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Should I cite every study that supports my point?
Suppose I'm writing a paper and at some point in the paper (e.g. the background section), I write that "Vanilla ice cream is healthier than chocolate ice cream." I search EBSCO and find check all research studies that tested this and find and skim through 15 papers all supporting this claim, including the earliest pioneer research in the area up to the most recent. Is it then appropriate to affix in-text citations for all 15 of those studies to that sentence? What about if I find 50 studies?

Would you be writing "Vanilla ice cream is healthier than chocolate ice cream" before you had some reason to make that claim?

It depends on the purpose of the paper.
If it is a review article on the effects of different flavor of ice cream, it may well be appropriate to cite far more papers than it would be if you are merely establishing the point in a paper containing your original research on the subject. In the latter case you may even be able to cite someone else's review.
Generally speaking, new papers in a field only get published if there is an element of novelty to them. Thus it is unlikely to find 50 different papers saying exactly the same thing. If you need the citation to support your own project, you should be able to find a small subset of those that are most relevant to the question at hand (e.g. if I am using mouse models, I should probably cite prior work in mice over prior work in rabbit models). If you are reviewing a topic, you should be able to find the most important papers out of the group (e.g. the ones that were transformative to our understanding of ice cream health effects).
Additionally some papers will vary in quality or scope. Citing an initial, limited scope paper might be appropriate if you are discussing the history of a topic, but if you are just trying to establish a basis for a claim you may want to go with a later, more definitive study.
Many publications will give you a citation limit when writing for them. So you often won't have a chance to cite an entire library of previous work. You need to be able to pin down the papers that are best suited for your specific need.

The purpose of a citation is twofold:

It prevents you from taking credit for other person's work.
It can serve as an "external appendix" (the interested reader can read more in ...)

Neither requires that you cite everybody. If there is a large body of work done already, then typically one or more overview articles have already appeared. You can cite those, and combine both purposes: you indicate that it is not your finding and the interested reader can find a complete list of references in the overview article.

In case there aren't overview articles, you can always cite a few you like, and say something like "see these and the references therein."

In my field (particle physics), at least, when you give a citation for a result, it's traditional to cite the original result. Many papers that come later might also give the same result, some with the original derivation, some with updated derivations, some with experimental evidence (though that is really considered a separate result from the theoretical discovery in its own right), but they don't all get cited for that one result.
So it probably depends somewhat on the conventions of your field.

Of course, this practice also has its problems, especially when the original paper is very old, in an obscure journal and/or written in a language you don't understand. After all, you're also supposed to have read and (more or less) understood any articles you cite.

@IlmariKaronen I haven't read most of the papers where I am listed as a coauthor, let alone all of the papers that I put in the references section of my master's thesis. (Particle physics papers tend to list as coauthors everyone even tangentially related to the paper, in my very limited experience.) And I am as close to a nobody as you can be in the world of coauthors of particle physics papers.

It's mostly the large experimental collaborations which have long lists of authors that appear on every paper. In any case, I have gotten the sense people in particle physics don't always hold citations to that standard. For example if you cite an experimental result in a theory paper, the authors (who are theorists) would not be expected to understand the details of how the experimental apparatus works.

@yellowantphil: It may happen all too often, but most publication style codes do consider it improper to cite a paper none of the authors have ever read, at least unless the citation is clearly marked as indirect (e.g. "Lomonosov 1759, qtd. in Shiltsev 2014").

It depends on how important is that point to your paper. If you are studying the consistency of ice cream, and you find that vanilla has a better consistency, and furthermore, is healthier, you just need one good reference.
On the other hand, if that is a central point of your article (you are researching how to condition children into choosing vanilla instead of chocolate), you should make a strong point. In this case, is beneficial to put things in perspective:

The first work by Jones in 1976 suggested that Chocolate was not so healthy...

If there is a review, it can mostly replace all the older papers:

The fact was well established since the work by Marks, "Ice cream flavours, health, and little humans", 1998.

and possibly special mention mention those papers that are a substantial breakthrough or strength:

Smith 2003 followed the ice cream preferences of 10 000 white children...

+1 to Maarten's answer.
In addition: likely enough, the more recent of the 50 studies you mention already cite most of the earlier ones, so the reader can just follow the breadcrumbs back - no need for you to essentially repeat the literature survey that was already done in the papers you cite. Stick (mostly) with the recent literature.
Of course, you should cite papers that are most relevant to your study (e.g., similar protocols, similar questions etc.), and if you manage to find a relevant study that everyone else has overlooked, by all means include it.

This makes sense, unless there's a seminal paper.  A think a huge problem is that not enough people actually follow the breadcrumbs back before writing.

Usually one reference is best; sometimes you want more.
In general a single, well-chosen, citation is all that is needed. Select a paper that (a) you've read (b) clearly supports your assertion and (c) is well written and the job is done.
However, sometimes you may wish to include more than one references. The appropriate time to do this is if there is historical reason to do so (e.g. you may wish to cite the original paper and a more recent update), if you wish to emphasize the breadth of support for the point, if the point is - in your view - controversial or if you're giving a historical view and want to cite multiple papers to give the historical perspective on the point.


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Are TOEFL requirements waived for foreigners with US bachelors degrees?
I notice that perhaps most US graduate programs require non-native English speakers to get a certain mark on the TOEFL. Is this requirement typically waived for students who completed their bachelors degree in the US before applying to a masters program in another school also in the US?

Yes it is typically waived for students who did their undergraduate in the US

Could be university specific. check with universities.

I was in this position - as an international student applying to US graduate programs after being a US undergraduate. I contacted the graduate programs I was applying to to ask if they would waive the TOEFL requirement, and they all did (i.e. I didn't have to retake it). I heard recently that the requirement for a waiver (for my current university at least) is for an applicant to have been at a US university for four years.
My backup plan if the graduate programs had seemed unsure about a waiver was to call someone on the phone and essentially demonstrate that I am fluent in English.
(The TOEFL is expensive!)

Yet, it may take some doing to convince them. I know of a case of a eastern Europe citizen that did high school and bachelor, and was speaking with perfect Engish with the admission office, and they were still reluctant (but they accepted at the end).

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NSF graduate fellowship: how specific should the statement of purpose be?
Several of the students who have come to my group as summer students are planning to submit NSF graduate fellowship applications in the coming weeks. However, one question that I am not sure about is how specific the statement of purpose needs to be.
When I applied for the NSF fellowship (going on fifteen years ago), I had absolutely no clue what I wanted to do as a student, other than it was computational rather than experimental. Therefore, my application was all over the place, talking about three different types of projects I might want to work on as a graduate student (and I ended up choosing none of them in the long run!).
However, I get the impression that today such an essay wouldn't be suitable for the application, and that a more narrowly tailored essay is required. At the same time, there's also the challenge of ensuring that the research problem can be done at the school one has chosen, and not narrowing things so specifically that the student is too "boxed in" or too opaque for a review panel to see the merits of.
So how should students thread the gap between vagueness and specificity in writing these and other fellowship applications?

The fellowship is awarded to the student, not to the  research proposal.

Best bet is to check with your school's scholarship/fellowship office, as they tend to have copies of successful in-house applications. Use those as a guide for recent standards.

I think this is an issue that a lot of students struggle with; at least I did when I applied last year.  I was rejected, so probably take what I say with a grain of salt.  They say some things on their website that are important to note.

Keep in mind that NSF does not just seek to fund scientists and engineers; NSF seeks to fund future STEM leaders.
Use appropriate scientific form (hypothesis, figures, references) in the Graduate Research Statement.
Instead of elaborate details on theory, focus on the rationale for your studies and the existing literature as it supports your proposed work.

The students that I know that were given the award properly addressed these issues.  My proposal did focus on one research idea and that was rewarded with comments on the creativity and feasibility of my proposed idea.  One of the critiques I got in my review was "While the applicant does demonstrate an excitement of discovery and should be able to communicate his results to a large audience, ...  Broad societal impacts are not evident with respect to encouraging diversity and enabling the participation of underrepresented groups."
The feedback that I got was based on two scores: Intellectual Merit Criterion and Broader Impacts Criterion.  I would make sure that your students take both into account.  As far as the research proposal goes, I what JeffE said is true.  It is an opportunity for the students to show that they are familiar with the current research and are able to come up with an appropriate idea to pursue.

How the heck are results from scientific research (not in a field like sociology) supposed to increase diversity??

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Should remote teaching sessions be shorter than classroom sessions?
In normal years, when I teach in a physical classroom, I teach in sessions of ~90 minutes, with ~30 minutes break.
This year, all teaching is done via Zoom (in real-time), and I wonder whether I should split each lesson into a larger number of shorter sessions, for example, split each 90+30 session into two 45+15 sessions.
On one hand, students are used to the standard 90+30 sessions; changing it might confuse them. Some students may e.g. forget coming back after the break, and this may cause a waste of time after breaks.
On the other hand, in remote learning, it is much harder for students to focus, so maybe they need more breaks.
Is there any research / experience regarding the optimal length of a remote real-time teaching session? Is it indeed shorter than classroom teaching session, and by how much?

