2024 Gold-Glove Winners

Major League Baseball has announced its 2024 Gold-Glove winners.

What Happens in Seoul Stays in Seoul (2024 Edition)

I am off to Seoul to speak in a workshop on Theoretical Challenges in Network Science! I really enjoy visiting Seoul, and I am very happy to have another chance to visit.

Dodgers Win the 2024 World Series!!!!

The Dodgers have won the 2024 World Series!

Today was the 5th game of the series. The 5-run deficit that the Dodgers overcame is the largest comeback to win a clinching game in World Series history. Walker Buehler came into the 9th inning to get the save two innings after he started game 3. (Gerrit Cole of the Yankees threw more than 100 pitches today. He's the first pitcher to do that in the World Series in either 21 or 27 World Series games. The broadcasters indicated the number in the 6th inning, but I forgot which one it is.) Here is the game's box score.

Obviously, Freddie Freeman was named the series MVP.

Mookie Betts is now the only active player with 3 World Series rings.

I was very happy when the Dodgers won in 2020, but that season has a giant asterisk, and I have been able to enjoy things much more with this year's World Series championship in a proper season.

Thankfully, now that the World Series is over, I won't have to see any more of these damn political commercials anymore this year. Sweet relief.

"Using Mathematics to Study how People Influence Each Other’s Opinions"

Our article for teenagers and preteens about mathematical modeling of opinion dynamics has just been published in final form. Here are some details.

Title: Using Mathematics to Study how People Influence Each Other’s Opinions

Authors: Grace J. Li, Jiajie (Jerry) Luo, Kaiyan Peng, and Mason A. Porter

Abstract: People sometimes change their opinions when they discuss things with each other. Researchers can use mathematics to study opinion changes in simplifications of real-life situations. These simplified scenarios, which are examples of mathematical models, help researchers explore how people influence each other through their social interactions. In today’s digital world, these models can help us learn how to promote the spread of accurate information and reduce the spread of inaccurate information. In this article, we discuss a simple mathematical model of opinion changes that arise from social interactions. We briefly describe what opinion models can tell us and how researchers try to make them more realistic.

RIP Fernando Valenzuela (1960–2024)

Dodger great Fernando Valenzuela died today. I knew that he was really sick and he seemed to be in trouble, but of course I was hoping that he would pull through. Fernando is one of those players that will always be synonymous with the Dodgers, and I was very pleased when the Dodgers finally officially (and belatedly) retired his uniform number in 2023.

You can read more about Fernando Valenzuela on Wikipedia page.

Update: Here is ESPN's article about Valenzuela's death.

Update (10/24/24): I'll add a bit more detail.

For baseball in Los Angeles, Fernando Valenzuela is a legend.

Among other things, he changed the entire fan base of the Dodger organization. He is an absolutely pivotal figure in the history of the Dodgers.

On the performance side, he of course had an incredible beginning and an amazing peak. He started the All Star Game as a rookie, and he's the only player to win the Rookie of the Year and Cy Young Award in the same year. He's also the last MLB player with 20+ complete games in one season.

Update (10/26/24): Here is an obituary article by Jay Jaffe.

What Happens in Atlanta Stays in Atlanta (2024 Edition)

I am heading to Atlanta for the first time since DragonCon 2013. I will be attending the 2024 SIAM Conference on Mathematics of Data Science (MDS), and it even takes place in one of the Dragon*Con hotels. :)

The Dodgers are Going to the World Series!!!

The Dodgers beat the Mets in the 6th game of the National League Championship Series (NLCS), and we're now off to the World Series to face the Yankees!

This is the 12th time that Dodgers and the Yankees (our traditional rivals) are facing each other in the World Series, though it's the first time since 1981.

The Dodgers scored a record number (46) of runs for an NLCS (and the second-highest total for any league championship series), and — I think, if I understood the broadcast correctly — Shohei Ohtani reached base a record number of times for a postseason series.

The NLCS most valuable player (MVP) is Tommy Edman.

Dodgers Advance to the National League Championship Series!

After being on the brink of elimination, the Dodgers beat the Padres 2–0 to advance to the National League Championship Series!!!! We were down 2 games to 1, and we won the next two games to get past the Padres.

There was one home run from Kiké Hernández, and then later there was one home run from Teoscar Hernández. Therefore, it was also Hernández 2, Padres 0.

We'll be facing the Mets in a rematch of the 1988 NLCS.

What Happens in Boston Stays in Boston

I'm on my way to Boston for the workshop to celebrate David Campbell's 80th birthday! It will surely be chaotic. :)

2024 Nobel Prize in Physics Awarded for Applications of Statistical Physics to Machine Learning!

The 2024 Nobel Prize in Physics has been awarded to physicist John Hopfield and computer scientist Geoffrey Hinton.

The official prize citation is "for foundational discoveries and inventions that enable machine learning with artificial neural networks". However, I strongly prefer the phrasing along the lines of "for the statistical-physics basis of neural networks", which is how mathematical physicist Barry Simon described it.

Here is the information, press release, and other materials from The Nobel Foundation.

Naturally, I am strongly in favor of more Nobel Prizes being awarded for foundational interdisciplinary work, as that is the world in which I live. Unsurprisingly, many traditional physicists are arguing against and doing their common practice of staking territorial claim (as we also often see on the job market and in other arenas). This is an old battle, and we can look forward to a later phase when somebody gets a physics Nobel Prize for work in networks. That said, I am grateful to see people arguing about science, rather than about other ideological things!

