation protocol, but significantly higher than 1 ng/mL or lower concentration supplementation protocols. Likewise, COL2A1 expression reached a maximum among the static cultures when TGF-β3 supplementation was provided at a concentration of 100 ng/mL (403 fold) for a period of 2 weeks. Considering the expression of undesirable hypertrophic and osteogenic genes, we found comparable mRNA levels among all TGF-β3 supplementation protocols. Additionally, the expression level of the hypertrophic and osteogenic markers are statistically indeterminate from the unsupplemented controls. TGF-β3 supplementation modulates expression of chondrogenic markers without significantly altering the expression profile of the osteogenic panel. Genes with statistically significant regulation are highlighted with a red box. Statistically significance is indicated by asterisks For BMP-2 supplemented cultures, upregulation of genes from both the chondrogenic and osteogenic panels at high cytokine concentrations was evident (Fig. 5). When the culture medium was supplemented with BMP-2 in concentrations in excess of 10 ng/mL, the entire chondrogenic gene panel (SOX9, AGGRECAN, and COL2A1) was upregulated relative to duration matched cultures receiving BMP-2 supplementation at a concentration of 1 ng/mL or less. Hypertrophic marker COLXΑ1 also showed increases with respect to duration matched unsupplemented controls as BMP-2 concentration was increased. Regarding the osteogenic gene panel, OSTEOCALCIN was upregulated in cultures supplemented at 10 ng/mL or greater relative to duration matched cultures receiving 1 ng/mL or less for each culture period studied. RUNX2 and COL1A1 were also upregulated relative to the low supplementation groups (0 and 1 ng/mL), but only when BMP-2 supplementation was provided at a concentration of at least 100 ng/mL for a period of 2 weeks. BMP-2 supplementation modulates expression of both chondrogenic and osteogenic markers. Genes with statistically significant regulation are highlighted with a red box. Statistically significance is indicated by asterisks Effect of hydrodynamic loading on cytokine supplemented cultures Both BMP-2 and TGF-β3 produced strong differentiation of the MSC population utilizing the static culture platform, and provided a baseline for normalization of the hydrodynamically loaded cultures to control for the independent effect of the cytokines so that we might investigate whether stimulation via hydrodynamic loading can induce a synergistic effect on the gene expression profile of the differentiating cell population. BMP-2 supplemented cultures exhibited a strong shear coupling with respect to expression of SOX9, RUNX2, and all of the collagens studied, and was strongly biased towards high magnitude loading protocols (Figs. 6, 7 and 8). It is apparent that RUNX2 was strongly upregulated for all BMP-2 supplementation protocols with concurrent high magnitude hydrodynamic loading as evidenced by significant increases relative to time-matched static controls at each time point investigated as well as significantly high expression relative to the low magnitude loading when BMP-2 concentration was at least 10 ng/mL. In addition to changes in expression of RUNX2, it was also observed that COL1A1 was upregulated for the high shear condition groups. For the 1 ng/mL BMP-2 group, COL1A1 expression was significantly higher in the high shear group compared to the static controls at two weeks of culture. When the concentration was raised to 10 ng/mL (Fig. 7) it was observed that the behavior was sustained in addition to being significantly higher than the low magnitude loading group. When BMP-2 supplementation was provided at a concentration of 10 ng/mL or lower, there was no significant difference in expression between the static and low magnitude hydrodynamic groups for either RUNX2 or COL1A1. When BMP-2 supplementation was increased to 100 ng/mL (Fig. 8), however, it was observed that COL1A1 was significantly upregulated in the low magnitude loading group relative to the static control after 2 weeks of culture. Additionally, hydrodynamic modulation of OSTEOCALCIN expression was observed for the first time in these studies in the high magnitude loading group relative to the static control after 2 weeks of culture in cultures receiving at least 10 ng/mL of BMP-2. Even at low levels of BMP-2 supplementation, significant regulation of collagens and osteochondral transcription factors is observed. Genes with statistically significant regulation are highlighted with a red box. Statistically significance is indicated by asterisks Transcription factors and collagen modulation is maintained in cultures supplemented with 10 ng/mL. Osteocalcin regulation is also observed under high shear conditions, suggesting a commitment to the osteogenic differentiation pathway. Genes with statistically significant regulation are highlighted with a red box. Statistically significance is indicated by asterisks When BMP-2 is supplemented at a high level (100 ng/mL) shear stress is a significant modulator of all chondrogenic and osteogenic markers studied. Genes with statistically significant regulation are highlighted with a red box. Statistically significance is indicated by asterisks Regarding the chondrogenic markers, SOX9 was upregulated in high magnitude loading culture relative to the static control for all BMP-2 supplementation groups, but interestingly this effect was only considered significant at the 1-week time point. COL2A1 expression was observed to increase in high magnitude hydrodynamic cultures as well, as evidenced by significant increases relative to static controls at the 2-week time point for cultures receiving 1 ng/mL of BMP-2 and at both time points for culture receiving at least 10 ng/mL of BMP-2. This effect also appears to be sensitive the magnitude of hydrodynamic loading as significant differences were observed between the static cultures and low magnitude cultures as well as between the low and high magnitude cultures. Differences in AGGRECAN expression were only considered significant under high shear and high supplementation. It is also worth noting that expression of hypertrophic marker COLXA1 was significantly increased in the high magnitude loading group after 2 weeks of culture for all BMP-2 supplementation protocols relative to the static control for the low concentrations (1 ng/mL) and to both low magnitude and static cultures at elevated concentrations of BMP-2 (10 and 100 ng/mL). These results are not very surprising in light of the results from unsupplemented, hydrodynamically loaded construct group as two osteoinductive agents, hydrodynamic loading and BMP-2 supplementation, are at work simultaneously in these protocols. While the slight chondrogenic character of these cultures is not desirable, it is worth noting that modulation of chondrogenic markers (SOX9, COL2Α1) at high shear was of less than an order of magnitude and the order of the baseline control expression of these genes was considerably lower than their chondrogenic counterparts. COLXΑ1 expression increased by an order of magnitude over culture period and supplementation matched static controls for both low and high shear conditions at two weeks when cultures were supplemented with 100 ng/mL of BMP-2. While the inductive impact of hydrodynamic loading is not as great in magnitude as that of BMP-2 supplementation at high levels (one order of magnitude change vs three orders of magnitude), it none the less is an important modulator of osteogenic induction as no significant difference was observed between static cultures supplemented at 100 ng/mL and cultures supplemented at 10 ng/mL that were also subjected to high magnitude hydrodynamic loading in terms of total gene expression relative to the initial MSC population. When hydrodynamic stimulation was introduced in concert with TGF-β3 supplementation, it was observed that COL2A1 was upregulated relative to duration and supplementation group matched controls when the hydrodynamic loading condition was high (10 dyn/cm2) and TGF-β3 concentrations were low indicating a mild synergistic effect on the chondrogenic induction of the resident cell population (Fig. 9). When the supplementation protocol was increased to 10 ng/mL, high shear cultures resulted in upregulation of both SOX9 and COL2A1. No regulation of hypertrophic or osteogenic markers was observed at this supplementation level, and interestingly there was no effect on chondrogenic markers in low magnitude hydrodynamic cultures (Fig. 10). Upon increasing the TGF-β3 protocol to 100 ng/mL, shear magnitude dependent modulation of all three chondrogenic genes studied was observed. The chondrogenic panel was upregulated under high magnitude shear conditions relative to static controls after 1 week of culture and remained significantly high for subsequent culture durations (Fig. 11). There was no statistical difference between low and high shear conditions for COL2A1 and AGGRECAN expression, but there was a shear magnitude dependency observed for SOX9. Hydrodynamic loading has limited impact on MSC based constructs with cultivated with low concentrations of TGF-β3 (1 ng/mL). Modulation of COL2A1 was considered significant with high magnitude hydrodynamic loading after 2 weeks of culture relative to time and concentration matched controls. Noticeably, the regulation of osteogenic genes with shear observed in unsupplemented controls disappears. Genes with statistically significant regulation are highlighted with a red box. Statistically significance is indicated by asterisks TGF-β3 supplementation of 10 ng/mL is the most ubiquitous supplementation protocol for chondrogenic cultures found in the literature. When hydrodynamic loading is introduced in concert at these levels of exogenous supplementation, SOX9 and COL2A1 are modulated in high shear environments. Osteogenic markers remain at levels comparable to static controls. Genes with statistically significant regulation are highlighted with a red box. Statistically significance is indicated by asterisks High levels of TGF-β3 supplementation results in strong upregulation of chondrogenic genes in the presence of hydrodynamic loading. Genes with statistically significant regulation are highlighted with a red box. Statistically significance is indicated by asterisks Interestingly, changes in expression of the osteogenic gene panel were not considered significant for any of the hydrodynamic regimes studied. Expression of COLXΑ1, however, was upregulated relative to concentration matched static controls when conditions were such that high shear magnitudes (10 dyn/cm2) were paired with low (1 ng/mL) concentrations of TGF-β3 for a period of at least 2 weeks. No significant changes in COLXA1 were observed with moderate or high TGF-β3 supplementation. These observations hint at two potentially useful characteristics of this approach. First, chondrogenic differentiation is clearly positively influenced by the presence of hydrodynamic loading when presented in concert with at least 10 ng/mL of TGF-β3, and that TGF-β3 signaling appears to have an inhibitory effect the on the osteoinductive role of high magnitude hydrodynamic loading observed with the other supplementation protocols studied herein. Histology & immunofluorescence Histological staining and immunofluorescence of 2-week culture samples qualitatively supports the gene expression profiles observed through PCR (Figs. 12, 13 and 14). Toluidine Blue staining indicates increasing expression of sulfated glycosaminoglycans with increases in both BMP-2 and TGF-β3 supplementation, while Alizarin Red staining shows greater staining with increased BMP-2 supplementation. Alizarin Red staining was relatively uniform for TGF-β3 supplemented cultures for all hydrodynamic and supplementation protocols tested. Immunofluorescence indicates increasing Collagen type I and Collagen type II expression in the BMP-2 and TGF-β3 supplemented cultures of increasing concentration, respectively. Trends in collagen expression between shear conditions are less clear, but there appears to be more total collagen in BMP-2 supplemented cultures on the whole, and total collagen expression appears to increase with hydrodynamic loading. Histological and Immunofluorescence analyses of static cultures suggest increasing osteogenic character with BMP-2 supplementation and increasing chondrogenic character with TGF-β3 supplementation Histological and Immunofluorescence analyses of low shear cultures suggest increasing osteogenic character with BMP-2 supplementation and increasing chondrogenic character with TGF-β3 supplementation Histological and Immunofluorescence analyses of high shear cultures suggest increasing osteogenic character with BMP-2 supplementation and increasing chondrogenic character with TGF-β3 supplementation As the predominate source of cells for tissue engineered constructs has shifted from terminally differentiated primary cells towards progenitor cells of various differentiation potentials, the ability to spatiotemporally exert epigenetic control over the differentiation of stem cells within a tissue engineered construct has become desirable as a means to better reproduce native tissue complexity and reduce cultivation costs associated with traditional differentiation protocols. Subsequently, we decided to focus herein on the impact of the hydrodynamic environment on MSC differentiation due to its essential role in nutrient exchange during in vitro cultivation. The purpose of this study was to investigate how modulation of hydrodynamic loading affects the stability of the MSC phenotype during serum-free tissue culture and how this approach might enhance differentiation efficiency in the presence of morphogens known to be either osteoinductive or chondrogenic in nature. Our primary findings (Additional file 1: Table S3) were that hydrodynamic loading, in the absence of exogenous supplementation, promotes expression of hypertrophic and osteogenic genes. Although not investigated in this study, we suspect this observation is due to integrin signaling activated by deformation of the MSC pericellular matrix in response to the hydrodynamic loads as indicated by other studies in the literature [30, 31]. The influence of hydrodynamic loading on osteogenic markers was sustained for low levels of exogenous supplementation irrespective of the cytokine provided. Lineage specific upregulation towards chondrogenic and osteogenic phenotypes was observed under high magnitude shear conditions when hydrodynamic loading was presented in concert with high levels of TGF-β3 and BMP-2 supplementation respectively. Generally, the observed impact of hydrodynamic loading on the desired phenotypes was greater in longer term cultures, and in cultures receiving higher concentrations of exogenous cytokines. These findings are in agreement with prior mechanobiological studies in other osteochondral lineage cell sources. In studies based on osteoblastic cell lines, multiple studies have shown that hydrodynamic loading is osteopromotive [32–36], and often results in increases in type I collagen production and matrix mineralization. Hydrodynamic studies on MSCs from various donor species have also been previously shown to be osteoinductive [37–39]. Additionally, multiple studies on primary chondrocytes have shown that in addition to increases in type II collagen [40, 41]. Exposure to high shear environments can result in development of a fibrous layer rich in non-hyaline type I collagen at shear exposed surfaces [42], particularly when cultured with serum supplemented medium [43] versus serum free preparations. If we compare the extent of the impact of hydrodynamic loading on unsupplemented cultures in our study to that of other environmental induction schemes for MSCs, we find that the effect on gene expression is on the same order of magnitude as manipulations of scaffolding stiffness for osteoinduction [44] and both hydrostatic pressure [45] and dynamic unconfined compressive loading [46, 47] for chondrogenic induction. Unlike these prior studies, however, we found the impact of exogenous supplementation on gene expression to be considerably greater than the environmental stimulus applied. Our results converge again, however, when the mechanical stimuli were presented concurrently with TGF-β3 supplementation [45, 46]. As in our study utilizing hydrodynamic loading, dynamic compression and intermittent hydrostatic loading both resulted in additional increases in chondrogenic gene expression when presented in cultures supplemented with at least 10 ng/mL. The order of magnitude of the change, however, is considerably greater in our hydrodynamic study (>100 fold change) than either of the prior studies utilizing compressive (<10 fold change) and hydrostatic (<10 fold change) loading. Conversely, other studies have shown compressive loading to have a negative impact on glycosaminoglycan accumulation within the construct at the protein level [48]. It is unclear, however, if this effect is due to decreased synthesis or loss of glycosaminoglycans to the culture medium. Interestingly, the same study [48], also showed that dynamic compressive loading resulted in increases in COLXA1 in the absence of TGF-β3 supplementation, a result that mirrors our findings of both a hypertrophic influence of unsupplemented hydrodynamic loading and of the chondroprotective character of TGF-β3 supplementation. Our findings, herein, seem to indicate a comparable role of hydrodynamic loading to that of other environmental factors, particularly dynamic compression. Considering finite element analyses have shown interstitial fluid flow to be an effect of dynamic loading in biphasic materials such as those referenced herein, it is not surprising that these two loading conditions produce similar responses in MSC based tissue constructs. Our finding that high magnitude hydrodynamic loading promotes osteogenic gene expression in unsupplemented cultures is instructive and suggests that MSCs cultures intended for chondral therapies not be subjected to high shear hydrodynamic loading conditions during processing and cultivation. While the modified parallel plate bioreactor system utilized better utilized for experimental investigation than a scalable manufacturing process, the bioprocessing principles derived from its use could easily be incorporated into a more scalable suspension bioreactor system based on three dimensional microcarriers. It is our recommendation that the nutrient utilization of chondrogenic cultures in such a system be carefully considered such that fluid loading not be applied in excess of magnitudes needed to meet the convective transport demands of the tissue in order to avoid potential induction of a hypertrophic phenotype. Conversely, our findings also suggest hydrodynamic loading of osteogenic cultures can potentially be a means of either reducing culture dependence on exogenous cytokines or promoting increased matrix deposition provided the magnitude of loading is increased such that impacts cell viability in a negative manner [49]. The findings of this study bring forth a number of important considerations regarding hydrodynamic culture of MSC based constructs for tissue engineering applications. As evidenced by results from all cytokine supplementation groups, including serum-free expansion medium culture, it is clear that MSCs are tuned to their local mechanical loading environment, and that prolonged exposure to high magnitude fluid shear stresses induces a hypertrophic phenotype amongst the resident MSCs ultimately resulting in expression of osteogenic markers. 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Khademhosseini A, Langer R, Borenstein J, Vacanti JP. Microscale technologies for tissue engineering and biology. Proc Natl Acad Sci U S A. 2006;103(8):2480–7. No acknowledgements to report. Interdisciplinary Bioengineering Graduate Program, Georgia Institute of Technology, Atlanta, GA,, 30332, USA Stephen M. Goldman & Gilda A. Barabino G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA,, 30332, USA Stephen M. Goldman Department of Biomedical Engineering, City College of New York, 160 Convent Avenue, New York, NY,, 10031, USA Gilda A. Barabino Correspondence to Gilda A. Barabino. SMG and GAB conception and design of research; SMG performed experiments and analyzed data; SMG and GAB interpreted results of experiments; SMG prepared figures and drafted manuscript; SMG and GAB edited and revised manuscript; SMG and GAB approved final version of manuscript. Additional file 1 Table S1. Experimental Condition Matrix. Table S2. RT-qPCR Primers. Table S3. Summary of Transcriptome Analysis after 2-Weeks of Culture. Table S4. Gene Regulation Ratios. (DOCX 21 kb) Supplementary Methods. (DOCX 17 kb) Adherent cells were lifted from culture after one passaging and test for the presence of bovine MSC surface markers consisting of CD271, CD166, and CD44. Additionally, cells were tested for the absence of hematopoietic surface marker CD45. (TIF 2104 kb) Following confirmation of MSC surface markers via flow cytometry, MSCs from the bone marrow of three calves were pooled, plated, cultured and assessed for tri-lineage differentiation potential. From left to right MSCs culture in inductive media (top) and growth medium (bottom row) were stained with Oil Red O, Toluidine Blue, and Alizarin Red to confirm evidence of adipogenesis, chondrogenesis, and osteogenesis respectively. (TIF 26421 kb) Goldman, S.M., Barabino, G.A. Hydrodynamic loading in concomitance with exogenous cytokine stimulation modulates differentiation of bovine mesenchymal stem cells towards osteochondral lineages. BMC Biotechnol 16, 10 (2016). https://doi.org/10.1186/s12896-016-0240-6 Fluid shear stress Chondrogenesis Osteogenesis	CommonCrawl
What are two independent, uniformly distributed random variables on the unit interval? I have been dabbling in learning basic things about probability theory and (of course) being of the school of abstract nonsense I have tried to understand things in its language. I apologize if this question is therefore somehow obvious. As I understand it, if $X$ is a probability space with measure $\mu$ and $f \colon X \to \mathbb{R}$ is a random variable (measurable function), its "probability distribution function" is actually the pushforward measure $f_(\mu)$, which is only a function multiple of Lebesgue measure under some kind of regularity hypothesis that I'm not asking about now. If $g$ is another such random variable, the joint distribution is obtained by forming the map $(f, g) \colon X \to \mathbb{R}^2$ and pushing forward again, getting $(f,g)_(\mu)$. Independence of these random variables is Fubini's theorem, that for any $h(x,y)$ on $\mathbb{R}^2$, we have $$\int h(x,y) d(f,g)_(\mu) = \iint h(x,y) df_(\mu) dg_(\mu).$$ Okay. It therefore appears that when $X = [0,1]$, the following dream is possible: find a pair of functions $f,g$ as above, say with values also in $[0,1]$, each of which is uniformly distributed in that their distributions are both Lebesgue measure, which are also independent. Then $(f,g)_(\mu)$ is Lebesgue measure on $[0,1]^2$. This seems to me to be rather different from the usual construction. I can imagine what the pair $(f,g)$ must look like: it traces a curve in $[0,1]^2$ that is obviously space-filling, since the pullback of any small box must have positive measure, and so must at least be nonempty; i.e. the curve is dense. Question: Are the component functions of the standard space-filling curves (say, the Hilbert curve) independent and uniformly distributed? Can it be shown directly that they are independent, i.e. without constructing two-dimensional Lebesgue measure and invoking Fubini's theorem explicitly? Is this a valid way of getting Lebesgue measure on $[0,1]^2$? measure-theory pr.probability Ryan Reich Ryan ReichRyan Reich $\begingroup$ A friend of abstract nonsense should be satisfied with the following result: Two Polish spaces endowed with their Borel-sigma-algebra are isomorphic as measurable spaces iff they have the same cardinality. In particular, all uncountable such spaces are isomorphic to the unit interval. In particular, the at most countable product of the unit interval is isomorphic to the unit interval. Even nicer, any probability measure on a Polish space is the push-forward-measure induced by Lebesgue measure on the unit interval (or any othe atomless probability measure) under some measurable function. $\endgroup$ – Michael Greinecker Sep 29 '11 at 6:38 Let us consider more closely the question about space-filling curves. The Peano curve and the Hilbert curve, and several other variations of them, have parametrizations $[0,1]\to[0,1]^2$ that actually take the 1-dimensional Lebesgue measure on $[0,1]\, ,$ $\mathcal{L} _1\, ,$ to the 2-dimensional Lebesgue measure on $[0,1]^2\, ,$ $\mathcal{L} _2\, ,$ by push-forward. Notably, the Peano curve $\gamma: [0,1]\to[0,1]^2$ is originally defined in terms of ternary expansions of real numbers, which makes it particularly simple to check the independence of the coordinates. The Hilbert curve also admits a (slightly less) simple description in terms of binary expansions. Here are the details; I'll try to give you an abstract-nonsense-friendly description. Let's start by some well known facts. The map that takes a sequence $a:=(a_1,a_2,\dots)\in\ 3^\mathbb{N}$ (here $3:=\{0,1,2\}$ and $\mathbb{N}$ is the set of positive integers) into its value as ternary expansion, namely $\mathrm{v}(a):= \sum_ {n\ge1} 3^{-n}a_ n\in[0,1]$, is a continuous surjective map (and bijective, up to removing a certain countable, null subset $D$ of the domain) : $$\operatorname{v}:3^\mathbb{N}\to[0,1]\, .$$ Also, this map takes the measure $\mathbf{m}$, product of countably many copies of the uniform probability measure on $3$ to the measure $\mathcal{L} _1$ ("the base 3 digits of a real number are independent and uniformly distributed". Any other base of course works as well). Now, at the level of the ternary sequences we have the nice and simple Cantor bijection $3^\mathbb{N}\to 3^\mathbb{N}\times 3^\mathbb{N}$ "split the sequence of digits into the sequence of odd-position digits and the sequence of even-position digits" $$C:3^\mathbb{N}\ni (a_n)\mapsto \big(\, (a_{2n-1}), (a_{2n})\, \big) \in 3^\mathbb{N}\times 3^\mathbb{N} $$ which is easily seen to be a compact metric space homeomorphism that takes the measure $\mathbf{m}$ into the product measure $\mathbf{m}\otimes\mathbf{m}$. Note that this homeomorphism does not pass through the quotient map $\mathrm{v}$, for in general sequences with the same value do not produce sequences with the same value by extraction of a subsequence. However, removing the above mentioned countable set $D$ the map $\mathbf{v}$ becomes bijective and you do have correspondingly a bi-measurable, a.e. defined (or everywhere but non-continuous) map of the unit interval to the unit square that takes the measure $\mathcal{L} _1$ to the measure $\mathcal{L} _2$. All that is quite standard. Now your question cames quite naturally, as a request for a commutative square: Can we find another measure preserving homeomorphism $\Gamma:3^\mathbb{N}\to > 3^\mathbb{N}\times 3^\mathbb{N}$ that induces a map $\gamma: > [0,1]\to[0,1]\times[0,1]$ through the map $\mathbf{v}$, that is, such that $\gamma\circ\mathbf{v}=(\mathbf{v}\times\mathbf{v})\circ\Gamma$ ? Since $\mathbf{v}$ is a quotient map, this map $\gamma$ will be automatically a continuous surjection, that also takes $\mathcal{L} _1$ to $\mathcal{L} _2$. The answer is yes, and this is Peano's construction (he was not interested in the measure-theoretic property, but this also follows immediately from the definition). It's the way he constructed his example in the celebrated paper dated 1890 on Mathematische Annalen, " Sur une courbe, qui remplit toute une aire plane ". Here's Peano definition of the map $\Gamma$: extract as before the sequence of the odd-position digits and the even-position digits, but first invert every odd-position digit whenever there are an odd number of odd even-position digits before it, and invert every even-position digit whenever there are an odd number of odd odd-position digits before it. Here "invert" just means taking $x\in3$ to $2-x$, that is $0$ to $2$, $1$ to $1$, $2$ to $0$. Translating this definition in a formula, is not difficult to check it defines a homeomorphism of the form $\Gamma=C \circ \phi$, compatible with the map $\mathbf{v}$. The measure property is quite obvious, since the "inverting digit map" $ \phi:3^\mathbb{N}\to 3^\mathbb{N}$ is clearly an involutory preserving measure homeomorphism. For the Hilbert curve, the digit description has to be done in terms of binary representation, and it is slightly less simple (I have it written somewhere and will look for it and quote here at request) but everything works as well. Let me finish with an historical note. Of course, what is not easy in the short Peano's paper is to understand what's going on geometrically. He made no picture in this paper, although the graphical iterative construction was perfectly clear to him, and was with all probability his starting point —he made an ornamental tiling showing a picture of the curve in his home in Turin. His choice to avoid any appeal to graphical visualization was no doubt motivated by a desire for a well-founded, completely rigorous proof owing nothing to pictures, in the spirit of the program of arithmetization of analysis. In the conclusion of his paper he observed incidentally that the same construction may be made with all odd basis, and even basis too, although in the latter case, by slightly more complicated formulae (hence less elegant from his viewpoint). In order to make Peano's example more accessible to the mathematical community, a couple of years later Hilbert wrote on the same journal the very clear geometric construction that we know. He chose the Peano construction in base 2 because it is simpler from the graphical point of view. edited Sep 5 '13 at 17:29 Pietro MajerPietro Majer There's no particular reason to use a continuous space-filling curve, other than style points. Just expand x in binary and send the odd digits to $f$ and the even digits to $g$. To prove that you get the right measure you should only need to prove it on every box, therefore on every box with dyadic endpoints. These can all be expressed as simple statements about the binary expansion of $f$ and $g$, pull them back, then you're done. For a continuous space-filling curve, roughly the same thing should work. Approximate $h(x,y)$ with step functions on the various boxes that the nth step of the curve passes through, making closer and closer approximations with each n. Will SawinWill Sawin $\begingroup$ In your second paragraph, are you saying that any space-filling (continuous) curve will work? $\endgroup$ – Ryan Reich Sep 29 '11 at 18:10 $\begingroup$ I'm saying that any of the standard ones will. $\endgroup$ – Will Sawin Sep 29 '11 at 18:58 $\begingroup$ Indeed, you can use a similar construction to define an infinite sequence of iid uniform random variables on $[0,1]$. For instance, enumerate the primes as $p_i$ and send all the bits in positions which are powers of $p_i$ to $f_i$. You can also combine this with the fact that any probability distribution can be obtained as a function of a uniform random variable, and get a sequence of independent random variables with any desired distributions. You're now well on your way to the Kolmogorov extension theorem... $\endgroup$ – Nate Eldredge Sep 29 '11 at 19:36 Using binary digits of a uniformly distributed random variable on [0,1] is the first step in obtaining a variety of distributions in various spaces. In fact, distributions on almost any reasonable measurable space you can think of are pushforwards of Lebesgue measure on [0,1], see e.g., http://en.wikipedia.org/wiki/Standard_probability_space Yuri BakhtinYuri Bakhtin Let's not be so technical. Choose a number x in [0,1] whose decimal representation is .x_1x_2x_3x_4... . Then the random variables y=x_1x_3x_5... and z=x_2x_4x_6... are independent and uniformly distributed. Kenneth SchillingKenneth Schilling $\begingroup$ This was basically what Will Sawin suggested in 2011. $\endgroup$ – Nate Eldredge Feb 27 '20 at 21:59 Not the answer you're looking for? Browse other questions tagged measure-theory pr.probability or ask your own question. Function of independent random variables cannot be independent of each variable? Random walk with positive uniformly distributed steps Asymptotic Expansion of Distribution in Central Limit Theorem for Non-Identically Distributed Random Variables Uncountable family of random variables Sum of a random number of identically distributed but dependent random variables? Is it possible to construct any random variable on the Euclidean Probability space? Constructing an independent uniform random variable from two independent ones Frobenius norm of the principal submatrix of a uniformly distributed random orthonormal matrix Two independent function when considered as random variable over $([0,1],\mathrm{Lebesgue},\mathcal{B}_{[0,1]})$	CommonCrawl
On group symmetries of the hydrodynamic equations for rarefied gas KRM Home Mathematical modelling of charge transport in graphene heterojunctions June 2021, 14(3): 429-468. doi: 10.3934/krm.2021011 A mean-field limit of the particle swarmalator model Seung-Yeal Ha 1, , Jinwook Jung 2,, , Jeongho Kim 3, , Jinyeong Park 4, and Xiongtao Zhang 5, Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul, 08826, and Korea Institute for Advanced Study, Hoegiro 85, Seoul, 02455, Republic of Korea Research Institute of Basic Sciences, Seoul National University, Seoul, 08826, Republic of Korea Institute of New Media and Communications, Seoul National University, Seoul, 08826, Republic of Korea Department of Mathematics and Research Institute of Natural Sciences, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea Center for Mathematical Sciences, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan, 430074, China * Corresponding author: Jinwook Jung Received June 2020 Revised November 2020 Published June 2021 Early access March 2021 We present a mean-field limit of the particle swarmalator model introduced in [46] with singular communication weights. 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BMC Bioinformatics A novel target convergence set based random walk with restart for prediction of potential LncRNA-disease associations Jiechen Li1,2, Xueyong Li1, Xiang Feng1,2, Bing Wang3, Bihai Zhao2 & Lei Wang ORCID: orcid.org/0000-0002-5065-84471,2 BMC Bioinformatics volume 20, Article number: 626 (2019) Cite this article In recent years, lncRNAs (long-non-coding RNAs) have been proved to be closely related to the occurrence and development of many serious diseases that are seriously harmful to human health. However, most of the lncRNA-disease associations have not been found yet due to high costs and time complexity of traditional bio-experiments. Hence, it is quite urgent and necessary to establish efficient and reasonable computational models to predict potential associations between lncRNAs and diseases. In this manuscript, a novel prediction model called TCSRWRLD is proposed to predict potential lncRNA-disease associations based on improved random walk with restart. In TCSRWRLD, a heterogeneous lncRNA-disease network is constructed first by combining the integrated similarity of lncRNAs and the integrated similarity of diseases. And then, for each lncRNA/disease node in the newly constructed heterogeneous lncRNA-disease network, it will establish a node set called TCS (Target Convergence Set) consisting of top 100 disease/lncRNA nodes with minimum average network distances to these disease/lncRNA nodes having known associations with itself. Finally, an improved random walk with restart is implemented on the heterogeneous lncRNA-disease network to infer potential lncRNA-disease associations. The major contribution of this manuscript lies in the introduction of the concept of TCS, based on which, the velocity of convergence of TCSRWRLD can be quicken effectively, since the walker can stop its random walk while the walking probability vectors obtained by it at the nodes in TCS instead of all nodes in the whole network have reached stable state. And Simulation results show that TCSRWRLD can achieve a reliable AUC of 0.8712 in the Leave-One-Out Cross Validation (LOOCV), which outperforms previous state-of-the-art results apparently. Moreover, case studies of lung cancer and leukemia demonstrate the satisfactory prediction performance of TCSRWRLD as well. Both comparative results and case studies have demonstrated that TCSRWRLD can achieve excellent performances in prediction of potential lncRNA-disease associations, which imply as well that TCSRWRLD may be a good addition to the research of bioinformatics in the future. For many years, the genetic information of organism is considered to be stored only in genes used for protein coding, and RNAs have always been thought to be an intermediary in the process of encoding proteins by DNAs [1, 2]. However, recent studies have shown that the genes used to encode proteins only account for a small part (less than 2%) of human genome and more than 98% of human genome are not made up of genes that encode proteins and yield a big mount of ncRNAs (non-coding-RNAs) [3, 4]. In addition, as the complexity of biological organisms increases, so does the importance of ncRNAs in biological processes [5, 6]. Generally, ncRNAs can be divided into two major categories such as small ncRNAs and long ncRNAs (lncRNAs) according to the length of nucleotides during transcription, where small ncRNAs consist of less than 200 nucleotides and include microRNAs and transfer RNAs etc. However, lncRNAs consist of more than 200 nucleotides [7,8,9]. In 1990, the first two kinds of lncRNAs such as H19 and Xist were discovered by researchers through gene mapping. Since gene mapping approach is extremely time-consuming and labor-intensive, then researches in the field of lncRNAs have been at a relatively slow pace for a long time [10, 11]. In recent years, with the rapid development of high-throughput technologies in gene sequencing, more and more lncRNAs have been found in eukaryotes and other species [12, 13]. Moreover, simulation results have shown as well that lncRNAs play important roles in various physiological processes such as cell differentiation and death, regulation of epigenetic shape and so on [8, 14, 15]. Simultaneously, growing evidences have further illustrated that lncRNAs are closely linked to diseases that pose a serious threat to human health [16,17,18], which means that lncRNAs can be used as potential biomarkers in the course of disease treatment in the future [19]. With the discovery of a large number of new types of lncRNAs, many databases related to lncRNAs such as lncRNAdisease [20], lncRNAdb [21], NONCODE [22] and Lnc2Cancer [23] have been established by researchers successively, however, in these databases, the number of known associations between lncRNAs and diseases is still very limited due to high costs and time-consumption of traditional biological experiments. Thus, it is meaningful to develop mathematical models to predict potential lncRNA-disease associations quickly and massively. Based on the assumption that similar diseases tend to be more likely associated with similar lncRNAs [24, 25], up to now, a good deal of computational models for inferring potential lncRNA-disease associations have been proposed. For instance, Chen et al. proposed a computational model called LRLSLDA [26] for prediction of potential lncRNA-disease associations by adopting the method of Laplacian regularized least squares. Ping and Wang et al. constructed a prediction model for extracting feature information from bipartite interactive networks [27]. Zhao and Wang et al. developed a computational model based on Distance Correlation Set to uncover potential lncRNA-disease associations through integrating known associations between three kinds of nodes such as disease nodes, miRNA nodes and lncRNA nodes into a complex network [28]. Chen et al. proposed an lncRNA-disease association prediction model based on a heterogeneous network by considering the influence of path length between nodes on the similarity of nodes in the heterogeneous network [29,30,31]. However, for some time past, a network traversal method called RWR (Random Walk with Restart) has emerged in the field of computational biology including prediction of potential miRNA-disease associations [32, 33], drug-target associations [34] and lncRNA-disease associations [35,36,37] etc. Inspired by the thoughts illustrated in above state-of-the-art literatures, in this paper, a computational model called TCSRWRLD is proposed to discover potential lncRNA-disease associations. In TCSRWRLD, a heterogeneous network is constructed first through combining known lncRNA-disease associations with the lncRNA integrated similarity and the disease integrated similarity, which can overcome a drawback of traditional RWR based approaches that these approaches cannot start walking process while there are no known lncRNA-disease associations. And then, each node in the heterogeneous network will establish its own TCS according to the information of network distance, which can reflect the specificity of different nodes in the walking process and make the prediction more accurate and less time-consuming. Moreover, considering that for a given walker, while its TCS has reached the ultimate convergence state, there may be still some nodes that are not included in its TCS but actually associated with it, then in order to ensure that there is no omission in our prediction results, each node in the heterogeneous network will further establish its own GS as well. Finally, for evaluating the prediction performance of our newly proposed model TCSRWRLD, cross validation are implemented based on known lncRNA-disease associations downloaded from the lncRNAdisease database (2017version), and as a result, TCSRWRLD can achieve reliable AUCs of 0.8323, 0.8597, 0.8665 and 0.8712 under the frameworks of 2-folds CV, 5-folds CV, 10-folds CV and LOOCV respectively. In addition, simulation results in case studies of leukemia and lung cancer show that there are 5 and 7 out of the top 10 predicted lncRNAs having been confirmed to be associated with Leukemia and Lung cancer respectively by recent evidences, which demonstrate as well that our model TCSRWRLD has excellent prediction performance. In order to verify the performance of TCSRWRLD in predicting potential lncRNA-disease associations, LOOCV, 2-folds CV, 5-folds CV and 10-folds CV were implemented on TCSRWRLD respectively. And then, based on the dataset of 2017-version downloaded from the lncRNADisease database, we obtained the Precision-Recall curve (P-R curve) of TCSRWRLD. In addition, based on the dataset of 2017-version downloaded from the lncRNADisease database and the dataset of 2016-version downloaded from the lnc2Cancer database, we compared TCSRWRLD with state-of-the-art prediction models such as KATZLDA, PMFILDA [38] and Ping's model separately. After that, we further analyzed the influences of key parameters on the prediction performance of TCSRWRLD. Finally, case studies of leukemia and lung cancer were performed to validate the feasibility of TCSRWRLD as well. In this section, ROC curve (Receiver Operating Characteristic) and the score of AUC (Area Under ROC Curve) will be adopted to measure the performance of TCSRWRLD in different cross validations. Here, let TPR (True Positive Rates or Sensitivity) represent the percentage of candidate lncRNAs-disease associations with scores higher than a given score cutoff, and FPR (False Positive Rates or 1-Specificity) denote the ratio of predicted lncRNA-disease associations with scores below the given threshold, then ROC curves can be obtained by connecting the corresponding pairs of TPR and FPR on the graph. As illustrated in Fig. 1, simulation results show that TCSRWRLD can achieve reliable AUCs of 0.8323, 0.8597, 0.8665 and 0.8712 in the frameworks of 2-folds CV, 5-folds CV, 10-folds and LOOCV respectively, which implies that TCSRWRLD can achieve excellent performance in predicting potential lncRNA-disease associations. AUCs achieved by TCSRWRLD under the frameworks of 2-folds CV, 5-folds CV, 10-folds CV and LOOCV respectively Moreover, in order to further estimate the prediction performance of TCSRWRLD, we will obtain the P-R curve of TCSRWRLD as well. Unlike the AUC, the AUPR (Area Under the Precision-Recall curve) represents the ratio of all true positives to all positive predictions at every given recall rate. As illustrated in Fig. 2, simulation results show that TCSRWRLD can achieve a reliable AUPR of 0.5007. precision-recall curve achieved by TCSRWRLD Comparison with other related methods From above descriptions, it is easy to know that TCSRWRLD can achieve satisfactory prediction performance. In this section, we will compare TCSRWRLD with some classical prediction models to further demonstrate the performance of TCSRWRLD. Firstly, based on the dataset of 2017-version downloaded from the lncRNAdisease database, we will compare TCSRWRLD with the state-of-the-art models such as KATZLDA, PMFILDA and Ping's model. As shown in Fig. 3, it is easy to see that TCSRWRLD can achieve a reliable AUC of 0.8712 in LOOCV, which is superior to the AUCs of 0.8257, 0.8702 and 0.8346 achieved by KATZLDA, Ping's model and PMFILDA in LOOCV respectively. The AUCs achieved by TCSRWRLD, KATZLDA, Ping's model and PMFILDA in LOOCV based on the dataset of 2017-version downloaded from the lncRNAdisease database Moreover, in order to prove that TCSRWRLD can perform well in different data backgrounds, we also adopt the dataset of 2016-version downloaded from the lnc2Cancer database, which consists of 98 human cancers, 668 lncRNAs and 1103 confirmed associations between them, to compare TCSRWRLD with KATZLDA, PMFILDA and Ping's model. As illustrated in Fig. 4, it is easy to see that TCSRWRLD can achieve a reliable AUC of 0.8475 in LOOCV, which is superior to the AUCs of 0.8204 and 0.8374 achieved by KATZLDA and PMFILDA respectively, while is inferior to the AUC of 0.8663 achieved by Ping's model. the AUCs achieved by TCSRWRLD, KATZLDA, Ping's model and PMFILDA based on the dataset of 2016-version downloaded from the Lnc2Cancer database Analysis on effects of parameters In TCSRWRLD, there are some key parameters such as $ {\gamma}_l^{\prime } $, $ {\gamma}_d^{\prime } $ and ∂. As for $ {\gamma}_l^{\prime } $ and $ {\gamma}_d^{\prime } $ in the Equation (5) and Equation (11), we have already known that the model can achieve the best performance when the values of $ {\gamma}_l^{\prime } $and$ {\gamma}_d^{\prime } $ are both set to 1 [39]. Hence, in order to estimate effect of the key parameter ∂ on the prediction performance of TCSRWRLD, we will set the value range of ∂ from 0.1 to 0.9 and select the value of AUC in LOOCV as the basis of parameter selection in this section. As illustrated in Table 1, It is easy to see that TCSRWRLD can achieve the highest value of AUC in LOOCV while ∂ is set to 0.4. Moreover, it is also easy to see that TCSRWRLD can maintain robustness for different values of ∂, which means that TCSRWRLD is not sensitive to the values of ∂ as well. Table 1 AUCs achieved by TCSRWRLD in LOOCV while the parameter ∂ is set to different values from 0.1 to 0.9 Up to now, cancer is considered as one of the most dangerous diseases to human health because it is hard to be treated [40]. At present, the incidence of various cancers has a high level not only in the developing countries where medical development is relatively backward, but also in the developed countries where the medical level is already very high. Hence, in order to further evaluate the performance of TCSRWRLD, case study of two kinds of dangerous cancers such as lung cancer and leukemia will be implemented in this section. As for these two kinds of dangerous cancers, the incidence of lung cancer has remained high in recent years, and the number of lung cancer deaths per year is about 1.8 million, which is the highest of any cancer types. However, the survival rate within five years after the diagnosis of lung cancer is only about 15%, which is much lower than that of other cancers [41]. Recently, growing evidences have shown that lncRNAs play crucial roles in the development and occurrence of lung cancer [42]. As illustrated in Table 2, while implementing TCSRWRLD to predict lung cancer related lncRNAs, there are 7 out of the top 10 predicted candidate lung cancer related lncRNAs having been confirmed by the latest experimental evidences. Additionally, as a blood-related cancer [43], Leukemia has also been found to be closely related to a variety of lncRNAs in recent years. As illustrated in Table 2, while implementing TCSRWRLD to predict Leukemia related lncRNAs, there are 5 out of the top 10 predicted candidate Leukemia related lncRNAs having been confirmed by state-of-the-art experiment results as well. Thus, from above simulation results of case studies, we can easily reach an agreement that TCSRWRLD may have great value in predicting potential lncRNA-disease associations. Table 2 Evidences of top 10 potential leukemia-related lncRNAs and lung cancer-related lncRNAs predicted by TCSRWRLD Since it is very time-consuming and labor-intensive to verify associations between lncRNAs and diseases through traditional biological experiments, then it has become a hot topic in bioinformatics to establish computational models to infer potential lncRNA-disease associations, which can help researchers to have a deeper understanding of diseases at the lncRNA level. In this manuscript, a novel prediction model called TCSRWRLD is proposed, in which, a heterogeneous network is constructed first through combining the disease integrated similarity, the lncRNA integrated similarity and known lncRNA-disease associations, which can guarantee that TCSRWRLD is able to overcome the shortcomings of traditional RWR based prediction models that the random walk process cannot be started while there are no known lncRNA-disease associations. And then, based on the newly constructed heterogeneous network, a random walk based prediction model is further designed based on the concepts of TCS and GS. In addition, based on the dataset of 2017-version downloaded from the lncRNAdisease database, a variety of simulations have been implemented, and simulation results show that TCSRWRLD can achieve reliable AUCs of 0.8323, 0.8597 0.8665 and 0.8712 under the frameworks of 2-fold CV, 5-fold CV, 10-fold CV and LOOCV respectively. Additionally, simulation results of case studies of lung cancer and leukemia show as well that TCSRWRLD has a reliable diagnostic ability in predicting potential lncRNA-disease associations. Certainly, the current version of TCSRWRLD still has some shortages and deficiencies. For example, the prediction performance of TCSRWRLD can be further improved if more known lncRNA-disease associations have been added into the experimental datasets. In addition, more accurate establishment of Mesh database will help us obtain more accurate disease semantic similarity scores, which is very important for the calculation of lncRNA functional similarity as well. Of course, all these above problems will be the focus of our future researches. In this paper, the main contributions are as follows: (1) A heterogeneous lncRNA-disease network is constructed by integrating three kinds of networks such as the known lncRNA-disease association network, the disease-disease similarity network and the lncRNA-lncRNA similarity network. (2) Based on the newly constructed heterogeneous lncRNA-disease network, the concept of network distance is introduced to establish the TCS (Target Convergence Set) and GS (Global Set) for each node in the heterogeneous lncRNA-disease network. (3) Based on the concepts of TCS and GS, a novel random walk model is proposed to infer potential lncRNA-disease associations. (4) Through comparison with traditional state-of-the-art prediction models and the simulation results of case studies, TCSRWRLD is demonstrated to be of excellent prediction performance in uncovering potential lncRNA-disease associations. Methods and materials Known disease-lncRNA associations Firstly, we download the 2017-version of known lncRNA-disease associations from the lncRNAdisease database (http://www.cuilab.cn/ lncrnadisease). And then, after removing duplicated associations and picking out the lncRNA-disease associations from the raw data, we finally obtain 1695 known lncRNA-disease associations (see Additional file 1) including 828 different lncRNAs (see Additional file 2) and 314 different diseases (see Additional file 3). Hence, we can construct a 314 × 828 dimensional lncRNA-disease association adjacency matrix A, in which, there is A(i, j) = 1, if and only if there is an known association between the disease di and the lncRNA lj in the LncRNADisease database, otherwise there is A(i, j) = 0. In addition, for convenience of description, let NL = 828 and ND = 314, then it is obvious that the dimension of the lncRNA-disease association adjacency matrix A can be represented as ND × NL. And the like mentioned above, we can get a cancer-disease associations adjacency matrix which dimension is 98 × 668 (It comes from 2016-version of known lncRNA-disease associations from the Lnc2Cancer database) (see Additional file 4). Similarity of diseases Semantic similarity of diseases In order to estimate the semantic similarity between different diseases, based on the concept of DAGs (Directed Acyclic Graph) of different diseases proposed by Wang et al. [44, 45], we can calculate the disease semantic similarity through calculating the similarity between compositions of DAGs of different diseases as follows: For all these 314 diseases newly obtained from the lncRNAdisease database, their corresponding MESH descriptors can be downloaded from the Mesh database in the National Library of Medicine (http://www.nlm.nih.gov/). As illustrated in Fig. 5, based on the information of MESH descriptors, each disease can establish a DAG of its own. DAG of the digestive system neoplasms and breast neoplasms For any given disease d, Let its DAG be DAG(d) = (d, D(d), E(d)), where D(d) represents a set of nodes consisting of the disease d itself and its ancestral disease nodes, and E(d) denotes a set of directed edges pointing from ancestral nodes to descendant nodes. For any given disease d and one of its ancestor nodes t in DAG(d), the semantic contributions of the ancestor node t to the disease d can be defined as follows: $$ {D}_d(t)=\left\{\begin{array}{c}1\\ {}\max \left\{\varDelta \ast {D}_d\left(t\hbox{'}\right)\|t\hbox{'}\in children\kern0.17em of\;t\right\}\kern1em \begin{array}{c} if\;t=d\\ {} if\;t\ne d\end{array}\end{array}\right\} $$ Where Δ is the attenuation factor with value between 0 and 1 to calculate the disease semantic contribution, and according to the state-of-the-art experimental results, the most appropriate value forΔis 0.5 . For any given disease d, let its DAG be DAG(d), then based on the concept of DAG, the semantic value of d can be defined as follows: $$ D(d)={\sum \limits}_{t_i\in DAG(d)}{D}_d\left({t}_i\right) $$ Taking the disease DSN (Digestive Systems Neoplasms) illustrated in Fig. 5 for example, according to the Equation (1), it is easy to know that the semantic contribution of digestive systems neoplasms to itself is 1. Besides, since the neoplasms by site and the digestive system disease located in the second layer of the DAG of DSN, then it is obvious that both of the semantic contributions of these two kinds of diseases to DSN are 0.51 = 0.5. Moreover, since the neoplasms located in the third layer of the DAG of DSN, then its semantic contribution to DSN is 0.50.5 = 0.25. Hence, according to above formula (2), it is easy to know the semantic value of DSN will be 2.25 (=1 + 0.5 + 0.5 + 0.25). For any two given diseases di and dj, based on the assumption that the more similar the structures of their DAGs, the higher the semantic similarity between them will be, the semantic similarity between di and dj can be defined as follows: $$ DisSemSim\left(i,j\right)= DisSemSim\left({d}_i,{d}_j\right)=\frac{\sum_{t\in \left( DAG\left({d}_i\right)\cap DAG\left({d}_j\right)\right)}\left({D}_{d_i}(t)+{D}_{d_j}(t)\right)}{D\left({d}_i\right)+D\left({d}_j\right)} $$ Gaussian interaction profile kernel similarity of diseases Based on the assumption that similar diseases tend to be more likely associated with similar lncRNAs, according to above newly constructed lncRNA-disease association adjacency matrix A, for any two given diseases di and dj, the Gaussian interaction profile kernel similarity between them can be obtained as follows: $$ GKD\left({d}_i,{d}_j\right)=\mathit{\exp}\left(-{\gamma}_d{\left\Vert IP\left({d}_i\right)- IP\left({d}_j\right)\right\Vert}^2\right) $$ $$ {\gamma}_d={\gamma}_d^{\hbox{'}}/\left({\sum \limits}_{k=1}^{N_D}{\left\Vert IP\left({d}_k\right)\right\Vert}^2\right) $$ Here, IP(dt) denotes the vector consisting of elements in the tth row of the lncRNA-disease adjacency matrix A. γd is the parameter to control the kernel bandwidth based on the new bandwidth parameter $ {\gamma}_d^{\prime } $by computing the average number of lncRNAs-disease associations for all the diseases. In addition, inspired by the thoughts of former methods proposed by O. Vanunu et al. [46], we will adopt a logistics function to optimize the Gaussian interaction profile kernel similarity between diseases, and based on above Equation (4), we can further obtain a ND × ND dimensional adjacency matrix FKD as follows: $$ FKD\left(i,j\right)=\frac{1}{1+{e}^{\left(-12 GKD\left(i,j\right)+\log (9999)\right)}} $$ Integrated similarity of diseases Based on the disease semantic similarity and disease Gaussian interaction profile kernel similarity obtained above, a ND × ND dimensional integrated disease similarity adjacency matrix KD (ND × ND) can be obtained as follows: $$ KD\left(i,j\right)=\frac{DisSemSim\left(i,j\right)+ FKD\left(i,j\right)}{2} $$ Similarity of LncRNAs Functional similarity of LncRNAs We can obtain corresponding disease groups of two given lncRNAs li and lj from the known associations of lncRNA-disease. Based on the assumption that similar diseases tend to be more likely associated with similar lncRNAs, We define the functional similarity of two given lncRNAs li and lj as the semantic similarity between the disease groups corresponding to them. The specific calculation process is as follows: For any two given lncRNAs li and lj, let DS(i) = {dk \| A(k, i) = 1, k∈[1, ND]} and DS(j) = {dk \| A(k, j) = 1, k∈[1, ND]}, then the functional similarity between li and lj can be calculated according to the following steps [31]: For any given disease group DS(k) and disease dt∉DS(k), we first calculate the similarity between dt and DS(k) as follows: $$ S\left({d}_t, DS(k)\right)={\max}_{d_s\in DS(k)}\left\{ DisSemSim\left({d}_t,{d}_s\right)\right\} $$ Therefore, based on above Equation (8), we define the functional similarity between li and lj as FuncKL(i, j), which can be calculated as follows: $$ FuncKL\left(i,j\right)=\frac{\sum_{d_t\in DS(i)}S\left({d}_t, DS(j)\right)+{\sum}_{d_t\in DS(j)}S\left({d}_t, DS(i)\right)}{\mid DS(i)\mid +\mid DS(i)\mid } $$ Here, \|D(i)\| and \|D(j)\| represent the number of diseases in DS(i) and DS(j) respectively. Thereafter, according to above Equation (9), it is obvious that a NL × NL dimensional lncRNA functional similarity matrix FuncKL can be obtained in final. Gaussian interaction profile kernel similarity of lncRNAs Based on the assumption that similar lncRNAs tend to be more likely associated with similar diseases, according to above newly constructed lncRNA-disease association adjacency matrix A, for any two given lncRNAs li and lj, the Gaussian interaction profile kernel similarity between them can be obtained as follows: $$ FKL\left({l}_i,{l}_j\right)=\mathit{\exp}\left(-{\gamma}_l{\left\Vert IP\left({l}_i\right)- IP\left({l}_j\right)\right\Vert}^2\right) $$ $$ {\gamma}_l={\gamma}_l^{\hbox{'}}/\left({\sum \limits}_{k=1}^{N_L}{\left\Vert IP\left({l}_k\right)\right\Vert}^2\right) $$ Here, IP(lt) denotes the vector consisting of elements in the tth column of the lncRNA-disease adjacency matrix A. γl is the parameter to control the kernel bandwidth based on the new bandwidth parameter$ {\gamma}_l^{\prime } $by computing the average number of lncRNAs-disease associations for all the lncRNAs. So far, based on above Equation (10), we can obtain a NL × NL dimensional lncRNA Gaussian interaction profile kernel similarity matrix FKL as well. Integrated similarity of lncRNAs Based on the lncRNA functional similarity and lncRNA Gaussian interaction profile kernel similarity obtained above, a NL × NL dimensional integrated lncRNA similarity adjacency matrix KL (NL × NL) can be obtained as follows: $$ KL\left(i,j\right)=\frac{FuncKL\left(i,j\right)+ FKL\left(i,j\right)}{2} $$ Construction of computational model TCSRWRLD The establishment of heterogeneous network Through combing the ND × ND dimensional integrated disease similarity adjacency matrix KD and the NL × NL dimensional integrated lncRNA similarity adjacency matrix KL with the ND × NL dimensional lncRNA-disease association adjacency matrix A, we can construct a new (NL + ND) × (NL + ND) dimensional integrated matrix AA as follow: $$ AA\left(i,j\right)=\left[\begin{array}{cc} KL\left(i,j\right)& {A}^T\left(i,j\right)\\ {}A\left(i,j\right)& KD\left(i,j\right)\end{array}\right] $$ According to above Equation (13), we can construct a corresponding heterogeneous lncRNA-disease network consisting of ND different disease nodes and NL different lncRNA nodes, in which, for any given pair of nodes i and j, there is an edge existing between them, if and only if there is AA(i, j) > 0. Establishment of TCS (target convergence set) Before the implementation of random walk, for each node in above newly constructed heterogeneous lncRNA-disease network, as illustrated in Fig. 6, it will establish its own TCS first according to the following steps: Flow chart of constructing TCS for an lncRNA node j For any given lncRNA node lj, we define its original TCS as the set of all disease nodes that have known associations with it, i.e., the original TCS of lj is TCS0(lj) = {dk \| A(k, j) = 1, k∈[1, ND]}. Similarly, for a given disease node di, we can define its original TCS as TCS0(di) = {lk \| A(i, k) = 1, k∈[1, NL]}. After the original TCS has been established, for any given lncRNA node lj, ∀dk∈TCS0(lj), and ∀t∈[1, ND], then we can define the network distance ND(k, t) between dk and dt as follows: $$ ND\left(k,t\right)=\frac{1}{KD\left(k,t\right)} $$ According to above Equation (14), for any disease nodes dk∈TCS0(lj) and ∀t∈[1, ND], obviously it is reasonable to deduce that the smaller the value of ND(k, t), the higher the similarity between dt and dk would be, i.e., the higher the possibility that there is potential association between dt and lj will be. Similarly, for any given disease node di, ∀lk∈TCS0(di) and ∀t∈[1, NL], we can define the network distance ND(k, t) between lk and lt as follows: $$ ND\left(k,t\right)=\frac{1}{KL\left(k,t\right)} $$ According to above Equation (15), for any lncRNA nodes lk∈TCS0(di) and ∀t∈[1, NL], obviously it is reasonable to deduce that the smaller the value of ND(k, t), the higher the similarity between lt and lk will be, i.e., the higher the possibility that there is potential association between lt and di will be. According to above Equation (14) and Equation (15), for any given disease node di or any given lncRNA node lj, we define that the TCS of di as the set of top 100 lncRNA nodes in the heterogeneous lncRNA-disease network that have minimum average network distance to the lncRNA nodes in TCS0(di), and the TCS of lj as the set of top 100 disease nodes in the heterogeneous lncRNA-disease network that have minimum average network distance to the disease nodes in TCS0(lj). Then, it is easy to know that these 100 lncRNA nodes in TCS (di) may belong to TCS0(di) or may not belong to TCS0(di), and these 100 disease nodess in TCS (lj) may belong to TCS0(lj) or may not belong to TCS0(lj). Random walk in the heterogeneous LncRNA-disease network The method of random walk simulates the process of random walker's transition from one starting node to other neighboring nodes in the network with given probability. Based on the assumption that similar diseases tend to be more likely associated with similar lncRNAs, as illustrated in Fig. 7, the process of our prediction model TCSRWRLD can be divided into the following major steps: Flow chart of our prediction model TCSRWRLD For a walker, before it starts its random walk across the heterogeneous lncRNA-disease network, it will first construct a transition probability matrix W as follows: $$ W\left(i,j\right)=\frac{AA\left(i,j\right)}{\sum_{k=1}^{N_D+{N}_L} AA\left(i,k\right)} $$ In addition, for any node £i in the heterogeneous lncRNA-disease network, whether £i is a lncRNA node li or a disease node di, it can obtain an initial probability vector Pi (0) for itself as follows: $$ {P}_i(0)={\left({p}_{i,1}(0),{p}_{i,2}(0),\dots, {p}_{i,j}(0),\dots {p}_{i,{N}_D+{N}_L}(0)\right)}^T $$ $$ {p}_{i,j}(0)=W\left(i,j\right)\kern0.36em j=1,2,\dots, {N}_{D+}{N}_L $$ Next, the walker will randomly select a node §i in the heterogeneous lncRNA-disease network as the starting node to initiate its random walk, where §i may be an lncRNA node li or a disease node di. After the initiation of the random walk process, supposing that currently the walker has arrived at the node Γi from the previous hop node Γj after t-1 hops during its random walk across the heterogeneous lncRNA-disease network, then here and now, whether Γi is a lncRNA node li or a disease node di, and Γj is a lncRNA node lj or a disease node dj, the walker can further obtain a walking probability vector Pi(t) as follows: $$ {P}_i(t)=\left(1-\partial \right)\ast {W}^T\ast {P}_j\left(t-1\right)+\partial \ast {P}_i(0) $$ Where ∂ (0< ∂< 1) is a parameter for the walker to adjust the value of walking probability vector at each hop. Moreover, based on above newly obtained walking probability vector Pi(t), let Pi(t) =$ {\left({p}_{i,1}(t),{p}_{i,2}(t),\dots, {p}_{i,j}(t),\dots {p}_{i,{N}_D+{N}_L}(t)\right)}^T $, and for convenience, supposing that there is pi, k(k)=maximum{$ {p}_{i,1}(t),{p}_{i,2}(t),\dots, {p}_{i,k}(t),\dots {p}_{i,{N}_D+{N}_L}(t) $}, then the walker will choose the node ψk as its next hop node, where ψk may be a lncRNA node lk or a disease node dk. Especially, as for the starting node §i, since it can be regarded that the walker has arrived at §i from §i after 0 hops, then it is obvious that at the starting node §i, the walker will obtain two kinds of probability vectors such as the initial probability vector Pi (0) and the walking probability vector Pi (1). However, at each intermediate node Γi, the walker will obtain two other kinds of probability vectors such as the initial probability vector Pi (0) and the walking probability vector Pi(t). Based on above Equation (19), supposing that currently the walker has arrived at the node Γi from the previous hop node Γj after t-1 hops during its random walk across the heterogeneous lncRNA-disease network, let the walking probability vectors obtained by the walker at the node Γi and Γj be Pi(t) and Pj(t-1) respectively, if the L1 norm between Pi(t) and Pj(t-1) satisfies ‖Pi(t) − Pj(t − 1)‖1 ≤ 10−6, then we will regard that the walking probability vector Pi(t) has reached a stable state at the node Γi. Thus, after the walking probability vectors obtained by the walker at every disease node and lncRNA node in the heterogeneous lncRNA-disease network have reached stable state, and for convenience, let these stable walking probability vectors be $ {P}_1\left(\infty \right),{P}_2\left(\infty \right),\dots, {P}_{N_D+{N}_L}\left(\infty \right) $, then based on these stable walking probability vectors, we can obtain a stable walking probability matrix S(∞) as follows: $$ S\left(\infty \right)=\left[\frac{S_1}{S_3}\kern1em \frac{S_2}{S_4}\right]={\left({P}_1\left(\infty \right),{P}_2\left(\infty \right),\dots, {P}_{N_D+{N}_L}\left(\infty \right)\right)}^T $$ Where S1 is a NL×NL dimensional matrix, S2 is a NL×ND dimensional matrix, S3 is a ND×NL dimensional matrix, and S4 is a ND×ND dimensional matrix. And moreover, from above descriptions, it is easy to infer that the matrix S2 and the matrix S3 are the final result matrices needed by us, and we can predict potential lncRNA-disease associations based on the scores given in these two final result matrices. According to above described steps of the random walk process based on our prediction model TCSRWRLD, it is obvious that for each node Γi in the heterogeneous lncRNA-disease network, the stable walking probability vector obtained by the walker at Γi is Pi(∞) = $ {\left({p}_{i,1}\left(\infty \right),{p}_{i,2}\left(\infty \right),\dots, {p}_{i,j}\left(\infty \right),\dots {p}_{i,{N}_D+{N}_L}\left(\infty \right)\right)}^T $. Moreover, for convenience, we denote a node set consisting of all the ND+NL nodes in the heterogeneous lncRNA-disease network as a Global Set (GS), then it is obvious that we can rewrite the stable walking probability vector Pi(∞) as $ {P}_i^{GS}\left(\infty \right) $. Additionally, from observing the stable walking probability vector $ {P}_i^{GS}\left(\infty \right) $, it is easy to know that the walker will not stop its random walk until the ND+NL dimensional walking probability vector at each node in the heterogeneous lncRNA-disease network has reached a stable state, which will obviously be very time-consuming while the value of ND+NL is large to a certain extent. Hence, in order to decrease the execution time and quicken the velocity of convergence of TCSRWRLD, based on the concept of TCS proposed in above section, while constructing the walking probability vector Pi(t)=(pi, 1(t), pi, 2(t), …, pi, j(t), $ \dots, {p}_{i,{N}_D+{N}_L}(t)\Big){}^T $ at the node Γi, we will keep the pi, j(t) unchanged if the jth node in these ND+NL nodes belongs to the TCS of Γi, otherwise we will set pi, j(t)=0. Thus, the walking probability vector obtained by the walker at Γi will turn to be $ {P}_i^{TCS}(t) $ while the stable walking probability vector obtained by the walker at Γi will turn to be $ {P}_i^{TCS}\left(\infty \right) $. Obviously, comapred with $ {P}_i^{GS}\left(\infty \right) $, the stable state of $ {P}_i^{TCS}\left(\infty \right) $ can be reached by the walker much more quickly. However, considering that there may be nodes that are not in the TCS of Γi but actually associated with the target node, therefore, in order to avoid omissions, during simulation, we will construct a novel stable walking probability vector $ {P}_i^{ANS}\left(\infty \right) $ through combining $ {P}_i^{GS}\left(\infty \right) $with $ {P}_i^{TCS}\left(\infty \right) $to predict potential lncRNA-disease associations as follows: $$ {P}_i^{ANS}\left(\infty \right)=\frac{\ {P}_i^{GS}\left(\infty \right)+{P}_i^{TCS}\left(\infty \right)}{2} $$ The datasets generated and/or analysed during the current study are available in the LncRNADisease repository, http://www.cuilab.cn/ lncrnadisease. 10-Fold CV: 10-fold cross-validation 2-Fold CV: 2-fold cross-validation; 5-fold cross-validation AUC: Areas under ROC curve AUPR: Area under the precision-recall curve FPR: False positive rates GS: Global set H19: Long non-coding RNA H19 lncRNAs: Long non-coding RNAs LOOCV: Leave-One Out Cross Validation ncRNAs: Non-coding RNAs P-R curve: Precision-recall curve Receiver-operating characteristics RWR: Random walk with restart TCS: Target Convergence Set TCSRWRLD: A novel computational model based on improved rand walk with restart is proposed to infer potential lncRNA-disease associations TPR: True positive rates Xist: Long non-coding RNA Xist Crick FHC, Barnett L, Brenner S, Watts-Tobin RJ. 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The funder of manuscript is Lei Wang(L.W.),whose contribution are stated in the section of Author's Contributions. The funding body has not played any roles in the design of the study and collection,analysis and interpretation of data in writing the manuscript. College of Computer Engineering & Applied Mathematics, Changsha University, Changsha, Hunan, People's Republic of China Jiechen Li, Xueyong Li, Xiang Feng & Lei Wang Key Laboratory of Hunan Province for Internet of Things and Information Security, Xiangtan University, XiangTan, People's Republic of China Jiechen Li, Xiang Feng, Bihai Zhao & Lei Wang School of Electrical and Information Engineering, Anhui University of Technology, Anhui, 243002, Maanshan, People's Republic of China Jiechen Li Xueyong Li Xiang Feng Bihai Zhao JCL conceived the study. JCL, XF, LW improved the study based on the original model. XYL, BW and BHZ implemented the algorithms corresponding to the study. LW supervised the study. JCL and LW wrote the manuscript of the study. All authors reviewed and improved the manuscript. Correspondence to Lei Wang. Additional file 1. The known lncRNA-disease associations for constructing the known lncRNA-disease network. We list 1695 known lncRNA-disease associations which were collected from LncRNAdisease datasetit is the latest version in the database. The known 828 lncRNAs name Included in the 1695 known lncRNA-disease associations which were collected from LncRNAdisease datasetit is the latest version in the database. The known 314 diseases name Included in the 1695 known lncRNA-disease associations which were collected from LncRNAdisease datasetit is the latest version in the database. The known 98 human cancer,668 lncRNAs and 1103 confirmed associations between them from Lnc2Cancer database. Li, J., Li, X., Feng, X. et al. A novel target convergence set based random walk with restart for prediction of potential LncRNA-disease associations. BMC Bioinformatics 20, 626 (2019). https://doi.org/10.1186/s12859-019-3216-4 Received: 08 February 2019 Potential lncRNA-disease association prediction Heterogeneous network Networks analysis Machine learning for computational and systems biology	CommonCrawl
