RIP Gary Lorden (1941–2023)

Gary Lorden, a profesor emeritus of mathematics at Caltech, died last night. In addition to being a mathematics professor, Gary held many leadership positions at Caltech. He was the only statistician in Caltech's math department, and I TAed for him during my junior year in the inaugural edition of the so-called "new core", which included major changes in Math 1 and Math 2. I got my gig as a consultant for the movie "Meet Dave" through Gary. He was also a very kind person.

Update (10/30/23): Caltech has posted a short obituary.

Nicolas Bourbaki and The Traveling Wilburys

Nicolas Bourbaki was basically the mathematics version of The Traveling Wilburys.

What Happens in Providence Stays in Providence

I am heading off to Providence to participate in the first roughly 1.5 days of ICERM's workshop on Mathematical Challenges in Neuroscience Network Dynamics.

A New Secondary Appointment in UCLA's Department of Sociology

As a small bit of career news, I now have a secondary appointment (i.e., a "0% appointment) in UCLA's Department of Sociology, in addition to my primary appointment in the Department of Mathematics. I am looking out to hanging out and otherwise interacting with the sociologists! I guess that I now get to consider myself an honorary sociologist?

"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.

"Recurrence Recovery in Heterogeneous Fermi–Pasta–Ulam–Tsingou Systems"

Another of my papers was published in final form today. Here are some details.

Title: Recurrence Recovery in Heterogeneous Fermi–Pasta–Ulam–Tsingou Systems

Authors: Zidu Li, Mason A. Porter, and Bhaskar Choubey

Abstract: The computational investigation of Fermi, Pasta, Ulam, and Tsingou (FPUT) of arrays of nonlinearly coupled oscillators has led to a wealth of studies in nonlinear dynamics. Most studies of oscillator arrays have considered homogeneous oscillators, even though there are inherent heterogeneities between individual oscillators in real-world arrays. Well-known FPUT phenomena, such as energy recurrence, can break down in such heterogeneous systems. In this paper, we present an approach—the use of structured heterogeneities—to recover recurrence in FPUT systems in the presence of oscillator heterogeneities. We examine oscillator variabilities in FPUT systems with cubic nonlinearities, and we demonstrate that centrosymmetry in oscillator arrays may be an important source of recurrence.

"Non-Markovian Models of Opinion Dynamics on Temporal Networks"

One of my papers was published in final form today. Here are some details.

Title: Non-Markovian Models of Opinion Dynamics on Temporal Networks

Authors: Weiqi Chu and Mason A. Porter

Abstract: Traditional models of opinion dynamics, in which the nodes of a network change their opinions based on their interactions with neighboring nodes, consider how opinions evolve either on time-independent networks or on temporal networks with edges that follow Poisson statistics. Most such models are Markovian. However, in many real-life networks, interactions between individuals (and hence the edges of a network) follow non-Poisson processes and thus yield dynamics with memory-dependent effects. In this paper, we model opinion dynamics in which the entities of a temporal network interact and change their opinions via random social interactions. When the edges have non-Poisson interevent statistics, the corresponding opinion models have non-Markovian dynamics. We derive a family of opinion models that are induced by arbitrary waiting-time distributions (WTDs), and we illustrate a variety of induced opinion models from common WTDs (including Dirac delta distributions, exponential distributions, and heavy-tailed distributions). We analyze the convergence to consensus of these models and prove that homogeneous memory-dependent models of opinion dynamics in our framework always converge to the same steady state regardless of the WTD. We also conduct a numerical investigation of the effects of waiting-time distributions on both transient dynamics and steady states. We observe that models that are induced by heavy-tailed WTDs converge more slowly to a steady state than models that are induced by WTDs with light tails (or with compact support) and that entities with longer waiting times exert more influence on the mean opinion at steady state.

What Happens in Berkeley Stays in Berkeley

In a few hours, I'll have my flight to Oakland and then head over to Berkeley to spend most of September in residence at the institution formerly known as MSRI as part of the semester on Algorithms, Fairness, and Equity!

