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Can you post an article on arXiv while under peer review?
Would doing so go against the declaration many journals require that the author has not submitted the work anywhere else?

https://academia.stackexchange.com/questions/12603/is-it-ok-to-submit-a-paper-to-arxiv-after-copyright-transfer

Journals that do not have embargo periods do not care when you post to ArXiv.

"Submitted" is ambiguous. It most likely means "to a peer-reviewed journal", not exactly "posting on-line".

It depends on the journal.  If it is not found on their web site, ask them.

I'll note that in some fields the journals tend to be consistent one way or another. Math journals tend to be permissive. But, yes, ask to avoid problems.

You have to carefully read to be sure what "submitted anywhere else" really means. Depending on the field (e.g. math or physics), this might only mean that you have not submitted to any other journal, while posting it to a preprint server such as the arxiv is fine. For example, Physical Review Letters states

The manuscript has not been published and is not being and will not be considered by another journal while it is considered here.

clearly stating that this only refers to journals, and Nature Physics states

Nature Physics supports the posting of submitted manuscripts on community preprint servers such as arXiv and bioRxiv. We do, however, ask you to respect the following summary of our preprint policy:

The original submitted version may be posted at any time.
The accepted version may be posted 6 months after publication.
The published version—copyedited and in Nature Physics journal format—may not be posted on a preprint server or other websites.

BTW, interesting find while searching for the Physical Review policy on the arxiv: https://www.aps.org/publications/apsnews/201211/preprint.cfm.  Posting preprints can come with unexpected risks.

Nature Physics ought to update the last bullet point in their preprint policy. They just started allowing authors to publish under a CC-BY license, in which case anyone (presumably including the authors) should be able to freely share the published version.

@Anyon Though this probably means that you have to pay publication charges? The same holds for the hybrid and open access Phys Rev journals, I believe.

Yeah, and it'll cost a small fortune (unless using their Guided OA system where it's considered for three journals at the same time). I just think they should qualify that statement.

@Anyon Oh, indeed, I remember seeing insanely high figures.

Usually, yes, you can.
arXiv is a preprint server. Preprints are not like submitting a paper for review at another journal, they do not involve formal peer review, and arXiv is not a journal. Many (most?) publishers have explicit policies that deal with preprints as well, and they are usually minimally restrictive, e.g. Elsevier:

Preprint

Authors can share their preprint anywhere at any time.
If accepted for publication, we encourage authors to link from the preprint to their formal publication via its Digital Object Identifier (DOI). Millions of researchers have access to the formal publications on ScienceDirect, and so links will help your users to find, access, cite, and use the best available version.
Authors can update their preprints on arXiv or RePEc with their accepted manuscript .

with caveats

Some society-owned titles and journals that operate double-blind peer review have different preprint policies. Please check the journals Guide for Authors for further information.
Preprints should not be added to or enhanced in any way in order to appear more like, or to substitute for, the final versions of articles.

So you are usually free to post an article on arXiv, even before submitting it for peer review. Exceptions can apply if the journal you submitted to operates double-blind peer review.
Your question asks about something else, which is whether journal policies that say "has not submitted the work anywhere else" prohibits you from submitting to arXiv. Usually it doesn't, because this journal policy is typically of the form "if you submit here, your paper is not currently under review by another journal". Since arXiv is not a journal, there is no issue. Again here's another policy page from one of Elsevier's journals:

Submission declaration and verification
Submission of an article implies that the work described has not been published previously (except in the form of an abstract, a published lecture or academic thesis, see 'Multiple, redundant or concurrent publication' for more information), that it is not under consideration for publication elsewhere, that its publication is approved by all authors and tacitly or explicitly by the responsible authorities where the work was carried out, and that, if accepted, it will not be published elsewhere in the same form, in English or in any other language, including electronically without the written consent of the copyright-holder. To verify originality, your article may be checked by the originality detection service Crossref Similarity Check.


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Does publishing in multidisciplinary journals undermine perceived work quality or impact?
For example, Heliyon is Elsevier's multidisciplinary journal which I'm considering publishing in. Is publishing in a broad-scope journal such as this one or PLOS necessarily detrimental to one's career or the likelihood of the paper being impactful?

In Web of Science's Journal Citation Reports, there are 236 categories ranging from "Acoustics" to "Zoology". There is also one category called "Multidisciplinary Sciences". PLOS ONE is in that category (and Heliyon is still in the ESCI, so not assigned to a category yet).
If you sort Web of Science's list of categires by Aggregate Impact Factor, you will see that "Multidisciplinary Sciences" ranks at #10 out of 236 (as of early 2021):

Your question, it seems to me, is too general to answer properly, but perhaps this formal approach might indicate that the answer is: No, publishing in a multidisciplinary journal will not necessarily harm you. As Libor wrote in the comments, journals like Nature and Science belong to that category.
The response might be slightly different if you refer to Open Access megajournals. There are enough skeptics, I fear. But my own guess is that in the mid- to long-term, it will not harm you. The reason is the following:
Many university libraries increasingly set up bibliometric departments that analyze your scholarly outputs when you are a candidate for a research post at that university. And one of the positive indicators they look at is the share of Open Access publications. Publishing in such journals may underline your commitment to Open Science, which is a generally positive aspect. (But again, opinions may vary.)

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Prerequisite for research in discrete mathematics
I hope to apply graduate math department for MS/PhD in math. My area of interest are discrete math, combinatorics, graph theory... etc.Now I have few questions :

Which are the prerequisites for these courses ? and Which grade of my undergraduate are more important ?
I am also a bit confused that whether I will apply for a pure or applied dept ?

What country are you in? What country do you want to do your PhD in?

Usually the prequisites are listed in the syllabus. 2. You should find out the exact degree on the university website.

Have you looked at https://academia.stackexchange.com/q/13293/12339 and https://academia.stackexchange.com/q/14463/12339?

Can you talk with a local prof about that?

Combinatorics is an area where there are both very applied programs (in particular look at programs in "Combinatorics and Optimization" or "Algorithms, Combinatorics, and Optimization") and programs where combinatorics is studied as pure mathematics.

This is a US centric answer. If you are applying to a mathematics doctoral program in the US and have a mathematics undergraduate degree then the specialty you want to pursue isn't especially important. First, a broad based undergraduate degree has what you need to get started in a US doctoral program. If your undergraduate degree is other than math, you have a more complicated situation, but admission is still possible if you have, in general, "enough" math.
But one reason that this is the case is that such programs start out heavy in coursework, so if you need more combinatorics, for example, you will be able to get it before starting research.
The prerequisites you need for research are probably at the discretion of the advisor you will (later) choose to guide you. They may have some specific suggestions.
The one thing you might need to consider, however, is whether the pure and applied math specialties are contained within a single department or split between departments. Some splitting is common, as having statistics (different example, I know) separate from math. If pure an applied are in a single department, then you don't need to make a selection before applying, and you may be able to delay that decision for a year or two while you take some courses and learn more about possible advisors.
In other countries the situation might be drastically different, of course, with more expected on entry but a shorter time-frame for getting the degree.

Be aware that in some universities, discrete mathematics might happen in the computer science departments, e g at ETH Zürich.

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What facts constitutes as citation-worthy
If I were to state a fact that is simply a part of a field, do I need to cite a scientific article that supports this? Like, let's say I write something like this:

"... tryptamine being a monoamine protein in the body, involved in the regulation of serotonergic, dopaminergic and glutamatergic systems in the brain."