Rumor: inflation-related primordial B-modes to be announced on Monday BICEP2 near the South Pole might have found a gem Update, Monday 4 pm: The rumor was 100% true. Ahead of the press conference, official data have been released. They measured $n\sim 0.96$ and more importantly $r=0.20\pm 0.05$ or so (see a new graph) and could exclude $r=0$ at a 6-7 confidence level. The peaks are where we expect it from cosmic inflation, contamination by instruments seems very unlikely to them. See FAQ. See also a post-discovery blog post by Prof Liam McAllister. In the morning, Sam Telfer asked Matt Strassler, Adam Falkowski, and myself about the new buzz related to the B-modes. It turns out that he was ahead of us. But now, all of us know what is supposed to happen soon, and it is exciting. As an undergrad, your self-described non-athletic humble correspondent would be the sports commissar of the Academic Senate. I would establish a new "fitness gym course" that people could take instead of the logistically inconvenient volley ball and similar courses on the other side of Prague. I attended it myself along with mostly female fellow students. The female instructor stressed that without hormones, women can't really develop structured bicepses. The rumor is all about BICEP2, a small experiment at the Amundsen–Scott South Pole Station in the Antarctica (BICEP1 concluded with this paper; see also BICEP2 status in 2012). Focusing on the frequency $150\, {\rm GHz}$ i.e. wavelength 2 millimeters, it is trying to find the primordial B-modes, something that could be important to pick the winners among theories of cosmic inflation and possible alternative theories to cosmic inflation. What are the B-modes? They are one of the two components of anisotropies of the cosmic microwave background that may be separated by the Helmholtz decomposition (or its generalization for the celestial sphere). Well, not so fast. Recall that the cosmic microwave background (CMB) is a thermal black body radiation (the most perfect natural black body radiation we have observed in the Universe) at current temperature $2.7\,{\rm K}$. It used to be much warmer but it cooled down, because of the global cooling in the whole Universe (an inseparable consequence of the expansion of the Universe; no, there is no global warming in the Universe) that has lasted for 13.8 billion years. The cosmic microwave background was only created about 400,000 years after the big bang. Around that moment, atoms were born and the ionized plasma turned into a nearly transparent gas of neutral atoms. Since that moment, the photons were propagating through space almost uninterrupted. Their wavelength was just expanding proportionally to the expansion of the whole Universe and because longer wavelengths correspond to a lower frequency, energy, and temperature, the CMB was cooling down. The temperature (as given by the maximum-intensity frequency etc.) is almost constant in all directions, the variations only amount to (relative) 10 parts per million or so. The variations are nevertheless important, may be measured, and decomposed to spherical harmonics. Those graphs of the amplitudes as functions of $\ell$, the orbital angular momentum, provide us with some of the most spectacular confirmations of our theories about the very young Universe (including the scale invariance). So far, I have only talked about the intensity. But the microwave radiation may be polarized which means that one linear or circular polarization has a higher intensity (or, more precisely, a higher temperature by a microkelvin or two) than the other one. At some level, this polarization is inevitable. Because the CMB was created from a variable density $\kappa$, we may deduce the main components of the polarization from derivatives of this density field $\kappa$, see e.g. page 2 of this paper. Define\[ \nabla \kappa = \vec u \] and try to separate the density field $\kappa$ into $\kappa^E$ and $\kappa^B$ (yes, the letters coincide with the names of the electric and magnetic vectors in electromagnetism) so that\[ \nabla^2 \kappa^E = \nabla\cdot \vec u, \quad \nabla^2 \kappa^B = \nabla\times \vec u. \] So that's the basic separation into E-modes and B-modes, something that may be expressed in various other ways. The E-modes and B-modes try to isolate the "gradient" and "curl" parts of $\vec u$. These modes imprint themselves to the linear and/or circular polarization of the CMB in some way. There are two kinds of modes because there are two polarizations. In a plane, you could choose the usual bases but on the sphere, there is no universal x-polarization or y-polarization or right-handed polarization or left-handed polarization because you can't "comb the sphere". So the 2-dimensional basis has to be chosen more cleverly (in some sense, the problem is analogous to the addition of the angular momentum, $\ell+1$) and the E-modes and the B-modes happen to do the job well. In some sense, the B-modes denote/quantify/measure the "vortices" or "whirlpools" in the CMB as measured by the polarization of the photons. If I simplify a bit, B-modes are the part of the variable polarization of the CMB that has something to do with the "curl" and it's called in this way because it's the magnetic field's fault that any "curls" appear in Maxwell's equations, anyway. ;-) It's actually more accurate to define the B-modes not as the "curl-ful" part of the non-uniformities but as the "divergence-less" part (note that the divergence of a curl vanishes, $\nabla\cdot(\nabla\times \vec u)=0$). You may find the review of the modes by Wayne Hu of Chicago or Peter Coles' blog post or John Kováč's 40-minute-long talk (B-modes from the ground) much more helpful and informative than my modest remarks. The graph above was taken from this HHZ 2002 paper or some slides (page 2) and it is showing the relative strength of various E-modes and B-modes from different sources, as a function of $\ell$. In general, there are "gravitational lensing" i.e. "mundane" B-modes but if the inflation scale is sufficiently high (close enough to the Planck scale), for example near $2.6\times 10^{16}\GeV$ on the graph, the "primordial" waves prevail at lower values of $\ell$. To be a bit slower: The B-modes may have arisen "recently", from the self-attraction of the CMB photons (this is the mundane origin); or, more excitingly, "a long time ago" (these are the important "primordial" B-modes, probably created during inflation when the Universe was really, really young and we may be jealous about its GDP growth rate). The "primordial" B-modes should be evidence of the gravitational radiation (i.e. gravitational waves) caused by the cosmic inflation itself and the numerical data about these "primordial" modes should tell us something about the characteristic energy scale of cosmic inflation which is mostly expected to be near the GUT scale, $10^{15-16}\GeV$ or so. The closer the inflation scale was to the Planck scale, the stronger gravitational waves we expect. For any scale, there seems to be a maximum (bump) in the B-modes around $\ell=90$ where BICEP2 and others may have focused (the "mundane" B-modes from gravitational lensing are elsewhere, near $\ell\sim 1,000$). In the early Universe, B-modes behave just like tensor modes (those related to the metric-like tensor field). The tensor modes are the only conceivable source of B-modes during the extreme childhood of the Cosmos. Their emergence in cosmology would be exciting because so far, we have only seen signs of the "scalar" non-uniformities of the matter density in the outer space (via the CMB). Amundsen-Scott South Pole Station. The microwaves and millimeter waves are nicely observed at the South Pole because it's 2.8 km above the sea level – a thin atmosphere; because the atmosphere is stable as there are no sunrises and sunsets; the concentration of water vapor that could steal/absorb these waves is low. In Summer 2013 (Nature, Science Daily, arXiv/PRL), the "mundane" B-modes were finally observed by the South Pole Telescope with some help from the Herschel Space Observatory. BICEP2 focal plane with four detector tiles. Now it seems rather plausible that less than a year after the detection of the "mundane" B-modes, BICEP2 may actually detect the exciting "primordial" ones, too. And the announcement may be just 3 days from now! The rumor may also suffer from a bug. A positive signal would be sort of surprising because it was generally expected that the Planck satellite would be the first experiment with a chance to detect the "primordial" B-modes (see the current status of the Planck measurements; note that Planck has died due to a helium heart attack but papers should continue to be published up to Summer 2014 or so). WMAP saw no B-modes. And the same thing more or less holds for POLARBEAR in Chile that published its results earlier this week. Finally, the rumor. Finally, I may show you that I can also be a linker-not-thinker and overwhelm you with ten more URLs to sources that discuss the rumor and some anti-rumors: Spaceref.com: March 17th Press Conference on Major Discovery [official title, no rumor! Note by LM] at Harvard-Smithsonian Center for Astrophysics The Guardian: Gravitational waves: have US scientists heard echoes of the big bang? (By Stuart Clark) The Trenches of Discovery: "A major discovery", BICEP2 and B-modes (by Shaun Hotchkiss) Richard Easther's ExcursionSet.com: The Smoking Gnu [sic] Bruce Bassett's writing: Should you hold your breath for B-modes? Résonaances: Plot for Weekend: flexing biceps (Adam Falkowski) viXra: Primordial Gravitational Waves? (Phil Gibbs) Blank on the map: B-modes, rumours, and inflation (by Sesh Nadathur) Preposterous Universe: Gravitational Waves in the Cosmic Microwave Background (by Sean Carroll, a rather clean and meaningful intro added on Sunday) Prof Matt Strassler: Getting Ready for the Cosmic News (a brief comment added by an active particle phenomenologist on Sunday; see also his Brief History of the Universe, Saturday) You are invited to read the articles now. Czech, German, Italian, Dutch, and Spanish readers get a bonus link. Five more bonus links: Hank Campbell, Universe Today, Raw Story, IO9, Sky and Telescope. The first (Spaceref) article says that the Harvard-Smithsonian will be streaming a press conference on Monday at 5 p.m., Prague Winter Time (9 a.m., California Daylight Savings Time). Some contacts are mentioned there. You may already see all the secret data now (if you guess the right password). The Guardian and the Trenches emphasize that it would be a huge, potentially Nobel-prize-winning discovery of gravitational waves (the Nobel prize could go to the experimenters, to my former student Alan Guth [interview on B-modes] and his competitor Andrei Linde [both are rumored to attend the press conference on Monday], or others). Gravitational waves need to have a source but in this case, cosmic inflation itself may offer a source. "Trenches" also suggest that this could be the greatest hard-science discovery in astrophysics although cosmologists will surely consider it a discovery in cosmology. Tweets about "B-modes" Twitter may sometimes make you feel that something is happening in a highly specialized topic every minute. Richard Easther says a few words about the inflationary origin of the "primordial" B-modes and admits that the precise information in the rumor seems contradictory at this point. Some sources say that the discovered B-modes are stronger than other teams indicated, and therefore suggesting a contradiction or some really weird behavior of the early Universe; other sources say that the new observation is compatible with everything else. Bruce Bassett tries to use a combination of Bayesian inference and psychology to determine how strong a signal they may announce. He considers the physical and experimental priors and the likelihood that a big signal would leak or that it would need rechecks, and tries to use some experience with some Planck and Opera announcements to check his musings. Well, it is amusing but a bit too speculative. Rumors are of course unreliable but in many cases, I prefer to believe that the rumor is essentially accurate over these vague Bayesian inferences which are nothing else than a guesswork using fancy words. The graph includes both measurements and theoretical predictions. The horizontal axis is the primordial tilt $n_s\approx 0.96$ (according to observations); the tilt (expected around one in "clean inflation"; more generally known as the spectral index) is defined as the exponent from $P(k) = \langle \abs{\delta_k(t)}^2 \rangle\sim k^n$. The vertical axis is the T/S (tensor-to-scalar) ratio. You may see that e.g. T/S around $r\approx 0.05$ is preferred (and hoped for) by proponents of the (violet) natural inflation. Adam Falkowski at Résonaances wants you to look at this graph because it may be the last days when the graph looks like this. On Monday, it may change rather dramatically. Finally, Phil Gibbs adds some pessimistic remarks. Not such a long time ago, we were disappointed by the pre-hyped press conferences of AMS, LUX, and others. He adds some comments about the decomposition of the waves. And Sesh Nadathur is also skeptical, claiming that a truly positive signal would contradict the already published Planck and WMAP data: note that the $r=0.2$ vertical line on the graph above is above the recommended big "hill" in the middle of the picture. Nadathur suggests that the rumor also says that the T/S $r\approx 0.2$ which he finds incompatible with others but a reader says that both Planck and BICEP2 could be compatible with the real value around $r\approx 0.1$. Note that BICEP1 measured $r\approx 0.03\pm 0.25$ or so. It seems to me that the error margin of BICEP2 may be at most 5-10 or so times smaller, like $0.03$, so for the claim about a nonzero $r$ to be significant, the mean value should better be higher and close to $r\approx 0.2$, indeed. This 2010 talk comparing BICEP2 with others claimed that BICEP would reach $r\sim 0.03$ by 2013 so I wouldn't quite exclude the possibility that they will claim a discovery with a very low $r$, either. Originally posted on Friday, March 14th. Update: On Monday after 4 pm, everything became clear as the BICEP server became accessible. See Andrei Linde who heard the news and will probably get very drunk (via Stanford). They announced $r=0.20\pm 0.05$ or so, excluded $r=0$ at 6-7 sigma or so, and $n=0.96\pm 0.01$. This is consistent, for example, with the hilltop quartic inflationary model with many (60) e-foldings. HenryBowman419 Mar 14, 2014, 11:08:00 PM Unfortunately, NATO has proven itself to be an offensive organization, rather than a strictly defensive one (e.g., Serbia). One can argue that NATO's presence in Afghanistan, which poses virtually zero threat to European countries, is yet another example. It would be nice if EU countries told the U.S. to "shove it" whenever some U.S. warmongers want to use NATO, but as long as the U.S. pays the bills for (most of) the EU defense, they seem inclined to go along with the U.S. Curious George Mar 14, 2014, 11:50:00 PM In a conflict between David and Goliath, our sympathy is usually with David. I find it difficult to see Russia as David. Or the West, either. Many years ago I vacationed in Yalta, Crimea. I read an interesting account of some exiled revolutionaries arriving as foreign tourists and visiting rock towers of Ai Petri high above the city. A local guide showed them how to climb inaccessible rocks. They hanged several "Down with the Tsar" banners from the highest towers. Police did not dare to climb, so they asked for a military assistance. The army came with machine guns and actually shot down most the banners, except for one, which get caught on a rock spike by its bullet holes. I went to a local Intourist office to book a trip to Ai Petri. "Sorry, sir, the Ai Petri area is closed to foreign tourists". anony Mar 15, 2014, 12:03:00 AM http://youtu.be/DR91Rj1ZN1M Gordon Mar 15, 2014, 1:44:00 AM "The US never attacks anyone who can fight back, Lubos." You must be kidding, Cynthia. After all, the U.S. invaded Grenada... (also S. Dakota in 1890 to kill 300 Lakota :)) Yes, political correctness will not work with Putin. Kerry and Obama lecturing Putin on morality is delusional. It is like a tourist lecturing a grizzly bear on its behaviour. Putin does not, unlike Obama, have the Hamlet syndrome. Smoking Frog Mar 15, 2014, 2:38:00 AM Since this will be yet another in my series of attempts at humor, I think it's only fair to let you in on the secret that I fairly often disagree with you but refrain from saying so because I lack the energy and/or - maybe - sufficient knowledge. (Examples: unemployment; Templeton prize winner; Galileo.) I just don't want you to be misled. :-) Also, I strongly favor Slavic-American friendship because, what with the confusion in 1991, the KGB forgot to stop funding me. :-) With my extraordinary talent for recognizing patterns :-) (you'll remember the bit about infinite series), I've just discovered, completely by accident,, a remarkable connection between Russian nuking of America and what I said about the letter K in "creatures with poor memories." It turns out that Johnny Cash (of all people!) wrote an SF story in 1953 about a Soviet nuking of America and a subsequent occupation in which the letter K plays a significant role :-), owing to Soviet destruction of the English language. It's called "The Holografik Danser" and it was published in 2000. I haven't read it, and it's not online, but it contains the following line: Fil Gravr sat at the bak ov the klasrum where he always sat, paying no particular attenshun tu the techir, Professor Ivan Klewicki. BTW, Cash was a talented telegraph copier in air force intelligence, and he was the first Westerner to copy the news of the death of Stalin. He didn't understand what he was copying, though. See Google Books. Peter F. Mar 15, 2014, 3:37:00 AM The proof that you are most probably right is in that he is now, after all, a politician. People pay this kind of people too much respect, IMO. LOL, I have read similar improvements of the English - and German - language. But once the anarchy in the Americas is cured, the correct spelling will be: Fil Grávr set et dz bek ov dz klásrům uér hý ólvejz set, pejing nou pártikjular etenšn tu dz techír, Professor Ivan Klevický. mesocyclone Mar 15, 2014, 6:44:00 AM I think your fears are greatly overblown. Russian doctrine is to use nukes if attacked, because of the terrible state of Russian conventional forces. But those are tactical nukes to stop the attack, not a strategic conflict. Russia has way too much to lose in a strategic exchange, even if the US has more at risk. Part of MAD is to make leadership and command and control priority targets. Putin would very likely die. If he didn't, he wouldn't like the wreck he inherited. That the US was devastated would be little solace. If you research the effects of nuclear weapons, you'd realize how devastating a strategic exchange would be. It wouldn't be the end of the world, as the anti-nuke activists claim (but then, they were funded and pushed by the KGB). But it would be bad, really, really, really bad. Russia would suffer badly. The US would suffer badly. But more of the US would survive, because there isn't much of value in Russia outside of a small number of major cities, while that isn't true of the US. Unless Putin loses it (which is always possible), he isn't going to do this. Also, while the US is currently rather pathetic (which is why it is hectoring rather than acting), it has a history of savage response when attacked. Do not mistake the weakness of the current administration for a country which would fight almost to the last man to retaliate for an attack on the homeland. None of this is to justify the west acting too badly. But... in spite of the silly hectoring tone of our foppish President and Secretary of State, the US has a real interest in stopping Russia's misbehavior. The significant issues are not the Crimea, but Syria and especially Iran, where Russia has aided and abetted monsters who. In the case of Iran, those monsters fully intend to kill lots of Americans, beyond the thousands of American deaths they are already responsible. Should Russia invade the Ukraine proper, rather than just Crimea, the west would be forced to react strongly. I just wish the US leaders weren't so juvenile in how they speak about this. Russia isn't a child to be admonished, it's a pretty evil dictatorship, in a country which has been unimaginably evil in the not distant past - at least as evil as the Nazi's.. Looking at the picture, her B-nodes don't seem adequately inflated to me. I won't comment on the physics, because I'm not qualified to do so. LOL, are B-nodes the breasts or something inside them? David Nataf Mar 15, 2014, 7:39:00 AM Do you consider this a greater discovery than the Higgs Boson, if true? The breasts, I hope! Yes, I actually do, mostly because this one is in no way clear a priori, while the existence of the/a Higgs boson has been clear for decades. This discovery would also allow us to see how the laws of physics are organized at vastly higher energy scales than the scales associated with the Higgs boson - we could be looking at the GUT scale. Of course, whether those things are true and how much we may learn depends on what will actually be announced. ;-) This is a different kind of discovery than what we are used to and thus people may have a hard time following. There would be more news if the south pole telescope gad discovered the planet Nibiru / Nemesis. LOL, but I think that it should have penetrated a little bit into the popular culture. Sheldon Cooper did some experiments in the North Pole. I am not sure why he didn't go to the South Pole for the monopoles etc. - one doesn't have to swim all the time in the South - but the idea that interesting observations of the cosmos may be born at the poles is something that shouldn't be an alien concept. The term "B-modes" would appear in almost every deep enough talk on cosmology, as one of the "dreams" about the future insights that didn't seem to be coming. Various theories would predict various wonderful things but all of them would be on paper so far. Suddenly, they could become real. TheDOC Mar 15, 2014, 8:22:00 AM Both the article and the experiment are very wonderful. Pleasure to read. :D Though I don't really understand much of this article. I have tried to read up a little on this (I tried reading the paper you linked, but couldn't get past the abstract). If possible, could you state what inflation models are ruled out or confirmed with considerable confidence based on the most likely result of this experiment? When you report the results on monday, I will find the relevant sections in my cosmology book and tear out the pages of the false models. And I will also cancel the same topics in the index with a marker. With all the recent progress in physics I shall have to mutilate all my books in similar ways, since I'm too stingy to update my collection. :D Your optimism is nice but I don't see anything "tactical" about the current tension. The problems look strategic and systemic to me. Tactical nukes are used when the foe makes a localized mistake somewhere in a corner of Russia etc. But what the U.S. leaders seem to be planning is a harm against the whole Russia. So far it's a cold conflict but a very strategic one, I think. Also, I don't believe that Putin would have a huge trouble if Russia were damaged a bit as long as he would become the most powerful person in the world. Albert Zotkin Mar 15, 2014, 10:26:00 AM I always thought that the sources for each detected photon in the cosmic microwave background radiation are overly remote clusters of clusters of ancient galaxies beyond our cosmic horizon (one Hubble radius). Those sources would be so remote that we could only see one photon per each source at a time. I always thought those photons were produced in scattering processes of particles or in spontaneous (or induced) emissions of atoms or molecules. In your opinion, how many (and what kind of) sources are contributing to the production of the CMBR? Regards and congratulations for your contribution to the interesting buzz related to the B-modes Peter F. Mar 15, 2014, 11:27:00 AM WHAT - is Alan Guth A FORMER STUDENT of yours!!! Did he try to catch up on string theory? This is surprising since I thought he is at least 15 years older than you. (Just checked: He is 26 years ahead of you!) cynholt Mar 15, 2014, 12:13:00 PM For people who don't want to put on John Kerry's rose colored glasses and conduct foreign policy as a utopian demagogue, the fact is that Putin has probably done us a favor in Syria and Ukraine as well as some other areas. You've got two choices in Syria at this time, Assad or Al Qaeda. That's pretty much it. And those were always going to be the choices regardless of what the neocons say. Dreaming of another choice at this time does not make that choice realistic. Perhaps there may be some things the United States can do to help constitutional development take place in these areas over the next century or two. That doesn't change the choices that are available now. It is hard to imagine the protests in Ukraine leading to an actual coup were it not for help from militants in the Svoboda and Right Sector parties. (The ousted President pandered to these parties, but apparently not enough.) Some idealists are claiming that these forces represent a small percentage of the protestors. That doesn't matter. In an unstable country with no constitutional background, the people who move in after a coup like this are the people with the guns — which is why militants now occupy 8 cabinet level positions in the new government, including important positions in the military and outright control of the police. Yes, he wanted to be "in" in string theory so he attended my string theory course. While he slept throughout most of my monologues, he would still ask the best questions at the end. I am far from being the only one who reports the same combination of facts. ;-) The US is clearly the instigator of this crisis as revealed by Victoria Nuland's phone call to the US ambassador in Ukraine. Russia is a long way from perfect regarding personal freedom, human rights etc. but I cannot recall any expansionist incidents from them since Cuba. (Afghanistan is a local trouble spot to the Russians.) The US, on the other hand, has spread violence, destruction, and deceit the world over. Dilaton Mar 15, 2014, 12:35:00 PM Yes, this looks exciting indeed (from afar) :-) ! Last week I got slightly out of synchronization with TRF, as I tried to take up my work again, too many spare time events, etc ... I have to catch up a bit with the nice things here now ... I think I will also accept the offer of my employer to work only part time for some weeks, to have more time to read TRF etc ...:-P. More seriously, I noted that things are still exhausting me still a bit more than I first expected ... At least it is the week end now, such that I have time to follow the links in this artilce too :-) Of course Putin doesn't want a war. It does him no good, and a lot of harm. Europe still needs natural gas. There's been some delusional silliness that they could get the energy they need elsewhere, but the infrastructure and supplies don't exist. Russia and China even more so have global power based on selling things people need, not military intimidation and coercion. All their interests are defensive in nature. Putin's military preparations are set against armed ideological insurgents who want to let NATO set up operations on Putin's front porch, not against NATO itself. "U.S. surprises oil market with sale from strategic reserve" http://www.reuters.com/article/2014/03/12/us-usa-energy-reserves-idUSBREA2B12V20140312 This a very Anti-American thing to do, IMO. The strategic oil reserves are there for a REAL national emergency, not to be used as a poker chip in trying to illegally overthrow a government of a foreign nation. Gordon Mar 15, 2014, 12:51:00 PM Hmmm, Klingon script....? There are powerful NeoconCrazies like McCane who think we can (and should) win a preemptive nuclear strike against Russia. Our country is largely controlled by madmen who pull the strings on their puppet, Obama. And yes, the NeoCrazies work for the Banksters. Their media has control over 80% of the American sheeple. We truly live in dangerous times. I thought Syria a few months ago could lead to WW3. This one is just as dangerous. Smoking Frog Mar 15, 2014, 12:56:00 PM That would never fly - it requires smartening up. Cash's only requires dumbing down. You do know that's Johnny Cash the famous singer, don't you? There is no doubt that what has happened in the last decade is surreal, the psychopaths have taken over and pulling off their masks and the people of the US just yawn or don't notice. We in the USA are ruled by the likes of Insane McCain and surrounded by submissive sheeple, so don't count on the US population to help in any meaningful way. If we can make it pass March, I don't think this planet will end up a spinning ball of radiation. Keep you and yours safe and loved, because that is all that is meaningfully in the end anyway. Smoking Frog Mar 15, 2014, 1:00:00 PM McCain is having flashbacks again to those good old days when he spent time in the Hanoi Hilton after bravely ditching his jet and parachuting rather than shooting it out with the Vietcong. You should try knowing what you're talking about some time. http://en.wikipedia.org/wiki/John_McCain#Prisoner_of_war That really takes the cake. As I said, you should try informing yourself. cynholt Mar 15, 2014, 1:09:00 PM McCain's recent posturing along with many other members of "our" government should finally convince us that our "public servants" are more dedicated to keeping themselves in the news than in working at resolving problems to benefit the country. I think the U.S./EU will continue to support the neo-Nazis. But more and more people will gradually become aware of what Ukrainian nationalism actually stands for -- anti-gay, anti-abortion, anti-Semitic -- the polar opposite of the "Pussy Riot demographic" that the West is trying to persuade to support its Ukrainian folly. This -- hopefully -- will lead to an erosion of what little support Obama currently has for this latest neocon escapade. ;~) Bill Bogus Mar 15, 2014, 1:58:00 PM Be sure to note that the above quote is clearly in the context of military conflict, not the trade war. The point is, i think, that Russia may not be that strong economically, but when it comes to war, it is quite good at and determined to ruin your interests when you choose to ruin theirs. Once a war criminal, always a war criminal. McCain was shot down over Hanoi while bombing civilian targets: http://www.villagevoice.com/2008-07-29/columns/is-mccain-a-war-criminal-who-has-served-his-time/ "During the first six months of 1967, while McCain was part of an attack squadron of A-4 Skyhawks on the carrier Oriskany in the South China Sea, North Vietnamese officials said some 167 schools were bombed, along with 230 churches, three seminaries, and 23 pagodas. In late September—just a month before McCain's crash on his 23rd bombing run—U.S. planes managed to drop four massive container bombs (2,400 pellet bombs apiece) on a grade school in Thanh Hoa province, south of Hanoi. The school had just reopened after the summer recess and, according to Vietnamese reports, the attack killed 33 pupils, ages 8 to 12. Thirty more were wounded, including two teachers. That was a single incident. The American estimate is that the 1965-68 bombing campaign killed between 52,000 and 182,000 civilians; the Vietnamese claim the figure was several times higher." He also conspired to initiate the invasion of Iraq, which was without a doubt a war of aggression. He should be tried in the Hague and hanged. McCain wants all young soldiers to share his POW experience. He left his marbles in that POW camp. Let him and Lindsey Graham lead the attack force. Get that old nut away from me. The Arizona sun has fried his brain. If you can't fix a problem with a club, bomb, or bullet Senator McCain wants nothing to do with it. Eastern_European Mar 15, 2014, 3:25:00 PM I'm just wondering if the Czech Republic belongs to Little Russia or Greater Russia? Neither. It never has. Little Russia has been, up to the early 20th century, the (main) name of the territory now called "Ukraine". Given your previous comments, I am not surprised that you don't know these basic things. So good for you although I heard some troops visited you in 1968. You think that the Russian imperialism will stop in Ukraine. Don't be so sure. btw your knowledge of history seems to be based on Soviet or Putin's textbooks. And todays' Russian people themselves are in complete information blocade when anti-establishment media are being closed. It seems to me you are a little blinded by your anti-americanism. I agree that American liberalism (with their PC, hysterical feminism, etc.) are things that can easily cause one to vomit but it is an entirely different issue. Never mind. Good luck to you, Czechs. The future will show everything. Don't be suprised if one day you will see some troops from the east. Uncle Al Mar 15, 2014, 4:35:00 PM A fundamental spatial trace chiral anisotropy must not be acknowledged! Theory postulates the vacuum is absolutely isotropic over all time. Falsification is blackest heresy. SN 1054 never happened in Europe. The One True Church existed in unchanging heavens, by postulate. 10^(-13) difference/average chiral divergence is the geometric Eotvos experiment, 90 days on a bench top in existing apparatus, signal twice background noise. It is a terrible outcome - but is it true? hunterson Mar 15, 2014, 4:44:00 PM Lubos, The US will fold, as will the EU. Russia started this by buying up Ukranian politicians, and Ukranians woke up too late to resist. I find it ironic and sadly instructive to see that a child of the USSR empire like yourself, and whose grandparents suffered under appeasement to German demands inthe 1930's, would take the position you seem to take. Russia nuking the US over waht is turning out to be basically the US firmly lecturing against invading a country they specifically agreed not to invade is ridiculous. Sec. Kerry, many people agree, is a long winded pretentious buffoon. But he is not the one sabre rattling. He is in fact mostly talking about the most important thing in the world, global warming. And his boss is even sillier. My bet is that the first sanction Russia gets will be responded to by turning off the gas to Europe. Then it will settle down pretty quick. But maybe I am an optimist? You missed the point, Lubos. If this thing goes hot, Gordon, it's not gonna be like Iraq where we shot malnourished ragheads with 20 year old shotguns driving around in the back of 20 year old Toyota pickup trucks! I've learned a long time ago that when the US steps up to defend another nation, especially in the name of democracy and that country isn't Israel, the UK or France, I grab the encyclopedia. Why you may ask? Well, we do nothing unless it has a financial value. For example, Afghanistan's geographical location is a very important gas transit country. In fact the pipeline that is presently under construction to transport natural gas from Turkmenistan through Afghanistan into Pakistan and India is a $8 billion project with origins as far back as 1995. Why would the US and Russia have such a interest in having a presence in a nowhere country? Do you really think it's for 9/11, Communism or Democracy? Ukraine is pretty much in the same boat with the exception that it is in Russia's backyard. Ukraine is the transit country for natural gas from Russia to Austria, Bosnia, Bulgaria, Croatia, Czech Republic, Germany, Greece, Hungary, Moldova, Poland, Romania, Slovakia and Turkey. In addition, there have been recent discoveries of shale gas deposits. Russia will do everything it can to maintain some control of this country because not only is it in its backyard (and does not want a Western presence that close), Ukraine is also a patch of land between it and a decent revenue source. This rattling of sabers has nothing to do with the freedoms of people - just money. Calling the Ukranians 'neo-nazis' is not only factually incorrect, it makes you look like an ignorant bigot. I am a strongly pro-American person. You are just a deluded idiot. The point was to write a cheap, untrue, demagogic rant directed against myself, wasn't it? I understood the point very well. That is naive, Lubos. The impeached Ukranian President was a Putin sock puppet. Russia is no longer ruled by ideology, Gordon. It is now ruled by pragmatism. Putin would much rather keep selling gas/oil to Europe instead of fighting a war, but he's not going to sit idly by and watch the Western Jackals take bytes out of Russian flesh. He knows that Ukraine is just a trial for the takeover of Russia itself by the Western imperial hegemony. Obama may draw "red lines" with Michelle's lipstick. Putin draws them in blood! David Nataf Mar 15, 2014, 4:52:00 PM Galaxy clusters don't produce perfect blackbodies, and they're not all at the same redshift. I am not a child of any USSR empire, fucking asshole. My country has always been independent from USSR and it was always ahead of it. It just happened to adopt communist for 40 years, much like 1/2 of Europe. And the reason that my grandparents - most notably, my maternal granddad, an academic painter - were harassed by the Nazi regime is one of my main reasons why my attitudes in this tension are so clearcut. This tension is really a revived proxy for the Second World War and my preference in that is totally clear - Allies including Stalin Yes, Hitler No. A lot of French and British and others thought the same about Germany' s leader in the 1930's. Do you think the Czechoslovakian Republic was a free agent in the Cold War, with no USSR stranglehold? A Soviet backed coup is a strange way to 'adopt' something. I respect your attitude and your points. And if I pushed buttons you in a personal way, that was not my intent. Please accept my apology. SteveBrookliMA Mar 15, 2014, 5:28:00 PM Kerry is a gasbag. Russia will do what it wants and Kerry et al will move on to much more critical issues like Climate Change. The American media will obligingly stop reporting much about Ukraine. I doubt 10% of Americans even know or care about this issue now. Nobody will remember or care when it fades. Nareg Mar 15, 2014, 5:34:00 PM I wonder, what will be the reaction of Paul Steinhardt, Turok and other Inflation-bashing people? Although to be completely honest in their last paper they make it quite clear that their problem is with multiverse and measure so the probable detection of primordial gravitational waves isn't going to ring a bell for them whatsoever! LOL Steinhardt is a hater of inflation but he is its co-uncle, too. And a co-author of "natural inflation" that may very well be confirmed and he could very well be a Nobel prize candidate for something he bashes. ;-) if he a decline a Nobel prize that would be something! Cyclic cosmology is somehow a dual version of inflation in so many ways. But at the same time that dos not mean inflation doesn't have its own problems, do you see the mutiverse, eternal inflation and measure problem as severe as they consider it? Buzz Mar 15, 2014, 6:33:00 PM Thanks for an unending stream of extremely bellicose "peace-mongering," vicious scapegoating, and hysterical apocalyptic drivel. And it's curious to see what happens to such bursts of righteous indignation when flowing from the mouth of a sewer. "[Putin] knows that Ukraine is just a trial for the takeover of Russia itself by the Western imperial hegemony [by "Western Jackals"]." While I've few illusions that the reactive bumbling of the Obama administration is pursuing sensible measures during the present Ukraine crisis (and I find Lubos Motl's perspectives worth noting), nevertheless, I don't find any sense or wisdom in your hysterical tirades either. So, c'mon, enlighten us--what territorial designs do these "Western Jackals" have on Putin's Russia? mesocyclone Mar 15, 2014, 8:26:00 PM I agree that optimism can be dangerous. History shows that leaders and nations sometimes do stupid things. However, Russia would not be "damaged a bit" in a strategic exchange. It would be effectively destroyed. There wouldn't be enough left to stop an invasion by Latvia, much less China or other surviving powers. Tactical nukes can be used in a strategic situation. The "tactical" adjective refers to the usage (and to some extent, the size). A ground attack into Russia could (and would, per doctrine) be stopped with tactical weapons. The reason for this is that the use of strategic nukes is suicidal - as above. The doctrine you cite refers to existential threats - conditions where any nuclear nation would use whatever it had. Also, MAD requires that participants have a doctrine of, essentially, suicidal nuclear response to existential nuclear attack. However, there is nothing existential about current western threats. At worst, there would be significant economic hardship - not something one will blow up the world about. Furthermore, Russia has other ways of responding short of strategic nuclear war - such as cutting off European energy supplies, or more sharp meddling in the middle east, etc. There has been theorizing over the years of limited strategic strikes - such as nuking just San Francisco. I doubt any leader thinks seriously about such things - look at the immense US response to the mere bombing of a naval base not even in the United States in 1941 (Pearl Harbor). True. The Russian's military budget is the equivalent of 79.3 Billions Euros, whereas the US one is 406 Billions Euros. Putin is rising of 63% his military budget over the next 3 years(reducing on Health and Education). skeptic Mar 15, 2014, 10:26:00 PM So this is the level of "observational" evidence required in modern science? You guys are all turning crackpot. If such an observation has been made, then, first we wait for Planck satellite confirmation, and in the postive or negative case we then think about models of the early universe that might explain such an observation - not just go with the fashionable one, which is hardly even close to "proved" by this observation. Also, they are quite rude to publish in such haste a very dodgy observation, and not wait for Planck to corroborate. I hope for Harvard's sake they haven't got a loose cable. Dear Skeptic, theories explaining the relevant cosmological observations have been studied, strengthen, refined, and refuted since 1980, i.e. for 34 years. Sometimes people have loose cables - note that I was sure in advance that the OPERA superluminal result had to be wrong. But many experiments may be just right and they don't have to be called Planck. It's really bullshit that no other experiment is "allowed" to make a discovery without waiting "what Planck says about it". No one really sensible has bothered with early universe models because it's barely science. NOW, if these B-Modes are confirmed (In the Summer by Planck) - a lot of competent people mught turn their atttention to this crazy corner of science - and hopefully bring some really stromg mathematical reasoning to the theories - which are currently mostly back of the envelope imaginings. Svik Mar 16, 2014, 5:57:00 AM I am sure there is a loose network cable on there somewhere. Or maybe the b and e cables are mixed up. Ha Well. After ams on the space station I am not even inclinclined to listen in on Monday. Again, first, experiments are not "obliged" to wait for other experiments. Maybe you are confusing science with a special school where they were waiting for retarded children left behind such as yourself but science is something else. Second, discoveries in physics may be either made first theoretically (with predictions for the experiments), or first experimentally (with theorists trying to explain the existing data later). Both scenarios have occurred in physics many and many times. There is absolutely nothing wrong about the first route and it is in fact the more scientific, the more exciting route intellectually. Third, almost everyone who has the capability has been thinking on cosmology. With the data, the theoretical research may become more directed but it doesn't have to become theoretically different. Fourth, cosmic inflation is as solid science as you can get and folks like Alan Guth and Andrei Linde have done at least the same kind of solid science as Peter Higgs and Francois Englert. Those are totally analogous things. Pompous stupid creatures don't understand either. I have banned you because at 5 sigma, I've excluded the hypothesis that you may ever contribute anything valuable to this forum or the mankind, for the matter: aggressive promotion of the stupidest laymen's delusions about what science is are not welcome here. Why don't you go to one of the thousands of websites fully dedicated to nasty imbeciles like you? What about Not Even Wrong? Nareg Mar 16, 2014, 10:51:00 AM saying that we should wait until Planck confirmation makes me think that you might be in Planck team and you are annoyed that you've got scoped so you are saying something this nonsense. If there is a solid detection that we are going to find out about it on Monday there is absolutely no need to wait for Planck, of curse confirmation by Planck would be nice and welcomed. Planck and the south pole telescope don't measure the same thing. They have different spatial coverage and resolution of the cosmic microwave background. kiki Mar 16, 2014, 2:16:00 PM nice, thank for post you Mall di Jakarta anna v Mar 16, 2014, 4:01:00 PM He was not sleeping, he was thinking :). Jack Steinberger would seem to be napping during presentations, but his questions also were always to the point. BobSykes Mar 16, 2014, 6:35:00 PM They will have no place in the coming Mexicrat faction just as blacks had no place in the old Dixiecrat faction of the Demcrat Party. Blacks and Asians will also need a new home. Merida, Mar 16, 2014, 7:05:00 PM Milos , for my. " taste" you are a little bit "too eastern'" with your analysis , or I'd rather say very Russian and Serbian fanatic Gene Day Mar 16, 2014, 11:11:00 PM There is already a separatist movement among Mexicans? That's pure crap, Bob. Having watched California's ethnic makeup and California politics from the inside for 67 years I assure you that integration and assimilation are progressing nicely, just as for all the other ethnic groups that are blending together here. The only Californians that even give lip service to secession are those individuals on the far right who know their voices are dwindling into oblivion and who are unwilling to face reality. Hey, Cynthia, that's my state you're talking about. We welcome everyone, including you! cynholt Mar 17, 2014, 12:39:00 AM Strangely enough, in ITALY there is a poll as important as in Crimea; however, mass media has decided or been instructed to totally ignore it. Four million Venetians will go to the polls and vote on whether Veneto, one of Italy's three wealthiest regions, should secede from Italy and become an "independent and sovereign federal republic." They also vote on leaving the EU with their new republic, leaving NATO, leaving the EURO. This must scare the EU leaders so much that they decided not to have it covered in the news, to not cause ideas in other regions as well. So far only very little coverage in the media: http://www.express.co.uk/news/world/465108/How-a-vote-in-Venice-could-change-the-face-of-Italy Mazikeen Morningstar Mar 17, 2014, 12:48:00 AM lol oi vey, Lubos. That was brutal. HenryBowman419 Mar 17, 2014, 1:24:00 AM I grew up in the segregated South, as well, and I completely agree with your assessments, cynholt. The government continues to work to let racism permeate its every move -- who else asks what one's race is on a form? The dullards in the left-wing media are accomplices, of course. lukelea Mar 17, 2014, 3:28:00 AM You are ok I hope, Dilaton. (Remember me? I passed you on my way down while you were on your way up, several years ago? ha ha) davideisenstadt Mar 17, 2014, 4:22:00 AM where does any discussion of a secular government go when you refer to the ummah? the islamic people in france deserve all the deference and rights given to christians in saudi arabia. that is, none. cynholt Mar 17, 2014, 4:45:00 AM We live in a reverse Jim Crow society. Institutional racism permeates all government and educational institutions. Certainly, Obama has made no effort to conceal his racism when he sticks his nose into legal cases he knows nothing about and imposes his anti-white prejudice. Of course, he won re-election, so this whole country has degenerated into something that repels me. Gene Day Mar 17, 2014, 5:13:00 AM Right, there is zero political backing in the US for military intervention in the Ukraine and very little for economic sanctions. What we are hearing is face-saving bluster. No one is seriously concerned about military confrontation with Russia. Putin knows all this, of course. A Mar 17, 2014, 8:25:00 AM way to go! I am still on other SE sites where it is a lot of real science discussions happening (e.g Chemistry), but, i won't go near Physics.SE site either holy crap! So they took out their 2nd highest contributor (I have read some of Ron's posts - very informative!), alienated many more contributors... no wonder several physics topics go unanswered! I asked a colleague of mine, a very experienced astrophysicist about Physics.SE... his response was an eye roll and said "there are better places" (I have told him about PO - he is intrigued :) ). Coldish Mar 17, 2014, 10:11:00 AM Well written, Lubos. I know we have disagreed on a number of issues, but here you really are showing the world the way to go. Well done. papertiger0 Mar 17, 2014, 11:18:00 AM the concentration of water vapor that could steal/absorb these waves is low. and the most powerful substance known, carbon dioxide? How could the detectors, which have to flee all the way to the ends of the Earth to escape water vapor, even hope to see through the glare of heat trapping carbon dioxide? Luboš Motl Mar 17, 2014, 11:25:00 AM LOL, a good question. Incidentally, this Antarctic logistics was linked to another topic remotely mentioned on this blog, in the second part of http://motls.blogspot.com/2013/06/asymmetric-fates-of-rivers-of-pilsen.html?m=1 Antarctic explorers... During a talk by an explorer, I won several small prizes, e.g. for the answers what Antarctica is "best at". I said it was the most Southern continent LOL, which was new to him, but he wanted that it was the driest continent etc., too. NOW, CO2 only absorbs at higher frequencies, really infrared, see the charts http://clivebest.com/blog/wp-content/uploads/2010/01/595px-atmospheric_transmission.png The wavelength relevant for the CMB is about 2 millimeters so it's not really infrared anymore, it's between microwaves and radio waves. CO2 doesn't matter for those. markusmaute Mar 17, 2014, 11:55:00 AM They should have named them "God modes", not B-modes :-) LOL, B must stand for Bog/Bůh, the Slavic/Czech word for God. I guess I should never mind the fact that you seem to believe that McCain ditched his plane, that the "Hanoi Hilton" was a hotel, and that if he hadn't ejected he could have "shot it out with the Vietcong" in North Vietnam? Should I never mind the fact that if McCain is a war criminal, the same must be true of thousands of aviators of modern history, not only American? Should I never mind the problems with believing North Vietnamese authorities' statements at the time? Instead of posting all the stuff you have, you could make things a lot easier simply by posting, "I hate America." If you reply, I won't answer. Just try reading your own messages and asking yourself why anyone would get involved with you. CentralCharge15 Mar 17, 2014, 2:03:00 PM No, only you and 10k+ users can see the thread now after deletion. Not all registered users can. Is it on the wayback machine? I think everybody should see what the SE Overlords ant their associated lynch mob are capable of doing... However, there are still enough examples of what they did to Math SE, Jeff Atwood behaving like a real asshole, insulting capable mathematicians who disagree with him, suspending pfofessors, etc ... You can find all this when searching for a thread with the title Threatening emails from Jeff Atwood and related discussions. Even though the SE Overlords strongly and negatively interfered with the mathematicians repeatedly, that community somehow (conversely to Physics SE) succeeded in staying rather free and independent and keeping its nice collegial community spirit. Czech guy Mar 17, 2014, 3:09:00 PM Mr. Motl here confirmed his close relation to late president of Czech Republic Vaclav Klaus. But, I don't think that Motl's or Klaus' views are representative of Czech Republic or Eastern Europe inhabitants' views. The truth is that Putin's position was severally weakened by deposition of Ukrainian president Janukovich. Putin reaction was to take back what he sees as his own - Krym. Nobody seriously objected to this. Not even Ukrainians. Krym is Russian. What is in play right now is East Ukraine. Putin can still decide to take it back as well. However, by invading Ukraine Putin can expose himself to unsymmetrical military reaction. Obviously, Ukraine army is no match for him, but western secret services could support local Ukraine nationalist and make Ukraine living hell for Putin. Something like what Iraq was for US or Afganistan for USSR and NATO. The outcome won't be nuclear confrontation between USA and Russia but low intensity conflict between Ukraine nationalists supported by western secret services and Russian police and army. If Putin takes Ukraine by force it will be great opportunity for CIA to play games not for US to launch nukes. Russia didn't nuke US during its Afganistan campaign in 80s so why they should nuke US because of Ukraine? Dear Czech guy, "close relations" might be a bit too strong word. The views' being or not being representative of Czechia or Eastern Europe doesn't affect their being right. Incidentally, I didn't synchronize my views about Ukraine with President Klaus in any way. The Czech Republic is a country in Central Europe, not Eastern Europe, and by its historical experience, it belongs to the Western Europe. You probably wanted to say that it was a post-communist (European) country. That's something else than "Eastern Europe". Which kind of a source do you expect me to mention as a reference to correct your terminological problem? http://www.klaus.cz/clanky/3396 Good that you agree that Crimea is, by its character, a Russian territory. Good luck to your CIA Agent 007 games in Eastern Ukraine LOL. You're joking, right? For a "low-intensity conflict" in Eastern Ukraine, the agents would be almost useless. Such a conflict would really be just a business-as-usual work - the same kind of work as our cops' operations against the Czech skinheads in DSSS. It of course is on the wayback machine, but the latest version I have it's HTML backed up here: http://psiepsilon.wikia.com/wiki/Ron_Maimon_Suspension nnon Mar 17, 2014, 5:24:00 PM I think it's a toad, not a frog:) Ron Tal Mar 17, 2014, 6:30:00 PM I moved to California for work about 18 months a go to the Bay area. Until I moved here I guess I was susceptible to propaganda of California doom and gloom due to Mexican immigration. At least in NorCal I can attest that while Mexicans are very visible, they are mostly just as well integrated as the Chinese and Indian tech migrants who take a generation and a half to fully assimilate (not necessarily lose their cultural identity). Also, while they are obviously a major voting bloc, their progress in climbing up the socio economic ladder is not very fast, meaning that they are still under represented in political leadership. The ones that do establish themselves (like Mayor Villanueva of LA) seem to be well assimilated in American culture and way of thought. Thanks for telling your friend about PhysicsOverflow, he will be highly welcome :-) If I really cant hold questions back, I am at most spamming around on Astronomy a bit, but it sometimes helps not much, this site is going very slowly and I am not sure how long it will be tolerated ... oleg Mar 18, 2014, 3:13:00 AM Another very reasonable assessment of the situation by Paul Craig Roberts , takes an hour though : https://www.youtube.com/watch?v=AhxZxL56B00 Pelle Mar 18, 2014, 3:22:00 AM Very good! I agree. yonason Mar 18, 2014, 4:30:00 AM Lots of posts here, so I apologize if I'm repeating what anyone else might have said, but aren't their things that Russia could do to blunt Obama's foolishness without going to all out war? E.g., if the US puts sanctions on Russia, what will happen to this relationship? If I were Russia, I would be tempted to say "you're on your own, pal." Oh, and thanks to Lubos for the benefit of his experience and insights gleaned while behind the iron curtain. Holy cow, I just opened Russia Today on YouTube, something that I was doing pretty regularly in recent weeks, and see what I found: https://www.youtube.com/user/RussiaToday/ Unbelievable. You will have a hard time to convince me that this is a coincidence that it happened today. America is no longer the country of the free. This kind of censorship matches what we knew in the Soviet bloc. A Mar 18, 2014, 11:03:00 AM I had a look at Astronomy, looks interesting. A little out of my subject area. But, I am enjoying my 'main' site - Chemistry.and my 2nd site - Sustainable Living - there, the discussions are purely on the topics. TomVonk Mar 18, 2014, 12:43:00 PM In Czechoslovakia, the citizens have also had "highly non-uniform opinions" on whether the country should be split. Most Czechs would oppose the Slovak independence for quite some time. This deserves a comment. As I remember it, the opinions in the Czech lands (yes, I am including Moravia) and in Slovakia were pretty much homogeneous. A very significant minority of the same order of magnitude (around 40%) supported separation in both lands (f.ex http://www.nytimes.com/1992/10/09/world/at-fork-in-road-czechoslovaks-fret.html but there were other polls giving similar results too). As anecdotic evidence I remember my discussions from that time too and in my Czech sample almost all people fluctuated between indifference and support for separation. Arguments for separation from the Czech part was mainly that one cannot live in the same country with somebody who is calling you " a colonial power" and you must surely remember that the Czechs were historically considered by the Slovak media and politicians as "colonial power" and "exploiters". Of course this argument was basically emotionnal and probably not shared by all Slovaks but it was not far from a 50% support either. Finally if one added those favourable for separation and those indifferent, it would certainly give a very similar figure above 50% in both lands so that if a referendum had been organised, a "Yes" for separation would have won in both lands with probably, as you wrote, a slightly higher margin in Slovakia. This is clearly seen in the apparent paradox that while "only" about 40% supported separation, a quasi unanimity considered that a separation will take place anyway. So it was this vastly shared indifference in the Czech and Slovak lands which enabled the separation to be velvet. If somebody asked me my opinion back then, I would surely say "If they want to leave, they may go. Who cares anyway ?" and I think the same thing today. Arguably the only negative consequence of the separation was ice hockey. Instead of having one top world class team able to beat on a regular basis Canda and Sweden, we have now 2 teams that are merely good without being top world class :) A second comment on : Your story about the contract in 1953 is funny, I have never heard of it. I assure you that since 1948 if not 1945, Czechoslovakia was the closest friend of the USSR, and it wasn't just on paper. The tight relationships were widespread. I have already noticed that you had a kind of light russophilia streak which is probably explained by your personnal history. However, and I am pretty sure that you know it, a crushing majority of Czechs that had at least 10 years in 1968 would passionnately hate USSR and the Russians, so that one can forget completely about any form of "friendship". For many it was already the case in 1948 - for instance my grand mother despite having lost her husband and brother in law in Terezin (Theresienstadt) was always speaking about "ty posrany bolsevici" and wouldn't definitely admit any qualitative difference between Hitler and Stalin. As she also lost a son in law in Jachymov, this opinion was justified and shared by many. Of course the analysis is relatively hard because in the post 1948 attitudes towards Russia was always a mixture of anti-communism (prevailing in Czechia, a bit less in Slovakia) and anti-russian/soviet empire yet at the same time one couldn't deny that we were ethnically if not culturally close. Personnaly I feel also a bit ambiguous. One one side I still remember those bewildered, stupid, helmeted young faces emerging from the red starred tanks and I know that I hate them. What is not clear is whether I hate them because they were arrogant, stupid and russian or because they symbolised the communism that we all hated too. Obviously when I am in Russia I feel rather close to the average Russian and with the significant exception of all kinds of militia, security and guards I even like them a bit. OK, Tom, but these are polls from the time when the split was already negotiated (October 1992). You can't use it as a measurement of the Czech opinions when it was being decided whether the federal state would be preserved. A vast majority of Czechs wanted to preserve the common state as recently as before the 1992 elections. MikeN Mar 18, 2014, 2:42:00 PM I think you are letting the Czech experience color your views. Crimea is very important to Russia strategically. Its naval base had its lease extended by the last(and legally current) Ukrainian leader. Without that base, the Black Sea Fleet would have to leave until they built a new base. It doesn't stop with Crimea either. Much of Eastern Ukraine has Russian sympathies as well. And then Latvia, Lithuania, and Estonia could follow, even though they are NATO members. http://www.powerlineblog.com/archives/2014/03/will-russia-use-lawfare-to-pave-the-way-for-an-invasion-of-eastern-ukraine.php Dear MikeN, it is a duty of NATO signatories to protect others who are attacked. Concerning the continuation of Russia to parts of Eastern Ukraine, well, you may be thinking that you are scaring me but you aren't because, indeed, I support the plans of Russia to gain some control at least over Eastern Ukraine, too. It would surely be better for the citizenry over there - and for the external world - than the current sketch of the failed government we may be seeing. Martin Mar 18, 2014, 6:19:00 PM I hope that even when Russia attempts such a thing (but I still belive that it will not come to this because I am living in the states) US are well prepared to intercept incoming missiles.http://en.wikipedia.org/wiki/Strategic_Defense_Initiative This is where their technological superiority comes to play...I really doubt that Russia has systems on this level. I doubt that SDI at this level is more able to defend than the Russian tools and technologies are able to attack. It must be so easy to fire a missile from a submarine or any other place so that there is almost no chance to intercept it in time... I just got this video: https://www.youtube.com/watch?v=lMJi0JIVZas It has English subtitles, the Czech ones are here: https://www.youtube.com/watch?v=W5Unk0MDTsE Looks rather impressive. I may bet on Russia in the case of its high-level conflict with someone else. H Mar 21, 2014, 7:33:00 AM Well, am going to leave the entire SE network... tired of the whole opinion over science thing going on several sites. Any wonder many academics that I know do not regard SE as a viable scientific site spoke too soon - same thing on Chemistry.SE to a degree... US citizen Mar 22, 2014, 2:07:00 AM I am afraid if we apply your assumptions to post WWII, we must reach the conclusion that the US destroyed the Soviets in a nuclear war, or vice versa. You seem to neglect the fact that Putin is not a figure of Sauron like self-sufficiency and power, but rather is a figure who is dependent on various people's support, who have, until now, benefited from Putin's tenure. If he becomes a detriment, his hold on power becomes far more tenuous. Putin my not care about external forces, but his power base does, acutely. We are in a period of high level confusion similar o that of the Carter years. Thanks to American democracy, a man was found who knew how to deal with a threat far greater than Putin's, and end it. Putin seems an intractable problem who must be appeased, because that is the thinking of Obama, and, therefore, the entire press corps. It is time or leaders in Congress to clarify what the US considers its vital interests vis a vis the world. William Mar 22, 2014, 4:16:00 AM Is it just me who remembers the invasion of Panama by the U.S. in 1990? I see this as having a similar situation to Ukraine. Although I'm an American and certainly sympathize with the Ukrainians (eastern European ethnic cousins, from my father's side), I think the U.S. should stay the (you know what) out of this, and apply only economic pressure (if they decide to). Gavinal Mar 24, 2014, 5:38:00 AM Put the nuclear U.S. missiles around Russia's borders, Let Putin push the first button. M J Mar 25, 2014, 2:53:00 AM Lubos has made a lot of good points, but what I do not see discussed, (despite the length of his article) still surprises me. Did you forget about MAD? The US still has the capability to do horrific damage to Russia even if Russia launches first. US missiles are still more accurate, we do not NEED to cover the whole area of Russia, since so much of that space is uninhabited or very lightly inhabited. There is also good reason to believe, even though details are (of course) classified, that the US has kept its nuclear weapons in better shape. This is one thing the US and Russia have in common that Europe forgets: unlike Europe, we both have a lot of wide open spaces. But if any of this happens, it will be a disaster not only for both sides, but for the rest of the world. Putin knows this, so I really doubt he is going to use nukes -- unless the US goes first, which is also extremely unlikely. More likely, he is letting subordinates say rash things like that because it looks good in the Russian press. That is, he is letting them say this because it project the image of strength he wants to project in front of the domestic audience. Putin's approval rating is very high right now, he wants to keep it that way. Projecting that image of strength is the way to do it. Actually doing it (using nukes) would lose that approval rating -- and so much more. BTW: official Soviet policy was never to use nukes first, but to respond with everything they have got once even a single nuke falls on Soviet soil. Russian policy is still the same, mutatis mutandis -- despite what hotheads say for press attention. M J Mar 25, 2014, 6:35:00 PM Russia has been having problems with capital flight since 1991. The first three months of this year were worse than all of last year (in terms of capital flight). It will only get worse now after what Russia has done in Ukraine, as would-be Western partners decide Russia is too risky for investment. Bunch43 Mar 27, 2014, 4:06:00 AM Lubos, interesting conjecture. Reality is that if shooting starts, all lose. MAD is still a certainty. What Putin and Russia are gambling on is Western weakness displayed by Obama and Nato. Give Ukraine back the nukes which were removed with Budapest Agreement and this whole issue becomes moot. No war, no problem. Weakness assures aggression, Strength yields Peace. Mike Mar 27, 2014, 4:17:00 AM It's not optimism, it's reality. Putin would have absolutely no chance, not even a .001% chance of emerging the most powerful person in the world. Russia has a very minimal offensive nuclear force outside of silo and mobile-based launchers and all of their nukes reside in Russia. You're forgetting that the US has closer strike points to Russia's mainland than Russia has to the USA's mainland. You're forgetting that out Ohio-class submarines outnumber any of Russia's non-land based missile delivery systems in size, number, speed, power and payload. You're forgetting NATO's missile defense program. You're forgetting Aegis. You're forgetting programs that the public isn't supposed to know about, such as nuclear-tipped cruise missiles and nuclear B2 stealth bombers in Poland. You're forgetting the nuclear arsenal in Israel that has never been acknowledged. You're forgetting that no matter who doesn't like us, India and Pakistan thrive off of a healthy global economy and heavily foreign-dependent US economy, which will cripple their economies in the event of a nuclear war. Who would India and Pakistan likely target to prevent a WW3 and lose the world's largest stabilizer in terms of war and market? It sure wouldn't be the US that they target. Russia is large, but only a small percentage of the entire country is developed and inhabited. The structural, functioning land totals of Russia are MUCH, MUCH smaller than the country's vast land totals. Russia's Vice PM has even acknowledged that the American Conventional Prompt Global Strike (PGS) strategy is superior and faster than anything that Russia has. Don't forget the US has an arsenal that isn't in books, on YouTube and on Wikipedia. You think that stealth chopper in the Osama raid was the gist of America's unknown weaponry? Rest assured that the US has functioning hypersonic missiles and delivery systems that are constantly targeting the largest nuclear threats from Russia. Russia doesn't have a practical defense network against our nuclear strike, they can simply try to overload our defenses (Aegis, NATO missile defense, etc.) with a barrage of missiles which we would likely destroy the majority of in a first-strike scenario. Ohio-class submarines, B2 bombers, strategic bombers, nuclear tipped cruise missiles, missile silos and probable allies would be sending a volley of nuclear strikes against Russia that would obliterate the country, all while every Aegis system we have would be targeting in-flight ICBM's from Russia. I'm just completely confused by your logic. Keep thinking that the current administration is in control of the nuclear arsenal in the event of a war. An all out barrage would follow a Russian nuclear strike. I can't believe you'd even think there would be a hesitation or delay in US response. The US has an insane first-strike policy against Russia, but you think they're going to delay in a response? Every functional nuclear weapon would be activated against Russian targets. I've never claimed that the U.S. wouldn't send these arms to Russia. I just care somewhat less about it than about whether the West will be crippled by Russian weapons. And I simply don't want that to be the case. Nuked big cities in the West would be a huge problem and a nuked Volgograd wouldn't "fix" it for me - on the contrary, I would find it a terrible event, too. If the Western folks' thinking is at least slightly similar to mine, they will have to tolerate a Russian Crimea - and already perhaps do, except for meaningless moralizing propaganda which I ignore - and they will probably have to tolerate a Russian takeover of the whole Ukraine, too. All this is just some stuff on paper. And a cherry-picked one. Our perspectives are clearly not compatible at all. Like your silly claims about the 0.0001% chance for Putin to become the #1 person after a conflict. One could make a good case that Putin already is the most powerful person in the world now. A complete lack of strategic thinking under Obama has contributed to it. While Putin is pretty much free to retake the territories inside the ex-USSR, Obama has been reduced to take pictures with the wet rag Rompuy and the Maoist Barroso and claim that the whole West is united and Putin is isolated. But what is it supposed to mean? The Western countries' citizens are not united because they're democracies. For example, I stand largely on Putin's side in this tense situation, and so do dozens of percent of others in the West. And what does the isolation of Russia mean? Russia is the territorially largest country in the world. It's almost equally justified to say that Russia is isolated; and to say that the rest of the world is isolated. Moreover, it's not really the rest of the world that is isolated (by being against Russia), it's just the West. Russia is doing totally OK with China, India, Latin America, and many other places. What does it achieve for Obama to dismiss Putin "just as a regional power"? The relevant region for Russia is the whole Europe and Asia - and the U.S. isn't even a regional power when it comes to acts. Right, that's why there will be peace in Ukraine under the Russian control and why there can't be peace under the weakness-driven, EU-supported Maidan government etc. I don't think that MAD is certainty - there's still a huge distance from some random nuclear exchanges to a universal destruction - but what I am sure is that MAD is in no way a "tie" from my viewpoint. It is the ultimate catastrophe and I am much more willing for my own country to be controlled from the Kremlin than to see MAD. Mike Mar 27, 2014, 9:11:00 PM Neither one will come out the #1 on top. The fact that you think Russia wouldn't be turned to ash is just astounding. Both countries will be rendered functionally destroyed. Every other NATO member and super power will be in higher standing than the US or Russia. Russia has virtually NO way to prevent a first strike or even full-scale retaliatory nuclear strike. Have you not been following the US Air Force's clean up in the past six months and firing of officers in the nuclear program? Russia would be isolated from the world if they take over Ukraine. You think everyone will be bullied into maintaining trade with Russia because they have nukes? Russia takes Ukraine, all super powers place sanctions and cut all trade with Russia. You think just because Putin stomps his feet and screams and cries, that EU and the West will continue trade just to avoid an angry nuke threatening Putin?	CommonCrawl
