"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.

Albert Pujols Hits 700th Career Home Run!

Albert Pujols just became the 4th player in Major League history with 700 or more career home runs (in the regular season). He hit a 2-run homer against the Dodgers in the 3rd and then a 3-run homer against the Dodgers in the 4th. Now we need to work to erase that 5-run deficit. Obviously, congratulations to Albert! What a career!

Yadier Molina and Adam Wainwright Make their Record 325th Start as Battery-Mates

Yadier Molina and Adam Wainwright of the St. Louis Cardinals started their record 325th game as battery-mates. They tied the old record last week. Take a look at the Wikipedia page for "battery (baseball)" to see the other top battery-mates.

The new record is going to stand as the record for a very long time, and I'm not sure if it will ever be broken.

Additionally, quoting the ESPN.com article above: "Only six current major league players — Albert Pujols, Nelson Cruz, Miguel Cabrera, Zack Greinke, Rich Hill and Justin Verlander — were active when Wainwright and Molina made their first start together."

What Happens in Milwaukee Stays in Milwaukee

I am in Milwaukee to give a talk at Marquette tomorrow (and also to see a double-header between the Brewers and the Giants in my first in-person baseball game since before the pandemic). (We arrived during the 6th inning of the first game.) Today was the first non-COVID double-header had Miller Park since 2000. This visit, which was originally slated for May, is my first time in Wisconsin. I have already had some frozen custard, of course.

An Infinite Loop in the Game Dominion

I managed to construct an infinite loop in Dominion: I am going to break the infinite loop, but you can see in the attached that my turn will last infinitely long if I keep using the 'Shepherd' function that I attached to Estates with Inheritance.

Also, I am almost guaranteed mathematically to be able to do this every turn (and get a Province if I choose to stop); this probability does lessen slightly with each new Province that I acquire. I also pick up a new Estate every turn by using my Hill Fort.

RIP Abdul-Aziz Yakubu (1958–2022)

A couple of weeks ago, I heard the very sad and unexpected news that Abdul-Aziz Yakubu had died. Aziz was great.

Like others, I also have some Aziz stories (but the one that I wanted to tell seemed a bit too light-hearted to tell immediately on social media): I know Aziz from my days helping out with MTBI as a PhD student. On one occasion, when somebody — one of the students? — was being a bit formal with my name as I entered a room and was also using my last name or something, I made the mistake of loudly proclaiming "I'm like Madonna. I only need one name." With a quietly wicked sense of humor (and with the knowledge that we'd all be amused by this, including me), Aziz proceeded to jokingly call me "Mason Madonna" for the next several years.

You can read more about Aziz in his 2020 Mathematically Gifted & Black profile.

RIP Vin Scully (1927–2022)

I'm watching the game, and the Dodger broadcasters announced about 20 or so minutes ago that broadcasting legend Vin Scully died today. (Scully's death was announced by the Dodgers in the tweet to which I just linked, along with other simultaneous social-media posts.) Vin was the greatest broadcaster who ever lived. I listened to Vin broadcast literally thousands of games across four decades. Vin was one of the key voices of my childhood (and much of my adulthood). For so long, Vin was not only the voice of the Dodgers, but was also (along with Tommy Lasorda) the pulse of the Dodgers.

Here is Vin's Wikipedia page.

Update: ESPN has now posted an article about Vin Scully's death.

RIP James Lovelock (1919–2022)

James Lovelock, who proposed the Gaia hypothesis (which postulates that the Earth functions as a self-regulating system) died today. You can read more about him on his Wikipedia page.

When I was in high school, I did a report on the Gaia hypothesis. I suppose that that was my start in complex systems?

(Tip of the cap to Alun Lloyd.)

What Happens at Santa Fe Institute Stays at Santa Fe Institute

I am heading off to Santa Fe Institute (SFI) for a bit.

RIP Pogo (1998–2022)

Pogo, the infamous cat of Somerville College, died on 26 June at the wizened age of 23 years and 10 months. Pogo's ashes will be scattered in his favorite spot in College just after the memorial for Dame Fiona Caldicott (who, of course, was Pogo's alter ego). That is immensely fitting.

RIP Mike Brito (1934–2022)

Longtime Dodger scout Mike Brito died today. For many years, Brito was a familiar sight behind the dugout with his cigar.

Retirement Conference for Colin Please

Unfortunately, I just checked and I am still COVID positive, so regrettably I will be missing the retirement conference and party for my Oxford colleague Colin Please. (Alhough I am far from perfect, I feel well enough to have attended if I weren't still testing positive. I may chat with some people during a break outside and from a safe distance.)

A more general thing to point out, and it relates to the fact that I already interacted with Colin several years before he joined the Oxford faculty — I wonder if he remembers my antics during the 'mock tutorial' part of his Oxford interview? — is that I have always admired and enjoyed just how tightly know the British applied-mathematics community is. People across some many of the institutions know each other really well and often "randomly" show up at events in nearby cities even when their affiliations are different. I miss that.