I assume you mean real-time sessions rather than recorded. Yes? And what happens or is expected to happen during the breaks?

@Buffy yes, I mean real-time sessions. During the breaks I usually make myself a cup of tea, and I assume the students do the same..

So you teach 90 minutes, then have a 30-min break, then another 90-minute lecture immediately, for a total of 3h30?

@FedericoPoloni If it's a 4-academic-hour lesson, then yes, it's 90+30+90. There are also 3-academic-hour lessions, which are 90+30+45.

Are students considered to be "in class" during the break? Or are they two separate classes back-to-back. I ask because That half hour time may not be yours to claim back anyway.

Relevant: "Zoom Fatigue" - https://www.nationalgeographic.com/science/2020/04/coronavirus-zoom-fatigue-is-taxing-the-brain-here-is-why-that-happens/

@AzorAhai--hehim in my university, the partition of time between lecture and break is entirely flexible and up to the lecturer.

@ErelSegal-Halevi Well them I would definitely recommend not doing 90/30/90 in any situation. Ninety minutes is too long to focus and half and hour is too long to stay on topic. I'll leave the answers below because I like them.

More on Zoom Fatigue. This might merit its own question.

If you search using Google or another search engine for something like "research on maximum effective lecture time" you will get some ideas. In general, long lectures are less effective than short ones because of the student's attention span. Video lectures should be very short, say 10-15 minutes for effectiveness. And with required activities at the end of each short session. So, a long "lecture" can be presented as a sequence of short but complete segments. Real time is a bit different, but keep all of that in mind in course design.
But it really depends on what you and the students are doing in the given time period, rather than the length itself in any absolute sense. A talking head writing on a board or (worse) showing a bunch of slides gets old and boring very fast. If the students have a chance to break it up with questions or some problem solving activities it is better and the class-period can be longer and still effective. Class discussion sessions is another way to break the monotony, but harder online and nearly impossible with video unless there is an effective communication channel shared by every student.
I used to teach a couple of courses that lasted all day and only met once a month. But the face time was usually broken up into small segments and we used very effective, but simple, communication tools so that students could "engage" with the course and the instructors (two of us) at any time through the period between face-time sessions.
The key is to keep the students active and engaged. Once they lapse into passivity you are lost. Some students have the skills and background to keep themselves engaged in sub-optimal environments, but not all do. Perhaps not even the majority.

@TheoreticalMinimum, actually there is research on that point, but I've forgotten the source. It is mentioned in another post on this site. Video is too passive. For example, you can break up an hour math session according to the theorems introduced and proved. One per session. Most won't require even 15 minutes if done well. If well labelled they are easy to return to for review, rather than scanning a long video.

@TheoreticalMinimum, hmmm. Was that professor "entertaining"?

@TheoreticalMinimum, no the goal is not to reduce the total engagement time, but to chop it up into semantically meaningful chunks.

Its not just shopping videos on YouTube. This analysis from EdX (one of the biggest providers on educational video online) shows that students stop learning after around 6 minutes. https://blog.edx.org/optimal-video-length-student-engagement/

"10-15 minutes"  Pretty sure it's less than that.

@AnonymousPhysicist, yes, but people seriously resist the six minutes that would be better. I gave an outer limit.

No research here, just a small amount of experience to chip in. :) And no answers, just observations...
First, they're coping with many changes that roll in on the news daily or weekly, many of them more of an upheaval than taking the same number of instructional hours and cutting it into smaller blocks. I don't think you should decide based on unfamiliarity in COVID times.
In my experience, your intuition is right: 90 minutes is a long time to be continuously focused on Zoom, but 45 minutes is very doable. Worse, many people (try to) multitask during remote learning, and 90 minutes is a long time to be dividing attention.
On the other hand, I think a longer break is a good idea. Students seem to find it hard to really break on Zoom. They turn off their mic and video or run to the washroom, but it's hard to do the necessary dissociation: standing up, moving their legs, bustling and talking and sharing impressions with peers, getting a breath of fresh air. If they stare at a screen during break, they won't come back with a fully refreshed ability to sustain attention for another block. For this reason I suspect that 30 minutes of break with explicit reminders to get up and away from the computer is more useful than 15 minutes. But 15 is better than 10 and 10 is better than 5.
As for coming back late and wasting time: not your problem. It's no different from deciding to get a snack and wander luxuriously when learning in person. If they're not back on time, the lesson doesn't stop for them.
How about the problem of momentum? Four blocks with three breaks between them is pretty significant as far as stopping and starting. You would need to be very much on point and purposeful to avoid transition/inertia eating into the 45 minutes from both sides.
One idea is to designate each 45-minute block for a different purpose. For example, if all four are direct instruction, the repeated pattern will accentuate the dreaded feeling of sameness. "Is this the third block or the fourth? Did he teach us that earlier today or last week?" Whereas if you teach the first 45-minute block, give them exercises the second one, teach the third, and give them exercises the fourth, that's quite a nice rhythm.
The same strategy also helps mitigate a 90-minute block. Being present and working while the instructor supervises / is present for questions is not taxing; what's taxing is being attentive while the instructor talks and shows slides (on a screen you may not be viewing or have snapped to half of the screen).

I challenge the "45 min is very doable" assertion. I think for delivery content in a lecture in real life 45min is the absolute limit. On zoom I don't think it still works because the intensity of the other person being in the same room is missing.

Yes, I would agree that 45 minutes of uninterrupted instructor speech would still be very taxing. But 45 minutes on Zoom with some speech, some reading, some diagrams, some discussion, and other (hopefully) normal varied lecture stuff is OK for most, I think.

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A paper review I've undertaken turning out to be harder than expected
I recently agreed to review a journal paper (in theoretical computer science). After I started to read it in depth, I found out it is much harder than I expected - over 60 pages with over 20 theorems with detailed proofs. Also, the topic is not exactly my expertise - I do not know a lot of the related works that the authors base their results on.
So far, I managed to verify about 10 of the shorter theorems. They seem correct, though I have some minor comments. The other theorems seem so long and complex that it will take me weeks to review, especially if I would need to read and understand the theorems in the cited papers that these theorems are based on. What should I do?
I thought of writing to the editor and explaining the situation in detail. Maybe the editor will be able to find another reviewer that will verify the other theorems. But I do not know how such letter will be perceived. In particular:

Is it common for a reviewer to review only a part of the paper, and leave the rest of the paper to other reviewers?
On the other hand: is it my duty, as a reviewer, to complete my review, regardless of how much time it takes?

is it expected that you review and 99% confirm theorems? I thought in math fields it is acceptable to publish work that might be later proven to be wrong

@aaaaaa - Most people believe that reviewers should believe beyond a reasonable doubt that all theorems are correct AND all proofs have sufficient detail for an expert audience.  This doesn't necessarily mean checking every proof in detail.  It's definitely embarrassing for all involved (more so for the authors and less so for the editors and reviewers) to publish work that is later shown wrong, though it is understood that honest mistakes occur.

"...is it my duty, as a reviewer, to complete my review, regardless of how much time it takes?" Surely the editor won't want to wait longer than a certain amount of time.

"it will take me weeks to review" Um. It's sixty pages. How could you possibly review something of that length in mere days or hours?

If I submit a 60 page paper, I don't expect to hear from the editor in less than a year.

Is it common for a reviewer to review only a part of the paper, and leave the rest of the paper to other reviewers?

I have done that on at least two occasions. Sometimes it is the only honest option.

On the other hand: is it my duty, as a reviewer, to complete my review, regardless of how much time it takes?

Not really. It is commonly considered a duty of a career mathematician to contribute to peer review of mathematical works (at least) proportionally to their own publishing. Whether you achieve this by refereeing some really tough papers or a lot of simple ones is up to you.

Consult the editor
Adding to @darijgrinberg's answer: Consult with the journal's editor(s) before making any decisions.
They might:

Tell you more about what's common in a situation such as the one you're in.
Possibly decide they want to switch reviewers or divvy up the review work
Tell you what they expect from you (including telling you or hinting at you what they would regard as unethical).
Pressure you into continuing (not such a great outcome - but I have to add this in fairness)

Don't feel awkward or inappropriate about taking this up with the editors, it's the responsible thing to do.