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S. Pattanaik, V. B. Varma, … R. V. Ramanujan Using operando techniques to understand and design high performance and stable alkaline membrane fuel cells Xiong Peng, Devashish Kulkarni, … William E. Mustain Aluminum electrolytes for Al dual-ion batteries Kostiantyn V. Kravchyk & Maksym V. Kovalenko Puchanee Larpruenrudee1, Nick S. Bennett1, YuanTong Gu2, Robert Fitch1 & Mohammad S. Islam1 Metal hydrides (MH) are known as one of the most suitable material groups for hydrogen energy storage because of their large hydrogen storage capacity, low operating pressure, and high safety. However, their slow hydrogen absorption kinetics significantly decreases storage performance. Faster heat removal from MH storage can play an essential role to enhance its hydrogen absorption rate, resulting in better storage performance. In this regard, the present study aims to improve heat transfer performance to positively impact the hydrogen absorption rate of MH storage systems. A novel semi-cylindrical coil is first designed and optimized for hydrogen storage and embedded as an internal heat exchanger with air as the heat transfer fluid (HTF). The effect of novel heat exchanger configurations is analyzed and compared with normal helical coil geometry, based on various pitch sizes. Furthermore, the operating parameters of MH storage and HTF are numerically investigated to obtain optimal values. ANSYS Fluent 2020 R2 is utilized for the numerical simulations. Results from this study demonstrate that MH storage performance is significantly improved by using a semi-cylindrical coil heat exchanger (SCHE). The hydrogen absorption duration reduces by 59% compared to a normal helical coil heat exchanger. The lowest coil pitch from SCHE leads to a 61% reduction of the absorption time. In terms of operating parameters for the MH storage with SCHE, all selected parameters provide a major improvement in the hydrogen absorption process, especially the inlet temperature of the HTF. A move away from fossil fuel-based energy resources towards renewable forms of energy is underway at a global scale. Since many forms of renewable energy provide electricity in a dynamic way, energy storage is required to balance load. Hydrogen-based energy storage is receiving much attention for this purpose, not least because hydrogen can be employed as a 'green' alternative fuel and energy storage medium, because of its characteristics and portability1. Furthermore, hydrogen also offers a higher energy capacity per mass compared to fossil fuels2. There are four main types of hydrogen energy storage: compressed gas, underground storage, liquid storage, and solid storage. Compressed hydrogen gas is the main type that has been used in fuel-cell vehicles such as buses and forklifts. However, this storage provides a low volumetric hydrogen density (around 0.089 kg/m3) and presents safety concerns regarding high operating pressure3. Liquid storage will store hydrogen in liquid form, based on the converting process with a low temperature and ambient pressure. However, there is around 40% energy loss during the liquefaction process. Moreover, this technique is also known for higher energy consumption as well as being time-consuming compared to the solid storage technique4. Solid storage is a feasible option for the hydrogen economy that stores hydrogen by combining it within solid materials through absorption and releasing hydrogen through desorption5. Metal hydride (MH) is one of the solid material storage technologies that has recently attracted significant interest in fuel cell applications because of having a high hydrogen capacity, low operating pressure, and low cost compared to liquid storage, for both stationary and mobile applications6,7. Moreover, MH materials also offer safe performance as high-volume efficiency storage8. However, there is one problem that limits MH performance: MH reactors suffer from low thermal conductivity9, resulting in slow hydrogen absorption and desorption. Appropriately transferring heat during the exothermic and endothermic reactions is the key to improving MH reactor performance. For the hydrogen charging process, the generated heat must be removed from the reactor in order to control the hydrogen charging flow at the desired rate with the maximum storage capacity10. In contrast, heat is required to improve the hydrogen release rate during the discharging process. To improve the heat and mass transfer performances, many researchers have studied the design and optimization based on several factors including operating parameters, MH structure, and MH optimization11. MH optimization can be done by adding high thermal conductivity materials such as the metal foams into the MH bed12,13. By this method, the effective thermal conductivity can be increased from 0.1 up to 2 W/mK10. However, adding solid material significantly reduces the MH reactor capacity. For the operating parameters, improvements can be achieved by optimization of the initial operating conditions of the MH bed and heat transfer fluid (HTF). The MH structure can be optimized by the reactor's geometry and the arrangement of heat exchanger designs14. In terms of heat exchanger configuration of the MH reactor, approaches can be classified into two types. These are an internal heat exchanger, which is embedded in the MH bed, and an external heat exchanger such as fins, cooling jacket and water bath that cover the MH bed15. For external heat exchanger, Kaplan16, analyzed the performance of a MH reactor by employing cooling water as a jacket to reduce the temperature inside the reactor. The results were compared to a reactor with 22 circular fins and another reactor that cools by natural convection. They claimed that having a cooling jacket significantly reduced MH temperature resulting in a better absorption rate. The numerical study of the MH reactor with water jacket from Patil and Gopal17, indicated that the hydrogen supply pressure and temperature of HTF are the key parameters to affect the hydrogen absorption and desorption rates. Increasing heat transfer area by adding fins and heat exchangers embedded inside MHs are key for improving heat and mass transfer characteristics that lead to the enhancement of MH storage performance18. Several internal heat exchanger configurations (straight tube and helical coil tube) have been developed in order to circulate cooling fluid throughout the MH reactor19,20,21,22,23,24,25,26. With an internal heat exchanger, the cooling or heating fluid will transfer local heat inside the MH reactor during the hydrogen sorption processes. Raju and Kumar27, employed several straight tubes as heat exchangers to improve MH performance. Their results indicated that the absorption time was reduced when using straight tubes as heat exchangers. Similarly, using a straight tube also reduced the hydrogen desorption time28. A higher flow rate of cooling fluid increases hydrogen charging and discharging rates29. However, increasing the number of cooling tubes positively affects MH performance rather than the flow rate of cooling fluid30,31. Raju et al.32, investigated the performance of multi-tube heat exchangers inside the reactor by using LaMi4.7Al0.3 as MH materials. They reported that the operating parameters significantly affect the absorption process, especially supply pressure, followed by HTF flow rate. However, the absorption temperature was found to be less significant. The performance of MH reactors was further improved by utilizing a helical coil heat exchanger, as it enhances the heat transfer compared to straight tubes. This is because of secondary circulations that result in better heat removal from the reactor25. Moreover, the helical tube provides more surface area for heat removal from the MH bed to the cooling fluid. This method also produces a more uniform distribution of the heat transfer tubes when it is embedded inside the reactor33. Wang et al.34, studied the effect of hydrogen absorption duration by adding a helical coil in the MH reactor. Their results indicated that the absorption time decreased when increasing the heat transfer coefficient of the heat transfer fluid. Wu et al.25, studied the performance of a MH reactor based on Mg2Ni and helical coil heat exchanger. Their numerical study showed a reduction in the reaction time. The enhancement of the heat transfer mechanism in a MH reactor is based on a smaller ratio of helical pitch to the helical diameter and non-dimensional pitch. The experimental study of using a helical coil as an internal heat exchanger by Mellouli et al.21 proved that the initial temperature of HTF significantly affects the improvement of hydrogen absorption and desorption times. The combination of various internal heat exchangers has been made by several studies. Eisapour et al.35, studied MH storage by employing a helical coil heat exchanger along with a central return tube in order to improve the hydrogen absorption process. Their results indicated that a helical tube along with a central return tube significantly improved heat exchanged between cooling fluid and MH. A lower pitch of the helical tube and a higher tube diameter increased the heat and mass transfer rate. Ardahaie et al.36, employed flat spiral tube planes as a heat exchanger for heat transfer enhancement inside a reactor. They reported that the absorption duration was reduced by increasing the number of flat spiral tube planes. The combination of various internal heat exchangers has been made by several studies. Dhaou et al.37, improved the MH performance by employing both helical coil heat exchanger and fins. Their results showed that this technique reduces hydrogen refilling time which is a 2 times reduction comparing to without fins. The annular fin was incorporated with the cooling tube and embedded inside the MH reactor38. The results from this study showed that this combination technique obtains more uniform heat transfer compared to the MH reactor without using fin. However, combining various heat exchangers will negatively affect the gravimetric and volumetric of the MH reactor. A comparison of different heat exchanger configurations was made by Wu et al.18. These included a straight tube, fins, and helical coil. The authors reported that the helical coil has the best effects on the heat and mass transfer improvements. Similarly, a double coiled tube has a better effect on the heat transfer enhancement compared to a straight tube, spiral tube, and straight tube incorporating with spiral tube39. The study from Sekhar et al.40, proved that using a helical coil as an internal heat exchanger and an external cooling jacket with fins obtained a similar improvement in hydrogen absorption. From the above mentioned example, using a helical coil as an internal heat exchanger offers a better heat and mass transfer improvement compared to other heat exchangers, especially straight tube and fin. Therefore, the aim of this study is to further develop a helical coil to increase heat transfer performance. A novel semi-cylindrical coil has been firstly developed from the traditional helical coil for MH storage. The expectation from this study is to enhance hydrogen storage performance due to the structure of a novel heat exchanger that provides a better heat transfer area arrangement by considering the constant volume of the MH bed and HTF tube. The storage performance of this novel heat exchanger is then compared with a normal helical coil heat exchanger based on various coil pitches. From the available literature, the operating conditions and coil pitch are the main factors that affect the MH reactor's performance. To optimize the design of this novel heat exchanger, the effect of coil pitch on the hydrogen absorption time and the MH volume is investigated. Furthermore, to understand the relationship between a novel semi-cylindrical coil and the operating conditions, the secondary aims of this present study are to investigate the reactor's performance based on various operating parameter ranges and identify an appropriate value for each operating parameter. The performance of hydrogen energy storage in this study is investigated based on two heat exchanger configurations (including a helical tube for case 1 to case 3 and a semi-cylindrical tube for case 4 to case 6), and sensitivity analysis on the operating parameters. The performance of a MH reactor is firstly examined based on the helical tube as a heat exchanger. Both HTF tube and the outer shell of the MH reactor are made of stainless steel. It should be noted that the size of MH reactor and the diameter of the HTF tube is constant for all cases, while the HTF pitch sizes vary. In this section, the impact of HTF coil pitch sizes is analyzed. The height and outer diameter of the reactor are 110 mm and 156 mm, respectively. The diameter of HTF tube is fixed as 6 mm. The detail regarding a schematic diagram of MH reactors with a helical tube and two semi-cylindrical tubes can be found in the Supplementary section. Metal hydride reactor with helical coil heat exchanger and semi-cylindrical coil heat exchanger Figure 1a presents the MH reactors with a helical tube and its dimensions. All geometrical parameters are provided in Table 1. The total helical tube volume and MH volume are approximately 100 cm3 and 2000 cm3, respectively. From this MH reactor, air as the HTF is injected from the bottom part into the porous MH reactor through a helical tube, while hydrogen is injected from the upper surface of the reactor. Characteristics of selected geometries for metal hydride reactors. (a) With helical tube heat exchanger, and (b) with semi-cylindrical tube heat exchanger. Table 1 Geometrical characteristics of MH reactors for the helical tube (case 1 to case 3) and the semi-cylindrical tube (case 4 to case 6). In the second part, the performance of the MH reactor is then investigated based on the semi-cylindrical tubes as heat exchangers. Figure 1b shows the MH reactors with two semi-cylindrical tubes and their dimensions. Table 1 presents all geometrical parameters for a semi-cylindrical tube that are kept constant except the pitch sizes. It should be noted that the semi-cylindrical tube from case 4 was designed by considering the constant volume of HTF tube and MH alloys from the helical tube (case 3). Regarding Fig. 1b, air is also injected from the bottom part for both HTF semi-cylindrical tubes, whereas hydrogen is injected from the opposite direction of MH reactor. Due to the new design of the heat exchanger, the objective of this section is to identify appropriate initial values for the operating parameters of the MH reactor that is incorporated with SCHE. For all cases, air is employed as the HTF to remove the heat from the reactor. Among HTFs, air and water are commonly selected as the HTF for the MH reactor due to having a low cost and less environmental impact. Due to a high operating temperature range of magnesium-based alloy, air is selected as the HTF for the present study. Moreover, it also has better flow characteristics compared to other liquid metals and molten salt41. Table 2 represents the properties of air at 573 K. For sensitivity analysis, only the best configuration of MH-SCHE performance case (among case 4 to case 6) is then applied to this section. This section is evaluated based on various operating parameters, including an initial temperature of the MH reactor, loading pressure of hydrogen, inlet temperature of HTF, and the Reynolds number, which is calculated by changing the velocity of the HTF. All operating parameters for sensitivity analysis are included in Table 3. Table 2 Thermo-physical properties of air at 573 K35. Table 3 Operating conditions for sensitivity analysis. This section describes all the necessary governing equations for the hydrogen absorption process, turbulent flow and heat transfer of the heat transfer fluid. To simplify the solution of the hydrogen absorption reaction, the following assumptions are made and provided; During the absorption process, the thermo-physical properties of hydrogen and metal hydride are constant40. The radiation heat transfer is neglected in the metal hydride reactor42. Hydrogen is considered as an ideal gas, local thermal equilibrium conditions are therefore considered43,44. The pressure gradient effect of hydrogen injection is negligible45. $$N=\frac{{\uplambda }_{e}M{L}_{gas}^{2}\mu }{{P}_{aeq}\frac{{\Delta H}^{2}}{{RT}^{2}}{\rho }_{g}K{L}_{heat}^{2}}$$ where ${L}_{gas}$ is the tank radius and ${L}_{heat}$ is the axial height of the tank. The hydrogen flow in the tank can be omitted in the simulation without obtaining a significant error when N is less than 0.0146. From this present study, N is far lower than 0.1. Therefore, the pressure gradients effect is negligible. The reactor's walls for all cases are well insulated. Thus, there is no heat transfer between the reactor and the ambient47. Magnesium-based alloys are known for having favourable hydrogeneration properties as well as a high hydrogen storage capacity, that is up to 7.6 wt%8. In terms of solid-state hydrogen storage applications, these alloys are also known as lightweight materials. Moreover, they also have excellent heat resistivity and good recyclability8. Among several magnesium-based alloys, magnesium-nickel alloys based on Mg2Ni is one of the most suitable choices for MH storage due to the hydrogen storage capacity that can be up to 6 wt%. Mg2Ni alloys also provide faster kinetics of absorption and desorption processes compared to magnesium hydride48. Therefore, Mg2Ni is selected in this study as the metal hydride material. Governing equations Absorption process The energy equation is expressed based on the thermal equilibrium between hydrogen and Mg2Ni hydride as25: $$\frac{\partial \left({\left(\rho {C}_{p}\right)}_{e,MH}T\right)}{\partial t}=\nabla \cdot \left({\uplambda }_{e,MH}\nabla T\right)+\frac{{\rho }_{MH}wt\left(1-\varepsilon \right)\Delta H}{{M}_{{H}_{2}}}\frac{dX}{dt},$$ where the effective heat capacity and conductivity are given as: $${\left(\rho {C}_{p}\right)}_{e,MH}={\varepsilon }_{MH}\times {\rho }_{{H}_{2}}\times {C}_{p,{H}_{2}}+\left(1-{\varepsilon }_{MH}\right)\times {\rho }_{MH}\times {C}_{p,MH}$$ $${\uplambda }_{e,MH}= {\varepsilon }_{MH}\times {\uplambda }_{H2}+\left(1-{\varepsilon }_{MH}\right)\times {\uplambda }_{MH}.$$ The hydrogenation reaction of Mg2Ni bed ($\Delta H$) is determined as: $${Mg}_{2}Ni+{2H}_{2}\leftrightarrow {Mg}_{2}Ni{H}_{4}+\Delta H.$$ X is the amount of hydrogen absorption on the metal surface in $wt\%$ that is calculated from the kinetic equation in the absorption process $\frac{dX}{dt}$ as follow49: $$\frac{dX}{dt}={C}_{a}\left(\frac{{P}_{{H}_{2}}-{P}_{a,eq}}{{P}_{a,eq}}\right)\left(\frac{x-{x}_{f}}{{x}_{0}-{x}_{f}}\right){exp}^{\left(\frac{-{E}_{a}}{RT}\right)},$$ where ${C}_{a}$ denotes the reaction rate and ${E}_{a}$ refers to the activation energy. ${P}_{a,eq}$ is the equilibrium pressure inside the metal hydride reactor for the absorption process which is determined using the Van't Hoff equation as follows25: $$\frac{{P}_{a,eq}}{{P}_{ref}}={exp}^{\left(\frac{\Delta H}{R{T}_{m}}-\frac{\Delta S}{R}\right)},$$ where ${P}_{ref}$ is the reference pressure of 0.1 MPa. $\Delta H$ and $\Delta S$ are the reaction enthalpy and reaction entropy, respectively. The properties of Mg2Ni alloys and hydrogen are provided in Table 4. A list of nomenclatures can be found in the Supplementary section. Table 4 Thermo-physical properties of hydrogen and metal hydride in model equations25,51. Heat transfer fluid The fluid flow is considered as turbulent due to its velocity and the Reynolds number (Re), which are 78.75 m s−1 and 14,000, respectively. The realizable k–ε turbulence model is selected in this present study. It was observed that this method provides more accuracy when compared with other k–ε methods and also provides less computational time than the RNG k–ε method50,51. Details about the governing equation for heat transfer fluid can be found in the Supplementary section. Initial and boundary conditions At the initial time, uniform conditions are applied for the temperature inside the MH reactor with the average concentration of hydrogen as 0.043. The outer boundary of the MH reactor is assumed to be well insulated. The magnesium-based alloys usually require a high operating temperature for the reaction to store and release the hydrogen from the reactor. For the Mg2Ni, this alloy requires the temperature range of 523–603 K to achieve the maximum absorption and the temperature range of 573–603 K to complete the desorption52. However, the experimental study by Muthukumar et al.53 proved that using the operating temperature at 573 K could achieve the maximum hydrogen storage capacity of the Mg2Ni storage which is equal to its theoretical capacity. Therefore, the temperature at 573 K is selected for the initial temperature of the MH reactor in the present study. $${T}_{MH}={T}_{0}=573\, {\mathrm{K}},\,\,\,{P}_{0}=1.8\, {\mathrm{MPa}},\,\,\,{x}_{0}=0.043$$ At the shell of the reactor: $$\frac{\partial {T}_{MH}}{\partial \overrightarrow{n}}=0,$$ At the heat transfer fluid inlet $${u}_{x}={u}_{z}=0,\,\,\,{u}_{y}={u}_{in},\,\,\,T={T}_{in},$$ At the heat transfer fluid outlet $$p={p}_{s}={p}_{a}.$$ Grid independency Various grid sizes are established in order to verify and achieve reliable results. The average temperature at selected locations for the hydrogen absorption process from four different element numbers are provide in Fig. 2. It is worth mentioning that only one case for each configuration is selected for grid independency checks due to having similar geometries. The same meshing methods are applied to other cases. Therefore, case 1 for the helical tube and case 4 for the semi-cylindrical tube are chosen. Figure 2a,b demonstrates the average temperature in the reactor from case 1 and case 4, respectively. The three selected locations represent the bed temperature contour at the top, middle, and bottom parts of the reactor. From temperature contours at the selected locations, the average temperature becomes stable and shows minor changes at the element numbers of 428,891 and 430,599 for case 1 and case 4, respectively. Therefore, these grid sizes are selected for further computational calculations. The details about the average bed temperature for the hydrogen absorption process for various mesh size and the successively refined grids for these two cases can be found in the Supplementary section. Average bed temperature at selected location for the hydrogen absorption process in the metal hydride reactor under various grid numbers. (a) Average temperature at selection location for case 1, and (b) average temperature at selected location for case 4. Model validation and numerical schemes Validation for metal hydride bed and turbulence model The magnesium-based metal hydride reactor from this present study is validated against experimental results from Muthukumar et al.53. In their study, they employed Mg2Ni alloy for hydrogen storage with a stainless-steel tube. The copper fins were used to improve the heat transfer inside the reactor. Figure 3a shows the comparison of the average bed temperature for the absorption process between the experimental study and the present study. The selected operating conditions from this experiment are 573 K for the initial MH temperature and 2 MPa for supply pressure. According to Fig. 3a, it is clearly shown that there is a good agreement between this experimental and present results in terms of the average bed temperature. Model validation. (a) Code validation of the Mg2Ni metal hydride reactor by the comparison of present study and experimental works from Muthukumar et al.52, and (b) validation study of the turbulence model in helical tube by the comparison of present study and Kumar et al.54. To validate the turbulence model, the results from this present study are compared with the experimental results from Kumar et al.54, in order to validate the selected turbulence model. Kumar et al.54, studied the turbulent flow in a tube-in-tube helical heat exchanger. Water was employed as both hot and cold fluids which were injected from opposite directions. The hot and cold fluids temperature was 323 K and 300 K, respectively. The Reynolds number for the hot fluid varied from 3100 to 5700, and 21,000 to 35,000 for the cold fluid. The Dean number for the hot fluid was 550–1000, and 3600–6000 for the cold fluid. The diameter of the inner tube (for hot fluid) and outer tube (for cold fluid) were 0.0254 m and 0.0508 m, respectively. The helical coil diameter and pitch were 0.762 m, and 0.100 m. Figure 3b shows the comparison of the experimental and present results in terms of various Nusselt numbers and Dean numbers for hot fluid at the inner tube. Three different turbulent models were performed and compared with experimental results. As shown in Fig. 3b, the results from the realizable k–ε turbulence model obtain a good agreement with experimental data. Therefore, this model was selected for this present study. Numerical schemes The numerical simulation in the present study is performed by utilizing the ANSYS Fluent 2020 R2. User-defined functions (UDFs) were written and applied as a source term of the energy equation in order to calculate the kinetic characteristics of the absorption process. The PRESTO scheme55 and PISO method56 are employed for the pressure–velocity coupling and pressure correction. The Green-Gauss cell-base is chosen for the variable's gradients. The momentum and energy equations are solved by the second-order upwind method. In terms of under relaxation factors, 0.5, 0.7, 0.7 are set for pressure, velocity components and energy, respectively. The standard wall function was applied for the HTF in the turbulence model. This section provides the results of numerical simulation of the heat transfer improvement inside the MH reactor by using a helical coil heat exchanger (HCHE) and semi-cylindrical coil heat exchanger (SCHE) for the hydrogen absorption process. The effect of the HTF pitch on the reactor bed temperature and absorption duration is analyzed. The critical operating parameters for the absorption process are investigated and presented in the sensitivity analysis section. Geometrical parameters Effect of helical coil pitch Three heat exchanger configurations with different pitches were examined in order to study the effect of coil pitch on the heat transfer in the MH reactor. Three different pitches of 15 mm, 12.86 mm, and 10 mm are assigned as case 1, case 2, and case 3, respectively. It should be noted that the tube diameter is fixed as 6 mm under the initial temperature of 573 K and loading pressure of 1.8 MPa for all cases. Figure 4 presents the average bed temperature and hydrogen concentration of the MH bed during the hydrogen absorption process for case 1 to case 3. In general, the reaction between metal hydride and hydrogen is exothermic for the absorption process. Consequently, the bed temperature rapidly increases due to the initial moments when hydrogen is first injected into the reactor. The bed temperature is continually increasing until reaching the maximum value and gradually decreasing because the heat is removed by the HTF, which has a lower temperature and acts as a cooling fluid. As shown in Fig. 4a, the bed temperature rapidly increases and continually decreases due to the previous explanation. The hydrogen concentration for the absorption process is usually based on the bed temperature of the MH reactor. When the average bed temperature decreases to certain temperatures, the metal surface will absorb the hydrogen. This is because of the acceleration of physisorption, chemisorption, diffusion of hydrogen and its hydride formation in the reactor36. It can be seen in Fig. 4b, the rate of hydrogen absorption from case 3 is lower than other cases due to having a lower pitch value of the coil heat exchanger. This results in higher tube length in total and higher heat transfer area of HTF tube. The absorption time from case 1 is 46,276 s for the average hydrogen concentration as 90%. Comparing to the absorption duration from case 1, the absorption duration for case 2 and case 3 decreases 724 s and 1263 s, respectively. The temperature contours and hydrogen concentration contours at selected locations of the HCHE-MH bed are provided in the Supplementary section. Effect of coil pitch on average bed temperature and hydrogen concentration. (a) Average bed temperature for helical coil pitch, (b) hydrogen concentration for helical coil pitch, (c) average bed temperature for semi-cylindrical coil pitch, and (d) hydrogen concentration for semi-cylindrical coil pitch. Effect of semi-cylindrical coil pitch To improve the heat transfer performance of the MH reactor, two SCHEs are designed under a constant volume of MH (2000 cm3) and helical coil heat exchanger (100 cm3) from case 3. This section also considers the effect of coil pitch as 15 mm for case 4, 12.86 mm for case 5, and 10 mm for case 6. Figure 4c,d presents the average bed temperature and concentration for the hydrogen absorption process based on initial temperature at 573 K and loading pressure at 1.8 MPa. According to the average bed temperature from Fig. 4c, a lower coil pitch from case 6 significantly results in lower temperature compared to the other two cases. The lower bed temperature leads to higher hydrogen concentrations (see Fig. 4d) for case 6. The hydrogen absorption time for case 4 is 19,542 s which is over 2-times lower than using HCHE as case 1–3. In addition, the absorption time with lower pitch values from case 5 and case 6 also reduces 378 s and 1515 s compared to case 4. The temperature contours and hydrogen concentration contours at selected locations of the SCHE-MH bed are provided in the Supplementary section. Performance comparisons between the MH reactors with helical coil heat exchanger and semi-cylindrical coil heat exchanger To study the performance of two heat exchanger configurations, the temperature profiles at three selected locations are made and presented in this section. The MH reactor with HCHE from case 3 is selected to compare with the MH reactor incorporated SCHE from case 4 as having constant MH volume and tube volume. Operating conditions for this comparison are 573 K as an initial temperature and 1.8 MPa as loading pressure. Figure 5a,b presents all three selected locations for temperature profiles from case 3 and case 4, respectively. Figure 5c represents temperature profiles and bed concentration after 20,000 s of the hydrogen absorption process. According to Line 1 from Fig. 5c, the temperature around HTF from case 3 and case 4 reduces because of having convective heat transfer from the cooling fluid. This leads to a higher hydrogen concentration around this area. However, using two SCHEs results in higher bed concentration. A more rapid kinetic reaction was found around the HTF area for case 4. Furthermore, a maximum concentration of 100% was also found around this area. From Line 2, located at the middle part of the reactor, the temperature from case 4 is significantly lower than for case 3 for all locations except at the center of the reactor. This leads to the maximum amount of hydrogen concentration for case 4 excepted around the center of the reactor where it is far away from the HTF. However, the concentration for case 3 is insignificantly changed. The huge difference in temperature and bed concentration was observed at Line 3, which is near the HTF inlet. The bed temperature from case 4 significantly reduces, resulting in full hydrogen concentration at this area, while the concentration line from case 3 still fluctuates. This is due to the heat transfer acceleration from SCHEs. The details and discussion regarding the comparison of the average temperature of the MH bed and the HTF tube between case 3 and case 4 are provide in the Supplementary section. Temperature profiles and bed concentration at selected locations of the metal hydride reactor. (a) Selected locations for case 3, (b) selected locations for case 4, and (c) temperature profiles and bed concentration at selected locations after 20,000 s of hydrogen absorption process for case 3 and case 4. Figure 6 displays the comparison of average bed temperatures (see Fig. 6a) and hydrogen concentrations (see Fig. 6b) during the absorption process between HCHE and SCHE. From this figure, it is evident that the MH bed temperature significantly reduces because of an increasing of heat transfer area. Having more heat removal rate from the reactor leads to a faster hydrogen absorption rate. Although both heat exchanger configurations have a similar volume, the hydrogen absorption time based on SCHE as case 4 significantly reduces at 59% compared to using HCHE as case 3. For more analysis, the hydrogen concentrations from both heat exchanger configurations are displayed as contours in Fig. 7. This figure shows that the hydrogen starts to be absorbed in the bottom part around the HTF inlet for both cases. A higher concentration was found at HTF areas, while a lower concentration was observed at the center of the MH reactor due to being far away from the heat exchangers. At 10,000 s, the hydrogen concentration from case 4 is significantly higher than case 3. At 20,000 s, the average hydrogen concentration inside the reactor rises to 90% for case 4, while there is only 50% hydrogen for case 3. This can be explained by the reason that incorporating two SCHEs have a higher effective heat removal which leads to having lower temperature inside the MH bed. Thus, more equilibrium pressure declines inside the MH bed and then causes faster hydrogen absorption. Comparison of average bed temperature and hydrogen concentrations between two heat exchanger configurations as case 3 and case 4. Comparison of hydrogen concentrations at 500 s, 2000s, 5000 s, 10,000 s, and 20,000 s after the start of the hydrogen absorption process between case 3 and case 4. Table 5 summarizes the hydrogen absorption durations for all cases. Moreover, the hydrogen absorption time in percentage is also presented in this table. The percentage is calculated based on the absorption time from case 1. From this table, the absorption time from the MH reactor with HCHE is around 45,000 to 46,000 s, while the absorption time incorporating SCHE is around 18,000 to 19,000 s. When compared to case 1, the absorption time from case 2 and case 3 reduces only 1.6% and 2.7%, respectively. By employing SCHE instead of HCHE, the absorption time significantly reduces by 58 to 61% from case 4 to case 6. It is evident that incorporating SCHE inside the MH reactor significantly enhances the hydrogen absorption process and MH reactor performance. Although inserting the heat exchanger inside the MH reactor will reduce the storage capacity, this technique obtains a significant heat transfer improvement compared to other techniques. Moreover, the reduction of pitch values will increase the SCHE volume which leads to reducing the MH volume. In case 6, which has the highest SCHE volume, there is only a 5% reduction in the MH volume capacity compared to case 1, which has the lowest HCHE volume. Furthermore, during the absorption process, case 6 indicates faster and better performances with a reduction of 61% in absorption duration. Therefore, case 6 is selected to further investigation regarding sensitivity analysis. It should be noted that the long hydrogen absorption time is due to the storage capacity which contains the MH volume at around 2000 cm3. Table 5 Summary of hydrogen absorption times for all six cases. Sensitivity analysis of operation conditions The operating parameters during the reaction process are essential factors that can be positively or negatively impact the performance of MH reactor in actual utilization. The sensitivity analysis is considered in this study to identify appropriate initial values of operating parameters for the MH reactor that is incorporated with SCHE, this section investigates four main operating parameters based on the best reactor configuration from case 6. The results from all operating conditions are presented in Fig. 8. Hydrogen concentration diagram for various operating conditions in the use with the semi-cylindrical coil heat exchanger. (a) Loading pressures, (b) initial bed temperatures, (c) Reynolds numbers of heat transfer fluid, and (d) inlet temperatures of heat transfer fluid. Effect of the loading pressure on the hydrogen absorption process Four different loading pressures of 1.2 MPa, 1.8 MPa, 2.4 MPa, and 3.0 MPa were chosen based on the constant initial temperature at 573 K and HTF flow velocity at 14,000 of Reynolds number. Figure 8a reveals the effect of loading pressure and the SCHE on the hydrogen concentration with respect to time. The absorption time is reduced by an increment of loading pressure. Employing exerted hydrogen pressure with 1.2 MPa is the worst case for the hydrogen absorption process with the absorption duration over than 26,000 s for achieving 90% of hydrogen absorption. However, higher loading pressure results in the reduction of absorption times by 32 to 42% from 1.8 to 3.0 MPa. This is due to higher initial hydrogen pressure causing a larger difference between the equilibrium pressure and exerted pressure. Thus, this generates a greater driving force for hydrogen absorption kinetic25. At the initial moment, the hydrogen is rapidly absorbed because of the greater difference between the equilibrium pressure and exerted pressure57. With loading pressure at 3.0 MPa, 18% of the hydrogen is rapidly stored within the first 10 s. The hydrogen is stored at 90% of the reactor at the final stage with 15,460 s. However, the absorption time is significantly reduced by 32% from the loading pressure at 1.2 to 1.8 MPa. Other higher pressures have less effect on the improvement of the absorption time. Consequently, the loading pressure at 1.8 MPa is recommended for the MH-SCHE reactor. The hydrogen concentration contours for various loading pressures at 15,500 s are provided in the Supplementary section. Effect of the initial temperature on the hydrogen absorption process Selecting the appropriate initial temperature of the MH reactor is one of the main factors that influence the hydrogen sorption process, as it will affect the driving force of the hydride-producing reaction. To study the effect of SCHE on the initial temperature of the MH reactor, four different temperatures were chosen under constant loading pressure at 1.8 MPa and Reynolds number at 14,000 of HTF. Figure 8b presents the comparison of various initial temperatures, including 473 K, 523 K, 573 K, and 623 K. In fact, the Mg2Ni alloy will have effective performance for the hydrogen absorption process when the temperature is above 230 ℃ or 503 K58. However, the temperature will rapidly increase at the initial moment when hydrogen is injected. Thus, the MH bed temperature will be over 523 K. For this reason, hydride formation is then promoted due to the absorption rate enhancement53. From Fig. 8b, the hydrogen is absorbed faster when the initial temperature of the MH bed is reduced. When having a lower initial temperature, it leads to generating lower equilibrium pressure. The larger different pressures between equilibrium pressure and exerted pressure cause a faster hydrogen absorption process. By 473 K initial temperature, the hydrogen is rapidly absorbed to 27% within the first 18 s. Moreover, the absorption time from lower initial temperatures is also reduced from 11 to 24% compared to the initial temperature at 623 K. The absorption time with the lowest initial temperature at 473 K is 15,247 s which is similar to the best case of loading pressure. However, reducing initial reactor temperature results in lower hydrogen storage capacity. The initial temperature of MH reactor should not be less than 503 K53. Furthermore, the maximum hydrogen storage capacity of 3.6 wt% can be achieved by using the initial temperature of 573 K53. Focusing on the hydrogen storage capacity and the duration of the absorption, there is only a 6% time reduction by the temperature between 523 and 573 K. Therefore, the temperature at 573 K is recommended for the initial temperature of the MH-SCHE reactor. However, the effect of initial temperature on the absorption process is less significant compared to loading pressure. The hydrogen concentration contours for various initial temperatures at 15,500 s are provided in the Supplementary section. Effect of the Reynolds number of the heat transfer fluid on the hydrogen absorption process The flow velocity is one of the essential parameters for both hydrogeneration and dehydrogenation because of its ability that affect the turbulence and heat removal or heat supplying regarding hydriding and dehydriding processes59. A large flow velocity will generate a turbulent stage and cause faster fluid flow through the HTF tube. This reaction will result in faster heat transfer. Various inlet velocities of HTF are calculated based on the Reynolds number as 10,000, 14,000, 18,000, and 22,000. The initial temperature of MH bed is fixed at 573 K with the loading pressure at 1.8 MPa. The result from Fig. 8c proves that utilizing a higher Reynolds number incorporated with the SCHE leads to a faster absorption rate. With the increase of the Reynolds number from 10,000 to 22,000, the absorption time reduces approximately 28 to 50%. The absorption time from the Reynolds number at 22,000 is 12,505 s which is lower than the absorption time based on various initial temperatures and loading pressures. The hydrogen concentration contours for various Reynolds numbers of the HTF at 12,500 s are presented in the Supplementary section. Effect of the initial temperature of the heat transfer fluid on the hydrogen absorption process The effect of the SCHE on the initial HTF temperature is analyzed and displayed in Fig. 8d. Four initial temperatures of 373 K, 473 K, 523 K, and 573 K are chosen for this analysis under the initial MH temperature at 573 K and loading pressure of hydrogen at 1.8 MPa. Figure 8d indicates that the decrease in inlet HTF temperature leads to a shorter absorption time. Compared to the base case with inlet temperature at 573 K, the absorption time reduces around 20%, 44% and 56% for inlet temperature of 523 K, 473 K, and 373 K, respectively. At 6917 s with the initial temperature of the HTF at 373 K, there is a 90% of hydrogen concentration inside the reactor. This can be explained by the enhancement of convective heat transfer between the MH bed and the HTF. A lower HTF temperature will increase the heat removal rate and result in an improvement of the hydrogen absorption rate. Among all operating parameters, improving the MH-SCHE reactor's performance by increasing the inlet temperature of the HTF is the most suitable method as the end of the absorption process is lower than 7000 s while the minimum absorption time from other methods is greater than 10,000 s. The hydrogen concentration contours for various initial temperature of the HTF at 7000 s are presented in the Supplementary section. The present study first introduces a novel semi-cylindrical coil heat exchanger embedded inside the metal hydride storage unit. The hydrogen absorption capacity of the proposed system is investigated under different heat exchanger configurations. The effect of operating parameters between the metal hydride bed and heat transfer fluid on the heat exchanged are examined, in order to find optimal conditions for the metal hydride storage with a novel heat exchanger. The key findings from this study are summarized as follows: Using a semi-cylindrical coil heat exchanger, heat transfer performance is improved as it has more uniform heat distribution in the magnesium bed reactor resulting in a better hydrogen absorption rate. Under the constant volume of the heat exchanger tube and metal hydride, the absorption reaction time is significantly reduced by 59% compared to a normal helical coil heat exchanger. Reducing the pitch size of coil heat exchangers positively affects the absorption duration because of having more heat transfer area. Among other pitch values, there is a 61% reduction of hydrogen absorption time when using semi-cylindrical coil heat exchangers with a pitch size of 10 mm. With this size, there is around a 5% reduction in the metal hydride volume capacity compared to the highest pitch size. Therefore, using a semi-cylindrical coil heat exchanger with 10 mm pitch size is recommended. Increasing the loading pressure of hydrogen injection leads to a lower hydrogen absorption time. The absorption duration significantly reduces, by 32%, with loading pressure at 1.8 MPa compared to 1.2 MPa. However, other higher values have less effect on the absorption duration. Therefore, the loading pressure at 1.8 MPa is recommended for the storage with a new heat exchanger. The lower initial temperature of the metal hydride bed results in a faster hydrogen absorption rate. However, to maintain the storage capacity with a Mg2Ni-based alloy, the initial temperature should not be less than 503 K. Considering the storage capacity and the absorption duration, the initial temperature at 573 K is recommended for the storage with a semi-cylindrical coil heat exchanger. The initial conditions of heat transfer fluid are the main parameters that significantly affect the improvement of storage performance with a novel heat exchanger. Higher Reynolds number of the heat transfer fluid positively influences hydrogen absorption duration because of having higher fluid flow velocity. Furthermore, a lower inlet temperature of heat transfer fluid also improves the convective heat transfer between the bed and the cooling fluid. By these two parameters, the absorption duration is significantly reduced by 50–56%. The results from this study provide a heat transfer improvement regarding the absorption process of magnesium-based hydrogen energy storage under a novel heat exchanger configuration with optimized operating conditions. The comprehensive study on this proposed system could be beneficial for industrial applications. To improve the hydrogen absorption duration, the metal hydride storage with a novel semi-cylindrical coil heat exchanger will be further incorporated with other heat exchangers in the next study. 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M.S.I. concept, simulation, validation, review and writing, supervision. Correspondence to Mohammad S. Islam. Larpruenrudee, P., Bennett, N.S., Gu, Y. et al. Design optimization of a magnesium-based metal hydride hydrogen energy storage system. Sci Rep 12, 13436 (2022). https://doi.org/10.1038/s41598-022-17120-3 Received: 31 May 2022	CommonCrawl
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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 37B05, 20M20, 37C25, 11B83 Retrieve articles in all journals with MSC (2000): 37B05, 20M20, 37C25, 11B83 Michał Misiurewicz Affiliation: Department of Mathematical Sciences, IUPUI, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216 MR Author ID: 125475 Email: [email protected] Ana Rodrigues Affiliation: Universidade do Minho, Escola de Ciencias, Departamento de Matematica, Campus de Gualtar, 4710-057 Braga, Portugal Email: [email protected] Received by editor(s): November 26, 2003 Additional Notes: The authors were partially supported by NSF grant DMS 0139916. The second author thanks the hospitality of the Department of Mathematical Sciences of IUPUI Communicated by: Michael Handel The copyright for this article reverts to public domain 28 years after publication.	CommonCrawl
Traditional knowledge and cultural importance of Borassus aethiopum Mart. in Benin: interacting effects of socio-demographic attributes and multi-scale abundance Kolawolé Valère Salako ORCID: orcid.org/0000-0002-7817-36871, Francisco Moreira2,3, Rodrigue Castro Gbedomon1, Frédéric Tovissodé1, Achille Ephrem Assogbadjo1,4 & Romain Lucas Glèlè Kakaï1 Eliciting factors affecting distribution of traditional knowledge (TK) and cultural importance of plant resources is central in ethnobiology. Socio-demographic attributes and ecological apparency hypothesis (EAH) have been widely documented as drivers of TK distribution, but their synergistic effect is poorly documented. Here, we focused on Borassus aethiopum, a socio-economic important agroforestry palm in Africa, analyzing relationships between the number of use-reports and cultural importance on one hand, and informant socio-demographic attributes (age category and gender) on the other hand, considering the EAH at multi-scale contexts. Our hypothesis is that effects of socio-demographic attributes on use-reports and cultural importance are shaped by both local (village level) and regional (chorological region level) apparency of study species. We expected so because distribution of knowledge on a resource in a community correlates to the versatility in the resource utilization but also connections among communities within a region. Nine hundred ninety-two face-to-face individual semi-structured interviews were conducted in six villages of low versus high local abundance of B. aethiopum spanning three chorological regions (humid, sub-humid and semi-arid) also underlying a gradient of increasing distribution and abundance of B. aethiopum. Number of use-reports and score of importance of uses of B. aethiopum were recorded in six use-categories including medicine, food, handcraft, construction, firewood, and ceremonies and rituals. Data were analyzed using Poisson and ordered logistic models. Informants listed 121 uses for B. aethiopum: medicine (66 uses), handcraft (16 uses), food (16 uses), construction (12 uses), firewood (6 uses), and ceremonies and rituals (5 uses); but food use was the most culturally important use (2.45 ± 0.03), followed by construction (0.61 ± 0.03), medicinal (0.57 ± 0.03) and handcraft (0.56 ± 0.03), firewood (0.29 ± 0.02), and ceremonies and rituals (0.03 ± 0.01). Food use was the most important for women who were specialized in hypocotyls and fruits collection for commercialization. Men valued more the species for handcrafting, construction, and medicine. The number of use-reports was significantly dependent on age category and gender, and differences between age categories (young, adult, and old) in particular were dependent upon local and regional apparency. In particular, discrepancies among age categories were higher in areas of low abundance and distribution, which may be linked to different speed in the process of knowledge acquisition. In areas of low abundance, the species past abundance was also found instrumental in understanding current knowledge distribution. Findings suggest that studies aiming at understanding relationship between current TK and cultural importance of a resource on one hand and socio-demographic attributes on the other hand should consider the resource current local and regional apparency but further its local past abundance. The study also confirms that B. aethiopum is a socio-economic important species in Benin. The overall trend of biodiversity loss [1] and the need to develop effective strategies for its conservation has led to emergence of several paradigms and principles of conservation. One of them, the principle of "conservation through use or trade" has been proposed as a key mechanism to provide incentives for the conservation of species and habitats by turning them into sources of income [2, 3]. The main idea is that conservation is more successful and livelihoods are improved when social and community beliefs and rights are understood and addressed in conservation programs [4]. This has resulted in increasing interests over local communities which in turn have led to a growing interest in the traditional knowledge (TK) they have on their environment [4, 5]. Ethnobotany, which aims at documenting interactions between humans and plants, has therefore become a core subject of conservation biology [6]. The need to better understand factors that determine spatial and intergenerational variation in TK has emerged, and quantitative tools are increasingly being developed to cope with the related issues [6]. Previous studies have shown that knowledge on the use of plant resources and its actual practices are a compounded effect of socio-demographic attributes, including people's gender and age [4, 7, 8] with women and older people tending to have greater knowledge [8, 9]. Historical gender divisions of space and labor in households and societies [10], and increasing knowledge accumulation through time [6], have been often used respectively to explain such patterns. In addition, the most highly available plants are more likely to be encountered, hence subject to greater experiment and, consequently, broader use and greater local importance [11]. This is referred as the ecological apparency hypothesis (EAH). Although this hypothesis has received mixed support in the literature [12, 13], partly because human culture is more complex to be influenced only by appearance [14], it is still central in ethnobotany [14]. The EAH has been often tested in studies dealing with the compared use of multiple species [15, 16] and rarely used for the study of a single species. In the latter case, the EAH predicts that people living in a landscape of high visibility (abundance) of a species have more knowledge of its uses than people in a landscape of low visibility. However, ecological apparency can be assessed at either local (e.g., village) or larger (e.g., chorological region) scale [17]. At local scale, ecological apparency hypothesis is expected to be a consequence of the direct contact between people and the used resource. However, at the regional scale, the amount of knowledge does not only result from the direct visibility of the species locally but also knowledge exchange between people of different communities/villages trough connectivity and networks. Whether and how local and global visibility of a species affect distribution of knowledge on its uses against age and gender has been poorly investigated. In an area of high abundance of a given resource, we might expect no or little difference of TK between age categories and to some extent between genders because the resource is so common that everyone knows and likely uses it. In contrast, in an area of low abundance, great discrepancies are predicted between both age categories and genders. Understanding such relationship is crucial for conservation biology in general and ethnobiology in particular. For example, this understanding would clarify on whether for documenting TK on a given taxon, sampling area of higher abundance is always better than area of lower abundance. In addition, it will also provide better insights in drivers of knowledge distribution in local communities. There are several evidences that patterns of plant selection and use by local people, as well as the importance of plants, are driven by complex interactions of biophysical, social, cultural, cultual, political, and economic contexts [14, 18], including resource availability [19]; informant age, gender, and ethnic affiliation [20]; urbanization and informant education level [10, 21]; market importance, nutritive value, and number of complementary uses of species [22]; informant social network [23]; and taboos [24]. As such, TK on use of plants and their importance cannot be simplified to only resource abundance and socio-demographic attributes such as age and gender. The overarching goal of this study was rather to examine whether and how both local and regional apparency of a resource mediate gender- and age-related distribution of traditional knowledge on its uses as well as its cultural importance. To our knowledge, this issue has so far been little explored. We used the case study of the palm species Borassus aethiopum Mart. in Benin, West-Africa. B. aethiopum is one of the most important wild palm species in West Africa [25]. Although the overall IUCN threat category of B. aethiopum is least concern (LC), the species suffers from local over-exploitation for palm wine and several other threats (http://www.iucnredlist.org/details/195913/0), hence considered threatened across its distribution range [26,27,28,29]. In Benin, B. aethiopum is found in traditional agroforestry systems and natural forests [30] but faces a serious threat of regeneration, and its populations are aging [26]. Based on IUCN Categories and Criteria of threat, B. aethiopum was categorized as "vulnerable" in Benin because of human disturbances on its populations [26]. Although several ethnobotanical reports exist on the species over its distribution range [28, 31,32,33,34,35], they are often narrowed to a locality or a small part of a country [35] and rarely used quantitative approaches to decipher complex interactions between humans and the species. Yet, such understanding could provide important baseline information for its sustainable use and management. The main research question addressed here is whether (and how) local and regional abundance of B. aethiopum influences the relationships between TK and cultural importance on one hand and socio-demographic attributes (gender and age) on the other hand? We predicted that (1) TK and cultural importance of B. aethiopum increases with increased local and regional apparency, (2) TK and cultural importance of B. aethiopum are influenced by gender and age, and (3) both local and regional apparency influence the relationships between TK and cultural importance of B. aethiopum and socio-demographic attributes, with greater discrepancies between age and gender where the species is less apparent. The study also sought to document the countrywide uses and importance of B. aethiopum in Benin. The study was conducted in Benin (6° 25′ N–12° 30′ and 0° 45′ E–4° E), West Africa (Fig. 1) [36]. Benin is characterized by three contrasting chorological regions [37], northwards: the Guinean region (humid climate), the Sudan-Guinean region (sub-humid climate), and the Sudanian region (semi-arid climate) regions [38]. The country's native vegetation has suffered severe degradation as a result of various intense anthropogenic activities. The vegetation becomes dominated by woodland and savannah northwards. The resident population in 2013 was nearly 10 million inhabitants, unequally distributed across the territory [39]. The population is mainly young (more than 40% are < 15 years old) and slightly female-biased (51.2%) [39]. The local economy is agriculture-based [39]. More than half the population (53.9%) live with less than 1 US dollars per day [40]. The average size of farmland per farmer is 1.7 ha, and more than 1/3 had less than 1 ha [41]. Regardless of socio-cultural groups, women have no or limited access to land [41]. Map of the republic of Benin showing the three chorological regions and the study villages Study species The African fan palm, B. aethiopum (Fig. 2), belongs to family Arecaceae, subfamily Coryphoideae [42]. It is widespread and common across sub-Saharan Africa where it is a well-known and conspicuous component of savannas. B. aethiopum has a large and straight stem to 25 m tall and may reach 80-cm diameter. The fruits are massive, ovoid, and orange at maturity (Fig. 2). The mesocarp is pulpy and fragrant with many longitudinal fibers [25]. In Benin, B. aethiopum is found in all three chorological regions but with great differences in regard with distribution and abundance [30]. Overall, B. aethiopum becomes common with higher abundance northwards, but in all three regions, there exist areas of local low and high abundance [30]. A female tree of B. aethiopum showing its fruits (white circle) in Northern Benin. Credits to Salako et al. [30] Sampling and data collection In Benin, B. aethiopum has a wider distribution and larger abundance (trees ha−1) in the semi-arid region (24.54 ± 1.51) than in the sub-humid region (16.24 ± 1.79), and than in the humid region (7.06 ± 0.56) [30]. However, these chorological region patterns hide strong local differences within each region, where it is possible to identify areas with low and high local abundance. Based on previous studies [30], we therefore identified villages with high (> 20 adult trees ha−1) and low (up to 10 adult trees ha−1) local abundance of B. aethiopum. In each chorological region, we randomly selected one village with high abundance and one with low abundance (Fig. 1). Abundance at chorological regions was assumed as an indicator of the regional apparency, while abundance at village level represented local apparency. Following [43], three age categories were considered (age < 30 years for young; 30 ≤ age < 60 years for adults; age ≥ 60 years for old persons). Gender (men and women) was also considered. Primarily, it was planned to select in each village 30 informants for each combination of gender and age category, making a total of 1080 informants. But because of insufficient informants in some villages, 992 informants participated to the work (Additional file 1). Data were collected using face-to-face individual interviews based on a questionnaire (Additional file 2). The goal of the study in terms of gathering knowledge on B. aethiopum for a PhD research (this study was part of the PhD research of the first author on the conservation biology of B. aethiopum in Benin) was first explained to village authorities and next to each of the informant as to have their consent for participation before starting the interviews. Only individuals that consented to participate in the study were considered. Interviews were conducted with assistance of a local translator when necessary. The questionnaire comprised three main sections. The first was related to informant's socio-demographic information (age, gender, and ethnic affiliations). The second consisted of a free-listing of the use-reports of B. aethiopum, defined as each specific use mentioned by the informant per plant part in the sense of [44]. For example if an informant mentioned use of fruits to cure malaria and the use of leaves to also cure malaria separately, we considered them as two separate use-reports. Use-reports were arranged per plant part in six use-categories adapted from [45]: food, handcraft, construction, firewood, medicine, and ceremonies and rituals. The use-report does not distinguish between "knowledge" and "real use", as various potential uses may be known but real use may be different [46]. To account for that, the third section of the questionnaire focused on the real use of the species by asking the informant to score the six use-categories based on the importance of their actual uses. The score varied from 3 ("high use") to 0 ("not used") with score 1 for "medium use" and score 1 for "low use" [7]. Informants were additionally asked to rank each plant part based on the importance of their actual uses. Each interview lasted between 2 h and 2 h 30 min. Knowledge on the uses of B. aethiopum First, for each use-report of B. aethiopum, the relative frequency of citation defined as how often a use-report was mentioned was calculated using the fidelity level (FL) [47]. Only significant use-report (with FL > 5%) were reported here. $$ \mathrm{FL}\left(\%\right)=100\times x/n $$ where x is the number of informants who mentioned a specific use and n is the total number of informants. Knowledge on uses of B. aethiopum was measured using the relative use-value (UV) [7] which is a modified version of the use-value method introduced by [11]. This modified version of UV allows capturing of all the known uses by an individual within and between use-categories [7]: $$ \mathrm{UV}=\sum \limits_{\mathrm{uc}=1}^{n_{\mathrm{uc}}}{\mathrm{UV}}_{\mathrm{uc}}=\sum \limits_{\mathrm{uc}=1}^{n_{\mathrm{uc}}}\sum \limits_{i=1}^n{\mathrm{UR}}_{\mathrm{uc},i}/n $$ where URuc, i is the number of use-report mentioned by informant i in for a given use-category uc. In our dataset, URuc, i varied from 0 to maximum (URuc,i) = 6, meaning that the maximum number of use-report mentioned by an informant in a use-category was 6. UVuc is the use-value for a given use-category uc which is the mean of URuc, i for that use category; nuc is the number of use-categories in the study (nuc = 6); n is the number of informants. UV stands as a mean of URuc,i and could vary from 0 to n × nuc × 6 (in case all informants mentioned all use-categories and that all informants cited a number of use-report equals to 6 in each use-category). Because URuc,i is a count data, a generalized linear model (GLM) with Poisson error distribution [48] was used to assess variation of UV (response variable) with respect to region, local abundance, age category, and gender of informants (predictors). All predictors were categorical with respectively three (humid, sub-humid, semi-arid), two (high, low), three (young, adult, old), and two (women, men) levels. Interaction terms in the model included (i) interaction of region with age category on one hand and gender on the other hand, (ii) interaction of local abundance with age category on one hand and gender on the other hand, and (iii) interaction of age category with gender. Non-significant terms were sequentially removed from the model. Likelihood ratio test was used to assess the goodness of fit of the final model. The deviance-based pseudo-R2 was also computed to assess the explanatory quality of the final model. Cultural importance of B. aethiopum The cultural importance of B. aethiopum was assessed using the importance index (IP) adapted from [49]: $$ \mathrm{IP}=\sum \limits_{\mathrm{uc}=1}^{n_{\mathrm{uc}}}{\mathrm{IP}}_{\mathrm{uc}}=\sum \limits_{\mathrm{uc}=1}^{n_{\mathrm{uc}}}\sum \limits_{i=1}^n{\mathrm{S}}_{i,\mathrm{uc}}/n $$ Si,uc is the score of importance attributed by informant i (i = 1,…, n) for the use-category uc; nuc is the number of use-category (nuc = 6). IP is the overall importance value of B. aethiopum and IPuc, the importance value of the use-category uc of B. aethiopum. Values of IP and IPuc vary from 0 to 18 (in case all informants scored all six use-categories as "high use") and 0 to 3 (in the case all informants scored the use-category uc as "high use") respectively, with higher values indicating higher cultural importance. Ordered logistic models were used to model the effect of age category, gender, local abundance, and region on the variation in the use importance score of B. aethiopum. Backward elimination as described in [50] was used to select the most parsimonious models. All statistical analyses were performed in the R software v.3.3.2 [51]. Package fmsb [52] was used to compute Naglekerke's pseudo-R2. Ordered logistic models were run using the function clm2 within the package "ordinal" [53]. Diversity of uses Countrywide, 121 different use-reports of B. aethiopum were recorded as follows: medicine (66), handcraft (16), food (16), construction (12), firewood (6), and ceremonies and rituals (5). However, only 28 of all those use-reports were found to be significant (Fidelity Level > 5%) (Table 1). The significant use-reports included 9 food uses (human), 6 construction uses, 5 medicinal uses, 5 handcraft uses, 2 firewood uses, and 1 ceremonies and rituals' use indicating that consensus was high on food uses than the other uses, medicinal uses being the use-category where the least consensus was observed (only 5 significant uses out of 66 uses) (Table 1). Table 1 Significant use-report of B. aethiopum per plant part and use category: processing method, forms of use, purpose of use and fidelity level (FL) per chorological region (Hu = Humid, Sub-hu = Sub-humid, Sem = Semi-arid) with illustrations on Fig. 3. Only uses with FL ≥ 5% in at least one region are displayed The number of significant use-reports per plant part was higher for fruits (6 uses) and leaves (6 uses). Stem was involved in four uses while seeds, hypocotyles, and petioles were each involved in three significant use-reports. Roots had only two significant use-reports (Table 1). Uses of plant parts of B. aethiopum (see Fig. 3) varied across regions. Fruits and leaves had multiple forms of use, some uses being reported by more than 50% of the informants. These two plant parts in addition to hypocotyl were involved in uses with the highest fidelity level, up to 86% in some regions. Seed uses were relatively not common, with fidelity level less than 15%. Use of root was mentioned only in the humid and sub-humid regions where it is used either to treat malaria or to strengthen children (Table 1). Processing methods were also not similar across regions (Table 1). For example, ripe fruits are toasted (Fig. 3b, c) only in the semi-arid region, while boiled (Fig. 3d) in the humid region before consumption (Table 1). In the semi-arid region, fruits are often boiled in association with cereals (either maize or millet or sorghum) (see Fig. 3e). The hypocotyles were consumed either boiled (Fig. 3g–i) (in all regions) or toasted (only in the semi-arid region) (Table 1). The use of fruits to discard shrews and snakes from homestead or chicken coop was essentially reported in the sub-humid region. There was no mention of this use in the semi-arid region. Many handcraft products (e.g., fan, mat, hat, sponge; see Fig. 3l–q) are made from leaves and petioles of B. aethiopum. It is worth noticing that other plant parts including bark and flowers of male and female trees were involved in medicinal and ceremonies and rituals uses that were not significant (FL < 5%), hence not presented here. Illustrations of some use-reports of B. aethiopum in Benin. a Fruits with removed flesh. b, c Toasted fruits. d, e Boiling the ripen fruits in water with corn (maize, rice or millet). f Almond after germination. g Freshly harvested hypocotyls. h Boiled and packaged hypocotyls ready for sale. i Boiled hypocotyls not cut yet. j Fresh hypocotyls cut and put in palm alcohol. k Solid potash from incinerated seed hulls. l An old man making sieve. m Samples of sieves. n Fans made from leaves. o Sponge made from petioles. p Battledore from petioles. q Gate from petioles. r Implement made of leaves for ceremonies in Berba region. s A farmer logging a male tree. t Stem used in construction. u Canoe made from stem. v Seat made from stem at public places. w Fruits sowed on farm for hypocotyls production. x Fruits sowed at home for hypocotyls production. y Petioles stored for firewood. z Soap "koto" made from seeds hull. Credits to Salako et al. [30] Based on the ranking of plant parts with respect to their importance for informants, fruit was ranked first and was followed by hypocotyl (Fig. 4) due to their food uses and commercial value. These two plant parts were the most sold on the local market either in rural or urban areas mainly by women and children. Fruits are collected from the wild. Hypocotyles are either collected from the wild or harvested from fruits sown on farm or at homestead (Fig. 3w–x). Apart from fruits and hypocotyles, the following plant parts were successively leaves, petioles, and stem (Fig. 4). Average actual use rank of plant parts of B. aethiopum Use-value of B. aethiopum: effect of region, local abundance, gender, age category, and their interactions Main effect of local and regional abundance, gender, and age category on overall and by use-category UV There was a significant (p < 0.05) relationship between overall knowledge of B. aethiopum uses and age category, gender, local abundance and region, either as main effect or in a significant interaction term (Table 2). Informants in the drier regions have more knowledge on the species use. Informants in the humid region reported less uses (mean ± standard error; 3.21 ± 0.08) than in the sub-humid (5.32 ± 0.14) and semi-arid (4.07 ± 0.11) regions. The younger the interviewee is, the lesser he has knowledge on the species uses. Young informants reported less uses (3.80 ± 0.11) than adults and old informants who reported similar number of uses, 4.36 ± 0.11 and 4.24 ± 0.14, respectively. Men (4.31 ± 0.10) were more knowledgeable than women (3.98 ± 0.10). Informants from areas with high local abundance reported more uses (4.19 ± 0.09) than informants from areas with low local abundance (4.09 ± 0.10). Table 2 Predictors in the best Poisson and ordered logistic models showing the relationship between socio-demographic attributes (gender and age category), regional (Region) and local abundance, with use-value and importance index, respectively for B. aethiopum (−, non-significant term) Knowledge on the uses of B. aethiopum varied greatly across use-categories (Fig. 5). Irrespective of the examined factors, knowledge was higher for food use (1.87 ± 0.04) followed successively by handcraft (0.72 ± 0.03), construction (0.60 ± 0.03), medicinal (0.41 ± 0.02), firewood (0.36 ± 0.02), and ceremonies and rituals uses (0.18 ± 0.01) (Fig. 5). Knowledge on food use was higher in the semi-arid region than in the sub-humid and humid regions that had similar knowledge (Fig. 5a). Knowledge on medicinal, construction, and handcraft uses were higher in the sub-humid region than in the other regions (Fig. 5a). Knowledge on food use was higher in areas with low local abundance while higher in areas with high local abundance for handcraft and ceremonies and rituals uses (Fig. 5b). Regarding gender, men always reported more knowledge than women irrespective of the use-category except for firewood use where the UV was higher for women (Fig. 5c). With respect to age category, knowledge was always lower for young than adults and old informants who had similar knowledge, except that for the food uses, the differences were relatively narrower than for the other use-categories (Fig. 5d). Radar chart showing the main effect of region (a), local abundance (b), gender (c), and age category (d) on the UV of B. aethiopum across use-categories Interacting effect of region and local abundance with socio-demographic attributes Among socio-demographic attributes, only age category was involved in significant interactions with local abundance (Table 2). Young, adult, and old informants had similar knowledge in areas with high local abundance while greater differences were observed in areas with low local abundance, in particular between young and both adult and old informants who had similar knowledge (Fig. 6). Interacting effect of age category and local abundance on the UV of B. aethiopum Main effect of region, local abundance, gender, and age category on the overall and by use-category importance There was a significant (p < 0.05) relationship between overall importance (IP) of B. aethiopum and region, local abundance, gender and age category; either as main effect or in interacting effect (Table 2). B. aethiopum was more important (higher IP) in the sub-humid region (mean ± standard error; 5.65 ± 0.08) than in the semi-arid (4.54 ± 0.08) and humid (3.51 ± 0.13) regions; slightly more important for men (4.52 ± 0.10) than for women (4.50 ± 0.09); more important in areas of high local abundance (4.55 ± 0.08) than in area of low local abundance (4.46 ± 0.10); and more important for adults (4.71 ± 0.10) and young (4.44 ± 0.12) than old informants (4.34 ± 0.12). The IP varied greatly among use-categories and for each of the examined predictors (Fig. 7). Irrespective of the predictors, food use was the most important (2.45 ± 0.03) followed by construction (0.61 ± 0.03), handcraft (0.57 ± 0.03), and medicinal (0.56 ± 0.03) uses and then firewood (0.29 ± 0.02) and ceremonies and rituals uses (0.03 ± 0.01) (Fig. 7). Considering region, food use was more important in the semi-arid and sub-humid regions than in the humid region (Fig. 7a). Medicinal use was more important in the sub-humid region while the firewood use was roughly not important there (Fig. 7a). Considering local abundance, food and medicinal uses were more important in areas with high local abundance than in areas with low local abundance (Fig. 7b). Handcraft and construction uses were more important in areas with low local abundance than in areas with high local abundance (Fig. 7b). With respect to gender, food and firewood uses were more important for women than men while handcraft use was more important for men than women (Fig. 7c). Regarding age categories, food use was more important for young and adult than old informants. Contrary to food use, medicinal and construction uses were more important for adults and old informants than young (Fig. 7d). Radar chart showing the main effect of region (a), local abundance (b), gender (c), and age category (d) on the IP of B. aethiopum across use-categories There was no significant interaction involving local abundance and either socio-demographic attributes. However, significant effect was observed for the interaction of region and age category for the overall importance of B. aethiopum (p = 0.036; Table 2). B. aethiopum was more important for young and adults in the sub-humid and semi-arid regions while less important for young in the humid region (Fig. 8a). There was also significant interaction of gender and age categories (p = 0.047; Table 2). Accordingly, B. aethiopum was relatively more important for young women than young men, similarly important for adult men and women while relatively more important for old men than old women (Fig. 8b). Interacting effect of region and age category (a) and gender and age category (b) on the IP of B. aethiopum This study reported on the relationships between traditional knowledge (TK) and cultural importance (CI) of B. aethiopum on one hand, and informant socio-demographic attributes (age categories and gender) on the other hand, considering the ecological apparency hypothesis (EAH) at both local and regional scale. It was found that TK and CI of B. aethiopum varied greatly across use-categories: first, food use and then successively handcraft, construction, medicinal, firewood, and ceremonies and rituals uses (1). Significant difference was also observed among age categories, younger informants reporting less uses than adults and old informants who reported similar number of uses (2). Men reported more uses than women (3). Local abundance had significant effect on TK and CI: informants in areas of higher abundance reported more uses and higher score than informants in areas of lower abundance (4). Also, regional abundance determined TK and CI, region of low abundance (humid region) reporting less uses and lower score than region of larger abundance (sub-humid and semi-arid regions) (5). It was also found that local abundance influences relationships between TK (respectively CI) and age categories: young, adult, and old informants having similar knowledge in areas of high local abundance while greater differences were observed in areas of low local abundance in particular between young and both adult and old who had similar knowledge (6). Interacting effect of age categories, gender, local abundance, and region as drivers of TK Our data support the general trend that TK depends on age categories and gender [4, 54, 55]. Young informants often reported less uses than adults and old informants, hence congruent with the assumption that TK is a time-dependent process of learning [6]. Therefore, informants from older age category, having spent a longer time with their natural environment, would normally have more knowledge than informants from younger age category [4]. Although women are reputed to have more contacts with NTFPs than men [56], the fact that men often have more knowledge than women in our case study may be because women are often specialized in some uses of a species, most often food and to some extent medicinal uses while men uses expand to other uses (e.g., construction, ceremonies and rituals). This utilization pattern of resources is often dictated by differences in activities and roles of men and women within households [54] and sometimes to cultural taboos or prohibitions [7]. The EAH has multiple implications in conservation biology. For example, a positive relationship between species visibility and their use imply gradual elimination of the more apparent species by predatory collection through the constant pressure for domestic/commercial use [17]. The finding that TK was globally higher in areas of higher apparency (either local or regional) supports the ecological apparency hypothesis. Previous studies using abundance as a quantitative predictor of UV have come to similar conclusions [57, 58]. However, others found either no link or at best a weak relationship [15, 16]. Therefore, the EAH would not always explain pattern of uses of species, and other aspects such as socio-cultural, economic, and political aspects should be accounted for [14] and may explain the failure of our model to capture about 60% of the variation in TK. Indeed, human decision processes are complex and cannot be reduced to only ecological or economic considerations; other factors such as social and cultural are important in the processes involved in choosing and harvesting a plant [59]. Informants in drier regions reported more uses than informants in the wettest region which is congruent with the EAH prediction at the regional scale following the regional pattern of B. aethiopum across the country: B. aethiopum abundance and distribution is proportional to dryness, increasing northwards (from the wettest to the driest region) [30]. In Benin, previous studies have shown that diversity of wild edible plant species and plant in home gardens declines towards the semi-arid region [60,61,62], suggesting a likely higher intensity of use on a narrow number of species when the climate becomes drier which may in turn results in more knowledge on the resource at least as food use is concerned. At a local scale, the EAH also overall proved true: the higher the local abundance, the higher the knowledge informants have on the species. However, looking at patterns within each region (not statistically tested because of lack of replicates), this seems to not be the case in the semi-arid region where informants in the village of low local abundance reported up to two times more uses than informants in the village of high local abundance (low abundance: 5.50 ± 0.14 use-reports, high abundance: 2.89 ± 0.09 use-reports), compared to the sub-humid (low abundance: 3.70 ± 0.21 use-reports, high abundance: 6.49 ± 0.13 use-reports) and humid regions (low abundance: 3.24 ± 0.14 use-reports, high abundance: 3.19 ± 0.10 use-reports). As such, differences in TK due local apparency could be related to regional apparency. This pattern suggests two hypotheses. First, in the village of low local abundance in the semi-arid region, B. aethiopum was abundant in a recent past and likely has undergone rapid decline as reported by informants in that village (Additional file 3). This thus raises the importance of understanding the species past abundance in understanding current patterns of knowledge people have on them. Second, in the village of high abundance, the spread of uses of B. aethiopum is narrowed because other species fulfill the role of B. aethiopum observed in the village of low local abundance as suggested by the diversification hypothesis. The diversification hypothesis considers that the presence of multiple species in an environment amplifies the spectrum of alternatives [63] for subsistence, health, and livelihoods in general, thus reducing the pressure (use) on a single species, hence knowledge of its use. Apart from the regional apparency, one additional factor that may explain between regions differences for a given local abundance (e.g., considering villages of high abundance) is differences in ethnic affiliations [61, 64, 65]. Different ethnic groups have often different life style, beliefs, and perceptions of their environment that translate in different knowledge of resources of their environment [64] as previously reported for many other species in Benin [65,66,67]. This study also provides empirical evidence that pattern of knowledge distribution across age categories depends on local and regional apparency of the studied resources as we predicted. The most common (locally or regionally) a species is, the most likely knowledge on its utilization is similar across age categories. In contrast, the less common a species is, the relatively greater is the gap of knowledge among age categories, especially between young on one hand and adult and old people on the other hand. While knowledge acquisition as time-dependent process [6] is straightforward in explaining the often lower knowledge of younger informants as compared to older informants, local or regional apparency may provide interesting potential explanation of the magnitude of the gap of knowledge among age categories. Our proposition is that higher local or regional apparency seems to speed the process of knowledge acquisition resulting in similar knowledge among age categories. At the opposite side, lower local or regional apparency slow the process of knowledge acquisition and therefore result in greater discrepancies among age categories, in particular between younger and older informants. Additional studies on others species would be needed to clarify this proposition. Understanding the cultural importance of plant resource is crucial for an informed management [7]. Differences in form of uses across regions (see Table 1) are mostly linked to cultural differences due to different ethnic affiliations. For example, Gourmantché people from the semi-arid region toast the fruit before consumption. Such use was not mentioned in the other regions. Most culturally important uses of B. aethiopum in study regions were successively food, handcraft, construction, and medicine. These use-categories are also the most known and important for palm species in Latin America [68, 69]. Irrespective of regions, local abundance, gender, and age categories, food use was the most culturally important, clearly indicating that B. aethiopum is primarily a food palm species in Benin, particularly in the sub-humid and semi-arid region. This corroborates Assogbadjo et al. [60] who reported B. aethiopum as a priority wild edible tree species in these two regions. The finding that food uses was more important for women than men confirms the previous hypothesis of women specialization in the food use category but also stress on the relationship between patterns of plant uses and activities/roles in African households [54]: women are responsible for kitchen and most often are the sellers of food products in markets. This is further confirmed by the greater value of importance index for use-categories handcraft, construction and medicinal for men than women since culturally, men are often responsible for constructions and health care of the household members [70]. The fact that fruits and hypocotyles were the most important plant parts added to its greater commercial value are an additional evidence that B. aethiopum is a food palm species. Moreover, the greater commercial value of these two plant parts for women than men confirms B. aethiopum as a "women-palm" species (Fig. 9) as also reported in Brong Ahafo region in Ghana [35]. However, this great cultural and commercial value of fruits and hypocotyls if not well controlled may reduce regeneration potential in natural stands of B. aethiopum, threatening its population rejuvenation as reported for other species, e.g., Pentadesma butyracea [71]. An old women and children on the way back to home from collection of B. aethiopum fruits in northern Benin. Credits to Salako et al. [30] Leaves were the second plant part with the highest number of significant use-report and the third most important plant part. They were often harvested from saplings and juveniles because adults are often taller (up to 20 m, see) and it is not easy to climb [30]. As reported in other studies [25, 72], stipe of B. aethiopum is a much appreciated material for construction and likely explain why it was so culturally important in the study regions. For example, roughly all houses in the village Loumbou-loumbou are made of B. aethiopum stipe (Salako, field observations; Fig. 3t). Gamba Begounou, an 83-year-old women, said "B. aethiopum is the only one good tree for house construction here. It is very resistant and can lives more than two hundred years". Medicinal use of B. aethiopum was also culturally important for surveyed informants and aligned with [35] who reported its medicinal use in 14 out of 28 African countries where it occurs and as the third most used palm species in traditional medicines in Africa. However, in spite of having four times more uses than food use-category (66 versus 16), only 5 were significant, suggesting a lack of consensus on most of the medicinal uses. This is likely due to the fact that the medicinal uses were mostly ethnic-specific. The common use of fruits against malaria also consensually reported in this study has been recently confirmed by pharmacological prospects [35]. Surprisingly, the use of sap commonly reported for B. aethiopum in other countries (e.g., Cote d'Ivoire, Senegal and Guinea; see [28, 32, 33]) was not mentioned in our study. In the humid region, this may be due to the fact that people reputed for palm wine extraction preferred Elaeis guineensis which is the ancestral source of palm wine in Benin [73]. In the sub-humid and semi-arid regions where E. guineensis is roughly absent, this may be due to (but not limited to) the fact that palm wine extraction is not their habit and that they do not have such knowledge. However, the use of fruits to discard shrews and snakes appears as a "new" reported use for B. aethiopum. This property may have potential for biological control of pests and hence required phytochemical screening prospection. Dearth of information on traditional knowledge and cultural importance of species has been implicated for their non-sustainable utilization. This study confirms that traditional knowledge is closely linked to gender and age but provides additional evidence that this relationship is further influenced by local and regional apparency of the resource: greater discrepancies between younger and older informants in areas of lower apparency. We propose that this is linked to the speed of knowledge acquisition which we postulate is lower in areas of lower apparency. Therefore, study reporting on knowledge distribution among age categories should account for the local and regional availability of the study resources in explaining the observed patterns and further shade this by the past abundance of the resource in the study environment. Additional studies on others species are needed to clarify this proposition. This study also showed the paramount local importance of B. aethiopum in Benin in particular for people of the sub-humid and semi-arid regions, providing them with fundamental good and services (food, medicine and materials for house construction) with a high potential to generate cash income for women. B. aethiopum is therefore a particularly important tree species which deserves more attention than it is currently given. From a management perspective, women should be trained for good practices of fruits and hypocotyls collection to avoid overutilization. From a domestication perspective, further studies should with priority focus on fruits and hypocotyls. As a first step, traditional classification will provide good insights, and because of their specialization, women could provide valuable knowledge. Women also should be of particularly interest when selecting "plus trees" for desired traits in fruits and hypocotyls. Davis SD. Plants in danger: what do we know? 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The authors are very grateful to the local people for kindly sharing their precious knowledge. This research was supported by the International Foundation for Science, Stockholm, Sweden, through a research grant to VKS (no. D/5448–1). Additional funding was obtained from a PhD research fellow of the University of Abomey-Calavi under the project "WILD-PALM" also attributed to VKS. FM was funded by FCT (IF/01053/2015). The datasets used and/or analyzed in the current study are available from the corresponding author on reasonable request. Laboratoire de Biomathématiques et d'Estimation Forestières, Faculté des Sciences Agronomiques, Université d'Abomey-Calavi, 04 BP 1525, Cotonou, Bénin Kolawolé Valère Salako , Rodrigue Castro Gbedomon , Frédéric Tovissodé , Achille Ephrem Assogbadjo & Romain Lucas Glèlè Kakaï REN Biodiversity Chair, CIBIO/InBIO – Centro de Investigação em Biodiversidade e Recursos Genéticos, Universidade do Porto, Campus Agrário de Vairão, 4485-601, Vairão, Portugal CEABN/InBIO – Centro de Ecologia Aplicada "Professor Baeta Neves", Instituto Superior de Agronomia, Universidade de Lisboa, Tapada da Ajuda, 1349-017, Lisbon, Portugal Laboratoire d'Ecologie Appliquée, Faculté des Sciences Agronomiques, Université d'Abomey-Calavi, 03 BP 1974, Cotonou, Bénin Achille Ephrem Assogbadjo Search for Kolawolé Valère Salako in: Search for Francisco Moreira in: Search for Rodrigue Castro Gbedomon in: Search for Frédéric Tovissodé in: Search for Achille Ephrem Assogbadjo in: Search for Romain Lucas Glèlè Kakaï in: SVK conceived the work with advices from AAE, GKR, and MF. SVK collected the data with assistance of RCG. SVK and TF processed the data with contribution of RCG. SVK drafted the manuscript with contribution of MF and RCG. All authors read and approved the final manuscript. Correspondence to Kolawolé Valère Salako. Individual consent to participate in the study was obtained prior to implementing the questionnaire. Only individuals that consented to participate in the study were considered. Written informed consent for publication was obtained for photographs related to individual persons in Figs. 3 and 9. A copy of each consent form is available for review by the Editor of this journal. Socio-demographic attributes (ethnic group, age category and gender) of informants and local names of B. aethiopum. (DOCX 13 kb) Questionnaire for assessing use-value and cultural importance of B. aethiopum. (DOCX 15 kb) Local perception on the dynamic of B. aethiopum. (DOCX 28 kb) Salako, K.V., Moreira, F., Gbedomon, R.C. et al. Traditional knowledge and cultural importance of Borassus aethiopum Mart. in Benin: interacting effects of socio-demographic attributes and multi-scale abundance. J Ethnobiology Ethnomedicine 14, 36 (2018) doi:10.1186/s13002-018-0233-8 Received: 03 December 2017 Knowledge distribution Wild palm Borassus aethiopum Mart.	CommonCrawl