During this period, I'll spend a couple of days at ICERM for a workshop on mathematical neuroscience. I'll return close to the end of September for the start of our new school year (and will spend my first full day back figuring out what I'll do for the next day's lecture in my graduate-level mathematical-modeling course).

What Happens in Seoul Stays in Seoul

I have a couple-day pitstop in Seoul before heading back to LA.

What Happens in Tokyo Stays in Tokyo

Today I am off to Tokyo, where I will be participating in the ICIAM 2023 conference.

I'll be giving a talk on Monday.

What Happens in Daejeon Stays in Daejeon

I am flying to Asia for a couple of conferences. My first stop is Daejeon for an ICIAM satellite conference on stochastic modeling and data analysis for biological systems.

Fernando Valenzuela's Number is Finally Getting Retired Tonight!

Tonight the Los Angeles Dodgers are finally retiring Fernando Valenzuela's number 34. This is long overdue. Fernando is a Los Angeles icon.

No Dodger has worn Fernando's number since he left the team, and now no other Dodger will ever wear it again.

Update: Here is ESPN.com's article about the jersey retirement ceremony.

What Happens in Sunnyvale Stays in Sunnyvale

I am off to Sunnyvale for the weekend to attend the wedding of one of my former Ph.D. students. I have many friends in the area, so I will also hang out with some of them, given that I'll already be in the area.

RIP Sinéad O'Connor (1966–2023)

Sinéad O'Connor has died.

She was only 56. But, to be honest, I am surprised that she lasted this long. She seemed to always be struggling.

You can read more about her in her Wikipedia entry.

What Happens in Richland Stays in Richland

I'll soon be visiting Pacific Northwest National Laboratory as part of a Directory Advisory Committee.

Serendipitous Convergence of the Dodgers and Tarzan Boy

On a few occasions this year, I had noticed the Dodger organist playing Tarzan Boy, and I was wondering why.

I had thought it was for something like certain leaping catches in the outfield, but it turns out that it is specifically for rookie James Outman. I figured that out last night because they played it when he got a hit in his first at bat. (I revised my opinion from seeing this when Outman was at the plate and running for a hit, with his locks flowing.) I thought it might have been because of his luxuriantly flowing hair.

I decided to google it to confirm whether I was right, and indeed Tarzan Boy is played specifically for good James Outman action, although it seems to actually be because of a nickname that is catching on. (I hadn't known about eh nickname.)

I am very amused by the fact that this is a convergence between the Dodgers and Tarzan Boy, given how many people from my Lloyd House days at Caltech would associate each of those two things individually with me.

What Happens in Dallas Stays in Dallas

Well, unfortunately, I won't be making my connection (annoying flight delay), and I will be staying an unintended night in Dallas before resuming my journey in the morning.

But at least I won't be liveblogging from the Dallas airport, as I did 16 years ago.

"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.

"Lonely Individuals Process the World in Idiosyncratic Ways"

One of my papers that came out a couple of months ago now also has its final volume and page numbers. Here are some details about the article.

Title: Lonely Individuals Process the World in Idiosyncratic Ways

Authors: Elisa C. Baek, Ryan Hyon, Karina López, Meng Du, Mason A. Porter, and Carolyn Parkinson

Abstract: Loneliness is detrimental to well-being and is often accompanied by self-reported feelings of not being understood by other people. What contributes to such feelings in lonely people? We used functional MRI of 66 first-year university students to unobtrusively measure the relative alignment of people’s mental processing of naturalistic stimuli and tested whether lonely people actually process the world in idiosyncratic ways. We found evidence for such idiosyncrasy: Lonely individuals’ neural responses were dissimilar to those of their peers, particularly in regions of the default-mode network in which similar responses have been associated with shared perspectives and subjective understanding. These relationships persisted when we controlled for demographic similarities, objective social isolation, and individuals’ friendships with each other. Our findings raise the possibility that being surrounded by people who see the world differently from oneself, even if one is friends with them, may be a risk factor for loneliness.

What Happens in Beaver Hollow Stays in Beaver Hollow

I am off to Beaver Hollow for our 2023 Mathematics Research Community on Complex Social Systems.