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How to best address authorship issues with PI?
I am a postdoc working with the same supervisor who supervised my PhD thesis. During my PhD time, it was tacitly assumed that my work is his work too. It went as far as me doing the entire planning and execution of a paper and writing the first draft, while he later looked over the draft and made suggestions on what to expand and what to change. None of the suggestions were fleshed out. Yet we are the only two authors on this paper and he wrote in the author contributions footnote that he and I both conceived of the study, I did the experiments, and both wrote the paper.
Since the paper used some of his data as well as experiments funded by a grant given to him, I obviously cannot publish anything on my own.
However, now, in my postdoc function at the same institution, I find myself in a situation where a PhD student and I are doing a lot of work for a paper and there are two professors involved. My advisor and another professor.
The current paper grew out of another study for which I did all the experiments and coding with a lot of input from the other professor (not my advisor), while the advisor wrote the first draft. My advisor ended up as the first author, even though only the initial idea of working on the topic was his, but he barely contributed to the design of the study, nor does he understand the statistics used or the experimental design.
In this follow-up paper it is, once more, tacitly understood that my advisor will be first author and the other professor the senior author. The work, meanwhile, is done by the PhD student and me with some input and supervision from the other professor.
Is it possible to somehow broach this inequality in my/our position without destroying one's future?
Additionally, I'm getting more and more messages that sound like I'll be part of more papers where I'm clearly the only person doing all the work. Is it normal to have the lab leader as a senior author even though he doesn't contribute any work, nor any meaningful feedback (simply because the methods are not accessible to him)?
And also I've been getting signals that sound like if I publish my own work, not using the data gathered at work, I'd still have to run it by my PI, and possibly have him as a co-author. This last part is particularly disturbing. Has anyone ever been in a similar situation? How do you discuss these things?

Get a post doc position somewhere else and publish under your own banner.

Before you do something rash: you mentioned that the initial idea came from one of the senior authors. Note that identifying a good question to work on may require years of experience and prior thinking and you may underestimate the effort that went into it prior to your "hands-on" work. I do not say this is the case here, but take that into account as a possibility. Some people on SE say that ideas are cheap and easy to produce. That's perhaps true for mediocre ideas. It's not true for really outstanding ones. Of course, if your work is not properly appreciated, then it's time to leave.

@CaptainEmacs I agree with everything you say, but in my field, even the most amazing idea would not qualify for first authorship if someone else did all the heavy lifting of executing the idea.

@CaptainEmacs I agree that ideas should get recognized. Here however, it was not the central idea of analysis. It was more along the lines of "it should be on this topic", without a clear idea about how exactly. And as lighthouse keeper says, first authorship for merely having the idea to work on something -- even if it is a great idea -- is a bit much.

@story_without_a_title I am with you on the first authorship.

Your supervisor's conduct is blatantly unethical.  The current relationship is harming your career.  You need to find a new job.

I agree that having the professor as the first author seems wildly inappropriate. However, this can sometimes be the case in countries with labs that have a "lab head" and many young faculty underneath them. As many countries and schools only consider papers on which faculty are first or corresponding author in advancement and evaluation, it sets up perverse incentives for faculty to insist on first or corresponding authorship where it isn't deserved by most journals' ethical standards. If this is the case and is likely to remain so, then I agree with SolarMike's comments to find a new position if possible.
You don't say in your question what your relationship is like with the main advisor. Could you discuss this situation with them directly? If so, I would take a some time to cool off and make sure you aren't as dismissive of their contributions as you are in your question. Rather acknowledge their advising and support, but suggest that you and the PhD student be the co-first authors, while the professor and the other advisor be the co-corresponding authors. This would be the way we would untangle this Gordian knot in my institution.
Regarding including senior authors who may be distant from the day-to-day of running the experiments (but still qualify for authorship due to setting the directions, securing lab funding, etc.), this depends strongly on the customs in your field. Some fields go alphabetically, some have the "advisor" as the 2nd author, others the advisor is as the last author. However, the advisor is typically always included, even if their contributions were minor. Don't forget their funds paid your salary and the PhD students, got the equipment and whatnot for the lab, and other things without which the research would have remained an idea on a drawing board.
Regarding publishing papers entirely on your own, again this may be field and country-dependent, but I personally don't see anything "disturbing" about the advisor insisting on looking it over. This is standard practice in industry, for example, and your contract with the university may even say something to this effect. All of your intellectual output, even that created "on the side", typically belongs to the employer, who, at their discretion may choose whether or not to exercise their right to ownership if it's truly outside the bounds of your normal duties. As a post-doc you're not hired on a 9-to-5 basis, and as the bulk of the work is intellectual, there's no easy way to disentangle what ideas were developed "on the clock" versus developed on your own time.

I get the inclusion of the advisor on PhD-related papers, even though it is deeply unfair in cases where the advisor hasn't done any of the actual work. Additionally, having the advisor want to go over everything in their particular way often prolongs the process. I am, however, a bit confused about the concept of putting the advisor on my own work as a postdoc. Isn't the postdoc step supposed to be about personal growth as a researcher as well? And in my case I am definitely not downplaying his contributions, as he really isn't informed about the methods that I(we) use in the slightest.

again, this is field-dependent. there are almost no single-author papers in my field, for example. but keep in mind that the professor in question pays your salary, right? and you are using resources they procured for your research. this justifies their co-authorship to some degree. if they truly made very little intellectual contribution to your work, push to be listed as the corresponding author. this shows your academic growth.

Well, it's not like my salary is paid by my advisor, but I get the point.

Yes, there are hardly any single author papers in my field as well. It's more about the image projected. Being the corresponding author is a good step, I guess. It's happened in conferences that my advisor and a colleague's advisor had to admit that they don't quite know the answer during the q&a session of a paper lead by us "underlings". Yet they still have no qualms about presenting our work in their invited papers and saying "we" work on that. It's just that I've seen others say something along the line this research was done by my PhD student XY, while our advisors don' always do that.

if that's true, try and address it with your advisor. in a perfect world they would be highlighting your contributions in talks, and introducing you around to build your network. if they're not open or hostile to that kind of promotion, then you definitely need a new gig with a more supportive mentor.

I strongly disapprove of your claims the situation is ambiguous.  The asker has laid out a clear description of authorship misconduct.

@AnonymousPhysicist I don't think I ever claimed the situation was ambiguous. I clearly said that many aspects of what the asker described are very inappropriate.

It's in your very first sentence.  The fact that your answer is not internally consistent does not help either.

thank you for your feedback, I have edited the answer to clarify my meaning.

@AnonymousPhysicist Thanks for pointing out that this is clear authorship misconduct. I wonder how to address that without spoiling too much. One time I mentioned to another professor that part of what we ended up doing was an idea that came out "accidentally" while doing another experiment. But then my supervisor cuts in and claims that he had this idea a while back anyway. In that situation, I'm not able to do anything. A senior researcher is claiming, without any proof, that they had an idea and without documentation, they will be believed over me.


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My student: "As of now it is unknown, why...". I have very recently found out why. Do I tell him?
I'm supervising an undergrad student. STEM, if that's relevant.
Due to Corona, his contract ending and me leaving this job we haven't spoken in quite some time. He has now worked at home and has written his thesis. I am currently proof-reading his (pretty much) completed thesis which he send to me on 4 days ago.
In his thesis, and obviously last time he spoke, he didn't know why there was a bump in his results. Neither did I. In his thesis he writes something along the lines of "as of now it is unknown...". So far, so normal.
Two days ago I more or less coincidentally found out why. It turns out it is somewhat obvious once you know why. What should I do now?
I could write him a mail explaining why. But this wouldn't be his work. It also can't be solved. It is just a "quirk" of the method he used.
I could just say nothing: "as of now it's unknown" is perfectly acceptable, but I feel in this case it's also unnecessary. After all he COULD know why.
I thought about not saying anything and just be happy about a question I already have for the oral examn. But I am afraid it might be a little too difficult for the exam and he doesn't do too well with pressure.

Thank you all for your input. You helped shaping my thought process in a great deal.
I ended up writing a detailed email telling him which dots to connect and leaving the rest to figure out for himself with some pointers.
I did so for a simple reason:
His statistical analysis is wrong. Furthermore I don't understand from his thesis what he did. And after all I KNOW what he wanted to do. And I know for a fact: Somewhere something went wrong. And that I can't "let slide". Incompletion is one thing, errors another.
And in order to provide an explanation I needed to show him why his data doesn't make any sense which is easiest to explain with the underlying mechaism and so on.
I will, however, use this specific topic in the oral exam. I specifically told him to make sure he knows what's happening at this particular point and I feel this is more of a warning than he probably deserves.

What is your goal?

I want to help but I don't want to do his work for him. I myself have a LOT of work that I still have to get done in my last two weeks, but this is not an issue, neither of these approaches take up a lot of time. (Ironically this right now does...) So my goal is likely to get "this over with" as smoothly as possible while being the best supervisor I can.
I am not opposed to him succeeding at all.

Why don't you want to tell him? This is how science works. He can mention the source (i.e. you) if it's not a trivial insight (trivial in the sense that he should have seen it himself, in which case it would be encompassed in the acknowledgements). I would really loathe to see someone presenting work that is not - to the best of his and his supervisors/collaborator's knowledge - most complete in its conclusions and up-to-date if this is feasible in the allocated time. If it's an issue of time to prove this is the case, he could still formulate a hypothesis.

