What can be done (by the community as a whole) to make it easy (for persons other than the authors) to reproduce numerical results in a paper?

Given that creators have some rights to the things they create, you need to provide incentives for transparency to creators/authors. Hopefully they are positive incentives.

But many authors are hesitant to reveal all of their computer code or the actual data that they use in research. There are many reasons for this, some valid, even essential, and some less so.

Some (many) don't reveal all because they fear, reasonably or not, that their ideas will be stolen and that others will capitalize on them before they, themselves, have a chance to follow up.

Some don't reveal their computer code, realizing that it, in final analysis, isn't very good code and is a bit (or a lot) fragile. Or, again, they want to use it in future and don't want to enable others to "scoop" them using the revealed resources.

Another reason, especially for data, is that in many cases the data cannot be revealed for reasons of privacy. This is always an issue in any research with human subjects, even questionnaires on technical topics. It is difficult to anonymize data properly as statistical methods are pretty good at extracting information about individuals from many data sets. So, recognizing the difficulty, it often seems best to just keep it private.

However, I question the value of calling research reproduced if it relies on the same code (or other method) and the same data. If you want to properly reproduce research I suggest that you take the hypotheses of a paper and devise your own experiment independently and run it on independent data. If you get the same results then you have additional information about the value of the hypotheses. The simpler way (same code, same data) guards a bit against some sorts of academic dishonesty, but doesn't otherwise advance the state of knowledge very much.

But if you want to see the code and the data, you have to find ways to overcome the reluctance of the authors to make it public. I think that is easy in some cases and impossible in others, with everything in between pretty common. Moreover, the "easy" cases don't get you very far.

Let me note an important and disturbing current situation in the US. Since the current administration is hostile to science in too many ways, it has declared that scientific studies that are not completely transparent will not be considered in matters related to human health (air and water quality, etc) or climate change.

The effect is to make almost all human studies off limits for consideration, since the law also requires privacy of human subjects and much of the research on which, say, air quality standards depends was done under earlier (confidentially required) rules. Thus, only phony "science" provided by stakeholders (coal burning industries) will now be considered to set air quality regulations. In effect, the Environmental Protection Agency is now misnamed. The administrators are actually hostile to a safe and clean environment.

This is a strong negative incentive for transparency. Reveal all or be punished/ignored for your work. I hope this sort of thing ends soon.


What is the reason that some departments do not allow PhD students to be instructors of record?

My institution (which is a highly ranked R1 private university) tries to differentiate itself from other universities by advertising that all of our professors teach  and that the undergraduates -- if they choose to come here -- will learn directly at the feet of the greatest scholars in the world (blah blah blah..).

My cynical quip aside, we try very hard at least nominally to ensure this. All professors in the arts and sciences teach their own classes (research staff at the medical school are of course exempt), although some teach less than others.

Very few graduate students are permitted to be instructors of record -- only just a handful of 6th and 7th years are given this right, and only in very focused seminars.

For us, it's a bit of a matter of pride -- what differentiates us from some of the other R1s. But like most things in the neoliberal academy, there has been talk of bringing in adjunct faculty and other changes that will certainly dilute the claim made in the opening paragraph above.


Industry certifications as program entrance requirements?

Is there a comparative analysis of programs that allow industry
licensing/certification versus those that adhere to more traditional
entrance requirements like the GRE?

I am not aware of a formal analysis of the differences. One could probably divide graduate programs into two camps, with some gray area between. In a really general sense, academic research doesn't prepare you for industry jobs and industry jobs do not prepare you for research. Therefore, the two type of graduate programs are research targeted and industry targeted. I would argue that any program that accepts/requires/weights industry certifications falls into the industry targeted camp. The two camps are so different that trying to compare across them is silly.
As to your other questions

How do examinations, such as GSE/CISSP/CISM/etc, compare to the GRE in
terms of overall academic preparedness?
Is there is measurable difference in the comparative difficulty
between the different categories of examinations?
If you've taken both types of examination, industry and academic, is
one class of examination better or worse for gauging candidates, and
why?

Standardized tests in general are pretty rubbish metrics and that is why most admission committees also request transcripts, essays and recommendations. The GRE is likely marginally better at predicting success in research targeted programs and the industry exams will be marginally better at predicting success in industry targeted programs. As for difficulty, it really depends on the experience of the individual. Is an History exam more or less difficult than a Math exam?
Yes, but it depends on the individual. Individuals with an industry background will likely find the industry tests easier than the GRE, while those following a research based academic career path will likely find the GRE easier than the industry exams.


I plan to leave academia for good now. But I don't want to leave to
  live yet the same patterns in industry

You may find industry to be just as bad or even worse. People with power can be very nasty.

  Now, I am at a third lab to finish a thesis project for my degree. I
  thought that this lab would not be connected but recently they had
  been forging new relationships with close collaborators of previous
  supervisor. Things were going well at first in the sense there weren't
  any referential or odd remarks. Recently, however, I'm not so sure I
  can trust them either.

Due to traumatic past experiences, you have developed a "paranoia". It is highly unlikely that your previous supervisor (who seems to be a big shot, with multiple "close collaborators" and a large enough lab that he can treat his lab members disrespectfully and continue to have enough members to sustain his research) has the time or desire to go out of his way to badmouth a former undergrad to a group that is distant enough away that the connection is only through his close collaborators. He might even want you to succeed in this new lab, so that you are content/happy there and less likely to bother him again (asking him for letters of references, making complaints to his university administration for abuse/racism/academic-misconduct/etc.).

However, I appreciate that you will not be able to easily trust anyone anymore. You are vague though, about what happened that made you not so sure you can trust this new lab, so I'm limited in how much I can help you there. But what makes you think you will be able to unconditionally trust people in industry? You may consider also exploring this stack exchange: https://workplace.stackexchange.com/. You may find stories even worse than the one you've described here. Finally, part of your lack of trust for people, is in fact healthy, because as you get older you'll learn that you can't trust many people in this world.

  Has anyone successfully dealt with people like previous supervisor and
  gotten away from them? Any advice is greatly appreciated.

In the comments, I've given my email address and you can perhaps tell me which field you're working in so that I can see if I can help. Sometimes it's just a matter of finding the right lab, distant enough away from the previous one. Luckily this happened during your undergraduate years. While it will be impossible for you to fully appreciate this, you are in the very very early stages of your career (considering you did a masters and two undergrads, I'm guessing you are 1-2 decades behind my colleagues and I, so still very young). This means that the stakes are very low, and there is still a chance for you to have an upward rise in your career, which will help you to forget about all the nasty things that happened to you during your undergrad years. Trust me on this. When you get to my age your troubles as an undergrad become almost irrelevant.


Searching public domain works from a particular scholar

You might like to try Google Scholar, e.g.,

https://scholar.google.co.uk/scholar?as_yhi=1911&q=Condorcet+author%3AFrancis+Galton


infinite/sustainable hosting of a web-interface to a research database

I have the impression that quite a few university libraries are very interested in preserving and making available other things than just books. So talking to your university librarian would be my first stop. Even if your university library does not have expertice in this field, they may know of such a project somewhere else that you can apply for.

As to someone else maintaining the web-interface for you, I would not count on that happening. That will cost someone time and money, and unless you are rich enough (and willing) to set up a fund to preserve your project, you cannot count on someone else doing it for you. Instead I would keep the interface as minimal as possible. It may not look pretty, but it is more likely to keep working.


Appropriate way to discuss genetic conditions in a large lecture?

Poking around the LPA website, I found a list of discussion groups. I think that making a post there would be an excellent way to get feedback from people with the condition and get questions about terminology, etc. answered. The best way to design sensitive education is with the input of the people who it affects. I would also recommend calling LPA and asking them if they have any reference materials that they would encourage you to read.

This essay about where to draw the line when it comes to eugenics, written by a little person, might be a good thing to read before talking about that topic.

This profile of a late Harvard Law professor who was a little person might be another good person to talk about as an example of someone who has led a successful life. However, you should be careful with the tone of stuff like that. You don’t want to present it as “look! Some little people can manage to lead regular people lives!”


Reaching out to journal editors might backfire, I'd be careful with that approach.

Ultimately it's going to be up to your users to a) know how to cite your work and b) decide to do so. You have some control over a): you can display a short note with the preferred citation when the program starts. In the case of an R package, you can use the function .onAttach to display a message when your package is loaded. If it's a stand-alone program, put the message in your splash screen, or on the console, wherever a user might see it.

In the short term, you don't have any control over b), so I suggest you focus on maintaining the program and responding to users as best you can. As we use an increasing number of programs, deciding which ones get cited in any given paper is going to be a bit subjective. If my analysis depends on a bug fix or new feature that a developer implemented for me, they will definitely be cited!

Beyond that, your influence is limited to longer-term approaches to changing practices:

lead by example, so people become accustomed to seeing software getting cited
as an editor or reviewer, request citations be added where you think they should be
promote the idea to your students and colleagues


Possible that one dissertation in Computational Archaeology could earn two degrees?

