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.

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.

Friday, May 31, 2024

What Happens in Warsaw Stays in Warsaw

I am heading to Warsaw to participate a couple of days in the WAW 2024 conference. This is my first trip to Poland in several years, and unfortunately it's going to be very brief.

Wednesday, May 22, 2024

"Inference of Interaction Kernels in Mean-Field Models of Opinion Dynamics"

A paper of mine just came out in final form. Here are some details about it.

Title: Inference of Interaction Kernels in Mean-Field Models of Opinion Dynamics

Authors: Weiqi Chu, Qin Li, and Mason A. Porter

Abstract: In models of opinion dynamics, many parameters — either in the form of constants or in the form of functions — play a critical role in describing, calibrating, and forecasting how opinions change with time. When examining a model of opinion dynamics, it is beneficial to infer its parameters using empirical data. In this paper, we study an example of such an inference problem. We consider a mean-field bounded-confidence model with an unknown interaction kernel between individuals. This interaction kernel encodes how individuals with different opinions interact and affect each other's opinions. Because it is often difficult to quantitatively measure opinions as empirical data from observations or experiments, we assume that the available data takes the form of partial observations of a cumulative distribution function of opinions. We prove that certain measurements guarantee a precise and unique inference of the interaction kernel and propose a numerical method to reconstruct an interaction kernel from a limited number of data points. Our numerical results suggest that the error of the inferred interaction kernel decays exponentially as we strategically enlarge the data set.

Saturday, April 27, 2024

Shōgun (2024)

I just finished watching the 2024 Shōgun, which I enjoyed very much.

I read the book around December 1988 — followed over the next years of reading every single other Asia-saga novel that James Clavell wrote — during my elementary school's winter break. I was so captivated that that was basically all I did during that winter break. I was already a slow reader back then, and now I read much more slowly than I did back then. (I also don't have time to basically only read a book nonstop for a couple of weeks.) I was fascinated by the epic combined with the portrayal of how East and West saw each other through their interactions. This was the first book in my life that had ever captivated me that way, and I was really excited when I saw a poster for the new miniseries a few months ago.

The 2024 series did a great job of capturing that, and it was aspects of those interactions and contrasting views (and part of the scene of peeing in a garden to consummate an agreement, and I am pretty sure that I know which scene in the new tv series corresponds to that vignette) that really stood out to me. However, most of this runs together through all of Clavell's works, and I can't really separate Shōgun from the others. I had forgotten almost all of the plot, but from Wikipedia it seems that the new series adapted it very well.

I never watched the 1980 miniseries. There was a 1988 miniseries of Nobel House. I also never watched that one, but I did notice Shōgun and Tai-Pan (and knew that Nobel House was by the same author, and Tai-Pan also caught my eye because of the Apple II game of almost the same name that was inspired by the novel) on a bookshelf in my parents' house (nobody else in the household had read these epic books), so I picked up Shōgun, which became an important part of my own personal history, even though I forgot so much of it.

I suppose that a new Nobel House miniseries may be possible? That one, too, was a particularly awesome book. (I also enjoyed the others, although I gave up on Tai-Pan the first time and started over and read it only a couple of years after, because I could put up with the rougher writing of that earlier work with the thoughts of it as a prequel to Nobel House.)

Friday, April 12, 2024

What Happens in San Francisco Stays in San Francisco (again)

I am heading to San Francisco for a cousin's wedding.

Thursday, April 11, 2024

RIP David Goodstein (1939–2024)

David Goodstein (an emeritus physics professor at Caltech) died yesterday. This is the end of an era.

I watched many of The Mechanical Universe videos in high school. The beginning and end of each video showed Goodstein lecturing to students in the big Caltech physics lecture hall. I had Goodstein for Physics 1a (mechanics) in fall of my frosh year in that same lecture hall, and I remember how surreal it felt. That was one of my big "Wow, I am now at Caltech." things. Also, I came out of lectures feeling that I understood the material — but then I tried the homework and saw that I didn't actually yet understand it.

(h/t Barry Simon)

Tuesday, March 26, 2024

What Happens in Hanover Stays in Hanover

I am heading to New Hampshire for the first time ever. I'll be in Hanover to give the mathematics colloquium at Dartmouth College.

Monday, March 18, 2024

What Happens in New York City Stays in New York City

I'm heading off to New York City for the first time in many years. I'll be giving a talk at The Rockefeller University.

Tuesday, February 27, 2024

"Complex Networks with Complex Weights"

The published version of one of my papers came out today. Its title is one of my favorites among all of the papers that I've ever written. Here are some details about the paper.