Have told him to examine the method? That should be sufficient no?

@CaptainEmacs: I could give him proof. It just wouldn't be something he has done by himself (Reason 1). If we were in an earlier stage I would give him a series of tasks that would lead him there. This way he learns nothing. Also, and I don't know if I am taking this personally which adds another layer, I actually told him once or twice how I would like him to present his results which he just did not do. If he did as I told him he might have either found out himself OR it was much less of a "jump" to get there in the exam. This was also not the first time he disregarded a "suggestion" by me.

@SolarMike Not really. At the point in time the issue came up for the first time it didn't appear too important compared to other tasks still to complete.

Well, as you say he ignores suggestions from you, then perhaps you go ahead and ask at the oral exam.

@SolarMike I thought about that. However I don't want to be petty.
I am still unsure why he ignored it. Laziness? Forgetfullness? Didn't really listen? All of these are on the table.

Surely you have worked with that student long enough to be able to decide which of those answers "why"?

@SolarMike I have worked with him for over a year (he had a temp job prior to his thesis related work) yet I absolutely have no idea as to why. Since I am actually not a terrible judge of character that bothers me quite a bit, to be honest. I feel like he lives in his own little world. Also he still is nervous when we talk and it baffles me why. (I feel I am wandering a bit off topic right now.)

@Stefan Students that simply do not listen? Yes, that exists. There is nothing you can do about it. If you think it will not outright founder him, you can use this as a point of discussion during the exam, but if he is a nervous person, it's perhaps too much to expect this to work under pressure and it can derail him. You could suggest this to be added to the thesis with a (private communication) notice.

That last edit removes the point of the existing comments and the other answer... Shame. Op you have the right to revoke it...


text:
After the passing of my supervisor, the department forces me to start again from zero. How to respond?
I have had a very rocky PhD candidacy. My first supervisor left academia half way through my candidacy; the replacing supervisor passed away a year after that. So two and a half years through a three-years PhD candidacy, the head of the department gives me two choices: Either I have to change my topic of research and start over from zero again and somehow finish "in time" (how this will be done is unclear, and I am supposed to hash it out myself with one of the available supervisors), or I have to withdraw from the program.
Their justification is that no one in the department understands the content of my works. Is this a proper/normal justification? I cannot believe that an academic department belonging to a top university can seriously use “we fail to understand the candidate’s work“ as a justification to force me to do something that I deem to be completely infeasible.
So, assuming I cannot dispute this decision, given the fact that I have to start over from zero again anyway, with a department that readily admits that its people do not have the competence to understand and therefore will throw away wantonly what I have produced after two and a half years of working nine hours every single day without a single day off, should I just leave and apply for another PhD program? Whatever that will be coming out from this attempt to salvage my PhD will probably lead me nowhere except a piece of paper anyway. If I withdraw for this reason, how will this be seen by other universities? How will this be seen by people in the industry?
My goal is a career in academia. I am someone who has severe social anxiety and so I find it impossible to survive in the industry. I have always thought I might have a chance to be accepted in the academic world instead, but I have now realized that someone like me probably belongs nowhere.

Can you talk to someone higher up in the hierarchy than the head of your department?

What's your general academia area?  Engineering, physical sciences, medicine, humanities, etc.?

This is totally going to depend on your field, I'm afraid. The culture of supervising is very different in humanities than in the physical sciences. In physics, it could be easily possible for there to only be two people in a department who could be competent to evaluate your work.

My impression (may be wrong) is that humanities profs are more flexible about supervising work that is not so closely related to their expertise.

@Nat My area is mathematical finance, but I lean too much towards the mathematics side than the finance side apparently. I honestly do not think this is the case, because the works in the literature, at least in the topic that I am working on, use techniques that are well beyond what I am doing.

Mathematical Finance really sounds like a rosy sort of field to be in here!  It's usually accessible enough that most academics in related fields should be able to follow it, and presumably it tends to have some pretty immediate market applications.  So, erm, what exactly are they having trouble with?  Are you in a Business department where there's not anyone inclined toward math, or a Math department where there's not anyone who likes finance?

@Nat I am in an economics department. I do not know other academics well aside from the two supervisors that I had, but I presumed that they were capable of understand the mathematical techniques that I am using, because these techniques are not that advanced, certainly nowhere near the level that, I imagine, would be required for a thesis in Mathematics, and most of the academic staffs in the department do have a PhD in Mathematics!

I think you may be underestimating some of the problems involved in getting a new advisor. For instance, I have worked extensively with SDEs and know some mathematical finance people. I could (with work) understand papers in that field. But I would never supervise a student working on that, because I do not know what is the state-of-the-art, I do not know what questions are interesting, and I have no specific unique expertise that would aid the student. It is possible that you are in a position where no one in the department feels they can responsibly supervise you in your current work.

This has happened to you through extreme bad luck (death and advisor leaving!), and I hope that some people will go out of their way to help, given this circumstance, but it may be impossible. Something similar happened to a friend, and she ended up transferring universities to find a new supervisor, rather than change fields. This does not necessarily indicate anything about whether you "fit" in academia - there may be a happy place for you! - but is merely the sort of bad luck that can happen, and no one is to blame.

Out of curiosity, did you ask the department head (non-rhetorically) exactly how he visualized a reasonable way for you to complete? Or is he just trying to throw you out and he's pretending that it's somehow possible for you to finish?

@ElizabethHenning I don't really know. Sadly, I am not someone who can read between the lines. I did ask that question directly, but he told me to work it out with the available supervisors. It did not seem to me that he had a clear plan, he just told me that it was possible if I did exactly as I was told and that was the end of that. Maybe the potential supervisors will be able to tell me how exactly this will work.

@AJK According to my own experience with my previous two supervisors, and my discussions with other students, that is not the way things are being done here. It seems like the modus operandi has always been that supervisors have very little knowledge about what the student is doing, and the student is expected to conduct his research independently from start to finish. It certainly has been my own experience, and three professors have told me that their own PhD experience was like that, that it is the same everywhere.

Also consider switching to a different university where there is a professor in your domain. Apparently your department just lost two... I can imagine that the remaining supervisors do come from very different subdomains.

@ProjectBook I think your department, even it is ivy league, is highly poisonous environment, I would suggest you to look into google scholar or research gate, in order to find ppl similar to your field and change department as soon as possible.

If your current university isn't willing to work with you, go somewhere else. The 3 year limit in the UK is not set in stone, generally it's the length of the scholarship, many people take longer and in exceptional circumstances (which this certainly is) you can get an extension to your funding. Considering the circumstances, I wouldn't expect you to finish "on time" even if you do find another supervisor, this is probably going to take 4 years considering the delay, but better to take an extra year than waste 2 and a half.

Would it be possible to reach out to your first advisor? They may be willing to help in such an unusual circumstance, whether that means functioning in an informal supervisory role or helping you transfer programs (perhaps to work with their thesis advisor).

Maybe someone else in the department can supervise your work and maybe they can't--the fact is that they won't, and that's what you have to work with. My (pessimistic) gut feeling is that the department head has essentially written you off as collateral damage. He's willing to push you through for a completion because that's good for the department, but he doesn't care that you want an academic career.
On the off chance that this isn't the case, you might try approaching the possible available supervisors and get a clear timeline from them about how you can finish with work that can launch an academic career. If they tell you it will take longer than the one year that the department head seems willing to allow, you can try going over his head to pressure him to agree to your new supervisor's timeline. But this is a rather delicate situation and you are probably better off shopping your work around at another school and explaining that you lost two supervisors through no fault of your own.

This answer is so real and hard truth. I think OP should change program also.

First of all, there are a country dependency here.  I assume you are in the UK, since you talk about a 3 year time limit.  In most other countries, there is no time limit for a PhD, and if you did start over with another supervisor, it would be a good reason for taking another 3 years to finish, and the department could probably find some way to fund you for the extra time.  Unfortunately, it seems like this is impossible in the UK.
Second, as a mathematician, I find it very plausible that no one else in the department can supervise your research.  I can legitimately say that, in my department of 14, I do not really understand the research of anyone else in the department.  There are 2 or 3 others whose students' work I would feel competent to evaluate if I had a reasonable amount of time to study, but I couldn't provide any useful research guidance to their students.  For the rest of my department, I would really have to spend a couple of years relearning material from some fairly basic graduate courses in order to understand their research.  It's a significant burden with minimal rewards to evaluate the research of the student of a deceased colleague; someone even in a related area could easily have to put in a full month or more of work to get up to speed on mathematical ideas they have not thought about in a long time.  It might not be possible to persuade anyone to put in that kind of work for essentially no gain.
If you found someone at another university working in your area who would be a suitable supervisor, then I think starting a new (possibly expedited) PhD there would make sense, and you would have a good chance of being admitted under the circumstances.  However, if you are planning to leave in order to start over in a new area somewhere else, I don't think that would look good.
EDIT: I want to add an additional consideration.  In mathematics, applications for research-oriented positions rely heavily on letters from senior researchers who can explain how your work fits in the broader context of work in your area, since it is likely that the hiring committee will not have enough expertise to understand this context on their own, and recent PhDs do not have a broad enough perspective to explain this context for themselves.  Having a supervisor who does not understand your research area well enough to write such a letter puts you at a severe disadvantage on the job market.