Do I need to cite this? Is there anything one can remember to guide oneself in situations where one wonders whether to cite or not?
(I'm writing a treatise, which has been defined to me at least, as  a text type somewhere between an essay and a scientific article)

Related: https://academia.stackexchange.com/q/46324/20058

Generally speaking commonly known facts, such as things that appear in encyclopedias or even undergraduate text books don't need to be cited unless quoted.
But that doesn't mean "known" to everyone. If they are common knowledge among experts, for example, then no citation is needed.
If you quote or closely paraphrase something from a source, then you should cite that source.
But it is probably better to err on the side of over citation than under and citations can also sometimes help the reader, depending on the audience. A

I see. Considering I'm writing this treatise for a larger audience than just experts within pharmacology, it would perhaps be helpful to include citations for facts that are known among experts, since it can help those non-expert readers?

Yes, it might be helpful. In fact, over-citation is probably better than under-citation in most cases.

Okay, thank you a lot :)


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Citation of a book chapter that was put online
I am trying to cite, using the ACS format, https://www.intechopen.com/books/cancer-causing-substances/heavy-metals-and-cancer, but I don't know whether it is considered a book or ebook chapter. How am I supposed to tell them apart? The link is under "books" on the website, but seeing as it is online, wouldn't it be considered an ebook? If I cite it as a book, it'll be pretty weird for me to include a link and the date accessed, won't it?

I would cite this as a book section, including the DOI (because that's where you found it/how others will be able to find it) but not including "date accessed", because that is intended for more volatile resources like web pages. (If a reference has a DOI you can usually treat it as non-volatile.)
Sticking as precisely as you can to a reference format is important, but the most important thing is to make sure that the information is present that allows readers to (1) attribute credit appropriately and (2) re-locate the original source.

(1) Carver, A.; Gallicchio, V. S. Heavy Metals and Cancer. In Cancer Causing Substances; Atroshi, F., Ed.; 2018. https://doi.org/10.5772/intechopen.68247.

A book is a written work distributed by a publisher, in physical or digital form. (Books and eBooks needn't be distinguished, they contain the same content.) Book drafts are distinguished, they are distributed by authors.


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PhD salary for DFG (Deutsche Forschungsgemeinschaft) Collaborative Research Centre
I've been selected for a PhD position in a medical school at Lower Saxony in a DFG Transregio Collaborative Research Project. Even though I'm yet to receive my contract, I am curious to know if my salary will be according to the DFG payscale or the institute payscale (which is significantly lower than the DFG payscale)? My supervisor unofficially told me the scale would be 65% TVöD E-13, but he expects the salary might be between 1350 -1450 € per month for the first year (isn't that lower than 65% TVöD E-13?). On comparing with the DFG pay scale table 2021 (and after reading the first paragraph, of course), I want to know what salary can I actually expect in hand after tax deductions (I'm supposed to have some pension scheme, which I know nothing about)? Would the money be sufficient for 2 people in Hannover if I take my spouse with me? What % of salary will I be able to save, if at all?
Thank you.
P.S.: I'm very new to the German system and hence request to guide me. Any obvious issue which I don't know/haven't mentioned in my question can be happily addressed to give me an idea of my upcoming years.

Finding out about your salary in a TV-L or TV-ÖD setting is pretty straightforward. For TV-ÖD you can simply look it up here (note that Jochen Glueck's link in the comments refers to the table for 2020). Net salary for a 65% position would roughly be 1754.40 €. While the final amount depends on some personal factors (such as Steuerklasse), it should not be as low as suggested by your supervisor.
Now, the table provided by the DFG (you're probably referring to this one?) is not suitable to find out about your final salary, as is stated in that document ("Für die Ermittlung der persönlichen Vergütung sind sie weder vorgesehen noch geeignet"). This table gives numbers to be assumed as the Arbeitgeberbrutto, which corresponds to the amount of money your employer has to pay and is thus higher than the gross salary you receive. The purpose of this table mainly is to serve as a basis for calculating personnel costs in project proposals etc.
Whether your salary is sufficient for two people to live in Hannover completely depends on your expenses. The highest share of your income will probably be needed for rent, you can do a search for flats on the internet to get an idea. The university and/or Studierendenwerk should have an international office that may assist with further questions on living in Germany.

To add some more, probably helpful, information: TVöD, as can be seen here depends on: your work experience (Stufe, you might need to provide some details to your employer's HR, they would calculate what's applicable as experience), your taxes depend on your martial status -- Are you married? Do you have kids? Does your spouse work? Some "splitting" in who of both pays more taxes can be done (Lohnsteuerklasse).

Very good answer (and much more informative than my comments under the question, which I have thus deleted).

Can someone please illustrate about the pension scheme? What is that? Are you still considered a student if you are eligible for a pension scheme?

@user110134 Much more information is needed to say sth. meaningful about the pension scheme. (EU citizien? Planning to work for a longer period in Germany/EU?) For a PhD, I would say this should be the least of your concerns.

The DFG numbers say how much the DFG is giving through a grant, such as a CRC, for a PhD position applied for. This doesn't mean the university has to pay the same level (i.e. percentage of E13) to their students - they can pay more or less if they want to.
So you have to take whatever you are told (i.e. 65% E13) and use one of the available calculators (see erc's answer) to determine your net salary. (As a PhD student, you will get Stufe 1.) Whether this enough to live with 2 people in Hannover: I'd say yes, but it clearly depends on your standards. (Note that if you are married and your partner does not work, you should get tax class 3 which should get you some extra money, almost 2000€ net.)


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Can someone get his previous credits counted in a new Master's programme in the EU?
Suppose, someone studied in a 120ECTS MSc program in CS in a country 'X' in the EU. He obtained 60 ECTS there, but he also has some failed courses. He then abandons the program.
Now, he moves to a country 'Y' in the EU and gets admission to program CS in the country 'Y' after 5 years.
Can he get his 60 ECTS credits counted by the school offering CS?

Does "graduate" mean "PhD"? There is no such thing in Europe, mostly (in the sense of having to take courses, get ECTS points, etc.). Or do you mean Master studies.

Is this you? It's much easier to read in first person, IMO

5 years is a long time. I believe in quite a few programs you get kicked out after less years if you don't make enough progress. I doubt such old credits would be counted.

They will decide what credits / courses they will be prepared to accept.
All you can do is show what you have covered so far, even including syllabi may help make a case but, remember they get to decide what is accepted.

If the question is "does X work", "You have to check if X works" is not an answer. It is the question.

@user151413 Seems perfectly reasonable as an answer to me, this is basically the "it's up to your program" answer. It's a question that has to be asked of the specific program, no general answer can be given here.

@BryanKrause So you are saying the question should be closed.

@user151413 Indeed, that's how I voted.

If the only possible answer is "It depends on individual circumstances", then the question should be closed.

@BrianBorchers ... rather than answered.

@SolarMike Oh. I did. And I stick to my conviction.


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Co-authorship graph
I am currently building a reading list targeted towards a certain list of 5-10 authors. They all work under the umbrella of wireless communications (separated by their own subfields), and I would like to efficiently go through their recent works. To facilitate the search, I would like to know their "affinity" towards each other via co-authorship links. I am hoping this might shed light into the development of their ideas.
My question is: is there a resource for finding (possibly indirect) connections between authors?
The best I could find is DBLP but this only gives the list of authors who are direct co-authors. Also, this link suggests Visual Explorer from Microsoft Academic, but it seems to be no longer available.

You can have a look at csauthors.net. It uses the DBLP database to find the co-authorship distance between two authors, and also provides the list of papers co-authored by any two authors forming a link.
As with any such resource (including DBLP), you need to be careful about spurious links created due to confusing between authors with the same name. Unfortunately, if this does happen there does not seem to be any way to easily find the true shortest path, however.
Screenshot for reference:

Example for list of papers co-authored:

Note: I am not affiliated to this website in any way.


