"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.

RIP Betty White (1922–2021)

Iconic actress Betty White died today at age 99. January 17 was going to be her 100th birthday. You can read a lot about her on her Wikipedia page.

"Epidemic Thresholds of Infectious Diseases on Tie-Decay Networks"

Another paper of mine has just been published in final form. (Technically, one could say that it's almost in final form; the issue number has been determined, but its stamp is not yet on the .pdf file as I write this blog entry because some other articles from the same issue haven't yet been published.) Here are some details.

Title: "Epidemic Thresholds of Infectious Diseases on Tie-Decay Networks"

Authors: Qinyi Chen and Mason A. Porter

Abstract: In the study of infectious diseases on networks, researchers calculate epidemic thresholds to help forecast whether or not a disease will eventually infect a large fraction of a population. Because network structure typically changes with time, which fundamentally influences the dynamics of spreading processes and in turn affects epidemic thresholds for disease propagation, it is important to examine epidemic thresholds in models of disease spread on temporal networks. Most existing studies of epidemic thresholds in temporal networks have focused on models in discrete time, but most real-world networked systems evolve continuously with time. In our work, we encode the continuous time-dependence of networks in the evaluation of the epidemic threshold of a susceptible–infected–susceptible (SIS) process by studying an SIS model on tie-decay networks. We derive the epidemic-threshold condition of this model, and we perform numerical experiments to verify it. We also examine how different factors—the decay coefficients of the tie strengths in a network, the frequency of the interactions between the nodes in the network, and the sparsity of the underlying social network on which interactions occur—lead to decreases or increases of the critical values of the threshold and hence contribute to facilitating or impeding the spread of a disease. We thereby demonstrate how the features of tie-decay networks alter the outcome of disease spread.

"Classical and Quantum Random-Walk Centrality Measures in Multilayer Networks"

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

Title: Classical and Quantum Random-Walk Centrality Measures in Multilayer Networks

Authors: Lucas Böttcher and Mason A. Porter

Abstract: Multilayer network analysis is a useful approach for studying networks of entities that interact with each other via multiple relationships. Classifying the importance of nodes and node-layer tuples is an important aspect of the study of multilayer networks. To do this, it is common to calculate various centrality measures, which allow one to rank nodes and node-layers according to a variety of structural features. In this paper, we formulate occupation, PageRank, betweenness, and closeness centralities in terms of node-occupation properties of different types of continuous-time classical and quantum random walks on multilayer networks. We apply our framework to a variety of synthetic and real-world multilayer networks, and we identify notable differences between classical and quantum centrality measures. Our computations give insights into the correlations between certain centralities that are based on random walks and associated centralities that are based on geodesic paths.

"Motifs for Processes on Networks"

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

Title: "Motifs for Processes on Networks"

Authors: Alice C. Schwarze and Mason A. Porter

Abstract: The study of motifs can help researchers uncover links between the structure and function of networks in biology, sociology, economics, and many other areas. Empirical studies of networks have identified feedback loops, feedforward loops, and several other small structures as "motifs" that occur frequently in real-world networks and may contribute by various mechanisms to important functions in these systems. However, these mechanisms are unknown for many of these motifs. We propose to distinguish between "structure motifs" (i.e., weakly connected graphlets) in networks and "process motifs" (which we define as structured sets of walks) on networks and consider process motifs as building blocks of processes on networks. Using steady-state covariance and steady-state correlation in a multivariate Ornstein--Uhlenbeck process on a network as examples, we demonstrate that distinguishing between structure motifs and process motifs makes it possible to gain quantitative insights into mechanisms that contribute to important functions of dynamical systems on networks.

"Finding Your Way: Shortest Paths on Networks"

Another article of mine just came out in final form. Here are some details.

Title: Finding Your Way: Shortest Paths on Networks

Authors: Teresa Rexin and Mason A. Porter

Abstract: Traveling to different destinations is a major part of our lives. We visit a variety of locations both during our daily lives and when we are on vacation. How can we find the best way to navigate from one place to another? Perhaps we can test all of the different ways of traveling between two places, but another method is to use mathematics and computation to find a shortest path between them. In this article, we discuss how to construct shortest paths and introduce Dijkstra’s algorithm to minimize the total cost of a path, where the cost may be the travel distance, the travel time, or some other quantity. We also discuss how to use shortest paths in the real world to save time and increase traveling efficiency.

Tim Kurkjian Wins 2022 BBWAA Career Excellence Award!

