Comedic actor, musician, and painter Martin Mull dies yesterday.
I found out about him via the song "Dueling Tubas", which I first learned about in Physics 2a through an acoustics demo by now-Nobel Laureate David Politzer.
My musically-inclined classmates were in emotional pain.
My name is Mason Porter. I am a Professor in the Department of Mathematics at UCLA. Previously I was Professor of Nonlinear and Complex Systems in the Mathematical Institute at University of Oxford. I was also a Tutorial Fellow of Somerville College.
Friday, June 28, 2024
Tuesday, June 18, 2024
RIP Willie Mays (1931–2024)
The legendary Willie Mays died today. Mays was the oldest living baseball Hall of Famer; he took the mantle in 2021 when Tommy Lasorda died. You can see Willie Mays' statistics on this page.
I believe that Luis Aparicio is now the oldest living baseball Hall of Famer.
I believe that Luis Aparicio is now the oldest living baseball Hall of Famer.
Friday, June 14, 2024
"Emergence of Polarization in a Sigmoidal Bounded-Confidence Model of Opinion Dynamics"
A paper of mine was just published in final form. Here are zome details.
Title: Emergence of Polarization in a Sigmoidal Bounded-Confidence Model of Opinion Dynamics
Authors: Heather Z. Brooks, Philip S. Chodrow, and Mason A. Porter
Abstract: We study a nonlinear bounded-confidence model (BCM) of continuous-time opinion dynamics on networks with both persuadable individuals and zealots. The model is parameterized by a nonnegative scalar \gamma, which controls the steepness of a smooth influence function. This influence function encodes the relative weights that individuals place on the opinions of other individuals. When \gamma = 0, this influence function recovers Taylor's averaging model; when \gamma \rightarrow \infty, the influence function converges to that of a modified Hegselmann--Krause (HK) BCM. Unlike the classical HK model, however, our sigmoidal bounded-confidence model (SBCM) is smooth for any finite \gamma. We show that the set of steady states of our SBCM is qualitatively similar to that of the Taylor model when \gamma is small and that the set of steady states approaches a subset of the set of steady states of a modified HK model as \gamma \rightarrow \infty. For certain special graph topologies, we give analytical descriptions of important features of the space of steady states. A notable result is a closed-form relationship between graph topology and the stability of polarized states in a simple special case that models echo chambers in social networks. Because the influence function of our BCM is smooth, we are able to study it with linear stability analysis, which is difficult to employ with the usual discontinuous influence functions in BCMs.
Title: Emergence of Polarization in a Sigmoidal Bounded-Confidence Model of Opinion Dynamics
Authors: Heather Z. Brooks, Philip S. Chodrow, and Mason A. Porter
Abstract: We study a nonlinear bounded-confidence model (BCM) of continuous-time opinion dynamics on networks with both persuadable individuals and zealots. The model is parameterized by a nonnegative scalar \gamma, which controls the steepness of a smooth influence function. This influence function encodes the relative weights that individuals place on the opinions of other individuals. When \gamma = 0, this influence function recovers Taylor's averaging model; when \gamma \rightarrow \infty, the influence function converges to that of a modified Hegselmann--Krause (HK) BCM. Unlike the classical HK model, however, our sigmoidal bounded-confidence model (SBCM) is smooth for any finite \gamma. We show that the set of steady states of our SBCM is qualitatively similar to that of the Taylor model when \gamma is small and that the set of steady states approaches a subset of the set of steady states of a modified HK model as \gamma \rightarrow \infty. For certain special graph topologies, we give analytical descriptions of important features of the space of steady states. A notable result is a closed-form relationship between graph topology and the stability of polarized states in a simple special case that models echo chambers in social networks. Because the influence function of our BCM is smooth, we are able to study it with linear stability analysis, which is difficult to employ with the usual discontinuous influence functions in BCMs.