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What standards should I apply when evaluating a PhD thesis from a weaker university?
I have been asked to serve on the examination committee for a PhD thesis. It's in the area of machine learning. It's from a university in a developing country. My job is to provide a written report, recommending whether to award the degree (possibly with minor or major changes), or even not to proceed to defence. I won't be participating in the defence itself.
The quality is very bad. I would say it would receive a low grade, if evaluated as a 3-month MSc dissertation, in my university (in a developed country, but not a top-tier university). It's bad in every respect - novelty, experimental design, understanding, motivation, contact with literature, writing, reliance on "predatory" journals, even some (fairly benign) plagiarism. So, my instinct is to recommend it should not proceed to the defence.
My problem is that standards vary between countries and between institutions. How much allowance should I make for this? I do not want to perpetuate a "vicious cycle" which prevents high-quality work in developing countries (eg Breaking the (perhaps perceived) academic (poverty) cycle).
Part of my problem is that I don't know how much weight my report will carry. Maybe the department is used to receiving harsh reports from international committee members, and de-weights them. Or maybe a harsh report from an international member is enough for an immediate fail.
If I could allocate the blame in my review, I would say the supervisor surely deserves most of it. But it is the student who will suffer the most, if they fail. On the other hand, perhaps the supervisor's own PhD was the beneficiary of some lenient reviewing in the past, leading them not to know what standards are expected. I should not perpetuate that cycle either.
I hope my question does not sound condescending or insulting to scholarship in developing countries. I know that great research is done everywhere, and I have great respect for many individual researchers from the country in question.
Edit: of course, there are no right answers here, but I accepted @anon's answer because the "PhD = passport to worldwide community" concept was the most helpful in my thinking. In the end, I wrote a fully honest review from my point of view, and recommended it should not go to defence, but I added a note that I understand the local committee will apply the institutions' own standards. It goes without saying that I was constructive, not negative, and gave a lot of advice for accessible improvements. Thanks to all for a useful discussion!

I was in a similar situation, but the thesis in question is from a university in a developed country.  I applied the examination criteria, and provided evidence to justify my decision.  At the end of the day, as the name of examiners will be associated with a thesis for eternity, and if you pass a poor thesis, then think about what it says about you.

Did you receive, or have you asked for, any more detailed instructions about how to assess the thesis?  I believe universities typically have their own guidelines about theses.

Kimball, I haven't asked for extra detail, as I think my dilemma won't be resolved by them -- I don't think these extra details are going to say "low standards are ok, novelty is not required, ...".

Decline to write the report, but tell them exactly what you would put in it if you did. But one question: Why should a "non-top-tier" university have different standards than one of those with the big PR departments?

@Karl, if a professor from, say, MIT evaluated a PhD thesis from my university, they might find it fell short of the standards they expect (not as egregious as in my question, of course). This is pragmatic. I don't think PR is the difference between one "tier" and the next.

@Karl, I considered writing an informal "warning" so the chair would have the option to decide "ok this extern is gone rogue/too harsh so we'll get a different one".. but how are standards to be upheld? And this is not a normal part of the process - I don't really want to invent new process.

Oh, it's one difference. The other is their larger budget, which allows them to attract better, larger projects. But your teaching and scientific standards should be the same. Certainly the teaching varies all over the place also at those famous places. And there is no reason why poor countries should allow themselves to have low standards. It's often true, which is terrible for their students and for the development of those countries.

Standards can't be quite the same, because eg there is a big difference in the quality of the pool of applicants to the PhD programme.

What does it mean for a plagiarism to be "benign"? The student only copied the definitions, not the proofs? As someone who was subject to "benign plagiarism" in the past, it can be very annoying, and failing to remark on that is exactly how people move from benign to malign.

@Ink blot. It was some introductory-type sentences in some chapters which had been copied from blogs. From experience, some students don't realise they have to use quotation marks and citations. Nothing of substance in the PhD was plagiarised, to my knowledge. I agree that even benign/accidental plagiarism should be named and "punished".

@jmmcd I think you should write a new answer, because your comment above I think is a very pragmatic way to deal with this. Think of it the same way as writing a letter - you would not just silently write a bad one, you would let the interested parties know in advance that you are unable to write a sufficiently positive one and then have them act on this information any way they see fit.

External examiner = independent, disinterested, and candid expert
Universities engage external examiners in order to add the legitimacy of disinterested expert approval. Since the independence of the external examiner is a vital criterion, it is essential that the university not be allowed to dictate the terms on which you, as this disinterested expert, grant (or refuse to grant) approval. This is an occasion where you can and must be completely candid, acting without fear or favour. Whilst the internal examiner(s) and convenor are supposed to be similarly candid, they may be reluctant to be candid, since they may be too scared to "rock the boat".
[When I say disinterested, I mean you have no vested interests in the university or the candidate; of course, you have a vested interest in maintaing the integrity of scholarhip generally, and it is that interest which you represent in your capacity as external examiner]
As the external examiner, your responsibility is to evaluate the PhD thesis independently, since your duty is to scholarship, not to the university engaging you.
Therefore, you should judge it by the same standard as you would judge any PhD in the relevant field, irrespective of institution. Unlike Bachelor or Master's degrees, the principal criterion for the award of a PhD is universal and generic: a substantial original contribution to scholarship. As an expert in the relevant field (I hasten to add that only the candidate can be an expert in the work itself), it is your prerogative and responsibility to make a determine whether the thesis meets that criterion independent of what the university may or may not require.
A PhD is a 'passport' to recognition as a legitimate academic worldwide. Universities (and some vocational Higher Education institutions) are entrusted with the sacred responsibility to act as 'gatekeeper' to issuing this 'passport'. University regulations for PhD degrees are just a means to an end, existing to guide all parties towards determining what consitutes a substantial original contribution to scholarship. Ensuring compliance with such regulations is the responsibility of the internal examiner(s) and the convenor. The external examiner should disregard the bureaucracy and evaluate a PhD thesis solely on its own merits.
If the candidate has failed to comply with a university regulation (e.g.: he/she submitted too early or too late, did not attend some compulsory workshop, or did not comply with the word-limit) but his/her thesis is worthy of a PhD award (i.e.: the non-compliance is not a matter of academic integrity), that is for the internal examiner(s) and convenor to address, and not your problem as an external examiner.
If the candidate has complied with all university regulations, but his/her thesis is not worthy of a PhD award, it is your duty as external examiner to either recommend against awarding the degree (if the thesis is nowhere close to the standard required) or require corrections before the degree can be awarded (if the thesis is close to the standard required -- "pass subject to corrections" is the usual outcome in the UK). Of course, you should make your criticism constructive and useful, but you must not be lenient.
You are working for the global academic community, NOT for the university (despite the fact that it is the university which pays your fee and travel expenses)
Your responsibility as external examiner is to hold both the candidate and the university to account, and act as a vital line of defence (on behalf of the global academic community) against universities being too lenient (or, conversely, being too hostile to their own candidate... it can happen!). You also have a responsibility to defend the candidate against any absurdities of the university -- that is to say, you should have no qualms about disagreeing with university regulations if you feel they are inappropriate to the work at hand (e.g.: if you think the abstract is too long, you should demand, in your report, that the candidate make it shorter, regardless of how long the university regulations require the abstract to be).

This is a valid way to think about it, but as pragmatic advice goes I think this doesn't feel like very good advice. I would honestly recommend looking at @jmmcd's comments on the question, and consider to at least give the student and advisors a fair warning that you will not write a glowing report.

I suggest that you remember that you are evaluating the work, not its author, or the supervisor, or the university. Give it an honest evaluation, based only on what you see before you. If it doesn't measure up to your standards, then say so. Say why. Make suggestions if you have the time. But honesty is required.
One of the reasons, actually, for international reviewers is to give the home institution some assurance that they are producing students on a par with others.

+1 especially for "honesty is required."  I'd add that I can imagine situations where others might see this thesis and the report on it; in such situations, the report should be defensible.

