Accused of cheating on online final exam

It isn't up to you to prove your innocence. It is up to your instructor to prove your guilt. Insist that you did nothing wrong, assuming that is the case. Don't try to explain how you aren't guilty, but do explain, if asked how you solved any questions on the exam.
Let me note two things. Two correct answers are frequently likely to be the same, as that is just the nature of truth.
Second, all of the students had the same instructor and learning materials, so it is natural that they work in similar ways. It is natural that they approach problems in the same way. It is almost inevitable that there will be overlaps in how they solve problems.
No one can guarantee that injustice won't be done here, but similarity is not proof. Even using the same phrasing, if it is similar to that of the professor or the learning materials, is completely natural and to be expected. Especially from the better students.

You have a difficult task and can only suggest that if there is another faculty member who would be willing to speak for you at any hearing as your advocate, then it might make a difference. It is hard to stand alone against authority.

Also note that in technical subjects, there is frequently the situation that there are a limited number of ways to express something correctly. It is why some things in mathematics, for example, can't be copyrighted.
My personal opinion that a statement like "there is no way this could be a mistake", is both foolish and biased.


Previous interests in a subfield which is different from your perspective advisor's

It is not at all uncommon (especially at BSc level*) for people to go into vastly different areas; their knowledge and skills in one area can often add to their abilities in another.

For simplicity in what follows, let your original field be A and your newly taught field be B.

Things can get a little hairy if you are determined to stay in A for your project (or, at least, it might not be as successful as having a supervisor with strong knowledge within A). If you are willing to make the transfer to B, and if you are willing to accept that further academia in A may be rather impeded (again, compared with originally taking a project in A), I do not see any issue with such a switch at this point.

There might be some circumstances in which "belonging to the same parent field" does not mean that A and B are even remotely related in their approaches and terminology in the modern day, and catching-up might be a lot of hard work. It is, I suppose, up to you and your friend to figure this out with available literature.

I am probably not giving you any information above what you already know - but I had to say the above just in case. What I would really like to say is the following: If you want to follow a path, follow it. Prior knowledge adds something to the group - not only will you have some unexpected tricks up your sleeve, but you may become the "go-to guy" for certain problems, and their knowledge will provide you with yet another set of tricks. Such mixing rarely comes to a detriment of either side of the table, provided you are willing to learn and they are willing to stretch you.

But if you are unsure on a path, do not take it simply because you dont feel you have a choice. I personally fell into that trap - in my case, joining a doctoral training centre in a much more general field than my own (Theoretical Physics -> Nanoscience). It turned out to be so general that most of the material was hand-wavy and useless. Now I'm back doing what I love, but it was half a year of plain old misery for me.


Should I publish in a second rate journal published by a maybe disreputable publisher?

Of course not. If you spend the time to write a paper of decent quality, publish it in a journal of decent quality.
If a car salesman invites you to buy a car, would you do so because of the invitation, despite his questionable reputation?


Actually, I've never seen a paper where co-principal investigators (with respect to a grant) have been distinguished—and I was co-advised as a graduate student in exactly such a circumstance.

However, I don't think this is as big a problem as you think. If you were a co-PI, you would indicate the corresponding grant as part of your CV, as well as the resulting publications. So it shouldn't be too hard to figure out who contributed what.

Also, in my own circumstance, I am actively co-advising several students at the moment. In these collaborations, we assign the "senior author" position to the most "relevant" author for the publication. For instance, I'm in engineering and one of my collaborators is in CS. When we publish in a CS venue, he's the senior author; when we publish in an engineering venue, I'm the senior author.

If it's really important, though, to indicate the co-PI issue, you could mention this in the acknowledgments section, since that's where you'd list the grant support in any case. You could write something like

  F.O.O. and B.A.R. were co-principal investigators on grant XYZ from funding agency ABC.

or whatever comparable wording satisfies your needs as well as those of the funding agencies.


What are some tools available for drawing good figures for computer science research papers and presentations

Personally, I am a fan of the TeX-Package TikZ. It is easy to draw simple diagrams, include small pictures or create structures by using loops and conditionals.
It also supports relative positioning, which makes everything a lot easier than manual placement.

Since all of the input is plain text, it works great in combination with source control (e.g., git) and prior versions can easily be reverted back to.

I have to mention it takes some time to get used to the syntax, but the folks over at the TeX Stackexchange are usually very helpful. They have a great showcase of scientifc pictures, too! https://tex.stackexchange.com/questions/158668/nice-scientific-pictures-show-off

When images from other documents are to be included, I usually crop them out as vector graphics from pdfs by using Libreoffice Draw. With both tools in combination, I often get satisfying results since everything remains vector graphics for the entire diagram if i wish to.


Can one switch from the declared field of study in his SoP to another after acceptance?

(I'm a full prof at a top-5 American CS department, with a PhD from Berkeley.)

Yes, this is a common model for admissions in large engineering departments.  Admissions committees will assume that your statement of purpose accurately reflects your research experience, research interests, and professional goals.  Applications that describe interests in more popular areas (for example: machine learning) will face more scrutiny and stiffer competition than applications that describe less popular interests.

In the short term, this is important for funding decisions. Most CS PhD students at Ilinois at Berkeley are admitted with RAships, offered by individual faculty from their grants on specific topics.  We need strong evidence that you have the requisite background and interest in that research topic before offering you a job to work on that research topic.

In the longer run, this is important to make sure that the department will provide incoming students an environment that builds on their strengths.  We don't want to admit students who won't thrive, and we want to make sure that every incoming student can find an advisor, without overwhelming the faculty.

And yes, of course, PhD students can switch areas after they've been admitted, provided they can find an advisor in the new area.  After all, it's the student's degree, and the universe laughs at detailed plans.  That's why actual admissions decisions (in my department, at least) are made by a committee that includes faculty in all areas, rather than by the individual areas or individual faculty acting alone.  It's not enough for me to say that I would be happy to advise and fund a PhD applicant; there has to be strong evidence that the student will thrive even if they switch advisors or areas.

That said, it's a really bad idea to feign interest in a less popular area to get your foot in the door, and then try to switch to a more popular area.  As the Systers post you link to says: Popular areas have popular advisors.  Students who expressed interest in a popular area in their SoP have already been vetted by faculty in that area; students who did have not.  In practice, switching may not be possible.  And then you're stuck in a department that doesn't let you do what you really want to do!

Also, while allocating admissions slots to areas is a common model for admissions, it's not a universal model. Every department approaches admissions differently.  Some departments admit students under a general banner of excellence—under the quite reasonable assumption that most PhD applicants don't know what they want to be when they grow up—and then have everyone go through a common core of classes and group rotations.  A broader admissions model allows departments to take more risks, by admitting promising students who genuinely do not have specific research interests yet, which can lead both to huge payoffs and to more dropouts, but it can also put significant strain on the faculty in more popular areas.


How to approach principal investigators for internship/job positions

The absolute best way to approach someone to work in his group is to be recommended by another researcher in his field, preferably someone he has heard off previously. So, either a big name or someone with close or overlapping research interests.

So, I would advise you to approach some of the professors in the field you are interested in, at your current institution, and ask them if they know a research group or a professor meeting your criteria. Try to be flexible when you discuss possible names/places with them, to gather a relatively large list, even if you later decide against some of these names. Once you have decided on a few names, either you can get your professors to contact them for you or, barring that, you can contact the abroad PI and mention your shared acquaintance.


If I know how many questions I attempted/got wrong on GRE Math Subject test, can I estimate my score?

The official practice book for the Math Subject Exam describes how to score an exam.

According to this practice book, a typical scaled score in 2008-2009 for someone with a raw score of 41 (42 correct answer, 4 incorrect answers = 41 raw score) might be around 730, or 72nd percentile.

You can calculate the score for other possible scenarios following the procedure described in the practice book.

As for whether this is considered a "really low score," please see What is an acceptable math GRE subject score.


You might end up as competitors someday.  I've never felt like I was in competition with any of my former students or my own advisor, but some people are hyper-competitive, and others are unlucky enough to end up in awkward situations, so your mileage may vary.

Even though it could happen, you shouldn't waste time in graduate school worrying about hypothetical future competition.  There are more important things to think about, and you shouldn't let these worries interfere with learning as much as you can from your advisor.

Ultimately, becoming a successful researcher means developing your own research agenda.  Over time, you should drift away from your advisor as you explore your own interests.  (If you don't, it's a bad sign.)  In particular, as you become an established researcher your advisor will no longer play a central role in shaping your scholarly interests, and competition with your advisor will not be much more likely or worrisome than competition with other senior people in your field.


Best practices in sharing qualitative data such as interview transcripts alongside a paper publication?

If your research data comes from people, your sharing of the data needs to be approved through an ethical review process, or an exemption from that process must be obtained through the exemption process.
CSV format seems to be the most reliable data format; it does not matter if your data is quantitative of qualitative.  Your choice of repository should be guided by the customs of your field and your views of the repository's reliability, not the type of data.