It's hard to say something is definitely not possible, but I think this is a case where it just really isn't worthwhile. A PhD says you can do research; from there, it's more your research output that matters rather than the title of your degree.

What I would strongly suggest, however, is that you pursue having a mixture of faculty on your thesis committee. The exact rules will depend on your program and graduate school policies, but even if there is a requirement that official committee members come from a particular department, at a minimum you should be able to add some "outside" people who can help advise you in your second research area.

You should also pursue publishing papers in both fields.

Of course, all of this will depend on support from your main advisor, so when you look for particular programs, make that part of your search and part of the early conversations you have about your fit.


Is declining an undergraduate award which causes me discomfort appropriate?

I suggest a third way:

Write a concise e-mail to whoever is handing out the award that you would prefer to receive it silently for the reasons you cited (not wanting to be reminded of your disease), i.e., without being mentioned at the ceremony, but via mail or similar.

This has several advantages:

You spend at most as much energy on this as declining the award, probably less since you do not have to worry about how to politely decline it, etc.
You avoid what you want to avoid.
You will never face regret for not taking the award and in the future you are completely free to use it or not (for your CV and similar).


Where you include the tables is entirely dependent upon how important the information within the tables is for the text.

Three pages of tables are a lot. An average paper is somewhere between 5 and 20 pages, so three pages of pure table in between the rest certainly disrupts the text, which speaks against option (1). Option (2) will force the reader to go to the appendix, depending on how important it is that they actually read the table. If you could extract the key information in text form, you could simply reference the large table and put it into the appendix. Supplementary data is more likely to be overlooked by people reading your article, as they are separate documents that can be found on the journal web page. Therefore, I would only choose option (3) if the actual values in the table are unimportant and the statistics can be extracted in form of text or a smaller table.

You say there are two additional tables that are important for your model. It sounds like these are a case for the appendix. Again, depending on the importance of actual values, they also might better fit into the supplementary data.


What to write in CV when transferring between schools?

The problem is I have not been student at New University since 2010 and I don't want to say that I'm a first year student. Also since I didn't get any degree from Old University I cannot have a separate entry for it.

Why does it matter whether you got a degree from Old University?  There's no rule that says the education section of your CV can only be organized by degree.  You just need to be clear and honest.

What you propose doesn't seem inappropriate, but I think this might be slightly clearer:

2014-2016 (expected) PhD in Computer Science from New University

2010-2014 PhD student at Old University (transferred to New University)

2007-2010 MS in Computer Engineering from Another University


Failed the preliminary PhD exam because the committee members rejected my already accepted publication

The advice to find a different university is probably the best you will get. The standards of the committee are apparently very high, as one would expect.
You could appeal to your advisor or to the committee, but it seems doubtful that any other action would work. Even an appeal to higher authority at the university might result in bad feelings that won't help you get your degree.
See if you can salvage good recommendations from this mess and find a way to move on. It isn't the end of the world. Many students change universities mid-stream.
I actually left one program in a somewhat similar situation: a dispute over a single answer on a prelim exam. I wound up at a better university with a much better advisor.


How to present a degree that was earned abroad on a business card?

I suggest that you present it as it was awarded, and perhaps list the university as well. Most people will accept it at face value, though you may get the occasional question about what it means.

Australia isn't so isolated that it can't accept international terminology.

This would be different if you are in a field that requires certain certification, but that is a question to be directed at those providing the cert.


Is it better to submit a new research grant proposal or an extension of previous work?

There is no one-size-fits all answer. The key factors to consider are: (1) alignment to the funder's mission and (2) credibility.
Alignment to the funder's mission. Different funding agencies have different motivations. Some have a particular capability gap (whether mundane or extraordinary) and want to fund the group most likely to fix it. Some routinely fund well-established university groups and just want to see progress. Others specifically exist to fund high-risk, high-reward endeavors. Whether to propose "incremental" advances based on past research or "revolutionary" advances will depend on the funder's needs.
Credibility. Even for high-risk programs, successful proposals will usually provide a basis of confidence that the proposed idea will be successful (i.e., simply writing down some crazy idea to "extend the boundaries of science" will not be enough). In some cases, this basis of confidence could be the involvement of the proposal authors themselves (due to their publication record or performance on other programs). In other cases, this could be that a proof-of-concept of the proposed idea was already carried out and gave good results.


How to find scientists that cited several of my papers?

You need to first get a database put together of all those who potentially might have cited your work, and the bibliography of their papers.  This is not trivial, esp. if you are in a field where you don't have pre-existing online citation databases for published works.

Are your works available in such a format?  If so, then just do a query which you think will capture all the related papers to your work.  If you are cited in MEDLINE, you can use the "paper like this" as well as exploded MeSH based searches.  Start with the MeSH terms assigned to your work, and spend a little time going over where those show up in the MeSH hierarchy.

Also, how are you defining a specific subset of your papers?  Is this something you know a priori or are you expecting that subsets fall out based on who cited your work?

If your subset is small, and/or you don't have many citing authors, this would  be quicker to just do by hand.  Just build a bibliography from those who cited you (e.g. export Google Scholar/MEDLINE entries, which will have all the authors), and you can then parse that (download them in an XML format and you can probably use XPath/XQuery to do what you need, or see of one of Zotero's report options will help).


Career in applied mathematics after MS in abstract mathematics?

If you already have a Master's degree in mathematics, you should be capable of learning additional mathematics topics yourself. If you are interested in a particular field in which mathematics is applied, you can always spend some time becoming acquainted with that field and the mathematics involved. The Society for Industrial and Applied Mathematics (http://www.siam.org/) is one  resource to get an idea of what's out there. You might look for a smallish project to test the water and pick up some experience in mathematical modeling and, if relevant, computational mathematics. Years ago as a student, I did a summer project on modeling measles epidemics using difference equations. It was a valuable experience and taught me more than merely reading about mathematical modeling in a book or on a website.

You may also wish to bear in mind that seemingly pure mathematics can often end up being very applicable, so you may be able to have the best of both worlds. For instance, Bernd Sturmfels has used algebraic geometry in statistics and computational biology and Robert Ghrist has applied algebraic topology to signal processing and sensor networks.


Note that the article you linked to is a review article. A review article summarizes primary literature, often reporting on the most important findings regarding a particular question or questions being addressed. In reviewing many articles, there may be papers that the author(s) reviewed in order to derive the results and major findings of the paper, but that didn't have anything interesting or exemplary of the major findings to report/cite directly in the manuscript. In that case, the author(s) would still need to cite the paper somewhere because it was part of the data collection component of the manuscript.
Journals may deal with those references in different ways. When feasible, authors may have few enough references such that they fit into a table in the manuscript, or they may report papers used in the data collection as supplementary data. If neither of those options is used, the author must cite those papers somewhere in the manuscript because they were a part of the study, and an "Uncited References" section may be one option for doing that.


How should the CV for the application of a pure math PhD applicant be structured?

I don't think a "detailed account" is necessary for anything that's a standard part of the math curriculum: a simple list would suffice. (Note that this would also apply to any other discipline with a "standard" curriculum, such as chemistry or physics!)

I would not include research interest and test scores, as they may be "restrictive" and turn off potential readers. (Test scores, if needed, must be provided in a more official way than just a CV listing, so you might as well leave it off.)

As for honors and awards and experience, I'd include specific information if it is relevant to your career aims; otherwise, a simple listing suffices.


Reproducible, open, transparent, ethical Research when confronted to (patient) data anonymization : is it at all possible in practice?

Its totally normal practice for patient data to be allowed to be stored only on properly secured, regulated and monitored servers.

In my field (genomics), databases exist where researchers can deposit anonymized patient data, that is not "publically" available, but can be accessed by users that can demonstrate that they have good reason to use the data, that their use falls within the consent agreement and have the IT systems in place to keep the data safe (see for e.g. dbGaP and EGA) by making an application to a data-protection committee.

Code can be written in such a way that no patient data is in the code (loaded from secure locations, etc), so that the code can be shared.


Should I convince my advisor that thesis work is not finished yet?

Working full-time as both a software engineer and a Ph.D. student is unsustainable. If writing a thesis based upon the results you have is likely to suffice (speak to fellow students, read theses of prior students, speak to your advisor), I'd suggest you take that route. Reduce your workload to something more sustainable. Your thesis needn't be your best work; your thesis need only get you a PhD. Graduate, pursue the next step.


Where can I find correlation between US News ranking and IPEDS database?

I uploaded a file to wikisend (free and no sign-up file hosting service) with the correlation.

US News and IPEDS ID

Actually pastebin never expires so here's a link to it on pastebin:

http://pastebin.com/FNEaJ1vC


How good do I actually have to be to get into a top graduate program from an average undergraduate program?

From what you have said about yourself, I think you're very well prepared for graduate school at a very good institution. There are always a few incredibly bright, very young mathematicians that fit the image you have in your mind of students at top tier universities. I know of a few myself. However a very large number of math graduate students are much like you (and I).

