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Discussing diversity and underrepresented groups in personal history statement for PhD application
I am applying for a PhD program in US. The university has asked to address the following in personal history statement:

How your perspectives or activities contribute to social or cultural diversity and/or make you sensitive to the experiences of underrepresented groups

Honestly, the statement does not make sense. What is social or cultural diversity? Why it is important? Who are exactly underrepresented groups? What is experiences of underrepresented groups? I would be grateful if someone help me to understand this statement and give some examples about it. Many thanks.

What field is this?

What country are you from?

The discussion about whether diversity statements are a good idea has been moved to chat; future comments on this topic will be deleted without warning.

"How your perspectives or activities contribute to social or cultural diversity and/or make you sensitive to the experiences of underrepresented groups"
I think a useful way to approach this question is to not think about it in terms of race, but instead consider what it means to be socially diverse. As an example, consider this brief response to the question:
"Growing up in a small farming community in Canada has given me an opportunity to see how many of those in my community - many of which have never stepped foot on a university campus - can benefit from feeling represented in institutions that they might not naturally feel apart of. Growing up in a rural community gives me the advantage of being able to personally relate to people who might not have college degrees, or even high school degrees, and develop a level of trust when communicating scientific information that might be the topic of the day in the news. When I come to U of X, I hope to be able to share and encourage this level of empathy among my peers to help unify communities that might otherwise feel divided."
So, what's happening here? In this paragraph I mention that I am an international student - as I assume you are - and I am reflecting on how my own experience in my country might be able to bring about some type of positive change to the United States and the immediate community I am hoping to be in. In the example that I listed above, the 'underrepresented community' happens to be just the local people I grew up with. What I believe you should do is examine your own lifestyle in your home country and think about what you have experienced that might bring about positivity in your studies. Your response does not have to include gender or race because there are TONS of communities that might be relatively disadvantaged to you - these could even be immigrants from your own country that are not in touch with the institution you want to attend.
The question you ask is a challenging one, because it's actually a somewhat divisive question: Do you talk about racial disparities? Do you talk about gender disparities? What you want to really try to reflect on is how your own story can bring about some type of positive change when you go to the institution that you want to attend. It's a tough question to answer, but hopefully this response gives you some type of idea about what you want to say.

I think you are missing some key text from the prompt. I searched the exact text you did include, and found a prompt posted elsewhere that seems to match. It might not be the exact full prompt you were given, but please read yours carefully.
Here's the text I found posted by another applicant here... Bold is added by me.

Applicants for our graduate programs are selected using a holistic evaluation system. This essay will assist both the admissions committee and fellowship review committees to evaluate your background and motivation for graduate study. In your personal history statement, please describe how your personal background informs your decision to pursue a graduate degree. A sample of topics that you might address in your statement is below. However, please structure your statement in any way that you feel best represents your personal history. Please do note that there is a 1200 word maximum for the statement.

Any educational, familial, cultural, economic or social experiences or opportunities relevant to your academic journey

Challenges and/or obligations you have had to address in order to achieve your educational goals and how you addressed them

Employment while an undergraduate

How your perspectives or activities contribute to social or cultural diversity and/or make you sensitive to the experiences of underrepresented groups

You are not meant to address all four bullet points, but rather address a suitable topic that is relevant to your own life experiences. Different people are going to have different types of answers to a broad question like this - that's kind of the point.
I dug up one of my own statements from applying to grad schools over a decade ago, and although I don't have the exact prompt I was responding to, it looks like what I wrote would have fallen best under the first and third bullet points here.
I wrote about a job I had as an undergrad in which a big part of my role was in bringing biology to engineers, wrote about the challenges and benefits in working with experts having different knowledge and skill sets, and how I benefited from (and enjoyed) being in the middle.
I also wrote about a subject that I minored in as an undergraduate (the history of science and technology), that I thought would be uncommon among other applicants, and how I thought those perspectives were important to the practice of modern science.
I think for these statements the answers should show that you are thoughtful and have some ability to measure your own perspective; they aren't meant to check some magic "diversity box" that only certain people are qualified for.

This question suggests you are not prepared for doctoral study at the University of California.  Sign yourself up for a diversity training program.
In my opinion, the prompt is code for "Tell us how you will work effectively with people who are different from you."  Answer that appropriately for the context of your discipline, and you will be okay.

Your first paragraph also seems not to be in line with what the University of California is looking for with that text.

@wimi Please explain yourself.  I argue that the asker isn't ready for doctoral study until they have had diversity training.  The university is asking how the prospective doctoral student will contribute to diversity.  This is exactly in line.

the OP is possibly not from the US and is not familiar with how diversity is considered important and often discussed in the US. This is because OP comes from a different background. Telling them outright that this makes them unsuitable for study in the US is the opposite of promoting diversity. Promoting diversity would be acknowledging this difference and answering their question to let them know what is expected of them. I do not think taking a diversity training course is expected of every international PhD student in the University of California.

@wimi "unsuitable" and "not prepared" are totally different.  PhD students are expected to have completed an undergraduate degree, and an undergraduate degree should have taught the answer to this question.  If this student's undergraduate degree did not prepare them to answer the question, additional formal training is the right answer.

The downvotes here are crappy (I upvoted), but your first paragraph is glib. If the OP is in fact not from the US, there's no reasonable way they can be familiar with the nuances of who is underrepresented in the US and why. I'm sure the admissions committee knows this. Your second paragraph is 100% correct, but it's not just code: the rest of the prompt (linked by Buffy) actually says that they want to know how you yourself contribute to diversity and how you would serve underrepresented groups.

@wimi  "I do not think taking a diversity training course is expected of every international PhD student in the University of California". Perhaps not yet, but it is (quite regrettably, IMHO) moving in this direction. What is expected nowadays is, unfortunately, not treating people of all origins and orientations with respect, but swearing unconditional loyalty to the latest liberal ideas. I guess you have heard of the latest outcry around an article by Abigail Thompson (if not, look it up). Needless to say, all this stuff just moves people like myself to the other side of the barricades.

@fedja You made that up and your comment is just a rant.

@ElizabethHenning I will be extremely happy to learn that you are right and even have a secret hope that the future events will demonstrate it beyond doubt. As for today, I'll just let everyone judge for themselves :-)


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Will it be beneficial to my application if I include in a research proposal the fact that all my papers improve papers published at top conferences?
During my undergraduate studies, I was actively engaged in reading research papers and even discovered a significant result. However, after spending about 10 months trying to write a paper on it, a team of five researchers from a prestigious US university published the same result before I could. This experience led me to avoid tackling problems that seemed to require lengthy solutions, and as a consequence, my subsequent work has been less theory-dense.
Most of my papers now improve upon results that were presented at top conferences, yet none of my papers have been accepted at these top venues. I suspect that one other reason for the rejections might be the lack of recent activity in the areas I'm exploring.
Will it be beneficial to my research proposal if I include in a research proposal the fact that all my papers improve papers published at top conferences?

Application for what, exactly?

@Buffy Research proposal.

More precise please. For doctoral admissions? Masters admissions? Grant application? Faculty application? Something else?

Are you in academia or trying to enter it in some way?

By "improve" are you in a field like ML where "improvement" means some marginally better performance by some measure (computational speed, "accuracy", etc)? The sorts of "improvement" papers you describe in that field are mainly junk, even if they are popular to publish in certain venues. The improvements rarely generalize, the specialization is rarely justified.

Are these improvements that are obvious and not done previously because other people just thought it was too easy to bother with, or improvements that required genuine insight?

If it looks like an excuse and quacks like an excuse - it is an excuse. You keep looking to make excuses. Start looking for positive reasons some committee should support your proposed work.

@Buffy It's a grant application. The papers that I have were presented or published at A-rated conferences.

@AlexanderWoo The improvements were to problems that may have been avoided by more serious researchers as they likely have known that the benefits of solving them didn't outweigh the effort/time cost of solving them. But I don't think they are trivial in any way.

@Kupp - In my field, funding is so scarce that a researcher at your level (or mine) would not even bother applying for grants.  Only people with successful approaches to the most interesting problems get them.

@AlexanderWoo, my word, you are pessimistic about funding acquisition... it is not always/everywhere as bad as you suggest.

I would try not to emphasize the fact that your work is unoriginal and simply piggybacks off existing works, regardless of how good those original works are, and the fact that you may have "improved" them.
I would think really hard about what you brought that is unique and try to shift the focus on what your unique contributions are, rather than on the perceived prestige of the original works you have decided to "improve".
Your rejections from top conferences are because you are likely presenting marginal "improvements" or peripheral studies to original works.

Yes it's true my improvements are considered marginal but they are far from being trivial. These problems may be avoided by more serious researchers as they likely know that the benefits of solving them probably don't outweigh the effort/time cost of solving them. I was thinking of just putting a single line in my application about the fact that most of my papers improve papers that were published at top conferences. What do you think?

Was your work published at top conferences? If no, then the community has decided that it is not of that level, so it does not matter where the work you are following up was published. I think it is best to avoid all focus on the derivative factor of your work, and rather focus on what you bring to the table, especially if you say the work is non trivial. If you cite your statements in your proposal accurately, then readers can look it up and come up with their own opinion as to the impact of the area you are working in.

