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.

"Oscillatory and Excitable Dynamics in an Opinion Model with Group Opinions"

The published version of one of my papers just came out today. Here are some details.

Title: Oscillatory and Excitable Dynamics in an Opinion Model with Group Opinions

Authors: Corbit R. Sampson, Juan G. Restrepo, and Mason A. Porter

Abstract:

"Minimizing Congestion in Single-Source, Single-Sink Queuing Networks"

Another of my papers has appeared in final form. Here are some details about it.

Title: Minimizing Congestion in Single-Source, Single-Sink Queuing Networks

Authors: Fabian Ying, Alisdair O. G. Wallis, Mason A. Porter, Sam D. Howison, and Mariano Beguerisse-Díaz

Abstract: Motivated by the modeling of customer mobility and congestion in supermarkets, we study queueing networks with a single source and a single sink. We assume that walkers traverse a network according to an unbiased random walk, and we analyze how network topology affects the total mean queue size Q, which we use to measure congestion. We examine network topologies that minimize Q and provide proofs of optimality for some cases and numerical evidence of optimality for others. Finally, we present greedy algorithms that add edges to and delete edges from a network to reduce Q, and we apply these algorithms to a network that we construct using a supermarket store layout. We find that these greedy algorithms, which typically tend to add edges to the sink node, are able to significantly reduce Q. Our work helps improve understanding of how to design networks with low congestion and how to amend networks to reduce congestion.

"Bounded-Confidence Model of Opinion Dynamics with Heterogeneous Node-Activity Levels"

One of my papers came out in final form today. Here are some details.

Title: Bounded-Confidence Model of Opinion Dynamics with Heterogeneous Node-Activity Levels

Authors: Grace J. Li and Mason A. Porter

Abstract: Agent-based models of opinion dynamics allow one to examine the spread of opinions between entities and to study phenomena such as consensus, polarization, and fragmentation. By studying models of opinion dynamics on social networks, one can explore the effects of network structure on these phenomena. In social networks, some individuals share their ideas and opinions more frequently than others. These disparities can arise from heterogeneous sociabilities, heterogeneous activity levels, different prevalences to share opinions when engaging in a social-media platform, or something else. To examine the impact of such heterogeneities on opinion dynamics, we generalize the Deffuant-Weisbuch (DW) bounded-confidence model (BCM) of opinion dynamics by incorporating node weights. The node weights allow us to model agents with different probabilities of interacting. Using numerical simulations, we systematically investigate (using a variety of network structures and node-weight distributions) the effects of node weights, which we assign uniformly at random to the nodes. We demonstrate that introducing heterogeneous node weights results in longer convergence times and more opinion fragmentation than in a baseline DW model. The node weights in our BCM allow one to consider a variety of sociological scenarios in which agents have heterogeneous probabilities of interacting with other agents.

RIP Abdul-Aziz Yakubu (1958–2022)

A couple of weeks ago, I heard the very sad and unexpected news that Abdul-Aziz Yakubu had died. Aziz was great.

Like others, I also have some Aziz stories (but the one that I wanted to tell seemed a bit too light-hearted to tell immediately on social media): I know Aziz from my days helping out with MTBI as a PhD student. On one occasion, when somebody — one of the students? — was being a bit formal with my name as I entered a room and was also using my last name or something, I made the mistake of loudly proclaiming "I'm like Madonna. I only need one name." With a quietly wicked sense of humor (and with the knowledge that we'd all be amused by this, including me), Aziz proceeded to jokingly call me "Mason Madonna" for the next several years.

You can read more about Aziz in his 2020 Mathematically Gifted & Black profile.

Retirement Conference for Colin Please

Unfortunately, I just checked and I am still COVID positive, so regrettably I will be missing the retirement conference and party for my Oxford colleague Colin Please. (Alhough I am far from perfect, I feel well enough to have attended if I weren't still testing positive. I may chat with some people during a break outside and from a safe distance.)

A more general thing to point out, and it relates to the fact that I already interacted with Colin several years before he joined the Oxford faculty — I wonder if he remembers my antics during the 'mock tutorial' part of his Oxford interview? — is that I have always admired and enjoyed just how tightly know the British applied-mathematics community is. People across some many of the institutions know each other really well and often "randomly" show up at events in nearby cities even when their affiliations are different. I miss that.