I had a very strong affinity for math as a young child but grew up in one of the worst academic environments in the US. A highly nontrivial amount of students in my area didn't graduate high school, even fewer went to college and fewer then even went to universities that were not the crappy local universities. I lucked out because one of the best high schools in the nation was in my area yet I didn't feel very challenged and more or less coasted along and didn't try. Ended up with a GPA of about 3.0 at the time of graduation. I even spectacularly failed statistics with a 40 or so from lack of effort.

Undergrad rolled around. I flourished in the environment: took lots of math classes, took plenty of courses outside my degree to broaden my horizon, did lots of research, but like you I was a big fish in a small pond. I felt similar to you - that I only looked good in comparison to all of the others. I almost had a 4.0 in math and had a 3.8 overall with a couple of years of research under my belt. When it came time for grad school applications, I cast a bit of a wide net, but got rejected from a lot of universities. (This was largely my fault since I seemed to mess something up on every application. Having not really done undergraduate applications, I was a bit overwhelmed and scatterbrained.) I actually got into my top choice university which surprised me a lot.

When I started my master's, I did notice that there was a bit of a gulf between me and the other students once I got there. My undergraduate institution didn't have nearly the course selection or resources that the other students had. However in terms of math capability, I was at least middle of the pack; so while I had a bit of a learning curve and some growing pains, I think I ended up being one of the stronger master's students because I fully dedicated myself and didn't give up. I did spend a ridiculous amount of time in my office the first semester, though. I went to school around 9:30 in the morning and went home at midnight many days.

For all of it, I grew incredibly and am doing quite well in my PhD program. Coursework is a cinch now, research is going well and I'm writing up a couple of papers which I hope to submit in the not-too-distant future. With your background and love for mathematics, I think you'll be in a much better position than I was in terms of applications. Your GPA is better, you seem much more fluent in many areas of mathematics and are much more mathematically mature. The biggest factor in determining your success (outside of pure genius - which is incredibly uncommon, even amongst mathematicians!) is your unwillingness to give up. Even if you're slightly weaker than some of your future fellow graduate students right now, once you get there, all of those disparities will quickly melt away if you put in the time and effort. Where you came from does not have to dictate where you end up. You are more than your past if you allow yourself to be.

Here is some general off-topic advice regarding grad school since you seem to be lacking in advising: just because you want to go to a top tier university and get in to one does not mean you should necessarily go. For undergrad, this is not the case; if you get into MIT, Stanford, Harvard, etc. and have the financial means, you should definitely go as it is a great opportunity and can directly impact your future. At the graduate level, things are so much more nuanced. (For example, the reputation of the university doesn't directly dictate your future success provided that you put in 100%. In the internet age, it is much easier to do really meaningful research and network with top researchers at any respected university since you have access to all of the information you want.)

When you apply, you are not applying to the university more than you are applying to a professor (or professors) or at least this is the philosophy I think one should have. You should have an idea of what kind of things you want to pursue for research and you should look to those people who do research in that direction. I don't mean to say that you need to know exactly the project you want to do but have a rough idea of the field you are interested in, say commutative algebra or functional analysis or harmonic analysis. If you apply to a university in which no one really pursues what interests you, you're going to be without a future advisor or you'll have to settle for second best. Applying to a graduate program just because of prestige doesn't guarantee success or happiness. Granted, at the top universities, this tends not to be an issue as they have very broad reach but it is something to be wary about. Just because it is a great university or great department does not mean it is a great fit for you.

There are also other factors to consider when applying to schools: Could you deal with the super competitive atmosphere (or alternatively the extremely laid back atmosphere)? Could you stand to live there for four to six years, e.g. if you're from a very hot climate, could you survive the very harsh winters in upstate NY or if you're from upstate NY, could you handle a Texas summer? If you cannot see yourself being happy with (or tolerating) a lot of these extra-academic aspects of where you are, you might want to reconsider.

A PhD is very demanding and can be soul-crushing at times. You'll often run into really difficult road blocks in coursework or research and if everything else in your life makes you miserable as well, you're going to have a really bad time. Your mental health is very important. You will be pushed to the extreme at times and in many ways throughout your PhD and your environment shouldn't amplify this. If you're having a tough time in research, the weather is absolutely miserable and you cannot stand your fellow graduates for whatever reason, your mental wellness might take a turn for the worst. I have seen this happen first hand and it is really unfortunate. These are not things academic advisors often tell students who wish to do graduate school because they are easy to overlook, but it is something to keep in mind. Hopefully this has been helpful.


Plagiarism of former supervisors copying from my master thesis

I can accuse my former supervisors of plagiarism, contacting the editor of the journal and proving that a very large portion of the paper is taken from my thesis, which is not cited. Although my thesis is not available online, the authors could have included it in the list of references, and I can prove that they have a copy of it;

Yes, you can do that.

  I can ask to be included as author of the paper, since most of the work published is based on my master thesis, and not only the "simulations", as the authors wrote in the acknowledgements.

Yes, you can also do that.  Based on the information in the question, you should be an author on the paper.  I suggest you contact your supervisors and ask them to fix the author list first.  If that is unsuccessful, you should follow your university's grievance procedure.  Contacting the editor should be the last resort.


To answer the "who funds a company" question, which is not the same as "who funds a study":
Real biotech companies are usually pretty easy to get information on. Take Editas for example. Lots of information there about funding cause it's a real company and it helps make investors less nervous when there's transparency (and they can see other real investors have skin in the game).
Your example has no public information because it's not a real biotech company. It's a shell company that's brokering IP in a way that probably relies on "Political connections", which often means something that is poorly distinguishable from bribery. Any public information is just more ammo for a US attorney if they start poking around.


How to evaluate a postdoc offer, if I'm not sure I'd be able to do the work?

A postdoctoral position is first and foremost advanced training that prepares you to be an independent researcher above and beyond the training you received as a graduate student.  Your postdoctoral training should incorporate material that you are unfamiliar with, and a training plan for you to learn that material.  If you are concerned that you barely understand the research project, I would recommend identifying specific aspects of the project you are unfamiliar with (background literature, methodology, unanswered questions, etc) and talk with the PI about how, if you accepted the position, the lab would set up a specific training plan for you to learn that material.  I would only decline the position if they seem unwilling or unable to provide that training.

Personally, I struggled with the same concern when I started my post-doc, but my postdoctoral PI repeatedly reminded me that she hired me not because of what I already knew, but because she knew I was excited about the field and was confident I could learn. I've been productive thus far, and feel well positioned for the coming job search.  Plus, now I have distinct skill sets from my predoctoral and postdoctoral work, which helps distinguish me from others in the field.


Referencing a mathematical result already obtained

Since your proof is essentially the same as the proof in the literature, you have to state a good reason for including it anyway. Something like "although this argument has already appeared in [citation], we include a proof to demonstrate its connection with our other results, and also for completeness." But the longer the proof is compared to the length of your paper, the less valid a justification like this will be. If this proof takes up more than say 25% of your paper*, I recommend removing it, and simply mentioning the relationship between that theorem and your other results. There's nothing wrong with short papers, if the results are good.

Either way, understand that your paper will be judged on what's new in it, and write your introduction accordingly.

*People may disagree with this number in either direction, but it gives you a rough idea. Certainly 50% would be too much, and 10% is probably fine.


Where to submit an article of applied maths for physics

Remember that J. Phys. A and J. Math. Phys. are quite top journals and they reject lots of reasonable papers not because they would be off-topic but because they are "not good enough for them" (whatever that means).

IMHO, if you feel that your identities are something completely new to the world of maths, you should find a reasonably good math journal, because they are likely interesting to math people as well. On the other hand, if you feel that the results are interesting only to (theoretical/mathematical) physicists, go for a journal in this branch.

I don't know any mathematical physics journals personally.

For math journals about identities/symmetries in PDEs, you can check the list of publications in MSC class 35B06. For the mathematical physics journals, I suggest trying to find the proper MSC class in the MSC catalog, there you can see which journals would be suitable.


Chances of getting admitted to USA universities for Fall 2021

This is going to depend on your field, and the schools that you apply to and what their individual situation is, among other factors.  As someone in the US, that's also not to say that things won't be competitive in Canada or Europe either, as there are Canadian universities, as well as possibly European universities, that are just as reputed as some of the top universities in the US (at least as far as what I know in my field), so it's a flawed assumption, at best, to assume you'll be admitted to a program if you apply to Canadian/European universities.
The only advice I can give would be to contact the programs you are interested in and ask what their situation would be for the upcoming admissions cycle and if you're better off applying in a future cycle.  What I will say is that graduate admissions is generally competitive and a crapshoot no matter what the timing is.  Therefore, if you want to apply to US universities, and see where you get lucky/hope for the best, since the worst they can do is say no.


Suggestions for working effectively with international students from a non-western culture

I have found communication to be a problem and I strongly sense it has cultural roots.