Triviality is not binary but a continuum.  If, on a scale of 1 to 10, what you're calling trivial is everything that is a 1, and your work is a 3, it's still not good enough to get funded.

@AlexanderWoo I would say the average result is about 7 on your scale of difficulty. They are elementary results that are probably difficult to discover.

Yes, including that all your papers improve upon work published at top conferences can significantly strengthen your research proposal. It highlights your ability to push the boundaries of current knowledge and positions you as a competitive and impactful researcher. Just ensure to support this claim with specific examples or metrics if possible.

Actually the correct claim here is that the OP thinks they have improved on other people’s work, and this is highly subjective unless the OP is very clear on what has been improved and how.  So it’s a gamble to push this kind of storyline as the other side of the bet is that someone will read the relevant literature and might disagree or just find the claim exaggerated, neither of which are good outcomes.

@ZeroTheHero doubt the author of the answer can answer your comment, as it's likely a GenAI answer, not their own.

@ShadowWizard interesting observation re: possible AI-generate contents.

@ZeroTheHero well, this user posted more obvious GenAI answers on different sites, so it's just a pattern. On some sites it's allowed (sadly), but I hope here it's not.

@ShadowWizard amen to that!

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Are old (>35) faculty candidates discriminated against all over the world?
I think that in India research institutes will never take a faculty candidate who is over 35. Is it so all over the world?
I am asking this question from the point of view of if someone starts their PhD. at the age of 27 then its unlikely they will be faculty candidates till they are 40.

In many fields, possibly most, 13 years to go from starting a PhD to faculty candidate is on the long side. In many European countries and fields 3 years can be enough.

This really depends on how you define "faculty candidate". In the classical German system without tenure track positions (which still holds for the most part), the average age of obtaining a permanent faculty position in 2011 was 41.1 years (and this number was fairly consistent across disciplines). However, this position will usually be at the associate professor level or above.

35 years is not old for a faculty candidate, at least in Europe or the USA. Many folks don't finish their PhD until they're at least 30, and the youngest "normal" age to finish a PhD would be 26 or 27. Add a couple of postdocs and a candidate could easily be over 35.

Employment discrimination on the basis of age is illegal in the UK and many European countries, and probably others that I'm less familiar with.

Your first statement is not true. I received a graduate  degree from a research institute in India and my thesis adviser was well over 35 before he joined the department.I can point out numerous counterexamples if requested. Please edit this sentence.

@Shion Can you kindly name the institutes? Did your professor join as an "assistant professor" or in any other higher post?

Three cases where I can think of assistant professors joining when they were over 35 years old are Indian Statistical Institute (my personal example), Indian Institute of Science and Tata Institute of Fundamental Research.

@JackAidley, discrimination on the basis of age is indeed illegal. But, if an older candidate and a younger candidate are competing for the same job, then the younger candidate might seem more attractive because they're able to compete, which eliminates the discrimination factor. This isn't an issue if the older candidate is better.

Absolutely not.
Age discrimination is explicitly illegal in the US.  (I believe the same is true in Canada and most European countries.)  Even as the chair of my department's recruiting committee, I am forbidden to ask the age of any applicant.
If you're worried, just don't put your date of birth on your CV.  But this really is a non-issue.

My understanding is that age discrimination is not illegal in much of Europe.  For example, in Germany universities typically cannot hire a professor who is older than around 50 (depending on the state).

US federal age discrimination laws only protect people over 40, though your state/institution may have stronger laws/policies.

@NoahSnyder This is not exactly true  - the age limit only applies for hiring professors as civil servants (for which there is a different, usually better, social security scheme). After that, the university can still hire someone as a regular employee (with standard social security coverage); the age limit can also be waived in exceptional cases. How willing the university is to deal with the paperwork (especially in the latter case) depends, of course. In any case, this is an administrative matter and not in the hands of the hiring committee.

If you're worried, just don't put your date of birth on your CV. -- Most folks probably don't include their date of birth on their CV. For those who did their graduate studies later in life, however, it is relatively easy for a search committee to determine the candidate's age based on the year they received their undergraduate degree, which is often listed on a CV.

@user11192: Well, sort of.  At most, you can determine a lower bound on their age.  Many applicants have had a significant break between high school and college, to serve in the military, for example.  (This is a common feature of applicants from Israel.)

Even if a birthdate is lacking on the CV, a CV with more experience listed will generally correlate with older age, thus it's hard not to age-discriminate (for or against) a candidate.

ETH Zurich "discourages" applications from candidates older than 35.

@n1000 Source, please?  I don't see any such discouragement on their list of open faculty positions,

@JeffE It is written in the actual application page. E.g. "Assistant Professor (Tenure Track) of Data Science and Analysis for Health" > "Please apply online" > "Next" > "Please note: ETH Zurich does not have formal age limits for professorships, but as a general rule, the academic age of assistant professors (e.g. without the time period of maternity leave, industry experience, military service, etc.) should be 35 years or under at the time of appointment and on the associate and full professor level ETH Zurich's prime target group are scientists 45 or younger at the time of appointment."

"Academic age" means "years past PhD".  So "academic age ...should be 35 years of under" means (modulo the listed exceptions) "Your PhD should be less than 35 years old."  Since people typically earn their PhDs in their late 20s, this tells me they don't want to hire people over 60, presumably because Switzerland has compulsory retirement at age 65.  It does not mean that they discourage applicants born more than 35 years ago.

I think this answer needs more evidence than just citing the law. There are many kinds of discrimination that are illegal but happen all the time. Legality would certainly impact whether a university would have a written policy about it, but "X is illegal" is by no means a definitive answer to the question "Does X often occur"!

(This started out as a comment on JeffE's answer, but became too long, and I don't want to clutter his post.)
This is a gross simplification, but what hiring committees care about is your future research potential. In the absence of a crystal ball, they have to extrapolate from your previous achievements: The more in less time, the better. For this, your actual age is irrelevant - it is only important how long you have been an active independent researcher, which usually starts after your PhD. (This also touches on the point @user11192 made.)
Tl;dr: It's not age, but age minus time of PhD, divided by number of publications (and grant money squared).

Or, as it is sometimes put, it's "PhD-age" that may be relevant, that is, number of years since PhD, as a gauge for research accomplishment.

In some countries academic studies will only start at an age of ~22 due to factors such as military/civil service etc. which may yield:
22 + BSc (3 years)  + MSc (2 years)  + PhD (4-5 years) + (Postdoc 3-4 years) = 35 to 37
In this case 35 would be considered a typical, or even relatively young age for a candidate.

This answer stems from a few comments I made to a related question.

Are old (>35) faculty candidates discriminated against all over the world?

I can't speak to the worldwide aspect of the question. What follows will be specifically tailored based on my tenure-track job hunting experience in the U.S., although it may be applicable in other parts of the world.
As pointed out in another answer, it is illegal to discriminate on the basis of age in the United States.
However, I think the more interesting question to ask/answer is:
Even though it is illegal to discriminate against someone due to their age, does that mean that age plays no role whatsoever in tenure-track faculty hiring decisions?
Sorry to get your hopes up: I don't have so much a concrete answer to this question; however, I offer an example of something an "older" candidate may face when seeking a tenure-track faculty position.
Being an "older" candidate myself, I noticed on my unsuccessful interviews earlier this year that I seemed to get along just fine with tenured faculty; however, there was clearly some tension between myself and the "younger" tenure-track faculty at several places that I interviewed. If age did indeed play a role in this perceived tension, one may easily see why younger candidates would have an advantage. Furthermore, since most tenure-track candidates are from the same age group, the fact that an "older" candidate doesn't gel with his peers of the same academic rank for "some reason" makes you stick out like a sore thumb.
Ultimately, I think that if age does play a discriminatory role in faculty hiring decisions, it may be that it is an indirect discrimination. That is, in a direct sense, nobody cares about your age or have been trained to think that way. But if you don't have similar personality characteristics of those tenure-track faculty already in the institution's employ, then there is still some likelihood that you will be marked as a bad fit for the job. How high that likelihood is I cannot say.

Indeed... and/but the perception of "fit" might also be the opposite, if more senior (and mostly older) faculty are asking themselves whether the candidate shares their own sensibilities, rather than the sensibilities of the junior people.

short answer, no. There are 40+ year old new professors who will get tenure after starting work at a new school in the US. There are 35 year old first time science majors landing jobs because of their passion and I recently met a 55 year old who just completed an EET degree who landed a position at a decent firm with a good wage although he has a math phd as well from 30 years ago. It is mainly cultures where age discrimination is the disgusting norm and Google. India may be the worst country on earth in terms of age discrimination and bribery. There are job postings I saw (just out of curiossity from an article on this very subject) explicitly asking for no one over 26 where in the US those positions would say 10+ years of experience or a phd (experience preferred). If immigration is a possibility then it may be the best route. Some other countries have age discrimination issues as well but, generally with the exception of India, countries that were part of the British empire with its legal system tend to be more lenient. You have options. Age discrimination hurts everyone. Experienced professionals tend to demand less, are less restless, and require less training. Maybe a cultural shift is in order?