Congratulations to Colin on his retirement!

"Networks of Necessity: Simulating COVID-19 Mitigation Strategies for Disabled People and Their Caregivers"

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

Title: Networks of Necessity: Simulating COVID-19 Mitigation Strategies for Disabled People and Their Caregivers

Authors: Thomas E. Valles, Hannah Shoenhard, Joseph Zinski, Sarah Trick, Mason A. Porter, and Michael R. Lindstrom

Abstract: A major strategy to prevent the spread of COVID-19 is the limiting of in-person contacts. However, limiting contacts is impractical or impossible for the many disabled people who do not live in care facilities but still require caregivers to assist them with activities of daily living. We seek to determine which interventions can best prevent infections of disabled people and their caregivers. To accomplish this, we simulate COVID-19 transmission with a compartmental model that includes susceptible, exposed, asymptomatic, symptomatically ill, hospitalized, and removed/recovered individuals. The networks on which we simulate disease spread incorporate heterogeneity in the risk levels of different types of interactions, time-dependent lockdown and reopening measures, and interaction distributions for four different groups (caregivers, disabled people, essential workers, and the general population). Of these groups, we find that the probability of becoming infected is largest for caregivers and second largest for disabled people. Consistent with this finding, our analysis of network structure illustrates that caregivers have the largest modal eigenvector centrality of the four groups. We find that two interventions—contact-limiting by all groups and mask-wearing by disabled people and caregivers—most reduce the number of infections in disabled and caregiver populations. We also test which group of people spreads COVID-19 most readily by seeding infections in a subset of each group and comparing the total number of infections as the disease spreads. We find that caregivers are the most potent spreaders of COVID-19, particularly to other caregivers and to disabled people. We test where to use limited infection-blocking vaccine doses most effectively and find that (1) vaccinating caregivers better protects disabled people from infection than vaccinating the general population or essential workers and that (2) vaccinating caregivers protects disabled people from infection about as effectively as vaccinating disabled people themselves. Our results highlight the potential effectiveness of mask-wearing, contact-limiting throughout society, and strategic vaccination for limiting the exposure of disabled people and their caregivers to COVID-19.

What Happens in the United Kingdom Stays in the United Kingdom

I arrived in Oxford a bit over a week ago, but I forgot to blog about it. I then visited friends in Newcastle during the weekend and returned to Oxford on Monday. Unfortunately, I caught COVID and have thus delayed my return flight to the US. I am currently in a room in Somerville College (in Oxford) struggling through COVID and gradually (but bumpily) improving.

What Happens in Stockholm Stays in Stockholm

I am about to head to Stockholm for a networks conference that we were supposed to have in 2020. Only a bit late!

This is my first international flight during the COVID era. Meanwhile, I'll also be desperately trying to grade my final projects and finally finish the academic year.

RIP Roger Angell (1920–2022)

Famed writer and editor Roger Angell has died at age 101. Take a look at this article. I hadn't realized it before reading this article, but Angell is from quite a famous family.

Here is Angell's Wikipedia entry.

"How Do Our Brains Support Our Friendships?"

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

Title: How Do Our Brains Support Our Friendships?

Authors: Elisa C. Baek, Ryan Hyon, Mason A. Porter, and Carolyn Parkinson

Abstract: Have you ever wondered how your friends impact how you see the world? Or how you are able to keep track of the many different people in your life? To study these questions, scientists have begun to look at people’s social networks and their brains at the same time. In this article, we introduce this area of study and discuss how scientists use ideas from both neuroscience and mathematics to examine these questions. We also highlight some recent discoveries that reveal both how our brains support our ability to socialize with others and how our relationships with other people are related to how we use our brains.

What Happens in Davis Stays in Davis.

I am off to a short workshop at UC Davis.

However, I just almost accidentally boarded a flight to Hawaii.

I am flying to Sacramento for the workshop at UC Davis.

[I also just noticed: One of the PhD students in my class is actually here and probably on the same flight.]

A Great Visual Illusion: Radiating the Same Luminance

This is a great visual illusion.

The top and bottom chess pieces radiate the same luminance. (I did some sampling to check, and it seems to check out.)

(Tip of the cap to Luiz Pessoa.)

2022 Rock & Roll Hall of Fame Inductees

The Rock & Roll Hall of Fame has announced its 2022 inductees! They include Duran Duran, Eurythmics, Pat Benatar, and Harry Belafonte.

"Topological Data Analysis of Spatial Systems"

A book chapter of ours was just published in final form. It is Chapter 16 in this book. Here are some other details about it.