I think this is the first point to start with: Try to find out if your sense is right here and try to identify what kind of cultural difference may be the cause. In fact I am not sure if cultural differences are really the only (or most important) problem, but you may well be correct. However, there are very different cultures also in east Asia and also in the same country.

One thing that I have heard of is that in some Asian cultures it is impolite to ask questions to a professor (because it somehow shows that she did not explain things well). It may well be considered impolite to try answer questions for which the answer has not been well prepared in advance. (If this would be the case, you could, in principle, think about preparing questions in advance and hand them out a week early.)

If discussing of unprepared ideas is really important for the class, I am not sure what you could do. You may consider collecting different styles for the class such as

participants present prepared thoughts on homework questions in written form as a hand-out or orally (or both),
prepare handouts for some topics and distribute them in class, then let the participants work on them alone (or in groups), let them prepare statements and collect the statements,
have open discussion (prepared or non-prepared).

In any case, communicate the different modes clearly to the students, i.e. explain what they have to do, what you expect them to deliver and what (besides the actual content) they should learn in class. In this way you may get the message across, that "discussing" (and comparable skills) is really something that you expect the students to learn.


Pursuing other PhD offers, after accepting one too early

Policy Answer

As both an answer to this question and as a PSA, most major universities in the US are signatories to the "April 15th resolution," which gives students until April 15th to accept offers of admission/financial aid. A full list is here: http://cgsnet.org/ckfinder/userfiles/files/CGSResolution_RevisedOct2017.pdf

As part of that policy, most relevant sections bolded:

  In those instances in which a student accepts an offer before April 15, and subsequently desires to withdraw that acceptance, the student may submit in writing a resignation of the appointment at any time through April 15. However, an acceptance given or left in force after April 15 commits the student not to accept another offer without first obtaining a written release from the institution to which a commitment has been made.

Assuming the universities you are interested in are on that list, then, you can still change your mind according to policy. What remains to consider is the personal relationship with the institution/professor whom you have already accepted an offer to.

Interpersonal Answer

The institution itself is unlikely to care all that much since you are likely one of many graduate students - but do inform them quickly once a decision is made. Ideally it is most polite to give them as much time before April 15th to offer your funds to another prospective student. This might be different if it's a smaller program. Some professors at the institution might be a bit offended, but many will also understand the attraction of a fellowship over an assistantship, especially if the fellowship comes with any prestige. If you have accepted a position with an individual professor, that person is the person most likely to be offended, but this will depend entirely on their personality and how much stake they had in bringing you to their lab.

The ideal course of action would have been to wait to accept anything until you had all possible offers in-hand. It's unfortunate that no one gave you this advice while you were applying, but somewhat understandable that you would make this mistake simply because people don't typically apply to graduate programs more than once or twice in their lifetime.

Personally, I would probably not inform the school where you accepted simply that you are interviewing at the other school to avoid causing bad blood if you end up staying with the initial offer after all, but if you change your mind you must inform them immediately.

For your particular situation, consider also the duration of the package offered and the field you are in - a fellowship is nice, but in some fields a research assistantship effectively pays you to do your own research, and is only marginally better than a fellowship (besides any prestige of the fellowship). A one-year fellowship may be hardly worth changing your university choice. In other fields, a fellowship is a huge deal because RAs are not typically part of your personal research and degree progress.


In my experience (in math, in the US), no you cannot remain in your current position (for long).  While tenure is historically a means of protection for faculty from political forces, and thus a tool to provide academic freedom, pre-tenure periods often function as a sort of long-term provisional hiring period to make sure you're right for the university/department and getting tenure is sort of stamp of certification of your worth to the department and university.  So if you fail to get tenure, the reason is typically because someone decides you're not performing well enough in your current position.

That said, the university will typically give you another year in your current position which gives you time to look for jobs elsewhere.  People who don't get tenure usually move somewhere else, or have trouble getting another job.

Note: Sometimes people go up for tenure early (before the specified date in your contract).  I don't know what the standards are for consequences of not getting tenure then--when I've seen people go up early, they got tenure.


Reply an email from a potential professor?

This is a positive response in that you can apply to take the entrance examination and you can also apply for a scholarship.

There is no automatic position granted or stated for you, so you have to follow the enrollment process for entry in Fall 2021.

You don't have to reply to this except perhaps to say "thank you for the information, I will (or will not) be applying for admission for the fall 2021.

Up to you if you will apply.


Master's Thesis - using wikipedia contents in application

In a thesis you must reference any material/code that you did not solely created.

So in your case, I would suggest in the the background chapter, explain, the used data gathering techniques (e.g., using an API), and then add all the required references into it. So in later chapters, the reader knows what are these data and where they came from.


Travel reimbursement and "bonus programs"

Unless the funder has a specific policy (which they should tell you about), common practice is that "reward points" (including frequent flyer miles, etc) are yours to keep, and don't deduct from your reimbursement.

You're right that there is something a little shady about this, but basically, nobody has figured out a better way to handle it, and travelers are used to keeping their points and would get mad if they weren't allowed to.


How to evaluate potential advisers on grounds other than their research/publications?

There are a few things I would generally look at in a potential advisor beyond just their research/publications:

Who were the co-authors on their papers? Are they actively collaborating with people in your field - people who could be potentially useful for post-doc posts, etc.? Do their students often show up as primary authors on publications, or are they invariably buried in the middle of a long list of authors?
Personality. This goes beyond just do you like the person. Do they prefer frequent updates, meetings and the like, or is the occasional check-in enough? Are they a morning person and you prefer working nights, or the other way around? If you send a long email, would it get answered, or do they not often fail to answer emails? I've had some professors who I'm very fond of nevertheless would make poor advisors because of wildly disparate working styles.
How are their students funded? Your funding stream can have serious impact on your completion time and productivity. If every semester, its a desperate Pick-N-Mix of funded side projects, TAships, etc. you're going to have a lot on your plate that, while potentially an interesting experience, will slow down your progress.
Where do their students end up? Do they have decent career trajectories? Are they supportive of alternative paths like industry or government?
Rank and age. A young professor might be more aggressive and eager, on the other hand they're less established, don't necessarily have the same level of institutional support, and if they're not yet tenured, its possible they'll disappear. An older professor may be more established and stable, but might not use "cutting edge" techniques, or feel less of an internal drive to publish.


What are "Rare research subjects" ("Kleine Fächer")?

From the detailed description of the call:

  The so-called "rare subjects" (Kleine Fächer) often represent a comprehensive, significant and future-oriented canon of knowledge that is highly relevant for interdisciplinarity, internationality, and innovation.
  […]
  At the same time, these subjects are often characterized by precarious structures within universities.
  Above all, the human resources in these subjects are often scarce; there is a lack of structural sustainability for research and higher education.
  Moreover, they are particularly vulnerable to changing orientations in higher education policy, but also to socio-political change.

  […]

  The assessment will be based upon a comparative
  weighting of the following criteria:

  Does the proposed strategic concept focus on a “rare subject“? Is it about precarious knowledge?
  […]

So, the main criterion is that the subject is so small that it is “endangered” to die due to budget cuts and similar.

On the website of the call you can find a link to a conference on the subject, which in turn links to Portal Kleine Fächer (so there are other people using this term). This features a list of rare subjects, such as:

Albanology
Applied nuclear physics¹
Crystallography
Mining science
Rhetorics
Sign language
Film studies
Glaciology
Forensics
Medical physics¹
Ethics of medicine¹
History of science

As for distinguishing these subjects from subfields of other fields, that site’s definition particularly requires that the subject in question considers itself an own field, having its own societies, journals, and particularly own curricula at university level.
So, your typical specialisation of a big subject does not count here because practitioners of such fields first start the big subject and then specialise as opposed to studying the rare subject as they enter university.

In colloquial German you would rather call these Orchideenfach, but I suppose practitioners of the subjects avoid this term due to its negative connotations.

Please mind that I am mainly describing the usage by relevant sources and quote their examples. I do not completely agree with this.

¹ For which it is unclear to me how they meet the definition given by the site itself, despite having one of the respective institutes next door to me and having specialised on another of the fields to some extent.


Most university IRB's won't involve themselves in research that isn't conducted by employees and students of the university.  The alternative (widely used by pharmaceutical companies) is an "independent IRB" (the term is an oxymoron since the IRB isn't part of the institution that is doing the research...)

See the consortium of independent IRB's web site for some information about these IRB's.

http://www.consortiumofirb.org/


Using my published work on another paper

You have two options. If what you want to do is exactly what you would do if the previous paper were by someone else, then just do that. Quote yourself as if you were another author and give appropriate references.

However, if you wish to go beyond that and you have yielded copyright to the journal that published the first paper you need their permission - as stupid as that sounds.

I expect that most reputable journals would give you permission (in writing, of course) since the work is yours.

If you retain copyright though, you can copy it freely, but still reference the original.

Well, a third option, is to just create a new diagram without reference to the old one, even if that also seems stupid. The simplest thing, though, may just be go send readers to the other paper for the diagram.