It is the ratio of your accomplishments to age that matters. Generally accomplishments saturate with age and hence it appears that there is an age discrimination. I am sure a 50 year old Nobel Laurette will be hired directly as Professor at many Universities.

My university is planning to hire >100 senior faculty.  Presumably none of those people will be young.  The idea is to buy the university a world-class reputation.  I think other universities that have money and a desire to increase their rankings use a similar strategy.  Poorer universities hire younger faculty with an expectation they can be paid less.

Can you tell us which university this is?

@BenWebster Sorry, I'm unsure if this is intended to be public information.

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At the age of 27 is it worth changing graduate schools and starting again?
I am interested in areas of theoretical physics/mathematics which simply don't exist in my institute. I tried 2 or 3 different groups here which were not in my interest (but I felt I had some transferable skills) and it didn't work out.

This depends on many factors, such as your current situation, your ambitions, ... As it stands, this question seems impossible to answer.

Are you expecting an answer like, you should do it if you were 22 years old and you should not do it because you are already 27 ?

@MarcClaesen I am currently in a top-notch grad-school in the US just that it simply has no group in anything that interests me and my attempts to shift interests have failed. Any other data that you would want?

Age discrimination is illegal in the US.  By law, nobody cares how old you are, except maybe you.

Are you asking if your age is a problem in terms of an academic career?

@Bitwise May be...

@JeffE  The problem is if the selecting committee looks down upon the fact that in my current grad school I wasn't really attached to any specific advisor but was floating between different groups doing small projects in each. Will this be trouble?

There is no age limit for graduate studies. People are free to apply at whatever stage of life they choose, if they feel it's the right move for them.
As an example of this, a very good friend of mine was a social sciences major as an undergraduate, and worked in Washington, D.C., for a number of years before leaving politics and starting a PhD program in medical physics—and he did this in his mid-thirties. I've worked in the same department as other postdocs who made the career choice even later—they were in their early fifties!
So I would not look at your case as hopeless at all. If you find something else that inspires you, go for it.

@aesmail The problem is if the selecting committee looks down upon the fact that in my current grad school I wasn't really attached to any specific advisor but was floating between different groups doing small projects in each. Will this be trouble?

It depends on how long this went on. The longer you were there, the bigger a challenge it will be.

@aesmail Yeah..first year I was doing courses - and then 2 years more I shifted between 3 groups - doing small projects and trying to get myself interested (wrote a small paper from one and another result from another) - but all the while only feeling more frustrated that I wasn't getting to do the subjects I really wanted to! Finally I decided to try moving out!

Three years? That's going to be a tougher sell. But you've accomplished something. If you have the support of the professors for whom you've worked previously, you've got a shot.

As your question stands, the only honest answer is it depends but probably yes, it does.
Your question is lacking in essential information for a definite answer. Are you currently doing a masters or a phd? What is your background? Do you want to make a career in academia, ie. research oriented, or in the industry? Are you self-motivated? etc...
I would not rule out changing grad schools based on your age alone as there's no age limit to right a wrong. However, use common sense: be pragmatic and take time to analyze your options. Perhaps your advisor would allow you to collaborate with groups from other universities? Or maybe you could even do an exchange program? Is wrapping up what you have and moving on to something you're more interested in an option? If your project has been given a grant, ponder carefully the implications of leaving your current grad school.
If you feel that changing grad schools is your only option, then unless what is hidden behind starting again is that 400 lb gorilla, I see no obvious reason why you should not live a more fulfilling academic life.
Final note: if I were to review your application to a new grad school, I'd like to understand the reasons that brought you to your current grad school if no group was seemingly doing something that you're interested in.

what is the gorilla that you are expecting?

@user6818 it's that overwhelming and invisible thing in your head that keeps you from doing what you truly want.

If I am generous to myself, I would think that it was a stroke of terrible luck that I ended up at so-called top-notch institutes but never where there are people in my areas of interest. [..often its just so hard to explain to anyone the problem since from outside people tend to think that I am merely whining although I am at the "big" places...I have a hard time telling anyone that being at a "big" place is hardly a thing when the departmental focus is so different from what subjects excite me!...]

@user6818 I answered because I've been there myself: top-notch dept. in a top-notch university and on an insultingly high stipend. The kind of conditions for which 95% of grad students would easily kill each other without hesitation. Yet no amount of rational thinking like think of how lucky you are, grad students next door are in the basement and hunt for free-food will ever make up for absent/lost passion/excitement. I mistakenly down played my average interest in the field and realized that you cannot fool yourself through a phd. Through a masters, probably you can. Research is different.

@user6818 Research frustrates and makes you humble. So I could pull it for a while but the intellect feeds a lot on the satisfaction of achievements (articles, experiments, ah-ha! moments) and persistence in absence thereof. Oftentimes I saw my relationship to this phd like the one you probably already for a girlfriend (or boyfriend) for whom you have a strong attraction but without chemistry: You just know that there's a shelf life.

@user6818 The moral is but simple: everyone makes mistakes, no bigger deal than that. The fact that yours occurred now and in this form makes it all the bitterer. But look at the facts: you got into a top university once. You can and will probably do that again. This time around though you'll be a little less rookie with yourself and hopefully know better what dazzles you, and what doesn't. Find your arena and fight like a lion.

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How can I find if my viXra paper is cited?
I've published a paper in viXra and I would like to know if someone else cited it anywhere, but I don't know how. Is there a kind of global index for citations? Does it include “alternative archives” such as viXra?

I downvoted, for the usual reason: "This question does not show any research effort".

Most established academic journals are indexed in what are logically called “journal indexes”. These indexes commonly record all publication metadata, and usually also include a record of all citations. Such indexes are thus called citation indexes.
Now, the problem with viXra is inherent to its “alternative” nature: it is most definitely not indexed by conventional players (Web of Science, CrossRef, PubMed, CAS, etc.). You thus have two ways of looking for citations to your paper:

Google Scholar includes content from viXra in its results (see this search’s first hit, for example). It probably also records citations of such articles, but the quality of citation matching is limited by Google's heuristic algorithms. They're good, but not as good as DOI-based mechanism that commercial databases nowadays employ.
A regular web search with you name, or the title of your paper. This is not as automated, but it may give good results as to who is citing your work, especially if this is one of your first papers and you don't yet have a large web presence.
(Obvious caveat: if your name is John Smith or Li Wang, web search will not help much.)

Scholar does not seem to include vixra, at least systematically: http://vixra.org/faq

Vixra is indexed in Microsoft Academic Search, as of Aug 20, 2019. While potentially not as useful as Google Scholar, it does provide a similar portal; of course, Google itself also indexes Vixra papers (but not Google Scholar, which only apparently indexes the citations.)

Try using Google Scholar. There may be field-specific indexes too.

Scholar does not seem to include vixra, at least systematically: http://vixra.org/faq


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Is there a standard system example for writing papers which introduce a newly developed programming language?
I am writing a paper that describes a programming language that I am developing as part of my PhD. I think that writing the paper using an example can greatly improve how the paper is understood. Is there a "standard" example that is used in programming languages paper? A set of examples?

It depends, of course, on what you're trying to illustrate with your example. An example of a language is the untyped lambda calculus. Some algorithms and programs that are frequent examples are at Rosetta Code.
If you want to know more about what's typical in computer science, you might ask at Computer Science Stack Exchange or, if the relevance is specific to professional researchers in theoretical CS,  Theoretical Computer Science Stack Exchange.

It depends on what you want to show. Hello world is usually the minimum example, then Fibonacci for recursion, prime numbers in [2,100] for loops, etc. As you move to more fancy features the standardization fades (AFAIK, hopefully I'm wrong). More than focusing on a standard, I'd focus on an example that shows clearly the strengths of your language or the motivation. Finding the limitations or weaknesses is relatively easy, and frustrating, IMHO.

The biggest problem that you face when writing a programming language paper is explaining why the world needs another programming language, rather than a library or an API or something of the sort.
I would thus recommend skipping "standard" examples such as "Hello world" and recursive factorials entirely, and instead going straight to a set of minimal examples that illustrate the value of the new language.  Only in the case of a particularly extreme langauge will the standard examples be necessary to help understand the scientific concepts.
Note that documenting a programming language is an entirely different matter.

It would be helpful to learn about the specific strengths of your language, since good examples should illustrate its strengths (yes, this is more a meta-answer, but maybe exactly what you should be looking for).
The standard example is printing "Hello World"; everything else depends on the language and its features. E.g. you might want to demonstrate simple database queries, easy list processing, recursion, string manipulation, logic deduction, complex mathematics, ...


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How does one learn research methodology?
I am a multidisciplinary person. I have a bachelor's degree in computer science and now I'm working on my master's thesis on strategic intelligence studies. The experience I have in writing both of my master's and bachelor's theses, and the experience of using both of quantitative and qualitative methods show me that there are so many things to learn within the scope of research methodology, be it the methods, the paradigms, etc.
So, instead of being lured into one of the related disciplines that I've been exposed to, I'm far more interested in learning the research methodologies which are applicable to them. I want to  learn them all and I want to be able to devise such methods.
Thence my question, where should I begin my journey in learning and mastering research methodology? Is there any university offering such programme?