Is it acceptable to have a figure caption running to the next page?

300 words will be about 30-50% of the page. Such a large chunk of text seems substantial, so it's better to place it in the body of the paper.

In such situations, in the caption I usually just state what's in the figure, followed by "see text for details". And then I don't care if the text spills to another page.


How can I earn a professor's attention if I am not his/her student yet?

What's wrong with my actions and speaking?

Nothing's wrong with your actions, although they are not likely to lead to success.  As for your speaking, the paragraph you quote is not ideal, but I don't think that's why you are getting turned down.  Instead, the problem is that the system is just not set up to provide research mentors for high school students.  I regularly turn down requests for high school research supervision, for several reasons:

Like many faculty at research universities, I have more local students who would like to work with me than I have time to supervise.  This is particularly true for undergraduate research, and I end up turning away many undergraduates because of a lack of time.  The ones I end up working with typically have very strong backgrounds, and I'd be reluctant to turn more of them away to free up time to supervise high school students.
It's much easier to vet local students.  If they have never taken any of my classes, I can ask my colleagues about them.  By contrast, it's much harder to evaluate high school students.  It's already difficult to quickly gauge mathematical talent and background, and that's not even enough: I'd also want to know how hard working someone is, how overcommitted they are with other activities, etc.
I don't think high school research is particularly important, and I question whether it's even worthwhile.  For the vast majority of high school students (even ones who are exceptionally talented), spending a few more years studying the mathematics that's already known is at least as worthwhile as doing research.  The number of people who have genuinely reached the stage where they should be doing research, but who are not yet prepared to go to college, is minuscule.  By contrast, there are lots of people whose main motivation seems to be that doing research at a young age looks impressive, and I'm not eager to encourage this.

Of course not everyone will share these reasons, but I think they are reasonably widespread.  To maximize your chances of success, you should keep these issues in mind.

The most straightforward one to address is how to evaluate your background and talents.  You need external evidence, such as a letter of recommendation from a faculty member, ideally combined with some feedback and advice.  You could try taking an advanced course at a local university, or attending a summer math program for high school students.  Another possibility is strong performance on a math contest.  (That's less meaningful, since it measures only a limited form of talent and doesn't come with feedback/advice, but participating in a contest is less expensive than taking a course.)

It's worth applying to research programs specifically aimed at high school students, such as RSI.  There aren't very many of them, and they don't admit many people, so you may not have any luck with this.  If you target individual faculty members, you may have better luck if you choose people who have supervised high school students in the past, since you know they are in principle open to the possibility.  (You can sometimes tell this from their web sites or CVs.)  Faculty members at schools that don't have particularly strong undergraduates may be more excited by the idea of working with a great high school student, while faculty at Princeton have plenty of top undergraduates to work with.

If your search for a research supervisor works out, that's great.  But if it doesn't, you shouldn't worry that it's a negative judgment of you.  You're trying to do something the world basically isn't set up to facilitate.


First Presentation as a postgraduate student in a new workplace, messed it up!

When presentations go bad, and sometimes they do, it can give us a little PTSD. First, know that presentations get easier as your career progresses, because you have a better handle of the material. You will also experience more hiccups in your presentations (poorly-placed screens/laptops, unexpected interruptions, computer failures, etc), which will make you better prepared to give presentations under less-than-ideal circumstances. When I look back on my very-first lecture (more than a decade ago!), I cringe to remember how basically I read a outline for 50 minutes. Now I barely use notes for 3-hour lectures.

But bad presentations happen. A couple of years ago I was invited to speak to a room of 300+ healthcare providers on a technology my team was developing. On stage, it became painfully clear that the only people interested in the topic were the cinference's organizers who attentively sat up front while I watched 295 participants read their phones for 55 minutes. I also learned that I had to sit in the back of the auditorium to give the demonstration of our technology, leaving the stage empty for 10 minutes. It look me a good year to shake this off. Later, I realized that most of the problems were out of my control, but I prepared better the next time and it went great!

So, shake it off. Don't be so hard on yourself. Next time, ask someone else to change your slides, if the room set up is strange. It's okay to adapt to the situation! We have all been there and it will get better.


Manuscript went from 'awaiting referee selection' to 'awaiting decision'. What does this mean?

It means nothing. These status should not be taken seriously. Just give it some time; either you will get a decision or it will go for the review process.

It it is desk reject, then reviewer means the editor herself. If it is not a desk reject, then it will surely go to the external peer-reviewers for review.

Further, if you are thinking of sending an email to them, then I would say, don't. Wait! It is not late yet. Just ignore your paper for few months (of course, depends on your fields.).


Handling collaboration requests from the authors of double-blind reviewed papers (after submitting the review)

Given the timeline there is no ethical concern. You don't need to retract your review and you can agree to collaborate.
However, you should decline to review paper A if it goes to a next round. And in the short term you should refrain from telling the authors of your review. I don't see an issue in telling them later, after a final decision is made by others.
You might want to inform the program chair of the situation, giving the timeline. I doubt that they would have any complaint nor any reason to act.
Given what you say, the events seem to be entirely independent. Serendipity happens.


How do you defend against TA proctor false accusation of "seeing you look at others computer screen" to cheat on final

I think the evidence is weak unless you were extremely obvious about looking at other screens. Matching answers is almost never evidence of wrongdoing. In fact, matching incorrect answers can be evidence of poor question statements. And matching correct answers is just evidence of knowledge gained.

I would state what you have here. I didn't cheat. I had no need to cheat. I finished early. The proctor was simply mistaken.

Part of the problem in such situations is that no matter what we are doing or thinking, unless we have closed our eyes, they point somewhere. It is easy to misinterpret a look.

And a five month delay before being informed seems to be disqualifying to me. Presumably the proctor didn't have enough "evidence" to call you on it during the exam.

Sadly, no one can guarantee fair treatment in such cases.


What should I list as my academic affiliation in scientific publishing?

I would expect you to list both affiliations. This is very common at all levels of research.


Risks of shifting to post-publication review

In my mind, there are three semi-related problems with post-publication peer review:

It's difficult for the lay press to distinguish between pre- and post-publication reviewed papers, and for many "breaking" articles, I'd be concerned about reports of spurious results becoming more common, not less. For example, if I publish a paper on a risk factor for X disease, how long does the press have to wait to report it? Do they have to let peer reviews build up? Pre-pub at least ensures that someone has looked it over.
Article readership is nowhere near uniform, and there's no reason to believe reviews would be different. At the moment, every single paper published by a journal is subjected to some form of review, whether anyone else cares about that paper or not. Relying on post-publication, it's possible some papers will get few/no reviews. What's a non-expert to make of those papers? Similarly, what's a non-expert to make of a post-pub vaccine study that's been flooded with anti-vaxx rhetoric dressed up in technical jargon?
Post-pub peer review is inherently non-anonymous. I'm pretty sure Big Deal Figure in the Field is not going to be judged as harshly as New Grad Student even for the same work - and this will also likely effect those with clearly female or minority "sounding" names. Prominent scientists may be more likely to get a pass under the assumption that they're  right. In my mind, breaking review anonymity is a step in the wrong direction.


Advisor suggests to change my research topic after unsuccessful start, unsure what to do

You should be talking to your advisor(s) and you may have some good points to discuss.

If you think you have some relevant ideas, then you should discuss them with your advisor - one may be the "key" you are looking for.

If, after considering your points, the advisor still has good reason to think that there is no future, then you should accept that decision, clear in the knowledge that you put your points across.

So, discuss with your advisor and make an informed choice with them.


I generally avoid "I" in scientific texts altogether, though some authors are in fact using it if they are the sole author. I can't remember seeing it in a thesis though. In texts with a sole author, I usually understand "we" as meaning the author and the reader, and I'd suggest that it's fine to use it in places where it can have that meaning. For example something like "When substituting a by b, we get ..."

A generally useful advice would be to read into some of the theses written in your group, department, and university (in decreasing relevance), and see whether there is a common pattern.


German language for Phd courses in Germany

I know programs in other fields where the official graduate school language is English (e.g., my undergraduate alma mater - over 20 years back even), but am not personally familiar with engineering in Germany. You need to check the online program description for the universities you're interested in. They certainly exist - here is one example. The entire page is in English. It's an interview with international students about their experiences in the program, so it might be helpful, or at least interesting as well.

I had an Israeli professor who didn't speak German. He was tenured, taught in English even at the undergraduate level, and still managed to be probably the most popular teacher. While Germans generally speak some English, you just face a somewhat restricted social life, and should learn German while in the program to enjoy your time in a PhD more.


Can anyone help me to find out what resources are suitable for practicing the TOEFL exam reading section?