Received : 06 May 2021Revised : 08 July 2021Accepted : 06 August 2021 Microbubble-cloud behavior Simulation to Improve Focused Ultrasound Heating Effect using an Ultrasound Contrast Agent ShinKyoungwon1 YooByeongcheol2 ChoiHeungho3 (Research Institute (Attached), ASTERASYS Co., Ltd., Seoul, Korea [email protected]) (Research Institute (Attached), AirLab, Gimhae, Korea [email protected]) (School of Biomedical Engineering, Inje University, Korea [email protected] ) * Corresponding Author: Heungho Choi E-mail: [email protected] The thermal effect ability of an ultrasound contrast agent (UCA) in high-intensity focused ultrasound (HIFU) therapy was evaluated. This was done using a thermal effect simulation program using a microbubble-cloud model and modified Pennes Bio-Heat Transfer Equation (BHTE). In order to design the proposed simulation program, a spherical microbubble-cloud model was developed. Next, the proposed simulation program was experimentally investigated by ultrasound phantom experiments using commercial HIFU equipment and UCA, and the change of thermal effect according to the microbubble-cloud population ratio was measured. The HIFU thermal effect simulations using the properties of UCA were compared with the phantom experiments, which provided concordant results. HIFU, Microbubble, Simulation, Thermal effect Ultrasound is one of the most widely used diagnostics in the medical imaging field because it is non-invasive and generally less expensive than other imaging techniques. It also has developed into a very successful modality in clinical diagnosis because it can provide real-time images of soft tissue structures and blood flow. However, it does not have sharp contrast and is sometimes distorted due to its own artifacts. But with the development of ultrasound contrast agents (UCAs), including microbubbles, this problem can be partially resolved. The interaction of microbubbles with ultrasound has been studied in the last 30 years, and it is broadly used in diagnostic medical applications. As a UCA, microbubbles consist of 1 to 10-μm encapsulated gas-filled bubbles. One of their major characteristics is that they oscillate strongly under an external ultrasound field. The backscattering echo intensity is proportional to the change in acoustic impedance between the blood and microbubbles and acts as an echo-enhancer in diagnostic ultrasound. Another aspect that is impressive is the possibility of using microbubbles to carry various drugs to a target region and rupturing them by localized ultrasound energy. There are numerous results that show that they may also have therapeutic applications as drug or gene-delivery agents and as a mechanism for bypassing the blood-brain barrier [1,2]. Therapeutic ultrasound was considered as a tool for hyperthermia or thermal ablation of tumors. Ultrasound acoustic power induces destruction and collapse of a microbubble, produces a high-amplitude response, and can produce strong microstreaming. The local heat deposition is amplified when microbubbles are present as cavitation or microbubble-enhanced heating [3]. High-intensity focused ultrasound (HIFU) is a therapeutic medical technology where high-pressure acoustic radiation is focused on an Region Of Interest (ROI) within the body to heat tissue. HIFU has gained interest because it is non-invasive and has potential to treat cancers, such as those in the liver and brain [4,5]. But HIFU causes unwanted tissue damage during the treatment with long-treatment time and damages normal tissue before the target region. To reduce damage to target tissues, resting time has to be increased while modulating the intensity level [6]. Cavitation or microbubble-enhanced heating effects can be reduced by the acoustic intensity or treatment time required for the HIFU effect. Since the early 2000s, research to artificially induce the thermal enhancement effect by microbubbles and use it for HIFU treatment has been in progress. Kajiyama studied the optimal ultrasound pulse in a heating characteristic experiment that used HIFU after injecting a UCA [7]. Yu evaluated HIFU treatment using a UCA through the tissue necrosis rate depending on whether the UCA was injected into a rabbit liver [8]. Recently, as the potential for the efficacy and safety of HIFU enhancement using microbubbles has begun to draw attention, clinical trials for actual patients have been increasing. Wang Jingqi clinically tested 102 patients with adenomyosis. When HIFU treatment was performed after injection of ultrasound contrast medium, it was confirmed that it was safer than the result of treatment with only HIFU with less energy and reduced average power [9]. Cheng conducted clinical trials with 63 rabbits and 143 patients with uterine fibroids. As a result, it was confirmed that the group injected with UCA was able to treat fibroids in a much shorter time than the group without UCA, and there were no major complications [10]. However, most of the studies to date are limited to the research results through the experience that UCA can cause the thermal enhancement effect of HIFU. In order to be used clinically in practice, a quantitative analysis of microbubbles and a quantitative study under conditions close to reality are required. Gnanaskandan numerically analyzed the reinforcement effect of microbubbles using the Keller-Herring bubble dynamic equation and compared the simulation results with actual experimental results using the microbubble distribution model. However, the shape is different from a group of microbubbles actually formed by modeling microbubbles in a cube-shaped cylinder [11]. Kamei analyzed the non-linear HIFU enhancement effect by microbubbles, but there is still insufficient experimental content to verify the theory [12]. Therefore, we present a method for quantitatively analyzing and predicting the heat enhancement effect by a microbubble cloud collected during HIFU irradiation. To this end, the behavior of microbubbles was mathematically analyzed, and a simulation was performed by modeling a group of microbubbles, in which are collected form similar to the actual fluids field. In order to verify the simulation, an experiment was performed under the same conditions as the simulation. The paper is organized as follows. In Section 2, we introduce the background knowledge on a microbubble and its behavior equations and theories used in this study, such as the Rayleigh-Plesset equation, modified Herring model, and bio-heat transfer equation (BHTE). Section 3 describes a simulation program using the proposed microbubble behavior-analyzing method for quantitatively analyzing and predicting the heat effect. In section 4, the simulation condition and experimental variables are introduced. In Section 5, we describe the compared microbubble behavior results of the simulation and experiment for the heating effect. Finally, Section 6 explains the conclusions of this study and describes the limitations. In this section, theoretical studies are introduced to describe a microbubble that as a UCA. Also, we discuss a bio-heat transfer equation for ultrasound acoustic energy transfer to thermal energy. These discussed background studies are applied for the microbubble-cloud heating-effect simulation and experimental tests. 2.1 Microbubble used as UCA A microbubble UCA consists of a phospholipid coating film, which has surface tension and viscoelasticity. Because a phospholipid film suppresses vibrations caused by ultrasound irradiation, it acts as a basic variable in the behavior analysis. Surface tension ($\sigma $) is measured as a force per unit length, and the definition can be expressed by Eq. (1). σ = d y n c m = 1 e r g c m 2 = 1 10 − 7 m ⋅ N 10 − 4 m 2 The shear viscosity changes due to the continuously changing shear speed during the expansion of the gas bubble. The shear speed can be explained by Eq. (2), and the shear viscosity is defined by Eq. (3). r ˙ i = p i m i + r y i x ^ , p ˙ i = F i − γ p y i x ^ η = V k T ∫ 0 ∞ d t p x y 0 p x y t where $p_{xy}\left(t\right)$ is the non-equilibrium average of the pressure tensor using the dynamic equation of motion. 2.2 Microbubble behavior Equation Since 1917, several theoretical models have been introduced to study gas bubble dynamics in liquids, and early study on the geometric analysis of microbubble behavior began with Rayleigh's work, which focused on the application of fluid mechanics [9]. Later, Plesset conceived a mathematical model called the Rayleigh-Plesset equation based on Rayleigh's study [10]. This is the most commonly used formula to describe a single microbubble vibration. But these models are the simplest models because a microbubble is driven by just a low-amplitude sound field in an infinite fluid. This model ignores the liquid compressibility effects and assumes that the gas pressure in a microbubble is uniform and follows the polytropic law. The Rayleigh-Plesset equation is shown in Eq. (4): ρ R ¨ R + 3 2 R ˙ 2 = p g t − p 0 − p i t − 4 η R ˙ R − 2 σ R where $R_{0}$ is the microbubble radius at equilibrium, $\dot{R}$ and $\ddot{R}$ represent the first- and second-order derivatives of the microbubble radius $R$, $p_{0}$ is the hydrostatic pressure, $p_{i}\left(t\right)$ is the incident ultrasound pressure in the liquid at an infinite distance, $p_{g}\left(t\right)$ is the uniform gas pressure within the microbubble, and $\rho $, $\sigma $, and $\eta $ are the density of surrounding liquid, surface tension of the microbubble-liquid interface, and viscosity of the bulk fluid, respectively. In general, UCA is a form in which a film constrains a gas inside a bubble, and characteristics such as the thickness and viscosity of the film must be considered. De Jong and Hoff modeled encapsulated microbubbles by incorporating experimentally determined elastic and friction parameters into the Rayleigh-Plesset model. They studied it based on the Herring model, which considered the changes of pressure for liquid compressibility modified by Morgan [14,15]. The modified Herring model is shown in Eq. (5): ρ R R ¨ + 3 2 ρ R ˙ 2 = p 0 + 2 σ R 0 + 2 χ R 0 R 0 R 3 γ 1 − 3 γ c R ˙ − 12 μ s h ε R ˙ R R − ε − p 0 + P t where $\rho $ is the density of the surrounding liquid (assumed to be constant), $R$, $\dot{R}$, and $\ddot{R}$ are the radius, change in velocity, and acceleration of the microbubble, respectively, and $R_{0}$ is the initial radius. $p_{0}$ is the atmospheric pressure, and $P\left(t\right)$ is the external pressure (that is, the pressure by HIFU). $\sigma $ is the surface tension, $\chi $ is the elasticity of the microbubble shell, $\gamma $ is the polytropic index, $\mu $ is the viscosity of the medium, $\mu _{sh}$ is the viscosity of the microbubble shell, and $\varepsilon $ is the thickness of the shell. Through Eq. (5), the behavior according to the external pressure applied to a microbubble can be analyzed. The behavior of microbubbles generates additional acoustic pressure, and the pressure can be obtained from the pressure equation according to the distance defined in the Rayleigh-Plesset model. Eq. (6) shows the pressure equation according to distance: P r a d r , r b , t = ρ R r b 2 R ˙ 2 + R R ¨ where $r_{b}$ represents the distance away from the center of the microbubble. 2.3 Bio-heat Transfer Equation Ultrasound acoustic power-induced destruction and collapse of a microbubble produces high microbubble-enhanced heating in vasculature and tissue. The complex thermal interaction between the vasculature and tissue has been a topic of interest for many researchers. Harry H. Pennes presented the first quantitative relationship describing heat transfer in human tissue including the effects of blood flow on tissue temperature on a continuum basis [16]. For small volumes, the rate of heat generation is calculated by the attenuation coefficient in the tissue and the time-average intensity of the ultrasound. The transfer of heat takes place through mechanisms such as conduction, convection, radiation, metabolism, evaporation, and phase change. In consideration of this, Pennes proposed a heat transfer model called the Bio-Heat Transfer Equation (BHTE), as shown in Eq. (7): ρ C ∂ T ∂ t = ∇ · k ∇ T − W b C b T − T a + Q where $\rho $ is tissue density, $C$ and $C_{b}$ are the specific heats of tissue and blood, $W_{b}$ is the perfusion rate of blood, $T_{a}$ is the temperature of blood vessels, $k$ is the thermal conductivity of tissue, and $Q$ is the rate of heat production by ultrasound destruction and collapse. In this study, we developed a modified BHTE to understand the thermal effect propagation caused by microbubbles oscillation and explosion, which is given by Eq. (8): ρ C ∂ T ∂ t = ∇ ⋅ k ∇ T − W b C b T − T a + Q H i f u + Q B u b b l e where $Q_{Hifu}$ and $Q_{\textit{Bubble}}$ are the thermal effects induced by HIFU irradiation and microbubbles behaviors, respectively. 3. Simulation Program The thermal effect caused by the interaction between a microbubble cloud and the HIFU was simulated using a 3-D numerical model or structural model. This section is organized as follows. We first present a microbubble cloud behavior model that considers the microbubble's distribution in a cloud volume. Then, we introduce a program used to calculate the thermal effect of interaction between a developed microbubble cloud and the microbubble behavior model. 3.1 Microbubble Cloud Modeling The UCA does not exist as a single microbubble but exists in the form of a large number of microbubbles collected in an aqueous solution, so the clustered microbubble cloud should be considered. In addition, the distance of each microbubble is a very important variable for calculating the delivery pressure of the microbubble cloud, so it is important to set the cloud shape and the distance between the microbubbles in modeling the microbubble cloud. We first considered a cube-array bubble cloud suggested by Tatsuya Moriyama et al. [17]. The cube-array microbubble cloud method has the advantage of being simple and intuitive for modeling because all microbubbles are located at equal intervals. However, the distance between the microbubbles is very diverse because the focal point of the HIFU located in the center is very narrow and small. This is a major cause of slowing down the simulation processing speed. Therefore, in this study, a spherical array method involving spherical microbubble clouds with multiple layers of shells was chosen. The microbubbles on each shell have the same distance to the target. This means that the microbubbles on the same shell transmit the same pressure to the target, so the computation speed of the simulation can be improved. Fig. 1 illustrates the spherical microbubble cloud model. Fig. 1. Proposed microbubble cloud model: (a) diagram; (b) 3D simulation results. 3.2 Simulation Program Algorithm Fig. 2 shows the produced simulation program. The simulation presented in this paper was designed as follows. First, in order to analyze the behavior of microbubbles, the modified Herring model was solved using a 6$^{\mathrm{th}}$-order Runge-Kutta numerical analysis. Second, single microbubbles were placed on the modeled microbubble group model, and the distance to the target was calculated to obtain the total pressure applied to the target. Finally, the total pressure applied to the target was converted to thermal energy through BHTE, and then the expected temperature was calculated. Fig. 2. Developed simulation program UI and simulation parameters. MATLAB 2018b was used for all simulation procedures. This simulation program was designed to control the characteristics of the microbubbles, the concentration of the microbubble cloud, the size of the microbubble cloud, the characteristics of the medium, and the HIFU characteristics. It was also set to display a graph of the temperature rise over time. However, this simulation program and procedure have some assumptions: · First, all microbubbles are completely spherical and all have the same characteristics. · Second, all microbubbles are evenly spread in the microbubble group. · Third, the explosion of microbubbles all occurs within one cycle of HIFU ultrasound. · Finally, the interaction between microbubbles is ignored. 4. Outline of the Experiment In order to investigate the ability of UCA to increase the thermal effect of HIFU, several systems were assembled, and an experimental procedure was established. 4.1 The Contrast Agent To verify the UCA ability for the thermal effect, the commercially available SonoVue$^{\mathrm{TM}}$ was selected. It is a novel ultrasound contrast medium made of phospho-lipid-stabilized microbubbles of sulfur hexafluoride (SF$_{6}$) and a poorly soluble and totally innocuous gas. It presents outstanding stability and resistance to pressure. SonoVue$^{\mathrm{TM}}$ appears as a white, milky solution and is stable for hours. Because no sterilizing agent is present in the composition, SonoVue$^{\mathrm{TM}}$ should be used within 6 hours after reconstitution. SonoVue$^{\mathrm{TM}}$ is isotonic, and its viscosity is similar to that of blood. It does not contain protein-based materials (Table 1). Table 1. SonoVue$^{\mathrm{TM}}$ Characteristics. SonoVueTM Parameter Bubble diameter 2.5 [μm] Bubble volume concentration ~ 5 [μL/mL] Surface tension σ 0.051 [N/m] Polytropic gas exponent γ 1.07 [N/m] Shell elasticity χ Shell viscosity μ s h 0 to 8 [N/m] Shell thickness ε $1\times 10^{-9}$ [m] Table 2. Acoustic parameter of phantom and human. tissue NIPAM Polyolefin tube Sound velocity $\left[\mathrm{m}/\mathrm{s}\right]$ Attenuation $\left[\mathrm{dB}/\mathrm{cm}\right]$ Density [$\mathrm{kg}/m^{3}]$ Impedance [$\text{Mrayl}]$ Fig. 3. NIPAM phantom schematic and picture. 4.2 Ultrasound Phantom Parameters A phantom was fabricated using N-isopropylacrylamide (NIPAM), which is similar to soft tissue and has acoustic characteristics of the human body. We also used polyolefin tubes, which have similar characteristics to blood vessels and were implanted to inject the ultrasonic contrast agent (Fig. 3). In addition, in order to evaluate the temperature rise, a thermocouple intersected with the tube, and a liquid mixed with a blood-mimicking material filled the tube. Table 2 compares the acoustic parameters of human tissue and tissue-mimicking phantom materials Fig. 4. Experiment setup schematic and picture. 4.3 Experiment Setup To evaluate the thermal effect ability by UCA in HIFU therapy, an experimental system was set up as shown in Fig. 4. The phantom system ($30\times 30\times 30mm$$^{3}$) includes a polyolefin tube ($d=5mm$) for use in microbubble capture and a thermocouple implanted orthogonally to the polyolefin tube for measurement of temperature changes. The temperature changes were continuously monitored by Datalogger (Graphtec, Japan) from the implanted thermocouple. A set of a commercial focused ultrasound surgical units (ASTERASYS, Korea) that includes a HIFU transducer was used during the experiment. The HIFU transducer produces a peak acoustic intensity of $1.2MPa$ at the main lobe. The frequency was set to $4MHz$. For focusing point adjustment, a transducer was attached to a 3-axis jig system. The initial temperature of the blood-like substance mixed with microbubbles and the phantom was set to 25$^{\circ}$C 4.4 Experiment Procedure Prior to the main experiments, to evaluate the proposed spherical microbubble cloud model and simulation program, an experiment and comparison were conducted by changing the mixing ratio of the UCA and the blood-mimicking material from 1:4 to 1:1. The main experiment consists of measuring the change in the thermal effect according to the volume and the concentration of the microbubble cloud. First, a temperature increase was simulated by increasing the radius of the microbubble cloud from 0.5 mm to 1.5 mm at 0.25-mm intervals using a 30% concentration of UCA. Second, using a microbubble cloud with a radius of 1 mm, the temperature increase was simulated by increasing the concentration of UCA from 10% to 50% in 10% increments. Fig. 5 shows a diagram of the experimental procedure, and Table 3 shows parameters for the simulation study. 5. Evaluation Results 5.1 Spherical Microbubble Cloud Model To evaluate the spherical microbubble cloud model and simulation program, an actual experiment and comparison were conducted. Table 4 shows the simulation results, and Table 5 shows the results of HIFU irradiation experiments using an ultrasonic phantom. In the absence of microbubbles, the simulation results and experimental results increased by 5.12$^{\circ}$C and 5.1$^{\circ}$C to 30.12$^{\circ}$C and 30.1$^{\circ}$C, respectively. After that, in the case of mixed contrast agent, it was confirmed that both the simulation and experiment showed additional heat increase. Also, the heat-enhancing effect increased as the proportion of microbubbles increased. At a 1:1 ratio, a temperature increase of 6.92$^{\circ}$C was confirmed through simulation, and a temperature increase of 7$^{\circ}$C was confirmed in the ultrasonic phantom. Fig. 5. Flowchart of the experiment procedure. Fig. 6. Simulation and experiment results of the maximum temperature according to the ratio of solution. Table 3. Simulation parameter for UCA thermal effect. Microbubble-cloud radius [mm] UCA solution ratio Table 4. Temperature rise simulation result. Simulation Result Unit [℃] Non-bubble Init temp Peak temp Table 5. Temperature rise experiment result. Experiment Result Fig. 6 shows a graph of the simulation results according to the concentration of the ultrasonic contrast agent and the temperature rise result of the experiment using the ultrasonic phantom. Simulation results and experimental results using ultrasonic phantoms show that the temperature rise according to each condition has error within 0.2, and the temperature rise pattern is similar. This means that the analysis of the thermal enhancement effect through quantitative analysis of the microbubble cloud presented in this study is significant. 5.2 Thermal Effect of HIFU according to the Characteristics of Microbubble Cloud The thermal enhancement effect of HIFU according to the characteristics of the microbubble cloud was evaluated through simulation using the simulation program. The factors that have the greatest influence on the thermal enhancement effect of HIFU are the number of microbubbles in the medium and the distance between the focal point and the microbubbles. This is closely related to the size of the microbubble cloud and the concentration of the ultrasonic contrast medium. Therefore, in this study, the temperature increase was confirmed and evaluated through simulation while changing the volume of the microbubble cloud and the concentration of the ultrasonic contrast medium. Fig. 7 shows a simulation result of the temperature rise with no microbubbles. 5.3 Thermal Effect according to the Volume of Microbubble Cloud While changing the diameter of the microbubble cloud, the medium was fixed at 30%, and the microbubble group radius was increased from 0.5 mm to 1.5 mm. When the radius of the microbubble group was 0.5 mm, it increased by 0.1025$^{\circ}$C compared to when the microbubbles were not present. After that, it was confirmed that the temperature exponentially increased as the size of the microbubble cloud increased. In Section 3.2, microbubbles separated by more than 25 μm were found to have little effect. It is considered that the increase in the total pressure due to the increase in the number of microbubbles and the increase in the size of the microbubble cloud has more effect than the attenuation due to the distance. Table 6 and Fig. 8 show the heat rise results with increasing radius of the microbubble cloud. 5.4 Thermal Effect according to UCA Solution Ratio The radius of the microbubble cloud was set to 1 mm, and the temperature increase was confirmed through a simulation while increasing the collection density of the microbubbles (that is, the concentration of the ultrasonic contrast agent). The thermal enhancement effect of the microbubble group increased from 10% to 50% according to the increase in the concentration of the ultrasonic contrast agent. This confirmed that an additional exponential temperature increase occurred. When the ultrasonic focusing point and the microbubbles become closer, a large amount of microbubbles can be collected in a group of microbubbles of the same size, thereby inducing a synergistic heat effect. Table 7 and Fig. 9 show the results of thermal rise according to the microbubble concentration. Table 6. Simulation results according to microbubble-cloud volume. UCA Solution Ratio [%] Microbubble cloud radius Peak Temperature [°C] Table 7. Simulation results according to microbubble-cloud concentration ratio. Fig. 7. Temperature simulation result without microbubble cloud. Fig. 8. Simulation results according to microbubble-cloud volume. Fig. 9. Results of thermal rise according to the microbubble concentration. This study confirmed the effect of the characteristics of a microbubble cloud on the thermal enhancement during HIFU irradiation and analyzed it quantitatively. To do this, a microbubble behavior model was mathematically analyzed, and a microbubble group was modeled to simulate the microbubble distribution in ultrasonic contrast medium. After that, a simulation program to check the thermal enhancement effect was made using the microbubble behavior model and the microbubble group model, and the effect of the characteristics of the microbubble group on the thermal enhancement effect of HIFU was confirmed. The microbubble behavior of ultrasonic contrast medium was simulated using the modified Herring model. At this time, since the energy change according to the sound speed was limited, the change in the sound speed due to the HIFU pressure was not considered in the simulation. In addition, in the actual experiment, it was expected that there would be limitations in the collection of microbubbles and the temperature rise due to ultrasonic physical phenomena such as scattering. Therefore, it was expected that the accuracy of the temperature rise result could be improved if the conditions of the temperature saturation point are confirmed through additional experiments and applied to the simulation program. In addition, in the simulations produced by this study, all microbubbles had the same properties as the microbubbles spread out in the shell of the spherical microbubble cloud model. Practical results can be obtained by applying an algorithm that randomly applies the arrangement and characteristics of microbubbles to the extent physically possible. The results of this study are expected to contribute to the development of HIFU treatment research using ultrasound contrast agents. 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Mech., Vol. 16, pp. 277-282 Jong N. de, Hoff L., 1993, Ultrasound scattering properties of Albunex microspheres., Ultrasonics, Vol. 31, No. 3, pp. 175-181 Morgan Karen E., et al. , 2000, Experimental and theoretical evaluation of microbubble behavior: Effect of transmitted phase and bubble size., IEEE transactions on ultrasonics, ferroelectrics, and frequency control, Vol. 47, No. 6, pp. 1494-1509 Pennes Harry H., 1948, Analysis of tissue and arterial blood temperatures in the resting human forearm., Journal of applied physiology, Vol. 1, No. 2, pp. 93-122 Moriyama Tatsuya, Shin Yoshizawa, Shin-ichiro Umemura, 2012, Thermal simulation of cavitation-enhanced ultrasonic heating verified with tissue-mimicking gel., Japanese Journal of Applied Physics, Vol. 51, No. 7s Kyoungwon Shin Kyoungwon Shin is a graduate of Inje University's Master of Engineering program. He is a member of the Affiliated Research Institute, ASTERASYS Co., Ltd. Byeongcheol Yoo Byeongcheol Yoo is member of the Affiliated Research Institute, AirLab. He is a graduate of Inje University's Master of Medical Engineering program. Heungho Choi Heungho Choi is a professor of biomedical engineering at Inje University, Gimhae, Korea. In 1993, he was an exchange professor at the University of Tokyo, Japan. He served as an editor of the Korean Society of Medical & Biological Engineering. His research interests include medical ultrasound, health care, rehabilitation, and biological signal processing. Microbubble Thermal effect	CommonCrawl
Conditions to apply Source Coding Theorem I was wondering what are the conditions to apply source coding theorem (SCT). 1. Is it applied only to uniform-length coding, what about variable-length coding, does it also satisfy SCT? I was asking because in my lecture, SCT is only discussed in uniform coding section. 2. Is the result of SCT for uniquely decodable coding or is it for lossless coding? In Wikipedia SCT, it's said $f$ is unique decodable code, then we have SCT. In my lecture, it gives me an impression that SCT is generally applied to all lossless coding. information-theory coding-theory LoganLogan $\begingroup$ Uniquely decodable coding and lossless coding are the same thing. $\endgroup$ – Yuval Filmus Mar 14 '18 at 14:16 $\begingroup$ Yep, if within the context of uniform encoding, then lossless is equivalent to uniquely decodable. While if not, these two gonna be different concepts. $\endgroup$ – Logan Mar 15 '18 at 0:57 It is an average in bits/symbol and does apply to all coding schemes. You're correct, the number of bits/symbol needed is equal or larger than the entropy rate (asymptotically, though) of the source for any lossless code. If you allow for lossy coding, then a generalization called rate-distortion function is needed to lower bound the rate required. kodlukodlu The source coding theorem is a statement about uniform-length coding. It tells you how long the uniform length should be in order to guarantee high success probability. It can be proved using variable-length coding, but the statement itself just doesn't concern variable-length coding. It is meaningless to ask whether variable-length coding "satisfies" the source coding theorem. In more detail, suppose there is a source with entropy $H$. We want to encode $n$ i.i.d. samples of the source using as few bits as possible. Generally speaking, if you want to guarantee that the encoding always be decodable back to the original samples, then you cannot bound the length of the encoding (see the example below). Instead, we are content with a guarantee that the decoding will be successful with probability tending to 1. The source coding theorem states that such an encoding is possible using $nR$ bits if and only if $R>H$. To see why error is necessary, consider a source which is distributed geometrically $G(1/2)$, that is, with probability $1/2$ it equals $1$, with probability $1/4$ it equals $2$, with probability $1/8$ it equals $3$, and so on. The entropy of this source is finite (in fact, 2 bits), but since there are infinitely many potential outcome, if we want to guarantee that decoding will be successful, we must allow a message of unbounded length. One way to prove the if part of the theorem is using variable-length encoding. It is known that $m$ samples can be encoded as a prefix code using at most $mH+1$ bits in expectation. Taking $m = \sqrt{n}$, this shows that $n$ samples can be encoded using a variable-length encoding of length at most $nH + \sqrt{n}$ bits in expectation. If $R > H$ then for large $n$, $nH + \sqrt{n}$ will be much smaller than $nR$, and furthermore, it can be shown (using the law of large numbers) that it is highly likely that this variable-length encoding will use at most $nR$ bits. Therefore we can take as our uniform-length encoding the first $nR$ bits of this variable-length encoding (padding it arbitrarily if needed). The only if part of the theorem does have a counterpart for variable-length codes: any prefix code for a source with entropy $H$ must have expected length at least $H$. This is a nice exercise. As for your second question, lossless encoding is an encoding scheme which can be decoded exactly. This is in contrast to JPEG, for example, which is a lossy encoding – given an image, if you compress it to JPEG and then decompress it, you get a slightly different image. In contrast, uniquely decodable encoding is a term used to describe variable-length codes with the property that the concatenation of several codewords can be segmented uniquely into codewords. Every uniform-length code is automatically uniquely decodable. The two terms describe different aspects of the encoding. The first term states that the encoding aims to reconstruct the source exactly rather than approximately. The second term states that the encoding can be used to encode a sequence rather than just a single item. Not the answer you're looking for? Browse other questions tagged information-theory coding-theory or ask your own question. Source Coding Theorem: what happen when go below N⋅H(x) bits? Typical set in Shannon's source coding theorem Is the Source Coding Theorem straightforward for uniformly distributed random variables? Is Morse Code binary, ternary or quinary? Is there a generalization of Huffman Coding to Arithmetic coding? Kraft's inequality and Shannon's noiseless coding theorem for an encoding How to show that in noiseless coding theorem, the bound $\mathrm{MinACL}<H(P)+1$ is tight? Prove that the upper bound in the Noiseless-coding theorem is strict What is a symbol code? Is arithmetic coding restricted to powers of $2$ in denominator equivalent to Huffman coding?	CommonCrawl
BMC Pregnancy and Childbirth Risk factors for vaginal fistula symptoms in Sub-Saharan Africa: a pooled analysis of national household survey data Mathieu Maheu-Giroux1, Véronique Filippi2, Nathalie Maulet3, Sékou Samadoulougou4, Marcia C. Castro5, Nicolas Meda6,7, Mariève Pouliot8 & Fati Kirakoya-Samadoulougou9 BMC Pregnancy and Childbirth volume 16, Article number: 82 (2016) Cite this article Vaginal fistula (VF) is one of the most severe maternal morbidities with the immediate consequence of chronic urinary and/or fecal incontinence. The epidemiological evidence regarding risk factors for VF is dominated by facility-based studies. Our aim is to estimate the effect size of selected risk factors for VF using population-based survey data. We pooled all available Demographic and Health Surveys and Multiple Indicators Cluster Surveys carried out in sub-Saharan Africa that collected information on VF symptoms. Bayesian matched logistic regression models that accounted for the imperfect sensitivity and specificity of self-reports of VF symptoms were used for effect size estimation. Up to 27 surveys were pooled, including responses from 332,889 women. Being able to read decreased the odds of VF by 13 % (95 % Credible Intervals (CrI): 1 % to 23 %), while higher odds of VF symptoms were observed for women of short stature (<150 cm) (Odds Ratio (OR) = 1.31; 95 % CrI: 1.02-1.68), those that had experienced intimate partner sexual violence (OR = 2.13; 95 % CrI: 1.60-2.86), those that reported sexual debut before the age of 14 (OR = 1.41; 95 % CrI: 1.16-1.71), and those that reported a first birth before the age of 14 (OR = 1.39; 95 % CrI: 1.04-1.82). The effect of post-primary education, female genital mutilation, and having problems obtaining permission to seek health care were not statistically significant. Increasing literacy, delaying age at first sex/birth, and preventing sexual violence could contribute to the elimination of obstetric fistula. Concomitant improvements in access to quality sexual and reproductive healthcare are, however, required to end fistula in sub-Saharan Africa. In sub-Saharan Africa, maternal disorders are the second most important cause of death among women of reproductive age (15-49 years old) [1]. Disease burden attributable to maternal complications still remains important despite the significant declines in maternal mortality observed in this region since the mid-2000s [2, 3]. In fact, it is estimated that for every woman dying from maternal complications, another 20 women will have to withstand serious maternal morbidity [4]. Of all maternal morbidities, obstetric fistula is one of the most debilitating conditions with the immediate consequence of chronic urinary and/or fecal incontinence. Physical comorbidities, psychological distress, and social stigmatization usually follow [5–9]. The etiology of vaginal fistula (VF), an abnormal hole between the bladder (vesico-vaginal fistula) and/or rectum (recto-vaginal fistula) and the reproductive tract of a woman, is divided into two main categories: obstetric and traumatic. VF of obstetric origin are caused by an intertwined set of biological, socio-economic, and cultural factors that favor obstructed labor and triggered by insufficient or delayed access to quality emergency obstetric care [7]. VF of traumatic origin mostly results from sexual violence. The vast majority of VF in sub-Saharan Africa are of obstetric origins and prevalence of this condition in this region was recently estimated to be between 1.0 and 1.6 per 1,000 women of reproductive age depending on methodology [10, 11]. The epidemiological evidence regarding risk factors for VF is dominated by facility-based studies [12]. The numerous clinical series usually report socio-demographic characteristics of VF patients (age of marriage, marital status, literacy, parity, etc.) as well as circumstances of fistula occurrence (duration of labor, type of birth attendance, mode and place of delivery, etc.) [13–21]. This accumulation of hospital-based studies contributed to highlight the diverse characteristics of fistula sufferers who present to facilities [12]. A few case-control studies tackle individual determinants with the aim to confirm risk factors [22–24] or develop a fistula prevention index [25]. Other studies, often qualitative, reflect on cultural or health system factors to reduce the three delays causative of obstetric fistula and maternal mortality [21, 26–28]: delay in decision to seek care, delay in reaching care, and delay in receiving adequate care once in the health facility. Population-based studies could be less susceptible to selection bias than case series from facility and case-control studies but are rarely carried-out [11, 29]. In sub-Saharan Africa, the main sources of nationally representative health data are Demographic and Health Surveys (DHS) and Multiple Indicator Cluster Surveys (MICS). Since 2004, these surveys progressively began to include questions about VF symptoms. These data sources were recently used to estimate the prevalence of VF in sub-Saharan Africa [10], while adjusting for the imperfect accuracy of self-reports, but a thorough and systematic examination of individual risk factors has yet to be completed. We are aware of four population-based studies that examined determinants of VF [30–33]. These studies only included a small number of surveys, assumed that self-reports of VF symptoms were perfectly accurate, and none pooled surveys together, severely limiting their statistical power. The primary objective of this paper is thus to examine the association between selected individual risk factors and lifetime prevalence of self-reported VF symptoms, such as literacy status, education level, female genital mutilation (FGM), sexual violence, short stature, age at first sexual intercourse, age at first birth, and women's ability to get permission to seek health care. By pooling surveys from different countries, we hope to improve the representativeness and precision of the effect size measures for those risk factors. DHS and MICS surveys conducted in sub-Saharan Africa that included questions about VF symptoms were considered for this analysis. A comprehensive overview of DHS and MICS surveys can be found elsewhere [34]. Briefly, both DHS and MICS are household-based surveys that use a multistage stratified cluster sampling design to select a nationally representative sample of women of reproductive age (15-49 years old). Socio-demographic characteristics and information on selected health indicators are collected through face-to-face interviews by trained personnel and recorded in standard questionnaires. The majority of surveys administered the VF questions to all women of reproductive age but some restricted it to women that were ever married (Mauritania MICS 2011), ever pregnant (Swaziland MICS 2010 and Guinea-Bissau MICS 2010), or that had a live birth in the previous five years (Rwanda DHS 2005). The specific questions related to vaginal fistula symptoms varied slightly from survey to survey and a contingency question about knowledge of vaginal fistula was sometime incorporated. A full description of the VF and contingency questions (if any), their probes, and the coding of the outcome can be found elsewhere [10]. Based on previous studies and the information available from DHS/MICS surveys, we estimated the effect of the following risk factors: illiteracy, education level, whether the respondent has experienced female genital mutilation (FGM), short stature, experience of intimate partner sexual violence, young age at first sexual intercourse, young age at first birth, and women's difficulty to get permission to access health care. Literacy status was ascertained in the surveys by asking the interviewee to read a sentence on a card that was handed out to her. If the woman was able to read only part of the sentence, she was considered not being able to read properly. Women who reported having had some secondary education or higher were de facto assumed to be literate. For genital mutilation, we did not stratify our analysis by FGM type as a validation study of the DHS FGM questions in Sierra Leone demonstrated that they were accurate to determine FGM prevalence but inaccurate for determining cutting extent [35]. Not all surveys recorded information for these risk factors and the list of countries for which such data was collected is presented in Tables 1 and 2. As for women's anthropometric measurements, this information is not collected by MICS surveys and the women's height was recorded from a sub-sample of participants in most DHS surveys. Similarly, questions on domestic violence were often administered to a subsample of women, depending on the survey, and the questions about ever having experienced intimate partner sexual violence were only asked to ever married women (or those in a union). As for age at first sexual intercourse, inconsistent responses were disregarded and considered as missing (e.g., a women reporting never having had sexual intercourse but having given birth). Finally, most DHS surveys asked women if getting permission to seek health care was a problem. Those who responded that it was a big problem were considered as having limited ability to seek the care they need. Table 1 Number of vaginal fistula (VF) by survey datasets for the following risk factors: literacy status, education level, female genital mutilation (FGM), and short stature (<150 cm) Table 2 Number of vaginal fistula (VF) by survey datasets for the following risk factors: experience of intimate partner sexual violence (IPSV), young age at first sex (<14 years old), young age at first birth (<14 years old), and permission to seek health care The principal threat to the internal validity of our analyses is confounding of the exposure-outcome relationship. The main potential confounders for which information was collected by the survey questionnaires are age, literacy status, location of residence (rural versus urban), gravidity status, and religion. Socio-economic status and marital status were not considered in this analysis because these variables are likely both a cause and an effect of VF. That is, due to the cross-sectional nature of data collection, we do not have information on the temporal sequence in which changes in socio-economic status or marital status occurred. Three surveys (Chad MICS 2010, Mauritania MICS 2011, and Togo MICS 2010) did not record information on gravidity status and we assumed that all nulliparous women were also nulligravid – a reasonable assumption giving the high correlation observed between these two variables. Finally, four surveys did not record information on religion and these were coded using a missing variable indicator to retain them in the analyses (Mauritania MICS 2011, Niger DHS 2012, Swaziland MICS 2010, and Tanzania DHS 2010). To circumvent the lack of balance and overlap for some of the covariates, matching was used to make the group with the selected risk factor (i.e., exposed) as similar as possible to the group without (i.e., unexposed). By reducing model dependency through this semi-parametric data preprocessing, we aim to produce more robust inferences that are less sensitive to modeling assumptions [36]. Three of our risk factors are continuous and were dichotomized. Respondents with a height less than 150 cm, a commonly used threshold [12, 15], were defined as having a short stature. For age at first birth, visual inspection of the exposure-outcome relationship suggested that this variable could be dichotomized at less than 14 years of age at first delivery. This corresponds roughly to the 4th percentile of the distribution of age at first birth. The same threshold of less than 14 years was used to define young age at first sexual intercourse. All country datasets were pooled together as the low number of VF cases precludes data analysis at the country level for many surveys (i.e., all cases were either exposed or unexposed in these surveys). For the selected risk factors, a nearest neighbor algorithm was used to match women on sampling weight (for sexual violence, the sampling weight from the domestic violence questionnaire was used), age (continuous), and survey identifier. For this latter variable, exact matching was used for risk factors that consistently had more unexposed than exposed observations across surveys: short stature, intimate partner sexual violence, young age at first sexual intercourse, young age at first birth, and problem obtaining permission to seek care (otherwise, nearest neighbor matching was used). The matching ratio of exposed to unexposed units varied for each risk factor and was chosen as to minimize unbalance and maximize statistical power. Matching was implemented using the 'MatchIt' package [37] in R. Unmatched women were excluded from the analyses. Logistic regression models were used on the matched data to estimate the effect of the selected risk factors on lifetime prevalence of VF. Missing values for the selected risk factors and covariates were always less than 1 %, except for height (2.0 %) and age at first sexual intercourse (6.1 % of inconsistent or missing values). Observations with missing values were excluded from the analyses (with the exception of those for religion which were retained using a missing indicator). To provide for additional control of potential confounders, we adjusted for the following covariates: age (15-19, 20-29, and 30-49 years), literacy status (this covariate was not included for literacy status and education level risk factors), gravidity status (not included for age at first birth), location of residence (urban/rural), religion (Christian, Muslim, others, missing), and the survey's country. Such analyses have been described as doubly-robust because statistically consistent inferences can be made "if either the matching analysis or the analysis model is correct (but not necessarily both)" [37]. Surveys that had a different population denominator were included in the analysis since we matched on survey identifier and country fixed effects were included in the parametric analyses. These logistic regressions did not account for the clustered design of surveys as our preliminary analyses have shown that clustering the standard errors had no impact on our conclusions (also discussed in [10]). Importantly, women's self-report of vaginal fistula symptoms do not have perfect sensitivity and specificity, as compared to the gold standard of a pelvic examination. In order to account for non-differential misclassification of the self-reported outcome, we used a latent-class Bayesian statistical model [10, 38, 39]. The underlying assumption being that all surveys have a common sensitivity and specificity (see [10] for details). This model takes the following form: $$ \begin{array}{c}\mathrm{Likelihood}:\\ {}{y}_i\sim Binomial\left({p}_i,{N}_i\right)\\ {}{p}_i={\pi}_i(Se)+\left(1-{\pi}_i\right)\left(1-Sp\right)\\ {}\mathrm{logit}\left({\pi}_i\right)=\alpha +\beta {X}_i\end{array} $$ Because of our very large sample sizes and the computing-intensive nature of Bayesian calculations, we grouped observations with the same covariate patterns and used a binomial likelihood instead of the standard Bernoulli (i.e., grouped logistic regression). In this model, y i is the total number of women reporting VF symptoms with covariate pattern i; N i is the total number of women with covariate pattern i; p i is the observed probability of reporting VF symptoms, π i is the true probability of women having ever had VF symptoms; Se and Sp are the sensitivity and specificity of the survey instrument, respectively; α is the model's intercept; β is a vector of coefficients for the covariates included in X i . The model's specification is completed using the following prior distributions: $$ \begin{array}{c}\mathrm{Prior}\ \mathrm{distributions}\ \mathrm{f}\mathrm{o}\mathrm{r}\ \mathrm{model}\ \mathrm{parameters}:\\ {}\alpha \sim Normal\left(0,20\right)\\ {}\beta \sim Normal\left(0,20\right)\\ {}Se\sim Uniform\left(95.10\%,99.90\%\right)\\ {}Sp\sim Uniform\left(99.85\%,99.95\%\right)\end{array} $$ Both α and β are given non-informative priors that follow a normal distribution with a mean of zero and standard deviation of 20. For sensitivity and specificity, we used uniform distributions that match the 95 % credible intervals of the posterior distributions of these quantities, as estimated previously [10]. Posterior distributions were obtained using Markov Chain Monte Carlo sampling, implemented in R using the 'rstan' package [40]. Samples are obtained using the no-U-turn sampler, a computationally efficient variant of Hamiltonian Monte Carlo [41]. Inferences were based on three chains of 30,000 samples after an initial warm-up period of 2,500 samples per chain (total of 90,000 iterations used for inferences). Convergence was examined using traceplots and ensuring that the potential scale reduction factor was equal to one. All analyses were performed using the R statistical software [42]. Surveys characteristics A total of 31 surveys collected information on VF symptoms in sub-Saharan Africa. Of these, individual data records were not available for two surveys (Equatorial Guinea DHS 2011 and Guinea-Bissau MICS 2010), and two other surveys were excluded because the incontinence questions were considered to be non-specific (Côte d'Ivoire DHS 2011-12 and Malawi DHS 2004). Hence, 27 surveys, conducted between 2005 and 2014, informed our analyses. The main characteristics of the interviewees can be found in Additional file 1: Table S1. These 27 surveys pooled self-reports from 334,606 eligible women and 2,048 reported having ever experienced VF symptoms (742 had missing information on the outcome (0.2 %)). The specific sample size used in the regression models varied, depending on the considered risk factors, from 332,889 for literacy to 102,928 for intimate partner sexual violence (before matching). Detailed information on the risk factors and number of women reporting VF symptoms, stratified by surveys, can be found in Table 1 and Table 2. Briefly, a little over a third of women were able to read (38.6 %), a quarter had completed post-primary education (26.8 %), 42.2 % had experienced FGM, 8.7 % had a height below 150 cm, 9.0 % of ever married women had experienced intimate partner sexual violence, 11.0 % of sexually active women had their first sexual intercourse before the age of 14, 3.8 % of primi/multiparous women had their first birth before the age of 14, and 18.3 % of women reported that obtaining permission to seek health care was a big problem for them. Risk factors for vaginal fistula The sample size of the pooled datasets before and after matching are presented for each risk factors in a supplementary appendix (Additional file 1: Table S2). One-to-one matching was used for the risk factors that were most prevalent: being able to read, having a post-primary education, female genital mutilation, and degree of difficulty in obtaining permission to seek health care. For the other risk factors, the ratio was chosen as to minimize imbalances while retaining sufficient statistical power: one-to-two matching for intimate partner sexual violence, one-to-three for young age at first sexual intercourse, one-to-four for short stature, and one-to-eight for young age at first birth. Results from the matched logistic regressions are presented in Table 3. Preliminary results from the Bayesian models for young age at 1st birth and problem getting permission to seek healthcare suggest convergence issues with the country fixed effects. Since matched logistic regressions with and without country fixed effects for these two risk factors gave very similar results (data not shown), they were omitted from the Bayesian model. Table 3 Matched logistic regression results for the different risk factors for vaginal fistula symptoms Being able to read decreased the odds of VF by 13 % (95 % Credible Intervals (CrI): 1 % to 23 %). The impact of having completed some post-primary education also reduced the odds of VF by 10 % (95 % CrI: -6 % to 24 %) but the effect did not reach statistical significance. For these two determinants, it is likely that gravidity status lies on the causal pathway between literacy/education and occurrence of VF. If that is the case, the effect size measures reported above should be interpreted as the direct effect of literacy/education on VF (i.e., the effect not mediated through gravidity). By not controlling for gravidity status, we can calculate the total effect of literacy/education. The total effect of being literate is a 20 % reduction in the odds of VF (95 % CrI: 10 % to 30 %). For post-primary education, the total effect is a 21 % reduction in the odds of VF (95 % CrI: 7 % to 34 %). FGM had little effect on the odds of VF, after adjusting for outcome misclassification. Women with a short stature had odds of VF that were 31 % (95 % CrI: 2 % to 68 %) higher than their taller counterparts. Among the sample of ever married women (or in a union), the odds of having had VF for those that experienced intimate partner sexual violence were 2.13 times higher than those that never had (95 % CrI: 1.60-2.86). This finding was confirmed in the subsample of 13 surveys that asked all women (never married and ever/currently married) if they had ever experienced sexual violence (from anyone) with an odds ratio of 2.22 (95 % CrI: 1.72-2.90). Among sexually active women, the odds of VF for those that had sexual intercourse before the age of 14 were 41 % (95 % CrI: 16 % to 71 %) higher than those that had a sexual debut at an older age. Expanding our sample by including women that have not begun their sexually active life had little impact on this effect size estimate (odds ratio (OR) = 1.38; 95 % CrI: 1.14-1.66). Both of these findings are in line with the one from age at first birth. Indeed, having had a first live birth before the age of 14 was associated with odds of VF that were 39 % higher (95 % CrI: 1.04-1.82) than those that had their first birth at older ages. Finally, having difficulty obtaining permission to seek health care was associated with increased odds of reporting VF symptoms but this effect did not reach statistical significance (OR = 1.20; 95 % CrI: 0.99-1.47). Main findings Pooling data from up to 27 population-based surveys conducted in sub-Saharan Africa, we identified the following risk factors for VF: illiteracy, short stature, sexual violence, young age at first sexual intercourse, and young age at first birth. These results corroborate findings from previous studies on the importance of some individual-level risk factors for obstetric fistulas [12, 13, 15, 43]. Short stature, early sexual debut and young age at first birth are risk factors that are related, among other things (e.g., cultural practices, women's status, access to family planning), to a woman's anthropometry. Women that were young at first sex/birth, with immature pelvic bones, and women of short stature have increased incidence of cephalo-pelvic disproportion, which is a known risk for obstructed labor [44]. Illiteracy has been found to significantly increase the odds of VF and its effect went beyond that mediated by gravidity status. In contrast, we found no significant direct effect of post-primary education on VF occurrence. This could be explained by the fact that literacy was objectively measured whereas the quality of primary education in sub-Saharan Africa varies widely, even within the same geographical region [45]. Alternatively, it is possible that education beyond primary school has no impact on VF incidence, suggesting that fistula sufferers are the most disadvantaged of the disadvantaged. We did not evidence any relationship between FGM and VF. The DHS/MICS questionnaire, however, did not enable us to investigate if the most severe forms of FGM, such as infibulation and gishiri cutting, are risk factors for VF. Experience of intimate partner violence had a large effect on VF occurrence, as reported previously [31]. Taken together, these results suggest that empowerment and improvement of women's status could play a key role in reducing the burden of VF in sub-Saharan Africa. Strengths and limitations A number of strengths characterize this study. First, we have conducted what is believed to be the largest population-based analysis of risk factors for VF, pooling data from up to 23 countries (27 surveys) in sub-Saharan Africa. Second, we explicitly modeled uncertainty of self-reports of VF symptoms using a Bayesian Latent C lass model whereas the few other studies that have examined risk factors for VF using DHS/MICS surveys did not perform such adjustments. Finally, we used a doubly-robust method for inferences as a safeguard to bias of effect size estimates. This study has some limitations. First, some of the estimates could be affected by reverse causality. This is mostly true for intimate partner sexual violence since the majority of other risk factors are likely to have preceded the occurrence of VF symptoms. Hence, it is possible that women with VF have a higher probability of being affected by intimate partner sexual violence as VF impacts their status within marriage and community [46], for example by creating financial stress and/or affecting women's economic productivity. Living with fistula was found to interfere with sexual activity for 85.2 % of patients in a multi-country study [18]. Some physical and psychological consequences of VF persist after repair [47] and this could influence risk of sexual violence [18]. Second, we could not exclude from our sample fistulas that were not of obstetric origins as many surveys did not record the cause of VF symptoms. Since more than 90 % of VF in sub-Saharan Africa are from obstetric origins [10, 13], inclusion of VF from other causes should have little impact on our estimated effect size measures. Third, risk factors like intimate sexual violence, the degree of difficulty of obtaining permission to seek health care, and literacy were measured at the time of interview and we assumed these to be time-invariant. This assumption could be violated if these risk factors have changed since the women's onset of VF symptoms. Finally, the cross-sectional nature of the surveys, coupled with potentially important within-country migration, prohibited us from examining the effect of a number of other risk factors such as access to health services, quality of health services, and coverage of maternal health interventions that may ultimately represent important barriers to the prevention and elimination of obstetric fistula in sub-Saharan Africa. VF embodies many of the challenges of the post-2015 agenda, and, more specifically, of the unfinished reproductive health agenda. Despite a decade of maternal health improvements [2, 3], poor access to and quality of health services is the norm in most low and middle income countries with antenatal and perinatal care being the least equitable interventions [48]. The third sustainable development goal (SDG) aims at reducing the maternal mortality ratio to less than 70 per 100,000 live birth and to ensure universal access to sexual and reproductive health-care services, including family planning [49]. The fifth goal also calls for achieving gender equality and women empowerment, with the elimination of all form of violence against women and girls and of harmful practices such as early and forced marriage [49]. Attaining these objectives could have important synergistic impacts to reduce incidence of obstetric fistula [50], but quality of care should be emphasized as poor vulnerable women are often attended by "the most disenfranchised members of the health-care system" [4]. The importance of family planning and antenatal care should also be stressed. Indeed, universal access to sexual and reproductive health is emphasized in both the third and fifth SDG. Alongside, access to comprehensive emergency obstetric care should be viewed as a form of prevention [51, 52]. Yet, our study highlighted that fistula prevention could be most effective if accompanied with enhanced efforts on education and women empowerment. Our study confirms a number of important individual-level risk factors for VF, while adding precision to the effect size estimates, using population-based data from a large number of countries in sub-Saharan Africa. Increasing literacy, delaying age at first sex/birth, and preventing sexual violence could contribute to the elimination of obstetric fistula if concomitant improvements in access to quality sexual and reproductive healthcare are ensured. Informed consent was provided by all survey participants (or their guardian) before questionnaire administration. Further, all DHS survey protocols have been approved by the Internal Review Board of ICF International in Calverton (USA) and by the relevant country authorities for both DHS and MICS. Further information on the ethics approval can be found in the individual country reports published by DHS and MICS. Datasets containing individual-level records are in the public domain and can be obtained from The DHS Program (DHS surveys) and UNICEF (MICS surveys). credible intervals DHS: Demographic and Health Survey FGM: MICS: Multiple Indicators Cluster Survey SDG: VF: vaginal fistula IHME. GBD Heatmap. 2013 [cited 2015 August 12]; Available from: http://vizhub.healthdata.org/gbd-compare/heatmap. Kassebaum NJ et al. Global, regional, and national levels and causes of maternal mortality during 1990-2013: a systematic analysis for the Global Burden of Disease Study 2013. Lancet. 2014;384(9947):980–1004. WHO. Trends in maternal mortality: 1990 to 2013. Estimates by WHO, UNICEF, UNFPA, The World Bank and the United Nations Population Division. Geneva, Switzerland: World Health Organization; 2014. p. 56. Langer, A., et al., Women and Health: the key for sustainable development. Lancet, 2015;386(9999):1162–1210. Wilson, S.M., et al., Psychological Symptoms Among Obstetric Fistula Patients Compared to Gynecology Outpatients in Tanzania. Int J Behav Med, 2015;22(5):605–613. Siddle K et al. Psychosocial impact of obstetric fistula in women presenting for surgical care in Tanzania. Int Urogynecol J. 2013;24(7):1215–20. Wall LL et al. The obstetric vesicovaginal fistula in the developing world. Obstet Gynecol Surv. 2005;60(7 Suppl 1):S3–S51. Arrowsmith S, Hamlin EC, Wall LL. Obstructed labor injury complex: obstetric fistula formation and the multifaceted morbidity of maternal birth trauma in the developing world. Obstet Gynecol Surv. 1996;51(9):568–74. Goh JT et al. Mental health screening in women with genital tract fistulae. BJOG. 2005;112(9):1328–30. Maheu-Giroux M et al. Prevalence of symptoms of vaginal fistula in 19 sub-Saharan Africa countries: a meta-analysis of national household survey data. Lancet Glob Health. 2015;3(5):e271–8. Adler AJ et al. Estimating the prevalence of obstetric fistula: a systematic review and meta-analysis. BMC Pregnancy Childbirth. 2013;13:246. Zheng AX, Anderson FW. Obstetric fistula in low-income countries. Int J Gynaecol Obstet. 2009;104(2):85–9. Muleta M, Rasmussen S, Kiserud T. Obstetric fistula in 14,928 Ethiopian women. Acta Obstet Gynecol Scand. 2010;89(7):945–51. Hawkins L et al. Characteristics and surgical success of patients presenting for repair of obstetric fistula in western Kenya. Int J Gynaecol Obstet. 2013;120(2):178–82. Tebeu PM et al. Risk factors for obstetric fistula: a clinical review. Int Urogynecol J. 2012;23(4):387–94. Ijaiya MA et al. Vesicovaginal fistula: a review of nigerian experience. West Afr J Med. 2010;29(5):293–8. Holme A, Breen M, MacArthur C. Obstetric fistulae: a study of women managed at the Monze Mission Hospital, Zambia. BJOG. 2007;114(8):1010–7. Landry E et al. Profiles and experiences of women undergoing genital fistula repair: findings from five countries. Glob Public Health. 2013;8(8):926–42. Wall LL et al. The obstetric vesicovaginal fistula: characteristics of 899 patients from Jos, Nigeria. Am J Obstet Gynecol. 2004;190(4):1011–9. Tahzib F. Epidemiological determinants of vesicovaginal fistulas. Br J Obstet Gynaecol. 1983;90(5):387–91. Mselle LT et al. Waiting for attention and care: birthing accounts of women in rural Tanzania who developed obstetric fistula as an outcome of labour. BMC Pregnancy Childbirth. 2011;11:75. Melah GS et al. Risk factors for obstetric fistulae in north-eastern Nigeria. J Obstet Gynaecol. 2007;27(8):819–23. Roka ZG et al. Factors associated with obstetric fistulae occurrence among patients attending selected hospitals in Kenya, 2010: a case control study. BMC Pregnancy Childbirth. 2013;13:56. Barageine JK et al. Risk factors for obstetric fistula in Western Uganda: a case control study. PLoS One. 2014;9(11):e112299. Browning A, Lewis A, Whiteside S. Predicting women at risk for developing obstetric fistula: a fistula index? An observational study comparison of two cohorts. BJOG. 2014;121(5):604–9. Norman AM, Breen M, Richter HE. Prevention of obstetric urogenital fistulae: some thoughts on a daunting task. Int Urogynecol J Pelvic Floor Dysfunct. 2007;18(5):485–91. Wall LL. Overcoming phase 1 delays: the critical component of obstetric fistula prevention programs in resource-poor countries. BMC Pregnancy Childbirth. 2012;12:68. Turan JM, Johnson K, Polan ML. Experiences of women seeking medical care for obstetric fistula in Eritrea: implications for prevention, treatment, and social reintegration. Glob Public Health. 2007;2(1):64–77. Cowgill KD et al. Obstetric fistula in low-resource countries: an under-valued and under-studied problem--systematic review of its incidence, prevalence, and association with stillbirth. BMC Pregnancy Childbirth. 2015;15:193. Sagna M, Hoque N, Sunil T. Are some women more at risk of obstetric fistula in Uganda? Evidence from the Uganda Demographic and Health survey. Journal of Public Health in Africa. 2011;2(e26):108–11. Peterman A, Johnson K. Incontinence and trauma: sexual violence, female genital cutting and proxy measures of gynecological fistula. Soc Sci Med. 2009;68(5):971–9. Biadgilign S et al. A population based survey in Ethiopia using questionnaire as proxy to estimate obstetric fistula prevalence: results from demographic and health survey. Reprod Health. 2013;10:14. Johnson, K. and A. Peterman, Incontinence data from the Demographic and Health surveys: comparative analysis of a proxy measurment of vaginal fistula and recommendations for future population-based data collection, in DHS Analytical Studies No. 17. 2008, Macro International Inc.: Calverton, MD. Hancioglu A, Arnold F. Measuring coverage in MNCH: tracking progress in health for women and children using DHS and MICS household surveys. PLoS Med. 2013;10(5), e1001391. Bjälkander O et al. Female genital mutilation in sierra leone: forms, reliability of reported status, and accuracy of related demographic and health survey questions. Obstet Gynecol Int. 2013;2013:680926. Stuart EA. Matching methods for causal inference: A review and a look forward. Stat Sci. 2010;25(1):1–21. Ho D et al. MatchIt: Nonparametric preprocessing for parametric causal inference. Journal of Statistical Software. 2011;42(8):1–28. Maheu-Giroux M, Casapia M, Gyorkos T. On the validity of self-reports and indirect reports to ascertain malaria prevalence in settings of hypoendemicity. Soc Sci Med. 2011;72(5):635–40. McInturff P et al. Modelling risk when binary outcomes are subject to error. Stat Med. 2004;23(7):1095–109. Stan Development Team, RStan: the R interface to Stan, Version 2.5.0. 2014. http://mc-stan.org. Hoffman M, Gelman A. The no-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. J Machine Learning Res. 2014;15:1593–623. R Development Core Team. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing; 2013. Muleta M. Obstetric fistula in developing countries: a review article. J Obstet Gynaecol Can. 2006;28(11):962–6. Neilson JP et al. Obstructed labour. Br Med Bull. 2003;67:191–204. Murtin F. Improving Education Quality in South Africa. Paris, France: Organisation for Economic Co-operation and Development; 2013. Book Google Scholar Mwini-Nyaledzigbor PP, Agana AA, Pilkington FB. Lived experiences of Ghanaian women with obstetric fistula. Health Care Women Int. 2013;34(6):440–60. Mselle LT et al. "Hoping for a normal life again": reintegration after fistula repair in rural Tanzania. J Obstet Gynaecol Can. 2012;34(10):927–38. Barros AJ et al. Equity in maternal, newborn, and child health interventions in Countdown to 2015: a retrospective review of survey data from 54 countries. Lancet. 2012;379(9822):1225–33. UN, Open Working Group proposal for Sustainable Development Goals. 2014, Open Working Group of the General Assembly on Sustainable Development Goals: http://undocs.org/A/68/970. Wall LL. Preventing obstetric fistulas in low-resource countries: insights from a Haddon matrix. Obstet Gynecol Surv. 2012;67(2):111–21. Higashi H et al. Surgically avertable burden of obstetric conditions in low- and middle-income regions: a modelled analysis. BJOG. 2015;122(2):228–36. ICES, Vision & Priorities for the Sustainable Development Goals and the Post-2015 Development Agenda - Women's Equity and Essential Surgery Recommendations for Action. 2014, The International Collaboration for Essential Surgery. p. 3. MMG's research is supported by the Bisby prize and a postdoctoral fellowship from the Canadian Institutes of Health Research. FKS received a travel award from Fonds de la Recherche Scientifique-FNRS to complete this work. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Department of Infectious Disease Epidemiology, Imperial College London, St Mary's Hospital, London, UK Mathieu Maheu-Giroux Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, UK Véronique Filippi Institute of Health and Society, Université Catholique de Louvain, Clos Chapelle-aux-champs, Brussels, Belgium Nathalie Maulet Pôle Épidemiologie et Biostatistique, Institute de recherche expérimentale et Clinique, Université Catholique de Louvain, Clos Chapelle-aux-champs, Brussels, Belgium Sékou Samadoulougou Department of Global Health and Population, Harvard TH Chan School of Public Health, Boston, MA, USA Marcia C. Castro Centre Muraz, Ministry of Health, Bobo-Dioulasso, Burkina Faso Nicolas Meda UFR Sciences de la Santé, Université de Ouagadougou, Ouagadougou, Burkina Faso Institute of Food and Resources Economics, Section for Global Development, University of Copenhagen, Copenhagen, Denmark Mariève Pouliot Faculté de Santé Publique, Université catholique de Louvain, Brussels, Belgium Fati Kirakoya-Samadoulougou Correspondence to Fati Kirakoya-Samadoulougou. FKS developed the original research idea with contributions by SS and MMG. FKS, MMG, and NMa performed the background literature review for this paper. MMG assembled and managed the databases. MMG also performed the analyses with inputs from VF, MCC, MP and FKS. MMG wrote the manuscript with contributions by FKS and NMa. VF, NMa, SS, MCC, NMe, MP, and FKS contributed intellectual content to the paper and critically reviewed it. All authors have read and approved the final version of this manuscript. Characteristics of the study population, stratified by survey. Table S2. Number of surveys included in the analyses, sample size in the un-matched datasets, matching ratio, and matched sample size for the selected risk factors. (DOCX 22 kb) Maheu-Giroux, M., Filippi, V., Maulet, N. et al. Risk factors for vaginal fistula symptoms in Sub-Saharan Africa: a pooled analysis of national household survey data. BMC Pregnancy Childbirth 16, 82 (2016). https://doi.org/10.1186/s12884-016-0871-6 Accepted: 14 April 2016 vesicovaginal fistula rectovaginal fistula Submission enquiries: [email protected]	CommonCrawl
An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems JGM Home June 2014, 6(2): 141-166. doi: 10.3934/jgm.2014.6.141 Geometric characterization of the workspace of non-orthogonal rotation axes Bertold Bongardt 1, DFKI GmbH, Robotics Innovation Center, Robert-Hooke-Straße 1, 28359 Bremen, Germany Received August 2013 Revised May 2014 Published June 2014 In this article, a novel characterization of the workspace of 3R chains with non-orthogonal, intersecting axes is derived by describing the set of singular orientations as two tori that separate two-solvable from non-solvable orientations within $SO(3)$. Therefore, the tori provide the boundary of the workspace of the axes' constellation. The derived characterization generalizes a recent result obtained by Piovan and Bullo. It is based on a specific, novel representation of rotations, called unit ball representation, which allows to interpret the workspace characterization with ease. In an appendix, tools for dealing with angles and rotations are introduced and the equivalence of unit quaternion representation and unit ball representation is described. Keywords: rotation representation, rotation decomposition, kinematic analysis, Non-orthogonal Euler angles, singularity analysis.. Mathematics Subject Classification: Primary: 70B10; Secondary: 22E70, 15A1. Citation: Bertold Bongardt. Geometric characterization of the workspace of non-orthogonal rotation axes. Journal of Geometric Mechanics, 2014, 6 (2) : 141-166. doi: 10.3934/jgm.2014.6.141 B. Alpern, L. Carter, M. Grayson and C. Pelkie, Orientation maps: Techniques for visualizing rotations (a consumer's guide), in VIS '93: Proceedings of the 4th conference on Visualization, (1993), 183-188. Google Scholar S. Bai and J. Angeles, A unified input-output analysis of four-bar linkages, Mechanism and Machine Theory, 43 (2008), 240-251. doi: 10.1016/j.mechmachtheory.2007.01.002. Google Scholar O. A. Bauchau and L. 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Numerical Algebra, Control & Optimization, 2021 doi: 10.3934/naco.2021018 Zhen Lei. Rotation-strain decomposition for the incompressible viscoelasticity in two dimensions. Discrete & Continuous Dynamical Systems, 2014, 34 (7) : 2861-2871. doi: 10.3934/dcds.2014.34.2861 Palle E. T. Jorgensen and Steen Pedersen. Orthogonal harmonic analysis of fractal measures. Electronic Research Announcements, 1998, 4: 35-42. Danny Calegari, Alden Walker. Ziggurats and rotation numbers. Journal of Modern Dynamics, 2011, 5 (4) : 711-746. doi: 10.3934/jmd.2011.5.711 Michel Laurent, Arnaldo Nogueira. Rotation number of contracted rotations. Journal of Modern Dynamics, 2018, 12: 175-191. doi: 10.3934/jmd.2018007 Arek Goetz. Dynamics of a piecewise rotation. Discrete & Continuous Dynamical Systems, 1998, 4 (4) : 593-608. doi: 10.3934/dcds.1998.4.593 Xavier Buff, Nataliya Goncharuk. Complex rotation numbers. Journal of Modern Dynamics, 2015, 9: 169-190. doi: 10.3934/jmd.2015.9.169 Congming Li, Jisun Lim. The singularity analysis of solutions to some integral equations. Communications on Pure & Applied Analysis, 2007, 6 (2) : 453-464. doi: 10.3934/cpaa.2007.6.453 Tyrus Berry, Timothy Sauer. Consistent manifold representation for topological data analysis. Foundations of Data Science, 2019, 1 (1) : 1-38. doi: 10.3934/fods.2019001 Christopher Cleveland. Rotation sets for unimodal maps of the interval. Discrete & Continuous Dynamical Systems, 2003, 9 (3) : 617-632. doi: 10.3934/dcds.2003.9.617 David Cowan. A billiard model for a gas of particles with rotation. Discrete & Continuous Dynamical Systems, 2008, 22 (1&2) : 101-109. doi: 10.3934/dcds.2008.22.101 Mads Kyed. On a mapping property of the Oseen operator with rotation. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1315-1322. doi: 10.3934/dcdss.2013.6.1315 Jiao Du, Longjiang Qu, Chao Li, Xin Liao. Constructing 1-resilient rotation symmetric functions over $ {\mathbb F}_{p} $ with $ {q} $ variables through special orthogonal arrays. Advances in Mathematics of Communications, 2020, 14 (2) : 247-263. doi: 10.3934/amc.2020018 Jifeng Chu, Meirong Zhang. Rotation numbers and Lyapunov stability of elliptic periodic solutions. Discrete & Continuous Dynamical Systems, 2008, 21 (4) : 1071-1094. doi: 10.3934/dcds.2008.21.1071 Katja Polotzek, Kathrin Padberg-Gehle, Tobias Jäger. Set-oriented numerical computation of rotation sets. Journal of Computational Dynamics, 2017, 4 (1&2) : 119-141. doi: 10.3934/jcd.2017004 Ingrid Beltiţă, Anders Melin. The quadratic contribution to the backscattering transform in the rotation invariant case. Inverse Problems & Imaging, 2010, 4 (4) : 599-618. doi: 10.3934/ipi.2010.4.599 Suddhasattwa Das, Yoshitaka Saiki, Evelyn Sander, James A. Yorke. Solving the Babylonian problem of quasiperiodic rotation rates. Discrete & Continuous Dynamical Systems - S, 2019, 12 (8) : 2279-2305. doi: 10.3934/dcdss.2019145 Deissy M. S. Castelblanco. Restrictions on rotation sets for commuting torus homeomorphisms. Discrete & Continuous Dynamical Systems, 2016, 36 (10) : 5257-5266. doi: 10.3934/dcds.2016030 Héctor E. Lomelí. Heteroclinic orbits and rotation sets for twist maps. Discrete & Continuous Dynamical Systems, 2006, 14 (2) : 343-354. doi: 10.3934/dcds.2006.14.343 Salvador Addas-Zanata. Stability for the vertical rotation interval of twist mappings. Discrete & Continuous Dynamical Systems, 2006, 14 (4) : 631-642. doi: 10.3934/dcds.2006.14.631 Bertold Bongardt	CommonCrawl
