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Stream: deprecated: mathematics

Topic: Publishing papers

Patrick Nicodemus (Feb 17 2023 at 00:55):

I don't know anything about how publishing works.
I have a small theorem, it took like a month to prove, it is not entirely trivial but not the most interesting thing in the world. I know where I want to go next, I have a bigger theorem lined up which is more interesting. I have related questions:

• At what point do you cut your work off and say "This is a publishable chunk." When is it appropriate to just put up a small research note that establishes a basic theorem, maybe 5-15 pages, and say "More to come on this later" vs just folding it back into your work and waiting until you have the bigger thing ready
• How do you tell the level of significance that distinguishes between "just upload to the arxiv and move on", "maybe a conference paper", "worth publishing in a half-decent journal"

John Baez (Feb 17 2023 at 00:59):

I'm afraid I'd have to hear more about the theorem, because different people have completely different ideas about the meaning of "not entirely trivial but not the most interesting thing in the world". I know good mathematicians who don't bother to publish work that other people would love to publish, and also mathematicians who publish things that other people would find embarrassingly easy. If you want to tell it to me privately I promise not to steal it or share it with anyone. For now I can just offer limited advice.

John Baez (Feb 17 2023 at 01:02):

At what point do you cut your work off and say "This is a publishable chunk."

When it is, in fact, publishable. Different journals have different standards. To tell if something is publishable in Journal X, you need to look at a bunch of articles in Journal X. The only shortcut is to have an advisor who knows your work and has read Journal X. But even if you do have such an advisor, it's good to do this sort of reading yourself, where you look at journals just to see what they're like - not to understand the papers in detail, but just to see what it takes to publish a paper there.

Patrick Nicodemus (Feb 17 2023 at 01:03):

Ok, cool. This is a sensible answer. I will come back to this thread later once I have written up and double-checked the proof, and describe the theorem then. I have been trying to force myself to get more familiar with journals but it's hard.

John Baez (Feb 17 2023 at 01:05):

Great.

Mike Shulman (Feb 17 2023 at 04:03):

Ultimately, of course, the only way to really answer the question of whether something is publishable in journal X is to submit it there and find out whether it gets accepted. Looking at other articles in journal X can give you an idea, but you can get surprised in both directions. Sometimes the editor and the referee matter.

Mike Shulman (Feb 17 2023 at 04:16):

I do think there's more to deciding when to cut the work off and publish what you've got than only the question of whether you could publish what you've got. You don't always want to aim for the Minimum Publishable Unit.

My default approach is to work on a subject until I'm done working on it for now, and then figure out how to make zero or more publishable papers out of what I've got. Depending on the situation, "done working on it for now" might mean that I've proven everything I wanted to prove; or it might mean I've proven something and I wish I could prove more, but I'm out of ideas or time for working on it more right now. For instance, the latter is how I ended up writing four papers about the semantics of HoTT in higher toposes: each time I came back to it with a new idea and pushed it as far as I could at that time, even though the first three times that wasn't as far as I wanted.

However, sometimes it happens that I'm not done working on a project yet, but I reach a point where I have a pretty good guess that eventually I'll want to split it up into multiple papers, and I can tell that the material that'll go in one of those papers is basically complete. This is a bit dangerous because writing up and publishing that paper tends to distract me from actually continuing to work on the project, and so it takes longer to finish the other papers (if I indeed ever do). For instance, my work on LNL polycategories was originally intended to prove a 2-conservativity result for them, but developing the basic theory got so long that I published a paper about just that -- and I still haven't gone back to finish the 2-conservativity.

Mike Shulman (Feb 17 2023 at 04:20):

As for how I would split a project up into papers when it's finished, there are a lot of considerations. Usually my default approach is to start trying to write it as one paper, and see whether it starts collapsing under its own weight or trying to break itself in half, and if so whether there are parts it could be divided into that can stand on their own. Another thing to think about is whether different parts of the work are of interest to different communities and might benefit from being published in different venues, or at least unencumbered by other parts of the project that some readers might be intimidated or bored by.

For instance, right now I'm working on a theorem about semantics of modal dependent type theory. I have a pretty satisfying result about semantics in diagrams of 1-categories, and a less complete result about diagrams of $\infty$-categories, and I've been going back and forth about whether to put them in one paper or two. At the moment, I'm leaning towards publishing the 1-categorical version on its own, because it's more complete, doesn't require homotopy-theoretic background to read, and will probably be of interest to a wider audience. Then I'd take some more time to see whether I can get a better result in the $\infty$-case before deciding to cut off that work and publish it. But I might change my mind again!