I have had to take TOEFL about two decades ago since it was an admission requirement. Back then, as now, I believe that the biggest problem was in having full and unequivocal understanding of the questions. The general approaches to academic reading fail miserably on the question/answer sets. In general academic reading, you can afford a slightly superficial understanding, at least on the first reading, only to later drill down to get all the details clearly and dispose of the inevitable misunderstandings of the first reading.
Yet, when it comes to any sort of standardized-style examinations, superficial understanding of questions is never enough, and it will jeopardize any benefits you may have from deep understanding of the prompt itself (the text or the topic you're asked about).
The fact that you classify the questions as similar should be inconsequential: they are very stereotypical, and must be devised along some common patterns. That the similarity seems to be an obstacle means that you have only superficial understanding of the questions - an understanding that is insufficient to answer correctly. Your perception of similarity of questions should be a flag to yourself that you've got some work to do in the area of not glossing over details in the questions. So, if you are looking for some definite area you could focus on, it'd be to understand the nuance of the language used in the questions and answer sets. That language is to a large extent stereotypical as well, and full of patterns that you'll only find in the reading q/a sets and not anywhere else. You would probably not be mistaken in looking at it as if it was a technical jargon. Familiarity with it would go a long way in improving your results.
Think of it this way: the techniques useful in reading the prompt are different than those in reading the questions/answers. You can't afford the long time it would take to fully "dissect" the prompt before you tackle the questions. So you won't, in most cases, be able to have unequivocal understanding of the prompt a priori answering the questions. You need to acknowledge that some finer points of the text may have to remain unclear until a question is there to point you to go back and delve deeper if needed. On the other hand, the questions cannot be glossed over. You have to fully understand them, and then the similarities will be of no concern - a bit of trivia, but otherwise of little consequence. With full understanding, the differences between the questions will stand out, the similarities will become a background feature.
Remember that the people who write the prompts and the questions and answers do it as a matter of their job, and it's done en-masse. There's no way to be too creative at such a job. The prompts (the reading texts), the questions and the answer sets are all extremely stereotypical - you just lack the experience of seeing enough of them to see those patterns. So you may have to take me at my word that the authors of the prompt text, the questions, and the answers, are not really trying to be clever to "catch you" unaware or to trick you. No, I don't have any direct nor 2nd nor even 3rd-hand experience here: it's all based on my morbid curiosity in the workings of the standardized test "machinery". Very unfortunately, it is a "pay to play" field where the "research material" is firmly behind a paywall, and one is contractually forbidden from discussing some of the details. Thus, whatever I can divulge here is partly filtered by my sincere wish not to break the rules I willingly bound myself to.
I can only sympathize with the observation that lots of study materials are not representative of the difficulty of the test. That's because there are practical limitations to doing an adequate job when preparing such materials.
Let's now look at things from the perspective of a person who want to create test preparation materials ("study books" and such). There are only two  major avenues:

Repeatedly taking the test as often as allowed, having money to pay for it, and having the perfect memory to memorize everything and good enough writing skills to paraphrase the structure of the prompts, questions and answers. If all you want is TOEFL, and you're taking it in the US, then it's a $2k/month "hobby" if you want to take as many tests as you are allowed to. If you want to diversify, then GRE at maximum rate is $1k/year, SAT is $400/year (depending on how exactly how many administrations there are in a given year), etc.

Breaking the test contract if you are a test-taker (i.e. by using some obscured device to capture test content in violation of the rules you agreed to abide by), or breaking your employment contract if you happen to work for ETS, or breaking the law outright if you figure out how to get access to the test materials in spite of not working for ETS. In some jurisdictions/situations, breaking the rules of employment contract may in itself be a violation of the law as well.

Most people who want to make any sort of a career, even if brief, in test preparation world, will do well to avoid the 2nd option. The 1st option takes resources, dedication, and people with memory skills - and you need that up-front. The 2nd option carries, well, a false promise at best.
I've taken TOEFL some number of times over the years out of sheer morbid interest, and what I could reverse-engineer was:

The multiple-choice part of the test is selected from a permutation of a large pool of prompts and question/answer sets.
There may be a tendency to think it "easy" to leak those, maybe just slightly altered, to provide test preparations material. It's obvious that each person taking the tests within a certain time frame can be individually identified just from the multiple-choice material they leaked. As for the fallout - the contract one signs to take the test is telling. It's important. I imagine that in the best of cases, one would be "only" barred from taking any other ETS tests when caught - that's a problem in itself, since ETS also administers GRE, for example. Thankfully the academia is slowly weaning itself off of the unhealthy dependence on ETS as a gatekeeper. Worse consequences would all be of legal nature, I imagine. IANAL so that's all I know about it.

The essay part seems to be "organizationally constrained". A decade+ ago, the essays were clearly scored by humans. And those humans must be on a team. And that team has some leadership in place, surely to answer questions of those in the trenches, or review some of their scoring, etc. It's no different than in any other group setting where multiple employees make repetitive decisions along some pattern, e.g. in awarding bank loans. Only the timeframes may differ. My entirely made-up guess would be that, say, a test scoring person may have to score a 100 essays a day, but a banker may approve/process a couple house loans a day, on average, so there can be a 1-2 orders of magnitude disparity in rates, but the oversight process, and the relatively rigid guide set for each essay prompt or each type of a loan would remain.
The essays are so specific and different from each other that I bet it's impossible to be scoring different essays all at the same time. Maybe approving a couple different personal residential bank loan types may be within the ability of a good banker. When I imagine myself scoring an essay, there'd be just way too much to remember to be able to effectively score multiple essay prompts in succession. So, I imagine that most of the time the people who score would be working at one prompt (topic) at a time, and switch as needed, but such "switching" requires everyone to switch: the managers have to switch and familiarize with the new essay prompt just as the people who score.
My experience so far is that if you get multiple people to take TOEFL on the same day, it's highly probable they'll be writing the "same" essay. In the last few years, it became rather clear to me that some of the essays can't but be scored by software, and not a particularly clever software at that. That software used to be really easily fooled by syntactically correct writing that had a varied and "highly literate" vocabulary yet amounted to gibberish - it wouldn't pass by any human not totally asleep at their job. Nowadays, the software seems to be cleverer, but still distinguishable. I guess if you think of a future as a test scorer, it'll be a future of historical interest mostly at some point.

Each time I took the test, many of my curious friends did as well, and we all had the same essay prompt but our multiple-choice questions all varied and the best we could tell there was no overlap between them. Surely ETS has a huge pool of questions to pull from.


How to deal with fellow grad students who want to copy assignments?

Sometimes, as in your case, you want to protect your best interests without burning any bridges. That's understandable, as I assume some regions have a much higher culture of cheating than others. For example, I know of one nation where people used to hire proxies to take their exams. In this case, I assume you've already participated at some point, so the long-term goal is to protect yourself and wash your hands.

Make an excuse about how you haven't completed your assignment yet. You can easily extend this to the due date and claim you were working on it all night the day it is due. Any other excuses like not starting, and so on, while you have, to hide the fact that you've done so.

This also protects you from being further involved in academic dishonesty without making you look bad to your classmates. Your end goal should be to cover yourself, and lying about not being able to share your work is a significantly better endgame than being caught in a cheating ring.

As to reporting the academic dishonesty, I hate to say it, but I probably would not do so at this point. You're implicated, and if it's a small class, it'd be easy to track back to you.


How to get authoritative bibliographic information about journals

I always like to go back to first principles when considering questions like this.  The purpose of a citation is to allow another researcher to find the reference in question.

The conventions for citation were developed many decades ago, when documents were always looked up in print, having information like the publisher was critical. These days, we live in an era of search enginers and highly international publishers.  That means that:

Often there is no such thing as a definitive publisher name or address, because it depends on what perspective you take.
There is no unified database for anything, anywhere.  If it is valuable, there are many versions of it, and they will contain conflicting information.
Authors and title are typically all that's actually needed to uniquely identify a document.

What's typically really important to get right is: author, title, and publication venue (journal, conference, [chapter in] book).  Many citation formats won't even show the publisher or address.  Likewise, online-only publications like the PLoS journals don't even have a meaningful address or page numbers.  For the rest of the fields: don't give incorrect information, but any of the reasonable variants of correct information is fine.


Education or employment: What is a post-doc? What is a PhD student?

The legal situation in Israel

I mention Israel first since am involved in a legal case before the Israeli national labor court on this very question: Arguing that those PhD candidates who are required to work all week long, who are forbidden from working outside the university, who can be required to teach up to a limit according to the needs of their academic departments etc. etc. - who contribute significantly to the research (and teaching) "outputs" of the university, should be considered its employees, and the monthly "stipends" that they get should be recognized again as their salary. This is case ע'ע 5439-04-16 (Labor Appeal 5439-04-16). I've authored a booklet on the history of this struggle, which has an English version:

"These are student recipients of prizes": On the erasure of the Technion's junior researcher class

Or get the Hebrew version; in fact, if you can read Hebrew, you can find the court case documents here.