Current Search: Research Repository (x) » info:fedora/fsu:undergradhonors (x) » info:fedora/ir:thesisCModel (x) "It's Not Gay if They Don't Touch": Challenging Heteronormative Empire and Countering the 'Closeting of History' Through Art. Steel, Isabella, Department of Art My project revolves around the "closeting of history", which is the phenomenon in which evidence that suggests gay or bisexual behavior is omitted from the narratives of important historical figures, thus allowing them to be imagined as heterosexual by future generations (and depriving young people of gay and bisexual icons). I wanted to create artwork that counters this phenomenon, by placing historical figures and popular characters in situations that complicate their sexuality, removing... Show moreMy project revolves around the "closeting of history", which is the phenomenon in which evidence that suggests gay or bisexual behavior is omitted from the narratives of important historical figures, thus allowing them to be imagined as heterosexual by future generations (and depriving young people of gay and bisexual icons). I wanted to create artwork that counters this phenomenon, by placing historical figures and popular characters in situations that complicate their sexuality, removing them from the heterosexual narrative that they have been confined to. I first began to explore this concept with a series of drawings of several American presidents as drag queens, complete with drag names, such as Abraham "Babe" Lincoln. I want these and other art pieces of mine to challenge the idea of "normativity" as applied to sexuality by re-appropriating iconic figures such as presidents, who have been symbols of heterosexual masculinity and success, as tools for showing sexuality as a performance—something that is fluid rather than compartmentalized. I want key works to simultaneously tackle the discomfort associated with excessive femininity, particularly when that femininity is applied to powerful individuals, and to negate the idea of the effeminate as weak. My artwork consists primarily of colorful and playful drawings and paintings, inspired by the camp aesthetic and sense of humor. At the end of the day, I just want to confront people with fun images of gay male sexuality, so that they might question what it is about it that makes them uncomfortable, and whether their discomfort is truly warranted. "It's Really Overwhelming": Parent And Service Provider Perspectives Of Parents Aging Out Of Foster Care. Radey, Melissa, Schelbe, Lisa, McWey, Lenore M., Holtrop, Kendal, Canto, Angela I. Rates of pregnancy and parenthood among current and former foster youth are two to three times higher than non-foster youth peers. Repeat pregnancies among young mothers aging out of foster care also occur at higher rates than peers not involved with the child welfare system. Furthermore, mothers aging out of foster care demonstrate high levels of parenting stress and risk for child maltreatment. Indeed, this population is in significant need of help; however, beyond anecdotal evidence,... Show moreRates of pregnancy and parenthood among current and former foster youth are two to three times higher than non-foster youth peers. Repeat pregnancies among young mothers aging out of foster care also occur at higher rates than peers not involved with the child welfare system. Furthermore, mothers aging out of foster care demonstrate high levels of parenting stress and risk for child maltreatment. Indeed, this population is in significant need of help; however, beyond anecdotal evidence, little is known about the needs and day-to day experiences of this population. In order to tailor interventions to meet the needs of parents aging out, the perspectives of stakeholders must be taken into account. Using qualitative data gathered from separate small group interviews with parents aging out and service providers, this study examined participants' perceptions of parents' daily experiences, strengths, and needs. Findings indicated that parents aging out face overwhelming adversity and stress with little outside financial, emotional, or parenting support from family or friends. Yet, parents also expressed motivation to be good parents, resilience, and the desire to gain effective parenting skills. Although similar themes arose among parent and provider interviews, perceptions differed. Parents expressed hope and optimism in providing for their children while providers expressed systemic failure in preparing parents for independent living. Based on these findings, we conclude that parenting interventions specific to parents aging out may need to address three fundamental and key components: basic needs, social support, and effective parenting techniques. Published by Elsevier Ltd. FSU_libsubv1_wos_000381171100001, 10.1016/j.childyouth.2016.05.013 "Keeping Them Off the Streets": Examining the Media's Discussion of Youth Agriculture Projects. Philips, Allison, Boggs, George The "noble experiment" in Tampa: A study of prohibition in urban America. Alduino, Frank William., Florida State University Prohibition sprang forth from the Progressive Era--the widespread reform movement that swept across the United States at the turn of the century. Responding to the dramatic changes in American society since the end of the Civil War, the Progressive movement encompassed a wide array of individuals and groups advocating a far-reaching program of economic, political, and social reform. For over forty years temperance zealots strived to impose their values on the whole of American society,... Show moreProhibition sprang forth from the Progressive Era--the widespread reform movement that swept across the United States at the turn of the century. Responding to the dramatic changes in American society since the end of the Civil War, the Progressive movement encompassed a wide array of individuals and groups advocating a far-reaching program of economic, political, and social reform. For over forty years temperance zealots strived to impose their values on the whole of American society, particularly on the rapidly expanding immigrant population. These alien newcomers epitomized the transformation of the country from rural to urban, from agricultural to industrial., Rapidly-expanding urban centers were often the battleground between prohibitionists and supporters of the whiskey traffic. European immigrants, retaining their traditional values, gravitated to metropolitan areas such as Boston, New York, and Chicago. With the opening of the cigar industry in the mid-1880s, Tampa, Florida also began attracting large numbers of immigrants. Because of its pluralistic composition, the city might serve as a microcosm of the national struggle between the "wet" and "dry" forces., Using newspapers, oral interviews, and other primary materials, this study traces the various aspects of the prohibition movement in the city of Tampa. In addition, it details other peripheral areas associated with the advent of the Eighteenth Amendment including the drug and alien trades. Finally, this study examines the lengthy efforts to repeal the "Noble Experiment" and return legalized drinking back to Tampa. THE "OLD SUMPTER HERO": A BIOGRAPHY OF MAJOR-GENERAL ABNER DOUBLEDAY. RAMSEY, DAVID MORGAN., The Florida State University Abner Doubleday was an unusual and often a controversial person. Born into a family staunchly supporting Andrew Jackson, Doubleday reflected the determined Unionist position of the strong-willed president. Abner's attitude towards the Union was later vividly demonstrated at Fort Sumter. A mediocre career at West Point illustrated Doubleday's lack of desire to excel although he possessed the ability to do so. The controversy over the origin of baseball, although Doubleday was never directly... Show moreAbner Doubleday was an unusual and often a controversial person. Born into a family staunchly supporting Andrew Jackson, Doubleday reflected the determined Unionist position of the strong-willed president. Abner's attitude towards the Union was later vividly demonstrated at Fort Sumter. A mediocre career at West Point illustrated Doubleday's lack of desire to excel although he possessed the ability to do so. The controversy over the origin of baseball, although Doubleday was never directly involved in the question, was the first of several controversies with which Abner Doubleday's name is associated., Doubleday never seemed satisfied with his early life. In his papers he continually referred to people, prominent in later years, which he knew. While serving in the Mexican War, Doubleday continually felt the need to relate the dangerous situations in which he was placed. He seemed to want to demonstrate his personal responsibilities, which while actually meager, he viewed as of supreme importance. Doubleday apparently wanted to be a famous, bold cavalier, but realized he failed to accomplish his objective and stressed his "noble" deeds., Doubleday loved large cities and the benefits they offered a person. He liked being in the right social circles and enjoyed the "good life." By 1852, while serving as a commissioner for the Senate, Doubleday had come to despise Mexico and the Mexicans. By 1858, while serving in Florida, he disliked the inconveniences of chasing "savages." With secession in 1860 Doubleday no longer liked Charlestonians; later extending his revulsion to all Confederates., With the crisis at Sumter in 1861 Doubleday was greatly troubled. The affront to the United States government was almost more than he could bear. With the outbreak of the war, Doubleday was more than willing to fight the rebels. A dependable, if unspectacular soldier, Doubleday served well during the Civil War. While no one accused him of original thinking militarily, his men always fought well. Gettysburg was Doubleday's finest hour but became his final hour in the Civil War when he could not countenance serving under a junior officer., It seems strange that Doubleday served in the Freedmen's Bureau since his superior was none other than his old enemy from Gettysburg, O.O. Howard. Doubleday's service in California brought the controversy over the origin of the cable car. Retirement from the army in 1873 brought out several new qualities in Abner Doubleday. He wrote books, read French and Spanish literature, and became interested in the occult and became a believer in theosophy., Doubleday was a colorful figure in nineteenth century America. He was associated with several significant events in the growth of the nation. Doubleday represented, possibly to an extreme, the attitude of many American Unionists and supporters of Manifest Destiny. His commitment to a united nation is similar to Lincoln's attitude. Doubleday not only vocalized this sentiment, but, like Lincoln, was prepared to fight for his belief. Abner Doubleday was an intense American. He desired a strong, powerful United States and opposed those not supporting such a course. "One Must Actually Take Facts as They Are": Information Value and Information Behavior in the Miss Marple Novels. Kazmer, Michelle M. One perspective not often brought to the study of detective fiction is that from the field of information science. Among other topics, information science is concerned with information behavior, or how people behave with respect to information: needing, seeking, accidentally encountering, avoiding, evaluating, storing and so forth. Examining the solving of a mystery as an information behavior has potential for insights into the genre and into our twenty-first century readings of detective... Show moreOne perspective not often brought to the study of detective fiction is that from the field of information science. Among other topics, information science is concerned with information behavior, or how people behave with respect to information: needing, seeking, accidentally encountering, avoiding, evaluating, storing and so forth. Examining the solving of a mystery as an information behavior has potential for insights into the genre and into our twenty-first century readings of detective fiction. Current audiences are accustomed to modern information technology and the information behaviors afforded by it: amateur sleuths hack computer systems or professional detectives analyze trace evidence for DNA. Highly technologized contemporary information environments leave us to ask: in what ways do the manipulation of information value, and the sophistication of the information behaviors, in novels written by Agatha Christie in the early- to mid-twentieth century, continue to enthrall readers in the twenty-first? "Poverty Porn": The Narratives of INGO Media Campaigns. Costner, Monique, Kohli, Tanu International non-governmental organizations (INGOs) have different strategies of raising awareness and funds for their causes. Sometimes however, these strategies can rely on the use of stereotypical or dehumanizing depictions of people from the developing world. We have all seen the images of hungry children with bloated stomachs, presumably from some African or Asian country. To what extent do these narratives present a grossly simplified version of the struggles people in poverty face?... Show moreInternational non-governmental organizations (INGOs) have different strategies of raising awareness and funds for their causes. Sometimes however, these strategies can rely on the use of stereotypical or dehumanizing depictions of people from the developing world. We have all seen the images of hungry children with bloated stomachs, presumably from some African or Asian country. To what extent do these narratives present a grossly simplified version of the struggles people in poverty face? The term "poverty porn" has been coined to describe these kinds of shock-based images which reduce people to their vulnerability and helplessness. Narratives within INGO media campaigns can either contribute to, or combat stereotypical images of developing regions. The first section of this research will discuss representations of people from developing regions. Second, the research will examine strategies employed in several digital-based INGO media campaigns through their use of visual and verbal tools. Third, the research will analyze the ethical nature of media campaigns which contribute to or combat stereotypes. It is important for international non-governmental organizations and those within the field of international development to consider how communication strategies impact the understanding we have of developing regions. This research aims to look critically at INGO communications and provide best practices for organizations constructing their own media campaigns. FSU_libsubv1_scholarship_submission_1525459187_d84adacc FSU_libsubv1_scholarship_submission_1525459546_a796c8ef THE "SACRED HARP" SINGING GROUP AS AN INSTANCE OF NON-FORMAL EDUCATION. MITCHELL, HENRY CHESTERFIELD., The Florida State University The "State" of Behavioral and Demographic Analysis of Longevity Risk: A State-Aggregated Approach to Studying the Inter-Related Effects of Financial Education and Financial Literacy. Levine, Apple, Sirmans, Eleanor, Born, Patricia The "talk" of returning women graduate students: An ethnographic study of reality construction. McKenna, Alexis Yvonne., Florida State University This study looked at women's internal experience of graduate school. In particular, it focused on the experience of women returning full-time to graduate school after an extended time-out for careers and/or family. The questions examined were: (1) how do returning women "name and frame" their experience? (2) what, if any, is the relationship between the way the women "name and frame" their experience and their response to it? and, (3) what role does the researcher-as-interviewer play in the... Show moreThis study looked at women's internal experience of graduate school. In particular, it focused on the experience of women returning full-time to graduate school after an extended time-out for careers and/or family. The questions examined were: (1) how do returning women "name and frame" their experience? (2) what, if any, is the relationship between the way the women "name and frame" their experience and their response to it? and, (3) what role does the researcher-as-interviewer play in the construction of the data?, Data were collected through a series of three ethnographic interviews with 12 returning women, ranging in age from 28 to 50. Two of the twelve women were single, two were widowed, seven were divorced and one was divorced and remarried. Eight of the women had children., Analysis of the data showed that returning women, as a group, "named and framed" their experience in terms of change. Some women wanted to change self-image or self-concept while others wanted to acquire a new set of skills or credentials. Individually, the women "named and framed" their experiences in terms of an internalized "meaning-making map" acquired in the family of origin but modified through adult experiences. This "map" told them who they were and what kind of a life they could have. It gave their "talk" and behavior a consistency that could be recognized; it could make life easier or harder. A woman who felt she must "prove" herself, for example, found graduate school more difficult than a woman who wanted to "work smart.", The researcher-as-interviewer influenced the construction of data through her presence as well as through the kinds of questions she asked. The women understood and gave meaning to their experiences through the process of explaining them to the interviewer. The insights gained through this process of "shared talk" influenced future action and decisions. "To Benefit the World by Whatever Means Possible": Adolescents' Constructions of Global Citizenship. Myers, John This article reports on the ways that 77 students in an international studies programme constructed meanings for global citizenship. The focus was on their personal meanings for the topic and how they articulated a global identity with their national civic beliefs. Data was collected from online discussion boards, written essays and 20 interviews. A key finding was that the students' political language for global citizenship, examined here in terms of purpose, membership and relationship with... Show moreThis article reports on the ways that 77 students in an international studies programme constructed meanings for global citizenship. The focus was on their personal meanings for the topic and how they articulated a global identity with their national civic beliefs. Data was collected from online discussion boards, written essays and 20 interviews. A key finding was that the students' political language for global citizenship, examined here in terms of purpose, membership and relationship with national citizenship, was predominantly a moral commitment framed in universal language. A second finding was that the students understood global citizenship as a heterogeneous and complex affiliation shaped by a range of sources. The implication is that citizenship education emphasizing a narrow notion of patriotism may encourage students to disengage from civic life because it does not represent their lived experiences and identities. Insights for making citizenship education practices more inclusive are discussed., In this study, information about national identity and global citizenship were collected from 77 students enrolled in an international studies program through discussion boards, essays, and interviews. Results regarding global citizenship showed that participants' language was often framed in moral and universal terms, and that students saw global citizenship as complex and drew from diverse sources to understand what it meant. The article also discussed how citizenship education needs to be broader and more inclusive than the traditional focus on patriotism. FSU_migr_ste_faculty_publications-0007, 10.1080/01411920902989219 "Waiting to Fail" Redux: Understanding Inadequate Response to Intervention.. Al Otaiba, Stephanie, Wagner, Richard K, Miller, Brett This introduction to the special issue provides an overview of the promise, but also the ongoing challenges, related to Response to Intervention (RTI) as a means of both prevention and identification of reading disabilities. We conclude by describing the articles in this special issue and considering their implications for future research. FSU_pmch_25422530, 10.1177/0731948714525622, PMC4240019, 25422530, 25422530 #IfTheyGunnedMeDown: Social Media Activism in Ferguson, Missouri. Entralgo-Fernandez, Rebekah, Jones, Emilie, Carney, Sean The study focuses on the race issues and increased police militarization in Ferguson, Missouri related to the recent murder of Michael Brown. This particular part of the study focuses on the popular trend of the hashtag If They Gunned Me Down. Young activists on Twitter post pictures of themselves, both positive and negative, to highlight the media's opinion of people of color in the news. The tag is meant to show the obvious bias in media portrayal of black victims of police violence through... Show moreThe study focuses on the race issues and increased police militarization in Ferguson, Missouri related to the recent murder of Michael Brown. This particular part of the study focuses on the popular trend of the hashtag If They Gunned Me Down. Young activists on Twitter post pictures of themselves, both positive and negative, to highlight the media's opinion of people of color in the news. The tag is meant to show the obvious bias in media portrayal of black victims of police violence through personal images. During the study we studied these images and then complied a sample of 20 images per category (categories being aspects of their personality being highlighted). The tweets show two pictures per post, one negative and one positive, which we group together to find the most common traits presented. From these qualities we are hoping to gain an idea of the way the black community views the medias opinion of their worth. In addition to this information we are also qualitatively coding tweets related to race, black culture and marketing to find celebrities involvement and influence in the issue of police brutality of the black community. β-lactam synthesis. Holton, Robert A., Vu, Phong H. The present invention is directed to a process for the preparation of β-lactams. Generally, an imine is cyclocondensed with a ketene acetal or enolate to form the β-lactam product in a "one pot" synthesis, this process is generally performed at a higher temperature than conventional processes. FSU_uspto_7541458, 7541458, 711524, 11/449462, 6c9256d97d167832cbab694dc904bd27 'determinism' Is Just Fine: A Reply To Scott Sehon. De Marco, Gabriel Scott Sehon recently argued that the standard notion of determinism employed in the Consequence Argument makes it so that, if our world turns out to be deterministic, then an interventionist God is logically impossible. He further argues that because of this, we should revise our notion of determinism. In this paper I show that Sehon's argument for the claim that the truth of determinism, in this sense, would make an interventionist God logically impossible ultimately fails. I then offer and... Show moreScott Sehon recently argued that the standard notion of determinism employed in the Consequence Argument makes it so that, if our world turns out to be deterministic, then an interventionist God is logically impossible. He further argues that because of this, we should revise our notion of determinism. In this paper I show that Sehon's argument for the claim that the truth of determinism, in this sense, would make an interventionist God logically impossible ultimately fails. I then offer and respond to a weaker version of the argument for the claim that we should revise our notion of determinism. THE 'PRESENT ETERNITE' OF 'TROILUS AND CRISEYDE.'. LORRAH, JEAN., The Florida State University The 'True' Juvenile Offender: Age Effects and Juvenile Court Sanctioning. Mears, Daniel P., Cochran, Joshua C., Stults, Brian J., Greenman, Sarah J., Bhati, Avinash S., Greenwald, Mark A. Age is the only factor used to demarcate the boundary between juvenile and adult justice. However, little research has examined how age guides the juvenile court in determining which youth within the juvenile justice system merit particular dispositions, especially those that reflect the court's emphasis on rehabilitation. Drawing on scholarship on the court's origins, attribution theory, and cognitive heuristics, we hypothesize that the court focuses on youth in the middle of the range of... Show moreAge is the only factor used to demarcate the boundary between juvenile and adult justice. However, little research has examined how age guides the juvenile court in determining which youth within the juvenile justice system merit particular dispositions, especially those that reflect the court's emphasis on rehabilitation. Drawing on scholarship on the court's origins, attribution theory, and cognitive heuristics, we hypothesize that the court focuses on youth in the middle of the range of the court's age of jurisdiction—characterized in this article as "true" juveniles—who may be viewed as meriting more specialized intervention. We use data from Florida for court referrals in 2008 (N = 71,388) to examine the decision to proceed formally or informally and, in turn, to examine formally processed youth dispositions (dismissal, diversion, probation, commitment, and transfer) and informally processed youth dispositions (dismissal, diversion, and probation). The analyses provide partial support for the hypothesis. The very young were more likely to be informally processed; however, among the informally processed youth, the youngest, not "true" juveniles, were most likely to be diverted or placed on probation. By contrast, among formally processed youth, "true" juveniles were most likely to receive traditional juvenile court responses, such as diversion or probation. FSU_libsubv1_scholarship_submission_1460380390, 10.1111/1745-9125.12034 THE (CARBON-12,BERYLLIUM-8) AND (CARBON-12,CARBON-12) REACTIONS ON EVEN CALCIUM ISOTOPES. MORGAN, GORDON REESE., The Florida State University THE (CARBON-12,BERYLLIUM-8) AND (OXYGEN-16,BERYLLIUM-8) REACTIONS ON CARBON-12, OXYGEN-16, AND SILICON-28 NUCLEI. ARTZ, JERRY LEE., The Florida State University (oxygen-16 + thorium-232) incomplete fusion followed by fission at 140 MeV. Gavathas, Evangelos P., Florida State University Cross sections for incomplete fusion followed by fission have been measured for the reaction ($\sp{16}$O + $\sp{232}$Th) at 140 MeV. In plane and out of plane measurements were made of cross sections for beamlike fragments in coincidence with fission fragments. The beamlike fragments were detected with the Florida State large acceptance Bragg curve spectrometer. The detector was position sensitive in the polar direction. The beamlike particles observed in coincidence with fission fragments... Show moreCross sections for incomplete fusion followed by fission have been measured for the reaction ($\sp{16}$O + $\sp{232}$Th) at 140 MeV. In plane and out of plane measurements were made of cross sections for beamlike fragments in coincidence with fission fragments. The beamlike fragments were detected with the Florida State large acceptance Bragg curve spectrometer. The detector was position sensitive in the polar direction. The beamlike particles observed in coincidence with fission fragments were He, Li, Be, B, C, N and O. Fission fragments were detected by three surface barrier detectors using time of flight for particle identification. The reaction cross section due to incomplete fusion is 747 $\pm$ 112 mB, or 42% of the total fission cross section. The strongest incomplete fusion channels were the helium and carbon channels. The average transferred angular momentum for each incomplete fusion channel was calculated using the $Q\sb{opt}$ model of Wilczynski, and the angular correlation was calculated using the saddle point transition state model. The K distribution was determined from the Rotating Liquid Drop model. The theoretical angular distributions were fitted to the experimental angular distributions with the angular momentum J and the dealignment factor $\alpha\sb{o}$ as free parameters. The fitted parameter J was in excellent agreement with the $Q\sb{opt}$ model predictions. The conclusions of this study are that the incomplete fusion cross section is a large part of the total cross section, and that the saddle point transition state model adequately describes the observed angular correlations for fission following incomplete fusion. (tco4-)-tc-99 Remediation By A Cationic Polymeric Network. Li, Jie, Dai, Xing, Zhu, Lin, Xu, Chao, Zhang, Duo, Silver, Mark A., Li, Peng, Chen, Lanhua, Li, Yongzhong, Zuo, Douwen, Zhang, Hui, Xiao, Chengliang, Chen, Jing, Diwu, Juan,... Show moreLi, Jie, Dai, Xing, Zhu, Lin, Xu, Chao, Zhang, Duo, Silver, Mark A., Li, Peng, Chen, Lanhua, Li, Yongzhong, Zuo, Douwen, Zhang, Hui, Xiao, Chengliang, Chen, Jing, Diwu, Juan, Farha, Omar K., Albrecht-Schmitt, Thomas E., Chai, Zhifang, Wang, Shuao Direct removal of (TcO4-)-Tc-99 from the highly acidic solution of used nuclear fuel is highly beneficial for the recovery of uranium and plutonium and more importantly aids in the elimination of Tc-99 discharge into the environment. However, this task represents a huge challenge given the combined extreme conditions of super acidity, high ionic strength, and strong radiation field. Here we overcome this challenge using a cationic polymeric network with significant TcO4- uptake capabilities... Show moreDirect removal of (TcO4-)-Tc-99 from the highly acidic solution of used nuclear fuel is highly beneficial for the recovery of uranium and plutonium and more importantly aids in the elimination of Tc-99 discharge into the environment. However, this task represents a huge challenge given the combined extreme conditions of super acidity, high ionic strength, and strong radiation field. Here we overcome this challenge using a cationic polymeric network with significant TcO4- uptake capabilities in four aspects: the fastest sorption kinetics, the highest sorption capacity, the most promising uptake performance from highly acidic solutions, and excellent radiation-resistance and hydrolytic stability among all anion sorbent materials reported. In addition, this material is fully recyclable for multiple sorption/desorption trials, making it extremely attractive for waste partitioning and emergency remediation. The excellent TcO4- uptake capability is elucidated by X-ray absorption spectroscopy, solid-state NMR measurement, and density functional theory analysis on anion coordination and bonding. FSU_libsubv1_wos_000440413500007, 10.1038/s41467-018-05380-5 .beta.-lactams as taxol intermediates N-acylated. Holton, Robert A. .beta.-lactam compounds which are reacted with a metal alkoxide for preparing N-acyl, N-sulfonyl and phosphoryl substituted isoserine esters. FSU_uspto_5539103, 5539103, 711524, 08/351532, 600b83161da1122888348587dc18798c .beta.-lactams used in preparing taxol. A .beta.-lactam of the formula: ##STR1## wherein R.sub.1 is aryl, substituted aryl, alkyl, alkenyl, or alkynyl; R.sub.2 is hydrogen, alkyl, acyl, acetal, ethoxyethyl, or other hydroxyl protecting group; and R.sub.3 is aryl, substituted aryl, alkyl, alkenyl, or alkynyl; and the enantiomers and diastereomers thereof. 1-deoxy baccatin III, 1-deoxy taxol and 1-deoxy taxol analogs and method for the preparation thereof. Holton, Robert A., Somoza, Carmen, Liang, Feng, Tang, Suhan 1-Deoxybaccatin III, 1-deoxytaxol and 1-deoxy taxol analogs and method for the preparation thereof. 1-deoxy taxol analogs. 1-s2.0-S2352827318300272-main. 1.1-billion-year-old Porphyrins Establish A Marine Ecosystem Dominated By Bacterial Primary Producers. Gueneli, N., McKenna, A. M., Ohkouchi, N., Boreham, C. J., Beghin, J., Javaux, E. J., Brocks, J. J. The average cell size of marine phytoplankton is critical for the flow of energy and nutrients from the base of the food web to higher trophic levels. Thus, the evolutionary succession of primary producers through Earth's history is important for our understanding of the radiation of modern protists similar to 800 million years ago and the emergence of eumetazoan animals similar to 200 million years later. Currently, it is difficult to establish connections between primary production and the... Show moreThe average cell size of marine phytoplankton is critical for the flow of energy and nutrients from the base of the food web to higher trophic levels. Thus, the evolutionary succession of primary producers through Earth's history is important for our understanding of the radiation of modern protists similar to 800 million years ago and the emergence of eumetazoan animals similar to 200 million years later. Currently, it is difficult to establish connections between primary production and the proliferation of large and complex organisms because the mid-Proterozoic (similar to 1,800-800 million years ago) rock record is nearly devoid of recognizable phytoplankton fossils. We report the discovery of intact porphyrins, the molecular fossils of chlorophylls, from 1,100-million-year-old marine black shales of the Taoudeni Basin (Mauritania), 600 million years older than previous findings. The porphyrin nitrogen isotopes (delta N-15(por) = 5.6-10.2 parts per thousand) are heavier than in younger sedimentary sequences, and the isotopic offset between sedimentary bulk nitrogen and porphyrins (epsilon(por) = -5.1 to -0.5 parts per thousand) points to cyanobacteria as dominant primary producers. Based on fossil carotenoids, anoxygenic green (Chlorobiacea) and purple sulfur bacteria (Chromatiaceae) also contributed to photosynthate. The low epsilon(por) values, in combination with a lack of diagnostic eukaryotic steranes in the time interval of 1,600-1,000 million years ago, demonstrate that algae played an insignificant role in mid-Proterozoic oceans. The paucity of algae and the small cell size of bacterial phytoplankton may have curtailed the flow of energy to higher trophic levels, potentially contributing to a diminished evolutionary pace toward complex eukaryotic ecosystems and large and active organisms. FSU_libsubv1_wos_000439574700004, 10.1073/pnas.1803866115 10-desacetoxytaxol derivatives. Farina, Vittorio, Holton, Robert A., Chen, Shu-Hui The present invention relates to 10-desacetoxytaxol and derivatives thereof, which are useful as antitumor agents. These compounds have the formula ##STR1## wherein R.sub.2 is hydrogen, hydroxy or a protected hydroxy group; R.sub.3 and R.sub.4 are independently hydrogen, hydroxy, a protected hydroxy group, methyl, --SH, --NH.sub.2, or --NR.sub.8 R.sub.9 ; R.sub.5 is R.sub.10, or --OR.sub.10 ; R.sub.6 and R.sub.7 are independently hydrogen, alkyl, or aryl; R.sub.8 and R.sub.9 are independently... Show moreThe present invention relates to 10-desacetoxytaxol and derivatives thereof, which are useful as antitumor agents. These compounds have the formula ##STR1## wherein R.sub.2 is hydrogen, hydroxy or a protected hydroxy group; R.sub.3 and R.sub.4 are independently hydrogen, hydroxy, a protected hydroxy group, methyl, --SH, --NH.sub.2, or --NR.sub.8 R.sub.9 ; R.sub.5 is R.sub.10, or --OR.sub.10 ; R.sub.6 and R.sub.7 are independently hydrogen, alkyl, or aryl; R.sub.8 and R.sub.9 are independently hydrogen, alkyl, alkenyl, alkynyl, or aryl; and R.sub.10 is alkoxy, alkyl, alkenyl, alkynl, or aryl. 125-Iodine: a probe in radiobiology. Warters, Raymond Leon 14-3-3 and aggresome formation: implications in neurodegenerative diseases.. Jia, Baohui, Wu, Yuying, Zhou, Yi Protein misfolding and aggregation underlie the pathogenesis of many neurodegenerative diseases. In addition to chaperone-mediated refolding and proteasomal degradation, the aggresome-macroautophagy pathway has emerged as another defense mechanism for sequestration and clearance of toxic protein aggregates in cells. Previously, the 14-3-3 proteins were shown to be indispensable for the formation of aggresomes induced by mutant huntingtin proteins. In a recent study, we have determined that 14... Show moreProtein misfolding and aggregation underlie the pathogenesis of many neurodegenerative diseases. In addition to chaperone-mediated refolding and proteasomal degradation, the aggresome-macroautophagy pathway has emerged as another defense mechanism for sequestration and clearance of toxic protein aggregates in cells. Previously, the 14-3-3 proteins were shown to be indispensable for the formation of aggresomes induced by mutant huntingtin proteins. In a recent study, we have determined that 14-3-3 functions as a molecular adaptor to recruit chaperone-associated misfolded proteins to dynein motors for transport to aggresomes. This molecular complex involves a dimeric binding of 14-3-3 to both the dynein-intermediate chain (DIC) and an Hsp70 co-chaperone Bcl-2-associated athanogene 3 (BAG3). As 14-3-3 has been implicated in various neurodegenerative diseases, our findings may provide mechanistic insights into its role in managing misfolded protein stress during the process of neurodegeneration. FSU_pmch_24549097, PMC4189886, 24549097, 24549097, 28123 14-3-3 protein targets misfolded chaperone-associated proteins to aggresomes. Xu, Zhe, Graham, Kourtney, Foote, Molly, Liang, Fengshan, Rizkallah, Raed, Hurt, Myra, Wang, Yanchang, Wu, Yuying, Zhou, Yi The aggresome is a key cytoplasmic organelle for sequestration and clearance of toxic protein aggregates. Although loading misfolded proteins cargos to dynein motors has been recognized as an important step in the aggresome formation process, the molecular machinery that mediates the association of cargos with the dynein motor is poorly understood. Here, we report a new aggresome-targeting pathway that involves isoforms of 14-3-3, a family of conserved regulatory proteins. 14-3-3 interacts... Show moreThe aggresome is a key cytoplasmic organelle for sequestration and clearance of toxic protein aggregates. Although loading misfolded proteins cargos to dynein motors has been recognized as an important step in the aggresome formation process, the molecular machinery that mediates the association of cargos with the dynein motor is poorly understood. Here, we report a new aggresome-targeting pathway that involves isoforms of 14-3-3, a family of conserved regulatory proteins. 14-3-3 interacts with both the dynein-intermediate chain (DIC) and an Hsp70 co-chaperone Bcl-2-associated athanogene 3 (BAG3), thereby recruiting chaperone-associated protein cargos to dynein motors for their transport to aggresomes. This molecular cascade entails functional dimerization of 14-3-3, which we show to be crucial for the formation of aggresomes in both yeast and mammalian cells. These results suggest that 14-3-3 functions as a molecular adaptor to promote aggresomal targeting of misfolded protein aggregates and may link such complexes to inclusion bodies observed in various neurodegenerative diseases. FSU_pmch_23843611, 10.1242/jcs.126102, PMC3772389, 23843611, 23843611, jcs.126102 14-3-3 proteins are required for hippocampal long-term potentiation and associative learning and memory. Qiao, Haifa, Foote, Molly, Graham, Kourtney, Wu, Yuying, Zhou, Yi 14-3-3 is a family of regulatory proteins highly expressed in the brain. Previous invertebrate studies have demonstrated the importance of 14-3-3 in the regulation of synaptic functions and learning and memory. However, the in vivo role of 14-3-3 in these processes has not been determined using mammalian animal models. Here, we report the behavioral and electrophysiological characterization of a new animal model of 14-3-3 proteins. These transgenic mice, considered to be a 14-3-3 functional... Show more14-3-3 is a family of regulatory proteins highly expressed in the brain. Previous invertebrate studies have demonstrated the importance of 14-3-3 in the regulation of synaptic functions and learning and memory. However, the in vivo role of 14-3-3 in these processes has not been determined using mammalian animal models. Here, we report the behavioral and electrophysiological characterization of a new animal model of 14-3-3 proteins. These transgenic mice, considered to be a 14-3-3 functional knock-out, express a known 14-3-3 inhibitor in various brain regions of different founder lines. We identify a founder-specific impairment in hippocampal-dependent learning and memory tasks, as well as a correlated suppression in long-term synaptic plasticity of the hippocampal synapses. Moreover, hippocampal synaptic NMDA receptor levels are selectively reduced in the transgenic founder line that exhibits both behavioral and synaptic plasticity deficits. Collectively, our findings provide evidence that 14-3-3 is a positive regulator of associative learning and memory at both the behavioral and cellular level. FSU_pmch_24695700, 10.1523/JNEUROSCI.4393-13.2014, PMC3972712, 24695700, 24695700, 34/14/4801 14-3-3 proteins in neurological disorders. Foote, Molly, Zhou, Yi 14-3-3 proteins were originally discovered as a family of proteins that are highly expressed in the brain. Through interactions with a multitude of binding partners, 14-3-3 proteins impact many aspects of brain function including neural signaling, neuronal development and neuroprotection. Although much remains to be learned and understood, 14-3-3 proteins have been implicated in a variety of neurological disorders based on evidence from both clinical and laboratory studies. Here we will... Show more14-3-3 proteins were originally discovered as a family of proteins that are highly expressed in the brain. Through interactions with a multitude of binding partners, 14-3-3 proteins impact many aspects of brain function including neural signaling, neuronal development and neuroprotection. Although much remains to be learned and understood, 14-3-3 proteins have been implicated in a variety of neurological disorders based on evidence from both clinical and laboratory studies. Here we will review previous and more recent research that has helped us understand the roles of 14-3-3 proteins in both neurodegenerative and neuropsychiatric diseases. FSU_pmch_22773956, PMC3388734, 22773956, 22773956 14-3-3τ promotes surface expression of Cav2.2 (α1B) Ca2+ channels. Liu, Feng, Zhou, Qin, Zhou, Jie, Sun, Hao, Wang, Yan, Zou, Xiuqun, Feng, Lingling, Hou, Zhaoyuan, Zhou, Aiwu, Zhou, Yi, Li, Yong Surface expression of voltage-gated Ca(2+) (Cav) channels is important for their function in calcium homeostasis in the physiology of excitable cells, but whether or not and how the α1 pore-forming subunits of Cav channels are trafficked to plasma membrane in the absence of the known Cav auxiliary subunits, β and α2δ, remains mysterious. Here we showed that 14-3-3 proteins promoted functional surface expression of the Cav2.2 α1B channel in transfected tsA-201 cells in the absence of any known... Show moreSurface expression of voltage-gated Ca(2+) (Cav) channels is important for their function in calcium homeostasis in the physiology of excitable cells, but whether or not and how the α1 pore-forming subunits of Cav channels are trafficked to plasma membrane in the absence of the known Cav auxiliary subunits, β and α2δ, remains mysterious. Here we showed that 14-3-3 proteins promoted functional surface expression of the Cav2.2 α1B channel in transfected tsA-201 cells in the absence of any known Cav auxiliary subunit. Both the surface to total ratio of the expressed α1B protein and the current density of voltage step-evoked Ba(2+) current were markedly suppressed by the coexpression of a 14-3-3 antagonist construct, pSCM138, but not its inactive control, pSCM174, as determined by immunofluorescence assay and whole cell voltage clamp recording, respectively. By contrast, coexpression with 14-3-3τ significantly enhanced the surface expression and current density of the Cav2.2 α1B channel. Importantly, we found that between the two previously identified 14-3-3 binding regions at the α1B C terminus, only the proximal region (amino acids 1706-1940), closer to the end of the last transmembrane domain, was retained by the endoplasmic reticulum and facilitated by 14-3-3 to traffic to plasma membrane. Additionally, we showed that the 14-3-3/Cav β subunit coregulated the surface expression of Cav2.2 channels in transfected tsA-201 cells and neurons. Altogether, our findings reveal a previously unidentified regulatory function of 14-3-3 proteins in promoting the surface expression of Cav2.2 α1B channels. FSU_pmch_25516596, 10.1074/jbc.M114.567800, PMC4317001, 25516596, 25516596, M114.567800 14-hydrido-9β-hydroxytetracyclic taxanes. Suzuki, Yukio, Holton, Robert A., Somoza, Carmen, Shindo, Mitsuru Process for the preparation of a derivative or analog of baccatin III or 10-desacetyl baccatin III having a C9 substituent other than keto in which the C9 keto substituent of taxol, a taxol analog, baccatin III or 10-desacetyl baccatin III is selectively reduced to the corresponding hydroxy group. THE 1928 PRESIDENTIAL ELECTION IN FLORIDA. HUGHES, MELVIN EDWARD, JR., The Florida State University THE 1964 WISCONSIN PRESIDENTIAL PRIMARY: GEORGE C. WALLACE. WINDLER, CHARLES WILLIAM, JR., Florida State University In 1963, Alabama Governor George C. Walace defied a court order by Attorney General Nicholas Katzenbach to integrate the University of Alabama. This incident turned the governor into a national celebrity and led to a number of speaking engagements across the country. During one of these engagements, Wallace indicated an interest in entering certain presidential primaries in the North in order to campaign against the pending national civil rights legislation. The Wisconsin Democratic... Show moreIn 1963, Alabama Governor George C. Walace defied a court order by Attorney General Nicholas Katzenbach to integrate the University of Alabama. This incident turned the governor into a national celebrity and led to a number of speaking engagements across the country. During one of these engagements, Wallace indicated an interest in entering certain presidential primaries in the North in order to campaign against the pending national civil rights legislation. The Wisconsin Democratic presidential primary was the first of these races., Since President Lyndon Johnson had the Democratic presidential nomination for the asking, little attention was given to the Wallace candidacy. Governor John Reynolds was selected to run against Wallace as the Democraic favorite-son candidate, and the Republicans chose Representative John Byrnes as their favorite-son candidate. When the votes were cast on April 7, the entire nation was surprised at the large number of votes obtained by Wallace., Upon examination of the conditions and events prior to and during the presidential primary campaign, the following factors apparently contributed to the surprising showing of Governor Wallace: (1) An open primary system existed in Wisconsin that allowed a large Republican cross-over vote for Wallace; (2) The Republican favorite-son candidate had no opponent; (3) The Democratic party was divided over their favorite-son candidate, one of the most unpopular Governors in the political history of Wisconsin; (4) Wallace's opponents waged a personal defamation campaign based on Wallace's reputation as a racist to which Wallace did not respond; and (5) Some white residents of Wisconsin were afraid of the increasing civil rights demands of the black population. These factors served to gain support and sympathy for the Wallace candidacy and to focus national attention on the Alabama governor as he conducted subsequent campaigns in Maryland and Indiana. Center for Ocean-Atmospheric Prediction Studies (48) + - Education, Guidance and Counseling (221) + - Literature, Modern (200) + - Medical sciences (185) + - Education, Teacher Training (184) + - Physics, Nuclear (162) + - Psychology, Experimental (160) + - Sociology, Criminology and Penology (160) + - Political Science, General (154) + - Library Science (151) + - Home Economics (148) + - Literature, American (139) + - Chemistry, Organic (132) + - Theater (130) + - Adult (123) + - Steele, C. K. (Charles Kenzie) (1) + - Students for a Democratic Society (U.S.) (1) + - Apalachicola (1) + - Apalachicola (Fla.) (1) + - Bellwether Parish (Apalachicola, Fla.) (1) + - Freely accessible for non-commerical use. Subject to copyright laws. 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asymptotic statistics definition Significance testing refers to the use of statistical techniques that are used to determine whether the sample drawn from a population is actually from the population or if by the chance factor. The asymptotic regression model has the form: Figure 1. In mathematics and statistics, an asymptotic distribution is a … A Limiting Distribution (also called an asymptotic distribution) is the hypothetical distribution — or convergence — of a sequence of distributions. When b 1 >0, b 2 <0, and b 3 <0, it gives Mistcherlich's model of the "law of diminishing returns". We can simplify the analysis by doing so (as we know 2011, Soon-Mo Jung, Hyers–Ulam–Rassias Stability of Functional Equations in Nonlinear Analysis, Springer →ISBN, page 130 F. Skof investigated an interesting asymptotic property of the additive functions (see Theorem 2.34). Intuitively, I disagree: "unbiasedness" is a term we first learn in relation to a distribution (finite sample). However, hand calculation of the true probability distributions of many test statistics is … Example 3 (Sign test). Asymptotic theory or asymptotics occupy a focal point in the developments of the theory of rank tests. In particular, the central limit theorem provides an example where the asymptotic distribution is the normal distribution. Asymptotic statistics book 1998 worldcat. Asymptotic definition of asymptotic by The Free Dictionary. Many test statistics follow a discrete probability distribution. Suppose that a distribution of observations is defined by a real parameter $ \theta $ and that it is required to verify the hypothesis $ H _ {0} $: $ \theta = \theta _ {0} $ against the alternative $ H _ {1} $: $ \theta \neq \theta _ {0} $. It is remarkable that this is true under the present definition of convergence of experiments, which involves only marginal convergence and is very weak. Asymptotic Statistics Solution Manual Chegg com. Using asymptotic analysis, we can very well conclude the best case, average case, and worst case scenario of an algorithm. asymptotic statistics a w van der vaart trade paperback. Lecture 4: Asymptotic Distribution Theory∗ In time series analysis, we usually use asymptotic theories to derive joint distributions of the estimators for parameters in a model. Asymptotic theory of statistics and probability anirban. ... Browse other questions tagged mathematical-statistics independence asymptotics definition or ask your own question. In the related post over at math.se, the answerer takes as given that the definition for asymptotic unbiasedness is $\lim_{n\to \infty} E(\hat \theta_n-\theta) = 0$.. Barndorff-Nielson & Cox provide a direct definition of asymptotic normality. The plug-in principle is a technique used in probability theory and statistics to approximately compute or to estimate a feature of a probability distribution (e.g., the expected value, the variance, a quantile) that cannot be computed exactly.It is widely used in the theories of Monte Carlo simulation and bootstrapping. Asymptotic distribution is a distribution we obtain by letting the time horizon (sample size) go to infinity. ... Information and translations of asymptotic distribution in the most comprehensive dictionary definitions resource on the web. Asymptotic p-values are useful for large sample sizes when the calculation of an exact p-value is too computer-intensive. Asymptotic definition of asymptotic by the free dictionary. This model initially increases quickly with increasing values of x, but then the gains slow and finally taper off … by Marco Taboga, PhD. Synonyms for asymptotic in Free Thesaurus. Remark 1. This book is an introduction to the field of asymptotic statistics. This example is from Van der Vaart, but presents a different derivation than is found in the book. Asymptotic definition, of or relating to an asymptote. In mathematics and statistics, an asymptotic distribution is a probability distribution that is in a sense the "limiting" distribution of a sequence of distributions. Condition (HI) is a standard assumption needed to ensure asymptotic stability of the underlying system; similar remarks apply to (H4). $\begingroup$ Asymptotic variance refers to the variance of a statistic (appropriately normalized by first subtracting the expected value and multiplying by the square root of the sample size) when the sample size approaches infinity. Asymptotic Distribution Theory • In Chapter 5, we derive exact distributions of several sample statistics based on a random sample of observations. 1 word related to asymptote: straight line. There are several distinct approaches to the definition of the asymptotic efficiency of a test. In these situations, we rely on approximate results that are based on It appears then more natural to consider "asymptotic unbiasedness" in relation to an asymptotic distribution. One of the main uses of the idea of an asymptotic distribution is in providing approximations to the cumulative distribution functions of … A w van der vaart asymptotic statistics pdf ebook. Pdf asymptotic statistics by a w van der vaart. Definition of asymptotic distribution in the Definitions.net dictionary. 9780521784504 Asymptotic Statistics Cambridge Series in. • In many situations an exact statistical result is difficult to get. See also. Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. asymptotic statistics springerlink. A line or curve that is asymptotic to given curve is called the asymptote of . The plug-in principle. 'The term asymptotic means approaching a value or curve arbitrarily closely (i.e., as some sort of limit is taken). See more. Usually, statistical significance is determined by the set alpha level, which is conventionally set at .05. Asymptotic regression model. Antonyms for asymptotic. Asymptote definition is - a straight line associated with a curve such that as a point moves along an infinite branch of the curve the distance from the point to the line approaches zero and the slope of the curve at the point approaches the slope of the line. Asymptotic developable definition is - the developable surface generated by the tangent planes of a ruled surface whose rulings are supposed not to be minimal lines. Asymptotic theory of statistics and probability Anirban DasGupta (auth.) springerlink. Asymptotic Definition of Asymptotic at Dictionary com. Asymptotic analysis of an algorithm refers to defining the mathematical boundation/framing of its run-time performance. Statistics 553 Spring 2020. Some of these distributions are well-known. The asymptotic representation theorem, Theorem shows that every sequence of statistics in a converging sequence of experiments is matched by a statistic in the limit experiment. The treatment is both practical and mathematically rigorous. 2 Lecture 19: Asymptotic Relative Efficiency Definition 2 (Asymptotic relative efficiency). Asymptotic meaning in the cambridge english dictionary. asymptotic variance an overview sciencedirect topics. One of the main uses of the idea of an asymptotic distribution is in providing approximations to the cumulative distribution functions of … In statistics, asymptotic theory (or large sample theory) is a generic framework for assessment of properties of estimators and statistical tests.Within this framework it is typically assumed that the sample size n grows indefinitely, and the properties of statistical procedures are evaluated in the limit as n → ∞.. The confidence intervals can be of two types that are asymptotic and non-asymptotic. Asymptotic statistics ideas repec. asymptotic definition of asymptotic at dictionary. (mathematics) Pertaining to values or properties approached at infinity. In mathematics and statistics, an asymptotic distribution is a hypothetical distribution that is in a sense the "limiting" distribution of a sequence of distributions. Asymptotic normality synonyms, Asymptotic normality pronunciation, Asymptotic normality translation, English dictionary definition of Asymptotic normality. The term asymptotic means approaching a value or curve arbitrarily closely (i.e., as some sort of limit is taken). A line or curve that is asymptoticto given curve is called the asymptote of .' Asymptotic Statistics A W van der Vaart Google Books. asymptotic statistics a ulm university. Perhaps the most common distribution to arise as an asymptotic distribution is the normal distribution. Suitable as a text for a graduate or Master's level statistics course, this book also gives researchers in statistics, probability, and their applications an overview of the latest research in asymptotic statistics. What are synonyms for asymptotic? Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Hardy and Wright (1979, p. 7) use the symbol to denote that one quantity is asymptotic to another. Here is a practical and mathematically rigorous introduction to the field of asymptotic statistics. The analysis of several plausible nested alternative stock return generating processes suggests that stock returns with weak asymptotic tail dependence will produce CoVaR and MES hypothesis test statistic distributions that significantly overlap the sampling distributions of test statistics calculated from Gaussian returns. As it is hypothetical, it isn't a distribution in the general sense of the word. The asymptotic distribution theory attempts to find a limiting distribution to a series of distributions.. Asymptotic normality. This book is an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. Cite The Asymptotic Relative Efficiency (ARE) is the ratio of the squares of slopes between two statistics. Asymptotic Statistics SpringerLink. Aadhar Seeded Meaning In Kannada, Healthy Grilled Peaches, Egg Shell Uses For Health, Harry Potter Knight Bus 3d Puzzle Instructions, Triglyceride Omega Liquid Pump, School Of Planning And Architecture Recruitment, Makita Xdt15zb Review, Microsoft Exam Dumps Pdf, Port Of Tauranga Vessel Arrival, Curry Sauce Made With Baked Beans, asymptotic statistics definition 2020	CommonCrawl
On optimal autocorrelation inequalities on the real line New general decay result for a system of viscoelastic wave equations with past history Adel M. Al-Mahdi 1,, , Mohammad M. Al-Gharabli 1, and Salim A. Messaoudi 2, The Preparatory Year Program, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia Department of Mathematics, University of Sharjah, P. O. Box, 27272, Sharjah. UAE Received November 2019 Revised September 2020 Published November 2020 Fund Project: This work is funded by KFUPM under Project #SB191037 This work is concerned with a coupled system of viscoelastic wave equations in the presence of infinite-memory terms. We show that the stability of the system holds for a much larger class of kernels. More precisely, we consider the kernels $ g_i : [0, +\infty) \rightarrow (0, +\infty) $ $ g_i'(t)\leq-\xi_i(t)H_i(g_i(t)),\qquad\forall\,t\geq0 \quad\mathrm{and\ for\ }i = 1,2, $ $ \xi_i $ $ H_i $ are functions satisfying some specific properties. 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Santos, Decay rates for solutions of a system of wave equations with memory, Electron. J. Differ. Equ., 2002 (2002), 1-17. Google Scholar I. E. Segal, The global Cauchy problem for a relativistic scalar field with power interaction, Bull. Soc. Math. Fr., 91 (1963), 129-135. Google Scholar Tomasz Szostok. Inequalities of Hermite-Hadamard type for higher order convex functions, revisited. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020296 Lingfeng Li, Shousheng Luo, Xue-Cheng Tai, Jiang Yang. A new variational approach based on level-set function for convex hull problem with outliers. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020070 Bahaaeldin Abdalla, Thabet Abdeljawad. Oscillation criteria for kernel function dependent fractional dynamic equations. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020443 Serge Dumont, Olivier Goubet, Youcef Mammeri. Decay of solutions to one dimensional nonlinear Schrödinger equations with white noise dispersion. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020456 Cung The Anh, Dang Thi Phuong Thanh, Nguyen Duong Toan. Uniform attractors of 3D Navier-Stokes-Voigt equations with memory and singularly oscillating external forces. Evolution Equations & Control Theory, 2021, 10 (1) : 1-23. doi: 10.3934/eect.2020039 Xiaopeng Zhao, Yong Zhou. Well-posedness and decay of solutions to 3D generalized Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 795-813. doi: 10.3934/dcdsb.2020142 Yang Liu. Global existence and exponential decay of strong solutions to the cauchy problem of 3D density-dependent Navier-Stokes equations with vacuum. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1291-1303. doi: 10.3934/dcdsb.2020163 Hassan Mohammad. A diagonal PRP-type projection method for convex constrained nonlinear monotone equations. Journal of Industrial & Management Optimization, 2021, 17 (1) : 101-116. doi: 10.3934/jimo.2019101 Manuel Friedrich, Martin Kružík, Jan Valdman. Numerical approximation of von Kármán viscoelastic plates. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 299-319. doi: 10.3934/dcdss.2020322 Hai Huang, Xianlong Fu. Optimal control problems for a neutral integro-differential system with infinite delay. Evolution Equations & Control Theory, 2020 doi: 10.3934/eect.2020107 Yifan Chen, Thomas Y. Hou. Function approximation via the subsampled Poincaré inequality. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 169-199. doi: 10.3934/dcds.2020296 Jing Zhou, Cheng Lu, Ye Tian, Xiaoying Tang. A SOCP relaxation based branch-and-bound method for generalized trust-region subproblem. Journal of Industrial & Management Optimization, 2021, 17 (1) : 151-168. doi: 10.3934/jimo.2019104 Barbora Benešová, Miroslav Frost, Lukáš Kadeřávek, Tomáš Roubíček, Petr Sedlák. An experimentally-fitted thermodynamical constitutive model for polycrystalline shape memory alloys. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020459 Xiaoping Zhai, Yongsheng Li. Global large solutions and optimal time-decay estimates to the Korteweg system. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1387-1413. doi: 10.3934/dcds.2020322 Alessandro Fonda, Rodica Toader. A dynamical approach to lower and upper solutions for planar systems "To the memory of Massimo Tarallo". Discrete & Continuous Dynamical Systems - A, 2021 doi: 10.3934/dcds.2021012 Youshan Tao, Michael Winkler. Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 439-454. doi: 10.3934/dcds.2020216 Bimal Mandal, Aditi Kar Gangopadhyay. A note on generalization of bent boolean functions. Advances in Mathematics of Communications, 2021, 15 (2) : 329-346. doi: 10.3934/amc.2020069 Adel M. Al-Mahdi Mohammad M. Al-Gharabli Salim A. Messaoudi	CommonCrawl
Accuracy of imputation using the most common sires as reference population in layer chickens Marzieh Heidaritabar1, Mario P. L. Calus2, Addie Vereijken3, Martien A. M. Groenen1 & John W. M. Bastiaansen1 Genotype imputation has become a standard practice in modern genetic research to increase genome coverage and improve the accuracy of genomic selection (GS) and genome-wide association studies (GWAS). We assessed accuracies of imputing 60K genotype data from lower density single nucleotide polymorphism (SNP) panels using a small set of the most common sires in a population of 2140 white layer chickens. Several factors affecting imputation accuracy were investigated, including the size of the reference population, the level of the relationship between the reference and validation populations, and minor allele frequency (MAF) of the SNP being imputed. The accuracy of imputation was assessed with different scenarios using 22 and 62 carefully selected reference animals (Ref22 and Ref62). Animal-specific imputation accuracy corrected for gene content was moderate on average (~ 0.80) in most scenarios and low in the 3K to 60K scenario. Maximum average accuracies were 0.90 and 0.93 for the most favourable scenario for Ref22 and Ref62 respectively, when SNPs were masked independent of their MAF. SNPs with low MAF were more difficult to impute, and the larger reference population considerably improved the imputation accuracy for these rare SNPs. When Ref22 was used for imputation, the average imputation accuracy decreased by 0.04 when validation population was two instead of one generation away from the reference and increased again by 0.05 when validation was three generations away. Selecting the reference animals from the most common sires, compared with random animals from the population, considerably improved imputation accuracy for low MAF SNPs, but gave only limited improvement for other MAF classes. The allelic R2 measure from Beagle software was found to be a good predictor of imputation reliability (correlation ~ 0.8) when the density of validation panel was very low (3K) and the MAF of the SNP and the size of the reference population were not extremely small. Even with a very small number of animals in the reference population, reasonable accuracy of imputation can be achieved. Selecting a set of the most common sires, rather than selecting random animals for the reference population, improves the imputation accuracy of rare alleles, which may be a benefit when imputing with whole genome re-sequencing data. Using dense single nucleotide polymorphism (SNP) panels, genomic selection (GS) and genome-wide association studies (GWAS) have become common in animal and plant genomic breeding programs. Both GS and GWAS exploit linkage disequilibrium (LD) between SNPs and causative mutations. Increasing the density of SNP panels is therefore expected to contribute to improved accuracies of genomic prediction and GWAS [1, 2]. However, higher density of SNPs means higher genotyping cost which is still a key constraint in implementing GWAS and GS in animal breeding programs. To overcome this constraint, selection candidates can be genotyped for a low-density SNP panel after which a higher density SNP panel is obtained through imputation. Animals may be genotyped for different SNP chips due to the expansion of available genotyping technologies, for design reasons, or due to the coexistence of several genotyping products [3]. Thus far, different SNP chips have been developed for chicken. For instance, the publicly available chicken 60K SNP chip [4] from Illumina and the 600K SNP chip [5] from Affymetrix. Another SNP chip, containing 42K SNPs, has been developed as a proprietary tool in chickens [6]. These SNP chips have been widely used for purposes such as GWAS [7, 8], GS [9–13], fine mapping of quantitative trait loci (QTL) [14] and identification of selection signals [15]. Because of genetic variation within and between domesticated and commercial chicken breeds [16] and because of differences in LD patterns between different chicken breeds [17], a higher density SNP chip would be useful to address different purposes mentioned above (GS, GWAS, identification of selection signals and fine mapping of QTL) in a diverse range of chicken breeds and populations. In the future, additional SNP chips or even whole-genome sequence data may replace the current SNP chip data in avian genetic and genomic studies. As higher density SNP chips are put into use, the re-genotyping of previously genotyped individuals with these new chips would be costly. Imputation from the lower density chip towards the higher density chip could then be a cost-effective strategy. With two different SNP chips, a combined dataset with all SNPs genotyped on all individuals would be desired. Imputation could be used, but the feasibility and accuracy of SNP imputation between the SNP chips needs to be tested. Druet et al. [3] performed imputation between two SNP chips in cattle data, where the SNPs specific to the Illumina Bovine SNP50 (50K) chip were imputed for Dutch Holstein bulls that were genotyped using a custom-made 60K Illumina chip (CRV, Arnhem, the Netherlands) and vice versa [3]. Their results showed an imputation accuracy of 99 %. Imputation accuracy is of special interest for SNPs that have low minor allele frequency (MAF). Many studies that used SNP chip data [18–23] and also sequence data [24] to perform imputation have demonstrated lower imputation accuracy for SNPs with low MAF. However, the effect of reference population design on imputation accuracy of low MAF SNPs is largely unknown. Using simulation, Meuwissen and Goddard [25] found that the error rate was much improved when relatives were sequenced, and Khatkar et al. [26] suggested that selecting animals for genotyping based on pedigree is a strategically optimised method if pedigree information is available. Several factors influence the accuracy of imputation including the genetic relationship between the animals in the reference and validation populations [27], the size of reference population [27], MAF of the SNP to be imputed [18], the proportion of missing genotypes on the low and high-density panel [28], the population structure and levels of LD [29], the imputation method and, if applicable, the parameter settings of the applied imputation algorithm [30]. One important factor is the genetic relationship between the animals in the reference and validation populations [27, 31]. When close relatives of target animals are genotyped at high density, the missing SNPs can be recovered through linkage and segregation analysis [32], where haplotypes can be traced across generations of directly related individuals by the Mendelian inheritance rules. The algorithms used for imputation use either LD information such as Beagle [33] and IMPUTE2 [34] or both LD and pedigree information such as AlphaImpute [35]. If a pedigree-free imputation method is used, the most important factors to increase the accuracy of imputation are: the size of the reference population and the availability of a representative reference population which maximises the accuracy of imputation and captures the highest proportion of genetic variation in the validation population. Few studies have investigated imputation accuracy in poultry compared with other livestock species (see review [36]). Thus far, they have demonstrated that the application of imputation methods is effective in chickens. Comparing imputation accuracies across studies is difficult, since applied imputation softwares, size of reference populations, imputation measures, density panels, and population-specific parameters (e.g. LD and effective population size (N e )) differ substantially across studies. In general, high imputation accuracies were found in broiler chickens (ranging from 0.94 to 0.99) [37, 38] and also in brown egg layer chickens (ranging from 0.68-0.97) [39–41]. Most studies in chicken imputed missing genotypes from a very low density such as 384, 1K or 3K to a medium-density (20K, 36K or 60K). For instance, Wang et al. [38] and Hickey et al. [37] imputed from 384 SNPs to 20K and 36K, respectively. Vereijken et al. [39] imputed from three low-density panels (384, 1K and 3K) to 57K on six chromsomes of brown layer chickens. This study had two objectives. The first was to investigate the accuracy of imputation of 60K genotypes from lower density SNP panels (3K and 48K) using a small reference population of the most common sires. Imputation from 48K to 60K was performed not only to assess the impact of having a higher density panel as reference (compared with 3K) on imputation accuracy, but also to mimic the imputation of genotypes between two different SNP chips with similar densities. The second was to investigate the factors that affect imputation accuracy, namely: the size of reference population, the level of genetic relationship between the reference and validation populations, and the MAF of imputed SNP. In this study, the accuracy of imputation to 60K genotypes from lower density SNP panels (3K and 48K) was assessed in genotype data from GGA1 of layer chickens, when using a small reference population of the most common sires that are influential in the validation population. In addition, we evaluated the factors affecting imputation accuracy such as the size of reference population, the level of genetic relationship between the reference and validation populations (imputation in three discrete generations), and the MAF of imputed SNPs. Animal-specific imputation accuracy (rcorrected) was used as the measure of imputation accuracy. For the 3K to 60K scenario, imputation accuracy ranged from 0.46 to 0.63 (Table 1). For the 48K to 60K scenario, imputation accuracies in the first generation of the validation population (G0) ranged from 0.68 for MAF class < 0.10 to 0.88 for MAF class 0.3-0.4 with only 22 animals (Ref22) in the reference population (Table 2, Fig. 1). Increasing the reference population size to 62 animals (Ref62) improved the accuracies to values from 0.80 to 0.93 for the same range of MAF classes (Table 2, Fig. 1). From G0 to G1, imputation accuracies decreased to 0.60 for MAF class < 0.10 and to 0.86 for MAF class 0.3-0.4 when Ref22 was used (Table 2, Fig. 1). From G1 to G2, imputation accuracies increased to 0.72 for MAF class < 0.10 and to 0.89 for MAF class 0.3-0.4 when Ref22 was used (Table 2, Fig. 1). Similar to the results for G0, imputation accuracies substantially increased for G1 and G2 by increasing the size of reference population in these generations (Table 2, Fig. 1). Table 1 Animal-specific imputation accuracy (rcorrected) on GGA1 for 3K to 60K scenario Table 2 Animal-specific imputation accuracy (rcorrected) and the standard errors on GGA1 for different MAF classes in G0, G1 and G2 validation populations (48K to 60K scenario) Imputation accuracies in G0, G1 and G2 for 48K to 60K scenario. Imputation accuracies (rcorrected) for different MAF classes and different reference sizes for G0, G1 and G2 validation populations. The x-axis represents different classes of MAF and y-axis shows the imputation accuracies. The black dots are the mean imputation accuracies across individuals in each MAF class Imputation from 3K to 60K Imputation based on a lower density SNP panel in the validation population, from 3K instead of 48K, resulted in lower imputation accuracies, as expected (Table 1). In comparison with the 48K to 60K scenarios (Table 2, Table 5), the 3K to 60K scenario gained more in imputation accuracies from enlarging the reference population (Table 1). The increase in imputation accuracies from Ref22 to Ref62 was 0.13 (0.50 to 0.63), 0.12 (0.46 to 0.58) and 0.10 (0.50 to 0.60) for G0, G1 and G2 (Table 1), respectively. Factors affecting the imputation accuracy Size of reference population As expected, accuracy of imputation increased as the size of the reference population increased. The increase in average imputation accuracies (average across MAF classes) from Ref22 to Ref62 was 0.07 (0.82 to 0.89), 0.07 (0.78 to 0.85), and 0.04 (0.83 to 0.87) for G0, G1 and G2, respectively (Table 2, Fig. 1). Selection of animals for the reference population Animals for Ref22 were selected for being influential, having the highest relationships with animals in the validation population. The proportion of diversity represented by the 62 sires and maternal grandsires of G0 are in Additional file 1: Table S2. The 22 and 62 sires and maternal grandsires captured 39.85 % and 75.54 % of genetic variation in the target population. In comparison, a subset of 22 randomly selected animals captured between 0.68 % and 3.36 % (on average 2.10 % across 10 subsets) of the genetic variation in the target population. The biggest impact from randomly selecting 22 animals in the reference was observed for MAF class < 0.10, where accuracy dropped by 0.07 (Table 3). A drop of 0.03 was observed for MAF class 0.4-0.5. The other MAF classes showed no changes in accuracy. Table 3 Animal-specific imputation accuracy (rcorrected) with 22 randomly selected animals (Ref22rand) in the reference population Relationship between the reference and validation population The average of the top five genomic relationships of a given animal in the validation population with all animals in the reference population Ref22 was 0.14, 0.13, and 0.11 for G0, G1, and G2, respectively. With Ref62, these averages were 0.21, 0.16, and 0.13 for G0, G1, and G2, respectively. Although the average top five relationships decreased across generations, average accuracies did not follow this declining pattern with more distant validation generations. From G0 to G1, the average imputation accuracies across all MAF classes reduced by 0.04 for both Ref22 and Ref62. From G1 to G2, the average accuracies increased by 0.05 for Ref22, and by 0.02 for Ref62 (Table 2). Also, only small differences in imputation accuracy were observed between animals that had only their sire, only their maternal grandsire, or both these ancestors in the reference. Imputation accuracy in the 48K to 60K scenario for these groups of animals was always within 0.02 of the accuracy observed across the whole validation population (Table 4). Also, in the 3K to 60K scenario, the imputation accuracies were nearly the same for these three groups (Table 4). Table 4 Animal-specific imputation accuracy (rcorrected) of G0 for three groups depending on their direct ancestors in the reference population Ref62 Minor Allele Frequency (MAF) Imputation accuracies were lower when MAF of the masked SNPs was lower. SNPs with low MAF were more difficult to impute correctly (Table 2) and exhibited more variation in their accuracy of imputation (Fig. 1). The difference in imputation accuracy for low and higher MAF SNPs was smaller with the larger reference, showing that even if imputation accuracy is already moderate for higher MAF SNPs, the accuracy for low MAF SNPs can still be improved by increasing the reference size. When SNPs were masked and evaluated based on their MAF in the validation population, instead of in the reference population, the average imputation accuracies across MAF classes were slightly reduced, by 0.01 on average (Additional file 2: Table S3). Compared with the scenario where SNPs were masked based on their MAF in the reference population (Table 2), an increase in the accuracy was observed when SNPs were masked independent of their MAF. Average accuracies (average across MAF classes) were higher by 0.08 and 0.04 for Ref22 and Ref62, respectively (Table 5). Again, the benefit was larger for SNPs with lower MAF and within the smaller reference population (Ref22). Table 5 Animal-specific imputation accuracy (rcorrected) with SNPs masked across the different MAF classes when G0 validation population was used for imputation Parameter to measure imputation accuracy Our main measure of accuracy, rcorrected, can only be measured when masking data in an experimental setting, which means it cannot be computed for common imputation tasks where the true genotypes are unknown. The Beagle software, however, estimates the "allelic R2" value, based on the posterior probability of the most likely genotype (see Methods). The allelic R2 predicts the reliability of imputed genotypes, and we compared it with the mean imputation reliabilities that were obtained as the squared correlation between true and