Copyright law is a minefield. Self-plagiarism is a thing.


What happens if I get a grant for my PhD project but I decide to quit and start another PhD somewhere else?

Of course you are not forced, nor obliged, to finish your current project.

But it might very well be that, depending on your grant conditions, you will have to pay back the grant money, fully or partially, when you do not finish the project.

Furthermore, it might be wise to try to keep being on good terms with your current professor and colleagues. This is most likely achieved by involving them in your decision and motivations (which you might already be doing, as you write in your question).


How to approach a PhD if I want to have a career in academia?

If you want to stay in academia, these are some of the elements that prospective PIs/Institutions will be looking for: 1) published material; 2) conference participation; 3) ability to attract funding; 4) prizes/awards (although this should be of low priority if you are an early-career researcher, given how unlikely it is to get a prize at that stage). You should also focus on showing that you can have original ideas and that your PhD wasn't simply doing what you have been told to do. Other thing that is important, and I cannot stress this enough, is networking. No matter how ridiculous or incorrect it may seem, the people that you know will make a difference in getting jobs and positions.


I asked for a graduate student position from a professor. He replied "welcome". What does that mean?

I'd be a bit wary of working with this person if this is really them and is really their communication style.

20 minutes is plenty of time to determine a student is not a fit and to politely deny them. 20 minutes is not really enough time to commit to supervising a student.

This level of communication might be typical from some professors, but I think those are the worst to have as advisors:

  "What do you think of my research ideas?"

"Good"

  "Where should we try to submit this paper?"

"Journal"

  "I'm worried I'm not making progress towards my thesis"

"Ok"

I would look at the admissions process for this university. If the process is such that you need to have some professor's sign off to apply, then maybe that's all they are trying to convey: that you get their sign off, and they aren't putting more effort in because the application process tends to winnow students.

In that case, clarify they are willing to sponsor your application, and go ahead and apply, but make sure you get a chance to meet further with this person before you take them as an advisor, and continue to apply elsewhere: you should not take this as a sure thing by any means, nor should you be sure yourself. If there are other people there you are interested in working with, by all means contact them.

Good luck.


Why do papers not have a table of contents?

The purpose of an overview paragraph and a table of contents are different:

The table of contents serves to quickly find a specific section of a document so you can start reading there or extract a specific information. This is something that rarely makes sense with most papers, except if you start at the conclusion/discussion, which is however easy to find anyway. Even if you want to do this, finding the table of contents would cost you more time than it saves you, given the shortness of most papers. So my answer to your titular question would be: Because there is no need for it.

The main exception to this are long review papers, which however usually have a table of contents.
The overview paragraph serves to briefly summarise the paper and explain its semantic structure to the reader, usually somebody who is reading the paper from back to front. This serves to address certain expectations the reader may have had after the introduction (“don’t worry, we didn’t forget this important aspect”) and draw connections between sections (“our work in Section 3 provides us with a framework to evaluate our method in Section 4”). All of this is not possible in a table of contents.

Now, some papers just have a straightforward structure, and there is nothing about it that needs to be elaborated to the reader. In this case an overview paragraph would indeed be nothing but a written-out, tedious-to-read table of contents and should be skipped in my opinion.


When is it okay to publish when doing enterprise?

The results have undeniable commercial potential

You don't mention which industry you work in, but within the industries I'm familiar with, companies own everything that comes out of their employees' brains.  By default, your ideas, techniques, code, and results are almost certainly the property of your employer—even if you developed them at home on your own time using your own personal equipment— and they may not be inclined to let you exploit them commercially.  Read your employment contract very carefully.


Obstacles in job hunting for US citizens in non-US nations

There a multiple levels on which this problem operates. This is especially true for places saturated with immigrants. (For instance, USA with Indians/Chinese)

Getting the Job

This problem itself has a million subdivisions. Firstly, it is fairly difficult for immigrants (who studied in that country) to get jobs without exhibiting something really outstanding. The problem is not so bad for sectors such as computer science and electrical engineering wherein professionals are required by the dozen. The problem, however, is really bad in areas such as Theoretical Physics or Chemistry (or basic sciences). With limited vacancies and a million outstanding candidates, it is really difficult to crack that "top job".
Working in Sensitive Sectors

I don't even want to get started on sectors like Aerospace. More often than not, graduates from the top universities in USA and Europe have returned to their homelands because all companies stress on citizenship. For EU, it is fairly difficult for a Non-EU resident to get a job in the first place, add to that defense and secrecy and you have a useless degree. In USA, it's even better, if you graduate with a PhD in Aerospace Control Systems from say, Stanford, you are still worthless for US companies because they don't ask just for citizenship anymore but also Top Secret (or Lower) Security Clearance! That's at least 10 years for a foreign citizen.
Immigration and Visa

Getting a job is one part, getting the necessary immigration documents cleared is another. I mentioned about Aerospace engineering being a potential problem as far as jobs are concerned. But thats not all! USA has published a list called the technology alert list which requires screening of candidates before granting a visa.

The immigration laws in the Europe aren't very friendly for Non-European to begin with but as far as I know, they don't maintain a strict segregation between "things non-citizens can't do" and "things they can". However, rising far-right politics, things don't seem to get any better in the future.


Is this plagiarism or just a bad practice?

Referencing your source, but in a somewhat ambiguous way, does not open you to charges of plagiarism.

It's good to want to get this right, and the first example you give is slightly less clear than it could be.  However, given that you have referenced your source right in that paragraph, no one is going to think you are plagiarising.  This is an minor issue of style and clarity; it comes nowhere near academic misconduct.

The repeated references in your second example remove the ambiguity, but they are rather annoying and distracting to the reader (though it is less of a problem in more concise style conventions).

To cite a source for a whole paragraph or section of text, add an introductory sentence and then put the reference there.

This will make it clear that the source was used for the whole discussion, without needing to repeat yourself.  It also tends to be clearer, better writing in general. For example:

  The blah blah blah website is one example that illustrates this phenomenon (Smith 2010, p. 1-2)  One can use this website to write about various activities and interests such as music, art, science, etc... and one can also get in touch with the founder. However, to use the website, a person has to register and pay a fee. The website founder is known for his IT expertise. More people are joining nowadays than ever...

Or something like.

  Smith et. al. provide a description of the website functionality (Smith 2010, p. 1-2).  One can use this website to write about various activities and interests such as music, art, science, etc... and one can also get in touch with the founder. However, to use the website, a person has to register and pay a fee. The website founder is known for his IT expertise. More people are joining nowadays than ever...


Junior professorship (W1) in Germany without full German proficiency

You can certainly apply. I don't think German language proficiency will have a major impact on your chances, as long as your research record/profile is good and you are able to at least understand some German in case a student asks in German. Computer science students usually need to be able understand at least some English...

I disagree with earlier posts that you would be "expected to give undergraduate-level lectures". On the contrary, they would usually prefer you to give smaller (=specialized) classes until you have some more experience... Sometimes, you can find this in the advertisement.

However, German academia is very competitive!

We do not have a lot of professor positions, and it appears quite common to take 6-12 months to fill a position (make that 12-24 months for full professor positions)... according to Times Higher Education, Germany has the worst student-to-professors ratio (source). You may say, the German system is very efficient. We have few professors, yet we have a very high output of very educated people!

As far as I can tell, you need to:

be the best match for their plan
have had some third-party funding
have a strong track record (papers in top venues, awards, 100+ citations)
have been at different universities
have some teaching experience
convince them in person

So don't be surprised if you don't hear anything back (not even an invitation to present) on your first applications. Maybe you will get a negative reply after a year or two, when the new professor has arrived at his position. Maybe not even that. So, do not wait for an answer when you apply. Continue sending applications and making backup plans.

There is a reason why Postdocs ("Mittelbau") complain a lot in Germany (according to a recent study, even 50% of Junior Professors consider quitting academia because of the lack of perspective - most junior professor positions are currently not tenure-track). They do a lot of the work (both in research and teaching) and usually have only up to three years of work contract.


I would look for new positions at your university. There's no need to sound the alarm. It's pretty common for students to rotate around different labs during the first year and then make a decision at the beginning of the second. Where I did mine, they had a soft requirement that you had to do a rotation in at least 2 labs before you were allowed to decide.

Getting involved with the right project is (arguably) the single most important decision you can make to set yourself up for a successful PhD. If it takes you an extra 6-8 months to find the right project for you, then that is absolutely worthwhile. I had a friend change labs after 2 full years of working on a project. I thought he was crazy but he was able to find a different project in another lab and received his degree, just the same as the rest of us.


Can I ask my supervisor how long would it take to complete my PhD before beginning my PhD studies and post getting acceptance letter?

This question doesn't really make sense, the supervisor has relatively little control over how long it takes for a student to produce a thesis.  Questions you could ask which do make sense:

How long is funding guaranteed, and in practice what happens when students run out of guaranteed funding?
Do you have any additional standards or requirements for a thesis, such as requiring it to include an accepted paper, or requiring it to consist solely of singly-authored material?
How long have your students typically taken to graduate, and what factors played a role in that time?
How does a students career choices effect your advising process?