"Adapting InfoMap to Absorbing Random Walks Using Absorption-Scaled Graphs"

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

Title: Adapting InfoMap to Absorbing Random Walks Using Absorption-Scaled Graphs

Authors: Esteban Vargas Bernal, Mason A. Porter, and Joseph H. Tien

Abstract: InfoMap is a popular approach to detect densely connected "communities" of nodes in networks. To detect such communities, InfoMap uses random walks and ideas from information theory. Motivated by the dynamics of disease spread on networks, whose nodes can have heterogeneous disease-removal rates, we adapt InfoMap to absorbing random walks. To do this, we use absorption-scaled graphs (in which edge weights are scaled according to absorption rates) and Markov time sweeping. One of our adaptations of InfoMap converges to the standard version of InfoMap in the limit in which the node-absorption rates approach 0. We demonstrate that the community structure that one obtains using our adaptations of InfoMap can differ markedly from the community structure that one detects using methods that do not account for node-absorption rates. We also illustrate that the community structure that is induced by heterogeneous absorption rates can have important implications for susceptible–infected–recovered (SIR) dynamics on ring-lattice networks. For example, in some situations, the outbreak duration is maximized when a moderate number of nodes have large node-absorption rates.

Shohei Ohtani Joins the 50/50 Club (and Has One of the Best Single-Game Performances in Baseball History)

Shoehei Ohtani makes a habit of doing things that none of us have ever seen before.

During today's game, he became the inaugural member of the "50/50 Club", as he now has both 50+ home runs and 50+ stolen bases this year. No member of the 50-home-run club had ever stolen even as many as 30 bases before.

He also joined the club in spectular fashion today with a game for the ages. Ohtani's performance today was one of the best single-game performances in Major League Baseball history. He went 6 for 6 with 2 doubles, 3 home runs, 10 runs batted in, 4 runs, and 2 stolen bases. There have been only 16 games in Baseball history in which a player has 10+ RBIs; this is the first one by a Dodger. This is the first time in Baseball history that a player has had 3+ home runs and 2+ stolen bases in the same game.

Since the RBI became an official statistic in 1920, Shohei Ohtani is now the only player in Baseball history who has a game — any game, so they each can occur in different games — in their career with 10+ RBIs, 6+ hits, 5+ extra-base hits, 3+ HRs, and 2+ SBs. Any game. Ohtani did them all in the same game. Amazing!

I have never seen any game like this in my life before.

(P.S. The Dodgers clinched a playoff berth with their victory today.)

2024 Ig Nobel Prizes

The 2024 Ig Nobel Prizes were awarded in a ceremony this evening.

There are so many great ones this year that it's hard to pick my favorites.

What Happens in Ann Arbor Stays in Ann Arbor

I am off to Ann Arbor, Michigan. I'll be visiting University of Michigan to give a colloquium in their Department of Computational Medicine & Bioinformatics.

What Happens in Los Alamos Stays in Los Alamos

I am heading over to Los Alamos for a networks workshop.

That's right. I'll be spending a few days in the wild, wild West.

"Persistent Homology for Resource Coverage: A Case Study of Access to Polling Sites"

One of my paper was published in final form last week. Here are some details.

Title: Persistent Homology for Resource Coverage: A Case Study of Access to Polling Sites

Authors: Abigail Hickok, Benjamin Jarman, Michael Johnson, Jiajie Luo, and Mason A. Porter

Abstract: It is important to choose the geographical distributions of public resources in a fair and equitable manner. However, it is complicated to quantify the equity of such a distribution; important factors include distances to resource sites, availability of transportation, and ease of travel. We use persistent homology, which is a tool from topological data analysis, to study the availability and coverage of polling sites. The information from persistent homology allows us to infer holes in a distribution of polling sites. We analyze and compare the coverage of polling sites in Los Angeles County and five cities (Atlanta, Chicago, Jacksonville, New York City, and Salt Lake City), and we conclude that computation of persistent homology appears to be a reasonable approach to analyzing resource coverage.

What Happens in Glasgow Stays in Glasgow

I am off to Glasgow for the 2024 World Science-Fiction Convention (i.e., WorldCon). I am involved in a talk and some panels.

What Happens in Frankfurt Stays in Frankfurt

I am going to be in Frankfurt for a few days for a workshop on metric networks that I coorganized.

What Happens in Oxford Stays in Oxford

I am off to Oxford to spend most of the next few weeks. I'll also have a short embedded trip to Frankfurt and will be heading to Glasgow after my time in Oxford.

RIP Barry Wellman (1942–2024)

I'm very sad to hear about sociologist Barry Wellman's death.

He was one of the people who welcomed me warmly to the Sunbelt community (though he did make a point to inform me, with much spittle flying in the process, of course, that the Dodgers shouldn't have left Brooklyn).

I figured (but never officially knew) that Barry had been sick for a while, given his sudden lack of activity starting a couple of years ago on Facebook and SOCnet after always making a point of stressing that the point of such social gathering spaces (including social media) was to be very active, so he always purposely did that.

(h/t through the SOCnet mailing list)

RIP Martin Mull (1943–2024)

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.

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.