How do you evaluate the work without a rubric for evaluating? What if he's actually the top student in this developing country? No one in this country can ever receive a PhD? Perhaps the standards there are also quite different for what constitutes acceptable research. I think "honest evaluation" doesn't apply if you don't know what you're being honest about.

@Behacad If the top student in a country plagiarises and doesn't produce novel research of course they shouldn't pass. How could it be otherwise?

@Behacad "what you're being honest about" Being honest about science and truth. However, if the thesis is about humanities, you may have a point. A political view from a developing country may be different from a developed country. Still, plagiarism should not be tolerated.

The question is very difficult. One reason developing countries are developing because there are issues in the culture of learning, teaching and research which hold them back, amongst other authority-based or rote-based learning, focusing on unproductive criteria etc.
Now, there are amazing talents in these countries and some very interesting curricula (whose carriers often end up in good position in a 1st world country), but, on the whole, the system is not going to change overnight. On the other hand, the advent of the internet has brought the world's greatest library (ignoring the paywalls) to the fingertips of virtually anybody on this planet. In other words, the essence of a great academic institution which used to be its library, is no longer exclusive. Thus, even developing countries have now, in less resource-intensive topics, the perspective of improving the standing of their academic institutions.
To avoid the structural problems of nepotistic and political considerations, neutral external evaluations are increasingly sought. Research programs are now more and more evaluated by evaluators from established academic locations. It is clear that it is unlikely that the quality of such programs is going to match anything that, say, a top university regularly comes up with, but in a comparative setup, one can still fairly assess which of the proposals are the better of the submitted lot.
The OP's situation is more difficult. They have not been asked to rank, but to decide on a pass/fail. I would be careful not to assign blame to the supervisor, and possibly not even the academic institution - they have to work with what candidates they have, and their education level, existing tradition and resources. The question is, why did they select OP as a reviewer? Because of their expertise field, to rubber stamp the thesis, or indeed because they wanted an objective, developed-country view on the quality of the thesis?
As an academic, I would find it difficult to just waive the requirements I expect from a doctoral level work. But, understanding the context in which it was created, you might consider formulating it politely, compassionately, constructively, and perhaps with indications of what would need to be done to get the work up to passable level.
[I would not put too much weight on downgrading due to publications that fell for predatory outlets - after all, not only can you not expect less internationally experienced supervision teams to be fully aware of that, predatory outlets are sometimes very well disguised.  For instance, I remember a case of a predatory conference which closely mimicried another conference which is well known, which managed to push their version to the top search engine ranking - this included name, location (it was in the same country as the real one inducing you to not note the discrepancy; basically a form of gaslighting). We ourselves discovered it by chance, by on/off noticing that there were two different versions of a Program Committee, one of them with none of the researchers you would expect.]
They invited you to evaluate this work. This means they want your opinion. Academic integrity would probably demand that you give them your real opinion, but, in view of the circumstances, with a compassionate and constructive attitude and showing the candidate a way towards passing.
Finally, in the end, I assume it is their local committee that has to evaluate the opinion and give the ultimate verdict. If you feel that the mitigating circumstances still might call for a possible pass, you might consider formulating your opinion in such a way that gives them a back route to pass the candidate should they choose to do so.
In my opinion, the thing to remember that, ideally, with a PhD, that person should be able to apply for a position as a postdoc in a developed country. The long-term goal is that, with time, a PhD from that institution should become trustworthy enough that any good university in the developed world would realistically consider a PhD from that institution as a viable candidate. You have now a small role in helping to move towards this endeavour.

The "hireable into a postdoc" standard is definitely field dependent.  Pure math PhDs from the bottom half or so of PhD-granting math departments in the US are very rarely competitive for a postdoc; before 2008, most were directly hired into tenure-track positions at non-research-intensive colleges and universities.

Yes, but the point stands for other types of jobs.

@jmmcd - not really; it depends on the job market.  Right now, there are a grand total of seven advertised tenure-track jobs open to pure mathematicians in the US, at a time when one would expect about half of the jobs to have been advertised.  (It looks like postdoc ads are down, though not nearly as severely.)  I don't think being competitive for one of these jobs is a fair measurement of anything.  This situation is of course due to the pandemic, but there are humanities disciplines whose job markets have been this bad for years.

@AlexanderWoo The postdoc is a kind of gauge of the qualification. It is an ideal picture; and I was talking about a "good" university, i.e. one that would select people with a reasonably strong research background.

@AlexanderWoo, I see your point, but the phrase "ideally" ("ideally, with a PhD, that person should be able to apply for a position as a postdoc") is enough to avoid this kind of temporary/contingent circumstances.

@jmmcd It was hardly implicit in Alexander's commentary that the current circumstances are unlikely to be, in essence, temporary. But I do think it's a side point--the idea that "if the global supply of PhDs were in any way regulated to the global demand for postdocs, then this person ought to be able to apply for a postdoc in a developed country" seems about right.

The idea that the internet has made the quality of the university library a non-issue is appealing but doesn't match up with my experience. I got my PhD from a university in the developed world, but spent a month at a university in the developing world during my studies. While I was at the developing world institution, we found a relevant looking reference in a paper we were looking at, but the librarians at the host institution were unable to locate a copy of the paper. In the end, we only got a copy because I asked my home institution to make an inter-library loan request, and got a PDF.

@James_pic In technical topics, preprints are often available freely.

Being honest is not incompatible with adjusting for context. Give your assessment honestly, but not just in absolute terms — also state how you judge the thesis relative to the expected standards of the institution.
Of course, you will probably have to ask/research a bit to find out those standards.  Perhaps ask your contacts to send previous examples of what they consider a strong thesis and a weak-but-passable thesis; perhaps ask them to send any official guidelines to follow; perhaps ask for a phone call for an off-the-record chat to get their personal guidelines.
If these turn out to basically agree with your usual standards, then things are straightforward.  If they’re much lower than your usual standards, then you can be clear in the report that you are writing with reference to them, along the lines of:

This thesis has major problems XYZ. These are significant scientific flaws, which must be addressed in order to produce good-quality research, and by my own university’s standards, I would not recommend proceeding to defence.  However, the thesis does meet Target Institution’s standard of acceptability to proceed to defence, according my best judgement and the guidelines I have received.

You are not compromising your honesty or candour, nor hiding the ways in which the candidate’s (and perhaps the institution’s) research standards need to be improved; but you are also not unilaterally imposing an external standard.

If you have the time, you could consider giving him the full truth. Not only what parts are poor, but also why they are poor and more importantly, what would have been a better way of doing it. You can't give him the full tutelage of a supervisor, but since he apparently has a poor supervisor now, some good advice might help this student a lot.

Let's first consider the question of whether a thesis from a weaker university should be evaluated differently. First, we must define what we mean by 'weaker' and 'stronger.' I believe that there are two relevant definitions for this use: one is degree-granting institution and the other is quality of institution. We may also wish to consider institutional prestige as an additional factor.
Now, we must consider the effects of evaluating based on these factors. If one evaluates based on institutional prestige or degree-granting status, then their evaluation will be heavily influenced by reputation and hearsay. Such evaluations can be prone to personal bias as well.
If one evaluates based on institutional quality, then they are evaluating solely on the merits of the research and not hearsay. However, I believe that this can also be prone to bias.
Consider that there are many excellent institutions which may not be well-known. These institutions may have excellent professors and students who produce fantastic research, but because the institution is unknown to most people this work will go unnoticed.
Conversely, there are many institutions which may not be so excellent. These institutions have professors and students who produce less-than-stellar research, but because the institution is well known this work will be noticed!
Therefore, it seems that there are two factors which influence whether or not a thesis will be noticed: quality of the work itself and reputation/prestige.


text:
Where to put the appendices in a paper based thesis?
I am writing my paper based PhD thesis, i.e., a collection of papers surrounded by a common introduction and preliminary section. Each of my papers has a relatively long (with respect to the overall length of the paper) appendix section. Is it more natural to leave each appendix after each paper or put all of them together at the end of the thesis (possibly in different chapters)?