The legal situation in the US

Another, perhaps more relevant, legal treatment of this matter can be found in the recent ruling of the National Labor Relations board, in the case of Graduate Workers of Columbia University, UAW, AFL-CIO vs the University of Columbia (NLRB 364-90: HTML PDF, all case files): The court has found that, indeed, Graduate students who perform meaningful research or teaching work as part of the course of their PhD program (and are paid), are considered university employees to the extent of the applicability of US labor law, especially the laws governing unionization and collective bargaining.

That decision reversed the unfortunate (3-to-2) decision in the 2004 case of Brown University (NLRB 342-42: HTML, PDF), which had itself reversed the 2000 decision in the case of NYU (NLRB 332-111: HTML, PDF).

See also the AAUP description of the Columbia U case and their position.

The actual answer

I can talk for hours, literally, about this subject, and I actually have... but in a nutshell:

Being an employee and being undergoing a process of education are not mutually exclusive; and you always learn when you're starting out in a new career path, be it in industry or in academia.
The common labor-legal criteria for being considered an employee can and do apply to many/most/all PhD candidates (depending on which state in the world, which kind of PhD work etc.)
A university is an organization whose ongoing objectives are to produce research findings and to teach students. If you contribute towards those goals (by performing research and teaching), even if you're also undergoing a process of education yourself, you should be recognized and remunerated as such.
Post-Docs only undergo any sort of education through their practical research work (which, of course, involves learning - but that's the case also for the most high-ranking Professors); they don't take classes, get homework and take exams to see whether they've studied well enough. so about them there should not be any doubt of being in relations of employment.

as for why have PhD candidates when you can have Post-docs - I've already written enough, let others discuss that :-)


What is considered a new submission and a resubmission?

If your experimental paper is rejected, and you submit a paper describing the same experiment, that is a resubmission.  It is not a new submission.  Changes to the analysis such as selecting different participants are not sufficient to make your old paper a new paper.
Exceptions may apply for particle physics, other research based on huge databases, and observational research that does not have experiments.


Applying for PhD position to multiple professors in the same department

It is ok, since she already told you no. It is your right to find new one and to apply to us many as possible positions.
I think you should know that if you would like to work on someone's projects, it is highly desirable to have experience.


Yes, there is an agreed upon standard and it is specified in the Guide to the expression
of uncertainty in measurement (GUM), section 7.2.2, prepared by the Joint Committee for Guides in Metrology (an ISO committee).

Both forms are equally valid, and people use them indifferently. The first form is just more compact and it is particularly useful in tables, abstracts etc.

For an uncommon usage of the first form, see also this answer of mine on Physics SE.


How often do Ph.D. holders hold faculty positions in different, but related, fields from their Ph.D.?

For interdisciplinary researchers, this sort of thing can happen fairly often.  For example, if you are a chemist working on ecological applications, you might well have started out in a chemistry department and end up in an ecology department, or vice versa.  This happens even more so when dealing with disciplines that may be categorized differently by different institutions: for example, is work on medical devices part of biology and the natural sciences faculty or part of electrical or mechanical engineering?  Generally, however, if it's going to happen, there is at least some logical trail that you can see how the faculty member got from point A to point B.


I would suggest to focus on the most important part of the essay, i.e. the part you feel the strongest about and where you really get into the details of the topic, and leave out introduction & conclusion for the most part and instead write an abstract which summarises these points. Of course do keep bits of the introduction & conclusion to lead into & out of the topic, but that might only be a sentence or two and mainly for readability.


Why are UK universities "disproportionately successful at winning EU-awarded research grants"?

Universities in the UK (and universities in Northern Europe in general) are just better on average, with better infrastructure, better English skills, the means to hire better people, attract better students and in the end to write better grants (that might or might not be written by professional grant-writers). These are Framework programme grants for which there is Europe-wide competition.

This isn't entirely fair, that's why universities/research projects in poorer European regions are funded by the EU using more localized grants, as part of the European Structure funds. Usually these grants are not open to Europe-wide competition, and the UK can't win them all.

Another comment on how "disproportionally successful" could be counted. If they just counted #grants-with-UK-participants / #grants the UK would come out ahead because of its large population (the same for Germany). Almost all grants will have UK / German groups involved, as it's hard to get 10 research groups & companies together without taking one from the UK (or Germany).


Why do we put so much weight on final exams?

What's the alternative?
Exams have been criticized since before I can remember, but if someone has come up with something better I'm not aware of it, e.g.

Oral exams would "work", except those would also be high-pressure examinations, and they are also very time-consuming. Furthermore, unless one records the oral exam, it would also be difficult to resolve grading disputes.
Homework-based assessment is vulnerable to cheating, since the student can get 3rd-party help with the assignments and it would not be easy to catch. Students can also work in groups, with associated problems (it's quite common for a few people in a group to do most/all the work and the rest just copy them).
Subjective assessment where the teacher simply assigns a grade to each student is vulnerable to biases (which is part of the reason why grading schemes and/or blinded assessment are common).
Finally, there's a school of thought that if you are unable to reproduce the learned material, under pressure, you haven't actually learned it.


Free Database to Verify the Accreditation of any College or University in the World?

For information about European institutions, the best starting point for such an online search is possibly the ENIC-NARIC network (European Network of National Information Centres on academic recognition and mobility) which lists the national accreditation organisations.

A list of accredited Swiss higher education institutions can be found at the site of the Rectors' Conference of the Swiss Universities CRUS.

A database of accredited study programmes in Germany can be found at the site of the German Accreditation Council.

The Accreditation Organisation of the Netherlands and Flanders NVAO has a similar database of Dutch and Flemish study programmes and institutions.


What are some characteristics of top quality research work in math?

Since you ask about top quality research, I'll say some things about the extremes. Perhaps you can extrapolate a bit from the extremes to come to an understanding.

The first kind of superlative mathematical work is one that settles an old problem that many have worked on unsuccessfully in the past.

The second sort, though it may take a while to recognize it as such, is a paper that opens an entirely new field of mathematics. Sometimes the originator may not even recognize his/her work as a fundamental advance.

So, really good math papers are those that, perhaps, approach one of these extremes in some way. An old, settled, result proved with a new technique might be interesting if the new way of proving something lets others think in a new way about other problems.

Non mathematicians often think of mathematics as a bunch of facts. Early learners in mathematics think of it as proving theorems. But before you can have a statement of a theorem you need the insight to see what might be true and provable from what is already accepted. Some of those insights turn out to be valid, others not. But it isn't about the facts, nor about the proofs of the facts, but an exploration of what might also be true and provable. If you can do that, you are doing real mathematics.


Two abstracts accepted for oral and poster presentation, but I prefer they are swapped

It does not hurt to ask. You can send a polite email explaining your reasons and ask if it is still possible to swap the talk with the poster. It is possible that the decision of the conference committee was based only on the number of slots available, and they will not hesitate to swap talks at all. It may be also that their decision, as you described, is based on some evaluation of strengths of the abstract and potential interest to it among the participants. In this case they will simply refuse to do as you ask, but you lose nothing but a bit of time.

The request to swap talks is not quite common, I guess, but also not unaccepted or weird. I would say, it is worth to try.


How important are poster sessions in conferences?

A poster session is a good way to disseminate your work: but it has nothing to do with how you get credit for your work.

Some computer science venues have moved to a model where papers are reviewed and accepted, but the vast majority of papers only get a poster presentation at the conference. Another model is where all accepted papers are invited to a poster session. So it really depends on your area and venue.


“When you feel your paper do not have high chances to get accepted”… then I suggest you don't submit it for publication in the first place!

It has happened that I have submitted a work which I continued to work on improving, but it was definitely in some very specific cases, where

the improvement in question was nice but absolutely not crucial to the paper,
had no impact an any of the conclusions of the paper,
I was not sure the improvement would actually work.

Basically, something like submitting the paper while continuing to tinker on Figure 2, thinking without adding or removing any data there might be a better way to present it, but it required getting a new software license and learning how to use it. Or submitting a paper while thinking that “hey, this is totally publishable, but if I continue running the simulation while the paper is submitted, maybe I can get the curve on Figure 3 with a little bit less noise”. But nothing as extensive as changing the text.

What should you do now? — Well, if you think reworking on the paper can in a significant way improve its chances of being accepted, I suggest you withdraw it from consideration. If you submitted not too long ago, the editor and referees might not even have wasted much time on it yet. So write to the editor, apologetically explaining that you've realized you made a mistake in submitting your paper too early, and would like to withdraw it. It's not a very nice thing to do, but I still believe it's in your interest.


Whatever general advice this forum can offer is in my opinion extremely unlikely to offer much insight into your specific situation (though I'd love to be proved wrong by other answers). As you said, this is an issue of departmental policy, so you need to have a good long conversation about the situation with your department chair or grad/undergrad (as applicable) program chair. It is their job to set a policy on such matters that is legal and reasonable and provide you with any resources you need to do your job effectively and without creating an unreasonable workload for you (source: I am a department chair). And of course you will be able to provide them the necessary details that you cannot mention here. Good luck!