"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.

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.

"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.

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.)

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

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

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)

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.

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.

"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.

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.

"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.

Want Happens in San Francisco Stays in San Francisco

I am off to San Francisco for the 2024 Joint Mathematics Meetings.

Dodgers Sign Pitcher Yoshinobu Yamamoto!

The Dodgers have signed star pitcher Yoshinobu Yamamoto, who is joining the Majors from Japan. Now we have our ace starting pitcher!

This follows on our recent trade for pitcher Tyler Glasnow and our signing of free agent Shohei Ohtani.

What the Dodgers do is Moneyball with money.

"Human-Network Regions as Effective Geographic Units for Disease Mitigation"

Another of my papers just came out in final form. Here are some details.

Title: "Human-Network Regions as Effective Geographic Units for Disease Mitigation"

Authors: Clio Andris, Caglar Koylu, and Mason A. Porter

Abstract: Susceptibility to infectious diseases such as COVID-19 depends on how those diseases spread. Many studies have examined the decrease in COVID-19 spread due to reduction in travel. However, less is known about how much functional geographic regions, which capture natural movements and social interactions, limit the spread of COVID-19. To determine boundaries between functional regions, we apply community-detection algorithms to large networks of mobility and social-media connections to construct geographic regions that reflect natural human movement and relationships at the county level in the coterminous United States. We measure COVID-19 case counts, case rates, and case-rate variations across adjacent counties and examine how often COVID-19 crosses the boundaries of these functional regions. We find that regions that we construct using GPS-trace networks and especially commute networks have the lowest COVID-19 case rates along the boundaries, so these regions may reflect natural partitions in COVID-19 transmission. Conversely, regions that we construct from geolocated Facebook friendships and Twitter connections yield less effective partitions. Our analysis reveals that regions that are derived from movement flows are more appropriate geographic units than states for making policy decisions about opening areas for activity, assessing vulnerability of populations, and allocating resources. Our insights are also relevant for policy decisions and public messaging in future emergency situations.

2023 Hank Aaron Awards

The 2023 Hank Aaron Awards for the best offensive player in each league have been awarded to Shohei Ohtani (formerly of the Angels and now of the Dodgers) and Ronald Acuña, Jr. (of the Braves).

"Low-Dimensional Behavior of a Kuramoto Model with Inertia and Hebbian Learning"

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

Title: Low-Dimensional Behavior of a Kuramoto Model with Inertia and Hebbian Learning

Authors: Tachin Ruangkriengsin and Mason A. Porter

Abstract: We study low-dimensional dynamics in a Kuramoto model with inertia and Hebbian learning. In this model, the coupling strength between oscillators depends on the phase differences between the oscillators and changes according to a Hebbian learning rule. We analyze the special case of two coupled oscillators, which yields a five-dimensional dynamical system that decouples into a two-dimensional longitudinal system and a three-dimensional transverse system. We readily write an exact solution of the longitudinal system, and we then focus our attention on the transverse system. We classify the stability of the transverse system’s equilibrium points using linear stability analysis. We show that the transverse system is dissipative and that all of its trajectories are eventually confined to a bounded region. We compute Lyapunov exponents to infer the transverse system’s possible limiting behaviors, and we demarcate the parameter regions of three qualitatively different behaviors. Using insights from our analysis of the low-dimensional dynamics, we examine the original high-dimensional system in a situation in which we draw the intrinsic frequencies of the oscillators from Gaussian distributions with different variances.

Shohei Ohtani is Joining the Dodgers!

This is straight from the horse's mouth and is the largest contract in North American sports history.

Jim Leyland Elected to Baseball's Hall of Fame

Former manager Jim Leyland has been elected to Major League Baseball's Hall of Fame in a vote of the Contemporary Baseball Era Non-Players Committee.

"Leyland received 15 of a possible 16 votes (93.8%), while Piniella received 11 (68.8%), White received 10 (62.5%) and Gaston, Johnson, Montague, Peters and West each received fewer than five votes." A candidate needed to receive 12 or more votes (i.e., from at least 75% of the committee) to be elected.

Jay Jaffe wrote a particularly compelling case in favor of Bill White.

Shohei Ohtani Voted Major League Baseball's 2023 Top Designated Hitter

Well, duh.

2023 Relievers of the Year

Félix Bautista of the Baltimore Orioles and Devin Williams of the Milwaukee Brewers are this year's Relievers of the Year in Baseball.

2023 Comeback Players of the Year

Reliever Liam Hendricks of the Chicago White Sox and outfielder (and also infielder, when he was with the Dodgers) Cody Bellinger of the Chicago Cubs have been named Baseball's 2023 Comeback Players of the Year.

"A Density Description of a Bounded-Confidence Model of Opinion Dynamics on Hypergraphs"

Another of my papers has now been published in final form. Here are some details.

Title: A Density Description of a Bounded-Confidence Model of Opinion Dynamics on Hypergraphs

Authors: Weiqi Chu and Mason A. Porter

Abstract: Social interactions often occur between three or more agents simultaneously. Examining opinion dynamics on hypergraphs allows one to study the effect of such polyadic interactions on the opinions of agents. In this paper, we consider a bounded-confidence model (BCM), in which opinions take continuous values and interacting agents compromise their opinions if they are close enough to each other. We study a density description of a Deffuant–Weisbuch BCM on hypergraphs. We derive a rate equation for the mean-field opinion density as the number of agents becomes infinite, and we prove that this rate equation yields a probability density that converges to noninteracting opinion clusters. Using numerical simulations, we examine bifurcations of the density-based BCM's steady-state opinion clusters and demonstrate that the agent-based BCM converges to the density description of the BCM as the number of agents becomes infinite.