Ask your supervisor what they, and the Uni, prefer.
Either is acceptable, but if the appendices are longer than the papers then I would put the appendices at the end of the complete document.
That way the papers ie the meat is easily found together.


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Is doing a research internship during MSc. studies worth exceeding the standard period of study?
Is doing a 3-6 months research internship during MSc. studies worth exceeding the standard period of study?
I am in my 3rd semester for my (course and thesis based) CS MSc. degree. The standard period of study is 4 semesters, but most students exceed it anyway by 1-3 semesters, judging by hearsay.
I have a good relationship with a professor, with whose research group. I will probably have published 2-3 conference papers in a few months.1 The professor would very well recommend me to some peers of theirs such that I could do a 3-6 months "research internship" at another lab in the same field.
Advantages

networking
strengthening my CV - I'd like to keep doing research later anyway, be it in academia or industrial research labs

Disadvantages

I will probably need 7-8 semesters, significantly exceeding 4.
As other labs are very close to ours, I could probably combine internship and thesis work. But my advisor already noted that in gneral time in internship >> time spent on MSc thesis there.
Instead, I could shorten my MSc studies to do a PhD soon afterwards (in Europe you usually need an MSc for starting a PhD)

I don't think the prolonged studies are a problem financially or from the side of the examination office. I much more fear that it could look bad on my CV having necessitated 7-8 instead of 4 semesters.
Does a research internship strengthen my academic CV enough to outweigh the disadvantages caused by overlong Master studies?
1 one paper got already accepted, another two are in progress.

I'll ask this the professor anyway - I'd just like to hear more opinions before.

How long is the internship? Based on "7-8 semesters", an extra two years?

This is a bit too personal for a good answer. "Worth it" to who, exactly? The tradeoffs are yours to judge.

Internshipper, if you have created two accounts, you can merge them by following these instructions.

This is a matter of balancing trade-offs and can be viewed in a variety of ways. While I won't go into all of the many ways, here are two ways that taking the internship could be perceived:
1) You were not able to commit to something you agreed to commit to at the start. Your leaving for a better opportunity may be interpreted by potential PhD supervisors as an inability to stick with a program.
2) You found an opportunity to build a new network of collaborators, gain new knowledge, experience, and perspective. You will also be making money, which can be used to make your life easier later on.
There are infinite ways to view the trade-offs, but only you can make that distinction.


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Medical Statistician: Concerned about missing authorship after conducting majority of project's data analysis, graphs, and figures
Dear Academia Community,
I am a young PhD candidate biostatistician and the lead data analyzer for a particular medical group's project. For context, the project is led by two medical students, who are under the guidance of MD physician professors. The two students came to me directly to statistically analyze all of their data. Happy to help, I eagerly dove straight in and churned out all of the data analysis, key figures, and graphs for these students. Normally, this project would take at least a month of analyses and work, but I was excited to help them finish in only 2 weeks because of their time request. Throughout their project, I helped consult with them on data interpretation as well.
After giving all my data analysis and interpretation, the two medical students never consulted for my help again and felt no need for me to contribute to the writing of the paper, even though I explicitly said that I want to help write the statistics portion of their paper. There was a period of silence after the last email, in which the two students said they were busy with their clinical work, and said they will reach back to me soon. As the naive trustworthy lad I am, I waited for them patiently. Later down the beeline, they get back to me to tell me their research paper was published. I was very shocked by this sudden announcement. They never even told me about this. Going into the paper, I find that 100% of their data graphs and figures were made by me. I am simply acknowledged in the Acknowledgments section, and I am very disappointed that I was not even added as an Author. I understand that 1st and 2nd author would be unreasonable, but still feel that my contributions should at least be rewarded with some authorship. I feel very misled by these two medical students, as they didn't even communicate with me that they were already writing the research paper. I am feeling a mix of emotions right now - mostly, frustration and sadness that all this work went into nothing. I also feel disrespected as a statistician - statistics consultation and data analysis are not easy - these students and many whom I've worked with believe that these data/figures/charts can be churned out quickly, with just a plug and chug after writing some 'code' or analyzing data. Little do they know, there is a lot of work going behind the scenes with creating the code, data management and cleaning, and analytics.
I would like to ask for your guys' advice. I know that I was not able to contribute to the writing of the paper because of the nature of the situation, but I still feel that my many data analysis contributions (and ALL OF THEIR GRAPHS/FIGURES) should at least be acknowledged with authorship, rather than an acknowledgment. How should I approach this situation? Also, in the future, how should I go about asking that I be included for "authorship" before accepting a project? I've become very jaded from this experience. I thank you for your time everyone.
New Update: Thank you everyone, for your answers, advice, and feedback. I decided to contact my supervisor and the med students' physician supervisor for a group meeting. We're still in the midst of the talks of possibly retracting the paper to include my name and resubmit. It also turns out that the physician supervisor did not know the extent of my work when the med students submitted the paper. Only that they "acknolwedged SW's contributions of statistical analysis." Apparently, the students had only told him that someone was helping the statistics and that was all; perhaps, the supervising professor was just very busy and did not think of this very much (of the absence of my authorship) before submission.
 During prior interactions with the 2 students, I also realize how stupid of me to just take the 2 students' verbal word that the physician knew about my contributions -  they also never copied in the supervisor's name during our email exchanges. Nevertheless, I would like to remain positive that they were not doing this out of any malice, but rather the students do not know very much of the etiquette and norms of academic research. This was also their first research project, and the group has apologized to me.
Anyhow, the possibility of my authorship is still up in the air in terms of talking to the journal, etc. But I have certainly learned several lessons, including discussing authorship before I contribute anything. I would like to thank everyone again for their thoughts, advice, and words of comfort as well.

Yes, you should discuss authorship before you contribute.  Did you talk to the students' supervisor about this?

Your frustration is fully understandable, and this kind of treatment of theoretical collaborators are not necessarily rare. What kind of communication/arrangement you have with this group? What does being a lead data analyzer mean? What kind of agreement you have about the collaborations with the project leader or with the supervisor of these students?

Lesson: agree on authorship status ahead of time if the work you do is beyond "a simple favour". 2 weeks is more than "a simple favour".

Note that from a legal standpoint, it sounds like you have a copyright claim to the material which was directly used in the paper, or where the paper made use of derivative works of what the you created. So, you are an author of the paper, not just from a academic point of view, but from a legal point of view. Unless you explicitly gave the other students the right to publish your work, or derivatives of that work, they did not have the right to do so.

You may be interested in When does a statistical consultant become a co-author or collaborator? Or your collaborators may (should?) be.

Could you give an update to help others understand how it concluded?

I'm sorry this happened to you. It is, unfortunately, all too common for those of us that have vital skills that are asked to contribute to research initated by others.
What can be done at this stage? There are only realistically three options:

The paper is retracted. Its possible it could be submitted for publication again with you as an author, but this would be a long an uncertain processes.
A correction is issued. This would be associated with the paper, but the authorship line in many databases would not change. See this case here: https://publicationethics.org/case/late-introduction-omitted-author-after-online-publishing
You can accept the situation as it is, perhaps with an appology, learn from the situation, and try to prevent it happening again.

I would start by contacting the corresponsding author of the paper, whether that is one of the students, or their supervisor. Explain that you did all the analysis, every graph in the paper is one you created. More than that, you should explain what your intellectual contribution was. State what your desired outcome is.
If writing to the corresponding author fails you could try their superior, be that the supervisor, or the chair of the department.
It is possible that you could make a formal complaint of research misconduct agains the students if you wished. You would probably start by contacting the journal editor, but they would likely reffer it to the institution for a misconduct investigation. I would think carefully before doing this, and certainly not do it until all other avenues have been explored.
In future, the lesson to learn is that however unpleasent it feels at the time, you must make sure you agree authorship before you embark on any analysis for someone else. If someone is reluctant, it probably means they don't understand your skills, and thus these are people you don't want to work with.