Congratulations to awesome baseball journalist Tim Kurkjian, who has won the 2022 BBWAA Career Excellence Award!

New Hall of Famers from Two of the Era Committees

We have some new Hall of Famers!

The Golden Days Era Committee has elected Tony Oliva, Jim Kaat, Minnie Miñoso, and Gil Hodges to the Hall of Fame. I'm glad that Oliva, Hodges, and (especially) Miñoso are finally in the Hall of Fame. However, Jim Kaat should not have made it, and fellow Golden Era candidate Dick Allen bloody well should be in the Hall of Fame. Take a look at this series of articles for discussions of each of the candidates.

The Early Baseball Era Committee has elected Bud Fowler and Buck O'Neil to the Hall of Fame. Take a look at this series of articles for discussions of each of the candidates.

You can track the regular Hall of Fame ballotting on the usual ballot tracker. I am guessing that they're going to throw a shutout for the second year in a row, but players such as Todd Helton and Scott Rolen (and some others) should make good progress towards eventual election.

Update (12/06/21): As discussed in this article, Dick Allen fell one vote short for the second time in a row. :( Maybe next time, although even then he is no longer alive to enjoy it.

What Happens in Salt Lake City Stays in Salt Lake City

I am heading off to Salt Lake City to give a talk at University of Utah!

"Nanoptera in Weakly Nonlinear Woodpile Chains and Diatomic Granular Chains"

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

Title: Nanoptera in Weakly Nonlinear Woodpile Chains and Diatomic Granular Chains

Authors: Guo Deng, Christopher J. Lustri, and Mason A. Porter

Abstract: We study ``nanoptera," which are nonlocalized solitary waves with exponentially small but nondecaying oscillations, in two singularly perturbed Hertzian chains with precompression. These two systems are woodpile chains (which we model as systems of Hertzian particles and springs) and diatomic Hertzian chains with alternating masses. We demonstrate that nanoptera arise from the Stokes phenomenon and appear as special curves (called Stokes curves) are crossed in the complex plane. We use techniques from exponential asymptotics to obtain approximations of the oscillation amplitudes. Our analysis demonstrates that traveling-wave solutions in a singularly perturbed woodpile chain have a single Stokes curve, which generates oscillations behind the wave front. Comparing these asymptotic predictions with numerical simulations reveals that our asymptotic approximation accurately describes the nondecaying oscillatory behavior in a woodpile chain. We perform a similar analysis of a diatomic Hertzian chain, and we show that each nanopteron solution has two distinct exponentially small oscillatory contributions. We demonstrate that there exists a set of mass ratios for which these two contributions cancel to produce localized solitary waves. This result builds on prior experimental and numerical observations that there exist mass ratios that support localized solitary waves in diatomic Hertzian chains without precompression. Comparing our asymptotic and numerical results for a diatomic Hertzian chain with precompression reveals that our exponential asymptotic approach accurately predicts the oscillation amplitude for a wide range of system parameters, but it fails to identify several values of the mass ratio that correspond to localized solitary-wave solutions.

2021 Baseball Comeback Players of the Year

Baseball's comeback players of the year for 2021 have been announced. The American League winner is Trey Mancini of the Baltimore Orioles, and the National League winner is now-retired Buster Posey of the San Francisco Giants.

2021 Baseball Most Valuable Player Awards

Baseball announced its 2021 Most Valueable Player Awards today as the culmination of this year's awards. Once again, the results are unsurprising. Shohei Ohtani of the Los Angeles Angels was a unanimous winner in the American League (duh), and Bryce Harper of the Philadelphia Phillies won in the National League.

2021 Cy Young Awards

Major League Baseball has announced its 2021 Cy Young Awards for pitching excellence. Robbie Ray of the Toronto Blue Jays won the award in the American League, and Corbin Burnes of the Milwaukee Brewers won in the National League.

The National League race was very close; Burnes narrowly beat out Zack Wheeler of the Philadelphia Phillies and the Los Angeles Dodgers' Max Scherzer wasn't horribly far away either. Walker Buehler of the Dodgers finished 4th in the balloting.

2021 Baseball Managers of the Year

Major League Baseball has announced its 2021 Managers of the Year. The Americal League Manager of the Year is Kevin Cash of the Tampa Bay Rays, and the National League Manager of the year is Gabe Kapler of the San Fransisco Giants.

As with the Rookies of the Year, neither winner is surprising.