Title: Topological Data Analysis of Spatial Systems

Authors: Michelle Feng, Abigail Hickok, and Mason A. Porter

Abstract: In this chapter, we discuss applications of topological data analysis (TDA) to spatial systems. We briefly review a recently proposed level-set construction of filtered simplicial complexes, and we then examine persistent homology in two cases studies: street networks in Shanghai and anomalies in the spread of COVID-19 infections. We then summarize our results and provide an outlook on TDA in spatial systems.

"Role Detection in Bicycle-Sharing Networks Using Multilayer Stochastic Block Models"

A new paper of mine was published in final form today. The project started in January 2017 as a group project by students in the first course that I ever taught at UCLA. It's taken awhile, but we're finally done!

Title: Role Detection in Bicycle-Sharing Networks Using Multilayer Stochastic Block Models

Authors: Jane Carlen†, Jaume de Dios Pont, CassidyMentus, Shyr-Shea Chang, Stephanie Wang, and Mason A. Porter

Abstract: In urban systems, there is an interdependency between neighborhood roles and transportation patterns between neighborhoods. In this paper, we classify docking stations in bicycle-sharing networks to gain insight into the human mobility patterns of three major cities in the United States. We propose novel time-dependent stochastic block models, with degree-heterogeneous blocks and either mixed or discrete block membership, which classify nodes based on their time-dependent activity patterns. We apply these models to (1) detect the roles of bicycle-sharing stations and (2) describe the traffic within and between blocks of stations over the course of a day. Ourmodels successfully uncover work blocks, home blocks, and other blocks; they also reveal activity patterns that are specific to each city. Our work gives insights for the design and maintenance of bicycle-sharing systems, and it contributes new methodology for community detection in temporal and multilayer networks with heterogeneous degrees.

A Gallery of Ancience d20 Dice

Here is a gallery of ancient d20 dice. I love it! (It includes the one that I discussed in this post. Also see this post and this post. The second of these also showed up in a previous post.

Also, this reminds me: I need more dice.

(Tip of the cap to Chris Klausmeier.)

Hence is the Relief Pitcher

Tink Hence, a relief pitcher, is a prospect in the Cardinal's farm system.

I hope that he makes the Majors, so that we can bring back more of these jokes. My favorite one was when Chin Lung Hu came up with the Dodgers; I always wanted him to reach first base.

And Hence's first name is also great. "Tink Hence" is such a great baseball name. Because.

Dodgers Sign Freddie Freeman!

The Dodgers have reached a deal with free agent Freddie Freeman. As usual with the Dodgers, it'a Moneyball with money.

"In-Degree Centrality in a Social Network is Linked to Coordinated Neural Activity"

Another paper of mine was just published in final form. Here are some details.

Title: In-Degree Centrality in a Social Network is Linked to Coordinated Neural Activity

Authors: Elisa C. Baek, Ryan Hyon, Karina López, Emily S. Finn, Mason A. Porter, and Carolyn Parkinson

Abstract: Convergent processing of the world may be a factor that contributes to social connectedness. We use neuroimaging and network analysis to investigate the association between the social-network position (as measured by in-degree centrality) of first-year university students and their neural similarity while watching naturalistic audio-visual stimuli (specifically, videos). There were 119 students in the social-network study; 63 of them participated in the neuroimaging study. We show that more central individuals had similar neural responses to their peers and to each other in brain regions that are associated with high-level interpretations and social cognition (e.g., in the default mode network), whereas less-central individuals exhibited more variable responses. Self-reported enjoyment of and interest in stimuli followed a similar pattern, but accounting for these data did not change our main results. These findings show that neural processing of external stimuli is similar in highly-central individuals but is idiosyncratic in less-central individuals.

XKCD FTW: Greek Letters

Today's xkcd is fantastic! This is a big win. The mouseover is also great (and I am guilty as charged).

Wait until Randall Munroe finds out about mathfrak…

What Happens in Austin Stays in Austin

I am in Austin for the wedding of an old college friend. Some of our mutual friends from college are also coming. Yay!

David Ortiz Elected to Baseball's Hall of Fame!

The Baseball Hall of Fame results were announced today, and David Ortiz is the only person who was elected by the writers this year. As usual, you can see all of the ballots that have been made public so far at this website. You can also see a discussion of winners and losers from this year's results.

Two of the era committees elected several Hall of Famers last month.

