RIP Erik Bollt (1967–2025)

My collaborator Erik Bollt died suddenly and unexpectedly last Sunday (the 7th). Erik is a well-known applied mathematician, and he was especially in the applied dynamical-systems community. Erik and I wrote two papers together, including our paper on mathematically modeling cow synchronization.

You can read about Erik's research on his web page and his Google Scholar page.

There will be a memorial article at some point.

What Happens in Boston Stays in Boston

I'm on my way to Boston for the workshop to celebrate David Campbell's 80th birthday! It will surely be chaotic. :)

Short Course on "Mathematical and Computational Methods for Complex Social Systems" at the 2021 Joint Mathematics Meetings!

An exciting announcement!

We (@hzinnbrooks + @michellehfeng + Me + @al_volkening) are organizing an @amermathsoc 'Short Course' on "Mathematical and Computational Methods for Complex Social Systems" at the 2021 Joint Mathematics Meetings (@JointMath)! https://t.co/A4rXWVOWSU pic.twitter.com/e9hTEDLCN4

— Mason Porter (@masonporter) April 28, 2020

My TDA (Topological Data Analysis) Origin Story

Based on what I saw as an undergraduate, I thought that algebraic topology was hopelessly abstract, and then I encountered Konstantin Mischaikow's work when I was a postdoc at Georgia Tech. He was using these ideas to analyze experimental data from areas like fluid mechanics. This stuck in my head, but I didn't work on these topics for many years. However, it stuck in the back of my head for about a decade, as this had made an impression on me. (I was aware of work of some others as well, but this is the one that made an impression, because of the close collaboration with experimentalists.) I was spending a bunch of time on granular networks as well as on generalizing network analysis from graphs to various more complicated structures (and I also had the desire to look more at "higher-order" interactions more generally).

During one of my daily arXiv routines, I noticed a paper by Konstantin and collaborators that used topological data analysis (TDA), so I saw that we were looking at the same systems, but in different ways. I contacted him, visited him early in 2013, and we started a joint TDA project --- but it turned out to be on spreading dynamics on networks, rather than on granular networks. Our first paper (which was led by Dane Taylor and coauthored with many other excellent people, including my Oxford colleague Heather Harrington) was published in final form in Nature Communications in 2015. I viewed this as just one paper; I never intended to start a large new direction in my research program. Back at Oxford, one student saw that I was part of that and wanted to work with Heather and me on applications of TDA. Then more students saw the 2015 paper and what this student was doing, and they wanted to work with us on TDA.

After I moved to UCLA, more students (starting with Michelle Feng) saw that I had some papers on TDA and wanted to work with me on those topics, partly because they wanted to do things with applications but also wanted to continue pursuing more theoretical mathematical subjects as well. I also really like the idea of taking "traditionally pure" areas of mathematics and bringing more and more of them into applications. It's a really exciting thing to do. And the work on applications also yields really great insights into the mathematical theory. (Because it does go in both directions, after all.)

Most recently, at least among people who have officially joined my group, Abby Hickok saw the work that Michelle and I have been doing, and she has ideas for building further on that work. And now TDA (along with work involving the intersection of dynamics, networks, and simplicial complexes) has become an important part of my research program,

Anyway, it was an all an accident.

What Happens in San José Stays in San José (2019 Edition)

I'll soon be going to San José, Costa Rica for the third time to work on a collaboration on dengue dynamics and control. I'll also be participating in a spiffy panel discussion, where I'll get to meet one of my coauthors in person for the first time.

Our Physics Today Obituary of Norman Zabusky

David Campbell, Alan Newell, and I wrote an obituary of Norman Zabusky for Physics Today. It just came out.

Previously, we wrote an obituary of Zabusky for DSWeb.

What Happens in Oxford Stays in Oxford

I arrived in Oxford last Sunday and will be here for a while, staying in Somerville and hanging out with my peeps (including some of my former students) from College as well as the Mathematical Institute. It's great to still be part of the extended family!

I'll also be participating and speaking at Howison-fest, a workshop in honor of Sam Howison's 60th birthday.

You Wouldn't Like These Functions When They're Angry

There is a family of special functions called Anger functions. You wouldn't like them when they're angry.

Here is the context: Physics Today has agreed to publish an obituary for Norman Zabusky, so I needed to find some information that they require to be part of it. This led me to Norman's PhD thesis, which I found online. It briefly mentions something called Lommel polynomials, with which I wasn't familiar. The definition in a thesis appendix was terse — it's not exactly an important part of the thesis — so I looked at Wikipedia, and I kept seeing links to special functions that weren't familiar to me, and I have followed a couple of them. Anger functions are one family.

These various special functions are closely related to Bessel functions.

Our Memorial Article for Norman J. Zabusky (1929–2018)

Along with David Campbell and Alan Newell, I have written a memorial article for my collaborator Norman Zabusky, who died in February. It was posted online earlier today.

Oxford Mathematics Alphabet: "'H' is for Homology"

The latest entry in the Oxford Mathematics Alphabet, 'H' is for Homology, is out today.

