• Brendan Fong, *The Algebra of Open and Interconnected Systems*, Ph.D. thesis, University of Oxford, 2016. (Blog article here.)

Kenny Courser is starting to look at the next thing: how one network can turn into another. For example, a network might change over time, or we might want to simplify a complicated network somehow. If a network is morphism, a process where one network turns into another could be a ‘2-morphism’: that is, a morphism between morphisms. Just as categories have objects and morphisms, bicategories have objects, morphisms *and 2-morphisms*.

So, Kenny is looking at bicategories. As a first step, Kenny took Brendan’s setup and souped it up to define ‘decorated cospan bicategories’. I want to tell you a bit about his paper:

• Kenny Courser, Decorated cospan bicategories, to appear in *Theory and Applications of Categories*.

In this paper, he shows that these bicategories are often ‘symmetric monoidal’. This means that you can not only stick networks together end to end, you can also set them side by side or cross one over the other—and similarly for processes that turn one network into another! A symmetric monoidal bicategory is a somewhat fearsome structure, so Kenny used some clever machinery developed by Mike Shulman to get the job done […]

]]>Does the Nyquist frequency/rate relate to Cauchy-Schwartz Inequality and Heisenberg Uncertainty?

Does Gibbs Phenomena model any phenomena involving other abrupt discontinuities, like black holes (and Hawking radiation), or evanescent wave tunneling?

Does Bayesian vs. Frequentist feud extend to wave vs. particle duality (in for instance say, Young’s Experiment)? ]]>

CIRM seminar TGSI’17 “Topological & Geometrical Structures of Information”:

http://forum.cs-dc.org/uploads/files/1484556914411-poster-tgsi2017.pdf

and MDPI Entropy Book on “Differential Geometrical Theory of Statistics” on some of these topics:

http://www.mdpi.com/books/pdfdownload/book/313/1

For some reason I’m not getting notifications of comments on that particular *n*-Café entry, so I just noticed and replied to your comments there today. They’re really exciting to me!

So exciting, in fact, that I finally wrote Part 2 of this series, both here and on the *n*-Café.

(In fact, I’m running this series of posts both here and at the *n*-Category Café. So far I’m getting more comments over there, so I suspect the serious helping will happen there. You may want to pop over there to see what people are talking about.)