On the basis of what you have described, you should have been included as an author on the paper. Regardless of the amount of time you spent on the project, you produced some of the figures that directly appeared in the paper. Leaving you off the author list is particularly egregious as you are yourself a student dependent on fair acknowledgement of your work, not a company or core facility providing a service.
However, sometimes junior researchers (in this case the medical students) are ignorant or careless when it comes to issues of authorship, rather than deliberately malicious. Therefore I would recommend against directly contacting the journal or trying to have the paper retracted (these are nuclear options).
If I was in your situation, I would:

Discuss the the issue with your supervisor, who may be able to give a more accurate appraisal of your level of contribution etc., or even to resolve the issue informally.
Contact the corresponding author on the paper (either directly or via your supervisor) describing your contribution to the paper, and why you believe you should have been included on the author list. Include a list or annotated manuscript showing all your figures and analyses that appear in the paper.
Say that you realise this was probably an oversight, but that you would like them to issue a correction adding you to the author list. Such corrections are not uncommon, and would not in any way damage the paper.

In future, it is of course ideal to discuss authorship in advance of doing work - but in reality this is not always possible. Projects change, and your contribution may end up being more or less than what you originally planned.

I'd strongly second this regarding a likely lack of malice; in my experience (part of my job is sometimes to consult as a statistician for projects led by physicians, exactly like OP's situation though I am not a student), a lot of people (even senior) doing research in the medical field don't have a whole lot of scientific training or experience, including around norms for authorship and such. Their expertise is in the subject, not the process. Definitely doesn't excuse it, but it's something to be aware of when collaborating with physicians, they might need a bit of your scientific training.

I would feel cheated in your shoes as well. But note that your contribution may not entirely satisfy what eg. The International Committee of Medical Journal Editors define as qualifying for authorship 1:

Substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data for the work; AND
Drafting the work or revising it critically for important intellectual content; AND
Final approval of the version to be published; AND
Agreement to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

Your contribution fits the first bullet, and that is not enough. But this should not have been. On the same link, it is explicitly stated that

...all individuals who meet the first criterion should have the opportunity to participate in the review, drafting, and final approval of the manuscript.

I would recommend that you write a polite, yet firm, email to the corresponding author - and their supervisor, if it is one of the students - saying that you don't think you have had a fair chance to obtain authorship. You can refer to your previous correspondence with the students. There are two things you could obtain from this, make it clear what you want:

An apology, and if sincere, an opportunity for future collaboration.

The nuclear option: A retraction of the manuscript, and a re-submission with your name on it which, all things said, is quite unrealistic. If this fails, contact their institution (as also stated in the guidelines), rather than the journal. The journal will rightly say that sorting out authorship issues is not their responsibility. The question then becomes whether the authors would rather deal with a retraction and re-submission, or an internal case regarding academic dishonesty. With this route, you can forget about ever collaborating with these people again.

The lesson to learn, is to never touch another persons' analysis until you have an explicit agreement regarding either a) authorship, or b) payment as a consultant. This may sound harsh, but it is the only way to make sure your skills are valued. The world is full of people who would like you to do their work for them for free.

I think this answer neglects to mention that intellectual property of the OP was used without his consent. This is clearly illegal and the journal will surely respect his intellectual property and retract the paper once the OP proves the graphs were his which should be possible by showing earlier versions and correspondence. (Unless the OP gave explicit permission in writing to use his work and figures, but this does not seem to be the case.) The very fact that the OP still has this option should help motivate the other authors to try to fix this to the OPs liking.

This case is not just a matter of academic misconduct since not just an idea/work was stolen. The OP's intellectual property was used without his consent which is a matter of law.

I did not mention IP on purpose. Such a case would be difficult to lift, I think (depending on location etc). If the figures are produced with a normal plotting package, the authors can very well claim that they ran it themselves, and I am in no way equipped to guide someone about the intricacies of such a case, except for one crucial piece of advise: If you consider going any kind of legal route, ask a lawyer, and not people on the internet.

Okay I understand that it complicates things. But I do think that the fact that explicit figures were used gives the OP more leverage if the discussion turns ugly. The journal will care more about the IP theft than about the academic issues. Yes the other authors can claim that they reproduced the figures, but it does not sound like they did and thus it would be a very risky thing to claim if things ever got to court. (They would risk additional fraud charges.) Of course if things ever get that far a lawyer needs to be consulted.

As a biologist myself, I can attest that the rule of thumb is that if you made a figure used in the paper, you are an author. Period. The person who did all of the statistical analysis and generated the figures should be an author, no question about it whatsoever.

@Kvothe: You say that 'the journal will care more about the IP theft that about the academic issues', and you are indicating that if the authors received some script over mail from the poster, and simply pressed go to produce a figure, then the poster would have a legal right to be credited, rather than acknowledged (which he or she did). Do you have something (exemplary cases, own experience, a link, a background in IP law in the posters' juristiction...) to support those claims? IP law is tricky business, and common sense is rarely enough.

@Kvothe: IANAL so I can't say if it would stand up in court, but I can tell you that journal specifically state that they do not adjudicate authorship disputes, I don't think it would give you much leaverage with them.

@IanSudbery, they might want to avoid it but in this case I think they would have little choice. The journal would be publishing a paper without having the rights to it, since they only got the rights from the other authors which did not own full rights to the work. So it is kind of like saying we ignore intellectual property rights and don't care whether the guy selling them (or in this case probably giving them away for free) actually owns them. But since actually going to court is not what you really want I agree that perhaps the leverage is not a strong as I thought.

As I said, I don't really know the legal ins and outs, I just know that having your work published without you as an author is probaly the single most common complaint on here, and something journals deal with every day, but I've never heard of a journal withdrawing a paper for copywrite reasons in such a situation.

@Kvothe Unless the OP did all the research at home, on their own computer etc. then in all likelihood the IP belongs to the university. It is a general feature of academic contracts (including studentships) that any IP produced at the university belongs to the university, and therefore the OP would have no standing to make a legal claim even if they wanted to. However, universities have disciplinary procedures to ensure fair attribution of work, so if the medical students refused to issue a correction then a complaint could be made via the university.


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How can I minimize the damage of my PhD advisor's bad recommendation when applying for industry jobs?
I did not get along well with my former PhD advisor. I was able to defend and graduate; however, I have learned that my advisor was giving bad recommendation letters. No wonder why all of my postdoctoral applications were unsuccessful even though I have good academic standing. Since we had several intense arguments in the past, I can conclude with confidence that any reference from my advisor would be damaging.
I have decided to go to industry (non-research) not just because of this problem but also because of poor job prospects in academia. Now, I am wondering how I can minimize the damage. I do not know how references work in industry, but I can certainly exclude my advisor in any list throughout a recruitment process. My PhD advisor also has several connections in HR. This can also be damaging if a company background-checks through the university HR department.

When you say that you have decided to go to industry, do you refer to research or non-research positions?

non-research positions. Is there a clear line between research and non-research positions in companies?

It is very likely that the HR department will be more circumspect, especially if you have lodged a complaint about unfair references - the department is there to protect the institution, not the advisor. If applying to industry, it may be appropriate to be totally frank with them, pointing out that poor relations with the advisor has soured your view and is the very reason you are now applying to industry. It's expected that academics can have strong views, and industry's opinion of academia is often low anyway. Use a better referee if you have one, and let your record also speak for itself.

Can this question be migrated to https://workplace.stackexchange.com/ ? Presumably, that's where the actual experts from outside academia can give answers!