imputed genotypes for each SNP (Table 6). Overall, the allelic R2 slightly overestimated the empirical imputation reliabilities across generations and reference populations. Average values of allelic R2 (average across generations) ranged from 0.64 to 0.82 for Ref22 and from 0.75 to 0.90 for Ref62 compared with empirical imputation reliabilities ranging from 0.59 to 0.81 and from 0.68 to 0.85, respectively (Table 6). For SNPs with higher MAF, the two measures were more similar than for SNPs with low MAF. For instance, the difference between the two measures was as much as 0.05 for low MAF (< 0.1) and only 0.02 for high MAF (0.4-0.5), when Ref22 was used for imputation. In general, the correlation between the two measures was moderate to high depending on the SNP density of the validation population. In the 48K to 60K scenario, the correlation between the allelic R2 and the imputation reliability was on average (across different MAF classes) 0.70, 0.69 and 0.58 in G0, G1, and G2, respectively, using Ref22. By increasing the reference size (Ref62), the correlation increased by 0.06, 0.05, and 0.09 in G0, G1, and G2, respectively (Table 7). Correlations between the allelic R2 and the imputation reliability were higher in the 3K to 60K scenario, compared with the 48K to 60K scenario, with increases of 0.11, 0.11 and 0.21 in G0, G1, and G2 using Ref22, and by 0.13, 0.13, and 0.17 in G0, G1, and G2 using Ref62, respectively (Fig. 2). Table 6 Average allelic R2 measure from Beagle and true imputation reliability on GGA1 for different MAF classes and different reference sizes (48K to 60K scenario) Table 7 Correlation between allelic R2 measure from Beagle and true imputation reliability on GGA1 for different MAF classes and different reference sizes in G0, G1 and G2 (48K to 60K scenario) Correlation between true imputation reliability and allelic R2 measure from Beagle. True imputation reliability is plotted against the allelic R2 when 96 % of SNPs were masked (3K to 60K scenario) in G0, G1 and G2. The red line is the regression line Size of the chromosome Imputation accuracies were obtained for GGA8 to investigate whether the imputation results for GGA1 were representative for other chromosomes. For GGA8, a similar pattern of accuracies was observed across generations, and across MAF classes. Average imputation accuracies across MAF classes were slightly smaller, by ~ 0.01, for SNPs on GGA8 across all generations (Additional file 3: Table S4). Several SNP chips with different densities (42K, 60K and 600K) have been developed for chicken and additional chips may be developed in the near future. In this study, we mimicked the imputation of genotypes between two different SNP chips with similar densities by imputing from 48K to 60K. We were specifically interested in imputation of low MAF SNPs when imputing towards one of the chips, because SNPs with low frequency may play an important role in complex traits and may have larger effects than the common SNPs in a population [42]. In addition, the accuracy of imputation of the 60K genotypes from a very low density SNP panel (3K) was assessed. In both scenarios (3K to 60K and 48K to 60K), imputation was performed using a small reference population of white layer chickens. The reference animals were carefully selected to include recent ancestors (sires and MGS of G0) or a subset thereof, chosen based on the proportion of their contributions to the validation animals. The results indicate that genotype imputation based on a small number of carefully selected reference animals resulted in low imputation accuracy for the 3K to 60K scenario (between 0.46 to 0.50 for Ref22 and from 0.58 to 0.63 for Ref62) and in moderate imputation accuracy for the 48K to 60K scenario (between 0.60 to 0.89 for Ref22 and from 0.73 to 0.93 for Ref62). Several studies have reported reasonable accuracies of imputation of SNP genotypes between different SNP chips in cattle [3, 26, 43]. For instance, Khatkar et al. [26] found error rates of 2.75 % and 0.76 % when imputing from 25K to 50K and from 35K to 50K, respectively. Druet et al. [3] found an error rate of 1 % when imputing from 50K to 60K. Also, in beef cattle, imputation from the public BovineSNP50K BeadChip to a proprietary 50K panel yielded imputation accuracies (allelic R2) in the range of 0.94 to 0.98 [43]. In all these studies, the reference populations were much larger than the reference population used in our study. Past studies showed that imputation accuracy depends on the size of reference population, the level of relationship between the reference and validation populations, and MAF of the SNP being imputed [18, 19, 21, 44]. In the current study, imputation accuracy depended on the size of reference population and the MAF of the SNP being imputed, but did not depend on the level of the relationship between the reference and validation populations. With Ref22, only little variation in the top five relationships was observed, while variation in the top five relationships was larger when Ref62 was used as reference population. However, with both Ref22 and Ref62, the imputation accuracy did not follow the pattern of variation in relationships. We found that the size of reference population was more important for obtaining higher accuracy when the validation population was genotyped at lower density (3K). With a higher SNP density in the validation populations (48K), the impact of reference size on imputation accuracy was less, showing that the factors influencing the imputation accuracy interact with each other. When the size of the reference population was small, the pedigree-free imputation method implemented in Beagle yielded low to moderate imputation accuracy. Badke et al. [45] obtained high imputation accuracy with two small reference populations consisting of 16 or 64 Yorkshire pigs with phased genotype data. Imputing the genotypes of a validation population (n = 200) resulted in accuracies of 0.90 and 0.95 using Beagle's default parameters [45]. In their data, the reference included both parents of all the validation animals, which probably has a beneficial effect on the imputation accuracy. This benefit could not be tested in our data, because female parents were not genotyped. In addition to having both parents in the reference, the use of a phased reference population is a factor that is expected to increase the imputation accuracy compared with our results [33]. Increasing the size of the reference population decreases the probability to miss a haplotype in the reference population [46] and increases the probability that multiple copies of alleles are present for making the correct haplotypes [47]. As expected, the accuracy of imputation increased with the size of reference population for both 3K to 60K and 48K to 60K scenarios, which is in agreement with other studies [19, 20, 27]. For example, in G0, the increase in average imputation accuracies (average across MAF classes) was 0.07 (from 0.82 to 0.89). With the 3K to 60K scenario, the average increase in imputation accuracy was larger (e.g. from 0.50 to 0.63 for G0; Table 1) from increasing the reference population from 22 to 62, indicating that when a lower density SNP panel is used for imputation, a larger number of individuals in reference population can, at least in part, make up for the reduced imputation accuracy. Beagle has been extensively applied to impute missing genotypes in human and animal genetics, and imputation accuracy with small reference populations has been reported to be moderate to high. Hayes et al. [19] obtained an imputation accuracy of ~ 0.8 when the reference population consisted of only 25 or 40 Border Leicester sheep. Vereijken et al. [39] used 57 brown layers to impute the missing genotypes of 249 animals and obtained a SNP-specific imputation accuracy in the range of 0.75 to 0.9 (average across different chromosomes) with different panel densities. While moderate imputation accuracies were observed in these studies, it has also been shown that with a very small reference population, the application of an appropriate imputation method is crucial [20]. With a small reference population, Beagle did not result in the highest imputation accuracies in a study on dairy cattle data [20]. Accuracies were higher with our Ref22 compared with the randomly selected reference populations, Ref22rand. There was no improvement in accuracy for the classes with MAF > 0.10, except for a small improvement of 0.03 for MAF class 0.4-0.5. The largest increase of 0.07 was found for the lowest MAF class (MAF < 0.10), indicating that including the most common sires as a reference population will mostly benefit the imputation of the most difficult class of SNPs, those with lower MAF. Pausch et al. [20] showed, in Fleckvieh cattle, that pre-selecting key animals was slightly beneficial for subsequent genotype imputation. The required size of the reference population to achieve high imputation accuracy differs across populations and has been suggested to depend mainly on the effective population size, N e [48], which is relatively low for this population (52). In populations with small N e , genotype imputation based on a small number of carefully selected reference animals was shown to yield a reasonable accuracy [49]. Several studies have shown that the relationship between the reference and validation populations influences the imputation accuracy in sheep [19], maize [21], beef cattle [44] and dairy cattle [26–28]. All these studies reported that the accuracy of imputation was greatest for individuals with the highest average genetic relationship to the reference population, which was attributed to them sharing more and longer haplotypes with the reference. Ventura et al. [44] reported that with removal of the 37 close relatives from the reference population of 313 Angus cattle, the imputation accuracy decreased by 2.3 % using Beagle. The reason given for this decrease in accuracy was that close relatives introduce conserved long haplotypes in the reference population, favouring an effective haplotype search in the imputation process [44]. In our dataset, however, only small differences in imputation accuracy were observed when animals had only their sire, only their maternal grandsire, or both these ancestors in the reference. One possible reason that the imputation accuracies are so similar among these three groups might be the small number of individuals in each of these groups which makes it hard to compare the imputation accuracies. Instead of the average relationship with the whole reference population, we compared imputation accuracy across the three generations with the average of the top five relationships. It has been shown that this measure correlates better with the accuracy of genomic prediction compared with the mean relationship [50]. With Ref62, the top five relationships decreased from 0.21 in G0 to 0.16 in G1, and 0.13 in G2. The average imputation accuracies (average across MAF classes) showed only a small reduction between G0 and G1, from 0.82 to 0.78 for Ref22 and from 0.89 to 0.85 for Ref62. From G1 to G2, the average accuracies increased slightly, despite the reduction in the top five relationships. The persistence of imputation accuracy in later generations is desirable, and may be a feature of small populations that are closed such that most common sires can be put in the reference. With a pedigree-based imputation method, the distance to the reference population might have had more impact on the imputation accuracy, because pedigree-based methods were found to be more dependent on having close relatives in the reference population than pedigree-free imputation methods [18]. Another factor that can explain the persistence of accuracies with increasing distance to the reference population is the high persistence of LD across generations (Fig. 3). Animals that are several generations apart will still share haplotypes, at least over short distances, and population level LD will hence only change slowly. For the calculation of LD measured as r [51], phased and imputed SNP data were used as described in [52]. Correlation (concordance) between values of r estimated in G0 or G2 was 0.93 (Fig. 3). For pedigree-free imputation algorithms such as Beagle, the LD pattern in the data is the only information that is explicitly used, although it has been shown that the LD-based imputation methods use the relationship information indirectly [26]. With higher LD, the algorithm can better identify the haplotypes, which is easier with 60K data in the validation population, compared with 1K and 3K in previously reported studies [19, 39]. In addition, it was argued that as the density of the validation panel increases, the effects of genetic relatedness will be less important, because at higher density shorter haplotypes can be imputed correctly, which makes it possible for haplotypes from more distantly related individuals to be imputed correctly [21]. Concordance of LD in G0 and G2. LD within each generation was measured as r (correlation) [51] between neighbouring SNPs Our reason for imputing to higher density is to improve accuracies in genomic prediction scenarios. High imputation accuracy is required in later generations to achieve accurate prediction of genomic breeding values in those generations. Wolc et al. [9] did not apply imputation, but they did find the accuracy of genomic estimated breeding values (GEBV) for brown layers to be persistent between generations two to five after the training data using real genotypes (42K SNP chip data). This result was obtained with real genotypes in all generations but it indicates that if imputation accuracy is high, prediction accuracy can be expected to also be persistent in later generations [9]. It has been suggested that SNPs with low frequency may play an important role in complex traits, and may have larger effects than the common SNPs in a population [42]. Hence, we were specifically interested in the accuracy of imputed genotypes for SNPs with low MAF. Accuracies of imputation were lower when MAF of the masked SNPs was lower, which may be due to a lower degree of LD with the 60K SNPs (selected for higher MAF), or due to a more challenging haplotype reconstruction when few haplotypes carry the minor allele. Inclusion of very rare SNPs may interfere with phasing, resulting in less accurately constructed haplotypes and ultimately leading to inferior imputation quality [53]. The decline in the imputation accuracy for lower MAF was smaller when the reference size was larger showing that the imputation accuracy probably depends more strongly on the number of copies of the minor allele in the reference population than the MAF itself. The lower imputation accuracy when MAF was low is in agreement with other studies that used chip data [18–23] and sequence data [24] in different species. However, various measures of the imputation accuracy were used in those studies, hampering a quantitative comparison. In this study, where we used the correlation coefficient corrected for gene content, a small decrease in imputation accuracy was observed with MAF < 0.1 compared with higher MAF SNPs. In another analysis with the same data, we observed a greater decrease in imputation accuracy for MAF < 0.05 [54]. Lin et al. [23] showed that the decline in imputation accuracy already started with MAF < 0.15 in human data. Hickey et al. [21] and Hayes et al. [19] also reported the decline in imputation accuracy for MAF < 0.1 in maize and sheep populations. Interestingly, the selection of the most common sires appears to especially benefit imputation accuracy of low MAF SNPs. Small differences in imputation accuracies were observed when SNPs were masked based on their MAF in the validation population, instead of in the reference population. Since the fraction of the SNPs that was monomorphic in Ref22 and Ref62, but polymorphic in the validation population (G0) was relatively low (3.86 % in Ref22 and 1.07 % in Ref62), little difference in imputation accuracies was expected by masking MAF from the validation populations. When SNPs were masked independent of their MAF, imputation accuracy was larger for SNPs with lower MAF and within the smaller reference population (Ref22) (Table 5), indicating that SNPs with low MAF can be imputed more accurately when SNPs with different ranges of MAF were used to impute them. This suggests that a genotyping panel to be used for imputing to higher densities should not contain SNPs with intermediate frequencies, as has been done for the currently available SNP chips. Comparison of true reliability and allelic R2 from Beagle The correlation between the allelic R2 reported by Beagle and the imputation reliability calculated in this study was moderate to high, (Fig. 2 (3K to 60K scenario) and Table 7 (48K to 60K scenario)). The correlations were higher when the reference size was larger and the MAF was higher, which is in agreement with [24]. Further, the correlations tended to be higher when the validation density was lower (3K to 60K). For the 3K to 60K scenario, the regression of imputation reliability on allelic R2 was close to 1 (low bias), ranging from 0.82 to 0.88 in different scenarios (Fig. 2), which allows us to predict the reliability when the true genotypes of missing SNPs are unknown. Hence, with a very low-density reference panel (e.g. 3K) allelic R2 may be used as a measure of accuracy when validation using masked data is not possible. For instance, imputation of all genotyped animals in a validation population using a small number of sequenced animals does not allow comparison with the true genotypes of the non-sequenced animals, and the reference population is typically too small to allow cross-validation. In this study, imputation accuracy was not very different between chromosomes of different size, which is in agreement with [39]. However, a study in Angus cattle [55] showed that there is a positive association between the chromosome size and the imputation accuracy. The reported differences between the imputation accuracies on large and small chromosomes were, however, not large (less than 0.02 using Beagle) [55]. The reason for a slightly lower accuracy on smaller chromosomes would be the reduced accuracy at the beginning and end of the chromosome which would have a relatively larger effect for small chromosomes. In another study in cattle, it was shown that the number of SNPs per centi-Morgan influenced imputation error rate more than the chromosome size [30]. In a scenario to mimic the imputation of genotypes between different SNP chips of similar densities, we found that moderate levels of imputation accuracy can be achieved even with a very small number of animals in the reference population. Selecting animals for the reference population from the most common sires, rather than selecting random animals for the reference population, considerably improved imputation accuracy for SNPs with low MAF, and slightly for SNPs with the highest MAF. Accuracy could be further increased by adding animals to the reference population particularly when the validation population was genotyped for a low-density panel (3K) or the SNPs targeted for imputation had low MAF. The allelic R2 estimated by Beagle gave a good indication of imputation reliability when the density of validation panel was very low (3K) and the MAF of the SNP and the size of the reference population were not extremely small. The study was performed with data from a commercial white layer line of chicken. Animals that were genotyped with the Illumina Infinium iSelect Beadchip (60K chip) (Illumina Inc., San Diego, CA, USA) [4] came from four generations of training data, preceding the three generations of selection candidates (G0, G1, and G2) which were selected by genomic best linear unbiased prediction (GBLUP) method. Total number of genotyped animals was 2140. More details about the structure of data are in [54]. Data from 8623 SNPs on chromosome 1 (GGA1) and 1700 SNPs on chromosome 8 (GGA8) were used to assess imputation accuracy on two chromosomes of very different size. SNPs were removed if they had a MAF < 0.01, a call rate < 0.9, or > 10 % parent-progeny Mendelian inconsistencies. Animals were removed if their genotype call rate was < 0.9. After filtering, 4485 SNPs on GGA1, 824 SNPs on GGA8, and 2140 animals remained for further analyses. Of 2140 genotyped animals, 62 were sires and/or maternal grand sires (MGS) of animals in G0. The actual number of sires and maternal grandsires of G0 was 67, but 5 of them had no DNA sample available. Of these 62 sires and maternal grandsires, 22 most common sires were chosen as the reference population (Ref22). These 22 most common sires will be sequenced for further investigation of GS with (imputed) whole-genome sequence data. Ref22 was chosen based on their "proportion of genetic diversity" [56] in order to capture the greatest possible proportion of genetic variation in the target population. Capturing a large part of the genetic variation by selecting the most common sires should provide a high accuracy of genotype imputation. The details of the method are described in the next section. For this study, imputation was performed using 60K genotype data on GGA1 and GGA8. The results obtained from 22 reference animals were compared with the results obtained with 62 reference animals. Proportion of genetic diversity The genomic relationship matrix from SNPs (G matrix) [57] was obtained for 2140 genotyped animals. The proportion of diversity was calculated as: Pn = G n −1 cn, where G n was a subset of the genomic relationship matrix (n = 62 genotyped sires and maternal grandsires), c n was a vector with the average genomic relationship of the n sires and maternal grandsires with the target population, and P n was a vector of the proportion of the genetic diversity captured by the n sires and maternal grandsires. Imputation scenarios In the "3K to 60K" scenario, imputation from a very low-density SNP panel (i.e. a 3K panel) to a medium density SNP panel (60K) was tested by masking ~ 96 % of 60K SNPs in a structured way (virtually designed and evenly spaced) across the genome. The same reference and validation populations were used as above. Imputation from 48K to 60K The imputation accuracy from the "48K to 60K" scenario was compared with those from 3K to 60K scenario to investigate the impact of SNP density in the reference on imputation accuracy. Moreover, imputation from 48K to 60K mimics the imputation of genotypes between two different SNP chips with similar densities. In five different classes of MAF (see next section), each containing approximately 20 % of all the SNPs, genotypes were set to missing in the validation population, creating five panels of 48K SNPs. Imputation accuracy was assessed when using the 62 sires and maternal grandsires (Ref62), or Ref22 as the reference population. In an additional analysis, with validation population G0, 22 animals were randomly selected as reference population from the training population (that consisted of the four generations before G0) which included the 62 common sires. The random selection of reference animals and subsequent genotype imputation and validation was repeated ten times (Ref22rand). The three validation populations consisted of the animals in consecutive generations G0, G1, and G2. The number of animals in G0, G1 and G2 were 367, 395 and 148, respectively. Comparison of imputation accuracies in G0, G1 and G2 will give an insight on the effect of distance to the reference population on imputation accuracy. Further, to assess the impact of an animal's relationship to the reference population on imputation accuracy, accuracies were determined within each generation and compared with a measure of genomic relatedness which was the average of the top five relationships [50] with animals in the reference. Additionally, imputation accuracy was also computed for three groups of G0 animals, separated by the type of direct ancestors they had in the reference population Ref62: (1) animals who had just their sire (GR_S, n = 34), (2) just their maternal grand sire (GR_MGS, n = 23), or (3) both their sire and maternal grandsire (GR_SMGS, n = 310) in the reference population. The relationship between MAF of SNPs to be imputed and the imputation accuracy was investigated by masking SNPs in five different classes of MAF ranging from 0.008 to 0.5: [0.008-0.1], [0.1-0.2], [0.2-0.3], [0.3-0.4], and [0.4-0.5] (Additional file 4: Table S1). Imputation was done separately for all combinations of the two reference populations (Ref22 and Ref62), the three validation populations (G0, G1, and G2), and the five MAF classes. To investigate the impact of choosing SNPs to mask on imputation accuracy, some scenarios were repeated with: first, SNPs being masked based on their MAF in the G0 validation population instead of the reference, and second, SNPs being masked independent of their MAF class, i.e. SNPs from all different MAF ranges were masked and imputed in one analysis. Imputation accuracy was then computed within different MAF classes. In all these scenarios, approximately 20 % of all the SNPs from the 60K panel were set to missing in the validation population. As mentioned earlier, these scenarios were therefore identified as 48K to 60K scenarios. Imputation methods Masked SNPs were imputed using Beagle version 3.3.2 [33]. Beagle uses a localized haplotype cluster model to cluster haplotypes at each marker and then defines a hidden Markov model (HMM) to find the most likely haplotype pairs based on the individual's known genotypes. Beagle predicts the most likely genotype at missing SNPs from defined haplotype pairs [33]. In our previous study [54], we showed that the accuracy of imputation was very low in a preliminary analysis that applied the default parameters. We therefore tested several parameter settings of Beagle for the current analyses. Most importantly, Beagle was run for 50 iterations of the phasing algorithm rather than the default number of 10 iterations. Changing other parameters such as increasing the number of samples (number of haplotype pairs to sample for each individual during each iteration of the phasing algorithm) and number of imputations (average the posterior probabilities over multiple imputations) was also tested. However, we found no increase in imputation accuracy when these parameters were changed and default settings were therefore applied [54]. Measure of imputation accuracy Animal-specific imputation accuracy (rcorrected), computed as the correlation between the true genotypes (coded as 0, 1, or 2 minus the mean gene content) and the imputed genotype (the most likely genotype minus the mean gene content) as suggested by Mulder et al. [28], was used as the measure of imputation accuracy. Mean gene content was computed per SNP as the mean of the genotypes represented as 0, 1, and 2, and was based on genotyped reference animals in each scenario. The reason for correction (subtracting the mean gene content from true and imputed genotypes) is that different SNPs have different MAF and therefore SNPs have distributions with different means. By correcting for the gene content, it is assumed that the correlated variables are bivariate normally distributed. Besides calculating animal-specific imputation accuracy for each individual, the imputation accuracy was also computed per SNP across individuals (SNP-specific imputation accuracy). SNP-specific imputation accuracy was computed as the correlation between the true and imputed genotypes (the most likely genotype) for each masked SNP coded as 0, 1 and 2 for genotypes A1A1, A1A2, and A2A2, respectively. We then compared the square of SNP-specific imputation accuracy ("true" imputation reliability) with allelic R2 generated by Beagle. Allelic R2 is the squared correlation between the allele dosage of the most likely imputed genotype and the allele dosage of the true genotype. The estimated A2-allele dosage was obtained from the imputed posterior genotype probabilities as: 0 * P(A1A1) + 1 * P(A1A2) + 2 * P(A2A2) [33]. The results of rcorrected were given and discussed throughout this paper as the main measure of imputation accuracy for different scenarios. Allelic R2 was compared with true imputation reliability in a separate section (see Discussion). Calculation of effective population size (N e ) N e was estimated from the observed LD values (r 2) between SNPs. The r 2 was related to N e based on Sved's equation [58]: $$ {r}^2=\frac{1}{1+4{N}_ec} $$ The genetic distance between SNPs (c, in Morgan units) was obtained by converting the physical distances (in base-pairs) to genetic distances (in Morgan) using the recombination rate values as reported by International Chicken Genome Sequencing Consortium (ICGSC) [59]. This estimate of N e has been obtained under the assumption of constant population size [58]. Blood samples were collected as part of routine data and sample collection in a commercial breeding program. According to the local legislation, it was not needed to have permission from the ethics committee. GS: Genomic selection GWAS: MAF: Minor allele frequency Single nucleotide polymorphism LD: QTL: Quantitative trait loci N e : Effective population size GBLUP: Genomic best linear unbiased prediction MGS: Maternal grand sire Genomic relationship matrix HMM: Hidden Markov model GEBV: Genomic estimated breeding values ICGSC: International chicken genome sequencing consortium Meuwissen T, Goddard M. Accurate prediction of genetic values for complex traits by whole-genome resequencing. Genetics. 2010;185(2):623–31. Spencer CCA, Su Z, Donnelly P, Marchini J. Designing genome-wide association studies: sample size, power, imputation, and the choice of genotyping chip. PLoS Genet. 2009;5(5):e1000477. Druet T, Schrooten C, de Roos AP. Imputation of genotypes from different single nucleotide polymorphism panels in dairy cattle. J Dairy Sci. 2010;93(11):5443–54. Groenen MAM, Megens H-J, Zare Y, Warren WC, Hillier LW, Crooijmans RPMA, et al. 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Linkage disequilibrium and persistence of phase in Holstein-Friesian, Jersey and Angus cattle. Genetics. 2008;179(3):1503–12. Liu EY, Buyske S, Aragaki AK, Peters U, Boerwinkle E, Carlson C, et al. Genotype imputation of Metabochip SNPs using a study-specific reference panel of ∼4,000 haplotypes in African Americans from the women's health initiative. Genet Epidemiol. 2012;36(2):107–17. Heidaritabar M, Calus MPL, Vereijken A, Groenen MAM, Bastiaansen JWM. High imputation accuracy in layer chicken from sequence data on a few key ancestors. Proceedings of the 10th World Congress on Genetics Applied to Livestock Production (WCGALP), 2014, https://asas.org/docs/default-source/wcgalp-posters/660_paper_8829_manuscript_574_0.pdf. Sun C, Wu X-L, Weigel KA, Rosa GJM, Bauck S, Woodward BW, et al. An ensemble-based approach to imputation of moderate-density genotypes for genomic selection with application to Angus cattle. Genet Res. 2012;94(3):133–50. Druet T, Macleod IM, Hayes BJ. Toward genomic prediction from whole-genome sequence data: impact of sequencing design on genotype imputation and accuracy of predictions. Heredity. 2014;112(1):39–47. VanRaden PM. Efficient methods to compute genomic predictions. J Dairy Sci. 2008;91(11):4414–23. Sved JA. Linkage disequilibrium and homozygosity of chromosome segments in finite populations. Theor Popul Biol. 1971;2(2):125–41. Hillier LW, Miller W, Birney E, Warren W, Hardison RC, Ponting CP, et al. Sequence and comparative analysis of the chicken genome provide unique perspectives on vertebrate evolution. Nature. 2004;432(7018):695–716. We would like to thank Hendrix Genetics for providing the genotype and pedigree data. This project was financially supported by Agriculture and Food Research Initiative competitive grant no. 2009-65205-05665 from the USDA National Institute of Food and Agriculture Animal Genome Program. This work was further supported by additional funding from Wageningen University and Hendrix Genetics, the Netherlands. Mario Calus and John Bastiaansen acknowledge financial support from the Dutch Ministry of Economic Affairs, Agriculture, and Innovation (Public-private partnership "Breed4Food" code KB-12-006.03-005-ASG-LR). Animal Breeding and Genomics Centre, Wageningen University, P.O. Box 338, 6700 AH, Wageningen, the Netherlands Marzieh Heidaritabar , Martien A. M. Groenen & John W. M. Bastiaansen Animal Breeding and Genomics Centre, Wageningen UR Livestock Research, P.O. Box 338, 6700 AH, Wageningen, the Netherlands Mario P. L. Calus Hendrix Genetics Research, Technology and Services B.V., P.O. Box 114, 5830 AC, Boxmeer, the Netherlands Addie Vereijken Search for Marzieh Heidaritabar in: Search for Mario P. L. Calus in: Search for Addie Vereijken in: Search for Martien A. M. Groenen in: Search for John W. M. Bastiaansen in: Correspondence to Marzieh Heidaritabar. Conceived and designed the experiments: MH, MPLC, AV, JWMB, MAMG. Analyzed the data: MH. Wrote the manuscript: MH. Discussed and improved manuscript: AV, JWMB, MPLC, MAMG. All authors read and approved the final manuscript. Additional file 1: Table S2. Proportion of diversity for 62 sires and maternal grand sires (MGS) of G0. Animal-specific imputation accuracy (rcorrected) for SNPs classified by MAF in validation population Animal-specific imputation accuracy (rcorrected) on GGA8 for different MAF classes and different reference sizes in G0, G1 and G2. Total number of SNPs masked for different MAF classes in 48K to 60K scenario. Heidaritabar, M., Calus, M.P.L., Vereijken, A. et al. Accuracy of imputation using the most common sires as reference population in layer chickens. BMC Genet 16, 101 (2015) doi:10.1186/s12863-015-0253-5 Imputation accuracy Layer chickens Reference population design	CommonCrawl
How do we know galaxy GN-z11 is as far away as it is? The news media recently reported that galaxy GN-z11, formed just 400 million years after the big bang, is much further away than originally thought at perhaps 13.2 billion light years. They say, The key to the discovery was precisely measuring the shift of the galaxy's light into longer, redder wavelengths, which correspond to how far the photons had traveled before reaching Hubble's eye. (Reuters). So, suppose I'm standing next to, but safely away from, some train tracks. As the train approaches, sounding its whistle constantly, the pitch will appear to increase until it reaches me, upon which I will briefly hear the whistle's 'rest pitch' (the pitch of the whistle as if I were aboard the train), then it would decrease as the train moves away. Thus, the lower the pitch, the further away the train is. I hope that's right. So, if we know the rest frequency of galaxy GN-z11, its measured frequency indicates how far away it is from earth. Trouble is, how do we know what the rest frequency of light coming from this distant galaxy is? galaxy distances doppler-effect Michael LeeMichael Lee $\begingroup$ This might help explain it to you (astro.wku.edu/astr106/Hubble_intro.html), but basically they can measure rest wavelengths in a lab because they are looking for particular emission or absorption lines in elements such as Hydrogen. These are fundamental properties of all elements, no matter where they are in the universe, so by pinpointing them on the spectrum, they can calculate by how much they are red-shifted. $\endgroup$ – Dean Mar 6 '16 at 17:09 $\begingroup$ Thank you so much for the reference Dean. I appreciate it! $\endgroup$ – Michael Lee Mar 6 '16 at 19:16 So GN z-11 is the latest "furthest away" galaxy. It has a claimed redshift measurement of $z=11.1$, meaning that we are seeing the light it emitted about 400 Myr after the big bang (dependent on an assumed set of cosmological parameters). To get the redshift measurement, the discoverers used grism (relatively low resolution) spectroscopy in the near infrared. What they were looking for is the rest-frame Lyman alpha continuum break, which would be redshifted into this wavelength range. The Lyman alpha continuum break is caused by the absorption of nearly all ultraviolet photons with wavelengths smaller than 121 nm. These high energy photons are capable of photoionising the neutral hydrogen present in the intergalactic medium at a range of lower redshifts. This neutral hydrogen is present in abundance at redshifts greater than 6, as it had not yet been re-ionised by quasars and starlight. The consequence is that no light is expected to reach us from rest-frame wavelengths shortwards of 121 nm, but a galaxy's light can reach us from rest-frame wavelengths that are longer than this. When one observes the spectrum, we see flux at long wavelengths which suddenly cuts off at shorter wavelengths. The wavelength of the break is $\lambda = 121 \times (1+z)$ nm, where $z$ is the redshift. It is this Lyman alpha continuum break that has been identified at an observed wavelength of 1470 nm. This leads to the redshift estimate of $z= (1470/121)-1 = 11.1$. The details are presented in Oesch et al. (2016). The continuum break is the only thing visible in the spectrum. The authors are confident that this is what it is because their previous broadband photometry had given them an estimated redshift of $>10$ (which is why they observed this candidate in the first place). Rob JeffriesRob Jeffries Not the answer you're looking for? Browse other questions tagged galaxy distances doppler-effect or ask your own question. Can we know whether any distant galaxy is moving away in same direction or in opposite direction w.r.t. our galaxy? Can we tell how fast bodies are moving away by measuring their frequency? Do far away stars that we observe today still exist? How do we have photos of galaxies so far away? How far away is this galaxy? How far would EGSY8p7 be away now? Will intergalactic travel be impossible in roughly 15 billion years?	CommonCrawl
Fishermen do more than fish: local ecological knowledge of raftsmen about the arboreal species used to construct rafts (Bahia, Brazil) Isis Leite Medeiros Mascarenhas Andrade ORCID: orcid.org/0000-0001-9655-30881, Marcelo Schramm Mielke2, Nivaldo Peroni3 & Alexandre Schiavetti4 Traditional raft (jangada), piúba wood raft (jangada de pau de piúba), six-log raft (jangada de seis paus), and wooden raft (jangada de pau) are some of the names given to the traditional Brazilian watercrafts created from the buoyancy of bound logs. The traditional raft is a watercraft used and built by artisan fishermen who have, throughout generations, kept and improved knowledge related to this practice and the use of the plant species they need as raw materials. Active groups of these fishermen and their watercrafts are distributed along 200 km of the coast of the state of Bahia. The fishermen interviewed in this study are at the southern limit of distribution for the use of this type of vessel. This study aimed to characterize the use of the arboreal species applied in the construction of the traditional raft in the municipalities of Uruçuca, Ilhéus, and Canavieiras in the southern State of Bahia, Brazil. For this purpose, structured and semi-structured interviews were individually conducted with 36 fishermen, and walking tours were conducted with specialists in the construction of the watercraft. We observed that the raftsmen use 21 species to construct the traditional raft. The features of the wood, such as density, flexibility, and availability, are the main criteria applied to choose the arboreal species. Some species are preferred, such as pau de jangada (Apeiba tibourbou) and biriba (Eschweilera ovata), which are the most frequently employed in watercraft manufacturing. The southern Bahia population is familiar with the different tree species that are linked to their fishing activities. The main link between the fishermen and the useful species is present in the practice of raft construction. Currently, the restricted access to raw materials limits this practice, which consequently results in the cultural erosion of this community. The ecological knowledge of artisanal fishers about the environment in which they fish is already well documented. However, this knowledge goes beyond fishing activity. It is a knowledge that accesses information from various components of the ecosystem, including the species used in the construction of fishing technologies, such as materials used for the manufacture of tools and the construction of vessels [1,2,3]. The production of fishing technologies relies on the choice of the plant species adapted to the ecological and cultural conditions related to fishing. The abilities of the fishermen to produce this technology come from the successful capture of fish through an optimized choice of the utilized plant species [3, 4]. Several ethnobotanical studies were conducted in artisanal fishing communities in Brazil and worldwide. Many of them aimed to analyze the plant usage by these communities [5,6,7,8], while others focused on the use of plants with medicinal purposes [9, 10], and some addressed studies of plants utilized for the construction of vessels and fishing tools in communities [2, 11,12,13]. These studies present a high interdependence between the knowledge and usage of terrestrial and marine biodiversity [1, 7, 14, 15]. The Brazilian maritime patrimony is formed by a rich set of traditional watercrafts that belong to the history and the landscape of the country, representing the geographical specificities according to the historical, environmental, and cultural features. For example, the raft (jangada), found in Northeast Brazil, is characterized by the junction of many logs. Similarly, the tolda canoes are present in the São Francisco River, which is located between the northeast and southeast regions of Brazil [16]. Relatively to the large number of watercrafts and the cultural richness that these boats represent, few ethnobotanical studies have been conducted that aim to characterize how plant resources are used in the construction of these traditional watercrafts and in fishing activities [17,18,19]. The traditional raft (jangada), piúba wood raft (jangada de pau de piúba), six-log raft (jangada de seis paus), and wooden raft (jangada de pau) are some of the names given to the watercraft created from a construction that ensures the buoyancy of many wooden logs joined together [20]. These watercrafts are considered to be adapted to the environment and the fishing style, and they are formed by the hull, mast, and support devices. The construction is handcrafted by fishermen using fittings and ties and without the need for nails, screws, or any other hardware [20]. Although the traditional raft has disappeared in many locations on the northeast shore where they were common in the past [21], there are active spots where the traditional rafts are still used and built by raftsmen. The most active region is located in a strip approximately 200 km south of Bahia State [19,20,21,22]. Along with this shore strip, there are semi-desert beaches rounded by the Atlantic Forest, where arboreal species are used as plant resources necessary for the construction and maintenance of the rafts [23,24,25]. With an understanding of the cultural importance of the raft as a traditional watercraft used by a group of experienced fishermen, this study aimed to evaluate how arboreal species are used in the construction of traditional rafts by groups of raftsmen settled in the southern region of the state of Bahia. We expect that our results may be applied to the development of conservation strategies and actions that aim to preserve the Atlantic Forest and traditional fishing. Such strategies should also consider the impact of the human groups who know the biome's importance for the development of their daily activities. The state of Bahia has the largest seacoast in Brazil with 1188 km of continuous shore. Along with this coast, there are 44 municipalities and approximately 350 fishing communities. The state's fishing fleet is mostly formed by non-motorized vessels [26]. Fishermen who use traditional rafts are distributed along 200 km of the coast of the state of Bahia. The fishermen interviewed for this study were in the southernmost part of the Brazilian Northeast region. The raft is also used by small groups of fishermen on the north boundary of Bahia within the state of Sergipe [21] (Fig. 1). Map of the coastal strip of South of Bahia where the study was conducted Groups of fishermen from the southern part of the Northeast region are located in the surroundings of the Atlantic Forest, a biome that is an international hotspot and a priority area for conservation due to the extinction of a large part of the plant cover in an area with a high level of endemism and biological richness [27,28,29]. The study area comprised the municipalities of Canavieiras, Ilhéus, and Uruçuca (Fig. 1). These towns are located in the southern part of the state of Bahia, a region that has a hot and humid tropical climate without a dry season, with over 1300 mm of precipitation/year and with the most intense rainy period occurring between March and September [30]. Raftsmen We considered all artisan fishermen who use the traditional raft as a watercraft as raftsmen when we conducted our research. Among them, we were able to identify the raftsmen who mastered the techniques to construct the rafts when the individual interviews were conducted. The total population of fishermen who used the rafts as fishing vessels was 46 raftsmen, among whom 36 agreed to participate in the research. The interviewed fishermen were placed in five groups according to their geographic location in the studied municipalities (Fig. 1). Then, we characterized the groups by examining the number of raftsmen per group, the location, the proximity to protected areas [31, 32], and the width of the continental platform, which is the distance of the seabed from the continental platform at the spots where the rafts were found [33]. The fishing strategy, the type of raft used, and the distance traveled by the raft are presented in Table 1. Table 1 Numerical and spatial characterization of the raftsmen studied groups, Southern Bahia, Brazil Ethnobotanical research Data were collected from March to December 2015 by the individual interview method [34, 35]. All interviews were recorded with audio at the time and place set by the interviewees. The interviews had an average duration of 50 min. The interviews were conducted in semi-structured and structured forms. In the structured interview, all interviewees responded to a set of stimuli that were as identical as possible through the use of a questionnaire, a free listing, and a visual stimulus [34, 35]. The information obtained was complemented and enriched by using 'walking interviews' [36] to avoid errors in species identification, as the raftsmen pointed to the species mentioned in loco [37]. Samples of the specimens were collected and later herborized, identified, and incorporated into the HUESC herbarium collection, and duplicates were sent to the CEPEC herbarium. The identification of the species was conducted by consulting specialized literature, by the supervision of a botanist and a para-botanist, by comparing specimens from national and international herbaria with a high-resolution image available online [38, 39], and through field observations. Next, we examined the association between the uses of the species and their applications available in the specialized literature. Plants were classified according to their origin: native (originally from Brazil) and exotic (introduced from another country) based on the List of Species of the Brazilian Flora [40]. Data collection was conducted in three stages: (1) identification of the area and population, in which we characterized the traditional rafts by visiting the communities where the raftsmen live and (2) execution of the semi-structured and structured interviews to determine socioeconomic aspects through the questionnaire and to collect information about the knowledge related to the traditional raft and the fishing activity through a guided semi-structured interview. During the interviews, we used free listing to identify the tree species useful in the construction of the traditional raft. After the listing was asked of each interviewee, the reason for choosing the tree species used in raft construction was determined. To assist this process and to have all parts of the raft identified, visual stimuli through photographs of all raft structures were used. (3) The walking interviews that occurred in parallel with the second stage were performed only with the raftsmen who mastered the construction of the raft and who were able to participate in this stage of the research. At that time, we collected fertile specimens (with flower and fruit) for identification and herborization. We measured and tabulated the height, width, length, and diameter of each raft that was found to elaborate technical drawings of the models. Data related to the characterization of the interviewees were treated using descriptive statistics. Data were qualitatively classified through an ethnobotanical inventory confirmed with the register of the mentioned species (folk and taxonomic names) containing family, scientific name, popular name, origin, uses, and parts used [34]. The species referred to as useful for the production of the traditional raft were associated with each raft component. With the use of descriptive statistics, we calculated the average number of mentions of the valuable species to the production of each component of the raft, according to the calculation: $$ \boldsymbol{M}=\left(\sum X\right)/n $$ where M is the average number of mentioned uses of the component, X is the number of times that the species was mentioned as being useful for that component, and N is the total number of species used for the production of the component. Therefore, species with more remarks than the average for one component were considered as preferential for the production of this particular raft element. This calculation was done to determine the preferred species for the set of interviewees and was separately applied to groups with a sample more significant than one raftsman (groups 1, 2, 3, and 5) to determine the preferential species for each group. The arboreal species mentioned were quantitatively evaluated by the use value (UV). The UV [41] is represented by the number of uses the species has and is calculated by dividing the sum of mentions of use for a determined species by the total number of informants. The equation, as suggested by Rossato et al. [42], is $$ \mathbf{UV}=\left(\sum \mathrm{Us}\right)/N, $$ where UV is the use value of the species, Us is the number of mentioned uses by each informant for the species, and N is the total number of informants. For species used to build the rafts, we calculated the specific UV according to the use of the species in the construction of the watercraft. For that purpose, the use was associated with the presence of the species in the different components of the traditional raft. For example, knowing how many different manufacturing components the mentioned species is used for is useful. In addition to the UV calculation, we also calculated the Index of Cultural Significance (ICS), as established by Turner [43], to numerically express the role of plants in a culture. This index is calculated by a score given by the researcher leading to the species value. The formula adopted in this research was adapted by Silva et al. [44], where the values given to the variables (i, e, and c) are 2 or 1 for each mention of the use of each species. This adaptation gives the formula a more objective character: $$ \mathrm{ISC}=\sum \left(i\times e\times c\right)\ \mathrm{FC}, $$ where i considers the impact of the plant in the daily life of the community; the value 2 is given to species that are grown, managed or manipulated, and the value 1 is given to the species found in the area that are still free from any management or conservation practices; and e is the preference of the use of a species compared to some other uses for a determined function. The value 2 is suggested for a species that is preferably used for a specific purpose, and the value 1 is suggested for other available species that are non-preferential for this purpose; c is the frequency of use. The value 2 is given to plants that are effectively known and used, and 1 is given to plants that are rarely mentioned; FC is the consensus among the informants. This value is obtained from the number of informants mentioning the species divided by the number of informants mentioning the most mentioned species. The calculation of the UV and ICS considered the total mentions in the set of interviewees, and thereby, the UV and ICS of the species were obtained individually for each group. Moreover, the UV and ICS of the species mentioned by each group were obtained by considering only the remarks for the respective groups. To analyze whether the builder raftsmen tend to refer more to useful species than the non-builder raftsmen, we applied the Wilcoxon-Mann-Whitney nonparametric test. These statistical analyses were conducted after testing the normality of the data (Shapiro-Wilk) with the software R [45], α = 0.05. Socioeconomic characterization and knowledge related to fishing with a traditional raft All interviewees were male with an average age of 50 years. Sixty-one percent of the subjects of the study were born where they currently live. Most of the raftsmen counted on fishing with a traditional raft as their primary income source, and many of them worked in other activities to complement or replace fishing. The most significant complementary occupations were farmer, bricklayer helper, servant, and carpenter. However, 10 individuals identified fishing as their only income source. Of the interviewed population of raftsmen, 27 were literate. The average time of fishing activity with the traditional raft of the interviewed fishermen was 34 years. We observed that 25 of the raftsmen could build rafts. Moreover, we identified that the origin of the raftsmen's knowledge was mostly related to shared experiences with older fishermen. There was a high frequency of positive responses (32 of those interviewed) about the transmission of this knowledge to other fishermen. Regarding the changes perceived by these raftsmen, 33 alleged noticing some remarkable differences throughout the years in which they were fishing with a traditional raft. Among these, 31 and 24 classified these changes as adverse and positive, respectively. The most mentioned adverse changes were related to the reduction of fish (23 of those interviewed) and to the limits at the time on removing and transporting trees from the forest (18 of those interviewed). On the other hand, the most mentioned positive change was related to the introduction of the engine to the traditional raft (20 of those interviewed). Localization and characterization of the traditional rafts We identified traditional rafts made by the five groups of raftsmen, totaling 34 rafts, in which 20 were active rafts and 14 were inactive rafts (useless or in maintenance) (Fig. 2). Traditional rafts found in Southern Bahia, Brazil. a Group 4 traditional raft. b Group 2 traditional raft. c Group 3 traditional raft. d Group 1 traditional raft Thirteen elements were identified, totaling 25 pieces for the composition of the traditional raft (Table 2; Fig. 3). Table 2 Traditional raft components used in the South of Bahia (Brazil) with their functions, characteristics of wood allocated by the raftsmen to the species used in the production of these components Technical drawing of the traditional raft used in Southern Bahia, Brazil, with all components in side and front view The raft of group 1 had ballast, a mast, and support devices, and one more component: the engine along with its bank. The raft of group 2 had ballast and support tools. Group 3 used rafts with ballast and stools as support devices. The raft of group 4 was simpler, being constructed only with ballast. The raft of group 5 was very similar to that of group 2, although it did not have the stretch component (Fig. 4). Technical drawing of the traditional raft models found in Southern Bahia, Brazil, with components in upper view The five groups of raftsmen presented differences related to the type of traditional raft used, how they fished, and average distance they traveled in the sea to reach the fishing boat or the fishing spot (Table 1). Usage of the species in the traditional raft in southern Bahia We found 21 arboreal species that belonged to 17 families that are useful for the construction of the traditional raft (Table 3). Table 3 Species cited as useful in building the traditional raft by rafters of Southern Bahia, Brazil Raftsmen who built the rafts demonstrated significantly increased knowledge about the diversity of useful plants when compared to those who did not manufacture them (W = 210; p = 0.01246). Figure 5 highlights the species mentioned for the production of each component. Among the elements, the ballast, mast, lathe, aracambu, stool, and morão were made of just one preferred species. The canga, carrinha, hand paddle, and driving paddle components were composed of more than two preferential species. Figure 5 also highlights that biriba is the preferential species for the production of four elements, the morão, aracambu, lathe and stool, and that the pau de jangada, in addition to being the preferred species for ballast construction, is also exclusively used to produce this component. Species used in the making of the traditional raft's components, South of Bahia, Brazil The criteria to choose the species used in raft construction are associated with the functions of the components, and these factors are directly related to the features of the wood of the species (Table 2). The preferential species were determined for the set of interviewed raftsmen and individually for each of the groups of raftsmen (1, 2, 3, and 5) (Fig. 6). Moreover, we observed that only three species were preferential for all groups to produce the same component: massaranduba to produce the mast, pau de jangada to produce the ballast, and biriba to produce lathes and stools. Venn's diagram representing the preferred species in the traditional raft building for each of the groups analyzed in South of Bahia, Brazil. 1-Apeiba tibourbou, 2-Manilkara maxima, 3-Eschweilera ovata, 4-Brosimum rubescens, 5-Anacardium occidentale, 6-Caryocar brasiliense, 7-Xylopia frutescens, 8-Annona glabra, 9-Genipa americana, 10-Aniba intermedia, 11-Pinus sp., 12-Diplotropis incexis, 13-Albizia polycephala, 14-Symphonia globulifera, 15-Conocarpus erectus, and 16-Laguncularia racemosa Using a Venn diagram (Fig. 6), we identified that there are preferential species for each group: louro for group 1, sucupira and muanza for group 2, alandi for group 3, and mangue manso and mangue de botão for group 5. It is noticeable that groups 1 and 2 have the most substantial number of common preferential species and that there are three common preferred species for all the analyzed groups. Additionally, we observed that biriba had a higher UV value for both the set of interviewees and for the groups. Of the 21 species used in the construction of the traditional raft for all the interviewees, 19.05% showed UVs higher or equal to 1: taipóca, biriba, conduru, and pau de jangada. Species having UVs between 0.58 and 0.83 represented 33.33% of the species. The most significant percentage (47.6%) represented species with UVs between 0.08 and 0.50. Regarding the ICS results, the highest percentage (66.66%) represented species that obtained values higher than 1. The species that had ICS values between 0.50 and 0.78 represented 19.05% of the species. Only 14.28% of the species had ICS values lower than 0.50. Like the UV result, the more prominent ICS value was observed in biriba for both the set of interviewees and for the groups (Table 3). General aspects of the raft and the raftsmen Fishing with a traditional raft by raftsmen in southern Bahia is mostly practised by men and is becoming increasingly scarce along the northeast coast [21, 46]. Despite the existence of active spots for traditional raft fishing in this region, we observed a small number of fishermen joining this raft population (Table 1). Raft fishing and building techniques were learned from the life experiences of older fishermen without any kinship required. The way that knowledge is transmitted between the interviewed fishermen is different compared to other artisanal fishing communities, where knowledge is transmitted throughout the family circle [18, 46, 47]. The knowledge shared between the raftsmen is associated with the number of raftsmen building the rafts. This result contrasts with those found for groups of handcrafted canoe builders in the state of Piauí, corresponding to nearly 7% of all the fishing community [17]. Throughout the years of experience, these fishermen have actively transmitted their knowledge to other generations [22] by teaching new apprentices. The interviewed raftsmen population practises artisanal fishing, which is the income for nearly 25 of the population regarding both the sale and the consumption of fish. The raftsmen have been politically and socially active throughout the history of the country and are aware of the needs and difficulties that face the development of their daily practices [48, 49]. The studied population revealed itself to be perceptive to the changes that occurred and influenced the practices related to the traditional raft. Like the artisanal fishing community from Carne de Vaca beach in the state of Pernambuco [50], 83% of the changes with positive influence on the raftsmen interviewed in this study were associated with the adaptability of the watercraft compared to other motored watercrafts. However, the changes with negative influence on their practices were more noticeable and represented the opinion of 31 of the raftsmen. The most significant complaint was associated with the reduction of the fishing stocks. Raftsmen reported that there was increasing competition with large vessels next to the fishing spots. Another negative aspect was related to the difficulty of obtaining the necessary natural resources to construct the traditional raft due to inspection at the time of extraction or deforestation. These two factors were also reported in other communities as being among the main factors limiting the construction of artisanal watercrafts [2, 12, 17, 50]. Some authors [21] believe that the reduced use of the traditional raft in the northeast Brazilian region is mostly related to the lack of plant resources necessary for its construction. However, given the presented results, it is evident that there are many factors that can contribute to the reduction and replacement of the traditional raft by other types of watercrafts. According to the National Historic and Artistic Heritage Institute—IPHAN (2011), the traditional Brazilian raft is a watercraft threatened by extinction. The disappearance of traditional watercrafts with cultural importance to the local communities has already been reported in studies developed in Peru and in Polynesia, where authors highlighted that the association between culture and the environment is strengthened with the traditional practices of the communities [12, 13]. Therefore, the disappearance of a watercraft that was kept for such practices consequently leads to the alienation of these local communities from the environment and the natural resources surrounding them. Use of the species in the traditional raft in southern Bahia To analyze how plant species are used in the traditional raft, an understanding of how this watercraft is built and the models found along the seacoast studied is necessary. The traditional raft is derived from a simple indigenous watercraft formed by joining wooden logs with liana ties (ballast) and is used by indigenous populations mostly for river fishing [51]. After some structural changes influenced by Portuguese traditions, this watercraft became able to navigate in the high sea. Therefore, the traditional raft described by Cascudo [46] consists not only of the ballast but also of a structure to support the sail and at least two fishermen on the open sea. Models of the traditional raft observed along the studied area varied according to the groups of fishermen found. The models made by groups 1, 2, and 5 were similar to the rafts described in the literature, whereas the models of groups 3 and 4 were more similar to the watercrafts used by the indigenous population before Brazil's colonization (Fig. 4). The structural differences between the rafts found can be explained by the type of fishing chosen by the groups of raftsmen. Raftsmen from groups 1, 2, and 5 practise line fishing, so they need rafts with a sail to travel longer distances until they find fishing spots. On the other hand, groups 3, 4, and 5 practised trawling fishing, which dismisses the sail because there is no need to get far from the coast. However, to make it possible for this type of fishing to occur, it is necessary for a large continental platform to exist [30] at the spot chosen to displace the trawls. Only groups 3, 4, and 5 were favorably located to practise this type of fishing. Another adaptation observed in the raft built by group 1 was the introduction of a small engine previously used in the old flour mills (interview 18). The introduction of the engine might explain, for instance, the difference in the number of raftsmen in group 1 compared to the number of raftsmen in the other groups. The engine facilitates the activity by reducing the time spent arriving at the fishing spots by applying less effort to displace the raft and by increasing the possibility of exploring new fishing spots. In addition, the engine keeps construction and maintenance cost of the raft low compared to other motorized watercrafts. Therefore, the different models of traditional raft found are the result of each group's needs. In addition, all of the species occupy the technological category of use because their wood is used to produce the components of the watercraft. Moreover, this category represents the species that endure manipulation of their raw material to create useful elements (tools, furniture, watercrafts) [52]. Those pieces are individually made by the raftsmen who choose an arboreal species with a specific wood to produce each component. Thus, if some component, for instance, the carrinha, needs to be resistant enough to support the weight of the mast and the sailcloth, the raftsmen choose a species with wood that is resistant to this weight, popularly known as fixe wood. This specificity explains the diversity of species used to construct the traditional raft. The same chosen criteria for the usage of the species were observed in watercrafts built by fishermen on the Mediterranean western coast in Italy, in the construction of a canoe in Pohnpei, in the Federated States of Micronesia, and in the construction of a canoe on the island of Kabara in Polynesia. The authors had similar observations when compared to those in this study regarding the diversity of species used: 25 useful species in Italy, 27 in Micronesia, and 20 in Polynesia [2, 11, 13]. Altogether, we identified 21 species that are useful for constructing the traditional raft, but not all of them together compose the same watercraft. This selection occurs because the raftsmen have more than one species that can be applied to produce each component. In this way, it is expected that the specialists mention a more significant diversity of useful species in the raft because the raftsmen are aware of the similarity among species. In this way, the carrinha of a raft can be made of the pequi, massaranduba (cow-tree), roxinho (purple wood/purpleheart), sucupira, or jack tree wood. All of these wood types are recognized by the raftsmen as ideal to make this component because they have fixe wood. Therefore, each species cataloged is useful for a type of element in the raft, with the variation depending on the function that this component has in the raft and on the morpho-anatomical characteristics of the wood of each species. Consequently, each feature corresponds to a quantity of species capable of being used for its construction. Nevertheless, we detected that the same species have more frequent mentions than others concerning the production of some elements and that the number of useful species varies according to the created feature (Fig. 5). By calculating the average number of mentions of the valuable species needed to produce each part, it is possible to determine the favorite species for each component. The determination of the favorite species by the set of raftsmen studied was performed through the analysis of the mentions from all interviewees. This analysis was conducted with each group by considering only the mentions of the group. The observation by the group revealed that the favorite species of that population was very biased towards the species chosen by group 1. This observation likely occurred because group 1 had a more substantial number of raftsmen compared to other groups. Figure 6 shows the favorite species of each group that are uncommon between the groups and that some groups share more favorite species than others. Both situations may be related to the location of the groups, either because they are spatially close, as in groups 1 and 2, which share the same preferences, or because they are close to areas that favor the use of some species. This last observation was found in group 5, which is located near mangrove forest areas and selected two mangrove plant species as their favorite. It can also be noted that only 3 out of 21 species used by raftsmen are preferential to all the groups. Based on the number of species used to make each component and on the frequency with which the species were mentioned, we observed that biriba and pau de jangada were the most frequently used. Biriba was mentioned by all the raftsmen and was defined as being valuable for more than one component, which was observed by a higher UV in the raft and a higher ICS. This species was also the favorite for producing components (morão, lathe, aracambu, and stool). The diversity and frequency of usage of the biriba wood in the raft may be associated with its 'plastic' attribute—it is useful for more than one component, it is highly available, and it is practical to use. A raftsman declared that he found it "ready to use, with the right 'gauge'" and that "one can find biriba just by the roadside" (interview 28). On the other hand, pau de jangada wood was remarkably the species used exclusively for the ballast, with only muanza as a backup to make this component. However, the use of muanza in the raft is practised by groups 1, 2, and 3, and it is evident that the construction of the traditional raft by groups 4 and 5 would be impossible if the pau de jangada was not available. This information indicates that the existence of the traditional raft is directly associated with the availability of such species. Caruso [53] reported this in an interview with a raftsman: "Nowadays, unfortunately, this type of raft (six logs piúba wooden raft) does not exist anymore because the extraction of the tree has been forbidden. Now, you can only see the piúba raft in the museum". This affirmation is confirmed by the fact that one of the main components of the watercraft depends on the species pau de jangada. By considering the UV of the species, more than half presented low values (< 1.00). By examining the ICS, we observed the opposite (Table 3). This result indicates that the ICS represented a notable usage for these species in the traditional raft because its calculation includes not only the variables related to the type of usage of the species but also the frequency of usage, the preference for the species to the detriment of others available, and if there is an interaction, besides the extraction, between the species used and the fishermen. As a result, the species pau de jangada, taipóca, muanza, and cajueiro were better represented by the ICS than by the UV, which is mainly determined by the different uses of those species in the traditional raft. Given the cultural richness present in the traditional raft, the extensive knowledge obtained by the raftsmen concerning the natural resources they use, the native biodiversity of the Atlantic Forest, and the synergic interaction between these elements, the need to establish joint actions that guarantee their dynamics becomes evident. Moreover, the sites where people still practise actions that directly connect the survival of human groups to the use of natural resources may also be maintained. This direct relationship can be the key to making social groups feel like they are part of the environment due to their direct responsibility for preserving this area and consequently perpetuating their practices. Then, the imposing measures that are taken should be reduced in such a way that the existence of areas with rich biodiversity, such as the Atlantic Forest, can be guaranteed. Currently, the role of areas of protection [31] and of ongoing legislation to protect the species of the Atlantic Forest [54, 55] is essential to the existence of this fragile, naturally priceless biome. The recognition of the construction of the raft as a cultural heritage of the region could allow the permanence of the existing construction practice, even with the current laws of protection of biodiversity [31, 55] and the current change of fishing technology to synthetic materials. The permanence of this practice could maintain diverse relationships with the surrounding environment, allowing for even greater success in the conservation of resources. In several places in the world and in Brazil, there has been a substitution of natural resources for synthetic material, as described by Rodón et al. [12]. However, in the existence of a public policy that recognizes traditional knowledge and guarantees, if it is of local interest, its permanence would allow the perpetuation of local knowledge. The studied area is an example of a location with biological and cultural diversity, where strategies that involve both aspects can be developed to strengthen the local cultural identity and to guarantee the execution of traditional practices that would only be possible with local communities taking responsibility concerning the usage of the natural resources available. The raft-related population from southern Bahia is aware of the arboreal plant species connected to their fishing activity. The primary association between the fishermen and the species they use appears in the traditional practice of building the raft, which is done by the raftsmen themselves. Due to the high sophistication level in the construction of this watercraft, raftsmen need a more profound knowledge of the morpho-anatomical characteristics of the woods in the species used, which can guarantee the efficiency of the traditional raft in fishing-related activities. The models of the traditional rafts result from the necessities of the groups from each location. Moreover, the practicality and functionality of the watercraft in the face of the adversities found by the raft community are also remarkable. We identified the preferential usage of some species over others. Biriba wood has been found to be valuable for building such watercraft, and the pau de jangada wood was the only irreplaceable, or nearly irreplaceable, species in the production of the ballast of the raft. Faced with the need for the plant resources required for the practices of this population, developing strategies that combine the conservation of the natural resources available with the preservation of the local culture, while respecting the interrelation between "man-plant-sea," is essential. CEPEC: Cocoa Research Center HUESC: Herbarium of the State University of Santa Cruz IPHAN: National Historic and Artistic Heritage Institute Narchi NE, et al. 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Historical timbers of traditional rafts from along the coast of Pernambuco, northeast Brazil. Int J Dev Res. 2017;7(09):15490–3. To those, reason why this study exists, teachers of life and masters concerning to receptivity, the raftsmen. Among them, I have been blessed with delightful talking hours, learning motivating moments. To you, raftsmen, I am grateful for the opportunity of seeing grace and life in the simplicity of a raft. To José Lima da Paixão, for the support of the collection and identification of the species. To the UESC and the PPGDMA, for the support of the field activities, and to the CNPq, for the productivity scholarships to the last three authors. The PPGDMA financed the publication of this article. The data used and analyzed during the current study is available from the corresponding author on reasonable request, without disclosure of the interviewees. Programa de pós-graduação em Desenvolvimento e Meio Ambiente—PRODEMA (Master Degree Program in Development and Environment), Universidade Estadual de Santa Cruz (Santa Cruz State University), Ilheús, Bahia, Brazil Isis Leite Medeiros Mascarenhas Andrade Departamento de Ciências Biológicas (Department of Biological Sciences), Universidade Estadual de Santa Cruz (Santa Cruz State University), Ilhéus, Bahia, Brazil Marcelo Schramm Mielke Laboratório de Ecologia Humana Etnobotânica (ECOHE) (Laboratory of Human Ecology), Departamento de Ecologia e Zoologia (ECZ), Universidade Federal de Santa Catarina (UFSC) (Santa Catarina Federal University), Florianópolis, Santa Catarina, Brazil Nivaldo Peroni Investigador Asociado CESIMAR, CE- NPAT, Puerto Madryn, Argentina Alexandre Schiavetti Search for Isis Leite Medeiros Mascarenhas Andrade in: Search for Marcelo Schramm Mielke in: Search for Nivaldo Peroni in: Search for Alexandre Schiavetti in: ILMMA, MS, and AS designed the research project. IMMA performed the data collection and analysis and drafted the paper, with inputs from all co-authors. MS, NP, and AS provided theoretical inputs and comments on the draft manuscript. ILMMA, MS, NP, and AS provided financial support to research and manuscript translation. All authors read and approved the final manuscript and agreed to its submission. Correspondence to Isis Leite Medeiros Mascarenhas Andrade. This study was approved by the Ethics Committee on Research with Human Beings of the State University of Santa Cruz, with the presentation certificate for Ethics Assessment (CAAE: 42296514.6.0000.5526), and by the Biodiversity Authorization and Information System (SISBIO 49.650-1). The participating raftsmen have signed a free and informed consent form according to the ethical requirements of the National Health Committee (Resolution 196/96) and authorized the disclosure of the provided information. This manuscript does not contain any individual person's data and further consent for publication is not required. Andrade, I.L.M.M., Mielke, M.S., Peroni, N. et al. Fishermen do more than fish: local ecological knowledge of raftsmen about the arboreal species used to construct rafts (Bahia, Brazil). J Ethnobiology Ethnomedicine 14, 80 (2018) doi:10.1186/s13002-018-0279-7 Ethnobotanics Pau de Jangada Traditional raft Atlantic forest	CommonCrawl