I am also interested in the terminology associated with this. Like theory, theorem, hypothesis, assumption, conjecture, lemma, corollary, law, rule, principle, etc. Is that part of the question or should I open a new one? Sorry and thank you.

I'm really sorry Trylks but I don't have any intention in discussing academic terminologies. If you opened a new discussion, I would be more than glad to jump in :D

There is a strong need for learning research methodologies, and many postgraduate research courses require as prerequisite research methodology evidence.
The good news is that many institutions do offer specific courses in research methods; the better news is that many offer distance learning and there even some MOOC/Open learning options available. Below are some examples that I'm aware of (I'm sure there are many others):

Open Learning Initiative (Open)
City University London
University of Birmingham
University of Southampton
Saylor Academy (Open)
ACS

There are also a squillion books on research methods

thank you very much :) I've been reading research methodology books since, I don't know, the time I started to take an interest in it. Now it's time for me to find specific mentors and specialized classes to fill in my gap of knowledge in research methodology.


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Should we translate non-english university names?
In my country, several universities are prefixed by "Universidade Federal", which can be translated to "Federal University" (e.g., "Universidade Federal do Rio de Janeiro" to "Federal University of Rio de Janeiro"). When publishing a paper, should we translate this part of the name?
This is a obscure topic; I have some teachers that use "Federal University" and others that use "Universidade Federal". Once I heard that it is better to keep the original name of the university because it helps to keep its identity. However, even translated, it still is very easy to find. If you Google for both names, they will come up in the first positions of the ranking.
Should we translate or keep unstranslated?

More on the trivia side: translating can lead to ambiguities: for instance, the names of the Université libre de Bruxelles and the Vrije Universiteit Brussel both translate to "Free University of Brussels".

@FedericoPoloni: Same with the two Catholic Universities of Leuven, also in Belgium

And some others are partially untranslatable. "Complutense (de Madrid)", means "from Compluto", the (very) old name of a nearby city (where the university is not anymore).

@DaveClarke good examples - and those aren't even in the same city!

+1 to @FedericoPoloni. Please do not do this just because digital library people will be so mad. We are already frustrated disambiguating author names, we do not want to add university names to that.

The name of the institution is a proper name and IMO should not be translated. It would be the same as translating someone's name in conversation, and I certainly would not refer to a gentleman from Germany whose name was Johann Müller as "John Miller" just because I'm speaking English. The proper name of the institution you mentioned is Universidade Federal do Rio de Janeiro - I suggest you use it no matter what language you're writing or speaking in.

The first thing to do is to check if the university has any recommendations about this. If none exist, then the second aspect is to consider if the university is well known under one or another form of the name. The purpose of providing an affiliation and proper address is for the sake of communication. Before e-mail and Internet, most correspondence went by post so a proper address was very important. Now e-mail is used, which means the affiliation is mostly to identify the author and the author's affiliation. Web sites are usually bilingual so finding the university or department is possible in both English and the native language. Most will probably use the English translation because it makes most sense if the remainder of the paper is in English. A point to make is that if one uses the native language for affiliation etc. then problems will arise for those not familiar with, for example, Cyrillic, Chinese or Japanese. So it seems the best way to communicate affiliation/address is to use English translations that are hopefully officially accepted by the university.

+1 for checking university recommendations. I know mine has  specific guidelines for these issues.

Related to this is following the university's example. The English language home for Université libre de Bruxelles says "The Université libre de Bruxelles (ULB) is a multicultural university with almost one third of its students and researchers from abroad."

I think that most English speakers will recognise that "Universidade" means "University", especially in an academic context, so there's no need to translate the term. On the other hand, if you were referring to something less obvious to English-speakers, like 고려대학교, I'd add "(Korea University)".

And that illustrates the difficulty of translations generally.  고려 is "Goryeo", the name of a medieval Korean dynasty and the etymological basis for the exonym "Korea".  Koreans call their country 한국 "Hanguk", meaning roughly "this country".  An analogy would be if Koreans called England "Tudoruh", after the ancient royal house of Tudor.  Given all this, should 고려대학교 be rendered as Goryeo University or Korea University?

I think that using Hangeul or hanja characters when writing to a non-Korean audience would be counterproductive as it would limit the number of people who could read the paper. As someone said earlier, check with the institution to see what their recommendations are. In the absence of such recommendations, I'd say go with whatever you think is best - I think that either Goreyo or Korea would be fine. And thanks for a bit of Korean history.

@Malvolio What's Korean for "university", transliterated into English? If it's "university" then I suppose you could argue for either "Goryeo University" or "Korea University". But if the Korean word is something else, why would you write "Korea" in transliterated Korean and "university" in English?

@DavidRicherby -- I think you missed my point.  The university isn't named for country of Korea; it is named for something else entirely. There is in fact a Korea University -- but they transliterate the name!

authors: Bob Jarvis - Слава Україні


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Is it reasonable to hold the grade of a student who has graduated?
My son took an Undergraduate Thesis course this year, and he could not submit his thesis at the end of the school year. Even he has graduated now, he cannot submit his thesis. His advisor insisted that he should finish his current project, then submit the thesis. He got a temporary 80% on his transcript, even though he has published a conference paper and a workshop paper as a co-first author in top tier conferences in the past year.
It seems unreasonable to me and sounds that the professor is holding the grade as a hostage. It would be more proper to let him finish and submit the thesis on whatever the student got in the past year, and the professor judge the thesis and give a fair grade. The ongoing research can be continued as a collaboration and they could submit the paper together if more conclusive results have been obtained.

I don't understand: Your son has graduated. What grade is missing?

May I ask why you ask this and not your son?

I don't see how conference papers are relevant

How is the "current project" related to the thesis?

These papers are part of his undergraduate thesis. It is just a course for a year. The thesis should be submitted and graded at the end of school year. My son did his research in the group as well. For research, it carries on. For course, it ends at the end of the school year.

Why could he not submit his thesis?

The professor asked him to carry on working and submitted later.

I ask this because it is not reasonable from my 25 years experience of supervising graduate and undergraduate thesis.

If the student did not submit the undergraduate thesis by the deadline, the student should have a grade of zero.  Sounds to me like the student is getting a sweet deal.

Short answer is that I can't tell if it's ethical or reasonable given a lot of details are missing in your case. However, I can definitely say, accepting the graduation diploma with an unsettled grade is an incorrect decision. It should be a sustained "incomplete" grade and the student should never have agreed to take an 80% as a make-do grade.

even though he has published a conference paper and a workshop paper
as a co-first author in top tier conferences in the past year.

Yet, this is still not the thesis. Unless, the professor had promised (and the burden to show the proof is on the student) that a co-first author conference proceeding will be held as equivalent to the required thesis.

It seems unreasonable to me and sounds that the professor is holding
the grade as a hostage. It would be more proper to let him finish and
submit the thesis on whatever the student got in the past year, and
the professor judge the thesis and give a fair grade.

An important component that was not clear here is that what the contractual agreement between the student and the professor was. If the thesis proposal has three parts, A, B, C. And the student never finished C, but managed to publish a conference proceeding with materials in A & B. Technically speaking, the thesis is incomplete. And the professor is in the right to withhold the grade.
What is truly fishy to me is that, at least from what I know working in the US, graduation should not be possible unless all grades have been audited and finalized. If the professor gave an 80% and that grade got through audit, and then the student graduated. I really don't know how likely the institute will entertain a transcript revision.

Anyway I am disappointed that he received no award at the graduation
event even he got 100% on his other courses this year.

This is really besides the point. I'd suggest using this opportunity as a training for the child, know the right and learn how the system operates. It will be helpful along the way in future. Think about:

Now that graduation is all done, degree obtained. How much does the student want to get that thesis done? What kind of professional relationship would the student want to have with the said professor?

If there was alleged exploitation, can the student put together a case and ask for mediation or grievance with the academic department? Who can be the student's advocate?

If the student decided to follow through and complete the thesis, will the professor really be able to change the grade? What's the buy in? Can there be a documented procedure so that all parties involved (registrar, the department, the student and the faculty) are in agreement?

Keep written proofs on all communication on this issue from this point and on.

This is a course for an undergraduate, not a PhD thesis. A course ends at the end of the school year. The teacher must grade the thesis.

@ChrisJohnson I'm not sure why you remind us it's an undergraduate course. Penguin's answer has nothing to do with a PhD thesis. It sounds like your child did receive a grade (80%) so they could graduate, with the thesis to be finished informally, "offline." It is not clear whether your child agreed to that understanding the implications, or not

For a PhD thesis, the advisor and the student decide the content of a thesis and a (reasonable) time to graduate. For an undergraduate course, you just submit a thesis at the end of the school year. The professor has the responsibility to accept the thesis and grade it. I never saw this in my entire life. A good undergraduate thesis could lead to a future publication. Yet two top tier publications are not enough for a undergraduate thesis to be accepted? It seems to me that the professor is abusing the student and he has no right not to grade the thesis on time.