That is done here: https://workplace.stackexchange.com/questions/159260/bad-phd-advisor-and-industry-job-applications

You are worried to much.

My PhD advisor also has several connections in HR. This can also be
damaging if a company background-checks through the university HR
department.

First, HR is not allowed to say anything bad about you with no clear evidence (for fear of being sued). They will just give minimal information, and that's it.
Second, background check is often done by a third-party, who is only interested in ticking all the boxes that you declared. They are not interested in hearing some random stories.

I do not know how references work in industry, but I can certainly
exclude my advisor in any list throughout a recruitment process.

For non-research positions, nobody care about references.

I was a hiring manager in industry before retiring to teach.  I, at least, absolutely did care about references.  I also had an unwritten rule not to hire anyone who spoke badly about a previous employer.  The rationale was that I was looking for people who want to come to my organization, not to get away from someplace else.

I've been on both sides of the fence, and hired from academia into industry.
There is a lot of variability, of course, but generally references matter less and impression made during the interview a lot more for jobs in industry vs academia. Accomplishments and credentials continue to matter.
In industry, many people who change jobs are doing so since their previous job is not a great fit. Or have not let their current manager know they are looking elsewhere, so cannot use them as a reference. And getting a good reference from someone else is easily gameable. As a result, many reference checks -- at entry level in particular -- are purely formal ones, merely to make sure the candidate isn't a conficted fraudster or lying through their teeth about their prior experience.
To the extent you are applying for more senior and/or creative positions, there may be a desire to genuinely talk to someone to get a better sense of what kind of person you are. So you should think through what articulate and ideally industry-experienced contact, another faculty member or even a fellow research team member, you could supply if someone does want a reference.
By the way, we of course can't know about the specifics of your relationship with your advisor. But it is certainly possible that a dispassionate (as opposed to loyal) advisor may have given poor references during your academic job hunt not out of personal animus, but since they were not convinced (rightly or wrongly) that you are well suited to continuing in academia. They might be quite supportive of you seeking employment outside academia and even able to provide a good reference in that situation. Of course, this may not be the case at all, especially if you feel you cannot trust your advisor to not be two-faced.


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Am I taking a wrong approach while looking for an academic position in applied areas - brutal criticisms appreciated!
After a PhD in pure mathematic, I wanted to do work in applied areas where I could bring in my pure math expertise. So I did two postdocs in computational medical imaging where I could apply my pure math knowledge coupled with machine learning (which I also liked because of my pure math background). But the reason I wanted to do computational medical imaging were:
1) I felt the market for pure math would be hard, and it'd be difficult to obtain a permanent position. However, if I worked in imaging, then my CV would show that I was capable of doing both pure and applied stuff, hence would keep my options open to industry as well.
2) I looked through some papers in medical imaging, and what attracted me was the mathematical tools that they used in these papers, but I didn't pay much attention to the actual unsolved problems in medical imaging. It was definitely not like I didn't care about these problems in imaging, but they were not the main reason I got attracted to it. But I went ahead with the postdoc anyway, but worked mostly on problems that were of somewhat general nature (e.g. problems at the confluence of differential geometry and machine learning, of interest in imaging. I didn't really work with raw images, rather some heavily processed images that'd fit my differential geometric model).
After finishing these two postdocs, I tried to continue in medical imaging, but for reasons that were not under my control, I couldn't, and thereafter, I tried to switch to industry and worked unsuccessfully in several companies for short times, and currently I'm again looking to move back to academia.
The reason I ask this question here is that, I recently had a long talk with a friend of mine who's also a PhD and successfully transitioned into industrial R&D from applied math/machine learning to autonomous driving. He told me that I took a wrong approach to working in applied areas. The reason to work in applied areas should be "I want to solve this problem in this applied area (in my case medical imaging)" as opposed to "This applied area uses this and that tools, which I'm already familiar with and like using, hence I must like that applied area as well". The second one was my approach, and I'd like to know if I were wrong? Even to this day, what principally excites me in an applied area is the underlying math I can bring in to solve the problems there, hence in a project, I seek to stay on the theoretical side, rather than the practical one. For example, I'm definitely more at ease with pen and paper, but I can and do code for a problem that requires machine learning, but I'm no fan of e.g. keep tuning parameters to obtain the optimal model like they do in data scientist positions (I had some, didn't feel passionate about and was unsuccessful) - I rather like to write an algorithm, prove its convergence if needed, and test it on small and gradually bigger datasets. MY QUESTION: Am I being wrong in my approach? Please be brutally honest! Is there a middle ground that I can take, and how? Thanks in advance!!

What’s your question? This seems like  a question too dependent on your preferences, we are not the ones to say whether your preferences are right or wrong.

There is nothing to criticise here. You interests and approaches to research are your own. There is no one-size-fit-all approach for all pure or applied sciences. Different people and groups adopt different viewpoints and use different techniques. Your approach is as good as other. It's not clear from your question why you were not successful, and it's not enough information to suggest an advice.

Just want to point out that not all data scientist positions are about tuning parameters to obtain the optimal model. There are organizations out there where you aren't constrained to a single problem and instead are exposed to a variety of problems, many of which have limited discussion in the literature and don't have a lot of data to train on, but are still incredibly impactful. I work with multiple pure mathematicians turned applied/engineers and they've found their niche in this space.

@kjacks21 Tuning parameters was just an example - what I meant to say is that I'm no fan of building models based on already invented algorithms and use several softwares to integrate them into product or deploy the models, what I'm a fan of is actually coming up with a new algorithm. Just an other example, I don't like e.g. writing a code in TensorFlow to implement an RNN, but I like to write down the analytical expression of the cost function of RNN, and understand the gradient vanishing and blowing up problems from the scratch.

From my own experience and from several interactions with people, data scientist or machine learning researcher positions in industry are not generally of a fundamental nature, but rather utilizing already invented machinery - which I'm no fan of (not saying that's bad or anything like that, but it simply doesn't excite me).

@Stat_math thank you for clarifying your preference!

If you are making a mistake, it may be in narrowing your focus, closing off opportunities. Especially if it is you who is giving a too-narrow definition of your capabilities.
A math PhD should be able to teach (nearly) any undergraduate math course and many MS level courses. Every college and university teaches math and so needs people to teach those courses. The market is enormous. But for, say, medical imaging, there are few places that are truly interested. While it is also true that your skills should, and do, enable you to work on a vast range of problems, if you exclude those from consideration, or seem to, then your opportunities also close.
In a lot of ways a mathematician is like a Swiss Army Knife, being able to attack many problems, pure and applied, since they have a facility with abstract thought and how things fit together synergistically. But be careful, in any application, that you define yourself in a way that is flexible enough that others can see your potential.

Thanks for your answer! As you pointed out, it's true that a math PhD should be able to teach (nearly) any undergraduate math course and many MS level courses, and I can, too. But this doesn't mean the market is enormous, if you want to get a stable income. I'm in France, and when I look up 'mathematics' or 'mathematician' in any of the standard sites like indeed, glassdoor, or LinkedIn, I get two kinds of jobs: 1) data scientist/machine learning researcher position in industry which has nothing to do with math, and 2) contractual tutor position with 20€/hour salary. Even in the US, (contd)

(contd)  there're assistant prof. positions, and lecturer positions, and the later ones are called 'fast food positions' in academia from what I hear, as the lecturers are hired to deliver some courses, mostly for a temporary duration.
Having said that, thank you for your suggestion - I try to mention all my experiences in my CV, including pure math, machine learning and medical imaging, but I don't see abundance of jobs calling me. I've so far worked in only one big company (which recently let me go) and the rest are all small startups, who simply didn't value my passion for math.

