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).