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I am currently in the process of writing a paper for an international conference in image-processing area. One thing that bothers me somewhat is that the mathematical formulation I use is simple(specifically, I quantify a measure as a simple ratio). I happen to have just 2 equations in my paper. The formulation is sound,though, and is a natural outcome of the framework I have developed.

Ideally, simplicity or sophistication of equations occurring in a paper are not a measure of its worth, but I wonder openly -- what role does "density" and sophistication of mathematics used in the paper play in impressing the reviewers ? Just for clarification, I am not saying it should or should not. I would like to get a candid view of reviewer experiences and inclinations.

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    This is highly dependent on your target audience. In some computer science conferences, complex mathematical derivations are almost required (even when they are unnecessary); in others, they are essentially forbidden (even when they are necessary). Without specific knowledge about the community you're submitting to, there's really no way to answer this question. – JeffE Jan 2 '15 at 15:08
  • @JeffE As I mentioned in my question, the field is image-processing. – curryage Jan 2 '15 at 15:12
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    The answer may still depend on the specific conference. But in any case, you should first write the paper with whatever mathematical sophistication that your results require, and then send it to an appropriate venue, rather than artificially inflating/deflating the math in your paper to fit some target venue. – JeffE Jan 2 '15 at 15:27
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    Mathematical sophistication is surely not a requirement for the key equations of a paper, but an outcome that appears natural to you might not appear as natural to a reviewer, who, in turn, might ask you to add a mathematical proof of the fact that the simple parameter you are introducing is a good measure. – Massimo Ortolano Jan 2 '15 at 16:17
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Mathematical sophistication and mathematical density are often confused for one another, and this confusion often extends to reviewers and the "customs" of scientific communities. To my mind, the best mathematical presentation is the most lucid and simple, and it is certainly the case that important consequences often come from rather simple equations. The simpler your equations, however, the more that the contribution of the paper will depend on your exploration of those consequences (theoretically or empirically), rather than the mathematics per se.

It can be very tempting to "puff up" the perceived complexity of your mathematics by adding notational complexity or other baroquery. It may even work well when dealing with some communities (I know of some rather cynical and unfortunately successful experiments performed by certain colleagues of mine). I would strongly advise, however, against doing so. Write the paper as clearly and simply as possible, given the true nature of the mathematics within. Doing so may incur negative judgement from those who confuse "simple" and "trivial," but to do otherwise is scientifically dishonest. Moreover, if your work has value, it will show in the consequences of the mathematics rather than its nature, and writing it more accessibly is likely, in the long run, to increase its impact.

Finally, note that this dictum goes the other way as well: when you are presenting a complex mathematical result to an audience that does not appreciate mathematical complexity, do not attempt to pretend the mathematics is not complex. In this case, however, appendices and supplementary information is the way to go: keep only as much of key elements in the main text as is appropriate for the audience, and put the rest where those who are interested can readily find it without interrupting the flow of the main text.

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