80% (A-) is a stain on the transcript as all others are A+ and many are 100%. Yet the effort on the research is way more than that on other courses.

Giving an 80% grade pro tem allows it to be increased as needed and is “easy” on all parties.
Giving a higher grade that may need to be reduced is perfectly feasible just harder to do in front of all parties.
Once the thesis is submitted and has its proper grade then the final marks can be ratified.


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CV for PhD application: personal interests and non-academic skills
I am polishing my CV for PhD applications (Statistical Physics related). I was wondering about whether it is appropriate to list some personal interests and non-academic skills. This is my list (last line is the more uncertain, since during the lessons sessions I am not able to read much):
Additional Skills & Interests

Time planning skills --- Ability to take on new responsibilities --- Teamwork
Curious nature --- Problem solving skills --- Critical thinking
Keen hiker, runner and soccer player (informal level).
Passionate reader of classics and manga.

Personally, it feels cringey to see points like 1 and 2 in CVs. I don't think they will help your cause in any way. For 3 and 4, I think it is okay to share your interests. You are a human and they might help the other party to emphatize with you. Many academics mention their other interests in their webpages (see Ken Ono's for example). On the other hand it may backfire and they may think you are a pretencious snob. It is pretty much your call, but I advise you to keep them concise and reserve them to the very end.

My feeling about 1 and 2 for a Ph.D. application is that you may as well be saying you can breathe and you have a heartbeat.

My feeling is that while an academical might want to put hobbies and the likes in an official web page, that is most a "social" ,use. Unless common at the place you enquire, I wouldn't list any of the points you wrote here.

Focus on your academic skills. Stress the suitability of your background and your likelihood of success in any program. That is how you will be judged. For undergraduate admissions it can be a bit different (in the US, anyway), but not for doctoral study. Stick to business.
The other things may save you when you are in the process, but that is a personal thing you can draw on. Your SoP should be strongly oriented toward your expectations for the future and your willingness to work hard to get there.
But in some fields teamwork may be very essential. But don't just say you are a valuable team member. List team projects you were on that were successful.
Many of the other things are assumed. If you weren't curious, for example, you wouldn't be applying in the first place.

I do not like it when people write unqualified statements.
You say you have good time planning skills and good teamwork. How can you prove it? Did you successfully complete a complex project? Did you manage a team before? Did you collaborate with many people?
You say you have a curious nature and good problem solving skills. How can you prove it? Did you write a research paper? Did you win some physics/math competition?
Anyone can write anything on their CV. Without anything to back it up these statements are at best meaningless, and at worst seen as thinly veiled attempts to bolster a weak CV.
Personally I wouldn't write reading as a hobby. Hiking is fine, but I find that most people don't read these bits.

I'd only add interests if they're a bit different and demonstrate skills that are looked for in an ideal PhD candidate - determination, perseverance, creativity, intelligence, self-reliance etc. (e.g. triathlon runner, multi-lingual, high grade piano player etc.).
...And stick to only presenting one. You don't want to appear so involved with personal activities that you won't have time for your research project.
Hobbies and interests that are common place - enjoys reading, running, going to the cinema etc. are best to leave out.
Also avoid anything that might look like a huge time drain that could take you out of the lab regularly/for prolonged periods of time (i.e. a second job or travel blogger etc). These are not good to mention. As a general rule, supervisors want people in their lab who aren't hugely distracted by non-research activities.
Good luck with your application!


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Seeking evidence based answers: does day of the week have an effect on exams?
This question is related to, but (I think) distinct from, the recently asked Best day of the week to hold an exam?.  In that question, the author asks for the opinions of other instructors and students.  I am more interested in what the research has to say on the topic (if anything).

Question:  In the context of relatively high-stakes, summative assessments, does the day of the week have a measurable effect on student performance?  That is, what is the effect (if any) of holding exams on a particular day of the week?  Has this been studied at all?

I am looking for answers which are supported by research, rather than anyone's gut instinct or experience (these things are valuable, but I would prefer to see evidence which supports the conclusions or recommendations).
One of the answers to the above-cited question references Pope and Fillmore, "The impact of time between cognitive tasks on performance: Evidence from advanced placement exams" Economics of Education Review, Volume 48, 2015, Pages 30-40, https://doi.org/10.1016/j.econedurev.2015.04.002 .  However, this paper is primarily interested in the effect on AP exams, which seem (to me) to be somewhat different from regularly scheduled midterm exams in a college course.
I have spent some time looking for other articles on this topic but I have not found much that seems relevant.  That being said, (a) I am not an expert in this area of education research (hence I am not even sure which journals I should be looking at) and (b) my institution does not provide me with much access to academic resources (we are a small community college and lack the budget for access to many journals).  Further input from this community would be greatly appreciated.

If everyone picks the same day for exams, based on "evidence", then your goal will utterly fail if it includes making it possible for students to study effectively.

The solution isn't the "day" of the exam, but the type of exam. You can also avoid "high stakes" exams, no matter the day. One option is to have a daily very short quiz at the start of a lecture. One or two questions. Students hate it, I think (I did), but you got in the habit of studying every day.

What is the metric by which you define "best"? Do you want your students to get the highest scores? Your students to be the most relaxed?  (E.g., after a weekend) Do you want to make it easiest for you to fit grading into the schedule? (Monday) Do you want to make it easiest for your students to fit the exam into their schedules? (Friday 7-9pm) There are so many notions of what "best" might actually mean.

Those of us who have taught large enrollment courses, e.g., 300 or so students, know that other professors also teach big classes and, like Mick Jagger said: “You can’t always get what you want!” Good luck trying to find a solution.

@WolfgangBangerth Perhaps the question could be better phrased as "What is the effect of day of the week on student assessment?"  I have edited the question to highlight that.

@XanderHenderson Effect with regard to which variable? Exam grades? Student stress level? You will have to be specific about what effect you want to consider.

@WolfgangBangerth The question is, rather intentionally, somewhat broad.  Honestly, my intuition is that there should be no real effect (there are too many other variables).  But the linked question has a number of answers which seem to state with great vigor that there is an effect, and that we should care.  If day of the week has any consistent effect at all, on any variable that is interest, I would be quite surprised, and would want to know that.

While there is little research on this topic, I did find this paper from SUNY-Oswego. The methodology simply entailed giving surveys to 204 students several times a day over 10 weekdays. They claim that "productivity is lowest on Friday's [sic]."
Clearly this methodology leaves a little to be desired (and the apostrophe use is abominable). Further, it provides at best only a partial answer, since it considers only affective states and neglects scheduling issues. But you asked for evidence based, and this seems to be what there is.

With no research needed I'll declare (perhaps at some risk to my reputation here) that there is no solution. There is no best day. There are many reasons for this. First, is that if there were and every professor decided to use it, then it would automatically become the worst day since students would all get jammed up.
Second is that every student is different. Some have to work on week-ends (perhaps), some use it to study. Some to party. Some have a very heavy schedule, perhaps with report deadlines as well as exams. Every student is different.
I believe that there are a few universities that have a policy that every class has an exam on the last day of the week (there once were). This is "fair" at least, since everyone is in the same situation, though it isn't especially effective for actual learning. A slightly better system is to schedule major exams long in advance so that students that choose to have the opportunity to plan.
Another factor is the type of exam. Those that rely primarily on short term memory force some (many?) students to cram for the exam, losing sleep, perhaps, and doing worse than otherwise. Those exams that depend more on some competence learned only with practice and feedback will be less susceptible to such effects.
There are too many other variables than "day of week" that affect the individual performance and too many different student study techniques to make the question meaningful.
But, again, if there is a "best" day and everyone uses it, then it is likely to automatically become the worst day for many students.
My advice is to spread them out if possible, schedule them long in advance.
My more serious advice is to rely as little as possible on high stakes exams. There are better ways that actually enhance learning, not test-taking. And this is from a pretty effective "test taker" in my day.
Finally, optimize everything for learning, not for grading.

While it is true that this is just the opinion of an old codger who has taught something approaching 10,000 students, I think that is about all you will get for "evidence". The experience of teachers. The problem is that the number of variables that you would have to control to do a real research study with scientific validity is too large: field, course level, type of exam, student variability, ....
But if you simply want something that might have some, perhaps limited, validity for your own students, you could just ask them. I suspect you will get a variety of answers, but perhaps not (depending on all those variables). But if you also ask them "why" they prefer one day over another you might get an idea of the difficulty of the problem. And, of course, their own preference might be the deciding factor or not.

"With no research needed I'll declare..." -- leeway that we gladly provide to members of this group with a reputation of 214k ;-)

@WolfgangBangerth, thanks for that, but 40 years in the saddle at all sorts of colleges and universities provides the anecdotal background.

I do feel it does not really answer the question asking specifically about something evidence-based. Your insights are overall valuable, though, and "optimize everything for learning, not for grading" is the real highlight here.
Otherwise it's a severe XY problem - OP should be concerned with what makes them to teach better, not how they should grade things...