The "gain" would of course be fulfilling the department's obligation to the student, who has already put in more than two years' work. Which just underscores that (many) departments don't think they have any obligation to their students.

@ElizabethHenning: No I think it underscores that (many) professors don't think they have any obligations beyond the contracted ones to their departments or their universities.  I would venture that (many) professors think that their department has an obligation to the student, but that it's solely the job of the chair or the director of graduate studies to find a solution.

I was not aware that professors thought of themselves as contractors to the department. Thanks for the clarification.

For what it's worth: I believe both that the department has obligations to the student, and that I (as a faculty member) have obligations to the department beyond what is written in my contract. (I certainly don't view myself as a "contractor", and I don't know anyone who does.)  However, in both cases these obligations have limitations, and  they can be in tension with other obligations. In the case under discussion, taking on the student appears to be a very difficult assignment (in particular given the HoD's lack of flexibility in the case) that would be very likely to affect...

...the supervisor's other duties. Unless the department is really committed to achieving a good solution for the student, say by offering the new supervisor substantial accommodations in other workload, it seems difficult to imagine anyone volunteering for this job.

@Spiny I agree that the sticking point here is the HoD, since he is making it essentially impossible for anyone to volunteer for the job. But why isn't there another faculty member who, unlike the HoD, does think that the student is owed more than having to choose between being forced out of the program and writing a half-assed dissertation in a new field? It's disturbing that no one is advocating for this student, who is also a member of the department and is in this situation through no fault of their own.

Their justification is that no one in the department understands the content of my works. Is this a proper/normal justification?

I really empathize with this situation.  No one's understood my work for half my life now.  If it weren't for the fact that the stuff I make works, folks'd probably write me off as crazy.
Still, I passed a dissertation/defense pretty easily.  An advisor had suggested that I keep my mouth shut about how the stuff worked and just focus on showing its results.  The dissertation was mostly a bunch of how-to for the intro-level stuff.
I suppose that the dilemma is that, to pass you, the committee needs some means of appreciating that your work's meaningful enough to constitute a PhD.  For me, that was building stuff that worked.  For you, what might it be?  What can you do to show that your work has merit?

If I withdraw for this reason, how will this be seen by other universities? How will this be seen by people in the industry?

Individuals will likely have all sorts of different opinions.  Some might empathize; others might not.
When you go to interview for something, why should the interviewer believe your description of the situation?  How could they see that you have ability to be applied?  What should they think of your ability to contribute to their group's/company's efforts?
Ultimately, I think that this takes you back to the same dilemma - you need some means of providing others with a basis for appreciating your work.

My goal is a career in academia.

Academia's about building up a common knowledge base; some level of intellectual conformity is a prerequisite.  Otherwise, you'll be the person publishing papers that no one cites and hosting lectures that no one attends.
So if academia's your goal, you'll probably need to find some line of research that others can appreciate.  Something that they'll want to read about and attend lectures on.  Something that students'll want to take classes on.  Something that'll get traction when you write up a grant application.
Optimally, you'll pick a popular topic and increment it.  This works really well because there'll be a ton of academics reading papers on that topic already, and they'll liable cite your paper if it's the best on what they're trying to do.

I am someone who has severe social anxiety and so I find it impossible to survive in the industry. I have always thought I might have a chance to be accepted in the academic world instead, but I have now realized that someone like me probably belongs nowhere.

People'll judge you no matter what.  Just in academia, it'll be more about social esteem, while in industry, it'll be more about perceived market use.
If you have tons of anxiety, it'll be difficult for you to stand on your own as a free entity since that's exactly what stresses you out.  But if you're still able to get productive stuff done, then you'll often be able to find a place under someone's wing.
In academia, you might find a place as a researcher in another PI's group.  Or in industry, you might find a nice R&D lab.  You might not be a leader in either of those scenarios, but you'd still be a valued member.

Most of my works can be classified as "theoretical" so unfortunately I can't just show people that "it works" and be done with it. I have always had an affinity towards the abstract, and I chose to take my education up to this point because I believed that the people here appreciated what I could offer. I do not know if my previous two supervisors did "appreciate" it, but they certainly allowed me to work in this direction, and on papers, the department did too. But in the aftermath, it turned out that nobody knew what I was doing, and then after months of uncertainty, they decide to do this.

@ProjectBook Could you elaborate on "theoretical"?  I mean, theories are all about making real-world predictions; would you be able to make such predictions to show that your methods work?

One of the question I address is that suppose an investor cannot form a portfolio that pays, say 1 dollar, with certainty, then we can infer that the price of the stock satisfies certain statistical properties. This sort of result mainly (as far as I understand) allows one to justify why he/she can make certain statistical assumptions regarding the price of a stock (as well as give a rigorous argument to a conjecture that, intuitively, should be true), but in practice, it is virtually impossible to verify if either of the two equivalent conditions hold, hence "theoretical".

The equivalent to "the stuff I make works" for theory/pure math is publication and acceptance by the field. If you can get a prominent journal in your field to referee your work and find it valuable, that would be a sign that your work could be worth a PhD. However, since A) your work may not be at the stage to submit, and B) reviewing times are very long in pure math/econ, this probably would not help you with your academic situation.

I witnessed a similar situation in my field a few years ago:
A professor died suddenly, leaving a bunch of PhD students at a university where nobody had sufficient rank and expertise to evaluate their thesis and supervise them.
For those close to graduation, the following was done:
They joined a PhD program at another university where there was a professor capable of advising or supervising them, usually a collaborator of the late professor.
However, if they wanted to, they could physically stay at their old university, except for a few visits to the new university.
Also, their employments at the old university would continue.
All previous achievements were transferred to the new program, so the PhD students could basically continue without a considerable delay.
Whether this will be possible for you depends on the involved university’s guidelines, how PhD financing is organised in your country, and so on, so you have to get familiar with these.
Be aware that PhD programs differ a lot across different countries and universities.
If you can, find a supervisor at a university with a suitable program.
Being geographically and financially flexible helps of course.
For example, most German PhD programs officially only require you to have a reasonable prerequisite degree (e.g., a master’s), find a professor at the university who agrees to supervise you, stay in the program for at least a year, hand in a good thesis, and pass the defence (with the last two being the difficult parts).
Moreover, they often have a flexibility clause that allows them to waive certain criteria (such as staying in the program for a year) in exceptional circumstances such as yours.
Regarding your anxiety, consider that many professors in your field will happily take you:
You are already trained, probably productive in terms of publications, and having you as a graduate may contribute positively to all sorts of evaluations.
Moreover, you may become the ideal postdoc candidate, as you can be evaluated on the job.
Finally, keep in mind that a typical academic career would have involved switching locations for a postdoc soon anyway.
Now you do it a little bit sooner, but that’s easily explained on a CV given your circumstances.
Some random thoughts:

Are there any other supervisees of your late supervisor?
If yes, consider working together to get proper support from the department.
Consider finding professional help for dealing with your department.
Most universities nowadays have people whose job it is to support people having trouble with their advisor or similar.
Also, if you have a student union, they may help.
This won’t probably work given the attitude of your department, but it’s worth a try: If your late supervisor had other supervisees, in particular for a bachelor’s or master’s thesis (if that’s a thing in your country and field at all), these need supervision too. If you are good, you may help the department providing that supervision or even evaluating the respective theses (depending on your regulations). This won’t only give them a reason to keep and support you, but will also look good on your CV if you aspire an academic career.