"Supracentrality Analysis of Temporal Networks with Directed Interlayer Coupling" (Second Edition)

The unnecessary second edition of the book Temporal Network Theory is now out. It includes a second edition of a chapter that I coauthored. Here are a few details.

Title: Supracentrality Analysis of Temporal Networks with Directed Interlayer Coupling

Authors: Dane Taylor, Mason A. Porter, and Peter J. Mucha

Abstract: We describe centralities in temporal networks using a supracentrality framework to study centrality trajectories, which characterize how the importances of nodes change with time. We study supracentrality generalizations of eigenvector-based centralities, a family of centrality measures for time-independent networks that includes PageRank, hub and authority scores, and eigenvector centrality. We start with a sequence of adjacency matrices, each of which represents a time layer of a network at a different point or interval of time. Coupling centrality matrices across time layers with weighted interlayer edges yields a supracentrality matrix C(ω), where ω controls the extent to which centrality trajectories change with time. We can flexibly tune the weight and topology of the interlayer coupling to cater to different scientific applications. The entries of the dominant eigenvector of C(ω) represent joint centralities, which simultaneously quantify the importances of every node in every time layer. Inspired by probability theory, we also compute marginal and conditional centralities. We illustrate how to adjust the coupling between time layers to tune the extent to which nodes’ centrality trajectories are influenced by the oldest and newest time layers. We support our findings by analysis in the limits of small and large ω.

2023 Most Valuable Player Awards

Major League Baseball has announced its 2023 Most Valuable Players. To nobody's surprise, Shohei Ohtani of the Los Angeles Angels was the unanimous MVP in the Americal League. Also to nobody's surprise, Ronald Acuña, Jr. of the Atlanta Braves won the MVP award handily in the National League. Acuña, Jr. also won the MVP unanimously (which I hadn't expected), and this marks the first time that both MVPs were unanimous. Ohtani is the first baseball player ever to twice be name a unanimous MVP.

The National League MVP voting was interesting. Mookie Betts of the Los Angeles Dodgers got all 30 second-place votes, and Freddie Freeman (Dodgers) and Matt Olson (Braves) split all of the third-place and fourth-place voters (with Freeman getting 17 of the former and 13 of the latter to obtain 4 more points than Olson). Rookie of the Year Corbin Carroll of the Arizona Diamondbacks finished fifth in the voting and garnered 20 of the 30 fifth-place votes.

2023 Cy Young Awards

As with Major League Baseball's awards earlier this week, the 2023 Cy Young Awards were awarded to the expected pitchers. Blake Snell of the San Diego Padres won handily in the National League, and Gerrit Cole of the New York Yankees won unanimously in the American League.

2023 Managers of the Year

The Managers of the Year have been announced. Skip Schumaker of the Miami Marlins won in the National League and Brandon Hyde of the Baltimore Orioles won in the American League.

2023 Rookies of the Year

Baseball's 2023 Rookies of the Year are Gunnar Henderson of the Baltimore Orioles and Corbin Carroll of the Arizona Diamondbacks.

Both selections were unanimous, and it was clear that both selections would either be unanimous or very nearly so (and it was clear that Carroll would win unanimously).

What Happens in San Juan Capistrano Stays in San Juan Capistrano (2023 Edition)

I was just in San Capistrano for a bit more than a day to hang out with friends.

2023 Silver Slugger Awards

The 2023 Silver Slugger awards were announced today. This includes inaugural team awards for the Braves in the National League and the Rangers in the American League.

2023 Gold Glove Awards

Baseball's 2023 Gold Glove Awards were announced today.

What Happens in Pittsburgh Stays in Pittsburgh

I am off to Pittsburgh for a few days!

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.

"Detecting Political Biases of Named Entities and Hashtags on Twitter"

One of my papers came out in final form earlier today. Here are some details. (This is in collaboration with computer scientists, and stylistically it is rather different from much of my work. However, you'll still notice my hand in it. :P)

Title: Detecting Political Biases of Named Entities and Hashtags on Twitter

Authors: Zhiping Xiao, Jeffrey Zhu, Yining Wang, Pei Zhou, Wen Hong Lam, Mason A. Porter, and Yizhou Sun

Abstract: Ideological divisions in the United States have become increasingly prominent in daily communication. Accordingly, there has been much research on political polarization, including many recent efforts that take a computational perspective. By detecting political biases in a text document, one can attempt to discern and describe its polarity. Intuitively, the named entities (i.e., the nouns and the phrases that act as nouns) and hashtags in text often carry information about political views. For example, people who use the term “pro-choice” are likely to be liberal and people who use the term “pro-life” are likely to be conservative. In this paper, we seek to reveal political polarities in social-media text data and to quantify these polarities by explicitly assigning a polarity score to entities and hashtags. Although this idea is straightforward, it is difficult to perform such inference in a trustworthy quantitative way. Key challenges include the small number of known labels, the continuous spectrum of political views, and the preservation of both a polarity score and a polarity-neutral semantic meaning in an embedding vector of words. To attempt to overcome these challenges, we propose the Polarity-aware Embedding Multi-task learning (PEM) model. This model consists of (1) a self-supervised context-preservation task, (2) an attention-based tweet-level polarity-inference task, and (3) an adversarial learning task that promotes independence between an embedding’s polarity component and its semantic component. Our experimental results demonstrate that our PEM model can successfully learn polarity-aware embeddings that perform well at tweet-level and account-level classification tasks. We examine a variety of applications—including a study of spatial and temporal distributions of polarities and a comparison between tweets from Twitter and posts from Parler—and we thereby demonstrate the effectiveness of our PEM model. We also discuss important limitations of our work and encourage caution when applying the PEM model to real-world scenarios.