2021 Baseball Rookies of the Year

The 2021 Rookies of the Year were announced today. Jonathan India of the Cincinnati Reds won in the National League, and Randy Arozarena of the Tampa Bay Rays won in the American League.

Neither choice is surprising.

Some More Trips

I have had a few more short academic trips in the last couple of weeks. I spent a day at Harvey Mudd to talk to the students in Heather Zinn Brooks's class on mathematics and democracy. Then I took a trip to Michigan state to give an applied-mathematics colloquium, and now I am in San Diego State to give a mathematics colloquium.

Major League Relievers of the Year

The Mariano Rivera Award and Trevor Hoffmann Award have been awarded to the top relievers in the American League and National League, respectively. Liam Hendricks of the Chicago White Sox won the former, and Josh Hader of the Milwakuee Brewers won the latter.

"Pull Out All the Stops: Textual Analysis via Punctuation Sequences"

One of my papers, which has been available publicly for more than a year, is finally out in final form, with its coordinates (its page numbers and so on). Here are the details.

Title: Pull Out All the Stops: Textual Analysis via Punctuation Sequences

Authors: Alexandra N. M. Darmon, Marya Bazzi, Sam D. Howison, and Mason A. Porter

Abstract: Whether enjoying the lucid prose of a favourite author or slogging through some other writer's cumbersome, heavy-set prattle (full of parentheses, em dashes, compound adjectives, and Oxford commas), readers will notice stylistic signatures not only in word choice and grammar but also in punctuation itself. Indeed, visual sequences of punctuation from different authors produce marvellously different (and visually striking) sequences. Punctuation is a largely overlooked stylistic feature in stylometry, the quantitative analysis of written text. In this paper, we examine punctuation sequences in a corpus of literary documents and ask the following questions: Are the properties of such sequences a distinctive feature of different authors? Is it possible to distinguish literary genres based on their punctuation sequences? Do the punctuation styles of authors evolve over time? Are we on to something interesting in trying to do stylometry without words, or are we full of sound and fury (signifying nothing)?

In our investigation, we examine a large corpus of documents from Project Gutenberg (a digital library with many possible editorial influences). We extract punctuation sequences from each document in our corpus and record the number of words that separate punctuation marks. Using such information about punctuation-usage patterns, we attempt both author and genre recognition, and we also examine the evolution of punctuation usage over time. Our efforts at author recognition are particularly successful. Among the features that we consider, the one that seems to carry the most explanatory power is an empirical approximation of the joint probability of the successive occurrence of two punctuation marks. In our conclusions, we suggest several directions for future work, including the application of similar analyses for investigating translations and other types of categorical time series.

"Detection of Functional Communities in Networks of Randomly Coupled Oscillators Using the Dynamic-Mode Decomposition"

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

Title: Detection of Functional Communities in Networks of Randomly Coupled Oscillators Using the Dynamic-Mode Decomposition

Abstract: Dynamic-mode decomposition (DMD) is a versatile framework for model-free analysis of time series that are generated by dynamical systems. We develop a DMD-based algorithm to investigate the formation of functional communities in networks of coupled, heterogeneous Kuramoto oscillators. In these functional communities, the oscillators in a network have similar dynamics. We consider two common random-graph models (Watts–Strogatz networks and Barabási–Albert networks) with different amounts of heterogeneities among the oscillators. In our computations, we find that membership in a functional community reflects the extent to which there is establishment and sustainment of locking between oscillators. We construct forest graphs that illustrate the complex ways in which the heterogeneous oscillators associate and disassociate with each other.

Dodgers Advance to the National League Championship Series!

The Dodgers beat the Giants 2–1 in the elimination game of the NLDS to advance to the National League Championship Series against the Braves!!!

Today was game 5 of the National League Division Series. We were tied 1–1 entering the 9th inning and scored one run in the top of the inning. Max Scherzer entered the game in the bottom of the 9th and earned a save.

The called strike on the check swing to end the game was a really bad call.

Dodgers Win Wild Card Elimination Game on a Walk-Off Homerun!

The Dodgers have just beaten the Cardinals in the Wild Card elimination game!

We'll be going to face the Giants (in our first ever postseason series against them) in the National League Division Series!

The Dodgers and Giants had the two best records during the regular season.

Some Baseball Musings on the Last Day of the 2021 Regular Season

Despite some possibilities for drama, there won't be any Game 163 for any teams. (There was late-inning drama in two of the relevant AL games today, and that is why there won't be any of these extra games.)