(1) Your fear of working in industry, and how that may affect your life as a grad student.
Feeling boxed in isn't the best way to do a PhD.
I understand your fear of working in industry, but I will encourage you to face this fear, gently.  I think that if you do, some of that fear will dissolve, and you'll be able to continue your studies in a more positive way, with less energy wasted on fear-related stuff.
How can you face this fear?  Look around for people to shadow in industry.  "Shadow" means you follow your host around for a day, and watch and listen.  I've seen this called "career exploration."  Perhaps you could aim to do one shadow per month.
Believe it or not, there are people with severe social anxiety who are able to function pretty well in industry.
(2) The death of your advisor (on top of the departure of your first advisor).
You've had two significant losses.
I'm going to make two suggestions for you to consider:
(a) Get a doctor's note supporting a request for a leave of absence of a semester (or six months, if that is more compatible with your university's calendar).  Give yourself some time to grieve and recover after the death of your advisor.
(b) Regardless of whether you stick with your original research plan, or modify it somewhat, or start something brand new, you need an advisor.  It would be ideal if the advisor were hip to your research topic, but it sounds like that's not going to be possible.  Well, then you need an advisor who can be supportive in a more general, less specific way.  Since you are in a small department, you can consider each faculty member as a potential advisor.  Make yourself a short list of professors and get to know them a little bit, see if you can narrow things down some more.
Once you are feeling better, and once you have an advisor, you'll be in a better position to make some decisions about your thesis research and your thesis topic.
One possible way forward that I can imagine for you is that your new advisor helps you find a quasi-advisor at another university who can mentor you with your existing topic, or with a slightly modified version of your original topic.
When you feel ready, you should prepare to teach your new advisor about what you've been working on.

assuming I cannot dispute this decision

I recommend trying to:

two and half years through a three years PhD candidacy, the head of the department gives me two choices, either I have to change my topic of research and start over from zero again and somehow finish "in time"...or I have to withdraw from the program.

It is worth considering whether the head of the department has the legal right to actually do this. You have no-doubt signed a contract with the university and this contract grants rights to both parties. Perhaps the contract will support a third option:
Write your thesis and submit. Writing-up doesn't require supervision, so you can proceed without a supervisor.
I'd recommend proposing this solution to the head of department before exploring any legal avenue. (By "legal avenue," I don't necessarily mean using the legal system. I mean presenting an argument, perhaps in writing, to the department or university, that proposes a solution and provides some legal basis for why the department/university should accept. Such a legal basis need not be direct. That is, you needn't refer directly to any contract. You needn't threaten either. You just need to provide a reasonable solution that can be accepted.)

Their justification is that no one in the department understands the
  content of my works.

At this stage, there doesn't seem a need for supervision of your work. You're 5/6 complete.

should I just leave and apply for
  another PhD program? ... If I withdraw for this reason, how will this be seen
  by other universities? How will this be seen by people in the
  industry?

You presumably know some senior researchers (from other universities) at this stage. You could approach them and discuss the possibility of their supervising the remainder of your PhD, either at their university or your own. If you approach a senior researcher, rather than a university, then the university should follow the advise of their employee, so that shouldn't cause a problem. From a future employer's perspective, you'll have a tricky aspect to explain on your CV. That might be problematic for early positions, but it won't matter down the line.

The OP wrote "My goal is a career in academia."  Maybe he can somehow finish his PhD without a supervisor, but it is all but impossible for him to continue his academic career if he graduates this way.  In my opinion, it would be better in the long term to start in a new PhD program with a supervisor who can fully supervise, support and promote him.

@PeteL.Clark Why can he not continue his academic career?

My first response was going to be that you could say the following: "No!"
One key to this is not to follow up with any reasoning, as in fact you do not need to give reasoning--the reasoning is clearly implied by the situation. If you do give reasoning be careful they do not force you to eat away your own position of argument.  Since they have the lower stance, they may use such a strategy.    You have much more right to carry on with what you have started (started under the mutual agreement between you and the department) then they have for forcing you to drop all your work.
The above still stands, however, considering your personal situation, if you have concerns about communicating this strongly enough, then you may want to hire someone to represent you either formally or informally. You might consider the graduate student union, but the problem is are they good enough at your university? And are you ok approaching them?, if not then that is why getting your own representation is also possible.
By the way, there are definitely places where you belong, and university is one of them.
Also I'd like to address your question about their current justification. No it is not a valid argument.  For one if someone needs to know the stuff, they can go learn it just as you have learned it.  Learning is common and fundamental to professorial life. The other point is that the situation is not much different from when you had an advisor, as the advisor can not single-handedly give you a Phd, correct?

I'm curious why there has been negative votes to my answer, especially considering my answer is the only one which directly encourages the poster to stand up for what is their right without pulling any punches. The other posts are almost fatalistic, and thus indirectly in favour of the department's very unfair and authoritarian approach. I consider that wrongheaded, and feel the poster should take a solid stance against such injustice.

I would guess that you have received downvotes because your approach is highly confrontational and many of us have made the experience that in academia (and in life), being highly confrontational is rarely the way to achieve your goals, even and especially when dealing with unreasonable people. Your suggestion that the OP should "get representation" implies that they have a legal leg to stand on, which I find extremely questionable.

In addition, you also claim that "if someone needs to know the stuff, they can go learn it just as you have learned it." and assume that this is trivial. Instead, it is very likely that this would require months to years of focused work. Going up to anyone in any position and saying, "I have had bad luck, and therefore you must invest massive amounts of time to fix it" is not likely to end well, because it isn't reasonable.

@xLeitix Why is that? OP have every legal right to sue department

@SSimon Everybody has the legal right to sue anybody about anything. Whether it has a chance to even go before a court is a different story, and I can't imagine that this case has.

@xLeitix based on hwat?

Wow, we've been pushed around too much, but does that mean to down vote the messenger? That's horrible. Everyone has the right to sue, and everyone has a legal leg to stand on, especially if you have a lawyer representing you. The lawyer's job is to determine what to sue for. My guess it would be connected to the contractural agreement with the department to complete the PhD, lost income due to not working all those years, and lost career opportunities. I'm being confrontational because the department is being unjust!

I downvoted this because (with the exception of the third paragraph), the advice is so off-base so as to be likely damaging to the OP.  "My guess it would be connected to the contractural agreement with the department to complete the PhD." There is no such contractual agreement.  Instead, there is (probably) a yearly letter detailing the student's support and the conditions for it continuing...

...If the student is in a PhD program with a hard duration of three years, then they have been given three years of support, and there is no legal basis for extending the support.  Note well that this is true even when most departments and universities would elect to extend the support, and even when most would say that is "the right thing to do."  Not all justice is legal justice.  If the OP tries to sue the university in this matter, it is overwhelmingly likely that he will lose the suit, have to pay some attorney's fees, and have definitively worn through his welcome in his department.

@PeteL.Clark do you have any reference, such as court verdict or legal practice to back up your claims?

@SSimon: I am the current graduate coordinator of my department, so I sign all the contracts given to graduate students.  This is how I know there is no "contractual agreement with the department to complete the PhD."  If our department had a legal liability to extend a student's support past the time in which we guaranteed funding, we would be liable indefinitely beyond our own financial solvency, so we would not be able to offer a graduate program at all.  In terms of legal precedent: surely the burden should be on you to produce it, since you are advising the OP to take legal action.

@PeteL.Clark Many of such a cases. depend on the country of OP I can prove with ease. Don't forget that most of EU countries have the working type of contracts.

@PeteL.Clark "contractural [sic] agreement with the department to complete the PhD" might well have been written to mean  "contractual agreement with the department for the duration of the PhD" or (perhaps more likely) "contractual agreement with the department for three years."

@user2768: Maybe.  But of course a contractual agreement for three years is not a legal justification for continuing support beyond those three years.  I certainly can't speak for the entire academic world, but in all my experience, suing the department over a failure to continue funding past the initially guaranteed period is simply a non-starter.  Just saying "No!" is a similarly bad strategy.

@PeteL.Clark I completely agree that there "is not a legal justification for continuing support beyond those three years" and that "suing the department over a failure to continue funding past the initially guaranteed period is simply a non-starter."


text:
Found an error in my thesis
I've found a error in my thesis recently, after its submission. I made a mistake that wrongly accepted the hypothesis which should be rejected. What should I do??

It is normal that a thesis contains mistakes and wrong conclusions. If you did not yet do your defense, it is not a problem. The examiners may find and mentione it. Otherwise, you do it by yourself the day of your presentation, by indicating that honest mistake. You can then correct it in the final version of your thesis.
If your thesis is already in the library and you got evaluated for it, try to talk to your adviser and he will suggest either to ignore it or to add a correction on the website or as an extra document in the library.

Talk to your advisor!
This question could have very different answers, depending on lots of factors:

How significant is the error? Just in a minor statement, or does it invalidate the main results of your thesis?
What stage of the process are you at?  Have you already defended your thesis? received your degree? etc
What was your thesis contribution?  Significant original results that other people may wish to use? or mainly expository/survey work?
What are your institution’s culture and requirements around masters theses?
What is your field’s culture on how to treat errors in published work?

Your advisor is the person who can best judge the answer to these, and should be supportive for you.
That said, as a very rough general answer: in most situations, this should not hurt you badly.  If the mistake is minor, or if it is major but the thesis has already been defended/accepted, then probably all you need to do is put the correction on the record somehow (in my field, listing an erratum on your webpage would be reasonable).  If the mistake affects the main results of your thesis and you have not defended yet, then it’s more likely you should revise the thesis and postpone the defence.  But, again: this all depends on many situation-specific details, so the most important thing is to talk to your advisor about it.

I've submitted my thesis. But it is not gone for correction yet. Is there any chance to submit after having the error correction to the university??

