[EtDybNuvCu]

While it might seem arrogant of the author to take this stance, the Sampling Theorem generalizes extremely well and is considered an extremely stable result. My favorite generalized Sampling Theorem is https://arxiv.org/abs/1405.0324

[gowld]

It's hardly arrogant to vote in favor of a 100-year-old mathematical proof over a new supposed refutation.

[posterboy]

It is an argument from authority. That is asking a lot from the reader, i.e. to suspend believe or go research, the later of which is not too much to ask if direct at an acceptable audience.

"Arrogance" literally is akin to "to ask", e.g. interrogate ... unless the "a-" is akin to "anti" instead of "ad-" or whatever, so that arrogance would be like walzing in and taking without asking or making an assumption without due inquiry.

[gnulinux]

That's an extremely interesting paper. Do you have any other references if I were to read more about applications of Sheaf theory to signal processing or relevant fields like information theory, control theory, machine learning?

[thraway180306]

About signal processing AFAIK it's only this particular author, Michael Robinson https://scholar.google.com/citations?user=WxsA8yEAAAAJ&hl=en He's also got short book Topologica Signal Processing.

About all the other things, you want to follow the field of Applied Algebraic Topology. People such as Robert Ghrist, Shmuel Weinberger, Herbert Edelsbrunner, Gunnar Carlsson, Justin Curry whose thesis was on applied sheaf theory (it's nice and readable). Mostly the collaborations they part in, them just being in good places in the citation graph (OTOH Carlsson's Ayasdi Inc. is sadly very much a vapourware). Also, in over a decade of very active research in this area progress is being made mostly on the applicable algebraic topology part, not necessarily the applied part.

[gnulinux]

> Also, in over a decade of very active research in this area progress is being made mostly on the applicable algebraic topology part, not necessarily the applied part.

I'm not entirely sure what this means in terms of applied mathematics. Does it mean applied mathematicians produce these papers but applied fields like EECS, CS, biology etc never use them?

[thraway180306]

I mean the field's notions are being customized, but so far the language hasn't been shown to be all that insightful in numerous engineering fields probed. Algebraic topologists seem happy trying to be vaguely relevant though.