Does disability impact on prospects of employment in academia?

Self-identifying a disability at some stage during the interview process is usually in your best interest. Being upfront with a potential employer can make all the difference, especially because of the legal protections it affords you in most academic settings. It's also important because then expectations are properly set at the beginning of the process, rather than having to "adjust" later on.

Additionally, many application processes (at least in the EU) allow for self-identification of illnesses and handicaps that could "slow down" one's career. This allows one to "lengthen" the eligibility clocks for many programs. This helps to ameliorate the problems you mentioned of being judged against a cohort that has had more time to work.


What salutation to use for someone with a PhD who is a Lecturer or Reader in the UK?

The person's title in this case is (almost always) Dr, so "Dear Dr Last-name" would be the standard salutation for a first correspondence.  If they sign their reply with their first name, then you can consider yourself welcome to write "Dear First-name" in future.

Academics in the UK are very used to receiving email addressing them as Professor, so it's not a big problem if you do this, but there is probably a slight increase in the chance that they might view your email as spam (I say this because the overwhelming majority of emails I get which address me as Professor are at least somewhat spammy).
If someone's title is Professor, this will always be listed on the university website, so if you've done your research and found out that they are not a professor, it's probably best to use Dr.


Is a professor required to provide homework solutions?

No. The professor gets to decide if it would be more beneficial for students' learning to provide full solutions, partial solutions, or no solutions to homework problems.


how to find whether this paper is already available or not, if authors just changed the Paper title & author name?

There are several software available for checking plagiarism, which would also fit the problem you are investigating. The journal (actually the publisher) for which I am editor use iThenticate. I am not in a position to compare the numerous software and services around, some free, some commercial. However, a simple check that can easily be made is to to a Google search on bits of text. I have personally used this to check on similarities between manuscripts and earlier published articles to check on the degree of overlap and it works fine. It will give you a first indication at which stage you can decide on continuing with a more advanced analysis.

See also answers in What is the easiest way to check for plagiarism in student essay papers?


Should I indicate that definitions are from an article?

That is a great question for your advisor. :)

All I can give is my personal opinion on that, and your advisor might have a different opinion (and in the end, he grades your work, not me, so it might be good to find out what he is thinking):
There are two ways to quote a paper. One is to quote its general content, this is marked by something like

  The following section is based on multiple works by A and B [1,2,5,7].

If, as in your case, you want to directly quote something verbatim, I would make it clear, for example like this

  Definition 7 ([1, theorem 4.3])

Including the exact place where to find it in the original paper helps others to check that you really just quoted verbatim (don't get me started on people who change a quoted theorem to suit their claims...).
As a general rule, always try to make it as easy as possible for people to read and verify your work, without drowning them in unnecessary references. Quoting a famous 50 page research-novel might look good in your sources, but if you don't give the exact place in there, almost no one will have time to check what you are quoting.


How to tell whether invitation to special issue of a journal is worth being accepted?

First things first, Entropy is an MDPI journal. MDPI is a rather controversial publisher - see the "Controversies section of its Wikipedia page - and while I make no judgment on whether it's a predatory publisher, it's preferable to know the facts so you can make an educated decision on whether to publish with them.

If you conclude that it's worth publishing with them, then factors to consider are:

Do you have anything relevant to contribute to the special issue?
Do you know who the editors are? Are they authorities in your field?
How good is the journal? Have you read/cited papers published in it? If not, you can still look at the papers in its current issues and draw your own conclusions about its quality.
Which databases are the journal indexed in? This is usually a concern, but since you mention "impact factor", that means the journal is indexed by the Science Citation Index, and that's the index to be concerned about. If the journal is indexed there every other index doesn't really matter.
How much is the article processing charge, and can you afford to pay it? MDPI is an open access publisher, so you can only publish OA with them, which usually means there's an APC. It's possible they're offering you free OA (this is especially likely if you're an invited submission, similar to how invited conference speakers often have the conference attendance fee waived). Otherwise they might simply be letting you know that you might be interested in this special issue, in which case you'll probably need to pay the APC.

But in the end the final decision is up to you. If you submit, acceptance is not guaranteed, although I'll venture that your chances are relatively good. If yours is an invited submission, then you might get to list that prominently on your CV; even if not, it's still +1 to your publication count. But preparing a submission will take time, and if you have nothing really worth publishing available, that might not be time well spent. It's up to you.


Is there a bias in top tier PhD admissions at top tier universities to favor those with undergraduate degrees from other top tier universities?

Excuse my short answer: absolutely.

Obviously, a school with a good, or even a great name, will give a candidate a big boost in his/her application. This is a rational decision: the recruiting committee wants to minimize any risks and they don't have much time to delve seriously into the history of each candidate. So if you graduated from a top school with excellent credentials you will have an edge over those with equal credentials but lesser perceived schools.

Good references from colleagues of faculty in the department you're applying to, and good ties with your school are also strong factors for admission.


My degree (pure math) is from long ago and almost all my work was done working alone, though I had an office at the U. There were two exceptions. One was that the coffee lounge was both a good place for a break and a good place to bounce ideas around. The second was that we had a periodic seminar of a few faculty and students interested in the specific research area.
But both of these (other than someone else making coffee) are doable in the modern world with internet connections. There is no reason to give up the "contact" with others if you have access to email and zoom. Even the seminar environment can be replicated effectively.
One issue for some is the possible distractions of having family around as you work. I had two children by the time I finished, so working at home (pre internet) would have been pretty difficult, even though the work I did was mostly in my own head and not collaborative.

I suspect that in applied math, closer contact with colleagues is more important than in pure, but I don't have experience with that.
But, the world is as it is. We all need to learn better ways to cope with that.


Is it considered rude to enroll at a funded conference and then retract your enrollment?

The negative effect is that it may be difficult for the organizers to re-allocate the partial funding they'd allocated to you, so someone else missed the chance for funding to attend.

On the other hand, "the system" is not really actively worrying about your larger welfare, nor about the welfare of whoever missed funding due to your change-of-heart, and "the system" will not be "harmed" by your withdrawal. The organizers will scarcely notice whether you were there or not, funded or not. It's small potatoes.

Between those two extremes, granting that you yourself do have to reasonably play the odds for funded attendance at conferences, you should aim to be "a good sport", not inducing commitment of far more resources than you'd possibly use, thus, freezing them and denying use to others. But don't be exaggeratedly altruistic toward "the system", since the relationship is very unsymmetrical, not in your favor.


Entering Economics Ph D from M Sc Behavioural Science

I certainly don't see a MS in Behavioral Science as a negative, and I don't think any econ PhD program that does research in behavioral economics will either.  The reason you're interested in it is the same reason it applies well to that subfield.  That said:

You may make yourself more competitive in a program that emphasizes behavioral econ, at the opportunity cost of making yourself less competitive in a more traditional econ program, so make sure this is the field you really want to focus on.
You will still need the math.  So if you've studied multivariable calculus, differential equations, and real analysis anyway, then you've probably cleared many of the important bars.  If this MS you're considering would come at the cost of taking those core econ PhD pre-reqs, then that would be a problem.  Not necessarily an insurmountable one, however, if you can figure out how to fit those classes in.


For my PhD, should I go with the more prestigious university, or the one that is a better research match?

If you want to stay in academia, your top priority should be producing excellent research.  From your post, it sounds like this will be possible at either university.  Another helpful factor is your academic advisor.  Ideally, you can study under a very famous/well-respected/talented person.  Again it sounds like you have two good options in this regard.
If I may, it sounds like you have two good options.  This is a positive to me in that you cannot 'screw it up' and make the wrong choice.  One piece of advice is to consider the process of obtaining your degree rather than what happens when you're done.  You're looking at years of effort, so why not try to enjoy/maximize it instead of fretting about ultimate placement?  Live 'in the moment', as the millennials like to say.
A last cliche bit of advice is to flip a coin.  Heads = A, Tails = B.  Once you see the coin land, you'll either feel a quick sense of glee or sting of disappointment.  Then ignore the coin result and pick based on this feeling.  Good luck!


Single or double thesis for double major?

Write one thesis, so you only have to write one introduction and discussion section, and only have to go through the thesis formatting nightmare once. If you prefer two small projects, you can make two projects two separate chapters for your thesis and just try and figure out a way to relate them in your introduction and discussion.

Make the title of your thesis sound applicable to the field of study you want to get your masters in (no one will read your undergrad thesis on the admissions committee and I doubt anyone will care whether you wrote two theses or one).

You say you have a low GPA. Perhaps two smaller projects (still for one thesis) will allow you to collaborate with two different professors. Why is this advantageous? Because that is potentially two very strong letters of recommendation. Many undergrads have one good letter of recommendation and the rest are just professors that taught a course they took. If you have two very strong letters, that is quite impressive, and will do more to get you into graduate school than anything related to your thesis, short of publishing it in a peer reviewed journal.