@VijayalakmiVenugopal: that is the sort of thing which will depend on your university’s specific rules and procedures.

I've talked about the issue with my guide. He told me to put another two corrected thesis which would be submitted during the viva-voce. What if most of the null hypotheses is rejected in the chi-square test? Will it affect the result of the thesis?

@VijayalakmiVenugopal: again, that’s the kind of specific question which can best by answered by you, your advisor, and other colleagues who know your work.


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Do you need permission to use readability formulas in research?
I am considering using the Gunning Fog Index and the Flesch Reading Ease to calculate variable information for my dissertation. Do I need to obtain permission from someone to use these formulas? In other words are they considered to be copyrighted data collection instruments?

It's very doubtful that you'd need permission to use either formula. In any case, I'm not sure who you'd even ask. The formulae are simple, unpatented, and widely published, and both Gunning and Flesch are dead.
Both formulae were published by their developers, who actively encouraged their use (Gunning in his 1952 book The Technique of Clear Writing, Flesch as quoted by the University of Canterbury, NZ). The formulae are part of the existing literature, and it was clearly the authors' intention that these formulae be disseminated and used for relevant purposes.
The formulae, among others, are implemented in several pieces of software (including copyright-averse free software like LibreOffice) and online calculators. Even if there were some restriction on their use (which there doesn't appear to be), it is clearly unenforced, and hasn't been for a very long time.
It may, however, be appropriate to cite the work of Gunning and/or Flesch, depending on the norms of your field.


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Tenured professor wanting to go back to school for a PhD in a different field
I am a tenured professor in the field of education (learning sciences). I have been employed at my current university for six years now. Most of my research has been done in classrooms, researching the effects of instructional strategies on student achievement.
As I have been out in many different schools in different cultures and countries, I started to develop a new interest in the effect of physical environment on the behavior of students. Later I found out that the field is called environmental psychology and I am just so intrigued by the idea that school architecture and interior design can have impact on behaviors of students.
It has been about a year since I first started to feel passionate about the field. Now I am searching for graduate programs in the field. But giving up my current status and starting a new life as a graduate student requires a lot of courage. I have not heard of any professor who went for a second PhD degree in a different field. I don’t even know if they will let me in the program. I do feel like I can give up my current career for my passion in the new field.
Lots of people change their career during their lifetime. I have seen classroom teachers as old as fifty go back to university for a PhD. Why can’t a professor go back to school to change his/her field? But I guess I am afraid people will think I am crazy or that I might regret this later in my life. I am 40 years old, and I feel like perhaps this is my last chance for a field change. I would appreciate honest advice from other professionals in academia.

What you're doing now does not sound too different from what you would like to do. Don't you have the freedom to steer your research in that direction? Doing a second PhD is basically always a bad idea.

Just hire a PhD student and make him pursue your passion. And then try to be a great adviser.

PhD is not a cooking license or so. It is a proof that you are able to do research yourself. So just go, and start study the new field you are interested in, do research, apply for grants etc

@polfosol make him pursue your passion — I think you mean "Hire a PhD student who shares your passion and let them help you pursue it."

You're a tenured professor - you have all the latitude in the world to explore your ideas.  You want to do something new?  Do it!  You're past the part of your life where you need other people to give you a rubber stamp and a gold star.  Read some papers, make some contacts, write a proposal, go find some grant money, and get to work.

Look at your options for sabbatical.  Plenty of ways to catch up in a field short of getting a PhD at your stage.

You've already got a PhD, so you've already got the academic "union card". Is there some reason you can't do some research in the field that interests you? It certainly sounds like it has applicability to your current field.

The two fields are very close together.  (Both are essentially different types of applied psychology.)  There isn't really even a point in going back to school for this.  Just learn the stuff and practice it.  Once you have a Ph.D. in one field you can practice others.  Even ones that are more different like biology and physics.

Good point about PhD in one area and work in a very different one. The biophysics faculty of my wife (formally, a biology section) was 90% hard core PhD physicists (including all the senior staff and the head)

The other answers advising you not start over but rather refocus elsewhere, leveraging your tenure to allow you to move into a new research area are excellent.
There are a good number of fellowship/training programs that are specifically designed for experienced faculty to do exactly this. While they are might not be directly relevant to your specific situation, two that come to mind are NIH Research Career Development and Humboldt Research Fellowship for Experienced Researchers. As you move along in your career opportunities to explore new areas diminish, and programs like these are designed to address that.

There is no need quitting your present job. You can take a few online courses for free on internet if you feel that you are lacking background:
https://itunes.apple.com/us/course/environmental-psychology/id529650093
Then just follow advice that was already given to you.
However if EdD is what you have and it's not enough for your chosen field then it's a whole new game.

I was in a similar position to your a few years ago, except that I'm about 20 years older than you. I also work in education (teaching and doing research in instructional design). I had developed an interest in applied/professional ethics, and wanted to pursue this. Here is what I did: I pursued and online masters degree from a prestigious mainstream university in the United Kingdom (I live in the United States) - Russell Group university in if you know the UK ranking system. I did the master's in order to get a good solid grounding in the field. I did not feel the need to do a dissertation and get a PhD.
As other commentators have said, I would strongly advise you to consider alternatives to resigning your position. I was able to complete the master's in about 3 years, practically nobody in my department even knew about it (I kept it to myself). Now that I've completed it, I'm beginning to write and also teach one course. Good luck.

Are you a tenured professor in a primarily research university or do you have a huge teaching load? If you are at a research university and then you have freedom to steer your research career. Just hire a good PhD student or a postdoc as others have suggested and you can learn together. Go to conferences in the field, etc., etc. Since you have tenure you know how research works.
On the other hand if you have a huge teaching load and are not able to find to do your current research, let alone enter a completely new area, then you are certainly in a very tricky situation. But then you have to be realistic and ask yourself if a second PhD will land you in a better situation than your current one?
Also, as others have pointed out, a lot depends on where your tenure is (which country), which university you are at, and if you are happy with your environment there. Are you hoping to pursue a second PhD in a highly ranked university in the US? These details are not clear in your question.

authors: Bob Jarvis - Слава Україні


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Is it okay to directly copy a diagram/image from another research paper into yours?
We are writing a research paper and for our experiments using a model/architecture that was created by other researchers for a specific task. We are using the same model in a modified way for a different task, but the model at its core is the same.
Is it okay for us to directly lift the image/drawing/diagram of the model/architecture and post it in ours? We would give due credits of course. We thought about drawing it on our own again and posting it but we did not want it to seem as if we are hiding the fact that we are using someone else’s model and trying to pass it off as ours.
The paper in question is available in the open domain, so I doubt there will be any copyright issues.

available in the open domain – Can you specify this? Few papers actually are in the public domain. Paper that are published via open access are usually under a CC licence of some sort. Papers that are just freely available do not have any licence allowing for this.

No, it is not okey to use it without permission. Check the Reuse and permissions when clicking on the images on this paper for example on how in general the reuse it is done.

I am not sure about the license. I found a copy of the same on Arxiv. I could not see any fair usage guidelines for the as such.

@MysteryMan: The Arxiv page for each preprint tells you under which license it is published. (Just search the page for license; it’s rather hidden.) Unless it’s published by an open-access journal, it’s unlikely that this license grants you the right to do what you want to do.

You can always write the authors of the first paper and ask whether you can use the image. This is the most polite thing to do. And (assuming they don't ignore the email altogether) they will probably say "yes".


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Advice about the copyright in research work as a research associate
I need advice regarding the copyright of the work done as a research associate.
I am working for a university as a research associate and my principal investigator insists on publishing my work without my consent. She thinks that she is entitled to do so because i worked on her idea and she paid me the salary. So she has a right to publish my work without my consent and I have no right on that work any more.
Is this true?

Depends on the wording of your contract, but it is possible (it would be standard for industry contracts). Depending on jurisdiction, you may retain the right to have your name mentioned as originator of the work ("moral rights", they are usually given up in the contract in the US but inalienable in other places, e.g. France).


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What does it mean when a conference submission system asks if the first author is a student?
When I recently submitted a paper to a conference, there was a checkbox asking whether the first author is a student. Did you encounter anything like that? Does this means the reviewers will consider this and will be less strict?

Is there any kind of student paper award at this conference ?

No announcement about this.

@user79961 For further evidence, you can also check the websites of the conference's earlier editions. (But note that conference websites don't always announce the award winners.)

It can mean lots of things and only the conference organizers can tell you the reason. There could be student paper awards, travel awards, or student presentation sessions. There could be research speed dating or a desire to have more student presentations in each section.
Likely the peer review will not change, but the selection process might chnage. Paper selection is not just about the best paper, but about the best fit given the goals of the conference.

As suggested in @Distic's comment, the purpose of this question is probably to identify candidates for a student paper award.

does this means the reviewers will consider this and will be less strict?