Jean-Baptiste Vienney (Feb 17 2023 at 05:00):

Thank you to let us benefit from your experience. That's very interesting to me as well.

Jean-Baptiste Vienney (Feb 17 2023 at 05:10):

I have a related question. Is it okay to add a substantial amount of work to an already published paper by updating it on the ArXiv without making a new official publication or are people doing this only for minor corrections? It seems simpler to add the news to an already published paper than doing a new one each time and multiplying the number of papers.

David Michael Roberts (Feb 17 2023 at 06:49):

@Jean-Baptiste Vienney I would not seriously update a paper on the arXiv that was already published. If it's a substantial amount of work, it can be its own paper. Sometimes perhaps one is in the position Mike was in, but where the paper with the partial results weren't yet submitted, and then with a chunk more work, it turns out a complete story could be told. In that case it might be reasonable to update the arXiv paper, but definitely noting in the metadata that this is the case. The situation where this makes the most sense is where the additional work gives a stronger result, but which on its own seems like an incremental addition (regardless of how much effort went into finding the new resut).

For example, my first solo paper, post-PhD in TAC is different to how it was when I first submitted it, because in the very slow revision processes (I left academia temporarily, and other life stuff happened), I managed to make the results more general. So I updated the arXiv version, and the updated version back to the journal, upon which the referee was I think rather gracious in reading over a heavily-revised article (though the generalisation wouldn't have really been worth a sequel on its own, it just rewrote the main results in a way that was more general). I had to, at one point, cut this revision off, since I was in danger of writing a legitimately new paper, rather than merely strenthening the existing one.

John Baez (Feb 17 2023 at 08:20):

Jean-Baptiste Vienney said:

I have a related question. Is it okay to add a substantial amount of work to an already published paper by updating it on the ArXiv without making a new official publication or are people doing this only for minor corrections? It seems simpler to add the news to an already published paper than doing a new one each time and multiplying the number of papers.

You can't expect people to reread a paper that has been put on the arXiv after they've read it once, so - especially if you are hoping to eventually get a job - it pays to really finish a paper before putting it on the arXiv, and then if you have a new idea write another paper.

John Baez (Feb 17 2023 at 08:36):

Each paper you put on the arXiv should be a well-crafted thing that people will enjoy. Then people will start paying attention to you, like you, and maybe give you a job.

dusko (Feb 17 2023 at 09:41):

Mike Shulman said:

I do think there's more to deciding when to cut the work off and publish what you've got than only the question of whether you could publish what you've got. You don't always want to aim for the Minimum Publishable Unit.

My default approach is to work on a subject until I'm done working on it for now, and then figure out how to make zero or more publishable papers out of what I've got. [...]

if i understand correctly, the point is that research is a process of understanding things (ie finding ways to interact). publishing comes after some progress has been made in that direction, as means to understand things better together (and perhaps get paid and keep doing it longer...)

if this approximates your point, then i think it is a very important point. mounting the cart of publishing in front of the horse of research is a call for trouble, stress, and bad deals.

young people are confronted with a world of impact factors. i think they should be warned that even winning in that game is a bad deal. they signed up to do research, and they end up spending time on writing long versions of short papers and splitting long papers into publishable units, instead of doing research and writing new papers.

i don't know a way out of there, but there must be since it hampers science and civilization needs science.

dusko (Feb 17 2023 at 09:44):

"there must be some way out of here"
said the joker to the thief...
(maybe more like: said the thief to himself :)

Jean-Baptiste Vienney (Feb 17 2023 at 14:09):

John Baez said:

Each paper you put on the arXiv should be a well-crafted thing that people will enjoy. Then people will start paying attention to you, like you, and maybe give you a job.

I'm going to be be very honest. The point is that I'm already not heavily excited by the idea to get a postdoc later and then maybe accumulating several ones before finally abandoning doing math in academia because I don't find a stable position. Several past or potential relationship have already told me implicitly or explicitly that they changed their mind and don't want to stay with me or simply don't want to start if they don't know where and when I will have a normal job like people outside academia. Anyway I think I should continue because I would probably be really bad in another occupation than doing a phd in math today. But in these conditions it's harder to have the passion to carefully write well-crafted papers that people will enjoy. That's exactly my state of mind today.

John Baez (Feb 18 2023 at 02:34):

Well, if you're planning to not go into academia then you're more free to do whatever you feel like when it comes to writing math papers. But if you're sort of depressed and lacking in passion then any advice of mine may be irrelevant - because for me, at least, doing things well takes energy.