We (i.e., the Dodgers) have a win-or-go-home Wild Card 'playoff' against the Cardinals on Wednesday. I'll have it on silent at first while I am participating as a panelist in the UCLA math department job-application panel (which I suggested to our department head that we should do, and thankfully we're doing it), and then I'll have sound on for most of the game once the panel is over.

Trea Turner ended up winning the NL battle title handily. I have trouble picking an MVP, because I think the Padres going into the tank will hurt Tatis Jr.'s chances. That said, I still think he merits it, although if we're going to do pure performance after the Padres fall, maybe Juan Soto ultimately was somewhat better overall? The NL Cy Young award is hard to predict, as a lot of votes will get split. Right now, I think it will be Walker Buehler by a nose over Scherzer, Burnes, and Zack Wheeler. Urías will get some down-ballot votes, but despite the gaudy win totals, the other pitchers I mentioned (and some I have not) have been better them him. Jonathan India will when the NL ROY.

In the AL, Ohtani is the MVP. I think Gerrit Cole is a slightly better Cy Young choice than Robbie Ray, who many announcers seem to think is the heavy favorite. He's a good choice, but I think that Cole has been slightly better. Randy Arozarena is technically still a rookie, but I think I need to look more closely at some of the other viable options as well.

Finally, reports of Joey Votto's demise appear to have been greatly exaggerated (although he has changed his hitting style).

"Math Prof" (a parody of “Dentist” from Little Shop of Horrors)

“Math Prof”

(a parody of “Dentist” from Little Shop of Horrors)

[MATHEMATICS PROFESSOR]
When I was younger, just a small geeky kid,
My mama noticed nerdy things I did,
Like countin' all the lights in the ceilings
I'd find their patterns, and after these things
I'd create a small maze and see where it led
That's when my mama said

[POSTDOCS]
What did she say?

[MATHEMATICS PROFESSOR]
She said, "My boy, I think someday
You'll find a way
To make your natural tendencies pay
You'll be a math prof
You have a talent for countin’ things up
Son, be a math prof
People will pay you to be all stuck-up
Your temperament's wrong for the priesthood
And business would suit you still less
Son, be a math prof
You'll be a success

[POSTDOCS]
Here he is, folks, the leader of the proof!
Watch him be oh so aloof!
Oh, my god!
He's a math prof and he'll never ever be any good
Who wants a thesis defense with someone in that mood?

[STUDENT]
Oh that hurts! I don’t know!

[MATHEMATICS PROFESSOR]
Oh, shut up. Think faster. Now go!
I am your math prof

[STUDENT]
Goodness gracious!

[MATHEMATICS PROFESSOR]
And I enjoy the career that I picked

[POSTDOCS]
Really love it

[MATHEMATICS PROFESSOR]
I am your math prof

[STUDENT]
Proving theorems

[MATHEMATICS PROFESSOR]
And I get off on the pain I inflict

[POSTDOCS]
Really love it

[MATHEMATICS PROFESSOR]
I thrill when I ask a tough question

[POSTDOCS]
Tough question
[MATHEMATICS PROFESSOR]
It's swell though they tell me I'm maladjusted
And though it may cause my students distress,
Somewhere, somewhere in Heaven above me
I know, I know, that my mama's proud of me
Oh, mama
'Cause I'm a math prof and a success
Say pi!

[STUDENT]
Pi!

[MATHEMATICS PROFESSOR]
Say mu!

[STUDENT]
Mu!

[MATHEMATICS PROFESSOR]
Say nu!

[STUDENT]
Nu!

[MATHEMATICS PROFESSOR]
Now prove it!

2021 Ig Nobel Prizes!

The 2021 Ig Nobel laureates have been announced!

I think my favorite one this year is the prize in chemistry, but I of course have fondness for the winners in complex systems (especially with one of them published in Physical Review E).

What Happens in Boulder Stays in Boulder

I am taking my first trip since January 2020!

I'll be visiting CU Boulder to give an applied-mathematics colloquium. This will also be only my second in-person presentation (I gave one at IPAM a couple of weeks ago) since the start of the pandemic.

I haven't been to Boulder since around 2003 or 2004. I am looking forward to my trip, although traveling is even more nerve-wracking than before.

"Social Network Analysis for Social Neuroscientists"

A paper of mine that was posted in advanced access more than a year ago has now finally been posted in final form. It is a survey and perspective article on social network analysis for social neuroscientists. Here are some details.