It was written by doctoral students Bernadette Stolz (my collaborator and my former masters student, who I cosupervised with Heather Harrington, who is Bernadette's main doctoral supervisor) and Barbara Mahler (my doctoral student, who I am supervising along with Heather Harrington and Ulrike Tilmann).

Quote of the Day: The Volume of My Text

The following was pointed out by e-mail by my collaborator Peter Mucha, who is not my department chair: "During my time as a department chair, I received roughly 20K *work-related* (e.g., not personal and not spam) emails each year... Mason occasionally accounts for just over 2K of those himself."

2014 MacArthur "Genius" Awards

The 2014 MacArthur Fellows (i.e., the so-called "genius awards") have just been announced.

And I am super excited about them this year, because my coauthor Dani Bassett is one of the recipients! It is, unsurprisingly, richly deserved. (At age 32, she is also the youngest of this year's Fellows.) The work in which I was involved is cited among her major contributions --- especially this paper and several follow-ups. Major congratulations to Dani!

A couple of mathematicians are also among this year's winners, and of course that always makes me happy. (Among the mathematicians, it is particularly cool that Yitang Zhang won because of his career path.)

What Happens in Princeton Stays in Princeton

I am now in The Prince's Town to visit Kevrekidis the Elder.

What Happens in Chapel Hill Stays in Chapel Hill

I am now in Chapel Hill, North Carolina to visit my collaborator Peter Mucha at University of North Carolina. I will also be giving their applied mathematics colloquium on Friday.

And to describe dinner at the hotel restaurant tonight, let me just mention the following: Douchebags are drawn to sports bars like moths to a flame. [[...groan...]]

Facebook and Voting

Check out this new paper that was just published in Nature about voter participation and Facebook friendships. It was a collaboration between Facebook Data team, my collaborator James Fowler (who is a political scientist by training), and others at UC San Diego.

This paper is in the process of making waves. For example, here is what the New York Times had to say about it in its article. By the way, the research for this paper was funded in part by a joint grant that James and I have from the James S. McDonnell Foundation, though please note that I was not part of this project. (I did read an early draft of this paper over 1.5 years ago and gave some comments on it, and that is the extent of my involvement.) It is really cool that we get to mention this paper in our report to the funding agency, though!

Communities in Multislice Voting Networks

My latest Nonlinear Science Gallery paper officially came out today. Its title appears in the title of this entry. Note that this is the first time ever that Peter Mucha and I are the only two authors on a paper, which is interesting given that we have coauthored so many papers with students and other collaborators.

What happens in Sevilla stays in Sevilla (Take 2)

Tomorrow I take my second trip to Sevilla. In July, I went there for a nonlinear waves workshop, and this time I am visiting a collaborator. Thankfully, the weather should be much cooler than it was in July.

New to the Blogroll: ChaosBook

My collaborator Predrag Cvitanovic, who was my (unofficial) postdoc advisor on the physics side at Georgia Tech (Leonid Bunimovich was my postdoc advisor from the math side at Georgia Tech, and in that case it was official), now has a blog. Well, apparently, he had one before, but only since December 2009 has there been a decent amount of activity on it and only today did I find out about it.

The name of his blog comes from his award-winning (and I know, because I gave it the award) book on classical and quantum chaos.

There are certain comments that have appeared here over the past few years by anonymous posters that I suspect might have come from Predrag.

Connected: A new book about social networks

Given the media play it's received, I should mention my collaborator James Fowler's new popular book about social networks. The book, which James coauthored with Nicholas Christakis, is called Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives. The book should be an interesting read (I previously glanced through small parts of it in draft form), but I really think they should lose the term "network man". It's too corny.

(Tip of the cap to James for passing along this particular article.)

What happens in the Research Triangle stays in the Research triangle

I am now in the airport at San Diego, waiting for my red-eye flight to New Jersey, which will then go to Raleigh-Durham. I will be visiting my collaborator Peter Mucha at UNC, though I will also be stopping off at Duke on Tuesday (to give a math/physics seminar) and Wednesday (to give a social networks seminar, although that's more of an informal group meeting type deal). In fact, I will also be visiting a friend's lab at NC State on Saturday morning before she drops me off at the airport. I also have plans to see one friend from grad school who is now a postdoc at Duke as well as two friends from Caltech. Additionally, my collaborator JP Onnela will be flying down on Thursday for a bit of a synchronized visit and some additional work. It's definitely going to be both a fun and productive week.

Peter Mucha and I have numerous joint projects, though the one on which we'll probably spend the most time are our series of projects on Facebook networks. The American Physical Society press conference (held at the March Meeting) about our Facebook work is tomorrow morning (I think at 11am), and there will also be an APS press release (which I assume will come out tomorrow). They highlighted our student Mandi Traud's Tuesday talk at the conference, and she will be the one doing the press conference. We also have a poster in the GSNP Gallery at the meeting, and hopefully we'll have one of the winning entries. Stay tuned for more information about the media blitz...