@Lodinn My posing of the question was somewhat tongue-in-cheek and insincere.  I was rather shocked that the question I linked in my question here got such a positive reaction, when I considered the question to be nonsensical.  Buffy's answer is (essentially) the one that I would have given.  That being said, if there is actual research on the question, I would be interested to see it (since, as nearly every commenter here (though not at the other question) asserts, day-of-the-week is swamped by other variables).


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How to judge a Ph.D. applicant that arrives "out of thin air"
I just received an email from a student from a distant country, asking me to accept him as a Ph.D. student. I do not know this person, his advisors, his references or even the university he studied in.
His master's thesis looks good at first glance, but I cannot be sure since it is not in my field. He still wants to do Ph.D. research in my field.
I asked him to send me some refereed publications, but he replied that he has none yet, and then asked me to give him some work by which his application can be assessed.
I am very unsure about this - I am afraid to get stuck with a bad student that takes too much time to supervise. On the other hand, I do not want to block him entirely. So my plan is to give him an open problem that I and some colleagues tried to solve in the past but failed. If he fails and gives up, then he will have to look for another advisor;
if he does manage to solve the open problem, then I will be more than happy to be his Ph.D. advisor, and his solution will be a part of his thesis.
My reservation about this plan is that it might be unethical/unprofessional to give him such a difficult problem to start with. But, he asked for it, and of course he is not obliged to take it if he does not want to.
Is this plan reasonable? Is there a better plan?
UPDATE: based on the answers, I changed the plan as follows: (a) referred the student to register through my university's system; (b) asked the student what papers he has read on my research field, and what ideas he has for extending them; (c) Based on the student's answer, I decided on a research problem that was not solved yet in a publication, but for which I already thought of a solution, so that I can guide the student in case he gets stuck; (d) scheduled a video call. My plan is to start working together remotely in parallel to the registration process, and see how it goes.
Thanks a lot for all the insights and ideas!

I do not know this person, his advisors, his references or even the university he studied in. His master's thesis looks good at first glance, but I cannot be sure since it is not in my field. — Lots of red flags here. Without clear evidence of their suitability, why did you not just politely decline?

@JeffE it feels wrong to decline someone who's potentially capable because of my own ignorance. Someone somewhere out there is going to not know me/my references/my university as well, and I'd rather they give me a chance to prove myself too.

I'm confused about your characterization of this student as "out of thin air," since this just sounds to me like "applying." Isn't there some standard process for students who aren't referred through the old-boy network?

Is this your first phd student? How have you vetted other students in the past?

@Cecilia yes, I am a new faculty member and did not have Ph.D. students before. This is why I am confused about this situation.

Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on [meta], or in [chat]. Comments continuing discussion may be removed.

If the prospective student cannot realistically solve the problem - and it certainly seems so given that you + some colleagues couldn't solve it - then it does seem unprofessional to me. One could easily interpret your reply as a soft rejection, except it's dressed up to give the student some hope. Ambiguous signals are bad (just see how many literary plots involve one party in a romantic relationship giving ambiguous signals to the other).
I suggest instead using a problem which has already been solved, but the solution is not trivial. For example, you could take an exam question from a Masters-level course related to the student's field. The student should be able to solve it, although it will take effort. You can then assess how good the student is against the other students in the course. Alternatively, you could set some minor problem that will nonetheless need to be solved before a bigger one can be attacked. For example, "write a C++ program that numerically solves [this differential equation]" is not going to be easy, but if the student is able to do it, then you can maybe use that program on his thesis topic.
I'd avoid asking for something that takes more than several hours to do. The student is likely to be applying elsewhere as well, and it's not fair to expect him to sink a lot of time into one application.

They may not have found a solution as they may have only looked at it over the coffee break - but that does not mean that it does not have a solution...

But if it is just an exam question, how can I know if the student solved this by himself or just found the solution elsewhere / asked a friend to solve it for him?

@ErelSegal-Halevi I was thinking of an exam question whose answer is not easily Googled for. If you are concerned the solution might not have been produced by the student, you could ask for a Skype interview, and quiz the student about the solution then.

@ErelSegal-Halevi How could you verify anything that the student says (e.g. a solution to the problem your colleagues haven't solved) is produced by the student?

@SkeletonBow It's unlikely that the student will convince a colleague to work so hard, without getting any credit, just to help the student get accepted to Ph.D.

@ErelSegal-Halevi Anything that is not so hard as to be an unreasonable test for an entry-level Ph.D. student is also at a level where paid outsourcing is plausible. That's why a video interview is an important suggested stage in the interaction.

I don't see what's particularly unprofessional. I guess I'm the only person in the world who thinks impossible problems are fun. Though of course an overly-limiting way to test prospective students unless your application pool is really stellar. It would be interesting to see what they come up with in any case.

I would tell them what you expect from a PhD student: prove theorems/run empirical tests/conduct human studies or all the above. If their profile is a clear mismatch, I wouldn’t bother.
I would next ask them to review two papers of their choice out of your recent publications. One page review each. The review should include at least one idea for future directions.  It tells you whether they’re serious, what they want to work on, and whether they can reason about ideas in your field. It also guarantees that the problem is at least somewhat tractable (you’ve solved it after all).
If you’re happy with the write ups, schedule a video interview. You both are committing to 4+ years together, best to make sure you can discuss things together.
Good luck!

The issue is that, because (as you say) it's a commitment for 4+ years, I want to have a stronger evidence of fitness than just a single video interview..

@ErelSegal-Halevi by all means do more after the video interview, but as a start asking them to look into papers that you have published would make reviewing their work easy for you & is a good first step (assuming your looking for students & don't just want to ignore it completely)

If you have the money, you can offer them a 1 year/6 month research assistantship to see if you fit (after the first steps obviously)

What @Spark said. Even if you decided to take him on (which is not at this stage anyway) You could explain to him that because of his different background and lack of publications you would expect a trial period to assess his fit.

And if you don't have the money, it is perhaps not outrageous to ask the student to first get a master's degree in your field.

There are an awful lot of very fine but disadvantaged students out there who just don't have any good network to connect them into good schools. I know some excellent folks who are now top professors and researchers only because somebody decided to respond to their "out of the blue" email.
Unfortunately, there are also vastly more mediocre or terrible students who will do nothing but waste your time.  Moreover, these students are over-represented in perception because they email many more people than the good ones. Even just responding to their emails is usually a waste of time.
So how do I decide if a student who writes to me is likely to be worth responding to?  Simple: did they write to me, or did they just write to an authority figure who might be able to help them? Some heuristics that I find helpful in telling the difference:

Does the student talk about me at all, or just about themselves?
Does the student show some familiarity with my work beyond just the title of a paper or two?
Does the student explain how their interests may relate to mine?
Does the student have some vaguely plausible ideas about what sort of work they would want to do together with me?

If a communication passes all of these tests, then it shows that the person has spent some real time to think about this communication and that there is some real reason that there might be a potential match. It's an honest signal of effort that has been invested, and that's a big deal, because it means they're writing to me and not just a list of ten thousand people with Ph.D.s.
Now, this doesn't actually tell you if the student is actually any good or not---for that, things like the tests that others suggest are not a bad thing to do.  But this start gives some signals that seem to be fairly reliable in helping me distinguish between "application spammers" and potentially serious candidates to work with.

Indeed, now that I read his email again, I see that he mainly talks about himself, and does not show any familiarity with my research field except the general field name. Probably this is what made me suspicious in the first place.

A very good heuristic imho, since it allows to discard a good 95% of spammy applicants quite fast, while still giving a chance to the 5% remaining.

There are two separate issues involved in the discussion to this point:

How a faculty member should respond to a student who emails them directly asking about graduate studies
How to evaluate the credentials of a potential graduate student

Your question is a conflation of the two issues. But I will answer the first issue by saying what I do in these cases: I write them back with polite encouragement to officially apply to our graduate program, including the link to my department's admissions web page. And then I forget I ever got the email (unless something during the admissions process reminds me of it).
I don't see any point in trying to evaluate somebody from an email when there is a perfectly serviceable mechanism for gathering information on all applicants and evaluating them systematically.

This is the answer.

"perfectly serviceable mechanism for gathering information on all applicants and evaluating them systematically."  I wish this would be universally true...  Anyways the key takeaway is that universities make offers of admission, not professors.

At the OPs institution, a prerequisite for applying is to have the support of a professor there who agrees to advise them. In many parts of the world this is the order of operations, in others it is not. Your answer only applies in places where students first apply to a program.

Be wary.  This could be a con aiming at getting a study visa.  They apply for PhD courses, get accepted, get a visa and you'll never see them again.
Due diligence is required.

just received an email from a student from a distant country asking me to accept him as a Ph.D. student.

So far so normal.

I do not know this person, his advisors, his references or even the university he studied in.

If you don't know his university why are you even considering this ?  At the very least you should be seeing an accredited university (something that's easy to check).  Not seeing this, don't go any further and forget it.