What Happens at "Snowbird" Stays at "Snowbird"

Today I am off to the "Snowbird Meeting" (aka the SIAM applied-dynamical systems conference) for the latest instantiation of my favorite scientific conference series.

2023 Inductees to the Rock & Roll Hall of Fame

The Rock & Roll Hall of Fame has announced its 2023 inductees.

Of the acts on the ballot this year, the ones for which I cast a vote are Kate Bush (who made it) and Cyndi Lauper, New Order/Joy Division, and Warren Zevon (who didn't).

Song Parody: "They're Still ODEs to Me"

I felt inspired. :)

What Happens at SOCAMS Stays at SOCAMS

Today I am off to Irvine for the 2023 version of the SOCAMS conference to celebrate applied mathematics in Southern California.

What Happens in Vancouver Stays in Vancouver

I am off to Vancouver today for a little while. I'll be giving a talk tomorrow at University of British Columbia, and I'll also be staying with friends and hanging out with them for a while! (On this day 10 years ago, I flew away to visit the same people.)

What Happens in Potsdam Stays in Potsdam

I am heading to Potsdam, NY to partake in the 6th Northeast Regional Conference on Complex Systems.

"Theorems" (to the tune of ' "Heroes" ', by David Bowie)

"Theorems" (to the tune of ' "Heroes" ', by David Bowie)

I, I will be pure
And you, you will use rigor
And nothing will take it away
We can show them, just for one day
We can prove theorems, just for one day

And you, you can have bounds
And I, I'll take infinite time
We're joint authors, and that is a fact
We're coauthors, and that is that
Mathematics'll keep us together
It will not be just for one day
We can prove theorems for ever and ever
What do you say?

I, I wish I could prove
Like my teachers, my teachers can prove
Though sometimes it's hard to keep it together
I can show them, for ever and ever
Oh I can prove Theorems, just for one day

I, I will be pure
And you, you will use rigor
And nothing will take it away
We can prove Theorems, just for one day
We can do it, just for one day

I, I can remember (I remember)
Standing, by the board (by the board)
Arguments, far above our heads (over our heads)
And we tried, and we were never ignored (never ignored)
Our mentors, were always on our side
Oh we can show them, for ever and ever
Then we could prove Theorems, just for one day

We can prove Theorems
We can prove Theorems
We can prove Theorems
Just for one day
We can prove Theorems

We're students, and nothing will help us
Maybe it's hopeless, then you better not stay
But we could graduate, maybe one day

Oh-oh-oh-ohh, oh-oh-oh-ohh, maybe one day?

"An Adaptive Bounded-Confidence Model of Opinion Dynamics on Networks "

An article of mine just appeared in final form a couple of days ago. Here are some details.

Title: An Adaptive Bounded-Confidence Model of Opinion Dynamics on Networks

Authors: Unchitta Kan, Michelle Feng, and Mason A. Porter

Abstract: Individuals who interact with each other in social networks often exchange ideas and influence each other’s opinions. A popular approach to study the spread of opinions on networks is by examining bounded-confidence models (BCMs), in which the nodes of a network have continuous-valued states that encode their opinions and are receptive to other nodes’ opinions when they lie within some confidence bound of their own opinion. In this article, we extend the Deffuant–Weisbuch (DW) model, which is a well-known BCM, by examining the spread of opinions that coevolve with network structure. We propose an adaptive variant of the DW model in which the nodes of a network can (1) alter their opinions when they interact with neighbouring nodes and (2) break connections with neighbours based on an opinion tolerance threshold and then form new connections following the principle of homophily. This opinion tolerance threshold determines whether or not the opinions of adjacent nodes are sufficiently different to be viewed as ‘discordant’. Using numerical simulations, we find that our adaptive DW model requires a larger confidence bound than a baseline DW model for the nodes of a network to achieve a consensus opinion. In one region of parameter space, we observe ‘pseudo-consensus’ steady states, in which there exist multiple subclusters of an opinion cluster with opinions that differ from each other by a small amount. In our simulations, we also examine the roles of early-time dynamics and nodes with initially moderate opinions for achieving consensus. Additionally, we explore the effects of coevolution on the convergence time of our BCM.

The Dodgers are Finally Retiring Fernando Valenzuela's Uniform Number!

It took way too long, but the Los Angeles Dodgers announced today that they are finally retiring Fernando Valenzuela's uniform number. Given what Fernandro means to this franchise and this city, the team should have retired his number a very long time ago.