Transfer article to better Physical Review journal

Write to the editor and ask for a transfer, explaining the situation. The editor will tell you what the preferred action is. Asking for a transfer, rather than withdrawing and resubmitting on your own will not hurt your chances, rather the opposite, as the editor then knows what is going on - and you don't risk to fall under some rule of the manuscript need to only be submitted to one journal at a time. Since both journals are under the same umbrella, they should have no problem at all with this.


Pros and cons of doing PhD in a research group with a high number of post-docs?

There are too many variables for a general answer. How do the post-docs work? Do they work together? Is the lab environment friendly and helpful or cut-throat. Are they willing to help you? Are they new at this or beginners? All the combinations could balance out to something good or bad.

But most important is how interested your advisor is in helping you and spending the necessary time for it. The rest is probably just noise.

But a cooperative staff can be quite helpful if you are getting started. There is a lot of experience to draw on since the post-docs come from different institutions.

But do what you can to keep everything friendly and helpful. Establish a working relationship with your advisor. Don't be shy. Ask for help when you need it. Give help when you can.


The best advice I heard about this is: Write the thesis in the way you would like to have had it at hand when you started your thesis. Imagine yourself in a situation that you are a master's student and want to learn about the very topic of your actual thesis. What detail do you need? What background should you give? What literature should you refer to?

I often hear students say that their advisors do not really care about these issues, and indeed it's somehow true. As an advisor, you care much more about the content. This does not mean that the presentation does not matter, but it is not that much about what background you give, but how. Do you treat simple things at length but brush over more difficult things without proper reference? Do you provide proofs for standard facts but use advanced concepts without any argument?


Should I email Head of Depart. personally to seek faculty (unadervertised) positions?

I doubt that it would be appropriate and would be considered a bit odd. Most places, anyway. If there are no advertised positions, there are likely no positions at all. If there are advertised positions they will come with stated application procedures.

The department head normally isn't responsible directly for hiring faculty. It is a faculty committee decision and in some places the laws of the land require advertisements and fair consideration of candidates using published criteria.

I think it would be a waste of time to request a job. You don't say where you are, but I think that most in most places it would be improper to hire without advertising.

However, you might ask if the department contemplates hiring in the near future and where to look for announcements. But I wouldn't go beyond that.


In a camera ready paper (has been accepted), how to cite my own paper that is still under blind review?

While something is under review, it's in an indeterminate state and might not survive the review process. Once something is published, all of its critical supporting references need to be available.

Thus, I believe that the correct approach here depends on whether paper B actually depends on paper A, or if it's just a "related work" (e.g., "In Paper A, we solved a different problem from the same family of problems."):

If Paper B depends on Paper A, then I think you have no choice: put a preprint of Paper A into arXiv (or similar), and hope it doesn't hurt the blind review process---and in most cases it probably won't.
If citation of Paper A is only a "nice to have" for related work, then I would instead suggest simply dropping the citation, since the related work has not yet come into being. When I had much the same thing happen to me, I ended up following the second route, which was the right thing to do.

Nothing, however, can protect you entirely from the vagaries of the scientific publication process: in my own case, the first version of my Paper A was rejected partly because the reviewers took so long that they ended up complaining that I didn't cite my Paper B in it!


How do I effectively use tags to organize my bibliography?

Tagging is only useful if you use it with discipline. Look at Wikipedia or Stackexchange, most articles can be determined by 5-6 categories (science - math - geometry - euclidean geometry - metric). Stackexchange has a max. of 5 tags, often you only see 1-2 on questions, which is often pointless, as those tags will appear often in the question/paper title and abstract too. Wasted time.

So, if you decide to create a tagging system, use at least 4-6 tags depending on how interdisciplinary and specialized your paper/link collection is.

Also consider to not only tag by topic but also kind (review, letter, peer-reviewed, experimental results, theoretical analysis, explanation of new measurement method, meta-discussion...), year, personal rating (very interesting article you learned a lot from and should read again from time to time), rarely/often/top cited, new theory/model, strongly discussed in the research community

A last note. I use myself Copernic Desktop Search as a supplementary tool, I download all papers of possible interest (disk space is cheap ;) ), papers I read, will read or maybe will never take a look at. The point is that Desktop Search software often has more powerful search operators and sorting mechanisms than Google Scholar & Co. If you know how to use them, you can save a lot reading and tagging time or tagging at all. You know, if you are smart in using Google & search operators and have a good vocabulary, you don't have to ask a lot questions on internet boards.

Conclusion:

Don't use tagging for creating a pure thematic and linear directory structure, if finding again your papers or bits of information can be done by learning a good Desktop Search software. Use your tags in a personal way and remember, the point is not to structure your bibliography like a folder directory for categorized files, the point is to find again the bits of knowledge and most memorable papers, which will rather look like a strongly interconnected nonlinear tag cloud. If you look how people tag sites on del.ic.ious, often only 2 or 3 tags, sometimes using up to 10 pure thematic redundant tags, they are doing it imho wrong and waste a lot of time.


Can I still publish a paper on peer reviewed journals several years after publishing it on ArXiv?

You speak of ideas, yet ideas are worth close to nothing without results, at least in the academic understanding. Sure, they are the beginning, but are not intellectually protected by themselves. Anyone can have an idea, but it takes work to develop that idea into a solid contribution to science.

So, if you have real "discoveries" and "important advances", you shouldn't be afraid to submit them for peer-review, as that is the only way to scientifically validate your work. Otherwise, it doesn't matter if someone develops on your idea and doesn't cite you. Similarly, it doesn't matter where you put those ideas, it could be arxiv, your personal website, facebook, etc.

As stated in the comments, you can submit a preprint and also submit to a journal, the preprint puts a timestamp onto your work so you have time to publish it (even if it gets rejected and you retry). However, this holds only for work that has the chance to get accepted for publication, i.e. has some real contribution.


You can certainly add them to your CV. There's no general rule on how to write CVs so it's more or less personal preference. For an academic CV, teaching might be an important point, so I like to include "teaching experience" as a section but I prefer only mentioning "supervision of 5 bachelor theses and 2 diploma theses", otherwise it would get quite long.

In the end: if it makes sense and the information provided shows your qualification for the job then you should include it.


Is Manuscripts.io a legit tool? Any experience with it?

A good rule of thumb is that when you get something for free on the internet, you're the product, not the user.  There is often something being done with some or all of your user information or content you provide to generate some cash flow somewhere.  Or, you may be an advertising target.

An exception might be some academically developed mechanism supported by some society.

Poking around the website you point to, though, I see no Terms of Service immediately available, and this is a red flag.

There isn't necessarily anything inherently wrong with an arrangement like this.  You might find the service provided worth any use of your content/data or putting up with ads.  SE network, in fact, does this openly, and we're still here.


What does delegate registration mean in a conference?

Usually, this definition is extended to all the attendees of a conference, not just the presenters. So the delegate registration would be for anybody wanting to attend the conference


What is the most effective way to negotiate for more time while waiting for other offers?

You should consider how "in-demand" you are, both in general and for the positions in question. For the second position, if you have reason to believe that they will indeed make you an offer, you can approach them along the lines of "I would like to be able to consider your opportunity alongside my other current offers; could you give me some guidance as to when you expect to make a decision on my application?"

For the first position, they've made you an offer, so you need to judge whether they want you there enough to give you some extra time. You'll get differing advice on this point, but I would not mention that you're waiting for another offer (unless you are confident that they will wait). Again, this depends on whether you're in a buyer's or seller's market, so to speak. No harm in asking for extra time straight out, though.

If you need more time to decide once you have both offers in hand, I think it's best to be upfront that you're choosing between offers at that point.

In general though I think you have to be much more careful about pressing the first institution unless you really think you have leverage.


Telling a former supervisor you don't want to publish

Keep it short and sweet:

Dear [her name],
Thanks for the reminder about our project. I thought about it some more, and for personal reasons I won’t be able to continue with the work. Since you have all the data I suggest that you pursue publication by yourself or with other collaborators. And, if it matters, I do not care very much about the issue of coauthorship, so whatever you end up deciding about who should be a named coauthor of the paper once it’s finished is fine with me.
Regards,
Gerilk

An important point is that, since you’re worried she will try to pressure or guilt-trip you, you should not apologize for or explain your decision. Manipulative people are expert at using every sign of guilt or embarrassment to pressure people relentlessly until they get what they want from you. I can almost guarantee it from experience: if you give her a reason — any reason — she will find some counter-argument to make that reason look invalid or insufficient, and will repeat this as many times as necessary with any additional details you add to your explanation, until you give in. Do not give her an opening to do this. A firm “no” with no explanation is the only approach that works with this type of person.
Good luck!
Edit: there’s been an extensive discussion in the comments about whether the email should mention the subject of authorship. To clarify, I don’t think it matters very much if you mention it or not. I included that part since, first, it seems factually true based on what you said that you don’t care about authorship; and second, letting the former supervisor know this eliminates one possible pressure point she will surely try to use to keep pressuring and annoying you in the hope of getting you to change your mind.
But if you prefer not to mention this, that’s pretty much just as good and won’t particularly affect the outcome.