John Baez (Feb 18 2023 at 02:42):

When I first got my PhD, I didn't really want to go on with math, because my thesis wasn't very good and I didn't know what math I wanted to work on. I wanted to do either philosophy or music, but those both seemed even harder to get a job in.

So, I stuck with math more or less out of inertia, and got a postdoc. It took me a few years to figure out what I really wanted to do in math.

John Baez (Feb 18 2023 at 02:43):

I guess for a while my naturally high energy level made up, in part, for a lack of passion. Even when I'm miserable, doing work makes me feel better.

John Baez (Feb 18 2023 at 02:45):

In the end I learned a lot about how to publish papers. I've published about 117 papers and I really enjoy writing them and publishing them.

John Baez (Feb 18 2023 at 02:47):

So, I have huge amounts of specific advice about writing and publishing papers if you're interested. I think it's useful advice. But it takes work to implement it.

Jean-Baptiste Vienney (Feb 18 2023 at 06:24):

Thanks @John Baez . I appreciate a lot your message. I will write more soon but now it's the night so I will do it tomorrow.

Jean-Baptiste Vienney (Feb 18 2023 at 15:43):

I definitely have energy to do mathematics. I was just feeling really bad but when I wrote this message but this was maybe not so much related to mathematics. Gladly, I know exactly what math I want to do. I'm not sure doing math makes me feel better all the time. That's more the contrary. I'm thinking to math 24h a day 7 day a week and often I feel like in a jail and want to be able to stop thinking to it but don't succeed. Finally, I get tired and not productive for doing math or anything else. I do have questions about writing and publishing papers!

Jean-Baptiste Vienney (Feb 18 2023 at 15:45):

There are three papers that I have already at least half written.

Jean-Baptiste Vienney (Feb 18 2023 at 15:47):

One with JS Lemay on graded differential categories / linear logic. And two alone: "Higher order differential categories" and "symmetric powers in string diagrams". I don't have too much questions on the first two ones but I'm not sure what to do with the last one.

Jean-Baptiste Vienney (Feb 18 2023 at 15:50):

I proved something on symmetric powers in symmetric monoidal $\mathbb{Q}^+$-linear category. That's very simple. Given a family $(A_{n})_{n \ge 0}$ of objects such that $A_{0} = I$, you have a bijection between two type of family of maps. The first one is a system of symmetrization maps $(s_{n}:A_{1}\rightarrow A_{1}^{\otimes n}, r_{n}:A^{n} \rightarrow A_{1}^{\otimes n})_{n \ge 0}$ such that $s_{0},r_{0},s_{1},r_{1}$ are identities.

Jean-Baptiste Vienney (Feb 18 2023 at 15:52):

And the second one is a system of multiplication and comultiplications $(\nabla_{n,p}:A_{n} \otimes A_{p} \rightarrow A_{n+p}, \Delta_{n,p}:A_{n+p} \rightarrow A_{n} \otimes A_{p})_{nap \ge 0}$ such that when $n=0$ or $p=0$, each of the two types of maps are identities

Jean-Baptiste Vienney (Feb 18 2023 at 15:53):

and for every $n,p \ge 0$, you have two nice equalities which simplify $\nabla_{n,p};\Delta_{q,r}$ when $n+p=q+r$ and $\Delta_{n,p};\nabla_{n,p}$

Jean-Baptiste Vienney (Feb 18 2023 at 15:54):

The first system of maps defines symmetric powers as a split idempotent in an usual way.

Jean-Baptiste Vienney (Feb 18 2023 at 15:55):

But the second one gives a characterization as a "special and connected graded bialgebra".

Jean-Baptiste Vienney (Feb 18 2023 at 15:56):

And each of the two definitions give you a way to implement symmetric powers into string diagrams ! Using two different type of drawings.

Jean-Baptiste Vienney (Feb 18 2023 at 15:57):

That's a lot of fun (or not) and a lot of pages of diagrams to verify that it works. I think that's enough for a paper.

Jean-Baptiste Vienney (Feb 18 2023 at 15:58):

The issue is that I'm almost sure that you can generalize this result.

Jean-Baptiste Vienney (Feb 18 2023 at 15:58):

And I don't know if I must wait to have a more general version or not to publish it.