"The Professional Road that I have Traveled (so far)"

I was asked to write about my career trajectory for DSWeb, so I wrote this short article, which officially has the generic title of "Professional Feature — Mason A. Porter".

I really like my concluding sentence: "I want my mentees to continue to do excellent mentorship and research, be warm and kind-hearted, and not take any crap from anyone."

Scott Rolen Elected to Baseball Hall of Fame!

Yesterday, Scott Rolen was elected to Baseball's Hall of Fame in his 6th year of eligibility. He and Fred McGriff (who was elected to the Hall of Fame by an era committee in December) will be officially inducted into the Hall this summer. I am very pleased that both Rolen and McGriff are now in the Hall of Fame!

Scott Rolen is eminently merits his election, and it's great that he got in after several years of rising vote counts. Todd Helton and Billy Wagner made huge gains this year and should be joining the Hall in 2024. Andruw Jones and Gary Sheffield also made huge gains, although Sheffield is in his last year of eligibility for election by the writers in 2024 and is likely to instead be elected later by an era committee. It now looks like Andruw Jones will likely be elected by the writers in the next few years (but probably not in 2024) after getting under 8% of the vote (!) in his first year of eligibility. Jeff Kent, who was in his 10th and final year of eligibility, surged to 46.5% of the vote and is likely to be elected later by an era committee. Carlos Beltrán debuted on the ballot with 46.5% of the vote (matching Kent). I expect that Beltrán will get up to the high 50s in 2024, have some chance (but unlikely) of election in 2025, and probably be elected in 2026.

A strong set of players is debuting on the Hall ballot for the 2024 cycle. This set of players is led by Adrián Beltré, who will surely be a first-ballot Hall of Famer. Joe Mauer also is debuting on the ballot, but I think it will take 2 or 3 years (most likely 2, in my view) for him to get in. Chase Utley is also debuting in 2024. He'll make it eventually, but his counting stats don't stand out, so it's going to take a few years for him to get in (but I think that he will eventually.)

As in each of the past several years, I was closely tracking the Hall of Fame tracker during the past couple of months as writers released their ballots to the public.

Here is Jay Jaffe's recap of the voting results.

Here are some "way too early" predictions (from Bradford Doolittle David Schoenfield) of Hall of Fame results for the next few cycles. For the most part, my views are far closer to Schoenfield's than the Doolittle's.

Update (1/26/23): Jay Jaffe has written his annual ballot round-up of the candidates on this year's ballot.

Update (1/30/23): Jay Jaffe has written his 5-year Hall prognostication.

What Happens at the Joint Mathematics Meetings Stays at the Joint Mathematics Meetings (2023 Edition)

I am off to the in-person Joint Mathematics Meetings in Boston. I am giving three talks this year.

"The Topology of Data"

Our introduction to a topological data analysis (TDA) for a general physics audience was published today in Physics Today. Here are some details.

Title: The Topology of Data

Authors: Mason A. Porter, Michelle Feng, and Eleni Katifori

Lede: Topological data analysis, which allows systematic investigations of the “shape” of data, has yielded fascinating insights into many physical systems.

"Mixed Logit Models and Network Formation"

One of my papers was just published in final form about a week and a half ago. Here are some details.

Title: Mixed Logit Models and Network Formation

Authors: Harsh Gupta and Mason A. Porter

Abstract: The study of network formation is pervasive in economics, sociology, and many other fields. In this article, we model network formation as a ‘choice’ that is made by nodes of a network to connect to other nodes. We study these ‘choices’ using discrete-choice models, in which agents choose between two or more discrete alternatives. We employ the ‘repeated-choice’ (RC) model to study network formation. We argue that the RC model overcomes important limitations of the multinomial logit (MNL) model, which gives one framework for studying network formation, and that it is well-suited to study network formation. We also illustrate how to use the RC model to accurately study network formation using both synthetic and real-world networks. Using edge-independent synthetic networks, we also compare the performance of the MNL model and the RC model. We find that the RC model estimates the data-generation process of our synthetic networks more accurately than the MNL model. Using a patent citation network, which forms sequentially, we present a case study of a qualitatively interesting scenario—the fact that new patents are more likely to cite older, more cited, and similar patents—for which employing the RC model yields interesting insights.

Fred McGriff Elected to Baseball Hall of Fame!

The Crime Dog (i.e., Fred McGriff) finally has his day, as the latest (and ever-changing) incarnation of a veterans committee has elected him to Baseball's Hall of Fame. Finally!

McGriff was elected unanimously by the 16-member committee. 12 or more votes of the 16-member committee were necessary for election. The other three people who got enough votes for their vote counts to be released are Don Mattingly (8 votes), Curt Schilling (7 votes), and Dale Murphy (6 votes). Everyone else had 3 or fewer votes.

What Happens in San Juan Capistrano Stays in San Juan Capistrano

I am off to San Juan Capistrano to spend the weekend with friends!

"Nanoptera in Higher-Order Nonlinear Schrödinger Equations: Effects of Discretization"

A paper of mine has just been published in final form. Here are some details about it.