The abbreviation iff is generally understood in several fields outside logic, and in my experience it is well understood by physicists, but the golden rule is to define every abbreviation at its first use and/or provide a list of abbreviations. In this way, even those not familiar with an abbreviation will be able to understand the text.
However, in general, abbreviations may make a text less readable and therefore should be used judiciously. Thus, ask yourself if you will have to use the expression if and only if so frequently to warrant an abbreviation, sparing you just a bunch of characters, and think whether to limit its use to e.g. theorem statements.


How do I respond to a review of the wrong version of my paper?

Consider the pragmatic approach to this issue: you have already revised the paper according the reviewer’s suggestions, so only the response needs to be worked on. (Apart from other comments orthogonal to this main issue.)

Given that you already called the attention of the editor on the problem and he did not follow up on it, you clearly need to weigh carefully your response (unless you want to pick up a fight). I would suggest that you write a very detailed response letter, in which you explain how the manuscript addresses the reviewer's comments and questions. Do it point by point, quoting all the parts of your manuscript that are relevant (and locating them: page and line numbers).

Just do so by being slightly evasive about the exact evolution of the manuscript. Where you would normally say “we have added a paragraph at the end of section B”, just say “the revised manuscript includes a paragraph addressing the reviewer's question at the end of section B”. It's not untrue, though it is not perfectly clear.

Also, consider going for another journal. If you believe the editor has been treating somewhat badly, you might want to just let it drop and submit somewhere else. It's a complex decision.

Or, if you think it's worth it: make a stand for it. Appeal the editor's decision to the editor in chief, on the basis that a factual error was made. You need to be both strong and diplomatic in your appeal, and back it up heavily with facts. It will be easier if the incriminated review actually quotes some text that has changed in your revised manuscript, in which case the error is evident.


How to export Google Scholar keyword search results to Excel?

Check out Publish or Perish. You can run keyword queries on Google Scholar from there, and export the results to .csv, which you can later open from Excel


I graduated with 1st class honours - do I add it to the letters after my name?

No. The class of a degree is not written in your post-nominal qualifications. You can add it in he educational details on your CV.


What is the expected time commitment for a part time Research Master's Program?

Your planned schedule sounds reasonable, but I would be more concerned about the energy commitment with full-time employment, particularly with a learning disability. Depending on the nature of your disability, the kind of work you do at your job, and your schedule, you might find that you have very little left over for quality academic work after your job commitment. So try it for a semester, but have a backup plan in case you find yourself overloaded. Six years is a long time to run yourself ragged.


How technical should my oral PhD defense be?

You need to find out what the standard is in your department, since it varies. You can:

ask your advisor
attend other defense presentations in your department
ask students in your department who have successfully defended


What to do when the reviewer is wrong about your paper's scope, technically inaccurate, and clearly haven't read your rebuttals

Moving on is the best approach, as @lighthouse suggests.
If you don't like the best approach and prefer to combat it, you can ask the editor for another reviewer. Politely, on a day you feel great about everything else in your life and after being absolutely showered by compliments by all of your friends has put you in the very most positive mindset, write a rebuttal identifying the review's shortcomings and suggest to the editor that some bias seems to be preventing a good review and that you ask for another independent review.
If they send it to another reviewer, your fate is then in their hands. If they refuse, well, you're back where you started: move on, submit to another journal. You express concerns about an overlapping conference submission but if your field accepts conference papers as papers then the journal article doesn't matter, and if your field does not accept conference papers as papers then the conference doesn't matter.
"Bad reviews" like you describe - not bad in terms of negativity but intrinsically poor - are common.


What is the correct year to use in the reference list?

You can find this in books which are published at the end of a year. For instance, if books are published in November or December, publisher will state this year as publication year in their online catalogue. But the publisher has also assigned such a published book for the following year, because it will be mainly promoted and distributed to libraries, book stores etc in the next year.  Here is another example of 2 different years of publication of a book: publisher website states 2016 and google books shows in the book 2017  In case you have read the book and not the few pages on google books, I would say the year in the book is more reliable and would cite it as 2015.


How should I include a list of links in my thesis?

Personally, I am in favour of adding them as references in the bibliography section.

With that said, I am from a CS subfield that is very close to the "real world" in a way that related work is almost always a motley mixture of peer-reviewed publications, books, newspaper articles, technical standard documents (such as those by W3C), and actual innovative software or websites (whose concepts were never formally published in a scientific venue), i.e. sources with a continuously varying degree of reliability. Consequently, trying to find a well-defined rule about what to add as a footnote and what to add as a bibliography reference is certain to give you headaches (and uncertain to lead to a useful and consistent result).

However, I can see a few (maybe a bit subjective) general advantages of using bibliography items rather than footnotes for links (in no particular order):

Bibliography items tend to more or less have a fixed format. Frequently, meta-information such as year of publication or author can be provided for web resources just as it can for anything else. When using a footnote, authors may be tempted to just provide the link and skip the meta-information that would be naturally included in a bibliography item, thereby foregoing both any due attribution and any information required to possibly locate the resource again, should the link die.
I have seen styleguides that generally forbid the use of footnotes (e.g. "Please do not use footnotes at all!"), but I have yet to see a styleguide that generally forbids the use of a bibliography. By not using any footnotes, your manuscript is one step closer to being agnostic of the final formatting used (and thus matches with the ideal of separating content from layout).
If the same web resource is mentioned twice throughout your document, there is absolutely no problem if the link is provided in a bibliography item, which is simply referenced twice in your text, if appropriate (e.g. if the two mentions are sufficiently far apart). If the link is in a footnote, on the other hand, things are not so clear:

The footnote can be added several times in the document. However, this means a waste of space, and it may also confuse readers who expect some new information when reading a new footnote for the first time, or who might wonder whether they are looking at a copy-and-paste error where a previously unmentioned link should be provided. Personally, I consider this "solution" downright bad style.
The same footnote can be pointed to several times. While this may be slightly cumbersome in some typesetting software, it is definitely feasible. However, it significantly increases the effort for finding the footnote (it might be on any page in the document), and the need to switch to another page than the one the reader is currently on kind of defeats the purpose of footnotes, anyway.

As a reader, I find keeping track of references, figure numbers, and table numbers that I still want to look into after finishing or while reading the current paragraph or section hard enough. There is no reason to add yet another independent list for footnote numbers.
Also as a reader, I have a certain expectation what amount of information I will find when following a pointer to additional information. For bibliography references, it is clear that the pointer points to an entire external document. For footnotes, I conversely prefer it to be clear that the pointer points to no more than one or two sentences worth of additional information (for which I do not need to search for and/or open another document).


How to identify future directions in a saturated field without getting discouraged

If you browse through top 10 schools (or researchers') websites, you might get a "feeling" on where (or what) their research is heading towards! For example, you can check what their newest post docs are working on, PhD students' thesis titles etc. You can also do the same thing by checking NSF newly funded proposals. This may not give you a definite answer, but it might help you establish a "directional sense"

PS.
I'm in engineering not math.


At how many citations should I make my Google Scholar profile public?

As someone who is currently on a search committee for two tenure track positions in mathematics, I can tell you that "hiding" your profile certainly won't help.  In the job search process, potential employers are going to want to know about your research and its impact.  It's common to check on Google Scholar, Math Reviews, Web of Science, and similar databases to see what impact a candidate's research has had.  Many of the candidates for faculty positions that I've seen don't have public profiles, and in my opinion this makes them look weak in comparison with candidates who do.

If you don't have a public profile then someone trying to evaluate your research who looks at Google Scholar will probably find one or two of your most cited papers or perhaps find nothing and assume that you have essentially no citations.  Another possibility is that they'll find a confusing bunch of papers written by other authors whose names are similar to yours.  Having a public profile ensures that they'll see all of your publications and citations.  Even if there aren't many citations yet, this also shows that you're aware of the importance of documenting your research activity and its impact.


PhD opportunities when lacking publications

You have to make the case that your research potential outweighs your lack of research output.

The only places to make that case are your research statement and your letters.  Both your statement and your letters should make it clear that you are an active researcher, even though you are not yet published.  Your statement should describe the specific research problem(s) that you are pursuing, promising and specific partial results, and a specific and well-informed plan of attack.

Similarly, letters from faculty at your MS department should describe your independence, stubbornness, intellectual maturity, and so on, in specific and credible detail.  When you ask for letters, ask your references specifically if they can write a strong letter about your research potential.  Ideally, your references should admit that their department doesn't provide you with the environment that you need to thrive as a researcher.  And it really hurts to write “[Bravo] can do better than us,” so it better be true.