Advisors and references

These should be available to check at the university.  If you can find the university (!) but can't get in touch with these advisors or references (or they're not at the university) then it's a con ((or very likely one) and you just forget this.
Note : private emails and phone numbers should not be accepted.  You need email addresses and phone numbers from within the university.

my plan is to give him an open problem that I and some colleagues tried to solve in the past but failed. If he fails and gives up, then he will have to look for another advisor; if he does manage to solve the open problem, then I will be more than happy to be his Ph.D. advisor,

Ridiculous.
You and your colleagues (all better qualified) can't solve the problem but you expect a prospective PhD candidate to do better ?  This is just setting someone up to fail.  Why waste their time ?

My reservation about this plan is that it might be unethical/unprofessional to give him such a difficult problem to start with.

Difficult ???  It's impossible as far as you're concerned - you can't even solve it yourself !
How would you feel if someone did that to you ?

Is there a better plan?

Give a fair but difficult test if you must, but one you at least know the solution (and a reasonable time frame for it to be solved in).  This (like any test) will let you judge their competence.  You cannot judge their competence if you have no idea how to solve the problem yourself or how long it should reasonably take.
However I would not give a test until you have verified the university, references and advisors and confirmed they exist and know the student.
Remember : accredited third level institutes or you could end up with a fake university telling you everything is OK.

-1 because of the assumption that an applicant not be considered when you don't know their university. Also for being overly suspicious of it being a scam. However, definitely agree with what you said about OP's plan.

@einpoklum Did you miss the word "accredited" ?  It's not about "not knowing" the university, but the possibility that the university may be a university in name only.  As for "being overly suspicious", anyone dealing with online applications and new contacts who is not "overly suspicious" is being very naive.

Yes I did. Would you mind slightly rephrasing so I can un-downvote you?

@einpoklum If anything I was far too mild in my choice of language about the potential for online scams in this area, as anyone dealing with applications from overseas students should be aware.  Note that institutions can be held responsible for failing to do due diligence on these matters by the authorities.  This is a very serious issue.  Institutions should make staff more aware of these issues (clearly something the OP's employer failed to do).  My awareness is heightened by an acquaintance who ran a language school and was constantly receiving fake applications.

I'm just saying I can't un-downvote you without an edit; the site "locks" votes after a while. Also, note that a language school is very different from, say, a biotechnology lab, particularly w.r.t. applicant distribution.

@einpoklum You can edit the post yourself and add just a bunch of  , if you wish. (Yes, I know, that's a ridiculous policy on SE's part.)

Even if the school/references/everything is legitimate, it may still be a terrible school churning out effectively worthless degrees. Perhaps even where the norm is for everyone to cheat their way through. In fact I would consider this the default situation without either accreditation (in a developed country) or a reputation you know (i.e. of successfully feeding students to western schools).

One strategy is to query the student as to what specific part of your research program is of interest to him/her, and in what way is this student prepared for this kind of work, including papers (by you or others) or textbooks read on this topic.
As the path of least work is for the student not to read anything and move to a less inquisitive prospective supervisor, this should be enough to sieve however coarsely interested applicants from the “truly random” ones.  It is also a nice way to start to build a picture of the candidate as follow up questions can enlarge the discussion to cover background preparation.

tl;dr : Your plan's no good; do other things instead.

I do not know... his advisors, his references or even the university he studied in.

Then take a short while to read up on who those people are. Now, ok, if they're in art history and you're in chemical engineering, maybe you shouldn't bother, but I'm assuming there's at least some overlap between your applicant's former field of study and yours.
You could also consult colleagues of yours who are closer to that field, to get a basic opinion of that university and his advisors/references.

His master's thesis looks good at first glance, but I cannot be sure since it is not in my field. He still wants to do Ph.D. research in my field.

If he wants to switch to your field, he probably has some idea of what he wants to work on (not necessarily true but likely). Assuming that's the case, I'd consider having a remote audio or even video talk with him, to tell you about some specifics of his own interest and why he decided to approach you to be his advisor.

I asked him to send me some refereed publications, but he replied that he has none yet,

So, he just wrote a thesis but nothing was submitted anywhere? Or - did he submit somewhere but nothing's been accepted yet? If it's the latter, ask for a draft and promise you will read it in confidence.

and then asked me to give him some work by which his application can be assessed.

That is a bit of a weird request, although understandable if he's legit. Here's an idea: You probably teach some course in your field of research, no equivalent of which he has taken so far, being from another field. Give him some reading material, then finally when he says he's ready - a homework assignment from that course, with a limited amount of time for submitting it. Hopefully he would not be able to "cheat" effectively, or at all; and it would not be too hard; and maybe it'll help you see what his thought process is like

I am very unsure about this - I am afraid to get stuck with a bad student that takes too much time to supervise.

Hey, hey, you haven't committed to anything yet...

So my plan is to give him an open problem that I and some colleagues tried to solve in the past but failed.

Terrible plan. Even a legit Ph.D. candidate would likely fail. And if he resolves an open problem that even domain experts have not been able to crack - then he doesn't need much of your supervision, now does he? I'll chalk this one up to you being an inexperienced faculty member.

But, he asked for it,

He asked for something to prove his worth as a green candidate, not as an independent resolver of open research problems.

and of course he is not obliged to take it if he does not want to.

Very weak argument my friend...

Is this plan reasonable? Is there a better plan?

Not reasonable. Try the plan after the phrase "here's an idea" above. After doing that, consider inviting him for a visit, with him preparing a talk on the connections between your field and his old field (assuming one exists) for your research group or other such forum of people. That would be an opportunity to get to know him better. If you can, consider funding the visit.

Yes, this is reasonable and ethical, if you are willing to give serious consideration to an attempt at the problem that attains a standard manifestly commensurate with what you would require of a PhD student upon entry. Setting a very difficult problem/task can, framed properly, be a constructive method of assessing someone's capability and commitment, as long as you take interest in the journey/method rather than the result.
Tell the candidate that you do not necessarily expect him/her to be able to deliver a solution, but you want to see what he/she can do with the problem. You may want to set a deadline (I can see arguments both ways on whether to make it subject to a deadline or open-ended). Ask him/her to send you his/her worked-out attempts, and then schedule a video interview to discuss them (the latter part is important, to verify that the attempt is the candidate's genuine work).

I'm inclined to agree with this approach. The main problem I see with the OP's plan is that it's not going to provide any useful information about the student if he fails to solve the problem and it might not even provide useful information if he delivers a solution.

You will get more of these e-mails than the number of students that you are able to supervise. So, you should compare potential students to one another. It is likely that your university/department has a PhD application process; if so, refer the students to it (and then read the applications obviously!).
Also, talk to your colleagues --- they have more experience with the PhD admissions than you do.

I know there are many answers to this question, and there is likely overlaps in my answer and others' but I hope to give a different perspective.
I suggest you look at it from a different angle, instead of trying to validate the university and courses and degree, try to validate the "interest". It is not feasible for you or anyone to know all credible universities all over the world. It is however very feasible to discern a dedicated and well-informed candidate from a boilerplate application.
Some useful questions to ask might be:

"Why do you want to work with me/us?" - This question a lot of sense to see if the student has spent any thought on what working in your lab would give. It is especially relevant if, as you say, your current field is not immediately similar to the student's. I would say that if the answer is focused solely on how awesome your lab is or what the student has to gain by working with you, it's likely because the student just looked up some names and labs online, and applied to all/most. If on the other hand the student goes in to detail about your work, and why s/he finds it inspiring, you can get a better feel for if the student understands the key concepts in the field and has a "good-enough" prior knowledge. I feel people that have a good grasp of what they are interested in show that by their choice of words, and amount of detail they are comfortable getting into.
"What are your expectations for doing a PhD in my group?" - This is a twist on the previous question, by asking for what the student has for expectations, you can see if the student is actually well-informed about your current (not past) research, what type of a project the student is looking forward to work on. This question also has an additional benefit of checking if the student has realistic expectations for doing a PhD, for example with respect to amount of supervision, publications, conferences and courses, teamwork etc... Regardless of the level of prior knowledge, getting expectations aligned would be super helpful in mitigating future frustrations both on your part and for the prospective student.
"What would you like to work with, if you start in my group?" - Ask the student to pitch a project proposal. As I mentioned in the first point, by getting the student to elaborate on his/her goals you can see if they actually have a good enough grasp of the field. In order to avoid any kind of fraud, follow up on the project proposal with a skype interview. Ask follow-up questions on wherever the reasoning is "thin".

Obviously, my answer implies in taking some time into digging into the students intentions. If you feel like you don't want to invest the time to figure out if the student's interest is legit (which is fair enough since time is money) I suggest you politely decline rather than throwing tests at the student to see if s/he impresses you.
That approach is not entirely fair since if the student was capable of solving problems interesting enough for the field, it would be silly to apply for a PhD in the first place. A PhD student is supposed to be a student, learning to do science, not cheap labor for research groups produce results.
Hope that helps, or at least provides some insights

From the information you have in your OP, you don't know anything at all about this person.
Anybody can make up a plausible looking story about an unknown university, and take of copy of someone else's thesis, change a few names on the front pages, and pass it off as their own. Don't be naïve enough to think nobody would be so stupid as to try such a thing in real life.
Interviewing job applicants in industry who (allegedly) have at least bachelor's degrees, we now give ALL candidates the following simple test:
They are taken to an empty room, given some paper and a pen, and asked to spend 15 minutes writing a one-page summary of their CV, and a statement of what post they are applying for and why.
Believe it or not, some of them can't accomplish that task. And some who can at least remember what was on their professional-looking application are incapable of writing a simple English sentence with reasonably correct spelling and grammar.
Personally, I would just file this application in the trash and forget about it.