Title: Nanoptera in Higher-Order Nonlinear Schrödinger Equations: Effects of Discretization

Authors: Aaron J. Moston-Duggan, Mason A. Porter, and Christopher J. Lustri

Abstract: We consider generalizations of nonlinear Schrödinger equations, which we call “Karpman equations,” that include additional linear higher-order derivatives. Singularly- perturbed Karpman equations produce generalized solitary waves (GSWs) in the form of solitary waves with exponentially small oscillatory tails. Nanoptera are a special type of GSW in which the oscillatory tails do not decay. Previous research on continuous third-order and fourth-order Karpman equations has shown that nanoptera occur in specific settings. We use exponential asymptotic techniques to identify traveling nanoptera in singularly-perturbed continuous Karpman equations. We then study the effect of discretization on nanoptera by applying a finite-difference discretization to continu- ous Karpman equations and examining traveling-wave solutions. The finite-difference discretization turns a continuous Karpman equation into an advance–delay equation, which we study using exponential asymptotic analysis. By comparing nanoptera in these discrete Karpman equations with nanoptera in their continuous counterparts, we show that the oscillation amplitudes and periods in the nanoptera tails differ in the continuous and discrete equations. We also show that the parameter values at which there is a bifurcation between nanopteron solutions and decaying oscillatory solutions depends on the choice of discretization. Finally, by comparing different higher-order discretizations of the fourth-order Karpman equation, we show that the bifurcation value tends to a nonzero constant for large orders, rather than to 0 as in the associated continuous Karpman equation.

2022 Comeback Players of the Year

Baseball's Comeback Players of the Year for 2022 are Justin Verlander of the Detroit Tigers and Albert Pujols of the St. Louis Cardinals.

2022 Most Valuable Player Awards

Major League Baseball's Most Valuable Player (MVP) awards were announced today. There were no surprises. Paul Goldschmidt of the St. Louis Cardinals is the National League MVP, and Aaron Judge of the New York Yankees is the American League MVP.

The complete voting results for both the NL and the AL are available at this Web page.

2022 Cy Young Awards: Both Unanimous!

The 2022 Cy Youngs were announced today, and both of them are unanimous (i.e., received all 1st-place votes). Justin Verlander of the Houston Astros won the American League Cy Young Award, and Sandy Alcántara of the Miami Marlins won the National League Cy Young Award.

I expected Justin Verlander to win, but not to be unanimous. I would have been very surprised if Sandy Alcántara were not unanimous. No other pitchers were anywhere close to Alcántara this year. Only once before have both leagues had unanimous Cy Young Award winners in the same year. That was in 1968, when Denny Mclain won in the AL and Bob Gibson won in the NL.

2022 Managers of the Year

Baseball's 2022 Managers of the Year were announced today. Buck Showalter of the New York Mets is the National League Manager of the Year, and Terry Francona of the Cleveland Guardians is the American League Manager of the Year. This is Showalter's 4th MOY award (with four different teams and in four different decades), and this is Francona's third. Both of them will ultimately end up in the Hall of Fame.

2022 Rookies of the Year

The 2022 Rookies of the Year were announced today. Julio Rodríguez won in the American League in a landslide (no surprise), and Michael Harris II beat out teammate Spencer Strider in the National League.

Some Thoughts on "Statement of Purpose" (SOP) Documents for Graduate-School Applications

Lately, I have been going through statement-of-purpose (SOP) drafts for many UCLA undergraduates, and I have been giving them comments on it.

As a note, I am gearing this predominantly towards mathematics and applied mathematics. In the mathematical sciences in the US, one typically applies directly to graduate programs, rather than to individual faculty members. That entails much freedom in what one wants to work on (in contrast to, e.g., applying to a known project with known funding). Many of my comments should be relevant more broadly, but I wanted to give you this "Surgeon General's Warning" first, as some comments apply most directly to mathematical-science contexts (and especially in the US, as one also often applies directly to faculty or to more specific things in the mathematical sciences in other countries). Also, some parts of what I am writing are more for PhD programs than for Master's programs, but largely these ideas apply to both, aside from certain specifics (such as writing what person you may want as a PhD mentor).

Our students rightly view these documents as pretty mysterious, and these drafts often seem to be presented as chronologies of past experiences. That's not the point, and there is a resume/CV for such things anyway. Some past highlights are certainly relevant, but they need to be in the context of what the student wants to do now, how they got to where they are now and what they want to do, and how this relates to where they are going forward (including the context of the specific university where they are applying to do it). It is common to see too much detail and also to see mind-numbing timelines without the important context. The document should be present-looking and forward-looking.

When I am giving comments on my students' SOPs (along with more general advice on them), the way that I frame this document is as follows:

(1) The document should start with a terse statement of the student's current goal, at whatever level of specificity is accurate for that student. The analogy that I give is the start of a movie, such as an action movie. We start right in the middle of things (possibly in a really tense situation for our hero), and we don't know how they got there. That is also how an SOP should start. For example, I knew that I wanted to do a PhD in applied mathematics (so I applied to PhD programs in applied mathematics and more generally in mathematics) and that I wanted to study something (but I didn't know what) in the topic of dynamical systems. So that is what I said.

(2) One then needs to back up, as in an action movie, and briefly explain/summarize how we got to this point. The chronology and past highlights — including small bits of relevant experience and expertise, but don't overdue it and go at length into too much detail (because you're also submitting a transcript and a resume) — are part of this "backing up" process, but they should specifically be in the context of where one is now. I briefly discussed relevant courses that I had taken and also relevant undergraduate research projects (such as a summer project in geometric mechanics), but again not in too much detail. The idea is to convey how your current interest and goals developed, and past highlights (very specific parts of your personal chronology) can help do that.