Title: Complex Networks with Complex Weights

Authors: Lucas Böttcher and Mason A. Porter

Abstract: In many studies, it is common to use binary (i.e., unweighted) edges to examine networks of entities that are either adjacent or not adjacent. Researchers have generalized such binary networks to incorporate edge weights, which allow one to encode node–node interactions with heterogeneous intensities or frequencies (e.g., in transportation networks, supply chains, and social networks). Most such studies have considered real-valued weights, despite the fact that networks with complex weights arise in fields as diverse as quantum information, quantum chemistry, electrodynamics, rheology, and machine learning. Many of the standard network-science approaches in the study of classical systems rely on the real-valued nature of edge weights, so it is necessary to generalize them if one seeks to use them to analyze networks with complex edge weights. In this paper, we examine how standard network-analysis methods fail to capture structural features of networks with complex edge weights. We then generalize several network measures to the complex domain and show that random-walk centralities provide a useful approach to examine node importances in networks with complex weights.

Tuesday, January 23, 2024

Adrián Beltré, Todd Helton, and Joe Mauer Elected to Baseball Hall of Fame!

Adrián Beltré, Todd Helton, and Joe Mauer have been elected to the Major Legaue Baseball Hall of Fame! I knew that Mauer would make the Hall of Fame eventually, but he far surpassed my prediction for how he was going to do this year. I am pleasantly surprised to see him make the Hall on the first ballot, as I thought that he would need to wait a year or two to be elected. Adrián Beltré obviously sailed into the Hall on the first ballot.

Billy Wagner, who was named on 73.8% of the ballots, missed election to the Hall by only 5 votes. He'll make it in 2025, which is his 10th and final year on the writers' ballot. Gary Sheffield was named on 63.9% of the ballots in his final year on the writers' ballot. His Hall case is now in the hands of the various small commitees, and I think (and hope) that he'll make it eventually. Andruw Jones had a small gain to 61.6% and Carlos Beltrán made a sizeable gain to 57.1%. Beltrán has an outside shot to be elected in 2025, but I think that 2026 is more likely. Andruw Jones could also ultimately make it through the writers' ballot, but I think that Beltrán will surpass Jones in the vote total in 2025. One way or another, they'll both eventually make the Hall of Fame. Chase Utley got 28.8% of the vote in his debut on the ballot. He did much better in the public ballots than in the private ones. I do think that Utley will eventually make it, but it's going to be a long road for the more sabermetrically-minded folks to convince others that Utley belongs in the Hall of Fame.

In December, a small committee elected former manager Jim Leyland to the Hall of Fame.

As usual, I have been following the ballot tracker very closely these past couple of months.

A discussion of a few ESPN.com writers of this year's biggest winners and biggest losers, as well as an outlook on the 2025 ballot.

Of the players who can debut on the writers' ballot in 2025, the only plausible Hall of Fame candidates are Ichiro Suzuki and C.C. Sabathia. Ichiro will sail into the Hall of Fame in his ballot debut (and hopefully he'll be elected unanimously, but I am not holding my breath). Sabathia will eventually make it, but I think that it's going to take a few years (say, 4 years).

Update (which I forgot to include in the original text of this post): My prediction for the 2025 balloting is that Ichiro Suzuki and Billy Wagner will be the two players elected. I think that Carlos Beltrán will get around 70% of the vote next year and that Andruw Jones will be in the mid 60s (perhaps around 66%). I think that Chase Utley will probably end up at about 35%. Utley's candidacy appears to be the latest battle in the considerations of old-school versus new-school voters.

Update: Jay Jaffe has written a rundown of the results of this year's writers' ballot.

Update (1/24/24): Here is Jay Jaffe's candidate-by-candidate dissection of this year's writers' ballot.

Update (1/29/24): Here is Jay Jaffe's five-year forecast of Hall of Fame balloting.

Thursday, January 04, 2024

"Learning Low-Rank Latent Mesoscale Structures in Networks"

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

Title: Learning Low-Rank Latent Mesoscale Structures in Networks

Authors: Hanbaek Lyu, Yacoub H. Kureh, Joshua Vendrow, and Mason A. Porter

Abstract: Researchers in many fields use networks to represent interactions between entities in complex systems. To study the large-scale behavior of complex systems, it is useful to examine mesoscale structures in networks as building blocks that influence such behavior. In this paper, we present an approach to describe low-rank mesoscale structures in networks. We find that many real-world networks possess a small set of latent motifs that effectively approximate most subgraphs at a fixed mesoscale. Such low-rank mesoscale structures allow one to reconstruct networks by approximating subgraphs of a network using combinations of latent motifs. Employing subgraph sampling and nonnegative matrix factorization enables the discovery of these latent motifs. The ability to encode and reconstruct networks using a small set of latent motifs has many applications in network analysis, including network comparison, network denoising, and edge inference.

Tuesday, January 02, 2024