(The reason the last point is relevant is that if you want a research job it's quite simple, if you have good enough research to get a postdoc and you've actually written pages then you'll graduate.  But for a student with teaching or industry career goals there's more flexibility in trying to get a student out more quickly with a more minimal thesis.  Some advisors may be more understanding about a student's prioritizing getting out quickly for career reasons rather than produce the most compelling thesis.)


How are office hours for PhD classes different from office hours for undergraduate classes?

At every level of education, the purpose of office hours is to give students an open-ended opportunity to discuss the material that they are learning with their instructors, and particularly to get help and clarification in their understanding.

As an instructor, I found it greatly frustrating when students (or any level) reduce this opportunity into simply asking for help on homework questions.  I believe there are many other instructors who feel the same. In fact, I felt so strongly about this that I personally had a policy of refusing to help with homework questions per se, and would instead offer to work a related but different problem in order to try to get the student to learn the material rather than just solve the problem.

I find this attitude most widespread amongst undergraduates, but many graduate students have it to.  Hopefully, you are actually interested in the material that you are learning, rather than just your grade.  That attitude, then, can easily translate into requests for help that are about the material, rather than the problems.  For example, consider:

"Can you help me with problem 5?" vs.
"Problem 5 made me realize I don't really understand Urysohn's Lemma.  Can you help me understand that better?"

Whether graduate or undergraduate, if you ask questions of the second sort, any good instructor who cares about their students' learning is likely to appreciate it.


Can a postdoc change his/her supervisor in Sweden?

(I'm faculty at Chalmers University of Technology, a well-known private university in Gothenburg, Sweden)

The pragmatic question (whether it's a good idea to change supervisors mid-flight) is covered well by posdef, I'll focus on the legal angle here.

As you mention, PhD students have quite some rights in Sweden, but this is mostly because they are in a special type of employment largely governed by Swedish university law. This is not the case for postdocs - postdocs aren't students and they are not faculty (for which the law also knows some special privileges). Fundamentally, postdocs are just "employees", similar to research engineers, secretaries, or university accountants, and hence their tasks, rights, and privileges are exactly what the university has defined in their job profile. At Chalmers, I am not aware that there is any formalized "right" to be assigned a different supervisor. I suspect the situation in other universities is similar, but you may want to check your own contract first.

That said, and to echo the other answers a little, changing your supervisor is hard. Really hard. Even as a PhD student, when the law is on your side. Funding is a huge issue, but so is the fact that faculty tends to be sceptical of taking on students/employees where one of their colleagues has already made bad experiences. As always, there are exceptions, but in general you should figure out which faculty would take you on and take over your funding before talking publicly about changing supervisors. It's better to have a normal working relation with a supervisor that is not ideal, than to have an advisor who has been assigned by the department because nobody else took you on.


No Letterhead or official email id for Letter of recommendation

It's fine for the professor to use an email address and letterhead from the college where the professor works now.


Masters Admissions and Academic Dishonesty

However, in light of the academic dishonesty I'm not sure how it will affect my application, or if it's something that's redeemable?

From a graduate admissions point of view, relatively speaking, having a note on your transcript concerning your academic dishonesty violation is not as bad as being kicked out of undergraduate studies altogether (as noted in this answer here to the following question: Is it possible to do a Master's degree without obtaining a Bachelor's degree?).

So, your school is giving you another chance. It's up to you now to make the most of your remaining time in your undergraduate studies. In my view, here are some things you can do to improve your chances of admission at the graduate level:

Do really well in your remaining coursework.
Take up a research project (or two or three). You should do this anyway if you are serious about graduate studies.
Build a professional network, such as professors for your courses or your research project advisor. In addition to helping you become a better student/researcher, these folks will come in handy when it comes time to submit letters of recommendation along with your graduate studies application materials.

You already took some time off from your studies to reflect on your actions, but it bears repeating: Don't dwell on this indiscretion. All you can do is move forward and utilize every bit of time you have left in your undergraduate studies to increase the odds in your favor of admission to a graduate program.

Edit: OP mentioned that they are an RA, but my 2nd bullet point above is added for future users in a similar situation.


What to do when professor denies authoring an extremely negative letter of recommendation?

I think the question is unclear, so I'll try to cover all the scenarios.

If the professor is claiming that he submitted the positive letter and someone sabotaged it, then he should be very concerned that someone is falsifying letters. He should take the lead in helping you get to the bottom of this. If he says "oh well, someone sabotaged my letter but I don't care", then I would question his honesty.
If the professor is claiming that he did not author the letter at all, then it would seem that you've caught him in a lie. (This doesn't really make sense to me; doesn't the letter have his name on it?) Best to find another referee; if possible, you could even try to switch out the letters on your in-progress applications.
If you're not sure which of these is the case, you could express your concern that a letter was incorrectly submitted on their behalf, and ask for their help in fixing it. Or, if you have another referee, you could just try to swap them out without involving this person.


Ask the author of a paper for suggestions of where to publish replication results

Scientific method is based on the idea of reproducibility. So being able to replicate experimental findings, or not replicate them, is an important contribution to your community. Of course it would be more groundbreaking if you were NOT able to replicate results, as that would be a sign that there is more to learn. But even a mere replication using independent data would be make a solid paper. And of course, it matters all the most if the original paper found something really exciting.

It is a bit different for "theoretical" papers as putting forward ideas when somebody else did it already, does not add much to the community understanding. Unless you derived the same conclusions starting from very different assumptions, or following a very different path, replicating theoretical ideas typically does not warrant a publication.

As for what journal, again it depends on whether you are using independent data/though process, and how relevant was your original result. You could aim for the same journal of the original paper, and if that fails, aim for something just slightly lower in ranking, and more field-specific. Good luck!


What behaviors (desirable or not) are encouraged by an incentive system based on publication throughput?

This is a terrible question, because it presumes that publications are the goal of science, as opposed to an indicator of actual meaningful intellectual contribution.

Therefore, I will provide a solution that proves the metrics are meaningless per se:

Generate a sequence of N meaningless papers using Sci-Gen.
Have each of the meaningless papers cite K of the other meaningless papers in the sequence.
Identify a set of crap journals that do not perform meaningful peer review with the aid of Beall's list.
Publish the meaningless papers in series in the crap journals, thereby obtaining an i10-index of N and an H-index of K (assuming N>=K>=10).

If self-citations are excluded, then enlist (or fake) a colleague to do the same and cite each other's meaningless papers rather than one's own.  If Journal Impact Factor matters, then sequence the papers over three years.

Citation metrics are the shadows on the wall of Plato's cave.


Are references with indication of page number uncommon in computer science?

Specifying which part of a long book or article you are referring to in your citation is a sound practice, but in general section, theorem or equation numbers are more common than page numbers for this task: [52, Section 3.5] or [52, Equation 3.23] rather than [52, Page 132-134].

Personally I use page numbers only as a last resource where nothing else is available: that is, when the section or equation I want to refer to does not have a number of its own.

I do not have a compelling reason for this, if not that section numbers are more robust to minor pagination changes, but this is the behaviour that I have seen more commonly.


How detailed should my review of a very poorly-written manuscript be?

I view my job as a reviewer to be about triage and the "first order" issues with the manuscript.  Thus, for a very good manuscript, I will point out minor copy-editing issues, because those are the first-order issues remaining.  For a not-so-good manuscript, I will note if the manuscript needs language editing but focus on the scientific issues instead, because any specifics of copyediting are likely to be obsoleted in any case by the larger repairs that are necessary.


Undergraduate research in math, but no research paper, will this hurt me in graduate admissions?

Speaking as someone in field not too far from yours:  sure, it would help if you had done all of the stuff you've listed and written a paper about it.  But having a bunch of conference presentations under your belt (oral and posters) is still pretty impressive;  and there are many applicants to Ph.D. programs without any research experience at all.  The fact that you've done research, and that your advisor thought it was worth presenting at multiple conferences, is a pretty big item in your favor.

Oh, and it should go without saying that this professor should be one of your recommenders (absent any major falling-out or other complicating circumstances.)


Withdrawing paper from a conference after presentation due to error

You are overthinking it. A simple note is all you really need. "The paper needs to be withdrawn as we have found a serious error that we don't believe can be corrected in time for the conference."

This won't have been the first time that a paper has been withdrawn. It is a matter of scheduling sessions for the program committee but some of the members are probably familiar with that. There may be some scrambling, however, if proceedings have already gone to press. But they should have copyrights in order before that happens. If they don't, then it is their problem, not yours.

No, you don't need to detail the error, just that it exists and that you don't have a ready fix. If the conference is part of a continuing series you may have it ready by next year (or whenever).


If I drop out of a PhD program, do I have to pay back the university?