Admissions committees (at least the ones I've been on) do take applicants' previous institutions into account when judging research records.  We know that  applicants from most 4-year liberal arts colleges don't have as many opportunities for computer science research as applicants from (say) MIT, so our expectations for MIT applicants are higher.  So your lack of publications may not hurt you as much if your MS department is known to have a weak research atmosphere.

However: Do not suggest in your application that your lack of publications is your MS department's fault.  You may believe it's their fault, and you might even be right.  But if you actually write that it's their fault, you'll come across as someone eager to blame others for your weaknesses.  No matter how good you are at research, nobody will admit you if they think you're a jerk.


Why don't typical US colleges offer more online courses?

I think there are multiple reasons, I'll touch on some:

Currently online courses tend to fill a gap for students who otherwise would not be able to complete many courses.      This allows non-traditional students to have a chance at academically being competitive, although traditional students sometimes utilize them as well. They aren't designed to replace traditional courses, but to augment them.
It's harder to verify who is actually doing the coursework.
      This seems like  a fairly important issue, after all, you want potential employers to be confident that the degree a university bestowed means something - namely that you earned it. As a university, you want to be sure that your students aren't cheating.
Market saturation.      In-line with the previous bullet point, if classes were very cheap for many students, universities wouldn't be able to charge as much in general per student. This essentially translates to a lower value "per degree". This effectively tackles you point about joining "reputable" universities - the general train of thought is "If everyone can get in... is it necessarily reputable?" (Definitely a con from the university's point-of-view as they can potentially inflate their importance by limiting degrees conferred.)
Points of failure.      An online class, depending on the format, could potentially require a large amount of bandwidth. This means the university would be footing the bill to effectively run these courses, and the facilities to run quality web-based courses may not be cheap. While it's true the lectures could just be recorded or utilize some sort of learning software, decreased student interaction tends to lead to lower grades overall (Source: multi-year TA)
Decreased profit.     Arguably, I believe colleges make a fair amount of money by physically having the students on campus. "Butts-in-seats" mean that they charge more longterm for dormitories and food. Increased physically facility usage allows colleges to approach benefactors for more money, citing student use and need of expansion. Benefactors want a dorm with their name on it, not a server rack.
Collaboration.     Not the bad kind, mind you. Like @WetLabStudent mentioned, physically being at a college or university exposes you to ideals, people, and methodologies you might have never come in contact with. The ability to interact with a large spectrum of people is an important skill for the vast majority of students to develop.

This isn't an exhaustive list, but I hope it raises some of the issues. If I missed a few more major relevant points, feel free to comment.


Why do you need to study a subject at a university level to teach it at a high school?

On one hand, when I myself was in high school I was wondering about the same thing - especially that I learnt the whole high school material (in maths and physics, I mean) in the first year, so felt that I could have taught as well as a teacher. But indeed, as pointed out by Xander Henderson and Massimo Ortolano, only at the university (in fact, only during my PhD studies; well, in fact only as a post doc; well, in fact... hm, you get the idea) I learnt the bigger picture.

So, studies are so that if a student asks "what will I need the quadratic equation for?" you could give a better answer than "because it will be on the test".

What is a better answer in this case is a whole different issue. I have lots of friends who indeed, once they finished high school, never solved a quadratic equation again. But on the other hand, they also didn't need the knowledge about Hamlet, genetics, WW II history, etc., in everyday life. That doesn't mean that they, we, you shouldn't learn about those things. I have lots of knowledge that I don't need in my life - but I enjoy obtaining it, possessing and connecting it with other areas.


Why and how do professors go for sabbatical?

I think this will widely vary between professors, host institutions, and home institutions. I will try to address your questions, but always keep in mind that for each point there will be plenty of variations.

  When someone goes to another country, there are lots of unexpected expenses. High rent for a furnished house (for a year). They still have expenses in home country (like mortgage).

Sometimes the professor just foots a lot of it from his own pocket. Sometimes, especially if the host institution is not academic but a company research lab, the host institution will cover this through a stipend, or by providing housing. However, it should be noted that most professors eligible for sabbaticals are full professors, who are in an age and career phase where they are not anymore required to turn every penny twice.

  He will receive half of his salary from home university and zero from host university (not considering exceptions where getting paid for occasional tasks).

This isn't close to universal. In my institution, sabbaticals can be with close-to-full salary. Sometimes, the host institution pays the guest.

  Research Output: He cannot plan for a long-term research. Probably co-supervise some graduate students.

Generally speaking, the sabbatical is a phase of planning, and finding inspiration and future collaborations more than execution. For a senior professor, it may also be a rare chance to actually do some research her/himself again, precisely because one is not necessarily required to herd a dozen grad students to dissertations.

  It is not clear to me where is the place of a visiting professor. In a research group, he is not a postdoc to follow the PI plans to get hand in experimental works, and he is not the boss to plan and conduct others.

Well, the guest doesn't have a fixed place in the host lab as such. What the guest actually does all day will vary, depending on what the goals of the professor for the sabbatical and the plans of the host are. A few common ones that I have seen include:

The getting access to cool data sabbatical. Here, the prof. goes to a host institution (typically industrial in this case) with access to much more and better data. The guest uses his time there to validate (with the host professor and selected students) his theories on the data of the host institution.
The I wanna do this for real sabbatical. Here, he or she takes time off to actually apply his research in practice, either in an existing company or by creating a spin-off. He or she may or may not ever return from this sabbatical.
The setting up new projects sabbatical. Here, the guest ends up spending most of his time writing one or more project proposal(s) with the host professor and other academics in the area.
The marketing trip sabbatical. Here, the guest is primarily an ambassador of the home institution or lab, and spends a lot of time going through academic institutions in proximity of the host, giving talks and establishing connections.
The I really just needed a vacation sabbatical. Here, the guest ends up doing not much at all, except meeting up with some people and giving a talk here and there. The borders between this and the previous one are kind of blurry.
The entirely academia-unrelated sabbatical. And then there are of course the sabbaticals which are quite openly only on paper about anything academic. I have known professors that renovated their house during their sabbatical. I have known one who had medical issues and used the sabbatical to recuperate.


How shall I report an error in a given paper?

The same TA pointed out flaws (of fundamental nature, for example F = mv instead of F = ma) in the model, and once corrected allowed me to obtain the results shown in the paper.

The fact that after correcting the model you can actually reproduce the reported results seems to suggest that the authors did implement their model correctly, but made a mistake when writing the paper.

I think that it is best to first contact the authors, politely explain what you found, and give them the chance to take an appropriate action, e.g. publish an errata in the journal where they published their article (or on their website, if the mistake was really minor).

If they do not react at all, you might contact the journal directly. The editor will typically take care that an errata is published.

When nobody is responsive (I do not expect that in this case, but with a conference article or a fishy journal that might happen), and you consider it important that the scientific community is aware of the mistakes, you could decide to publish your correction somewhere (journal, conference, website, ...).


Is it bad to publish a scientific paper with wrong results?

Publishing things that you know are erroneous is a good way to get a really bad scientific reputation. Depending on how severe it is, it might go so far as to be labelled fraud and formally sanctioned, basically killing your career.

If it's important, then yes, you need to fix it.

If it's not published yet, then fix it before you publish it.  If it's published, then you will need to submit a correction or possibly even a retraction.  Good scientists do this, and it's much better to acknowledge your errors and retract than to have others expose you as a liar.


Is it plagiarism for my thesis advisor to publish a paper using content from my thesis without citation?

Whether or not the department holds the copyright to your thesis is irrelevant. Using someone else's ideas without appropriate attribution is plagiarism, period.

So, if your advisor used your original, non-trivial scientific ideas (or your non-trivial description of those ideas) in his paper without attributing them to you, then he has committed misconduct.

The only thing that may be questionable is whether or not your original intellectual ideas were actually used in the paper. What you describe definitely sounds pretty damning, and the more information you add, the worse it sounds; but as strangers on the Internet, we don't have the whole story.

For example: Given that the idea for the thesis was the advisor's, and the paper describes a non-trivial extension, it's possible (though perhaps not likely, depending on the scope of the work) that your advisor was working on the extended version himself independently of your thesis.

It's also possible that he considers your work to be a straightforward implementation of his idea, and not an intellectual contribution - that is, he believes you were doing the work of a staff programmer, not a scientist or engineer. In which case, an acknowledgement would probably have been appropriate, but it's not necessarily plagiarism to omit it.

The degree to which your work constitutes an intellectual contribution to your advisor's paper is impossible for strangers on the Internet to judge.

I suggest you email your former thesis advisor, tell him you've seen the paper, and ask (in a non-confrontational way) how it relates to your thesis work. Then decide how to proceed from there.

Note that pursuing the matter beyond that (i.e. formally accusing him of plagiarism) may involve some serious negative consequences for you, so consider this carefully before proceeding. The morally just course of action may or may not actually be in your best interests.