Congratulations to Colin on his retirement!

"How to Move a SIAM Minisymposium Online from the Comfort of your Home"

Several of us wrote a paper, from the perspective of both organizers and speakers, for DSWeb about our efforts to move a SIAM minisymposium online.

Authors: Heather Z. Brooks, Yuxin Chen, Michelle Feng, Yacoub H. Kureh, Mason A. Porter, Alexandria Volkening

An Awesome Ph.D. Defense by Dr. Yacoub Kureh!

Congratulations to my Ph.D. student Yacoub Kureh on an awesome defense of his thesis!

CONGRATULATIONS to Dr. Yacoub Kureh (@Yacoub_Kureh) on a successful and very impressive defense of his PhD thesis, called "Nonlinear opinion models and other networked systems"!!! pic.twitter.com/fXDNIE1GRX

— Mason Porter (@masonporter) May 28, 2020

A Spectacular Ph.D. Thesis Defense by Michelle Feng!

Congratulations to my Ph.D. student Michelle Feng on a superb defense of her thesis!

CONGRATULATIONS to Dr. Michelle Feng (@michellehfeng ) on a successful — and, in fact, spectacular — defense of her Ph.D. thesis, called "Topological Tools for Understanding Complex Systems"!!!!

You will be hearing a lot from her in the future. pic.twitter.com/gpjueTA6CW

— Mason Porter (@masonporter) April 28, 2020

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

"Quantifying “Political Islands” with Persistent Homology"

Here is a new expository article (in SIAM News) by my Ph.D. student Michelle Feng and me about our work on spatial topological data analysis.

I finally get to share my new @TheSIAMNews article (by @michellehfeng and me): "Quantifying “Political Islands” with Persistent Homology"https://t.co/ocpZN43EHg

— Mason Porter (@masonporter) January 28, 2020

You may also be interested in our associated research article and our recent follow-up article.

It's Applied-Mathematician Season

Or possibly duck season?

https://t.co/c0u86Szfc9 pic.twitter.com/6I1rK9viu6

— Conor Finn (@Conor_Finn) November 20, 2019

Awesome Talks by My Students and Postdoc at the Snowbird Conference!

Awesome talks by my students & postdocs at #SIAMDS19!

Heather Brooks (@HZinnbrooks): https://t.co/SDWGU4tTeR

Michelle Feng (@michellehfeng): https://t.co/EpOQTqrsom

Yacoub Kureh (@Yacoub_Kureh): https://t.co/Y31nfpCjm7

Alice Schwarze (@aliceschwarze): https://t.co/k9Ete7BkEv pic.twitter.com/MGojbXkqdH

— Mason Porter (@masonporter) June 10, 2019

RIP Richard Haberman (1945–2018)

I just got the e-mail to the applied dynamical-systems mailing list with the sad news that Rich Haberman died on December 31st. I used his book in a class my sophomore year (and our best TA was his former student from SMU), and then I met him through the Snowbird conferences, partly because he was one of the few senior people who sometimes did poster presentations. Rich was later my host for my job interview at SMU. My tweet below includes the preface of the second edition of his book.

RIP Rich Haberman (1945 – 12/31/2018).

I knew Rich and interacted with him at the Snowbird meetings (and he later hosted me for my job interview at SMU), but I used his PDE book in one of my classes before then.

He was an "unapologetic champion of Applied Mathematics". pic.twitter.com/JmCXkWqsAt

— Mason Porter (@masonporter) January 11, 2019

I'd also like to quote the obituary (written by Alejandro Aceves, Roy Goodman, and Peter Miller) in the e-mail that was sent to SIAM's dynamical-systems mailing list:

We are very sad to have to report that Richard Haberman passed away on December 31, 2018. Richard (Rich) received his BS (1967) and PhD (1971) at MIT. During his time as a graduate student, he met Mark Ablowitz, both of whom had the same advisor David Benney. Rich and Mark established a strong friendship that lasted until Rich's passing. They also co-authored papers which mark the start of Rich's contributions to nonlinear waves. In line with the times they worked on ways to generate isospectral flows which are equivalent to systems of nonlinear partial differential equations, including extensions to two and three dimensions, where as we know there are fewer known integrable models. The role of linear and nonlinear resonances leading to 'universal' evolution equations is best seen in their 1975 Journal of Mathematical Physics paper 'Resonantly coupled nonlinear evolution equations'. It is perhaps this aspect that points to the ease in which Rich's work blends nonlinear waves and dynamical systems in a natural way. More recent work with one of us (Roy Goodman) focused on explaining the two-bounce resonance phenomenon and chaotic scattering in the interaction of solitary waves in near-integrable and nonintegrable systems, which again blends nonlinear waves and dynamical systems.

Rich spent the bulk of his career at Southern Methodist University (SMU). An unapologetic champion of Applied Mathematics, he helped shape the Department of Mathematics to put emphasis in this direction. Throughout his almost 40 years as SMU, he mentored many young faculty, undergraduates, and graduate students. One of us (Peter Miller) was lucky to have been a beneficiary of this mentorship of undergraduates at SMU in the 1980's, and feels especially indebted to Rich for his training in applied mathematics and nonlinear waves in particular and his suggestion and support to continue study in graduate school. At the 2007 ICIAM meeting, he recruited one of us (Alejandro Aceves) to join SMU.

Rich's passion to teach the discipline with an applied flavor is best reflected in his books, most notably his book Elementary Applied Partial Differential Equations which has a world-wide audience and has been translated in many languages. This book is famous for its no-nonsense approach to a difficult subject and its clarity of presentation. Rich served for many years as Editor in Chief for the SIAM book series Mathematical Modeling and Computation. His last unfinished project with one of us (Alejandro Aceves) was to write a textbook in nonlinear dynamics based on many iterations of notes he had produced through the years.

Rich is survived by his wife of 50 years Liz Haberman, his children Ken and Vicki, and his granddaughters Leila, Gwyneth and Chloe. He was dedicated to his family and the profession. He was a friend, scientist, mentor and educator who will be sorely missed. The SMU Department of Mathematics is planning the creation of a scholarship in his name and more information about it will be posted on the Department website.

Which 2-Digit Parent Mathematics Subject Classification Should I Pick as my Primary Classification?

Suppose that you are in the situation that I am in terms of Mathematics Subject Classification, as shown in my tweet below (each term corresponds to one of these), and you are now supposed to pick one of these as your primary classification on the job market. (Note that I am not on the job market, but there was a time long ago when I was a junior scientist and I was faced with this situation.) Which one would you pick?

The Mathematics Subject Classification does an "awesome" job of classifying me: https://t.co/chQW9cCotC

This classification ontology is horrible for applied mathematicians in general, and that can really hurt them on the job market. pic.twitter.com/DnYYBI2Muh

— Mason Porter (@masonporter) November 16, 2018

Applied mathematicians face this all the time (though my own research portfolio is a particularly extreme case of MSC failure) on the job market in their job applications for postdoc and faculty positions in mathematics departments in the United States. They forced to submit the standard American Mathematical Society (AMS) cover sheet, and they are then categorized according to an ontology that fails them utterly. It is systematically unfair to applied mathematicians.

The MSC needs to be revamped.

Congratulations to Dr. Alejandro Martínez!

My doctoral student Alejandro Martínez has now officially finished his D.Phil. (i.e., Ph.D.), with a dissertation called Disordered Granular Crystals.

His thesis work includes several awesome papers, including this one, this one, this one, this one, and this one. (Alejandro also has additional papers from his thesis era that are in collaboration with other people.)

Alejandro is now a postdoctoral scholar in computational biology in Chile.

Referee Reports for the Watts–Strogatz 'Small World' Paper

This is a great document!

Steve Strogatz posted his referee reports (with annotations for their revision plans) about his genre-defining 1998 ‘small world’ paper with Duncan Watts.

It just goes to show that misguided, skeptical reports (see Referee 2 in the upper right) happen to the best of us.

Referee 2 was confused about the implications of the work to systems other than those studied (and possibly even to those applications)…

(The source is Steve's tweet. I posted the picture separately to orient it correctly.)

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.

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.