The Real-Analysis Trolley Problem

pic.twitter.com/sNJDBl7amH

— Oceans (@ShipSystem) November 15, 2019

(Tip of the cap to Ian Agol.)

RIP Philip J. Davis (1923–2018) and Writing Uncountably Many Articles

Philip J. Davis, an applied mathematician and very prolific writer, died on Tuesday.

I have a pet peeve in the above obituary: Don't write sentences like "He wrote countless books, articles, and book reviews imbued with his personal perspective." in the obituary of a mathematician, especially if he is an analyst (with much work in numerical analysis, in this case). Trust me: it's countable (and, actually, it's finite).

For most of us, we'll be more familiar with the many essays and (especially) book reviews that Davis wrote for SIAM News.

(Tip of the cap to the SIAM Twitter account.)

New XKCD: "Real Analysis is Way Realer Than I Expected."

Hell YES!!!!

Existence Proof https://t.co/LsVM88BDYZ https://t.co/ilYJsx2JKl pic.twitter.com/JxgXgUOsFJ

— XKCD Comic (@xkcdComic) June 28, 2017

"Why Classic Rock Isn't What It Used To Be"

Fivethirtyeight.com has an interesting analysis of regional variations in classic rock, and how more contemporary songs have snuck into it (in some regions more than others).

One could also do a similar analysis of others "genres" (or "radio formats", if you prefer), such as adult contemporary. I remember being surprised (many years ago now) the first time I heard Depeche Mode's "Enjoy the Silence" on an adult contemporary station.

Even More Average Than Before?

Former Major Leaguer Gabe Kapler offered some astute analysis about the Giants' playoff chances: "The loss of Pagan makes an already league average offense more average."

In related news, I subtracted 0 from 0, and I still have 0.

Note: Pagan's injury is a very big loss. Kapler had a sensible point in mind, but the way he phrased it is "fantastic".

"Inventive • Reserved • Efficient • Analytical • Sensitive"

An analysis of the words in my Facebook posts comes up with the descriptors "inventive", "reserved", "efficient", "analytical", and "sensitive". I can't argue with the results.

(Tip of the cap to David Williams.)

"A Method Based on Total Variation for Network Modularity Optimization Using the MBO Scheme"

One of my papers just came out in final form. Here are the details.

Title: A Method Based on Total Variation for Network Modularity Optimization Using the MBO Scheme

Authors: Huiyi Hu, Thomas Laurent, Mason A. Porter, and Andrea L. Bertozzi

Abstract: The study of network structure is pervasive in sociology, biology, computer science, and many other disciplines. One of the most important areas of network science is the algorithmic detection of cohesive groups of nodes called "communities." One popular approach to finding communities is to maximize a quality function known as modularity to achieve some sort of optimal clustering of nodes. In this paper, we interpret the modularity function from a novel perspective: we reformulate modularity optimization as a minimization problem of an energy functional that consists of a total variation term and an l_2 balance term. By employing numerical techniques from image processing and l_1 compressive sensing --- such as convex splitting and the Merriman-Bence-Osher (MBO) scheme --- we develop a variational algorithm for the minimization problem. We present our computational results using both synthetic benchmark networks and real data.


The really cool thing about this paper is what it does for "technology translation". We reformulate the modularity quality function in a way that relates it to compressive-sensing-like problems. One can thereby adapt methods from the latter to use for modularity optimization. One of the best compliments that we have received about this paper thus far occurred right after posting it on the arXiv: Somebody from the image-processing community told us that our paper was written in a language such that he could finally understand what people were doing with graphs. Given the goals of the paper, that was exactly what I wanted to hear!