Is the Nash Embedding Theorem a special case of the Whitney Embedding Theorem? The Whitney Embedding Theorem states that every smooth manifold can be embedded in Euclidean space. The Nash Embedding Theorem states that every Riemannian manifold can be embedded in Euclidean space. So I wonder: Can I regard Nash's theorem as a special case of Whitney's theorem? differential-geometry manifolds riemannian-geometry Haskell Curry hxhxhx88hxhxhx88 $\begingroup$ Nash's theorem says something stronger: every Riemannian manifold can be isometrically embedded in Euclidean space. $\endgroup$ – Zhen Lin Nov 13 '12 at 8:10 Just to add something to Jesse's answer, the idea behind the proof of the Easy Whitney Embedding Theorem is to place different pieces of the given $ n $-dimensional smooth manifold in 'general position' in $ \mathbb{R}^{2n + 1} $. The proof is not very hard to follow; I think that Munkres does a pretty good job in his book Topology. The Hard Whitney Embedding Theorem, which tries to embed a smooth $ n $-dimensional manifold in $ \mathbb{R}^{2n} $, requires a more technical proof. A clever idea, called 'Whitney's trick' nowadays, is the main idea behind the proof. Notice that we have no notion of distance on a general smooth manifold $ M $ unless some metric on $ M $ is specified. Hence, both versions of the Whitney Embedding Theorem do not talk about preserving distances between points when constructing the required smooth embedding. The Nash Embedding Theorem, however, is much harder. Not only must you embed the given Riemannian manifold in Euclidean space, you must do so isometrically, i.e., in a way that preserves distances between points. This requires the solution of a formidable system of partial differential equations that yields the required isometric embedding. Nash solved this PDE system using a special version of Newton's iteration method, called Newton's method with post-conditioning. When unmodified, Newton's iteration method, in general, fails to converge to a solution because each step of the iteration might result in the loss of derivatives, i.e., the order of differentiability is reduced. Nash recovered the lost derivatives by applying smoothing operators (defined via convolution) at each step of the iteration. This ensures that Newton's iteration method does actually converge to a solution. The application of a smoothing operator at each step is called post-conditioning. As you can see, Nash's result is definitely much harder and requires more technology to prove than Whitney's results. These two results also have different natures. The Whitney Embedding Theorem is more topological in character, while the Nash Embedding Theorem is a geometrical result (as it deals with metrics). However, the structure of smooth manifolds is sufficiently rigid to ensure that they are also geometrical objects (cf. my comment below Jesse's answer), to which the Nash Embedding Theorem can be applied. Haskell CurryHaskell Curry $\begingroup$ If you want embeddings (as opposed to immersions) you need to add $1$ to the dimensions you state: easy Whitney embeds into $\mathbb{R}^{2n+1}$ and as you say you can push the dimension down by one to $2n$. The example to keep in mind is the real projective plane which cannot be embedded into $\mathbb{R}^3$. The first chapter of Hirsch's book on differential topology contains a very good exposition of these ideas, too. $\endgroup$ – commenter Nov 13 '12 at 9:19 $\begingroup$ Yes, I accidentally stated the immersion result, which is not what I intended. Thanks for pointing that out! $\endgroup$ – Haskell Curry Nov 13 '12 at 9:21 $\begingroup$ Your explanation is quite heuristic, thanks very much! $\endgroup$ – hxhxhx88 Nov 13 '12 at 16:15 $\begingroup$ Very nice: I can't help feeling that the film A Beautiful Mind would have been much better if the above had been incorporated into the screenplay... $\endgroup$ – Georges Elencwajg Mar 13 '13 at 21:26 $\begingroup$ The Nash embedding states that given a Riemannian manifold $(M,g)$, there is an embedding $i:M\rightarrow \mathbb{R}^N$ for which $i^\ast g_0 = g$, where $g_0$ is the standard metric in $\mathbb{R}^N$. This is very different from saying the distance between points is preserved. For examples, a regular circle $S^1$ doesn't embed isometrically into any $\mathbb{R}^N$ using your defintion of isometric above. $\endgroup$ – Jason DeVito Nov 26 '18 at 22:04 It's really the other way around: Whitney's Theorem is (in some sense) a special case of Nash's Theorem. Whitney's Theorem says that every smooth manifold can be smoothly embedded in some euclidean space $\mathbb{R}^N$. Nash's Theorem says that every Riemannian manifold can be isometrically in some euclidean space $\mathbb{R}^N$, and hence smoothly embedded. While it's true that every Riemannian manifold is (by definition) a smooth manifold, it's also true that every smooth manifold can be equipped with a Riemannian metric (and thereby becomes a Riemannian manifold). Jesse MadnickJesse Madnick $\begingroup$ To see why every smooth $ n $-dimensional manifold $ M $ can be equipped with a Riemannian metric, first form an open cover of $ M $ consisting of subsets of $ M $ that are homeomorphic to open subsets of $ \mathbb{R}^{n} $. From these open subsets of $ \mathbb{R}^{n} $, pull back (via the individual homeomorphisms) the standard Euclidean inner product. Each member of the open cover is now equipped with an inner product. Next, construct a partition-of-unity subordinate to the open cover to consistently sum up all these inner products to get a global inner product on $ M $. $\endgroup$ – Haskell Curry Nov 13 '12 at 8:55 $\begingroup$ Got it. Thank you for answer!. $\endgroup$ – hxhxhx88 Nov 13 '12 at 16:17 Not the answer you're looking for? Browse other questions tagged differential-geometry manifolds riemannian-geometry or ask your own question. Riemannian Immersions into Euclidean Space? After Whitney embedding Question regarding Nash-Kuiper embedding theorem Whitney's Embedding Theorem Is the Whitney embedding theorem tight for all $n$? Can every Riemannian manifold be embedded in a sphere? Questions on J. F. Nash's answer about his errors in the proof of embedding theorem Whitney Embedding Theorem and the Riemannian Circle Isometrically embedding theorem	CommonCrawl
Phase space of partially coherent light with discontinuous surfaces Minyi Zhong1 & Herbert Gross1,2 An Erratum to this article was published on 08 July 2016 We propagate partially coherent light through discontinuous surfaces and analyze the optical effects in phase space. The discontinuous surfaces are classified into two types, those with discontinuity in space and those with discontinuity in slope. Results are discussed based on the Wigner function. This approach explains the performance of segmented elements during the transition from the refractive into the diffractive regime. At first the diffraction effects generated by a single discontinuity (e.g. a phase step and a linear axicon) are investigated. Later on we discuss surfaces with periodic discontinuities, e.g. gratings, to study the formation of multiple diffracted orders. A kinoform lens is given as a further example to visualize the change from pure refraction to diffraction. Moreover, we present the beam homogenizing effect in phase space generated by lens arrays. The Wigner function was first proposed by Wigner [1] in 1932 as a quasi-probability distribution to describe quantum mechanics in phase space. Later the Wigner function was introduced into optics by Dolin and Walther [2–4], to describe an optical signal in phase space. There are several remarkable advantages of using the Wigner function for analyzing optical systems. First, it describes optical signals simultaneously in spatial frequency and space. This idea resembles the concepts of angle and position in geometrical optics. Making use of this property we are able to propagate light in phase space with the ray transfer matrix (also known as ABCD matrix) [5, 6]. Second, phase space visualizes information in wave optics such as diffraction and interference effects. Here we use the Wigner function as a tool to investigate segmented elements during the transition between refraction and diffraction. Third, the Wigner function is able to represent a partially coherent beam in a straightforward way [7]. It visualizes the degree of coherence in phase space as the angular extent. An alternative method to analyze partial coherence is to decompose a beam into a summation of modes [8, 9]. However, it requires a convergent mode expansion dependent on each specific problem. By using the Wigner function we avoid performing such complicated mode decomposition. In this work we focus on light beams of spatial partial coherence, and propagate the beam through discontinuous surfaces. The optical effects are discussed in phase space. The content of this paper is divided into the following sections. Section 2 gives a brief introduction to the Wigner function. Section 3 discusses the diffraction effects generated by various discontinuous surfaces. We separate the discontinuous surfaces into two types, those with discontinuity in space, and those with discontinuity in slope. We limit the discussions to two dimensions spatially, i.e. in coordinates (x, z) where x denotes the transverse position and z is the propagation direction. The light is restricted to be monochromatic, paraxial and partially coherent in space. Provided we know the cross-spectral density function Γ(x1, x 2) (also known as correlation function) of a partially-coherent beam at a certain transverse plane, where x1 and x 2 are two arbitrary transverse coordinates, the phase space of light at this transverse plane is given by the Wigner function, $$ \mathrm{W}\left(\mathrm{x},\mathrm{u}\right)={\displaystyle \int \Gamma}\left(\mathrm{x}+\frac{\Delta \mathrm{x}}{2},\mathrm{x}-\frac{\Delta \mathrm{x}}{2}\right) \exp \left(-\mathrm{i}\frac{2\uppi}{\uplambda}\mathrm{u}\Delta \mathrm{x}\right)\mathrm{d}\Delta \mathrm{x} $$ where x = (x1 + x 2)/2, Δx = x1-x 2. By definition, the integration of all signals in the Wigner function over the spatial dimension results in an angular spectrum. Integration of all the signals over the angular dimension computes the light intensity in space. Figure 1 serves as an example to demonstrate the propagation of light inside a system by using Wigner functions. Inside the paraxial regions that can be described by ABCD matrices (e.g. z1-z6) we use Eq. 2 to propagate the Wigner function, Using the Wigner functions to propagate partially coherent light inside a system $$ {\mathrm{W}}^{\hbox{'}}\left({\mathrm{x}}^{\hbox{'}},\ {\mathrm{u}}^{\hbox{'}}\right)=\mathrm{W}\left(\mathrm{Ax}+\mathrm{B}\mathrm{u},\mathrm{C}\mathrm{x}+\mathrm{D}\mathrm{u}\right) $$ where W and W' denote the Wigner functions of light entering and exiting a region respectively. In other regions consisting of lenses or stops (e.g. d1-d4), it is more convenient to obtain the correlation function Γ behind the element by a Fourier transform of the Wigner function, then employ the thin element approximation (Eq. 3–5). In this approach the thicknesses d1- d4 of the elements are neglected. $$ {\Gamma}^{\hbox{'}}\left({\mathrm{x}}_1,\ {\mathrm{x}}_2\right)=\Gamma \left({\mathrm{x}}_1,{\mathrm{x}}_2\right)\cdotp \mathrm{t}\left({\mathrm{x}}_1\right)\cdotp {\mathrm{t}}^{}\left({\mathrm{x}}_2\right)\ \mathrm{or}\ \left({\mathrm{x}}_1,{\mathrm{x}}_2\right)=\Gamma \left({\mathrm{x}}_1,{\mathrm{x}}_2\right)\cdotp \mathrm{A}\left({\mathrm{x}}_1\right)\cdotp {\mathrm{A}}^{}\left({\mathrm{x}}_2\right) $$ $$ \mathrm{t}\left(\mathrm{x}\right)= \exp \left[\hbox{-} \mathrm{i}\frac{2\uppi}{\uplambda}\left(\mathrm{n}\hbox{-} 1\right)\Delta \mathrm{z}\left(\mathrm{x}\right)\right] $$ $$ \mathrm{A}\left(\mathrm{x}\right)=\left\{\begin{array}{c}\hfill 1,\ \mathrm{inside}\ \mathrm{stop}\ \hfill \\ {}\hfill 0,\ \mathrm{outside}\ \mathrm{stop}\hfill \end{array}\right. $$ In Eq. 3–5 Γ and Γ' represent the correlation functions of light entering and exiting the region, t and A referring to the modulation functions for phase and for amplitude from a surface, λ being the wavelength, n being the refractive index of the element and Δz defining the height of the surface. Because of the Hermitian properties of the correlation function, the Wigner function is always in real but not necessarily positive values. Negative values in the phase space indicate destructive interference [10]. In the following section we discuss the interpretation of diffraction effects in phase space with various examples. At first we introduce an important parameter Δϕ to denote the optical path difference generated by a phase step (Fig. 2c). A ray of light in the wavelength λ traveling through a refractive material with a height of Δz accumulates the phase term exp(i2πnΔz/λ), where n is the refractive index of the material. Meanwhile another ray of light next to the material traveling through air of the same thickness Δz carries another phase term exp(i2πΔz/λ). We define the normalized phase difference between the two different rays as Δϕ = (n-1)Δz/λ, i.e. the phase difference divided by 2π. In the special blazed condition, Δϕ is an integer. It means the optical path difference is of a multiple of the wavelength. Thus it results in no interference effects. In the following discussions we concentrate on cases of Δϕ being a non-integer to examine the diffraction effects. Phase steps of various heights. The parameters for the incident light source are σ = 1 μm, δ = 0.5 μm and M = 40 Phase step In this work the incident light source has a nearly flat-top transverse intensity profile, to insure a uniform illumination on the diffractive element. It is a superposition of multiple quasi-collimated monochromatic Gaussian Schell-model beams in the far field [11]. The source is characterized by three near-field parameters according to Eq. 12 in [11]: rms beam width σ, rms correlation width δ and the mode count M. The degree of coherence in our model decreases, when the value of σ increases. A larger integer of M produces a more flat-top profile of the far-field intensity. We define the refractive index n = 2.0 for all optical elements and the wavelength λ = 0.6328 μm. In Fig. 2 the step heights are defined as Δz = 50.0λ, 50.2λ, 50.5λ, 50.8λ and 51.0λ, yielding Δϕ = 50.0, 50.2, 50.5, 50.8 and 51.0 respectively (Fig. 2d-g). With Δϕ = 50.0 or Δϕ = 51.0 there is no change in the phase space between the incoming beam and the outgoing beam (compare Fig. 2a, d). That is because the light experiences no phase jump after passing the step. In the cases of Δϕ being a non-integer (Fig. 2e-g), ripples occur in phase space. They are the visualization of diffraction effects centered at the step location. These diffraction ripples are an indication of the Fourier series of the Heaviside step function. In the case of Δϕ = 50.5 the diffraction ripples are most pronounced and symmetric about the origin. In the intensity along the propagated beam (Fig. 2h) the destructive interference produces a minimum at the transverse intensity at x = 0. Besides, the phase space of Δϕ = 50.2 (Fig. 2e) is a 180° rotation of the phase space of Δϕ = 50.8 (Fig. 2g). The same applies to pairs of Δϕ = 50.3 and 50.7, Δϕ = 50.2 and 50.8, Δϕ = 50.1 and 50.9. It is worth mentioning that when the light source has a larger coherence length, the diffraction ripples are more pronounced. This is because a more coherent beam generates more noticeable interference effects. Conversely, as the coherence length of the light source decreases, the diffraction ripples become fainter. Axicon We take a linear axicon as another example to discuss the single discontinuity in phase. Compared to the phase step, a linear axicon is continuous in space but discontinuous in slope. Diffraction effects always happen when there is a slope discontinuity on the surface, even though there is no abrupt change for the step height. In this case Δϕ is no longer a criterion to evaluate the destructive interference. Corresponding results are shown in Fig. 3. The axicon splits a quasi-collimated incident beam (Fig. 3a) into two beamlets with different angles. This is indicated in the phase space (Fig. 3d) as two horizontal lines located at opposite angles. A split happens where the surface slope changes, i.e. x = 0. Phase space of a quasi-collimated Schell-model beam passing a linear axicon. The parameters for the incident light source are σ = 0.5 μm, δ = 0.2 μm and M = 40 In addition, diffraction ripples appear due to the phase wedge of the axicon. The ripples in Fig. 3d (i) and (ii) are connected to the two lines. They resemble the diffraction ripples generated by the phase step in Section 3.1. These ripples propagate with the beamlets and produce oscillations in the transverse intensity near the outer edges of the beamlets (Fig. 3g). Meanwhile the ripples in Fig. 3d (iii) near the origin are separate from the two lines. They result from interference between the two beamlets. The ripple frequency increases with the angle between the two beamlets [12]. When we integrate these ripples over the angular axes, they produce oscillations in the transverse intensity. For a longer propagated distance, the ripples are sheared and their effect on the transverse intensity diminishes. The axial range where oscillations can still be observed (z < 3 mm) in the transverse intensity is proportional to the coherence length of the incident beam. In the following we show several examples of phase space corresponding to various phase gratings. A binary grating can be considered as a periodic superposition of Heaviside steps. The phase space of a single Heaviside step is discussed in the previous section (Fig. 2d-g). Here we start with a grating composed of four Heaviside steps. The grating profile is overlaid on top of the phase space in Fig. 4b. On the line with u = 0 in phase space, negative values occur at four separate x positions. These positions coincide with the phase discontinuity of the surface. Another notable feature in Fig. 4b is the positive peaks on the line through u = 0.033 radian. The three horizontal lines of signals along u = 0 and u = ±0.03 radian form the 0 and ±1 diffracted orders, respectively. The angles of diffracted orders follow the formula sin u = mλ/d, where u is the diffracted angle, m being the diffracted order, λ representing the wavelength and d denoting the grating period. Phase gratings. The total spatial extent of the gratings in (c), (d) and (e) is from −0.5 mm to 0.5 mm along the x axis. We only show the grating profiles along the x axis from −0.05 mm to 0.05 mm for a clear visibility of the periods. The parameters for the incident light source are σ = 5 μm, δ = 0.8 μm and M = 40 In Fig. 4c the grating has the same period as the one in Fig. 4b, but covering a larger spatial extent. If we derive the angular spectrum from the phase space, there are sharper peaks representing the diffracted orders (not shown in the figures). However, the width of the peaks in the angular spectrum is also influenced by the angular extent of the partially coherent source. Figure 4d shows a binary grating with a larger period. According to the diffraction formula, a larger value of d results in a smaller diffracted angle u. The ±1 diffracted orders are at u = ±0.023 radian. Figure 4e illustrates a blazed grating (also called echelette grating). Due to the asymmetric profile of this grating, both refraction and diffraction take place. All the diffracted orders move along the angular axis. The 0 order is repositioned at the angle u = −0.12 radian. Moreover, the step height of the blazed grating defines the value of the normalized phase difference Δϕ. With Δϕ = 3.6, the −1 order contains more energy than the +1 order (Fig. 4e). For a binary grating, the energies in the +1 and −1 orders are always equal. Kinoform lens A kinoform lens can be interpreted as a grating with locally varying periods. When the periods can be approximated by a linear blazed grating, one may use the method proposed by Sinzinger [13] to analyze the diffraction effects based on Fourier analysis. In our work we express the profile of the kinoform lens as a conical surface with z = cx2/{1 + [1-(1 + k)c2x2]1/2}, where c denotes the curvature (i.e. the reciprocal of the radius) and k is the conic constant. We cut this surface into slices with an equal height Δz, and leave out all the coplanar parts. This cutting yields a kinoform lens with quadratically-decreasing zone widths from the inner to the outer region (Fig. 5a). The profiles of individual grooves remain conical. We discuss the diffraction effects generated by such a kinoform lens in Fig. 5, with c = 0.25 mm−1, k = −4 and various values of Δz. Kinoform lenses with various groove heights. The lens profile in (a) does not have perfectly uniform groove heights due to finite samplings. The zone widths vary from 10.4 to 41.8 μm in (c), from 7.8 to 34.6 μm in (d), from 7.8 to 36.6 μm in (e), from 11.7 to 47 μm in (f), and from 17.6 to 55.4 μm in (g). Figures of phase space share the color bar in (b). The parameters for the incident light source are σ = 5 μm, δ = 0.7 μm and M = 40 When the kinoform lens works in blazed condition we call it a Fresnel lens (Fig. 5c, Δϕ = 2.0). In this case the transmitted light is dominated by refraction. Ray optics is sufficient to describe its optical effects in the paraxial regime. In phase space the focusing effect of the Fresnel lens is expressed by a shearing of signals along the angular axis. The propagation of light is performed by an additional shearing along the spatial axis. At the focus position the signals in phase space form a vertical line. As there are no diffraction ripples in phase space, the intensity along the propagated beam is symmetric about the focal plane (z = 4 mm). When the kinoform lens does not fulfill the blazed condition, i.e. Δϕ being a non-integer, the phase mismatch generated by the groove height can contribute to significant diffractive phenomena. Multiple diffracted orders appear when the zone widths on the kinoform lens are in the range of several wavelengths. In Fig. 5c the phase space is composed of several stripes crossing each other at the origin. Each stripe represents one diffracted order. The central stripe is the 0 order indicating the refracted beam path. Thus the 0 order is always at the same location as the phase space signals in Fig. 5b. Any other higher orders (±1, ±2, etc.) are the outcomes of interference effects. The fine structures in phase space result from a superposition of all the interference effects generated by individual grooves. With Δϕ between 1.4 and 2.4 the diffracted orders are separated from each other by a large distance. In free-space propagation, each diffracted order produces its own axial focus. The energy ratio of the foci depends on the energy distribution among the diffracted orders. With Δϕ = 1.5, both +1 and −1 orders contain equal energy in phase space. Correspondingly the foci formed by the +1 and −1 orders share the same amount of energy. However, due to different numerical apertures, their peak heights are not equal. Meanwhile there is no intensity peak at z = 4 mm for Δϕ = 1.5 in Fig. 5d. That is because the integration of the phase space signals i the 0 order returns zero. The transition from diffraction to pure refraction happens when the zone width grows considerably larger than the wavelength (λ = 0.6328 μm). When the height of the kinoform lens is increased to Δz = 3.5λ, i.e. Δϕ = 3.5, the zone width is above 17 μm. The diffracted orders are no longer distinguishable (Fig. 5f). All the diffracted orders start to merge together. Individual foci in the propagated beam path are not separable any more. If the zone width is increased even more, diffraction effects gradually fade. Eventually this leads to one single focus as in ray optics. Due to manufacturing limitations, a Fresnel lens is commonly produced with linear saw-tooth grooves. In Fig. 6 we compare this type of Fresnel lens (Δϕ = 10.0) and a lens with conical grooves. Because Δϕ is an integer, the Fresnel lens with conical grooves gives exactly the same performance as a continuous conical lens. The axial intensity distribution along propagation is symmetric about the focus position (Fig. 6a). Correspondingly, a Fresnel lens with linear saw-tooth grooves is equivalent to a piecewise linear approximation of a conical surface. This approximation creates discontinuous slopes on the surface, although the groove height yields no phase mismatch due to Δϕ being an integer. The corresponding diffraction effects are seen in phase space as additional ripples. Furthermore, the linear profile on each groove bends the light into slightly non-focusing angles. Under the influence of ray effects and wave effects, an asymmetric axial focus is found in the propagated beam path (Fig. 6b). Fresnel lens with conical grooves (a) and linear saw-tooth grooves (b), both with a focal length of 10 mm. Figures with the same titles share the same color bars. The parameters for the incident light source are σ = 2 μm, δ = 0.3 μm and M = 40 Lens array The lens array is a common component in optical systems for beam homogenizing. Figure 7 shows two setups for this application. Setups for beam homogenizing. The focal length of the lens array is f1. The focal length of the condenser lens is f2. Plane A marks the plane right behind the array. Plane B lies on the back focal plane of the array. Plane C is the output plane for a homogenized beam Figue 8 shows the results based on the setup in Fig. 7a. The light leaving the array is distributed into five channels defined by the individual lenslets. This is indicated by five parallel tilted lines in phase space on the plane A (Fig. 8c). Between the adjacent lines there are additional diffraction ripples caused by the discontinuous slope of the array. Similar to the case of an axicon, ripples occur near the zero angle regions and at each end of the five lines (Fig. 8c (i) and (ii)). As the plane B is at the back focal plane of the lens array, five tilted lines in phase space on the plane A are sheared into a vertical orientation (Fig. 8d). By integrating the signals in Fig. 8d vertically we derive five narrow peaks in the transverse intensity on the plane B (Fig. 8f). They indicate five focused beamlets at the back focal plane of the lens array. The weaker intensity peaks in Fig. 8f originate from the non-uniform illumination. The ripples in Fig. 8d (i) give no contribution to the transverse intensity after the integration. Phase space results of the one-array system for beam homogenizing given by Fig. 7a. Figures of phase space share the color bar in (a). The parameters for the incident light source are σ = 1 μm, δ = 0.18 μm and M = 40 Since the plane B and the output plane C form a pair of Fourier conjugates, the phase space on the plane C is a 90° rotation of the phase space on the plane B. The ripples in Fig. 8g (i) produce oscillations in the transverse intensity at the edges of the beam (Fig. 8h). The only difference between the two setups in Fig. 7 is the second lens array. It is placed at the back focal plane of the first array, acting as a field lens. This field lens introduces an extra focusing effect. In phase space this is expressed as a vertical shearing of signals. Thus the ripples in Fig. 9a (i) are sheared into a symmetric distribution, compared with Fig. 8d. Physically it means the field lens captures light with large angles and bends them into the acceptable numerical aperture of the condenser lens. Thus the light falls into a better-defined spatial region on the output plane C. Figure 9c shows a more homogenized intensity profile than Fig. 8h. Phase space results of the two-array system for beam homogenizing given by Fig. 7b. Phase space in (a) and (b) share the color bar in Fig. 8a The Wigner function contains information about ray optics and wave optics. In this work the Wigner function helps us to understand the behavior of partially coherent light interacting with diffractive elements. We discuss two types of discontinuous surfaces, those with discontinuity in space and those with discontinuity in slope. The phase step, grating and kinoform lens belong to the first type. For surfaces of spatial discontinuity, the optical path difference is important to evaluate the destructive interference. For example, by varying this parameter we see the change of a kinoform lens from pure refraction to diffraction. This parameter also controls the energy distribution among the multiple foci formed by the diffracted orders of a kinoform lens. The axicon, Fresnel lens with linear saw-tooth grooves and the lens array represent the second type of surface discontinuity, i.e. discontinuity in slope. It always causes pronounced interference effects. The Wigner function is a useful tool for optical simulation. It facilitates the interpretation of intermediate optical effects, in particular for complex systems with partially coherent light and diffractive elements. Wigner, E: On the quantum correction for thermodynamic-equilibrium. Physical Rev 40, 749–759 (1932) Article ADS MATH Google Scholar Dolin, L: Beam description of weakly-inhomogeneous wave fields. Izv Vyssh Uchebn Zaved Radiofiz 7, 559–563 (1964) Walther, A: Radiometry and coherence. J Opt Soc Am 58, 1256–1259 (1968) Walther, A: Propagation of the generalized radiance through lenses. J Opt Soc Am 68, 1606–1610 (1978) Eppich, B: Die Charakterisierung von Strahlungsfeldern mit der Wigner-Verteilung und deren Messung. Doctoral dissertation, Technical University of Berlin, Germany (1998) Testorf, M, Hennelly, B, Ojeda-Castaneda, J: Phase-Space Optics: Fundamentals and Applications. The McGraw-Hill companies, New York (2010) Bastiaans, M: Application of the Wigner distribution function to partially coherent light. J Opt Soc Am A 3, 1227–1238 (1986) Wolf, E: New theory of partially coherence in space-frequency domain. Part I: Spectra and cross-spectra of steady-state sources. J Opt Soc Am 72, 343–351 (1982) Wolf, E: New theory of partial coherence in the space-frequency domain. Part II: Steady-state fields and higher-order correlations. J Opt Soc Am A 3, 76–85 (1986) Signer, W, Totzek, M, Gross, H: Handbook of Optical Systems-Physical Image Formation. Wiley-VCH, Weinheim (2005) Korotkova, O: Random sources for rectangular far fields. Opt Lett 39, 64–67 (2014) Hlawatsch, F: Interference terms in the Wigner distribution. Digital Signal Processing. 84 363–367 (1984) Sinzinger, S, Testorf, M: Transition between diffractive and refractive micro-optical components. Appl Opt 34, 5970–5976 (1995) This work is partially supported by the German Federal Ministry of Education and Research within the project fo+ (03WKCK1D). We thank Dr. Martin Kielhorn for comments and discussions which improved this manuscript. We are grateful to the reviewer for the constructive input. Friedrich-Schiller-University Jena, Institute of Applied Physics, Jena, 07743, Germany Minyi Zhong & Herbert Gross Fraunhofer Institute for Applied Optics and Precision Engineering IOF, Jena, 07745, Germany Herbert Gross Minyi Zhong Correspondence to Minyi Zhong. Both authors developed the simulation models together. The progress is a result of common contributions and discussions. MZ implemented the work and wrote the manuscript. HG proposed the original ideas, gave advices and offered the conditions for the project. Both authors read and approved the final manuscript. Zhong, M., Gross, H. Phase space of partially coherent light with discontinuous surfaces. J. Eur. Opt. Soc.-Rapid Publ. 12, 3 (2016). https://doi.org/10.1186/s41476-016-0004-x Received: 03 April 2016 Wigner function Segmented element Diffraction	CommonCrawl
Mathematics Meta Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Infinite Series $\sum\limits_{n=1}^\infty\frac{(H_n)^2}{n^3}$ How to prove that $$\sum_{n=1}^{\infty}\frac{(H_n)^2}{n^3}=\frac{7}{2}\zeta(5)-\zeta(2)\zeta(3)$$ $H_n$ denotes the harmonic numbers. real-analysis sequences-and-series complex-analysis closed-form harmonic-numbers edited Aug 3 '17 at 9:19 $\begingroup$ Typo: you meant $H_n = \sum_{k=1}^n \frac 1k$. $\endgroup$ – Stephen Montgomery-Smith Nov 7 '13 at 5:40 $\begingroup$ You can use the integral representation $B(p,q)$. Also, see here for related problem and techniques. $\endgroup$ – Mhenni Benghorbal Nov 7 '13 at 5:49 $\begingroup$ Generally speaking, $H_n\simeq\ln n+\gamma$, and $$\begin{align}\sum_{n=1}^\infty\frac{H_n^a}{n^b}&\simeq\sum_{n=1}^\infty\frac{\ln^an}{n^b}=\left\|\zeta^{(a)}(b)\right\|\simeq\\\\\\\\\\&\simeq\int_1^\infty\frac{\ln^ax}{x^b}dx=\frac{a!}{(b-1)^{a+1}}\end{align}$$ where the simpler formula $n!=\int_1^\infty\frac{\ln^nx}{x^2}dx$ can be obtained by a simple change in variable $t=\frac1x$ applied to Euler's first integral expression for the $\Gamma$ function: $n!=\int_0^1(-\ln x)^ndx=\int_0^1\ln^n\frac1xdx$. $\endgroup$ – Lucian Nov 9 '13 at 0:47 $\begingroup$ You should add explicitly what is $\large H_{n}$. $\endgroup$ – Felix Marin Nov 9 '13 at 6:19 $\begingroup$ Also, try and simply write the first few terms of each $\zeta$ from each product and simply multiply them, then group and order them, and notice the general form of the terms of each such product. $\endgroup$ – Lucian Nov 9 '13 at 7:04 One systematic way of proving identities like this is to write everything in terms of multiple harmonic sums and multiple zeta values . For integers $s_1,\ldots,s_k,n\geq 1$, we define the multiple harmonic sum (or MHS) $$ H_n(s_1,\ldots,s_k):=\sum_{n\geq n_1>\ldots>n_k\geq 1}\frac{1}{n_1^{s_1}\ldots n_k^{s_k}}\in\mathbb{Q}. $$ The MHS $H_n(1)$ is what you call $H_n$. We also define the multiple zeta value (or MZV) $$ \zeta(s_1,\ldots,s_k):=\sum_{n_1>\ldots>n_k\geq 1}\frac{1}{n_1^{s_1}\ldots n_k^{s_k}}\in\mathbb{R}, $$ where we need $s_1\geq 2$ to ensure convergence. The following relationship between MHS and MZV is easy to check, and will be useful: $$ \sum_{n=1}^\infty \frac{H_n(s_1,\ldots,s_k)}{n^s}=\zeta(s,s_1,\ldots,s_k)+\zeta(s+s_1,s_2,\ldots,s_k). $$ MHS's and MZV's satisfy what's called a quasi-shuffle identity. One instance of this is given by the following: \begin{eqnarray} H_n(1)^2&=&\left(\sum_{n_1=1}^n\frac{1}{n_1}\right)\left(\sum_{n_2=1}^n\frac{1}{n_2}\right)\\ &=&\left(\sum_{n\geq n_1>n_2}+\sum_{n\geq n_2>n_1}+\sum_{n\geq n_1=n_2}\right)\frac{1}{n_1n_2}\\ &=&2H_n(1,1)+H_n(2). \end{eqnarray} Using the relationship between MHS and MZV and the quasi-shuffle identity, the left hand side of your identity equals $$ 2\zeta(3,1,1)+2\zeta(4,1)+\zeta(3,2)+\zeta(5). $$ The expression $\zeta(2)\zeta(3)$ can also be expanded with a quasi-shuffle identity: $$ \zeta(2)\zeta(3)=\zeta(2,3)+\zeta(3,2)+\zeta(5). $$ This means your identity is equivalent to the MZV identity $$ 2\zeta(3,1,1)+2\zeta(4,1)+2\zeta(3,2)+\zeta(2,3)=\frac{3}{2}\zeta(5). $$ This identity is linear and homogeneous (that is, each MZV $\zeta(s_1,\ldots,s_k)$ that appears satisfies $s_1+\ldots+s_k=5$). There is a ton of literature on producing homogeneous relations among multiple zeta values. One general class of relations, called the extended double shuffle relations, is conjectured to include all relations. You identity follows by taking a linear combination of the following MZV relations, which can be found in the literature: the double shuffle relation applied to $\zeta(2)\zeta(3)$ (see Derivation and double shuffle relations for multiple zeta values, by Ihara, Kaneko, and Zagier): $$ \zeta(5)=2\zeta(3,2)+6\zeta(4,1), $$ duality applied to $\zeta(3,1,1)$ (this is a consequence of an expression of Konstsevich for MZV as iterated integrals, see The algebra of multiple harmonic series, by Hoffman): $$ \zeta(3,1,1)=\zeta(4,1), $$ and the sum formula (known in this case by Euler and proven in the general case independently by Granville and Zagier, the statement can also be found in The algebra of multiple harmonic series): $$ \zeta(2,3)+\zeta(3,2)+\zeta(4,1)=\zeta(5). $$ Julian RosenJulian Rosen Identities such as this can be proved with the help of Cauchy's residue theorem. If $f$ is a meromorphic function such that $\lvert f(z)\rvert=o(z^{-1})$ as $\lvert z\rvert\to\infty$ on a sequence of concentric circles about the origin then, the residue theorem gives $$ \begin{align} \sum_a {\rm Res}(f,a)=0.&&{\rm(1)} \end{align} $$ Here, the sum is over all poles of $f$ and ${\rm Res}(f,a)$ is the residue of $f$ at $a$. The tricky part is finding the right function $f$. Flajolet & Salvy1 show how to prove a whole set of identities of this form. For example (all sums are over $n=1$ to $\infty$), $$ \begin{align} &\sum\frac{H_n}{n^2}=2\zeta(3),\\ &\sum\frac{H_n}{n^3}=\frac54\zeta(4),\\ &\sum\frac{H_n}{n^4}=3\zeta(5)-\zeta(2)\zeta(3),\\ &\sum\frac{(H_n)^2}{n^2}=\frac{17}{4}\zeta(4),\\ &\sum\frac{(H_n)^2}{n^3}=\frac72\zeta(5)-\zeta(2)\zeta(3),&&{\rm(2)}\\ &\sum\frac{(H_n)^2}{n^4}=\frac{97}{24}\zeta(6)-2\zeta(3)^2,\\ &\sum\frac{(H_n)^3}{n^4}=\frac{231}{16}\zeta(7)-\frac{51}{4}\zeta(3)\zeta(4)+2\zeta(2)\zeta(5) \end{align} $$ We also have the set of identities due to Euler (for $q\ge2$) $$ \sum_{n=1}^\infty\frac{H_n}{n^q}=\left(1+\frac q2\right)\zeta(q+1)-\frac12\sum_{k=1}^{q-2}\zeta(k+1)\zeta(q-k). $$ It is mentioned in Flajolet & Salvy that identities of this form do not always exist and, in particular, there is unlikely to be any finite formula for $\sum (H_n)^3/n^q$ in terms of zeta values when $q$ is an odd number exceeding $10$. I'll give the function $f$ which generates the identity (2) asked for, following Flajolet & Salvy (specializing to this example). Let $\psi$ be the digamma function $$ \psi(z)=\frac{d}{dz}\log\Gamma(z)=-\gamma-\frac1z+\sum_{n=1}^\infty\left(\frac1n-\frac1{n+z}\right). $$ This is bounded by $O(\lvert z\rvert^\epsilon)$ on circles of radius $n+1/2$ about the origin and has poles at the nonnegative integers. To prove the required identity (2), it is easiest to break this down into three identities (although, you could add the three choices of $f$ below and do it in one go). Taking the function $f(z)=\frac13z^{-3}\left(\psi(-z)+\gamma\right)^3$, this has poles at the nonnegative integers. Expand each term about $0$ and positive integers $n\gt0$, $$ \begin{align} &\psi(-z)+\gamma=\frac1z-\zeta(2)z-\zeta(3)z^2-\zeta(4)z^3-\zeta(5)z^4+O(z^5)\\ &\psi(-n-z)+\gamma=\frac1z+H_n-\left(H_n^{(2)}+\zeta(2)\right)z+O(z^2)\\ &(n+z)^{-3}=n^{-3}-3n^{-4}z+6n^{-5}z^2+O(z^3) \end{align} $$ Here, $H_n^{(2)}$ is the generalized harmonic number $\sum_{k\le n}k^{-2}$. Multiplying the terms together and extracting the coefficients of $z^{-1}$ gives the residues of $f$. $$ \begin{align} &{\rm Res}(f,0)=2\zeta(2)\zeta(3)-\zeta(5),\\ &{\rm Res}(f,n)=n^{-3}(H_n^2-H_n^{(2)}-\zeta(2))-3n^{-4}H_n+2n^{-5}. \end{align} $$ Summing over $n$ and applying the residue theorem, $$ \begin{align} \sum\frac{H_n^2}{n^3}-\sum\frac{H_n^{(2)}}{n^3}-3\sum\frac{H_n}{n^4}+\zeta(5)+\zeta(2)\zeta(3)=0.&&{\rm(3)} \end{align} $$ Now, take the function $f(z)=\frac12z^{-4}\left(\psi(-z)+\gamma\right)^2$. This again has poles at the nonnegative integers. Using the expansions above together with $$ (n+z)^{-4}=n^{-4}-4n^{-5}z+O(z^2) $$ we can compute the residues as before $$ \begin{align} &{\rm Res}(f,0)=\zeta(2)\zeta(3)-\zeta(5),\\ &{\rm Res}(f,n)=n^{-4}H_n-2n^{-5}. \end{align} $$ Applying the residue theorem again gives $$ \begin{align} \sum\frac{H_n}{n^4}-3\zeta(5)+\zeta(2)\zeta(3)=0.&&{\rm(4)} \end{align} $$ Finally take $f(z)=\frac12\pi z^{-3}\cot(\pi z)\psi^\prime(-z)$ and use the expansions $$ \begin{align} &\psi^\prime(-z)=z^{-2}+\zeta(2)+2\zeta(3)z+3\zeta(4)z^2+4\zeta(5)z^3+O(z^4)\\ &\psi^\prime(-n-z)=z^{-2}+H_n^{(2)}+\zeta(2)+O(z)\\ &\psi^\prime(n-z)=\zeta(2)+n^{-2}-H_n^{(2)}+O(z)\\ &\pi\cot(\pi(\pm n+z))=z^{-1}-\frac13\pi^2z+cz^3+O(z^5)=z^{-1}-2\zeta(2)z+cz^3+O(z^5) \end{align} $$ (some constant $c$) to compute the residues $$ \begin{align} &{\rm Res}(f,0)=2\zeta(5)-2\zeta(2)\zeta(3),\\ &{\rm Res}(f,n)=\frac12n^{-3}(H_n^{(2)}-\zeta(2))+3n^{-5},\\ &{\rm Res}(f,-n)=-\frac12n^{-3}(\zeta(2)+n^{-2}-H_n^{(2)}). \end{align} $$ Summing over $n$ and applying the residue theorem, $$ \begin{align} \sum\frac{H_n^{(2)}}{n^3}+\frac92\zeta(5)-3\zeta(2)\zeta(3)=0.&&{\rm(5)} \end{align} $$ Adding identities (3), 3 times (4), and (5) gives the required result. I'll just add a note that the use of the digamma function, cotangent and residue theorem above are not really required. It has been mentioned in Noam D. Elkie's answer that such results can be proved by elementary, but clever, algebraic manipulations. Applied to rational functions, the residue theorem gives algebraic identities which can be easily verified. Also, the digamma function and cotangent can be expressed as sums over terms of the form $i^{-1}-(i+z)^{-1}$ over integer $i$. So, expanding the functions $f$ above as infinite sums over rational functions before applying the residue theorem reduces the argument to one involving summing over elementary identities. In particular, applying the residue theorem to the functions $\frac1{z^2}(\frac1i-\frac1{i-z})(\frac1j-\frac1{j-z})$, $\frac1{z^3}(\frac1i-\frac1{i+z})\frac1{(j-z)^2}$ and $\frac1{z^3}(\frac1i-\frac1{i-z})(\frac1j-\frac1{j-z})(\frac1k-\frac1{k-z})$ gives, respectively, $$ \begin{align} &\frac1{i^4}\left(\frac1j-\frac1{j-i}\right)+ \frac1{j^4}\left(\frac1i-\frac1{i-j}\right)+\frac1{i^2j^3}+\frac1{i^3j^2}=0,\\ &\frac3{j^4}\left(\frac1i-\frac1{i+j}\right)-\frac1{j^3(i+j)^2}-\frac1{i^3(i+j)^2}-\frac2{i^2j^3}+\frac1{i^3j^2}=0,\\ &\sum_{(ijk)}\frac1{i^3}\left(\frac1j-\frac1{j-i}\right)\left(\frac1k-\frac1{k-i}\right)=0. \end{align} $$ In the last identity, the summation refers to the sum over the three cyclic permutations of $i,j,k$. Summing these identities over positive integers $i,j,k$ and cancelling terms of the form $\frac1i$ and $\frac{-1}{i\pm j}$ leads to identities (3,4,5) above. 1 Euler sums and contour integral representations, P. Flajolet, B. Salvy, Experimental Mathematics Volume 7, Issue 1 (1998), 15-35. (link) George LowtherGeorge Lowther This is a known result; an explicit reference is [PP, equation (3c)]. The proof there is elementary (no need for digamma functions, definite integrals and contour integrals, etc.), but nontrivial, requiring clever manipulations with identities such as $1/XY = 1/(X(X+Y)) + 1/(Y(X+Y))$. As Julian Rosen noted, such sums are often expressed in terms of multiple zeta functions, such as the double and triple zetas $$ \zeta(a,b) = \mathop{\sum\sum}_{0<m<n} \frac1{m^a n^b}, \quad \zeta(a,b,c) = \mathop{\sum\sum\sum}_{0<l<m<n} \frac1{l^a m^b n^c}. $$ I found [PP] via Michael Hoffmann's list of References on multiple zeta values and Euler sums. [PP] cites a paper of Borwein and Girgensohn [BG], where the key triple-zeta value $\zeta(3,1,1) = 2 \zeta(5) - \zeta(3) \zeta(2)$ is given on page 21, together with the note that all such values of weight at most 6 appear in [M]. Indeed here the weight is $3+1+1 = 5 \leq 6$ and the result is the case $p=3$ of Theorem 4.1, listed explicitly as equation (4.2) on page 126. [BG] J. Borwein and R. Girgensohn, Evaluation of triple Euler sums, Electronic Journal of Combinatorics 3, research paper #23, 1996. [M] C. Markett: Triple sums and the Riemann zeta function, J. Number Theory 48 (1994), 113$-$132. [PP] Alois Panholzer and Helmut Prodinger: Computer-free evaluation of an infinite double sum via Euler sums, Séminaire Lotharingien de Combinatoire 55 (2005), Article B55a. Noam D. ElkiesNoam D. Elkies $\begingroup$ Since you are referring to the paper of Panholzer and Prodinger, it may be of interest for you that there's a typo in the main formula. If you like you may have a look at my answer to this question. The formula you are referring here is correct. Regards. $\endgroup$ – Markus Scheuer Sep 10 '14 at 21:29 $\begingroup$ Thanks for this warning and the link. $\endgroup$ – Noam D. Elkies Sep 10 '14 at 23:13 Since the sum in question belongs to the general category of non-linear Euler sums we use the following notation: \begin{eqnarray} {\bf H}^{(p,q)}_r(t) &:=& \sum\limits_{m=1}^\infty H_m^{(p)} H_m^{(q)} \cdot \frac{t^m}{m^r}\\ {\bf H}^{(p)}_r(t) &:=& \sum\limits_{m=1}^\infty H_m^{(p)} \cdot \frac{t^m}{m^r}\\ \end{eqnarray} Now by using my answer to Double harmonic sum $\sum_{n\geq 1}\frac{H^{(p)}_nH_n}{n^q}$ I have generated the following results: \begin{eqnarray} {\bf H}^{(1,1)}_2(+1) &=& \frac{17 \zeta(4)}{4}\\ {\bf H}^{(1,1)}_3(+1) &=&\frac{7 \zeta (5)}{2}-\zeta (3) \zeta(2)\\ {\bf H}^{(1,1)}_4(+1) &=&\frac{97 \zeta(6)}{24}-2 \zeta (3)^2\\ {\bf H}^{(1,1)}_5(+1) &=&-\zeta (5) \zeta(2)-\frac{5}{2} \zeta (3) \zeta(4)+6 \zeta (7)\\ {\bf H}^{(1,1)}_6(+1) &=&{\bf H}^{(2)}_6(+1)+\zeta(3)^2 \zeta(2)-8 \zeta (3) \zeta (5)+\frac{91 \zeta(8)}{12}\\ {\bf H}^{(1,1)}_7(+1) &=&-\zeta (7) \zeta(2)-\frac{5}{2} \zeta (5) \zeta(4)-\frac{7}{2} \zeta (3) \zeta(6)+\frac{55 \zeta (9)}{6}+\frac{\zeta(3)^3}{3}\\ {\bf H}^{(1,1)}_8(+1) &=&{\bf H}^{(2)}_8(+1)+2 \zeta (3) \zeta (5) \zeta(2)+\zeta (3)^2 \zeta(4)-10 \zeta (3) \zeta (7)-5 \zeta (5)^2+\frac{473 \zeta(10)}{40}\\ {\bf H}^{(1,1)}_9(+1) &=&-\zeta (9) \zeta(2)-\frac{5}{2} \zeta (7)\zeta(4)-\frac{7}{2} \zeta (5) \zeta(6)-\frac{9}{2} \zeta (3) \zeta(8)+13 \zeta (11)+\zeta (3)^2 \zeta (5)\\ {\bf H}^{(1,1)}_{10}(+1) &=&{\bf H}^{(2)}_{10}(+1)+2 \zeta (3) \zeta (7) \zeta(2)+\zeta (5)^2 \zeta(2)+2 \zeta (3) \zeta (5) \zeta(4)+\zeta (3)^2 \zeta(6)-12 \zeta (3) \zeta (9)-12 \zeta (5) \zeta (7)+\frac{23595 \zeta(12)}{1382}\\ {\bf H}^{(1,1)}_{11}(+1) &=& -\zeta (11) \zeta(2)-\frac{5}{2} \zeta (9) \zeta(4)-\frac{7}{2} \zeta (7) \zeta(6)-\frac{9}{2} \zeta (5) \zeta(8)-\frac{11}{2} \zeta (3) \zeta(10)+\frac{35 \zeta (13)}{2}+\zeta (3)^2 \zeta (7)+\zeta (3) \zeta (5)^2\\ {\bf H}^{(1,1)}_{12}(+1) &=& {\bf H}^{(2)}_{12}(+1)+2 \zeta (3) \zeta (9) \zeta(2)+2 \zeta (5) \zeta (7) \zeta(2)+2 \zeta (3) \zeta (7) \zeta(4)+\zeta (5)^2 \zeta(4)+2 \zeta (3) \zeta (5) \zeta(6)+\zeta (3)^2 \zeta(8)-14 \zeta (3) \zeta (11)-14 \zeta (5) \zeta (9)-7 \zeta (7)^2+\frac{19591 \zeta(14)}{840}\\ {\bf H}^{(1,1)}_{13}(+1) &=& -\zeta (13) \zeta(2)-\frac{5}{2} \zeta (11) \zeta(4)-\frac{7}{2} \zeta (9) \zeta(6)-\frac{9}{2} \zeta (7) \zeta(8)-\frac{11}{2} \zeta (5) \zeta(10)-\frac{13}{2} \zeta (3) \zeta(12)+\frac{68 \zeta (15)}{3}+\zeta (3)^2 \zeta (9)+2 \zeta (3) \zeta (5) \zeta (7)+\frac{\zeta (5)^3}{3}\\ {\bf H}^{(1,1)}_{14}(+1) &=& {\bf H}^{(2)}_{14}(+1)+2 \zeta (3) \zeta (11) \zeta(2)+2 \zeta (5) \zeta (9) \zeta(2)+\zeta (7)^2 \zeta(2)+2 \zeta (3) \zeta (9) \zeta(4)+2 \zeta (5) \zeta (7) \zeta(4)+2 \zeta (3) \zeta (7) \zeta(6)+\zeta (5)^2 \zeta(6)+2 \zeta (3) \zeta (5) \zeta(8)+\zeta (3)^2 \zeta(10)-16 \zeta (3) \zeta (13)-16 \zeta (5) \zeta (11)-16 \zeta (7) \zeta (9)+\frac{442323 \zeta(16)}{14468} \end{eqnarray} Note that whenever $r$ is odd then the result reduces to single zeta function values only. On the other hand if $r$ is even then one additional parameter appears. PrzemoPrzemo $\begingroup$ @ Przemo Well done. Did you also consider alternating sums ($t=-1$)? $\endgroup$ – Dr. Wolfgang Hintze Jun 6 '19 at 13:08 using the following identity : $$\displaystyle \frac{\ln^2(1-x)}{1-x}=\sum_{n=1}^{\infty}\left(H_n^2-H_n^{(2)}\right)x^n$$ multiply both sides by $\frac{\ln^2x}{x}$ then integrate both sides w.r.t $x$ from $0$ to $1$, we have: \begin{align} S&=\sum_{n=1}^{\infty}\left(H_n^2-H_n^{(2)}\right)\int_0^1x^{n-1}\ln^2x\ dx=\color{blue}{2\sum_{n=1}^{\infty}\frac{H_n^2-H_n^{(2)}}{n^3}}=\int_0^1\frac{\ln^2x\ln^2(1-x)}{x(1-x)}\ dx\\ &=\int_0^1\frac{\ln^2x\ln^2(1-x)}{x}\ dx+\underbrace{\int_0^1\frac{\ln^2x\ln^2(1-x)}{1-x}\ dx}_{x\mapsto1-x}=2\int_0^1\frac{\ln^2x\ln^2(1-x)}{x}\ dx\\ &=4\sum_{n=1}^{\infty}\left(\frac{H_n}{n}-\frac1{n^2}\right)\int_0^1x^{n-1}\ln^2x\ dx=4\sum_{n=1}^{\infty}\left(\frac{H_n}{n}-\frac1{n^2}\right)\frac{2}{n^3}=\color{blue}{8\sum_{n=1}^{\infty}\frac{H_n}{n^4}-8\zeta(5)} \end{align} where we used $\ln^2(1-x)=2\sum_{n=1}^\infty\frac{H_n}{n+1}x^{n+1}=2\sum_{n=1}^\infty\left(\frac{H_n}{n}-\frac1{n^2}\right)x^n$ rearranging the terms of the blue sides, we have: \begin{align} \sum_{n=1}^{\infty}\frac{H_n^2}{n^3}&=\sum_{n=1}^{\infty}\frac{H_n^{(2)}}{n^3}+4\sum_{n=1}^{\infty}\frac{H_n}{n^4}-4\zeta(5)\\ &=\left(3\zeta(2)\zeta(3)-\frac92\zeta(5)\right)+4\left(3\zeta(5)-\zeta(2)\zeta(3)\right)-4\zeta(5)\\ &=\frac72\zeta(5)-\zeta(2)\zeta(3) \end{align} The proof of $\sum_{n=1}^\infty\frac{H_n^{(2)}}{n^3}=3\zeta(2)\zeta(3)-\frac92\zeta(5)$ can be found here. Ali ShadharAli Shadhar Since $$\sum_{n=1}^\infty\frac{H_{n-1}}{n}x^n=\frac12\ln^2(1-x)$$ divide both sides by $x$ then $\int_0^y$ $$\sum_{n=1}^\infty\frac{H_{n-1}}{n^2}y^n=\frac12\int_0^y\frac{\ln^2(1-x)}{x}dx$$ Next multiply both sides by $-\frac{\ln(1-y)}{y}$ then $\int_0^1$ and apply that $-\int_0^1 y^{n-1}\ln(1-y)dy=\frac{H_n}{n}$ $$\sum_{n=1}^\infty\frac{H_{n-1}H_n}{n^3}=\sum_{n=1}^\infty\frac{H_n^2}{n^3}-\sum_{n=1}^\infty\frac{H_n}{n^4}=-\frac12\int_0^1\int_0^y\frac{\ln^2(1-x)\ln(1-y)}{xy}dxdy$$ $$=-\frac12\int_0^1\frac{\ln^2(1-x)}{x}\left(\int_x^1\frac{\ln(1-y)}{y}dy\right)dx$$ $$=-\frac12\int_0^1\frac{\ln^2(1-x)}{x}\left(\text{Li}_2(x)-\zeta(2)\right)dx$$ $$=\zeta(2)\zeta(3)-\frac12\int_0^1\frac{\ln^2(1-x)\text{Li}_2(x)}{x}dx$$ $$=\zeta(2)\zeta(3)-\frac12\sum_{n=1}^\infty\frac1{n^2}\int_0^1 x^{n-1}\ln^2(1-x)dx$$ $$=\zeta(2)\zeta(3)-\frac12\sum_{n=1}^\infty\frac1{n^2}\left(\frac{H_n^2+H_n^{(2)}}{n}\right)$$ $$=\zeta(2)\zeta(3)-\frac12\sum_{n=1}^\infty\frac{H_n^2}{n^3}-\frac12\sum_{n=1}^\infty\frac{H_n^{(2)}}{n^3}$$ Rearrange the terms $$\sum_{n=1}^\infty\frac{H_n^2}{n^3}=\frac23\zeta(2)\zeta(3)+\frac23\sum_{n=1}^\infty\frac{H_n}{n^4}-\frac13\sum_{n=1}^\infty\frac{H_n^{(2)}}{n^3}=\frac{7}{2}\zeta(5)-\zeta(2)\zeta(3)$$ where we used $\sum_{n=1}^\infty\frac{H_n}{n^4}=3\zeta(5)-\zeta(2)\zeta(3)$ and $\sum_{n=1}^\infty\frac{H_n^{(2)}}{n^3}=3\zeta(2)\zeta(3)-\frac92\zeta(5)$ Thanks for contributing an answer to Mathematics Stack Exchange! Infinite Series $\sum_{n=1}^\infty\frac{H_n}{n^32^n}$ A group of important generating functions involving harmonic number. Simple, yet evasive integral from zero to $\pi/2$ Double harmonic sum $\sum_{n\geq 1}\frac{H^{(p)}_nH_n}{n^q}$ An equality about infinite sums involving squared harmonic numbers Infinite Series $\sum\limits_{n=1}^\infty\left(\frac{H_n}n\right)^2$ Infinite Series $\sum\limits_{n=1}^\infty\frac{H_n}{q^n}$ Sum of Harmonic numbers $\sum\limits_{n=1}^{\infty} \frac{H_n^{(2)}}{2^nn^2}$ Elementary way to calculate the series $\sum\limits_{n=1}^{\infty}\frac{H_n}{n2^n}$ Infinite Series $\sum_{n=1}^\infty\frac{H_n}{n^5 2^n}$ Sum $\sum\limits_{n=1}^\infty\frac{H_n^2}{n^22^n}$ Compute $\sum_{n=1}^\infty\frac{H_n^{(2)}}{n^7}$ and $\sum_{n=1}^\infty\frac{H_n^2}{n^7}$ Advanced Sum: Compute $\sum_{n=1}^\infty\frac{H_{2n}H_n^{(2)}}{(2n+1)^2}$ Challenging Sum: compute $\sum_{n=1}^\infty\frac{H_n}{2n+1}\left(\zeta(3)-H_n^{(3)}\right)$	CommonCrawl
The higher education space: connecting degree programs from individuals' choices Cristian Candia1,2,3, Sara Encarnação4,5 & Flávio L. Pinheiro6 Data on the applicants' revealed preferences when entering higher education is used as a proxy to build the Higher Education Space (HES) of Portugal (2008–2015) and Chile (2006–2017). The HES is a network that connects pairs of degree programs according to their co-occurrence in the applicants' preferences. We show that both HES network structures reveal the existence of positive assortment in features such as gender balance, application scores, unemployment levels, academic demand/supply ratio, geographical mobility, and first-year drop-out rates. For instance, if a degree program exhibits a high prevalence of female candidates, its nearest degree programs in the HES will also tend to exhibit a higher prevalence when compared to the prevalence in the entire system. These patterns extend up to two or three links of separation, vanishing, or inverting for increasing distances. Moreover, we show that for demand/supply ratio and application scores a similar pattern occurs for time variations. Finally, we provide evidence that information embedded in the HES is not accessible by merely considering the features of degree programs independently. These findings contribute to a better understanding of the higher education systems at revealing and leveraging its non-trivial underlying organizing principles. To the best of our knowledge, this is the first network science approach for improving decision-making and governance in higher education systems. Many factors are known to determine the applicants' choices when entering Higher Education. Examples range from the socio-economic background of applicants [1–4] to their gender [5–8], but also include the expected earnings differentials between education fields [9, 10]; self-identification and career opportunities [11, 12]; ability beliefs and heterogeneous tastes [13–15]; political views, and applicants personality [16]. However, little is known on how these factors translate into organizational principles of higher education systems. Linking individual actions to higher-order organizational principles of human-made systems has been a long lasting problem in computational social sciences [17–22]. Such link plays a crucial role in our ability to design effective governance instruments and interventions. Indeed, the effectiveness of an intervention is arguably bounded by our understanding of how elements in a system can affect each other. In the context of higher education [23, 24], a lack of such knowledge materializes in our inability to answer simple questions, such as, how do changes in the demand of a given degree program spillover throughout the system? Would such variations be observed equally across all degree programs or would we, instead, observe a predictable and structured spillover dynamics? And what should we expect regarding other measurable features? Here, we propose the Higher Education Space (HES) as a data-driven mapping of the interdependence between degree programs, and thus as an instrument to improve the effectiveness of policy-making in higher education. Similarity between degree programs is measured by proxy from the revealed preferences of applicants when applying to higher education. The emerging structure, the HES, is a network that connects pairs of degree programs according to the likelihood that they co-occur in the applicant's preferences. Therefore, the HES represents 'how students, not administrators or faculty, think about the grouping of' degree programs [25]. This structure contrasts with the state of the art classification, the International Standard Classification of Education (ISCED) [26, 27], based on the similarity of degree programs according to their expected course content. Our work briefly presents findings that illustrate the relevance of the HES in different topics and in the context of the Portuguese and Chilean higher education systems. Both countries have a similar and centrally run application process to higher education. However, they also contrast in many socio-economic aspects, which help us to highlight possible universalities and contrasts. The HES reveals the existence of positive autocorrelations [28] among featuresFootnote 1 of degree programs. These features include gender balance, application scores, demand-supply ratio, unemployment level, first-year dropout rate, and mobility. The autocorrelations patterns indicate that features tend to be positively assorted throughout the network structure of the HES, meaning that, if a degree program exhibits a high prevalence of, say, female applicants, then, degree programs up to two/three links away will also show a similar prevalence. Furthermore, while some features (e.g., application scores and demand-supply ratio) also exhibit autocorrelations patterns with respect to temporal variations, others do not (e.g., gender balance). Results also show that autocorrelations regarding unemployment cannot be explained merely by matching elements with similar features. Indeed, the connectivity structure of a degree program in the HES seemingly plays a determinant role in the reported unemployment levels. In that respect, we observe that connected degree programs tend to have similar unemployment levels, even after controlling for feature-matched, but unconnected, degree programs. Naturally, this finding can have implications for applicants when weighing the potential future gains and costs of choosing a given degree program. This manuscript is organized as follows: Sect. 2 presents a short description of the data used in this study as well as the cleaning and preprocessing procedures; Sect. 3 presents the results along with a detailed discussion; and Sect. 4 concludes with final remarks and by summing up all contributions of this work and its societal implications. The data from both countries, Portugal and Chile, consists in a set of ranked preferences listed by applicants to the Portuguese (PHES) and Chilean (CHES) Higher Education Systems. In the PHES applicants' can list up to six preferences, while in the CHES they can list up to ten. Each preference corresponds to a pair of Institution and Degree Program. Each preference is unique, meaning that a specific pair of institution and degree program cannot appear twice in an applicant preference list. Here, we study the interconnection between Degree Programs, therefore, the same Degree Program (offered by different institutions) can show up more than once in the pre-processed preference list of an applicant. The PHES dataset includes application records to all public higher education institutions between 2008 and 2015, and it is not publicly available. The Portuguese data was obtained through a research collaboration with the Agency for Assessment and Accreditation of Higher Education, A3ES,Footnote 2 and sourced from the Directorate General for Higher Education, DGES.Footnote 3 The data is anonymized to make it impossible to identify specific individuals. The CHES dataset spans from 2004 to 2018, and includes all 36 institutions that belong to the Rectors' Council of Chilean Universities, CRUCHFootnote 4 and it also includes all the private institutions that participate in the Universal Admission System (SUA). The Chilean data was provided by the Department of Evaluation, Measurement and Educational Record, DEMRE,Footnote 5 which follows a standardized protocol for data protection. The Chilean datase can be obtained under request on the DEMRE website.Footnote 6 Concerning the PHES, degree programs are identified by a name, an unique 4-digit ID, and each is associated with a 3-digit ISCED code. Degree programs with the same name can have different IDs due to several distinguishable characteristics such as: 3-year (BA) or 5-year (BA + MA) programs; programs taught in different languages (Portuguese or in a foreign language) and programs taught during daytime (normal) or in a post-laboral (special) regimes. In order to clean and disambiguate these situations we have applied the following steps: (1) Discard all degree programs that are not taught in Portuguese; (2) Discard all degree programs that are not taught in the normal regime (daytime); (3) Aggregate degree programs with the same name but different IDs and (4) Discard all degree programs that are not offered in every year under study. After the above steps the list of degree programs was reduced from 1006 to 313. Concerning the CHES, each pair of degree program and institution is identified by a unique ID. Thus, for instance, all degree programs in Physics will have different identification IDs, one per institution. Besides, information on the ISCED classification is available only at first two levels. To map CHES data to ISCED classification, we disambiguate degree programs manually. We curated the dataset by aggregating all degree programs with similar name, description, curriculum, and ISCED classification. We also discarded the first two years (2004 and 2005) of data since the ISCED classification is not available for those years. Thus, from an initial pool of 1132 degree programs we obtained a list of 212 programs. Finally, in both higher education systems, CHES and PHES, we have also discarded applicants older than 21 years old, applicants with less than two preferences in their applications (after the pre-processing of the degree programs as detailed above, these are less than 5% in the PHES), and limited our analysis to the first application round. These last two conditions, effectively exclude applicants entering Higher Education System via special pathways. Considering all the filters applied, from the initial applicant pool of 561,752 (PHES) and 3,246,662 (CHES) we were left with 355,173 (PHES) and 691,159 (CHES) individual applications. Descriptive features of degree programs We collected descriptive features for each degree program to explore the existence of autocorrelation patterns, which might explain the organization of the Higher Education Space (HES), and to validate the emergent network structure. The features were engineered from the aggregated data of applicants (application scores, gender, degree program demand, and geographical origin) or from institutional reports (unemployment levels, academic supply, and first-year dropout rates). Each feature is standardized by year and across all degree programs in the HES for each country. For instance, the gender balance of each degree program is estimated by (i) computing the fraction of female enrolled students in each degree program, (ii) standardizing these values by subtracting the average fraction of enrolled female students among all degree programs and (iii) dividing by the standard deviation, thus obtaining a Z-score. Standardization of the features yields not only comparable results across time but also across degree programs of the entire system. In this work we focus on the analysis of the following features: Gender balance (PHES and CHES), computed from the fraction of female applicants enrolled in each degree program at the end of the application process; Application scores (PHES and CHES), reported in the dataset. These correspond to the combined marks obtained from the secondary school and the required nationwide exams of access to the Higher Education System. Application priority in each higher education system is given by the application score; Demand-supply ratio (PHES and CHES), given by the ratio between the number of applicants that chose a given degree program as their first choiceFootnote 7 by the number of open positions or academic supply (reported in the dataset) in that same degree program. This normalization ensures that demand is corrected for size effects (i.e., cases in which the sheer size of supply can drive demand). This indicator is similar, in spirit, to the "strength index" [29] sometimes computed to quantify institutions ability to fill the available offer from with the first choices of applicants; Geographical mobility (CHES only), estimated as the distance by car, in km, between the candidate's city of origin and the location of the main campus of the institution of enrollment. This distance was obtained using queries to google maps.; Unemployment level (PHES onlyFootnote 8), compiled and reported by institutions at the level of degree program; First year dropout rate (PHES onlyh), given by proxy from the enrollment situation of applicants at the end of the first year. The higher education space The Higher Education Space (HES) relates pairs of degree programs that exhibit a positive and statistically significant co-occurrence relationship in the applicants' preferences list [30–33]. To that end, we start by estimating the strength of the relationship between two degree programs using the methods of ϕ-correlation and then through two statistical tests we discard links whose statistical significance doesn't allow us to claim the existence of such relationships either due to small sample size or because the observer correlation can be just due to pure chance. The ϕ-correlation index between pairs of degree programs, i and j, which we define as $\phi _{ij}$, can be commputed as: $$ \phi _{ij}=\frac{M_{ij}Z-M_{i}M_{j}}{\sqrt{M_{j}M_{i}(Z-M_{i})(Z-M _{j})}}, $$ where $M_{ij}$ corresponds to the observed number of co-occurrences between degree programs i and j, $M_{i}$ is the total number of co-occurrences a degree program i participates ($M_{i}=\sum_{i} M _{ij}$), and N is the total number of co-occurrences in the dataset ($Z=\sum_{i} M_{i}/2$). Positive/Negative values of $\phi _{ij}$ indicate that increasing numbers in the prevalence of each degree program are likely to result in an increase/decrease in the number of co-occurrences between them. We discard all negatively correlated relationships, since these edges indicate pairs of degree programs whose co-occurrence pattern cannot be explained by the prevalence of each degree program alone. Next we filter links by performing two statistical tests. The first tests whether measured ϕ-correlations can be explained by pure chance alone, while the second tests if the identified ϕ values are different from zero given the sample size and the associated standard error. The first test is performed by comparing the observed $\phi _{ij}$ with a null-distribution obtained from an ensemble of $N=1000$ randomly generated networks. Each random network is generated by shuffling the preferences of the candidates in each year while maintaining constant the number of preferences of each candidate and the number of times each degree program was chosen in a year [34]. For each randomization k we compute the $\tilde{\phi }^{k}_{ij}$ associated a pair of degree programs. The ensemble of such values form the null distribution $\tilde{\varPhi }_{ij} = \{\tilde{\phi }_{ij}^{1}, \tilde{\phi }_{ij}^{2},\ldots,\tilde{\phi }_{ij}^{N}\}$. Using statistical inference methods [35] we estimate the p-value associated with $\phi _{ij}$ by calculating the upper tail probability of obtaining a value equal or greater than $\phi _{ij}$ from the cumulative frequency of the null-distribution $\tilde{\varPhi }_{ij}$. We discard links with a significance of p-value >0.05. Secondly, since the magnitude of observations varies across different degree programs we use a t-test to infer whether the positive correlations are significantly distinguishable from zero. To that end, we compute: $$ t_{ij}=\phi _{ij}\frac{\sqrt{D-2}}{\sqrt{1-\phi _{ij}^{2}}}, $$ where $D-2$ represents the degrees of freedom, which we take as $D=\max(M_{i},M_{j})$ [30]. We consider only links that are statistically significant with p-value ≤0.05 ($t _{ij} = 2.06$ for $D=25$, one tailed). To sum up, we discard links with negative ϕ-correlation and that fail two statistic significance tests with p-value ≤0.05. The first tests whether the identified ϕ-correlations are not just the result of pure chance, while the second discards links that due to the number of observations do not allow us to claim that the ϕ-correlation are significantly different from zero. Finally, we discard self-connections from the analysis, as we are interested only in relationships between different-degree programs. Figure 1 shows the HES network structures for Portugal and Chile. Nodes represent degree programs and are colored according to the nine groups of the first level of the ISCED classification: Arts and Humanities (dark blue), Social Sciences (dark green), Sciences (dark purple), Engineering (dark yellow), Agriculture (pink), Education (red), Services (light purple), and Health (light blue). The size of the nodes is proportional to the number of observations. The Higher Education Space for (a) Portugal, from 2008 to 2015 and for Chile, for (b) 2006 to 2011 and (c) 2012 to 2017. Following the 2012' addition of 9 new universities, the Chilean HE system was divided into two distinct networks (see Additional file 1). The color of the nodes identifies the Education Field of the degree program according to the first level of the International Standard Classification of Education (ISCED). Sizes of nodes illustrate the relative number of observations in relation to other degree programs in the same network, sizes of nodes are not comparable among different networks. Network layouts have been obtained using the SpringElectricalEmbedding algorithm implemented in Wolfram Mathematica The PHES network (Fig. 1(a)) results from all application preferences between 2008 and 2015, since no major and significant changes occurred in the system during that time interval. By contrast, the CHES network analysis is divided into two periods, due to the 2012's addition of nine new universities (see Additional file 1). The first period (Fig. 1(b)) considers applications between 2006 and 2011, while the second (Fig. 1(c)) analysis those between 2012 and 2017. The PHES and CHES networks are sparse (between 2% and 5% of the maximum number of relationships possible) and highly clustered (clustering coefficient measures between 0.46 and 0.49) when compared to random networks with similar density of links. The high clustering coefficient invites the use of network science methods (e.g., modularity-based network partition algorithms) to derive a classification/grouping of degree programs (see Fig. 2 and related discussion bellow). Each network exhibits a diameter between 6 and 11 links, and an average path length (APL) between 3.94 and 4.22. Both CHES networks have fewer nodes than the PHES network (177 and 179 against 312) but relatively similar connectivity per degree program—7.44 and 6.72 against 8.51. There are common elements in all three networks, viz. the existence of three main clusters: one dominated by degree programs in Engineering; a second one that involves degree programs in Biology, Sciences, and Health; and a third with a strong representation of degree programs in Arts and Humanities, and Social Sciences. Communities of the Higher Education Space in Portugal (a) and Chile ((b) and (c)). Nodes are colored according to the community they belong to (see main text for details). Panels (d) to (f) show the composition of each community in accordance with the first level of the ISCED classification Overall, the HES space is characterized by a doughnut-shaped structure with a few degree programs occupying a central region connecting opposite sides of the network. This topology is not new and similar networks were obtained when mapping science and research areas [36, 37]. Nonetheless, the above structures can have relevant implications for higher education policy development. For example, the centric role of Economics and Management (Commercial Engineering in Chile) connecting the Engineering, Arts and Humanities and Social Sciences clusters might hint to potential trans-disciplinary crossings when designing future changes in the system [38–40]. As mentioned above, the high clustering levels in all three networks invite for a classification/grouping of degree programs based on the network structure of the HES. Figure 2 shows the best partitions obtained using the Louvain algorithm [41], where nodes of the PHES (a) and CHES ((b) and (c)) are colored according to the partition they belong.Footnote 9 The best PHES partition has a modularity of 0.71 and explains 88% of the intra-group connectivity. When compared with the ISCED classification, these values correspond to an improvement of 42% in modularity and of 27% in intra-group connectivity. Likewise, the best partition of both the CHES networks exhibit a modularity of 0.67 explaining 83% of the intra-group connectivity with an improvement of 67.5% over the ISCED classification, see Fig. 2(d)–(f). The International Standard Classification of Education (ISCED) [26, 27] was developed in order to facilitate comparative statistics between different countries. It is also commonly used in academic studies and nationwide reports of the state of higher education. The ISCED premise is to group degree programs according to the their course content and does not represent the applicants nor educators perspective. Such premise contrasts with the data-driven and network-based approach derived here, which stems only from applicants perspective. Figure 2(d)–(f) shows the composition of each HES group according to the ISCED classification of its constituents. Colors among similar groups ($C_{1}$ to $C_{8}$) of different HES are kept consistent to ease comparison. Groups of similar color match groups located in similar regions of the PHES and CHES. For example, group 1 ($C_{1}$) in the PHES is composed of 14 degree programs from the Science Education Field, 1 degree program from the Agriculture field, 42 degree programs from the Engineering field, and 2 degree programs from the Services field. Communities have been named in order to make their composition comparable across the CHES and PHES networks, when possible. The observed diversity of ISCED scientific fields in each community shows that administrators and policy makers should take care in devising policies based on sectoral analyses developed by scientific fields only. This is specially relevant for policies aimed at solving access inefficiencies of the higher education system. This note of caution will be reinforced by the results found for positive assortment in the HES—see next section below. As expected, there are differences and similarities among the three HES. Firstly, the number of communities differs between the PHES (8) and the CHES (between 6 and 9) which might be explained by the size of each network and degree program diversity (see Additional file 1 for more details about each system). Secondly, the organization of the CHES network seems to have changed in the second time period, becoming more similar to the PHES network. This conjecture is backed-up by the number of communities and visual inspection requiring future validation, but raises interesting questions: 1) does globalization of higher education [42–45] lead different HES to evolve towards similar structures? and 2) since these structures are based on applicants' choices, are they adapting quickly to societal transformations and is policy on higher education able to follow suit? Feature assortment in the higher education space The Higher Education Space (HES) is estimated uniquely based on the applicants' choices and completely nescient about particular features that characterize each degree program. Thus, the emergence of three coherent and similar networks, in two different countries and for different time periods, naturally leads to the question of what explains the emergence of these same structures? The answer likely lies in a multiplicity of factors, some of which we briefly explore here by matching the HES network structures with available data on descriptive features of degree programs—e.g. gender balance or unemployment levels (cf. Sect. 2.2). It is important to keep in mind that other factors involved in the applicants' choices can certainly help to explain the structure of the HES. However, due to data limitations and the scope of this manuscript such exploration is left for future work. Figure 3(a)–(c) shows the PHES (a) and the CHES (b) and (c) where each degree program is colored according to the gender balance in 2015 (Fig. 3(a)), 2011 (Fig. 3(b)), and 2017 (Fig. 3(c)). Orange (Gray) tones identify an above average representation of female (male) applicants. The distribution of Gender prevalence among degree programs is not random or uniform but, in fact, it is clustered, resulting in the predominance of one gender over the other in particular regions of the HES. Similar patterns are observed for all other features such as application scores, unemployment levels, demand-supply ratio, mobility, and first-year dropout rates (see Additional file 1). Illustrates the positive assortment of features along the Higher Education Spaces of Portugal and Chile, nodes have been colored according to the gender balance of enrolled students during the 2015 applications in Portugal (a), 2011 (b) and 2017 (c) in Chile. Panels (d)–(q) show the autocorrelations between the aggregated characteristic of pairs of degree program separated by n links in the Higher Education Networks of Portugal (d), (g), (j), (m), and (p) and Chile (e), (f), (h), (i), (k), (l), (n), and (o). Bars represent the autocorrelation averaged over all observation years, and error bars the standard error in the estimation of the coefficients. Positive (negative) autocorrelation coefficients are shown in green (red). Bars in light colors indicate an autocorrelation that is not significantly different from zero (failed a t-test with $p > 0.05$. The characteristics under analysis correspond to the gender balance (d)–(f), application scores (g)–(i), demand-supply rate (j)–(l), unemployment levels (m), students mobility (n)–(o), and dropout rates (p) Figure 3(d)–(p) explores, quantitatively, these clustering patterns (i.e., positive assortment) over the HES. To that end, we compute, for each feature, the autocorrelations between pairs of degree programs at different distances in the HES network (i.e., measured by the minimum number n of links that form a path from one degree program to the other). Bars represent the autocorrelation averaged over all observation years, and error bars the standard error in the estimation of the coefficients. For example, an autocorrelation of 0.75 at $n = 1$ for gender dominance, means that degree programs separated by one link exhibit, in average, 75% of the proportion of Female students of a focal degree program. Positive (negative) autocorrelation coefficients are shown in green (red). Bars in light colors indicate an autocorrelation that is not significantly different from zero (failed a t-test with $p > 0.05$). These positive/negative relationships between pairs of degree programs seem to ascertain previous findings [3, 4], in that some groups of students tend to choose similar preferences based on similar determinants of choice. For example, a positive assortment in gender balance (Fig. 3(d)–(f)) confirms the existence of different preferences between gender groups, as found in [5–7, 46]. But more importantly, and a non-trivial finding of this approach, is to be able to show How and Where these similarities spread through the network and how neighbouring degree programs (nodes) influence or contaminate each other. In other words, how features spillover throughout the network structure of the HES. Returning to the gender balance example, Fig. 3(d)–(f) confirms what was already noticeable by visual inspection—the more female applicants apply to a degree program, the more female applicants are observed in neighboring degree programs, when compared with the average prevalence of female applicants in the entire system. This relationship is positive, significant up to two links, and holds for both Portugal and Chile. Positive autocorrelations, up to two neighbours, are also found, although not so strong, for application scores (Fig. 3(g)–(i)) and demand-supply ratio (Fig. 3(j)–(l)), in both countries. Due to data availability, autocorrelation patterns for unemployment levels (Fig. 3(m)) and First Year Drop-Out rates (Fig. 3(p)) are calculated for the PHES only. Both show similar behavioural patterns as in the previous features, although the positive relationship in unemployment levels extends to three-links of distance instead of two. Again, due to data constraints, the Student Mobility feature is only analyzed for the CHES (Fig. 3(n)–(o)). The positive relationship observed in the geographical mobility seemingly vanishes quicker with the network distance, although it remains statistically significant at distance = 2 being zero for larger distances. Two possible explanations for the lack of a positive autocorrelation away from the first neighbors can be: (1) most applicants assign a small weight to distance as a factor in the choice of a degree program, and (2) the majority of applicants has a tendency to apply to degree programs that minimize the distance to their local of origin. Although previous research seems to support the second hypothesis [47–52], a more in-depth future analysis is needed to answer this question conclusively. In sum, all features exhibit positive autocorrelations that extend up to two/three links of separation. The Higher Education Space captures information embedded in the interplay between degree programs, which is revealed by studying the preference patterns of applicants. These results are a natural outcome of all the information applicants' carry at the moment of their choices [53] (i.e., either contextual information used in the decision making or inherent characteristics of applicants), which in turn modulates the topology of the HES. Temporal variations in features In the previous section, we have shown How and Where certain degree programs are positively correlated, in several features, as a function of the network distance between them. In this section, we examine how temporal changes in these features can spillover throughout the HES. By understanding the When of the autocorrelations patterns, it is possible, for instance, to perceive how external shocks propagate through the system. As an example, we take the particular case of the building sector in Portugal—one of the most affected by the financial crisis that hit the country between 2010 and 2014 (a crisis that was preceded by a downward path since the beginning of the millennium and the global financial crisis of 2008 [54]). Figure 4(a)–(b) shows, for the PHES, the temporal variation in the demand-supply ratio for Civil Engineering (a) and Architecture (b) between 2008 and 2015. Also shown (light gray) are the temporal variations of their closest direct neighbors in the Higher Education Space network (averaged is highlighted in red). After the economic and financial crisis, the construction industry was one of the most negatively affected [55, 56]. A priori (without knowing the structure of the network), one could expect that both Civil Engineering and Architecture would suffer a similar impact on their demand-supply ratio given their close market relationship. However, a closer inspection of Fig. 4(a)–(b) shows that the negative impact on the demand for Civil Engineering is not observed for Architecture. More importantly, in both cases, the variations are consistent with the average behaviour of the nearest connected degree programs (temporal spillovers). This confirms and reinforces the above finding where both belong to two different clusters (architecture being closest to degree programs in Arts and Humanities than to Engineering), c.f. Fig. 1. Time variations and spillovers in the demand-supply ratio for Civil Engineering (a) and Architecture (b) and their direct neighbours, in the Portuguese Higher Education Network (PHES). The complete PHES network is colored according to the observed demand-supply ratio yearly variation between 2010/11 (c) and between 2014/15 (d). Two illustrative examples are shown that capture the variation in demand in a period when the number of applicants was in a clear decline (c) and another when it was growing (d) in the PHES. Orange denotes a positive variation (increase in demand-supply), black a negative variation (decrease in demand-supply) The spatial autocorrelation patterns, concerning the temporal variations of features, help to explain how the observed changes affect entire regions of the network in different ways and in different time periods. For example, a clearly discernible pattern in Fig. 4(c)–(d) reveals that variations in the demand-supply ratio reversed from one part of the network to the other in two distinct time periods (2010/11—Fig. 4(c) and 2014/15—Fig. 4(d)). These temporal spillovers are confirmed by the autocorrelation patterns of the yearly time variations of each feature, over all degree programs in the PHES (Fig. 5(a)–(b)). There are positive effects in time that remain up to two links of separation in the demand-supply ratio and application scores, suggesting that, not only these two features changed over time (thus reacting to conjunctural changes) but also that those changes spillover to their neighbours. Autocorrelations in respect to the time variations of different features for the PHES (a)–(c), CHES between 2006 and 2011 (d)–(f), and CHES between 2012 and 2017 (g)–(i) networks. Panels show the autocorrelations computed for the temporal variations of demand-supply ratio (a), (d), (g), application scores (b), (e), (h), and gender balance levels (c), (f), (i). We identify positive autocorrelations up to two degree of separation on demand-supply and application scores, the same is not shown in the gender balance. Bars in light colors indicate an autocorrelation that is not significantly different from zero (failed a t-test with $p > 0.05$) However, we do not find autocorrelation patterns among the temporal variations for all features. Certain features, such as the demand-supply ratio (Fig. 5(a), (d), and (g)) and application scores (Fig. 5(b), (e), and (h)), show a synchronous variation over time, suggesting that it responds to contextual changes. On the other hand, gender balance (Fig. 5(c), (f), and (i)) do not change over time, suggesting that it is likely to respond to more long-term structural changes, e.g., cultural mechanisms, and other socio-economic factors. Moreover, it is important to state that such effects although relevant in magnitude don't appear to be significant for the application scores in the CHES network (see Fig. 5(e) and (h)). Measuring unemployment similarity Thus far, we have identified prevailing autocorrelation patterns of features describing degree programs and applicants in both spatial distribution and temporal variations. But, how informative is the Higher Education Space on the higher education system? For example, can we explain the expected unemployment levels of degree programs just by looking at its connections in the HES? To explore this question we use a propensity score matching identification strategy. We define the treatment as the link between two degree programs in the HES. Thus, degree programs in the treatment group are necessarily connected in HES and the degree programs in the control groups are not connected in HES. Then, we compare the difference in unemployment levels in the treatment group against several control groups. To generate the control groups we match to each pair in the treatment group, a second unconnected pair of degree programs with an equivalent level of similarity in terms of features. Thus, we built five control groups: (1) gender level, (2) application scores, (3) demand-supply levels, (4) a control group with degree programs of the same ISCED field, and (5) all features combined. In addition, we built a randomly sampled control group, where pairs of nodes are taken at random disregarding any similarity. In Fig. 6, rows show the average of the absolute difference in unemployment levels between pairs of degree programs for each control group. In all cases, the differences are smaller for the treatment group (vertical black line) when compared to the control groups (all differences are statistically significant—t-test between the averages of the two groups with an upper-bound p-value of 0.001). These findings support the hypothesis that the HES represents a similarity mapping between degree programs from an applicants' perspective, that is not possible to access by estimating similarities using traditional features alone (e.g. gender, application scores or demand-supply). In other words, the network structure of the Higher Education Space captures information that enables us to improve our understanding of the higher education systems. Comparison between the absolute differences in unemployment levels of pairs of degree programs in a treatment group (black vertical line) against different control groups (horizontal). The treatment group corresponds to 1177 connected pairs of degree programs in the Higher Education Space. Each control group (of the same size as the treatment group) is a set of pairs of degree programs matched through the propensity score matching [57] with the pairs in the treatment group. Similarities measure the Euclidean distance among pairs of degree programs in different control groups: random (dark orange), education fields of the ISCED classification (purple), gender (red), application scores (green), demand-supply ratio (orange) and all the last three features (blue). Error bars in the control groups indicate the standard error in the estimation of the averages therein and the shaded area is the standard error for the treatment group. Statistical significance was measured by a t-test between the treatment and control averages—all differences are significant with $p\mbox{-values}< 0.01$ We should note that nodes in these networks do not incorporate any information about the institutions. These specificities can potentially change the results of the current model, especially in those cases where factors, such as the prestige of higher education institutions, the societal value of degree programs (e.g. medicine), and the relative location of institutions to their recruitment base can greatly impact the applicants' choices [58] and consequently, the structural organization of the HES. The ever growing worldwide complexity ensuing from technological, social, cultural, and economic changes demands the design of highly effective governance instruments that can support the management and policy development of higher education systems. To achieve those goals we need novel data-driven approaches [23, 24] that are able to capture the complex interplay between existing elements of the system and report new, comprehensive and reliable information about its functioning. By leveraging the information carried by the applicants to the higher education systems of Portugal and Chile at the time of their decision-making we have derived wider organizing principles common to both systems. We show that the Higher Education Space (HES) is sparse, highly ordered, modular, and able to capture multi-factorial information about the applicants' choices. Moreover, the HES reveals the existence of autocorrelation patterns among many features describing degree programs—gender balance, application scores, unemployment, mobility, demand-supply ratios, and retention rates—that stem from the aggregated characteristics of applicants and/or enrolled students. By construct, the methodology is blind to the applicants individual information, and as such, serves as evidence for validating the HES's utility as a source of non-trivial information about the system. For example, it informs that degree programs that are closer in the HES tend to be more similar in their features. It follows that these similarities among degree programs have a "contagious" effect between their closest neighbours. While spatial and temporal spillovers are identified in features that reflect conjectural changes (application scores and the demand-supply). In features that reflect structural changes, as gender balance, only spatial spillovers are identified. Moreover, the connectivity structure of the HES offers non trivial insights on certain features of degree programs, such as unemployment levels, than a proximity mapping using other traditional variables. This implies an important take away for applicants: prevalence of unemployment in some regions (i.e., sets of interconnected degree programs) can later manifest as a job mobility cost for graduates. As previously stressed by Baker [25], perception mismatches between students or applicants and educators or decision-makers need to be taken into consideration when developing new policies. In that sense, here we proposed a data driven characterization of degree programs that can serve as a complement to the ISCED classification. Through our approach degree programs are grouped according to the applicants' perspectives, not to their curricular content. Hence, the HES stems from a much richer and multi-factorial decision-making process than the ISCED classification, reflecting how actors in society perceive higher education. This work is a first approach and, thus, exploratory in nature, it aims at showing the potential of the Higher Education Space in supporting policy development and a better understanding of the organizing principles of higher education. Admittedly, much was left for future work, and our work suffered from several limitations that are noteworthy pointing out. Limitations include the number and scope of available features and the exploration of alternative network inference null models, which could capture the particularities of each application process. Building on that, we identify four main areas for future development: (1) exploring the practical and actual application of the HES in designing effective governance actions; (2) exploring the resulting topological features of the HES for a wider spectrum of countries, which can either highlight the universality of the HES or help us understand different cultural contexts and perspectives shape its structure; (3) in countries where application systems are not governed by a central body—such as in the United States and in Brazil—the methodology herein can be replicated by resorting to nationwide surveys that mimic the application process in countries such as Portugal and Chile. 