This year, Roger Clemens, Barry Bonds, Curt Schilling, and Sammy Sosa were all in their 10th and final years of eligibility. Clems and Bonds crept up to 65% of the vote, but that's still below the 75% that is needed for induction. Schilling, given his repeated crap, lost many votes. With Clemens, Bonds, Schilling, and Ortiz no longer on the ballot next year and few newcomers of note joining the ballot, holdover Scott Rolen (who went up to around 63% of the vote this year) will likely be elected in 2023 (yay!). Newcomer Carlos Beltrán is the only new person on the ballot next year with any chance. The weak ballot will help him, but we'll see how the Astros cheating scandal affects his vote total. Todd Helton and Billy Wagner finally surpassed 50% of the vote this year, and I expect Todd Helton to make another big jump next year. Both merit election, but it it may take some time for Wagner and I think that Helton is more likely to be elected in 2024 than in 2023. Andruw Jones surpassed 40%, so he's also trending upward. Support for Omar Vizquel tanked because of his shenanigans, and he doesn't belong in the Hall of Fame anyway. Jimmy Rollins and Alex Rodriguez were the only other newcomers to the ballot besides David Ortiz to get at least 5% of the vote.

We will see how the era committees deal with Bonds, Clemens, and Schilling. They'll get into the Hall eventually (as they should, even with their horseshit), but it may take a while.

Update (1/26/22): Also see the voting round-up from Jay Jaffe.

Update (1/27/22): Here is Jay Jaffe's candidate-by-candidate breakdown of the 2022 voting.

Update (1/31/22): Here is Jay Jaffe's five-year outlook of the Hall of Fame balloting in the writers' ballot.

"A Multilayer Network Model of the Coevolution of the Spread of a Disease and Competing Opinions"

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

Title: A Multilayer Network Model of the Coevolution of the Spread of a Disease and Competing Opinions

Authors: Kaiyan Peng, Zheng Lu, Vanessa Lin, Michael R. Lindstrom, Christian Parkinson, Chuntian Wang, Andrea L. Bertozzi, Mason A. Porter

Abstract: During the COVID-19 pandemic, conflicting opinions on physical distancing swept across social media, affecting both human behavior and the spread of COVID-19. Inspired by such phenomena, we construct a two-layer multiplex network for the coupled spread of a disease and conflicting opinions. We model each process as a contagion. On one layer, we consider the concurrent evolution of two opinions — pro-physical-distancing and anti-physical-distancing — that compete with each other and have mutual immunity to each other. The disease evolves on the other layer, and individuals are less likely (respectively, more likely) to become infected when they adopt the pro-physical-distancing (respectively, anti-physical-distancing) opinion. We develop approximations of mean-field type by generalizing monolayer pair approximations to multilayer networks; these approximations agree well with Monte Carlo simulations for a broad range of parameters and several network structures. Through numerical simulations, we illustrate the influence of opinion dynamics on the spread of the disease from complex interactions both between the two conflicting opinions and between the opinions and the disease. We find that lengthening the duration that individuals hold an opinion may help suppress disease transmission, and we demonstrate that increasing the cross-layer correlations or intra-layer correlations of node degrees may lead to fewer individuals becoming infected with the disease.

The `PrickRank' Algorithm

One way to gather information is to purposely write an incorrect 'factual' statement on social media.

People love to correct others (often obnoxiously, but at least one acquires info).

Google has PageRank, and social-media platforms like Twitter have this `PrickRank algorithm'.

(This monicker is destined to become a classic, just like FIPO.)

The Donkey Kong Visual Illusion

This visual illusion ought to be called the "Donkey Kong Illusion"

Horizontally aligned rows appear to tilt alternately. pic.twitter.com/80pfmXPql6

— Akiyoshi Kitaoka (@AkiyoshiKitaoka) January 9, 2022

"A Bounded-Confidence Model of Opinion Dynamics on Hypergraphs"

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

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

Authors: Abigail Hickok, Yacoub Kureh, Heather Z. Brooks, Michelle Feng, and Mason A. Porter

Abstract: People's opinions evolve with time as they interact with their friends, family, colleagues, and others. In the study of opinion dynamics on networks, one often encodes interactions between people in the form of dyadic relationships, but many social interactions in real life are polyadic (i.e., they involve three or more people). In this paper, we extend an asynchronous bounded-confidence model (BCM) on graphs, in which nodes are connected pairwise by edges, to an asynchronous BCM on hypergraphs, in which arbitrarily many nodes can be connected by a single hyperedge. We show that our hypergraph BCM converges to consensus for a wide range of initial conditions for the opinions of the nodes, including for nonuniform and asymmetric initial opinion distributions. We also show that, under suitable conditions, echo chambers can form on hypergraphs with community structure. We demonstrate that the opinions of nodes can sometimes jump from one opinion cluster to another in a single time step; this phenomenon (which we call ``opinion jumping") is not possible in standard dyadic BCMs. Additionally, we observe a phase transition in the convergence time of our BCM on a complete hypergraph when the variance $\sigma^2$ of the initial opinion distribution equals the confidence bound $c$. We prove that the convergence time grows at least exponentially fast with the number of nodes when $\sigma^2 > c$ and the initial opinions are normally distributed. Therefore, to determine the convergence properties of our hypergraph BCM when the variance and the number of hyperedges are both large, it is necessary to use analytical methods instead of relying only on Monte Carlo simulations.