Jean-Baptiste Vienney (Feb 18 2023 at 16:00):

First, it should work if you take a symmetric monoidal $\mathbb{Q}$-linear category and replace symmetric powers by exterior powers. Now you no longer look at the splitting of $\frac{1}{n!}\underset{\sigma \in \mathfrak{S}_{n}}{\sum}\sigma:A_{1}^{\otimes n} \rightarrow A_{1}^{\otimes n}$

Jean-Baptiste Vienney (Feb 18 2023 at 16:01):

but at the splitting of $\frac{1}{n!}\underset{\sigma \in \mathfrak{S}_{n}}{\sum}sgn(\sigma)\sigma:A_{1}^{\otimes n} \rightarrow A_{1}^{\otimes n}$

Jean-Baptiste Vienney (Feb 18 2023 at 16:06):

and I'm not sure how to adapt the equations for the bialgebraic definition. But I'm sure that it works because some people characterized symmetric algebras and exterior algebras in this way some dozen of years ago. I realized this after finding my result. But it was not done categorically, it was not symmetric/exterior powers but symmetric/exterior algebras, they didn't see the interpretation of the diagrams in term of differentiation and it wasn't related with any kind of logic or string diagrams, whereas I clearly do that because such a bialgebraic definition allows me to use a nice string diagrammatic calculus or a kind of linear logical sequent calculus for symmetric powers ! And I do think that my characterization in terms of powers is easier to understand that their ones. This is done in this paper: A Characterization of symmetric and exterior algebras in characteristic zero

Jean-Baptiste Vienney (Feb 18 2023 at 16:08):

A reason for making another paper for exterior powers is also that now you need a $\mathbb{Q}$-linear category so it no longer works for some models like $Rel$ which are not $\mathbb{Q}$-linear categories. And some people in computer science don't like negative numbers.

Jean-Baptiste Vienney (Feb 18 2023 at 16:12):

I think it's an interesting news for symmetric powers in string diagrams / logic which can be useful for categorical quantum mechanics and I think it's maybe better to focus only on symmetric powers in a first paper.

Jean-Baptiste Vienney (Feb 18 2023 at 16:14):

After exterior powers, as you told me Schur functors are also split idempotents. But I found the best way to express this split idempotent a few days ago by reading this wikipedia article: Gamas Theorem

Jean-Baptiste Vienney (Feb 18 2023 at 16:16):

So your idempotent for the Schur functor $S_{\lambda}$ where $\lambda$ is a partition of $n$ is now $\frac{\chi_{\lambda}(e)}{n!}\underset{\sigma \in \mathfrak{S}_{n}}{\sum}\chi_{\lambda}(\sigma)\sigma:A_{1}^{\otimes n} \rightarrow A_{1}^{\otimes n}$ (where $\chi_{\lambda}$ is the character of the irreducible representation of $\mathfrak{S}_{n}$ associated to $\lambda$ which can be defined more directly by the Frobenius formula).

Jean-Baptiste Vienney (Feb 18 2023 at 16:17):

But I have no ideas for the axioms in terms of graded bialgebra !

Jean-Baptiste Vienney (Feb 18 2023 at 16:19):

A result on Schur functors will trivially imply the ones on symmetric and exterior powers. That's why I'm not sure if I must publish something just on symmetric powers.

Jean-Baptiste Vienney (Feb 18 2023 at 16:20):

And I'm not sure even about exterior powers now.

Jean-Baptiste Vienney (Feb 18 2023 at 16:21):

I'm afraid if I try to do a paper on symmetric powers, then a one on exterior powers and then a one on Schur functors that people will tell "You just do three times the same things by modifying or generalizing a little bit each time!"

Jean-Baptiste Vienney (Feb 18 2023 at 16:22):

But I really need to write clearly the one on symmetric powers to have a clear mind to treat exterior powers and then I will want to write clearly everything about exterior powers to have a clear mind to treat Schur functors.

Jean-Baptiste Vienney (Feb 18 2023 at 16:25):

So my question is really if I must plan to do three papers or work until the end and just do one on Schur functors if it works for them.

Jean-Baptiste Vienney (Feb 18 2023 at 16:26):

The issue is that I don't succeed to go to the next step until the previous one is crystal clear. And the only way to make it crystal clear in my mind is to write a crystal clear paper about it.

Jean-Baptiste Vienney (Feb 18 2023 at 16:29):

I think there will be yet a lot of other things to work on if these characterization work! It's already clear that symmetric, exterior and Schur functors share a lot of similarities when you look at this: Determinant, Permanent, Immanant

Jean-Baptiste Vienney (Feb 18 2023 at 16:31):

Determinant and permanent are just a special case of immanant when you take the thin and long Young diagram or the the fat and short Young diagram (or the contrary, I never remember).