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Stud Higher Educ 35(4):371–389 CC and FLP acknowledge the financial support from the MIT Media Lab Consortia and the MIT-Masdar Instiute (USA—Reference 0002/MI/MIT/CP/11/07633/GEN/G/) initiative. CC acknowledges the financial support from Centro de Investigación en Complejidad Social. SE and FLP acknowledge the financial support of A3ES (2015–2017). SE acknowledges the financial support of FCT/MCTES through National funds, for project grants SFRH/BPD/1169337/2016 and by multi-annual funding of CICS.NOVA (UID/SOC/04647/2013). The authors are thankful to the Chilean Department of Evaluation, Measurement and Educational Record (DEMRE) for making the Admission Process to Higher Education data available for analysis. The authors are thankful to Carlos Rodriguez-Sickert for logistic support with the Chilean data set, Jorge Jara Ocampo for collecting data and to César A. Hidalgo, Cecilia Monge, Mary Kaltenberg, Aamena Alshamsi, Tarik Roukny, Vítor V. Vasconcelos, Diana Orghian, Alberto Amaral, Madalena Fonseca, Gustavo Castro-Dominguez, the Collective Learning Group at the MIT Media Lab, Laszlo Barabási and the Center for Network Science Research at Northeastern University for the helpful insights and discussions and the three anonymous reviewers for their contributions that greatly improved the clarity and quality of this manuscript. The findings, interpretations, and conclusions expressed by the authors in this work do not necessarily reflect the views of the Higher Education authorities in Portugal and Chile. The authors do not have the permission to share the raw nor the processed data used in this study. However, these can be made available upon request to the source authorities: DGES (Direção-Geral do Ensino Superior) concerning the Portuguese data, and DEMRE (Departamento de Evaluación, Medición y Registro Educacional) for the Chilean data. Kellogg School of Management, Northwestern University, Evanston, United States Cristian Candia Northwestern Institute on Complex Systems (NICO), Northwestern University, Evanston, United States Centro de Investigación en Complejidad Social (CICS), Facultad de Gobierno, Universidad del Desarrollo, Santiago, Chile Interdisciplinary Centre of Social Sciences (CICS.NOVA, FCSH), Universidade Nova de Lisboa, Lisboa, Portugal Sara Encarnação Applications of Theoretical Physics Group, Porto Salvo, Portugal Nova Information Management School (NOVA IMS), Universidade Nova de Lisboa, Lisboa, Portugal Flávio L. Pinheiro CC, SE, and FLP contributed equally for this manuscript. All authors read and approved the final manuscript. Correspondence to Flávio L. Pinheiro. The authors declare no competing interests. Cristian Candia, Sara Encarnação and Flávio L. Pinheiro contributed equally to this work. Supplementary describes in detail the data pre-processing and the analysis of degree program characteristics (PDF 1.2 MB) Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Candia, C., Encarnação, S. & Pinheiro, F.L. The higher education space: connecting degree programs from individuals' choices. EPJ Data Sci. 8, 39 (2019). https://doi.org/10.1140/epjds/s13688-019-0218-4 Higher education systems Network science Computational social sciences	CommonCrawl
Undecidable existence theorems Many conjectures about the natural numbers have the property that for any particular natural number, it is decidable (under some set of axioms like ZFC) whether or not the conjecture holds for that number. Nonexistence of odd perfect numbers and the Goldbach conjecture have this property, for instance. When is it possible for the conjecture itself to be undecidable in ZFC? Intuitively I would expect never, since if it were undecidable I could find a counterexample in the universe where the conjecture is false, "port" it to the universe where it is true, and get a contradiction. The top answer in this question, however, writes that this intuitive argument is flawed, since the natural numbers in one universe might contain elements that aren't natural numbers in the other. I don't understand how this is possible: can't I define $\mathbb{N}$ in a way that's provably unique (up to isomorphism) under ZFC? If so, how can adding an independent axiom to ZFC change the makeup of $\mathbb{N}$? Is there an easy example of how this can occur? The natural numbers are well-defined within ZFC -- so in any model of ZFC there is only one set that represents the natural numbers. However, if we have two different models of ZFC, their respective natural numbers do not need to be isomorphic at the metalevel. So if one of the models has something that, within that model, is an odd perfect number, then it is not necessary that this something has a counterpart in the other model. Intuitively (to the extent one can trust intuition in these matters), this is because ZFC is not strong enough to ensure that the $\mathbb N$ within a model is really the natural numbers -- there are models whose $\mathbb N$ is larger than the true naturals. That this must be so follows from Gödel's incompleteness theorem; there can be no first-order-theory that captures the the true natural numbers uniquely and is strong enough to do basic arithmetic. So adding a false-but-undecidable statement to ZFC as an extra axiom will just result in a theory where none of its models have "true" natural numbers. It can still be consistent, it just doesn't describe the set theory we intuitively expect to be working in. Henning MakholmHenning Makholm $\begingroup$ The existence of nonstandard models also follows directly from the compactness theorem, of course; it's not just an artifact of incompleteness. The theory of the reals is complete in the language of ordered fields, but it still has nonstandard models. $\endgroup$ – Carl Mummert Sep 28 '11 at 10:56 Adding to Henning's answer, the "flaw" that ZFC is not strong enough to determine the natural numbers up to isomorphism (i.e., if ZFC is consistent, then there are different models of ZFC with non-isomorphic $\mathbb N$'s) is due to the fact that ZFC is a first order theory. That is, quantification is over elements of the structure, in this case over sets. Every first order theory that has an infinite model (and all models of set theory are infinite) has arbitrarily large models. And there are models of ZFC with arbitrarily large versions of $\mathbb N$. Here large means when looked at from the outside. When one talks about undecidable statements in number theory, one usually considers not ZFC as the base theory, but some form of arithmetic, i.e., all the variables of our statements range over numbers. However, the problems are exactly the same as above, and the situation is even simpler, since you only have to consider models of arithmetic. But the problem remains. The first order theory of arithmetic does not determine $\mathbb N$ up to isomorphism. The connection to Gödel's incompleteness theorems is as follows: If ZFC is consistent (which we assume it is), then ZFC does not prove its own consistency (this is the second incompleteness theorem). It follows that ZFC together with the statement that it is inconsistent is actually consistent (mind bending, I know). This implies that there is a model of ZFC that knows a proof of $0=1$ from ZFC. Inside this model, that proof can be coded into a natural number in some computable way. Now that natural number does not correspond to an actual natural number that we know in the real world, because otherwise we would have a proof of the inconsistency of ZFC. But we assumed that we don't have such a proof. The same argument works for Peano Arithmetic, which has as its models just versions of $\mathbb N$, without any "sets" other than numbers. Stefan GeschkeStefan Geschke $\begingroup$ Everything here is true, but one should not conclude from it that moving to a second-order theory instead would fix all our troubles. A second-order theory for arithmeric (or, I presume, set theory) can fix a model uniquely up to isomorphism, but there can still be undecidable sentences because in the move from first to second order we lose logical completeness (the property that every statement that is true in all models has a proof). $\endgroup$ – Henning Makholm Sep 29 '11 at 23:26 $\begingroup$ "This implies that there is a model of ZFC that knows a proof of $0=1$ from ZFC" temporarily confused me. By "knows a proof" you mean the statement "there exists a sequence of lines which begins with the axioms of ZFC and ends in 0=1 such that blah blah blah" evaluates to true in this model. It doesn't know an actual proof, presumably--there will be a nonstandard version of "sequence of lines" or something else like that. $\endgroup$ – 6005 Nov 30 '15 at 6:26 Not the answer you're looking for? Browse other questions tagged logic or ask your own question. Undecidable conjectures Short open problems or undecidable statements in ZFC On the undecidability of the existence of odd perfect numbers How could it be possible for the Goldbach conjecture to be undecidable? Is it possible to construct sentences undecidable in first-order logic? Which "natural" problems are independent of ZFC? Decidability of the Riemann Hypothesis vs. the Goldbach Conjecture Is every true statement about the natural numbers provable in ZFC? Is Chaitin's constant well-defined? Definition of partial function using predicate that is possibly undecidable	CommonCrawl
Effects of ensemble and summary displays on interpretations of geospatial uncertainty data Lace M. Padilla1,2, Ian T. Ruginski1 & Sarah H. Creem-Regehr1 Cognitive Research: Principles and Implications volume 2, Article number: 40 (2017) Cite this article Ensemble and summary displays are two widely used methods to represent visual-spatial uncertainty; however, there is disagreement about which is the most effective technique to communicate uncertainty to the general public. Visualization scientists create ensemble displays by plotting multiple data points on the same Cartesian coordinate plane. Despite their use in scientific practice, it is more common in public presentations to use visualizations of summary displays, which scientists create by plotting statistical parameters of the ensemble members. While prior work has demonstrated that viewers make different decisions when viewing summary and ensemble displays, it is unclear what components of the displays lead to diverging judgments. This study aims to compare the salience of visual features – or visual elements that attract bottom-up attention – as one possible source of diverging judgments made with ensemble and summary displays in the context of hurricane track forecasts. We report that salient visual features of both ensemble and summary displays influence participant judgment. Specifically, we find that salient features of summary displays of geospatial uncertainty can be misunderstood as displaying size information. Further, salient features of ensemble displays evoke judgments that are indicative of accurate interpretations of the underlying probability distribution of the ensemble data. However, when participants use ensemble displays to make point-based judgments, they may overweight individual ensemble members in their decision-making process. We propose that ensemble displays are a promising alternative to summary displays in a geospatial context but that decisions about visualization methods should be informed by the viewer's task. Understanding how to interpret uncertainty in data, specifically in weather forecasts, is a problem that affects visualization scientists, policymakers, and the general public. For example, in the case of hurricane forecasts, visualization scientists are tasked with providing policymakers with visual displays that will inform their decision on when to call for mandatory evacuations and how to allocate emergency management resources. In other circumstances, the general public may view hurricane forecasts to make decisions about when and how to evacuate. Even though these types of decisions are costly and have a high impact on health and safety, the literature provides few recommendations to visualization scientists about the most effective way to display uncertainty in hurricane forecasts to a novice audience. Previous research has shown that novice viewers misinterpret widely used methods to visualize uncertainty in hurricane forecasts. The current work examines how novice users interpret two standard methods to display uncertainty in hurricane forecasts, namely ensemble and summary displays. We demonstrate how salient elements of a display – or elements in a visualization that attract attention – can influence interpretations of visualizations. We also provide specific recommendations based on empirical evidence for best practices with each technique. Ensemble data is the most commonly used type of forecast data across many scientific domains, including weather prediction and climate modeling (Sanyal et al., 2010). Scientists create ensemble datasets by generating or collecting multiple data values or 'ensemble members' (Brodlie, Osorio, & Lopes, 2012; Potter et al., 2009). Then, scientists plot all, or a subset of, the ensemble members on the same Cartesian coordinate plane, creating an ensemble display (Harris, 2000). Despite ensemble display use in scientific practice, it is more common to utilize summary displays for public presentations (Pang, 2008). Scientists construct summary displays by plotting statistical parameters, such as the mean, median, distribution, standard deviations, confidence intervals (CIs) and, with some advanced techniques, outliers, of the ensemble members (Whitaker, Mirzargar, & Kirby, 2013). Among the studies that have attempted to assess the efficacy of ensemble and summary visualizations, there is disagreement about the best method to communicate uncertainty to the general public. This work aims to test the efficacy of both approaches in the context of hurricane forecasts. Supporters of ensemble displays suggest that there are benefits to this visualization method, including (1) the ability to depict all or the majority of the ensemble data, making a representative portion of the data visually available (Liu et al., 2016); (2) the fact that ensemble displays depict non-normal relationships in the data such as bimodal distributions, perceived as discrete clusters (Szafir, Haroz, Gleicher, & Franconeri, 2016); (3) the preservation of relevant outlier information (Szafir et al., 2016); and (4) the fact that viewers can, in some cases, accurately report some statistical parameters depicted by ensemble displays such as probability distributions (Cox, House, & Lindell, 2013; Leib et al., 2014; Sweeny, Wurnitsch, Gopnik, & Whitney, 2015; Szafir et al., 2016), trends in central tendency (Szafir et al., 2016), and mean size and orientation (Ariely, 2001) (for comprehensive reviews see, Alvarez, 2011; Whitney, Haberman, & Sweeny, 2014). Sweeny et al. (2015) further showed that children as young as four could accurately judge the relative average size of a group of objects. Researchers argue that viewers perceive the aforementioned data parameters in ensemble displays because they can mentally summarize visual features of ensemble displays by perceiving the gist or integrating ensemble data into rich and quickly accessible information (Correll & Heer, 2017; Leib et al., 2014; Oliva & Torralba, 2006; Rousselet, Joubert, & Fabre-Thorpe, 2005). In relation to this, Szafir et al. (2016) detailed four types of tasks (identification, summarization, segmentation, and structure estimation) that are well suited for ensemble displays because they utilize ensemble coding or the mental summarization of data. In line with this work, Correll and Heer (2017) found that participants were effective at estimating the slope, amplitude, and curvature of bivariate data when displayed with scatter plots. In contrast, researchers found that viewers had a strong bias when estimating correlations from scatter plots but also demonstrated that the laws that viewers followed remained similar across variations of encoding techniques and data parameters such as changes in density, aspect ratio, color, and the underlying data distribution (Rensink, 2014, 2016). In sum, there is evidence that adult novice viewers and children can, in some cases, derive statistical information from ensemble displays and that ensemble displays can preserve potentially useful characteristics in the ensemble data. While previous research indicates that there are various benefits to ensemble displays, there are also some drawbacks. The primary issue with ensemble displays is that visual crowding may occur, which happens when ensemble members are plotted too closely together and cannot be easily differentiated, increasing difficulty in interpretation. While researchers have developed algorithms to reduce visual crowding (e.g., Liu et al., 2016), visual crowding may still occur when all of the ensemble data is plotted. Summary displays are an alternative to ensemble displays and are suggested to be easier and more effective for users to understand. Work in cartography argues that choropleth maps, which are color encodings of summary statistics such as the average value over a region, are more comprehensible than displaying all of the individual data values (Harrower & Brewer, 2003; Watson, 2013). Michael Dobson argued that the summarization in choropleth maps decreases mental workload and time to perform tasks while improving control of information presentation and pattern recognition (Dobson, 1973, 1980). Beyond choropleth maps, summarization techniques have been developed that can encode advanced summary statistics, such as quartiles, outlier data, and task-relevant features, in ensemble datasets (Mirzargar, Whitaker, & Kirby, 2014; Whitaker et al., 2013). However, researchers have also documented drawbacks to summarization techniques. First, displays of summary statistics, such as median, mean, and standard deviations, can hide important features in the data such as bimodal or skewed distributions and outliers (Whitaker et al., 2013). Second, summary displays that include boundaries, such as line plots of summary statistics, produce more biased decisions than scatter plots of the same data (Correll & Heer, 2017). Finally, studies have demonstrated that even simple summary displays, such as statistical error bars, are widely misinterpreted by students, the public, and even trained experts (Belia, Fidler, Williams, & Cumming, 2005; Newman & Scholl, 2012; Sanyal, Zhang, Bhattacharya, Amburn, & Moorhead, 2009; Savelli & Joslyn, 2013). In the context of hurricane forecasts, there is evidence that summary displays may result in more misinterpretations than ensemble displays (Ruginski et al., 2016). A notable example is the National Hurricane Center's (NHC) 'cone of uncertainty' (Fig. 1). An example of a hurricane forecast cone typically presented to end-users by the National Hurricane Center (http://www.nhc.noaa.gov/aboutcone.shtml) Forecasters create the cone of uncertainty by averaging a 5-year sample of historical hurricane forecast tracks, resulting in a border where locations inside the boundary have a 66% likelihood of being struck by the center of the storm (Cox et al., 2013). Even though the cone of uncertainty is used by the NHC, it does not follow well-established cartographic principles (e.g., Dent, 1999; Robinson, Morrison, Muehrcke, Kimerling, & Guptill, 1995), including hierarchical organization, which asserts that the level of salience should correspond to the importance of information in a display. However, the cone of uncertainty does support the general view that simplifying complex ensemble data will make decisions easier for users. Ruginski et al. (2016) compared five different encodings of ensemble data (three summary displays, one display of the mean, and one ensemble display) of hurricane forecast tracks, using a task where participants predicted the extent of damage that would occur at a given location. The three summary displays included a standard cone of uncertainty, which had a mean line, a cone without the mean line, and a cone in which the color saturation corresponded to the probability distribution of the ensemble data. Results revealed that, with the summary displays, participants believed that locations at the center of the hurricane that were at a later point in time would receive more damage than at an earlier time point. Strikingly, ensemble displays showed the reverse pattern of responses, with damage rated to be lower at the later time. Further, we found that participants viewing any of the summary displays compared to the ensemble display were significantly more likely to self-report that the display depicted the hurricane growing in size over time. In fact, the cone only depicts a distribution of potential hurricane paths and no information about the size (Cox et al., 2013). One consistency between the three summary displays was the growing diameter of the cone boundaries (as illustrated in Fig. 2a). A possible interpretation of this finding is that viewers focused on the increasing size of the cone, rather than mapping increasing uncertainty to the size of the cone. Examples of the cone (a, c) and ensemble display (b, d) visualization techniques of hurricane one (a, b) and two (c, d) More generally, one potential source of the misinterpretation of both summary and ensemble displays is their salient visual features. Salient visual features are defined as the elements in a visualization that attract bottom-up attention (e.g., Itti, Koch, & Niebur, 1998; Rosenholtz & Jin, 2005). Researchers have argued that salience is also influenced by top-down factors (e.g., training or prior knowledge), particularly for tasks that simulate real world decisions (Fabrikant, Hespanha, & Hegarty, 2010; Hegarty, Canham, & Fabrikant, 2010; Henderson, 2007). Hegarty et al. (2010) demonstrated that, in a map-based task, top-down task demands influenced where participants looked on the page, and then salience influenced what information they attended to in the region of interest. This work suggests that both top-down processing and salience guide attention. As described above, a salient visual feature of the cone of uncertainty is the border, which surrounds the cone shape and which grows in diameter with time (Fig. 2a). A salient feature of ensemble displays is the individual ensemble members and their relationship to one another (Fig. 2b). It is possible that the salient features of both the cone of uncertainty and ensemble displays of the same data attract viewers' attention and bias their decisions (Bonneau et al., 2014). The motivation for this work was to address both an applied and a theoretical goal. The applied goal was to test whether salient features of summary and ensemble displays contributed to some of the biases reported in prior work (Ruginski et al., 2016), whereas the theoretical goal was to examine whether salient visual features inform how viewers interpret displays. In the case of the cone of uncertainty, viewers may associate the salient increasing diameter of the cone with changes in the physical size of the hurricane. To test this possibility, in the first experiment, we expanded on our previous paradigm by having participants make estimates of the size and intensity of a hurricane with either ensemble or summary displays. In a second experiment, we focused further on the ensemble visualization and judgments of potential damage across the forecast, testing whether the role of the individual lines presented in an ensemble display would be misinterpreted because of their salience in the display. Finally, in a third experiment, we replicate the second experiment and extend the findings beyond a forced choice task. In line with our prior work (Ruginski et al., 2016), we hypothesized that participants viewing the cone of uncertainty would report that the hurricane was larger at a future time point. It was an open question whether judgments of intensity would also be associated with the depicted size of the cone. We predicted that those viewing the ensemble display would report that the size and intensity of the storm remained the same in the future because the size cue from the cone was not present. On the other hand, for ensemble hurricane track displays (Fig. 2b, d), it is possible that the individual tracks and their relationship to one another are the salient features used to interpret the hurricane forecast. The tracks in the ensemble display employed by Ruginski et al. (2016) became increasingly farther apart as the distance from the center of the storm increased, which could be associated with a decrease in perceived intensity of the storm. We predicted that participants viewing the ensemble display would believe that the storm was less intense where the individual tracks were farther apart (an effect of distance from the center of the storm). However, because the cone of uncertainty lacks this salient spread of tracks, we predicted that judgments of intensity when viewing the cone would not be affected by distance from the center of the storm. An example of the cone visualization, shown with the 12 possible oil rig locations. Only one location was presented on each trial (and km were not presented) Participants were 182 undergraduate students currently attending the University of Utah who completed the study for course credit. Three individuals were excluded from final analyses for failing to follow instructions. Of the 179 included in analyses, 83 were male and 183 were female, with a mean age of 21.78 years (SD = 5.72). Each participant completed only one condition, either size task with cone (n = 40), size task with ensemble display (n = 42), intensity task with cone (n = 48), or intensity task with ensemble display (n = 48). Stimuli were presented online using the Qualtrics web application (Qualtrics [Computer software], 2005). In each trial, participants were presented with a display depicting a hurricane forecast. The hurricane forecast images were generated using prediction advisory data from two historical hurricanes, available on the NHC website (http://www.nhc.noaa.gov/archive). The cone of uncertainty and an ensemble display technique were both used to depict the two hurricanes (Fig. 2). A custom computer code was written to construct the summary and ensemble displays, using the algorithm described on the NHC website (http://www.nhc.noaa.gov/aboutcone.shtml). The ensemble and summary displays were created using the code of Cox et al. (2013). The resulting displays were a subset of the five visualization techniques used in Ruginski et al. (2016), which depicted two hurricanes and were randomly presented to participants. All were digitally composited over a map of the U.S. Gulf Coast that had been edited to minimize distracting labeling. These images were displayed to the subjects at a pixel resolution of 740 × 550. A single location of an 'oil rig' depicted as a red dot was superimposed on the image at one of 12 locations defined relative to the centerline of the cone and the cone boundaries. We chose the following distances to place the oil rigs relative to the centerline of the cone, 69, 173, 277, 416, 520, and 659 km (Fig. 3), which correspond to 0.386, 0.97, 1.56, 2.35, 2.94, and 3.72 cm from the center line of the hurricane on the map. Relative points with respect to the center and cone boundary were chosen so that three points fell outside the cone boundary (277, 173, and 69 km), three points fell within the cone boundary (416, 520, and 659 km), and so that no points appeared to touch the visible center line or boundary lines. Underneath the forecast, a scale ranging from A to I was displayed along with visual depictions. For the intensity task, the scale was indicated by gauges, and for the size task the scale was indicated by circles (Fig. 4). Each circle was scaled by 30% from the prior circle. Each gauge was scaled by 1 'tick' from the prior gauge. The starting size and intensity of the hurricane were overlaid on the beginning of the hurricane track forecast for each trial. Three starting sizes and intensities (C, E, G) were presented in a randomized order. An example of the visual depiction of the Likert scales, which depicts intensity with gauges (top) and size with the diameter of the circle (bottom) Salience assessment To test the previously stated prediction about salience of features of ensemble and summary displays, we utilized the Itti et al. (1998) salience model. Prior research has employed the Itti et al. (1998) salience model to test the salience of cartographic images and found that this model is a reasonable approximation of bottom-up attention (Fabrikant et al., 2010; Hegarty et al., 2010). The Itti et al. (1998) salience model was run in Matlab (2016, Version 9.1.0.441655) using the code provided by Harel et al., (2007). The results of this analysis suggest that the most salient visual features of the cone of uncertainty are the borders of the cone and the centerline (Fig. 5a). Additionally, the salient visual features of the ensemble display are the relative spread of hurricane tracks (Fig. 5b). Example of the visual output generated using the Itti et al. (1998) salience model, which shows example stimuli used in this experiment. Brighter coloration indicates increased salience. a The summary display. b The ensemble display We utilized a 2 (visualization type) × 2 (hurricane) × 3 (starting size or intensity) × 12 (oil rig location) mixed factorial design for each task (size and intensity). Hurricane starting size or intensity and the oil rig location were within-participant variables, resulting in a total of 72 trials per participant. Participants were randomly assigned to one of two visualization conditions (summary or ensemble display) and one of two tasks (size or intensity) as between-participant factors. Individuals were first given a simple explanation of the task and visualization. Participants completing the size task were provided with the following instructions: "Throughout the study you will be presented with an image that represents a hurricane forecast, similar to the image shown above. You will be provided with the initial hurricane size (diameter) at a particular point in time, indicated by the circle shown at the apex (beginning) of the hurricane forecast. An oil rig is located at the red dot. Assume that the hurricane were to hit the oil rig (at the red dot). Your task will be to select the size that best represents what the hurricane's diameter would be when it reaches the location of the oil rig." Additionally, each trial included the text as a reminder of the task, "Assume that the hurricane were to hit the oil rig (at the red dot). Your task is to select the size that best represents what the hurricane's diameter would be when it reaches the location of the oil rig." For the intensity task, participants were provided the instructions: "Throughout the study you will be presented with an image that represents a hurricane forecast, similar to the image shown above. You will be provided with the initial hurricane wind speed at a particular point in time, indicated by the gauge shown at the apex (beginning) of the hurricane forecast. As the arm of the gauge rotates clockwise, the wind speed increases. For example, gauge A represents the lowest wind speed and gauge I the highest wind speed. An oil rig is located at the red dot. Assume that the hurricane were to hit the oil rig (at the red dot). Your task will be to select the gauge that best represents what the hurricane's wind speed would be when it reaches the location of the oil rig." Each trial also contained the instructions, "Assume that the hurricane were to hit the oil rig (at the red dot). Your task is to select the gauge that best represents what the hurricane's wind speed would be when it reaches the location of the oil rig." Following the instructions, participants completed all of the trials presented in a different random order for each participant. Finally, participants answered questions related to comprehension of the hurricane forecasts. These included two questions specifically relevant to the current research question: "The display shows the hurricane getting larger over time." and "The display indicates that the forecasters are less certain about the path of the hurricane as time passes." These questions also included a measure of the participants' understanding of the response glyphs used in the experiment by asking them to indicate which of two wind gauges had a higher speed or to match the size of circles. Participants who did not adequately answer these questions were excluded from the analysis (two participants for the wind speed gauges, one for the size circles). Multilevel models (MLM) were fit to the data using Hierarchical Linear Modeling 7.0 software and restricted maximum likelihood estimation procedures (Raudenbush & Bryk, 2002). Multilevel modeling is a generalized form of linear regression used to analyze variance in experimental outcomes predicted by both individual (within-participants) and group (between-participants) variables. A MLM was appropriate for modeling our data and testing our hypotheses for two major reasons. Firstly, MLM allows for the inclusion of interactions between continuous variables (in our case, distance) and categorical predictors (in our case, the type of visualization). Secondly, MLM uses robust estimation procedures appropriate for partitioning variance and error structures in mixed and nested designs (repeated measures nested within individuals in this case). We transformed the dependent variable before analysis by calculating the difference between the starting value of the hurricane (either size or intensity) and the participant's judgment. A positive value of the difference score represents an increase in judged size or intensity. In addition, although an ordinal variable by definition, we treated the dependent variable Likert scale as continuous in the model because it contained over five response categories (Bauer & Sterba, 2011). For the distance variable, we analyzed the absolute value of oil rig distances, regardless of which side of the hurricane forecast they were on, as none of our hypotheses related to whether oil rigs were located on a particular side. We divided the distance by 10 before analysis so that the estimated model coefficient would correspond to a 10-km change (rather than a 1-km change). The mixed two-level regression models tested whether the effect of distance from the center of forecasts (level 1) varied as a function of visualization (level 2). Visualization was dummy coded such that the cone visualization was coded as 0 and the ensemble display as 1. We tested separate models for the intensity and size tasks. Self-report measures of experience with hurricanes and hurricane prone regions were also collected. As the participants were students at the University of Utah, so few had experienced a hurricane (3%) or had lived in hurricane-affected regions (7%) that we did not include these measures as covariates. Results – Size Level 1 of our multilevel model is described by: $$ Chang{e}_{ij}={\beta}_{0j}+{\beta_{1j}}^{\ast}\left( Distanc{e}_{ij}\right)+{r}_{ij}; $$ and level 2 by: $$ {\upbeta}_{0\mathrm{j}}={\upgamma}_{00}+{\upgamma_{01}}^{\ast}\left({\mathrm{Visualization}}_{\mathrm{j}}\right)+{\mathrm{u}}_{0\mathrm{j}} $$ Where i represents trials, j represents individuals, and the β and γ are the regression coefficients. The error term rij indicates the variance in the outcome variable on a per trial basis, and u0j on a per person basis. Though people are assumed to differ on average (u0j) in the outcome variable, we tested to determine whether the effect of distance differed per person (u1j) using a variance-covariance components test. We found that the model including a random effect of distance fit the data better than the model not including this effect, and so the current results reflect that model (χ2 = 955.95, df = 2, P < 0.001). Including this term allowed us to differentiate between the variance accounted for in judgments specific to a fixed effect of distance and the variance accounted for in judgments specific to a random effect of person. Our primary hypothesis was that we would see greater size judgments with the cone compared to the ensemble display, reflecting a misinterpretation that the hurricane grows over time. Consistent with this prediction, we found a significant main effect of visualization type on average change in size judgments (γ 01 = −0.69, standard error (SE) = 0.33, t-ratio = −2.08, df = 80, P = 0.04). This effect indicates that, at the center of the hurricane, individuals viewing the cone visualization had a 0.69 greater increase in their original size judgment compared with individuals viewing the ensemble visualization (Fig. 6). However, the oil rig distance from the center of the storm did not significantly alter change in size judgments (γ 10 = 0.01, SE = 0.01, t-ratio = 1.43, df = 80, P = 0.16) and the effect of distance from the center of the storm on change in size judgments did not differ based on visualization type (γ 11 = −0.01, SE = 0.01, t-ratio = −1.32, df = 80, P = 0.19). Further, the main effect of visualization type on the average change in size judgment was also supported by results of the post-test question. A t-test, in which yes was coded as 1 and no as 0, revealed that participants viewing the cone (M = 0.70, SE = 0.04) were significantly more likely to report that the display showed the hurricane getting larger over time compared to the ensemble display (M = 0.39, SE = 0.05), t(176) = 4.436, P < 0.001, 95% CI 0.17–0.45, Cohen's d = 0.66. The effect of distance from center and visualization type on change in size judgments. Grey shading indicates ± 1 standard error. Accurate interpretation would be indicated by a '0' change score. A one-unit change represents a one-step change in circle size along a 9-point scale (see Fig. 4 for the 9-point scale) Results – Intensity The multilevel model used for the intensity data included the exact same variables as the size model. Similar to the first model, we found that the model including a random effect of distance fit the data better than the model not including this effect, and so the current results reflect that model (χ2 = 704.81, df = 2, P < 0.001). For intensity, we expected to see a greater effect of distance from the center of the storm on judgments with the ensemble display compared to the cone, reflecting participants' attention to the increasing spread of tracks as the distance from the center increase for the ensemble display. First, we found a significant main effect of visualization type on average change in intensity judgments (γ 01 = −0.85, SE = 0.33, t-ratio = −2.58, df = 95, P = 0.01). This indicates that, at the center of the hurricane, individuals viewing the cone visualization increased their intensity judgment by 0.85 (almost a full wind gauge) more than those who viewed the ensemble visualization at the center of the hurricane. Second, we found a significant main effect of distance from the center of the storm (γ 10 = −0.02, SE = 0.01, t-ratio = −3.28, df = 95, P = 0.001), which is qualified by a significant cross-level interaction between distance and visualization type (γ 11 = −0.02, SE = 0.01, t-ratio = −3.33 df = 95, P = 0.001). To decompose the interaction between distance from the center of the storm and visualization type, we computed simple slope tests for the cone and ensemble visualizations (Fig. 7). This revealed that the association between distance from the center of the hurricane and change in intensity judgment is different from zero for each visualization (cone visualization: Estimate = −0.02, SE = 0.01, χ2 = 64.74, P < 0.001; ensemble visualization: Estimate = −0.04, SE = 0.004, χ2 = 10.74, P = 0.001) and stronger for the ensemble visualization (χ2 = 101.89, P < 0.001). This result suggests that judgments of intensity decreased with distance more for the ensemble display than for the cone, consistent with a focus on the relative spread of hurricane tracks. In addition, using a t-test, a post-test question revealed that participants viewing the ensemble display (M = 0.53, SE = 0.04) were more likely to report that the display indicated the forecasters were less certain about the path of the hurricane over time compared to the cone (M = 0.39, SE = 0.05), t(176) = −1.97, P = 0.04, 95% CI −0.29 to −0.0003, Cohen's d = 0.29. Simple slopes of the interaction between distance and visualization type on change in intensity judgments. Grey shading indicates ± 1 standard error. Accurate interpretation would be indicated by a '0' change score. A one-unit change represents a one-step change in gauge intensity along a 9-point scale (see Fig. 4 for the 9-point scale) The results of this experiment showed that novice users interpret the size and intensity of a hurricane represented by ensemble and summary displays differently. Our prior work showed different damage ratings over time with the cone compared to the ensemble display, but it was unclear whether these were being driven by interpretations of size or intensity because a more general concept of 'damage' was used (Ruginski et al., 2016). In the current study, we found a similar pattern of greater increase in both size and intensity reported at the center of the hurricane with the cone, compared to the ensemble display. Furthermore, we found an effect of decreasing intensity judgments with distance from the center of the storm that was greater for the ensemble display than for the cone. These findings support our hypothesis that a salient feature of the cone is the border that shows the diameter of the cone, which is more likely to influence viewers' beliefs that the storm is growing over time compared to the ensemble display, which does not have this visually salient feature. We saw evidence of the participants' beliefs that the cone represented the storm growing in size with both objective judgments of size (which increased more relative to judgments made using the ensemble display) and self-reported interpretations of the cone of uncertainty. Our second hypothesis that participants viewing the ensemble display would believe that the storm was less intense where the individual tracks were farther apart was supported by results of the intensity task conditions. Here, while intensity ratings were higher for the cone compared to the ensemble display, the rate of decrease in ratings of intensity as distance from the center of the storm increased was greater for the ensemble display than the cone. Together, these findings demonstrate that, in the context of hurricane forecasts, the salient visual features of the display bias viewers' interpretations of the ensemble hurricane tracks. More generally, we suggest that summary displays will be most effective for cases in which spatial boundaries of variables such as uncertainty cannot be misconstrued as presenting physical boundaries. In contexts like cartography, where spatial layouts inherently represent physical space, ensemble displays provide a promising alternative to summary displays. Although our findings suggest that ensemble displays seem to have some advantages over summary displays to communicate data with uncertainty in a geospatial context, it may also be the case that ensemble displays provoke additional unintended biases. We tested one potential ensemble display bias in Experiment 2. While the findings of Experiment 1 suggested that viewers of the ensemble visualization are less likely to believe that the hurricane is growing in size, it is possible that ensemble displays also elicit unique biases. One possible bias is that the individual tracks of an ensemble display can lead a viewer to overestimate the impact of the hurricane for locations covered by a path. The storm tracks presented are only a sampling of possible ways the hurricane could go and not an exhaustive list of all routes. It would be a misconception to believe that a hurricane would travel the full extent of any one track. Further, it would also be incorrect to believe that locations that are not covered by a path have little to no possibility of being hit by the storm. Rather, the relative density of tracks indicates the comparative probability of a hurricane being in a given region at future time points. To test whether viewers' decisions are biased by the individual paths of the ensemble visualization, we conducted a second experiment in which the locations of the oil rigs were changed so that one oil rig was always superimposed on a hurricane path. We examined whether viewers would maintain the strategy to rate higher damage closer to the center of the storm, as reported in Ruginski et al. (2016) (i.e., selecting the closest rig to the center), or whether the salience of the ensemble track location would decrease the strength of the distance-based strategy (i.e., selecting the rig that was superimposed on a hurricane path, even when located farther away from the center of the storm). In this experiment, participants were presented with two oil rigs, one that was located on a hurricane path and one that was either closer (Fig. 8a) or farther from the center of the storm (Fig. 8b) than the one that was located on the path. Examples of the stimuli used in Experiment 2 depicting two hurricanes. a Condition in which the farther rig from the center of the storm was located on a hurricane track. b Condition where the closest rig was located on a hurricane track Participants were then asked to decide which of the two oil rigs would receive the most damage. Our hypothesis was that the likelihood of choosing the rig closer to the center of the storm would decrease if the rig farther from the center of the storm fell on a hurricane path, supporting the notion that the individual paths are salient features of the ensemble display that could lead to biased responses. In the rest of the paper we will refer to the close oil rig, meaning the oil rig that is closer to the center of the hurricane forecast display, and the farther oil rig, which is the rig farther away from the center of the hurricane forecast than the closer oil rig. Participants were 43 undergraduate students currently attending the University of Utah who completed the study for course credit; 12 participants were male and 31 were female, with a mean age of 23.56 years (SD = 7.43). Stimuli were presented using the previously detailed approach. On each trial, participants were presented with a display depicting a hurricane forecast and two oil rigs (Fig. 8). The distance between the oil rigs was roughly 100 km and remained constant for all of the trials. The 16 locations of the rig pairs were chosen selectively in areas where one rig was always located on a track and the other oil rig was at the same time point but not on a track, with an equal number of locations on each side of the hurricane. The rig on the track was either closer to the center or farther from the center relative to the rig that was not touching a track. Underneath the forecast, radio buttons were presented that allowed participants to indicate which oil rig they believed would receive the most damage. Damage was used for the response measure because it was found that participants were more likely to use a strategy based on distance from the center of the hurricane when making judgments about damage. This measure allowed us to determine if the colocation of an oil rig and a hurricane track modified the types of distance-based damage judgments reported in Ruginski et al. (2016). We utilized a within-subjects design, 2 (close oil rig on line or far oil rig on line) × 2 (hurricane) × 16 (oil rig pair locations), resulting in a total of 32 trials per participant. Oil rig on line refers to whether the closer or farther oil rig from the center of the hurricane were located on the hurricane track. Individuals were first given a simple explanation of the task and visualization. "Throughout the study you will be presented with an image that represents a hurricane forecast, similar to the image shown above. An oil rig is located at each of the two red dots. Your task is to decide which oil rig will receive more damage based on the depicted forecast of the hurricane path." Additionally, each trial included the text, "Your task is to decide which oil rig will receive the most damage from the hurricane." Following the instructions, participants checked a box indicating which oil rig they believed would receive the most damage. The trials were presented in a different random order for each participant. Finally, participants answered demographic questions and questions related to hurricane experience. A multilevel logistic regression model was fit to the data using the lme4 package in R and maximum likelihood Laplace approximation estimation procedures (Bates, Maechler, Bolker, & Walker, 2015). A logistic MLM was appropriate for modeling our data and testing our hypotheses because it uses robust estimation procedures appropriate for partitioning variance and error structures in mixed and nested designs (repeated measures nested within individuals in this case) for binary outcomes (choosing which oil rig would receive more damage in this case). $$ Close\kern0.5em Strateg{y}_{ij}={\beta}_{0j}+{\beta_{1j}}^{\ast}\left( Far\ Rig\ On\ Line\right)+{r}_{ij}; $$ $$ {\upbeta}_{0\mathrm{j}}={\upgamma}_{00}+{\mathrm{u}}_{0\mathrm{j}} $$ $$ {\upbeta}_{1\mathrm{j}}={\upgamma}_{10} $$ Far Rig On Line was dummy coded such that the farther rig overlapping with a line corresponded to 1, while the closer rig being on the line corresponded to 0. Our outcome variable, Close Strategy, was coded such that selecting the close oil rig to receive more damage corresponded to 1 and selecting the far oil rig to receive more damage corresponded to 0. We found that the model not including a random effect of On Line fit the data better than the model including this effect, and so the current results reflect the former (χ2 = 5.79, df = 1, P = 0.02). This indicates that there was a consistent fixed effect of On Line across people. The participants had very high odds of deciding that the closer oil rig would receive the most damage when the closer oil rig was on the line (and by design, the farther oil rig was not on a line) (γ 00 = 5.75, SE = 0.52, odds ratio (OR) = 314.19,Footnote 1 z = 11.19, P < 0.001). Expressed in terms of predicted probability, this effect indicates that participants chose the closer oil rig to receive more damage 99.68% of the time when the closer oil rig was on a line (Fig. 8). This very high proportion makes sense, as this condition combined properties of close location to the center and a location falling on the path. Importantly, our model indicated a strong effect of Far Rig On Line, such that predicted probability of choosing the closer oil rig as receiving the most damage decreased to 64.15% when the farther oil rig was on the line (γ 10 = −5.17, SE = 0.37, OR = 0.006, z = −13.85, P < 0.001; Fig. 8). In this condition, the far oil rig was chosen in 304 of the 688 trials, compared to only 12 of the 688 trials when it was not on the line. In other words, while participants chose the closer oil rig more often in both conditions, the result that the tendency to choose the farther rig increased by about 35% when the farther rig fell on a visual path strongly supports the use of the individual path as a salient feature influencing decisions (Fig. 9). Predicted probabilities of choosing the close oil rig to receive more damage. Bars represent 95% confidence intervals. Accurate interpretation would be to choose the close oil rig 100% of the time We found that non-experts almost always chose the closer oil rig to the center of the hurricane forecast when the oil rig fell on an individual hurricane track, consistent with prior work showing a strategy to report more damage to locations close to the center (Ruginski et al., 2016). However, when the farther oil rig visually overlapped with a single ensemble track, judgments were significantly biased by the individual path, decreasing the likelihood of choosing the close location. The results of the second study suggest that ensemble displays have their own set of interpretation biases, as individual ensemble members can be over weighted in participants' judgments. In an effort to replicate the prior study and test if the findings were robust to a non-forced choice task, a third study was conducted that was identical to Experiment 2 but with an additional response option of 'Equal Damage'. By adding an 'Equal Damage' response participants could indicate that neither oil rig A or B would receive more damage. The same methods and data analysis were used as Experiment 2. Participants were 35 undergraduate students currently attending the University of Utah who completed the study for course credit; 10 participants were male, and 24 were female, with a mean age of 22.06 years (SD = 4.5). As in Experiment 2, we used a multilevel logistic regression model to determine the impact of the colocation of an ensemble track and an oil rig. Prior to analysis, trials for which participants reported 'Equal Damage' (219 trials, 19.55% of total) were removed. Of the trials where participants reported equal damage, 79 occurred when the close rig was on a line and 140 occurred when the far rig was on a line. Models including fixed effects only and random effects fit the data equally well and results detail the more parsimonious model not including the random effect (χ2 = 0, df = 1, P = 1.00). This indicates that there was a consistent fixed effect of the oil rig touching an ensemble track across people. Consistent with Experiment 2, participants had high odds of deciding that the closer oil rig would receive the most damage when it was on the line (γ 00 = 10.94, SE = 1.52, OR = 56387.34,Footnote 2 z = 7.2, P < 0.001). In other words, participants indicated that the closer oil rig would receive more damage 99.99% of the time when it was on a line. This finding replicates the results of our prior experiment. Further, our results showed a similar effect compared to Experiment 2 for Far Rig On Line, such that predicted probability of choosing the closer oil rig as receiving the most damage decreased to 54.59% when the farther oil rig was on the line (γ 10 = −10.76, SE = 1.29, OR = 0.00002, z = −8.36, P < 0.001; Fig. 10). In this condition, the far oil rig was chosen in 238 of 420 trials, compared to only 1 of 481 trials when it was not on the line. In sum, Experiment 3 replicates the take home points of Experiment 2, but the SE increased in Experiment 3. It is likely that including the response option of 'Equal Damage' increased the variability of the responses by decreasing sample size (reducing trials) and choosing the far rig more often (almost 50–50) for those trials that were not decided as equal damage. In Experiment 3, we replicated Experiment 2, showing that participants were significantly biased by the colocation of an oil rig and an individual ensemble track. In the third study, in 19.55% of trials, individuals believed that the two oil rigs would receive equal damage, and about twice as many of these trials occurred when the far oil rig was on the line, providing additional evidence that the line competes with proximity to the center in evaluation of damage. For the rest of the trials where individuals chose either the close or far oil rig, results were consistent with Experiment 2, showing a decrease in the likelihood of choosing the close location when the far oil rig fell on the line. Together, these studies demonstrate that decisions about ensemble displays of hurricane forecast tracks change when making judgments about specific points that intersect with a track. More broadly, this work suggests that individual members of an ensemble display may be overweighed when the ensemble member happens to overlap with a point of interest. For example, individuals may be more likely to evacuate or take precautionary actions if a hurricane forecast track overlaps with their own town, but feel less concerned if not. These results suggest that visualization scientists should consider using ensemble displays in cases where users do not need to make decisions about specific points that may be influenced by an ensemble member. Instead, ensemble displays may be best suited for cases in which viewers are making judgments about patterns in the data or about areas, which is consistent with tasks proposed for ensemble displays by Szafir et al. (2016). Our findings may be influenced by the nature of the task in a geospatial context, where asking about a single point biases users towards more of an outlier-identification strategy (Szafir et al., 2016). Future work involving interpretation of geospatial uncertainty may help to disentangle this by implementing tasks that require individuals to make judgments about larger areas of space (such as a county), which may force individuals to summarize the visualization and be less biased by individual tracks. Correll and Heer (2017) provide support for the claim that tasks influence the nature of biases by demonstrating that viewers are not affected by outliers when making judgments about the overall trends in ensemble data. Our first study demonstrated that novice users interpret the size and intensity of a hurricane represented by an ensemble display and the cone of uncertainty differently, with relative lower size and intensity judgments over time for the ensemble display compared to the cone. These findings support our hypothesis that viewers of the cone of uncertainty are more likely to incorrectly believe that the visualization depicts the hurricane growing over time, consistent with the results of Ruginski et al. (2016). Furthermore, in the intensity task condition, we found a stronger effect of distance from the center of the hurricane for the ensemble display than for the cone. This result is in line with our predictions, providing evidence that a salient feature of the ensemble display is the tracks and their relationship to one another. In sum, these studies suggest that the type of visualization technique used to depict hurricane tracks significantly influences viewers' judgments of size and intensity – these effects are likely driven by the salient features of the displays, consistent with prior work (Correll & Heer, 2017; Newman & Scholl, 2012). Beyond hurricane forecasts, this work proposes that salient visual features in a display can attract viewers' attention and bias their decisions. Attention may bias viewers' judgments by manipulating the relative importance of features. Viewers may overweight the importance of salient features because they are attending to them more or they may devalue other features that they pay less attention to. Despite their benefits, ensemble displays are not free of biases that negatively affect uncertainty comprehension. Our second and third studies found that, while novice users predominantly make judgments as if ensemble displays are distributions of probable outcomes, they also indicate that locations that are touching an individual ensemble track will receive more damage. However, we speculate that individual ensemble members may only influence judgments of specific points and may not influence users making judgments about areas. This assertion is consistent with work that suggests ensemble displays are well suited to conveying the gist of a scene (Correll & Heer, 2017; Oliva & Torralba, 2006; Rousselet et al., 2005). Further, the types of tasks that Szafir et al. (2016) propose for ensemble displays all include identifying patterns in groups of data that are spatially organized rather than point-based judgments. This suggests that visualization scientists should consider the types of tasks that their users will be completing when selecting the appropriate visualization technique, and that ensemble displays are most appropriate for tasks that do not require judgments about specific points. Understanding human reasoning with static ensemble displays is a necessary first step to unpacking ensemble cognition; however, many visualization scientists may desire to present ensemble displays as animations or time-varying displays (Liu et al., 2016). Time-varying displays continually update the visualization with simulations, fading simulations out as a function of their time on the screen, which could reduce the salience of individual simulations. Directly manipulating the salience of features with animations, in line with Fabrikant et al. (2010) and Hegarty et al. (2010), is a possible future direction for this work. While animations may reduce biases produced by individual tracks, they may not be entirely beneficial (Tversky, Morrison, & Betrancourt, 2002) and often show little benefit when learning information from visualizations (Hegarty, Kriz, & Cate, 2003). However, the aforementioned work predominantly examined process diagrams and the negative impact of animations may not generalize to decision-making with uncertainty visualizations. Additionally, many animated visualization techniques also include user interaction capabilities. To determine the specific contributions of animation and user interaction to ensemble cognition, a systematic study is needed that tests both area and point-based judgments using these techniques. Future work is also needed to address claims of how ensemble and summary displays are used beyond geospatial weather forecasting. Hurricanes are an example of geospatial data forecasting involving movement over space and time. It is possible that interpretations of ensemble versus summary displays differ across data dimensionality (e.g., 1-D bar charts or violin plots, see Correll & Gleicher, 2014) as well as across domains. For example, GPS-location data visualizations elicit top-down influences that can modify viewers' judgments (Hegarty, Friedman, Boone, & Barrett, 2016). However, it is unclear if viewers of weather forecasting data visualizations demonstrate the same top-down influences. Additionally, the current studies provided limited information about the nature of the displays. This may have led viewers to rely more on visually salient features than they would have if provided with more specific instructions highlighting common misconceptions about uncertainty visualizations, including that changes in size of the display can represent other information than physical size changes and that ensemble members are not always an exhaustive representation of all of the data. If we had given participants more information about what the cone or ensemble represents, they might have misinterpreted it less. Future work could add supplemental instruction before display presentation and assess how effectively that information facilitates desired interpretations. Other biases may have resulted from the specific visual information depicted in the display. Perceptual biases and limitations of the visual system, such as simultaneous contrast effect and just noticeable differences, were not controlled for. Prior work shows that perception interacts with visualization techniques (e.g., Cleveland & McGill, 1986; Kosara & Skau, 2016). As such, future work is needed to generalize these findings beyond a geospatial context and to other visualization techniques. While there is disagreement about the optimal ways to visualize ensemble data, our work argues that both summary and ensemble displays have inherent biases based on their salient visual features. We propose that summary displays of geospatial uncertainty can be misinterpreted as displaying size information, while ensemble displays of the same information are not subject to this bias. On the other hand, when participants use ensemble displays to make point-based judgments, they may overweight individual ensemble members in their decision-making process. Overall, both user expertise and the intended visualization goal should be considered when visualization scientists decide to implement either summary or ensemble displays to communicate uncertainty. Current practice in visualization tends to emphasize the development of visualization methods more than testing usability (Isenberg, Isenberg, Chen, Sedlmair, & Möller, 2013), although there is a growing acknowledgment of the importance of incorporating human cognition and performance in visualization research (Carpendale, 2008; Kinkeldey, MacEachren, Riveiro, & Schiewe, 2015; Plaisant, 2004). As data availability and associated uncertainty visualization techniques continue to expand across the academic, industry, and public spheres, scientists must continue to advance the understanding of end-user interpretations in order for these visualizations to have their desired impact. 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From textures to crowds: multiple levels of summary statistical perception. In J. S. Werner & L. M. Chalupa (Eds.), The new visual neurosciences (pp. 695–710). Boston: MIT Press. We are thankful to Donald House and Le Liu for their assistance with stimulus generation. This work was supported by the National Science Foundation under Grant No. 1212806. All datasets on which the conclusions of the manuscript rely were deposited in a publicly accessible GitHub repository link. University of Utah, Salt Lake City, USA Lace M. Padilla, Ian T. Ruginski & Sarah H. Creem-Regehr Department of Psychology, University of Utah, 380 S. 1530 E., Room 502, Salt Lake City, UT, 84112, USA Lace M. Padilla Ian T. Ruginski Sarah H. Creem-Regehr LMP is the primary author of this study, and she was central to the experimental design, data collection, interpretation of results, and manuscript preparation. ITR also significantly contributed to experimental design, data collection, data analysis, and manuscript preparation. SHC contributed to the theoretical development and manuscript preparation. All authors read and approved the final manuscript. Correspondence to Lace M. Padilla. LMP is a Ph.D. student at the University of Utah in the Cognitive Neural Science department. LMP is a member of the Visual Perception and Spatial Cognition Research Group directed by Sarah Creem-Regehr, Ph.D., Jeanine Stefanucci, Ph.D., and William Thompson, Ph.D. Her work focuses on graphical cognition, decision-making with visualizations, and visual perception. She works on large interdisciplinary projects with visualization scientists and anthropologists. ITR received his B.A. in Cognitive Science and Religious Studies from Vassar College and his M.S. in Psychology from the University of Utah. He is currently a Ph.D. student in the Department of Psychology at the University of Utah. ITR's research interests include applying cognitive theory to uncertainty visualization design and evaluation, as well as the influence of emotional, social, and individual differences factors on perception and performance. SHC is a Professor in the Psychology Department of the University of Utah. She received her MA and Ph.D. in Psychology from the University of Virginia. Her research serves joint goals of developing theories of perception-action processing mechanisms and applying these theories to relevant real-world problems in order to facilitate observers' understanding of their spatial environments. In particular, her interests are in space perception, spatial cognition, embodied cognition, and virtual environments. She co-authored the book Visual Perception from a Computer Graphics Perspective, and was previously Associate Editor of Psychonomic Bulletin & Review and Experimental Psychology: Human Perception and Performance. The research reported in this paper was conducted in adherence to the Declaration of Helsinki and received IRB approval from the University of Utah, #IRB_00057678. Participants in the studies freely volunteered to participate and could elect to discontinue the study at any time. Consent to publish was obtained from all participants in the study. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Padilla, L.M., Ruginski, I.T. & Creem-Regehr, S.H. Effects of ensemble and summary displays on interpretations of geospatial uncertainty data. Cogn. Research 2, 40 (2017). https://doi.org/10.1186/s41235-017-0076-1 Ensemble data Summary display Visual salience Hurricane forecast Visualization cognition	CommonCrawl

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