So you're advocating to not even bother giving this applicant the opportunity to prove themselves, just delete it and continue on as if you'd never seen their email? That might be common practice, but it's not professional or courteous. And you're also not considering people who don't have English as their first language? There's plenty of intelligent and smart people that don't have a good command of English, yet are in ELL courses to get better.

All relationships have to start somewhere. You don't you 'anything at all' about anybody that you don't know yet.

@computercarguy No, but if the initial application sets off alarm bells then you send them a "thanks but no thanks" reply. As nice as it would be to give everyone a chance, you have one slot and multiple applicants, and it's normal to start triage there. As for language skills, there's a difference between being able to communicate in a second language and not being able to. If their English skills stop them communicating, they fundamentally cannot work at a uni where they need to communicate in English, so they're applying to the wrong place and need to be rejected.

The fact that some applicants in some industry are incapable of certain simple task does not at all mean OP's applicant is disingenuous or incapable. Your suggestion is completely unethical. -1.

I'm assuming this is a European thing for students to just cold-call professors about PhD programs. In North America, you go to the university's website and fill out the application. Of course, having prior contact with interested faculty is encouraged and sometimes can be required, but the professor is not expected to make any decision not contingent on the student actually receiving an admit.
The admission committee is supposed to take care of them "materializing out of thin air". They come up with standardized admission processes so that all applicants can be judged fairly, the best talent is attracted, that admitted applicants have the best fit and that they have the best odds of success. In exceptional cases (such as students who doesn't have requisite degrees from accredited universities) they can provide alternative means of verifying the student's eligibility, or make the judgment call that students who cannot satisfy the standardized requirements cannot apply.
I would suggest you not circumvent the admission committee by inventing your own ad-hoc application process just for this student. For one, the adcom might not appreciate it. Besides, there's a reason the current application systems exist.
Collaborating with this student, or giving him homework, is up to you. This should be done in the context of general edification of the student, rather than as in exchange of guaranteed admission (do you even have the power to give that guarantee?). You can say:

"Here's a problem we're working on, solve it with me and you can be co-author/acknowledgee".
"Here's some open problems in the field that are appropriate for you, solve them and you can publish on your own".
"I will pay you $x/hr to work on this problem for me, contract is attached".
"I volunteer to educate you, here is some homework that I will check for you, and also help you on if you get stuck".
"I volunteer to counsel you on your career, here are some books you should read and some topics you should learn, you can come ask me again about what to learn next"

You can choose from these depending on whether your goal is to actually collaborate and produce novel research, or if you are trying to selflessly help a disadvantaged student. Or if you are unwilling to commit any time, you can simply encourage him to check out the application instructions, and offer to answer any specific questions about the department and program/application process.
If you choose to associate with this student in the future, I suggest that you do this in the context of work that is itself beneficial to him. For example, if you give him a research problem, and he solves it, he can publish it. Don't make it so the main pay off is that if he gets admitted to your university's PhD program, he can become your student - then if he fails to be admitted, he has gotten no payoff for his work. Besides, once he does the work, maybe he will decide he wants to apply to other PhD programs. Or maybe he will dislike working with you and apply to your program, but seek other advisors. Creating a commitment to become your student seems a bit unethical and not really worth it.

You could as well request for his CV, then look into whatever you might be interested in from his background knowledge or something he has done before to have an idea into something he would like to do.
Then request a research proposal on any of two (or more) areas/topics that he is likely to have some basic familiarity with.
Access the proposal and you can ask him questions from the proposal via a Skype interview (as some others have suggested). That I think is a reasonable test of sincerity.
You might also need to ask about what motivates him most to do a Ph.D. and what he thinks a Ph.D. is like. Those things would hopefully give a clearer picture of who you would be likely working with.
Finally, you could seek to know two/three of those who have taught/supervised him in the past, then seek their opinion on his character and his level of dedication.
So many people "come from thin air" and publish very good contributions in prestigious venues. Peoples sincerity, dedication, background knowledge, interests, skills, and willingness to learn I think matters a lot in such circumstances.


text:
How difficult is it to change supervisor during a Marie Curie Individual Fellowship?
A couple of months ago I started my Marie Sklodowska-Curie Individual Fellowship. My relationship with the supervisor is pretty bad, which is surprising to me as she was involved and seemed to respect me when preparing the actual proposal a year ago.
She does not respect me, and sends me very unprofessional audio messages accusing me of not being 'wired for research', seems to think I should be available at all times for her and whenever we meet up. She is always late, at least 45 minutes late, every time without prior notice and never apologises. She is very condescending to me and it is getting to the point where I am starting to doubt myself and my research abilities. She always points out my flaws and there have been a couple of incidents where she's blown out at me and yelled. Whenever I have tried to fight my corner, I was met with "there is a hierarchy and you need to be aware of it and respect it"-kind of answer, which was extremely insulting. It is getting very toxic and since I do not want to quit the program, I am starting to consider the possibility of changing supervisor.
I wondered if anyone had any similar experience of changing supervisor and could tell me how easy/difficult it is to get it approved by the the European Commission.

Update Oct 2022
It ended up with me reporting my supervisor to the Student's Protection Board at my University for bullying and harassment. My supervisor also wanted to leave the supervision because she could see I was not backing down. From there they advised to tell the European Commission the supervisor was stepping down due to personal issues. I have another supervisor now but she is still employed as a Full Professor at the University, which stings but at least I don't have to put up with her constant belittling. EC asked no questions and I'd say changing supervisor was fairly easy.

Not posted as an answer, since the situation is quite different. I changed supervisors at some point, which was easily solved by contacting the project officer with the EC. This was more for formal reasons though, as my supervisor was no longer employed by the host institution, but still had an appointment with an affiliated institution, so in practice there was no real difference. Changing host institutions is much more difficult, apparently. I would expect the main concern for the EC is the potential impact on the research programme described in your proposal.

@PieterNaaijkens Thank you for your reply. I would not want to change host institution, the main problem is with my supervisor. I have thought about getting in contact with my project officer at EC, however, it seems that every time there is an exchange through the Funding&Tenders platform my supervisor gets a notification and has complete access to our exchanges, which I find odd... I guess I need to investigate a bit further and also speak to my coordinator at my host institution.

@Louic I have, very carefully and she tells me I need to be humble. She actually sent me a lengthy email saying I need to be very humble in my career, particularly when I start my secondment. She has also been verbally abusive to my coordinator at my host institution. Basically, she treats horribly people who she deems are "below" her. She has not helped me at all since the beginning of the scholarship and barely responds to my emails. It's beyond disappointing.

I've heard other cases in which changing supervisor was a smooth process, but recently it seems that they are becoming stricter. I would say that if the supervisor agrees that you change (as in your case), then there is no problem, but if the supervisor does not agree, it's very hard. The grant is not portable, so if a grantee wants to switch the supervisor in a different institution, it is possible that the transition won't be successful. The grant manager explained this to me recently.


text:
What to say when I contact my future advisor?
I haven't officially been accepted to the program yet, but I needed to secure an advisor prior to applying. I was accepted by an advisor and she has been great with helping me fill out the application. However, I have yet to be accepted by the school. The school said they were waiting to hear the results of my funding, which I found out that I got. However, my person of interest then left to go away on a research expedition (and has little access to internet). I suspect she MAY be the reason my application is not moving forward right now. I have to select courses in less than a month. She suggested that we talk over the phone about courses when she comes back in a couple days.
I would like to send her an email the day she gets back, but what should I say in the email? Also, how should I bring up the fact that my application hasn't moved forward without complaining (or blaming her)?

@MassimoOrtolano Person of interest. Sorry, I reworded the question and took that out.

I also removed the tag POI because I don't think we really need such a new tag.

If she's set a date for you to talk, don't email,  just be patient and wait. The postgraduate application process is designed to be a gentle introduction to the bureaucracy and idiosyncrasies of academia.

It's not clear why you need to send an email, if you and her already agreed to talk over the phone. Anyway, I guess you can send an email as a reminder and to set up an agenda for the phone call.
I would just say something like:

Dear NAME/TITLE/WHATEVER_IS_APPROPRIATE_IN_YOUR_CULTURE,
I'm looking forward to our phone call on DATE at HOUR.
Just so that we have a starting point for our conversation, I'd like to please get your advice on the courses I should take (the deadline for course selection is approaching soon).
Also, I haven't heard any final word about my application from the department since DATE. I know you just got back from your research expedition, but I was wondering whether you have any update about the status of my application. Thank you in advance.
Looking forward to talking to you soon,
NAME

The thing is is we haven’t officially set up a time or date to talk. She just said we should talk when she gets back.