It would be almost unheard of in the US for you to be asked to pay back money in such an arrangement. But note that you are probably paid monthly, and if you quit in the middle of a year, the monthly payments will stop then, and you won't see the entire amount.

You aren't promised the total, but only an amount that will come to that total if you see it through.


Is it common practice in the US for students to propose master thesis topics themselves, or do labs have a list of topics to pick from?

It's usually somewhere in between: the thesis topic is negotiated between the student and advisor.

Usually an advisor will have some topics already in mind, and can suggest them. The student can also suggest topics in which he or she is interested, and the advisor can decide if they would be appropriate. In the end, of course, they both have to agree.

It could also fall closer to one end of the spectrum or the other, depending on the advising style of the advisor. Some advisors might insist on one of the projects they have in mind, as they may not have the expertise or interest for any of the student's suggested topics. Or they might think the student's suggestions would be too easy, too hard, too obscure, etc. Other advisors may not have many topic ideas of their own, or consider that it is good experience for a student to find their own topic.


I am a first semester math PhD student who needs to transfer to a different school: how should I talk about my current program on applications?

While the notion of "transferring" has genuine substance for undergrad programs, and in many cases can be accomplished easily or even automatically, graduate programs work differently, certainly in the U.S. That is, operationally, there simply is no notion of "transfer" beyond applying to the program on an equal footing with everyone else. That is, the fact that you were admitted to one program does not guarantee anything about subsequent admission to some other program.

Even though grades will not be available by the application deadline, you can have them sent when they are available. Often the admissions committees don't really look at applications until (e.g.) January even when deadelines are in early December.

You'll also definitely want letters of recommendation from the graduate program you're in now, in part to allay potential suspicions that things were going badly for you so that you needed/wanted a fresh start.

In particular, such applications routinely require transcripts from all previous institutions, and this would include the place you've just begun the program.


What is the the history of Qualifying Exams in the US?

In the United States, Ph.D. qualifying exams or quals (also called comprehensive exams or comps, preliminary exams or prelims, and other terms) date back to the late 1930s and proliferated in the postwar period, according to Leonard Cassuto (Chronicle; also noted in the "Comprehensive Exams" chapter of his book The Graduate School Mess):

Comps seem as old as graduate school itself, so that tampering with them might appear the equivalent of rewriting the sacred scrolls. But comprehensive exams in the United States date back only to the late 1930s. They proliferated when graduate populations grew too large after World War II to manage by dissertation alone. Between the GI Bill and Sputnik-related research spending, the number of Ph.D.'s tripled in the 1960s. Against that backdrop, the dissertation defense became more of a formality, creating a need for so-called barrier exams beforehand.

Comprehensive exams had already existed in some departments for undergraduate students, but there was a lack of standardization for curricula at different colleges. For example, a graduate of another university who wanted to earn an MA from Princeton would have to take their senior comprehensive exam covering the undergraduate curriculum at Princeton. Economics professor Richard A. Lester, in "A Critique of Our Colleges" (The American Scholar, 3(4), 1934), uses this example to attack the insularity of graduate education at the time, which favored students from its own institution.
Still, occasional evidence for earlier PhD qualifying exams can be found. In a review for Jacob Viner: Lectures in Economics 301 in Journal of Economic Literature 52(2) (2014), a footnote cites PhD qualifying exams found in the Albert G. Hart papers at Columbia. "Hart had been a graduate student at Chicago from 1931 to 1936," indicating that PhD exams were in place in the economics department at the University of Chicago. That does not indicate that PhD exams were widespread, but only that deep dives into institutional archives might uncover earlier examples that Cassuto may not have been aware of.


You say the director of the program is sympathetic to you.  Why not talk to them?

This may be a case where the devil is truly in the details.  You might be able to take additional classes to bring up your GPA.  You may be allowed to retake classes.  These are the kind of high level alternative options that a program director will know.  Especially with the health issues and assault, the director may have a case to file some kind of waiver.  (Probably to allow you to retake one or more classes.)

You also have to be honest with the director (and yourself) about your workload & course load balancing.  Is it realistic to expect that you will be able to get straight A's from here on out while working full time to pay for expenses?  It sounds like that will be difficult.  Check with the director about other options (a semester off, becoming part time, grants, loans).

Being proactive and starting the conversation with the director is probably the best way to move forward.

Lastly, even if you find that walking away from this program is the right, best, "least worst", or only option for now, it does not mean that this is your one and only shot at a Master's degree.  My Undergraduate gpa was not stellar.  I was able to show that I had matured from that time (only four years before I applied) by taking graduate level courses and succeeding in them, which led to me getting two graduate degrees (not at the same time).  In my experience, grades alone are not the only thing that grad schools look at when you apply.


Are colleges prepared to offer a PhD position to one who already has a PhD

Certainly, it happens. I am currently pursuing a second PhD myself, in a field very different from my first. I just learned that one of my fellow graduate students in our department also has an earlier PhD, and hers is from a field very close to our department's.

As the thread linked by ff524 notes, there are many people who wish to earn a second PhD for all the wrong reasons. But you didn't ask whether it was a good idea to earn a second PhD, you asked whether Universities would admit you. The answer is that many will, but they certainly may be wary of this aspect of your application. As commenters have pointed out below, some universities flatly will not consider your application. Amongst those that will consider your application, some admissions committees will not like your previous degree, and others will not care. In my case, I felt the admissions committee did not really care about my earlier degree; they cared about my ability to demonstrate potential in my new field.

Furthermore, before applying to my current institution, I emailed roughly eight departments asking whether an application someone such as myself would be welcomed. Every single one of them replied to me to say that yes, it would; and several were encouraging about my prospects if I did apply.

Nonetheless you should be prepared to accept that some admissions committees will not like your previous degree, and you should be prepared to explain to them your good reasons for pursuing a second PhD.


how to be successful in CS field with inadequate background? Can just passion help for surviving grad school?

You do not sound like the strongest CS student. It appears that with luck, you will just "get by" in CS, and graduate near the bottom of the class. As long as you are resigned to that likelihood, and to just doing what you need to survive, you should continue.

The potential rewards could well make the effort worthwhile. Modern corporate development, particularly management, is about computing. I envision a "management" track for you, rather than a programming track. And if so, your skill level, such as it is, will give you the advantage over many managers. Your "passion" would be a big plus in this environment.

Your "endgame" may well be a degree in management, with CS only as a stepping stone. It might even make sense for you to leave CS, take a degree in management (MBA or Indian equivalent), and return to CS later when you have better idea of how to "manage" yourself in such a program. Some MBA programs even offer CS as a minor, so you could take "a few" more CS courses there without risking a whole degree.


I have accidentally given students assignment guidelines that conflict with the course coordinator's. How I can rectify my mistake?

Talk to the course coordinator immediately and coordinate your next steps.

Apparently, there was a serious breakdown in communication, and

  the course coordinator didn't provide any guidelines whatsoever

suggests to me that you are not the only one to blame.

Whatever your next steps will be, they need to be aligned with the coordinator and his expectations. You may be able to extend deadlines, adjust grading rubrics or something else.

Next time, make sure you know what the coordinator wants. (And the coordinator should make sure, too.)


Which quantitative metrics are there of the quality and prestige of journals, and how do they compare?

In short:

Impact factor is the traditional measure of mean citations per year shortly after publication.  It can refer to either the official Thomson-Reuters computation (which has lots of problems), or other competing similar computations.
SJR attempts to improve on impact factor by using an algorithm like PageRank to more heavily weight citations from "better" publication venues.
H-index for journals is just the same as for people, essentially looking for the volume of consistently good work.  The only large place I know of that applies this to journals is Google Scholar metrics.

All of these are subject to manipulation and gaming, all are highly field-dependent, and none are very good actual ratings of quality.  Still, they can be used to get a rough sense of the significance of a venue that you are unfamiliar with.


Do PhD students work alone in American universities?

The answer to this question is partly dependent on the field and the dynamics of the research group you are in. I used to work in a spectroscopy lab (in the US) where most of the work was experimental. My impression of the office was that periods of silent concentration were always interrupted by lively discussions, be it scientific or otherwise. We had white boards all over the office and they were never under-utilized. On the other hand, I've also worked in a lab with a more theoretical/computational focuses. There were more international students in the lab, and overall people in the lab were more reserved and largely focused on their own problems. However, I also know of theory labs that have a more lively atmosphere, so I hesitate to say that theory people are more prone to feeling isolated.

I think the solution to your problem is not necessarily moving to a different country. For whatever personal or external reason, collaboration may not be easy for you. But ultimately it is your responsibility to reach out to other people and build collaborations. The easiest targets are people in your research group and your cohort who entered graduate school at the same time. But also consider going to departmental talks and conferences to network with external researchers. As you learn more about your own projects and other people's research interests, it will become easier to start a conversation and explore the possibility of collaborations. It may not come easy to you, but it truly is a necessary training for you as a scientist.


How should I insist to be the first author?