(3) Now we have caught up to where our hero is now, and a reader of an SOP has caught up to where the applicant is now. Now you can briefly explain what topics you may want to explore now. That may be a continuation of a subtopic from before, it may be another topic in the same general area, it may be certain applications of that area, or it may be a progression to an adjacent area. Additionally, you don't need to know exactly what you want. Write this bit at whatever level of specificity gives an honest statement of where you are now. If you don't know what you want to work on, it's worth noting that some graduate programs are much more flexible than others. The specificity of what you think you want to work on may influence where you want to apply. Also, notice that I wrote "what you think you want to work on". Your interests will change. Maybe you'll learn about new topics that you didn't encounter before. Maybe some person who seems like a particularly great mentor is another area. Maybe something goes wrong with your intended mentor — unfortunately, this happens way too often — and your interests may change. Flexibility can be a major benefit of a graduate program. In my case, I don't particularly remember what I wrote here, but I expect that mostly just said that I wanted to continue doing dynamical systems. This then leads to connecting these goals and interests to the particular program to which you're applying. That is the next item.

(4) Now you need to briefly indicate why you are a good fit for the specific program to which you're applying, and vice versa. This often takes the form of a short paragraph that is somewhat different for each program to which you apply. For a given type of program (e.g., a PhD program in Mathematics), items (1)--(3) are mostly the same for all of your SOPs. If some programs are slightly different (e.g., some PhD programs and some Master's programs), then there could be two somewhat different versions. In this example, that is one basic one for the Master's programs and one basic one for the PhD programs. OK, I have digressed a bit, so I'll get back to item (4). It's good to indicate in general terms why that program is a good fit for you. In my case, my typical reason was that I wanted to go to places that were both generically "top schools" (where I note the various issues and complications of such a designation) and that were also really strong in applied dynamical systems. For example, that's why I chose to go to Cornell in applied mathematics. For PhD programs, it is also good to indicate potential PhD mentors; indicate who may be a good fit and why. This can simply be a matter of their work being intriguing, but it's good to indicate more direct potential overlap in scientific interests. If possible, listing at least two faculty members is good, and if there is only one person of interest to you, that often may not be the best program choice for you anyway. (See, e.g., my comment above about situations when there are issues with a supervisor.) When the SOP is examined by a committee, the presence of those names may increase the chance that somebody reading your application shows it to those people to ask their views. I have certainly gotten such requests (maybe a handful each year in most years) from my colleagues before. It also shows that you actually looked at the program website and did your homework. That's not bad to convey. Additionally, if there is anything else about the program that appeals to you, it is relevant to briefly mention that as well.

(5) Finally, you're ready to conclude. The movie (i.e., SOP) is about to end, and we need a denouement and the document to end. If you have any thoughts about what you want to do after you get your degree, indicate so. If there is a particular way that the university to which you're applying will help you get there, say that. I think that it's typically best for this text to take the form of a short paragraph. Many people don't know, and that is absolutely fine! But if you do know, it is useful to indicate it. I wanted to go on from my PhD program to a postdoc and then a faculty job, so that's what I said. One can also say that one wants to go to industry, a national lab, do data science for a nonprofit, or whatever else. One can also indicate a couple of these as possibility, since why should most people actually know definitively at this stage.



Good luck!



Note: If I didn't address anything that you feel that would be helpful for me to write in this blog entry, let me know, and I'll add something about it. Or, if I have nothing to say, I can at least remark that the issue exists and point out that I have nothing personal to add.

What Happens in Santa Fe Stays in Santa Fe

I am currently visiting Santa Fe for this event. There is some light snow.

"Analysis of Spatial and Spatiotemporal Anomalies Using Persistent Homology: Case Studies with COVID-19 Data"

I'm posting about one of my papers that was published in journal form a couple of months ago. I waited for a while because the journal made surprise, unwanted changes after the galley-proof stage — and unsurprisingly I objected very strongly to what they did — and I tried and failed to get those surprise changes addressed. They are very small, but they annoy me (and, as a matter of principle, they should not have made surprise wording changes between the version that we approved and the version that we published). Anyway, here are some details about the article.

Title: Analysis of Spatial and Spatiotemporal Anomalies Using Persistent Homology: Case Studies with COVID-19 Data

Authors: Abigail Hickok, Deanna Needell, and Mason A. Porter

Abstract: We develop a method for analyzing spatial and spatiotemporal anomalies in geospatial data using topological data analysis (TDA). To do this, we use persistent homology (PH), which allows one to algorithmically detect geometric voids in a data set and quantify the persistence of such voids. We construct an efficient filtered simplicial complex (FSC) such that the voids in our FSC are in one- to-one correspondence with the anomalies. Our approach goes beyond simply identifying anomalies; it also encodes information about the relationships between anomalies. We use vineyards, which one can interpret as time-varying persistence diagrams (which are an approach for visualizing PH), to track how the locations of the anomalies change with time. We conduct two case studies using spatially heterogeneous COVID-19 data. First, we examine vaccination rates in New York City by zip code at a single point in time. Second, we study a year-long data set of COVID-19 case rates in neighborhoods of the city of Los Angeles.

What Happens in Mountain View Stays in Mountain View

Well, duh.