"Long-Time and Short-Time Dynamics in a Weighted-Median Opinion Model on Networks"

One of my papers was published in final form late last month. Here are some details.

Title: Long-Time and Short-Time Dynamics in a Weighted-Median Opinion Model on Networks

Authors: Lasse Mohr, Poul G. Hjorth, and Mason A. Porter

Abstract: Social interactions influence people's opinions. In some situations, these interactions eventually yield a consensus opinion; in others, they can lead to opinion fragmentation and the formation of different opinion groups in the form of "echo chambers". Consider a social network of individuals with continuous-valued scalar opinions, and suppose that they can change their opinions when they interact with each other. In many models of the opinion dynamics of individuals in a network, it is common for opinion updates to depend on the mean opinion of interacting individuals. As an alternative, which may be more realistic in some situations, we study an opinion model with an opinion-update rule that depends on the weighted median of the opinions of interacting individuals. Through numerical simulations of our median-update opinion model, we investigate how the final opinion distribution depends on network structure. For configuration-model networks, we derive a mean-field approximation of the asymptotic dynamics of the opinion distribution when there are infinitely many individuals. We numerically investigate its accuracy for short-time opinion dynamics on various networks.

What Happens in Frankfurt Stays in Frankfurt

I am off to Frankfurt for a workshop on analog computing.

What Happens in Boston Stays in Boston

I am off to Boston to speak in the satellite conference on Physical Networks at the 2026 NetSci conference. (It's my triumphant return to NetSci!) As usual, I also helped organize the satellite conference on Network Science in Education (NetSciEd 2026).

"Ginzburg–Landau Functionals in the Large-Graph Limit"

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

Title: Ginzburg–Landau Functionals in the Large-Graph Limit

Authors: Edith J. Zhang, James Scott, Qiang Du, and Mason A. Porter

Abstract: Ginzburg–Landau (GL) functionals on graphs, which are relaxations of graph-cut functionals on graphs, have yielded a variety of insights in image segmentation and graph clustering. In this paper, we study large-graph limits of GL functionals by taking a functional-analytic view of graphs as nonlocal kernels. For a graph W_n with n nodes, the corresponding graph GL functional GL_ϵ^{W_n} is an energy for functions on W_n. We minimize GL functionals on sequences of growing graphs that converge to functions called graphons. For such sequences of graphs, we show that the graph GL functional Γ-converges to a continuous and nonlocal functional that we call the graphon GL functional. We investigate the sharp-interface limits of the graph GL and graphon GL functionals, and we relate these limits to a nonlocal total-variation (TV) functional. We express the limiting GL functional in terms of Young measures and thereby obtain a probabilistic interpretation of the minimization problem in the large-graph limit. Finally, to develop intuition about graphon GL functionals, we determine the GL minimizer for several example families of graphons.

What Happens in Santa Fe Stays in Santa Fe

I am off to Santa Fe to visit the Santa Fe Institute for a couple of weeks!

2026 Rock & Roll Hall of Fame Inductees

The Rock & Roll Hall of Fame has announced its 2026 inductess. They include Joy Division/New Order, Billy Idol, Phil Collins, Oasis, and others.

What Happens in the Bay Area Stays in the Bay Area

I am heading off to the Bay Area for a relative's bar mitzvah, with a game of Paranoia on the side. The Computer is my friend.