Insist may be the wrong approach. Given your #3 and #4 above, he may have a valid claim on it. You can ask, of course, and you can appeal to his "better nature" that it will boost your future prospects. That might be a win.
But if you balance off his good will and support against first authorship of a single paper it may turn to your profit to yield if he insists. Your first work, especially at the masters level, will, hopefully not be your best. It is a plus in your column no matter where you land in the authorship order. And if you trade it for a better and more enthusiastic letter of recommendation for your next steps it may be worth some sacrifice.
But there is a bit more to it here, since this is a conference paper and hopefully the conference will give you a chance to expand your circle of contacts. But that, too, might depend on having his good will.
Think strategically and for the long term. Don't compromise long term benefit for a short term "win".


How to proceed after failing exam to advance into PhD program, and subsequently losing motivation?

Two things:

A single exam is a high-variance way to measure the ability and potential of a complicated and multifaceted being called a human.  In other words, I wouldn't take a single failure too seriously.  Sometimes you have a bad day; some people simply don't perform well on tests even if they perform well "in real life."  And even if it turns out that you are less qualified than your peers according to the traditional standards of the field, that doesn't mean you don't have something unique and valuable to contribute.
Is there anything in your life right now that you're excited about?  If not, you might consider external factors.  Some days I'm fed up with my problem, and my research, and my career.  But after going for a run, eating well, spending time with friends, seeing a thought-provoking movie, and getting a good night's sleep, I often find (much to my surprise) that I am excited about my life and my work again.  In other words: don't underestimate the value of external factors.  (Especially exercise.  I cannot stress that one enough!)


Do non-Russian technical universities use Olympiad-style math/problem solving entrance exams?

In Japan, many universities have their own entrance exams.  For the entrance exams for mathematics that I've seen, there are several challenging problems (maybe about 5) to be solved in about 2-3 hours.  For instance, here is a recent exam from Tokyo University (this is the math exam for science students--humanities students get a different exam).  If you're a bit rusty on your Japanese, it's 2.5 hours for 6 problems.

Entrance exams in other east Asian countries are reputedly difficult also, but I haven't seen those exams to compare.  Maybe someone else can comment on that.


Is it ethical to omit the PhD credential from my resume?

Do you think that such a deception will help you significantly in landing the job? Several years of “work experience” at a university is going to look very suspicious and will probably raise some flags.

In general, you’re always better off stating the truth. There’s a smaller chance of things going sideways down the road if you do.


How to avoid supervisors with prejudiced views?

I will sound snarky with this answer, but have you tried talking to them?

Your question may ask well be asked as "How do I determine the values of another human being before I meet them?" And I would say that is not something you can truly learn and understand until you talk with them.

You may respond with, 'What if they lie?' And that's a very valid point. But I would tell you that all of human social interaction is this very problem, and that you will not gain the wisdom of how to interact with humans without interacting with them!


Should I submit a paper to a venue that is unlikely to accept it?

Without knowing all of the details, it's hard for random Internet strangers to make the call. You should only go for the GREAT conference if you meet all of the following criteria:

You've actually got a chance of making it in
You can resubmit to a GOOD conference if it's rejected
Someone else isn't likely to publish a similar result before you have a chance to resubmit
You don't need a publication on your CV right now

Even if the GREAT conference rejects it, you might get some valuable feedback that can help you make it even better. Personally, I'd take a shot at the GREAT conference if the chance was 15%, but the top conferences in my field get called crap shots anyway.

EDIT:

To expand my answer based upon changes in the question: There is nothing wrong with submitting to a conference if you think your paper stands a non-negligible chance of getting in. No one's going to black-list you for aiming high.

The only issue I can imagine is that a reviewer is working for both the GREAT and the GOOD conference and you don't update your paper to reflect any changes they suggest in their first review.


contacting advisor before admission can be helpful?

You could certainly talk with them and discuss your ideas and options and if you find the connection is a good one you could ask for a letter of recommendation from them, but short of a letter I don't think a professor has a whole lot of flex/power when it comes to admissions.

Certainly if they vouch for you that is a positive thing, but unlike a "job" I feel the role at the University is based more on your academic experience and aptitude than who you know.


Compiling ethical standards for coauthorship across academic fields and regions

This is excerpted from the Ethical Guidelines of the American Mathematical Society:

  I. MATHEMATICAL RESEARCH AND ITS PRESENTATION

  The public reputation for honesty and integrity of the mathematical
  community and of the Society is its collective treasure and its
  publication record is its legacy.

  The knowing presentation of another person's mathematical discovery as
  one's own constitutes plagiarism and is a serious violation of
  professional ethics. Plagiarism may occur for any type of work,
  whether written or oral and whether published or not.

  The correct attribution of mathematical results is essential, both
  because it encourages creativity, by benefiting the creator whose
  career may depend on the recognition of the work and because it
  informs the community of when, where, and sometimes how original ideas
  entered into the chain of mathematical thought. To that end,
  mathematicians have certain responsibilities, which include the
  following:

  To endeavor to be knowledgeable in their field, especially about work
  related to their research;

  To give appropriate credit, even to unpublished materials and
  announced results (because the knowledge that something is true or
  false is valuable, however it is obtained);
        To publish full details of results that are announced without unreasonable delay, because claiming a result in advance of its having
  been achieved with reasonable certainty injures the community by
  restraining those working toward the same goal;

  To use no language that suppresses or improperly detracts from the
  work of others;

  To correct in a timely way or to withdraw work that is erroneous.

  A claim of independence may not be based on ignorance of widely
  disseminated results. On appropriate occasions, it may be desirable to
  offer or accept joint authorship when independent researchers find
  that they have produced identical results. All the authors listed
  for a paper, however, must have made a significant contribution to its
  content, and all who have made such a contribution must be offered the
  opportunity to be listed as an author. Because the free exchange of
  ideas necessary to promote research is possible only when every
  individual's contribution is properly recognized, the Society will not
  knowingly publish anything that violates this principle, and it will
  seek to expose egregious violations anywhere in the mathematical
  community.

[Emphasis added.]


Will anybody actually read your research and teaching statements?

I am the chair of the faculty recruiting committee in a Very Good Department at a Big Research University.  I read research and teaching statements.

I need to know that you have a compelling agenda for your future research; your letters won't talk about that at all.  I need to know that you can describe and motivate your research agenda well enough to attract external research funding.  I need to know that you know why (not just "that") your work is interesting, visible, important, and likely to have high impact.  I need to know that you communicate clearly enough to be a good teacher, and that you care enough about teaching to formulate a coherent teaching philosophy.  I need to know that your research, teaching, and career goals—as you describe them—match those of my department.  I need to know that you are taking the recruiting process seriously.

In the long run, your publications (which I also read) and your recommendation letters are probably more important.  But saying that your statements have no importance is a dangerous exaggeration.

Also, I don't eat in the cafeteria.


Dive into a paper using a reading course

My experience was primarily as a (math) student many years ago but the course didn't focus on a single paper, but on a topic of which the paper was only an example. Maybe this is something you could use.
The basic meta concept is that reading isn't enough to learn and that students need to be more active if what they read/see/hear is to actually be learned.
So, if you organize a group around a topic and select, not one, but several papers that refer to that topic. Each student (or perhaps each pair of students) is responsible for creation of a presentation on that to the others, giving key concepts and any insights they manage to develop. But, all students are responsible for reading the paper.
A session, with everyone present, has two parts. First is the presentation of one of the follows by an open discussion at which questions can be asked and further ideas developed.
If the group meets once per week, then you "cover" one paper per week.
After the presentation and the discussion, the student could be asked to then develop a write-up.
This idea can be adapted to chapters of a book, also.
Note, however, that undergraduates can be expected to be awkward at this, so you need to be pretty understanding if it is a graded/marked activity. It is a useful skill to have, but one in which they have little or no experience.  And not every suggestion here need be incorporated. There can be many variations.

Edited to add:
Suppose, however that you have a large and long single paper. Such is difficult to divide up, since understanding early parts may be essential for reading later parts.
In such a case, the paper can be read in "sections" by everyone. One student (or a pair) is designated to lead the discussion of the "next" section and develop a set of initial questions. When the group meets that student leads the discussion. Alternatively, each student must turn in a written question or two on the section of the week. Or perhaps an insight along with a question. But, again, but the emphasis on student activities beyond reading and just making up questions on the fly. Insist on some actual preparation.

Over the horizon. Bonus points.
The following is probably too much to expect from undergraduates but you might offer bonus points (in any grading scheme) for any student or group of students who can come up with a research question that might arise from the paper. You could suggest what might lead there such as "changing some initial condition" or "generalizing" or "specializing" or whatever seems appropriate for the readings at hand. It might even happen, even if unlikely.


Applying for tenured positions while on sabbatical

Your sabbatical time may be able to be "bought out."

If you leave your job after your sabbatical, the school may just want reimbursement for your salary. It is possible that the new school will be willing to pay that in order to hire you.

One case of this happening, I believe, was when Matt Welsh left Harvard after getting tenure (although he left for a company).