In a decent conference, probably not. The audiences of these conferences expect that high standards are applied to submissions. These standards need to be enforced regardless of the authors' identities.

Sometimes reviewers don't even know who's paper they are reviewing at these things


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Dealing with non-contributing co-author when preparing an extended version of co-authored paper
Summary: A co-author on a manuscript under review hasn't really done anything. Should I remove their name (with or without notice), keep their name and tell them it's unfair, or do nothing.
Some time ago I met someone at a conference who works on similar topics. We had a nice conversation. Months later, this person contacted me about something I had worked on -- they had a few positive comments and some questions about methods. I appreciated the positive comments and answered the questions about methods.
Because I don't have a lot of collaborative papers, and I wanted to have more, I asked this person if they would be interested in collaborating on a paper to submit to a conference I had been planning to submit to anyway. They said yes.
In the following months we exchanged many emails, which were all positive in tone, discussing ideas and approaches. I began to notice that my collaborator would typically respond to my ideas, rather than propose something themselves. I asked my collaborator to send me some data they had, which they did. Eventually the submission deadline was approaching, so I wrote that I would work on a draft, then we could see about combining whatever they had prepared.
A few weeks later, I sent them my draft. They made a few editing suggestions, added a sentence or two, and added two additional references, one of which was to one of their own papers. They were not bad sentences or references, so I sent it off to the conference. The paper was accepted. My co-author said they wouldn't have time to attend to the conference. I wrote that was fine, they could send me some slide contents, if they wanted, and I would show them at the conference. I ended up presenting my own slides at the conference, because my co-author didn't send me anything. I wasn't really bothered by any of this, because I would have done more or less the same thing if I had submitted a single-authored paper to this conference.
After the conference, an organizer announced they were soliciting contributions of extended versions of conference papers for an edited volume with a well-reputed publisher, with a submission deadline six months hence. I forwarded the email to my co-author, with a note that I would not immediately commence work on the extended paper because I was simply too busy with other things. They were pleased at the prospect of submitting to the edited volume and wrote that we should work on it.
About a month after that, my co-author wrote that they had been approached by someone wanting contributions for an edited collection, in a different language, about a topic somewhat related to the one we had been working on. I responded that it sounded fantastic, and if they would write up a plan or a draft, I would try to work on it, but that although I knew that language, I didn't do a lot of academic writing in it. My co-author wrote that it was no problem, we could worry about that later.
So everything seemed to be progressing smoothly. My thinking was that as I had done almost everything for the conference paper, my co-author would take the lead with this manuscript, as a tit-for-tat, and also because they are in mainly writing in that language. So I imagined things to often work in collaborations.
Anyway, a few months later, my co-author wrote me that they had prepared a first draft for the other-language submission. The attached file was simply a translation of the introduction and methods section of our previous conference paper into the other language. I wrote back that I found it unsuitable, because the contribution should be about a different topic. In addition, the text appeared to have been machine-translated using copy-paste to a website.
As a response my co-author wrote that they actually didn't have very much time, so I could take the lead with the manuscript, as first author, and write up a draft. I wrote back that I did not have enough time to do that, nor sufficient expertise writing in their language. They responded that they would forego this submission.
I was disappointed, but didn't think about it too much. A few months later I finally got around to writing up the extended version of the conference paper. My co-author, although they knew of the deadlines, did not contact me about it, and made no contribution. I sent them the submission draft about a week before the deadline, but received no response. I submitted the manuscript with their and my names on it.
A few months later: My co-author wrote to me that the deadline for submission to the other-language edited volume had been extended, and they would have enough time to write something now, if I was still interested, and also, what was the status of the extended paper?. I wrote back very briefly as I had months earlier, that I was interested, and they should write up a draft, and that the extended paper was with the reviewers.
Cue to now: My co-author wrote again, stating once again that they didn't have enough time to work on the other-language contribution, and would signal to the editors that no contribution would be forthcoming.
Meanwhile, the reviews for the extended paper came back to me, and are positive. The changes requested by the reviewers will not require a great deal of time.
So my question is now: Should I
1)  Remove my co-author's name on the submitted extended paper, with the justification to the editors (and the co-author) that they contributed nothing, and inform my "co-author"?
2)  Remove my co-author's name on the submitted extended paper, with the justification to the editors (and the co-author) that they contributed nothing, and not inform my "co-author"?
3) Keep my co-author's name on the extended paper, but write them explicitly that I find it unfair that I have done everything and they are apparently not willing to reciprocate on other projects?
4) Keep my co-author's name and do nothing?
My feeling is that my "co-author" was hoping that I would write papers and add their name. I am also bothered by the rather ridiculous "draft" that they sent to me which was simply a translation of my own text.
I don't have a lot of experience with collaborations, so any advice is appreciated.

Very long, bt I would go for 3. You don't want to make such a conflict with yr colleagues. I am nt talking about what is fair and what is not because if see them from this perspective, so many things in Academia are not fair. I wrote papers and put my professor name and he did not even know what it is about. As a postdoc, I find it normal that he does not check after me but unfair because he didn't write a word. The problem is even worst with project proposals because he is the only acknowledged person. This is how it works and a paper will not make your co-author get promoted at your expense.

I tried to improve the summary so others won't have to read in full. @Zwentibold please do revert or edit further, if you want

Relevant question: When submitting an extended version, is it mandatory to include all authors of the original paper?

In most fields, there would be a great deal of difference between the bar for authorship and the bar for true equal contribution. In this situation, from your description, it seems that your co-author probably meets the bar for authorship, but of course not equal contribution. Below are some of your statements that were evidence for this, at least in my interpretation:

In the following months we exchanged many emails, which were all positive in tone, discussing ideas and approaches.

...

I began to notice that my collaborator would typically respond to my ideas....I asked my collaborator to send me some data they had, which they did.

...

A few weeks later, I sent them my draft. They made a few editing suggestions, added a sentence or two, and added two additional references, one of which was to one of their own papers. They were not bad sentences or references, so I sent it off to the conference.

I understand that you are frustrated that they have not contributed equally, but in general they have responded to your emails, made an effort to see where this work can be submitted, and been (partially) involved in the original work, although they have been very busy. It might be dishonest to exclude them now at the last minute. Additionally, it might be too late -- you can exclude them from the next follow-up thing you work on, but this was a thread of research that you began together, even if you did not finish it together.
In some cases, I would say that 5% actual contribution can be sufficient for authorship (though this depends on the field and the total number of co-authors). I have even seen at least one academic who lists on their CV their percent of contribution on various papers, and some are listed at 5 or 10 percent.
So my question to you is: does your co-author meet, say, a 10% bar for contribution, keeping in mind the intellectual ideas, not just the writing and editing work?
How you proceed will depend on the answer to this question. Let's consider the options you provided:

1) Remove my co-author's name on the submitted extended paper, with the justification to the editors (and the co-author) that they contributed nothing, and inform my "co-author"?
2) Remove my co-author's name on the submitted extended paper, with the justification to the editors (and the co-author) that they contributed nothing, and not inform my "co-author"?

These two options are terrible, because they treat this decision as yours to make, not in consultation with the co-author. Even if they did not do most of the work, they were a part of the project, and they should be able to have a say in whether they think they contributed enough to merit authorship.
Both options would likely cause a falling out with the co-author, and possibly some kind of minor scandal where (even if you are in the right), some people might believe you unfairly excluded them from co-authorship.

3) Keep my co-author's name on the extended paper, but write them explicitly that I find it unfair that I have done everything and they are apparently not willing to reciprocate on other projects?

This option is fair. But tread very carefully. Treat it as a question, not a request. Email your co-author and explain your concerns. Ask them if given the concerns, they feel they should still be on the paper. Be very clear that if they feel they did contribute enough to merit authorship, that you will include them. And follow through: actually include them if they feel they should be included.
You are already the first author, so it will be clear you have contributed more. But another way to phrase this request would be to ask if you should list "primary contribution" and "secondary contribution" as footnotes to your names (if this is appropriate in your field). In any case, even with this smaller request, be very careful and diplomatic.

4) Keep my co-author's name and do nothing?

If the answer to the question about whether the co-author contributed 10% or more is yes, then this would be my preferred option.

You absolutely cannot remove your coauthors name as they obviously (by your description) meet criteria for authorship.  Also you must give your coauthor the opportunity to review the final version of the manuscript in good time before you submit it.  A week is not normally enough time for this, unless the coauthor has agreed beforehand.  I would give at least two weeks.
There's no point being confrontational or burning bridges.  You can choose whether or not to work with somebody again.  And now somebody owes you a favour.  So option 4 for me.
If you want further advice you should consult the documents produced by the Committee for Publication Ethics (COPE) https://publicationethics.org/authorship.  Criteria for authorship vary across fields and disciplines (and sometimes with different journals and institutions), and are always open to interpretation.