@Roland Thanks for your comment! Yes I sincerely hope someone recognizes my potential : thanks to my varied background, quite recently I picked up some topics in probability theory and came up with original theoretical results in the domains of nearest neighborhood search ( a subtopic of machine learning), when I was working for a project in a big company, which was more of a fundamental nature.

In my opinion, your friend is more right than you.

This applied area uses this and that tools, which I'm already familiar with and like using, hence I must like that applied area as well.

means to me you are interested in the tools, not the application. The employer may think you'll leave if they change the tools. If that happens, they lose the investment on you.
Your friend's approach

I want to solve this problem in this applied area

means you are interested in the application regardless the tools they use. Your familiarity with the tools is a bonus to them. When and if they switch to another set of tools, they know you'll stay and learn how to use those new tools if necessary. After all, you are a PhD. You must be able to adapt yourself to new technology and tools with your previously acquired knowledge and rigorous math training.
My suggestion, use the combination of the two approaches. Emphasize your friend's approach, but also mention your familiarity with the tools, so the potential employers know you can jump to work right away without much training.

Thank you for your answer! I think you're right, I need to actually delve into the unsolved problems in an area first, and then only comes the question of using what tools I know.

There is nothing wrong with your approach, following along the lines of Dmitry Savostyanov's comment on your original question ("There is nothing to criticise here..."); however, here is another way to frame your thinking on this:
I've been guilty of having a tool, say a hammer, and looking for nails to hit with that hammer. In many cases where a nail wasn't there, but maybe a screw, I still used the hammer since I wasn't familiar with how to use screw drivers. I've also seen many others with this mentality, particularly in my field of computer science. This mentality ultimately limits the types of problems one can work on, can be off-putting to potential collaborators from other disciplines, and may even be detrimental. The book Range by David Epstein essentially argues this and has a chapter on "Learning to Drop Your Familiar Tools". One interesting anecdote of how only using tools one is familiar with on a variety of problems is a note by Rita Redberg in JAMA in 2015, that highlighted findings that "...adjusted mortality for high-risk hearth failure and cardiac arrest is lower at teaching hospitals during the cardiology meetings than during the rest of the year." [1]. In other words, patient outcomes were better when cardiac surgeons were away at conferences(!).
I don't think the above fits exactly how you are thinking, but it is related, hence the mention. Another point to make, based on your clarifying comment below:

Just an other example, I don't like e.g. writing a code in TensorFlow to implement an RNN, but I like to write down the analytical expression of the cost function of RNN, and understand the gradient vanishing and blowing up problems from the scratch.

Is that there are industrial R&D organizations that would benefit from this interest and do fundamental research. A few that come to mind are Facebook AI Research (FAIR) [2] and Google Brain [3]. Government funded labs may also be a good option, depending on the type of lab and the country you live in.
[1] Redberg, Rita F. "Cardiac patient outcomes during national cardiology meetings." JAMA internal medicine 175.2 (2015): 245-245. Link: https://jamanetwork.com/journals/jamainternalmedicine/article-abstract/2038976
[2] https://ai.facebook.com/research/
[3] https://research.google/teams/brain/

Mathematician working in industry here. I'll second scaaahu's answer and would like to offer an additional point of view.
Industrial employers have problems to solve. They are looking for solutions. Tools are only means to an end. As such, they will usually prefer candidates and employees who will use the most appropriate tool to solve the problem at hand - not search for problems they can apply their favorite tool to.
Thus, if the latter is your preferred approach, and especially if you communicate this ("What drew you to the field of medical image processing?" "I was looking for somewhere to apply differential geometry."), you may be limiting your employability. (And incidentally, also your personal growth.)
Of course, this doesn't mean tools are irrelevant. Switching tools such as technologies simply because a particular tool is better for a particular problem may be short-sighted if it requires much upfront/ongoing investment. And knowing tools that help you address problems is always a good thing, and you can become a guru for one particular tool. It's just that industry on balance prefers people that are driven by problems and solutions, less so by tools. And if you do go the guru way, you need to make sure your toolset stays in demand.

Thank you for your answer! I guess both academia and industry have problems to solve, but regarding the problems solved in industry though, I feel that because of the limitation on time and finances, the industry would often focus more on "quick and dirty" solution using pre-existing tools, rather than developing a new theory to solve the same. E.g. I've been told in interviews that the data scientists are were encouraged to perform linear regression for simplifying things, even if theoretically it didn't make sense to do so. (contd)

(contd) "Thus, if the latter is your preferred approach, and especially if you communicate this" It's not like it's my preferred approach, it's just that somewhat subconsciously this is the reason I keep getting attracted to applied areas, e.g. in my last job in telecom company, I was told in the interview that the project might use random matrices, and that made me interested, despite no knowledge of signal processing or telecom. But I think I get your point - I need to point out the actual problems in that area and how I can import my tools to solve them. Thanks again.

I would put it a little differently. Both industry and academia are trying to solve problems with constrained resources, and therefore, both take shortcuts where appropriate. In industry, this means applying methods even if they are wrong, as long as they work. (You'd be surprised how far a simple and inappropriate linear regression can get you, and it has the advantage of being easy to explain to a non-mathematician programmer, and to a customer.) ...

... Conversely, academia takes shortcuts in reducing problems. I work in forecasting, both in business and academically. Academics can get away with throwing away 5% of their time series that are problematic (and mentioning this in the paper, true). The business forecaster can't do that, he has to deal with all the data, and those 5% may cause more work than the other 95%. Similarly, academics in general pay much less attention to code quality, testing etc. After all, their code won't run for decades at many customers and potentially cause huge damage if it fails.

Finally, yes, the problems business and academia attack are different. In academia, advancing theoretical understanding is a value in itself. (It's what you get paid to do.) In business, it isn't. (You won't get paid to do so.)

Solving applied problems demonstrates your ability and willingness to perform in industry, which is probably more convincing in the job market in comparison with applying familiar tools, which only shows you have the right skills. You can adjust your self-promotion to improve your chances, e.g., by explaining that applying tools allowed you to hone your skills, which you're now ready to solve problems with. (There's a problem if those tools are now outdated.)

what principally excites me in an applied area is the underlying math I can bring in to solve the problems there, hence in a project, I seek to stay on the theoretical side, rather than the practical one.

You need to ask yourself whether transitioning to industry is for you. (You can be more at ease with pen and paper. Industry is awash with cash. You can specialise. Someone else can code, fine tune parameters, etc.) If you want to stay on the theoretical side, then why transition?


text:
Should I send a follow-up email or call again (to potential PhD supervisor)?
Sunday: I sent an email to a potential PhD supervisor.
Sunday 4pm: he responded asking me to call him tomorrow .
Monday 11am: I responded yes and asked if there's a preferred time.
Tuesday 1am: he emailed me back asking for my number and said he will try calling me on Tuesday.
Tuesday 8am: I responded with my cell and said there are two hours when I wouldn't be available but otherwise i would be happy to chat anytime.
Tuesday 5pm: still no call. So I sent an email to say I'm available rest of today and tomorrow.
I realized now that when he asked me to call him tomorrow on Sunday, I responded in email on Monday to ask for a time instead of calling on Monday... he was kind to have responded on Tuesday and said he will try calling me. But I still have not heard from him.
Should I email or call him today?

Try both? Tag, you're it.

Do you have his number? Either way, the ball is in his court, I'd give him another day or two.

I think it would be better to wait till the end of Wednesday, and then send a follow up email. It could be that he forgot to call or may be quite busy, given the (small) delay in his previous response. For the same reason, calling directly may not be a good idea.
In addition, do check that you did not miss any call or were unreachable at some point during the day. If so, you could mail immediately, apologize, and request to reschedule.
For future reference, it would have been better if you had mentioned your time constraints for the next several days and included your phone number in your first email that you sent on Monday. This would have made the scheduling much easier and the rest of the emails and the confusion after could have been potentially avoided.