John Baez (Feb 18 2023 at 17:45):

Jean-Baptiste Vienney said:

The issue is that I don't succeed to go to the next step until the previous one is crystal clear. And the only way to make it crystal clear in my mind is to write a crystal clear paper about it.

That makes sense. In your situation I would put three separate papers on the arXiv, making each one independently readable. So, example, the (n+1)st paper would summarize the results from the nth paper that are needed to understand the nth. If a result from the nth paper is only needed for a proof in the nth paper, not any theorem statement, you can just mention it in the proof and refer to the nth paper.

John Baez (Feb 18 2023 at 17:48):

I don't think people will be annoyed by 3 crystal clear papers on related themes, each building on the previous ones, as long as each paper can be read without reading the previous ones. (Note: by "read" I mean "read, trusting that the results referred to from the previous papers are correct". To fully verify the results in a given paper, people may need to check proofs in the previous papers - that's unavoidable and okay.)

John Baez (Feb 18 2023 at 17:49):

In particular, since the second paper works only for $\mathbb{Q}$-linear categories, it makes a lot of sense to have it be separate from the first, for the reasons you explained: it's a different flavor of mathematics, and different people will be interested in it.

John Baez (Feb 18 2023 at 18:20):

I think this should be a quite nice series of papers!

Jean-Baptiste Vienney (Feb 18 2023 at 20:48):

Awesome! So I'm going to try to make the first one and I'll tell you when I submit it!

John Baez (Feb 18 2023 at 21:20):

Great! By the way, your second paper is related to my paper with Moeller and Trimble. We do a detailed study of 2-rigs, which we define to be symmetric monoidal $k$-linear categories that are Cauchy complete, meaning they have finite biproducts and idempotents split. Here $k$ is any field of characteristic zero.

So, any 2-rig has an underlying symmetric monoidal $\mathbb{Q}$-linear category. And in your second paper you seem to want to split the idempotent

John Baez (Feb 18 2023 at 21:20):

$\frac{1}{n!}\underset{\sigma \in \mathfrak{S}_{n}}{\sum} \mathrm{sgn}(\sigma)\sigma:A^{\otimes n} \rightarrow A^{\otimes n}$

John Baez (Feb 18 2023 at 21:22):

So I'm guessing your results apply to 2-rigs. In our paper we study the symmetric and exterior power functors, but not in much detail by themselves: main along with all the other functors arising from Young diagrams ($\simeq$ irreducible representations of the symmetric groups).

John Baez (Feb 18 2023 at 21:23):

So it seems there's only a small amount of overlap in the results between your second paper and ours, but they are studying similar situations.

Jean-Baptiste Vienney (Feb 18 2023 at 21:24):

Sure, the third one, if things work, should be about all the Schur functors, although I quite don't understand how to do it right now.

Jean-Baptiste Vienney (Feb 18 2023 at 21:26):

John Baez said:

So I'm guessing your results apply to 2-rigs. In our paper we study the symmetric and exterior power functors, but not in much detail by themselves: main along with all the other functors arising from Young diagrams ($\simeq$ irreducible representations of the symmetric groups).

Yes, I don't want to require a $2$-rig because one can write down a sequent calculus where you will have only symmetric powers or only exterior powers or maybe only Schur functors without all the idempotents that split I guess. But I'm not sure.

Jean-Baptiste Vienney (Feb 18 2023 at 21:28):

Hmm I'm sure about that in fact. You can write a sequent calculus or string diagrammatic calculus which gives you a symmetric monoidal $\mathbb{Q}$-linear category with symmetric powers, where you have the morphism $\frac{1}{n!}\underset{\sigma \in \mathfrak{S}_{n}}{\sum} \mathrm{sgn}(\sigma)\sigma:A^{\otimes n} \rightarrow A^{\otimes n}$ but you don't have exterior powers

Jean-Baptiste Vienney (Feb 18 2023 at 21:32):

Also I can work without biproducts. But maybe adding biproducts can be another further step

Jean-Baptiste Vienney (Feb 18 2023 at 21:34):

In that case, I could try to use the Sheet diagrams for bimonoidal categories of @Cole Comfort @Jules Hedges, @Antonin Delpeuch and add Schur functors inside them. But please, right now I don't even understand if I can really do something about Schur functors so I only say that for the future.

Jean-Baptiste Vienney (Feb 18 2023 at 21:35):

And so it would be related with your conjecture about the biinitial object in the 2-category of bimonoidal categories.

Jean-Baptiste Vienney (Feb 18 2023 at 21:36):

I'm only 100% sure about my story for symmetric powers, 90% for exterior powers and I don't know for general Schur functors although it seems very attracting.