Title: Social Network Analysis for Social Neuroscientists

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

Abstract: Although social neuroscience is concerned with understanding how the brain interacts with its social environment, prevailing research in the field has primarily considered the human brain in isolation, deprived of its rich social context. Emerging work in social neuroscience that leverages tools from network analysis has begun to advance knowledge of how the human brain influences and is influenced by the structures of its social environment. In this paper, we provide an overview of key theory and methods in network analysis (especially for social systems) as an introduction for social neuroscientists who are interested in relating individual cognition to the structures of an individual’s social environments. We also highlight some exciting new work as examples of how to productively use these tools to investigate questions of relevance to social neuroscientists. We include tutorials to help with practical implementations of the concepts that we discuss. We conclude by highlighting a broad range of exciting research opportunities for social neuroscientists who are interested in using network analysis to study social systems.

Dodgers Acquire Max Scherzer and Trea Turner!

The Dodgers have made a huge splash in the trade market: they have acquired Max Scherzer and Trea Turner from the Washington Nationals for a load of prospects. This is exactly the trade that we needed. Scherzer, who will eventually be a Hall of Famer, is still an excellent and durable starter; and Turner is an outstanding infielder (who is also rather underrated, in my view, even amidst the wide recognition of his excellence), and I wouldn't be surprised if he eventually also makes the Hall of Fame. Just before then, the Dodgers also acquired pitcher Danny Duffy from the Royals.

Note: I didn't post this yesterday because I wanted to wait until the deal with the Nationals was done, rather than being something that the Dodgers were "finalizing".

XKCD and Flawed Data

XKCD nailed it yet again, especially with the mouseover text.

My Current Mathematics Genealogy

Here is my current mathematics genealogy.

My current Mathematics Genealogy (with doctoral students only): https://t.co/EAOiY0tasi

My MGP page (24 doctoral students): https://t.co/p35XlLXjoA

Current doctoral students: Abby Hickok, Grace Li, Jerry Luo, Kaiyan Peng, Mina Shahi

Also: I can't wait to have grandstudents! pic.twitter.com/dOU2wviu1V

— Mason Porter (@masonporter) July 16, 2021

"Tie-Decay Networks in Continuous Timeand Eigenvector-Based Centralities"

The paper based on one of my old projects finally appeared in final form. Here are some details.

Title: Tie-Decay Networks in Continuous Timeand Eigenvector-Based Centralities

Authors: Walid Ahmad, Mason A. Porter, and Mariano Beguerisse-Díaz

Abstract: Network theory is a useful framework for studying interconnected systems of interacting entities. Many networked systems evolve continuously in time, but most existing methods for the analysis of time-dependent networks rely on discrete or discretized time. In this paper, we propose an approach for studying networks that evolve in continuous time by distinguishing between interactions, which we model as discrete contacts, and ties, which encode the strengths of relationships over time. To illustrate our tie-decay network formalism, we adapt the well-known PageRank centrality score to our tie-decay framework in a mathematically tractable and computationally efficient way. We apply this framework to a synthetic example and then use it to study a network of retweets during the 2012 National Health Service controversy in the United Kingdom. Our work also provides guidance for similar generalizations of other tools from network theory to continuous-time networks with tie decay, including for applications to streaming data.

"Opinion Dynamics on Tie-Decay Networks"

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

Title: Opinion Dynamics on Tie-Decay Networks

Authors: Kashin Sugishita, Mason A. Porter, Mariano Beguerisse-Díaz, and Naoki Masuda

Abstract: In social networks, interaction patterns typically change over time. We study opinion dynamics on tie-decay networks in which tie strength increases instantaneously when there is an interaction and decays exponentially between interactions. Specifically, we formulate continuous-time Laplacian dynamics and a discrete-time DeGroot model of opinion dynamics on these tie-decay networks, and we carry out numerical computations for the continuous-time Laplacian dynamics. We examine the speed of convergence by studying the spectral gaps of combinatorial Laplacian matrices of tie-decay networks. First, we compare the spectral gaps of the Laplacian matrices of tie-decay networks that we construct from empirical data with the spectral gaps for corresponding randomized and aggregate networks. We find that the spectral gaps for the empirical networks tend to be smaller than those for the randomized and aggregate networks. Second, we study the spectral gap as a function of the tie-decay rate and time. Intuitively, we expect small tie-decay rates to lead to fast convergence because the influence of each interaction between two nodes lasts longer for smaller decay rates. Moreover, as time progresses and more interactions occur, we expect eventual convergence. However, we demonstrate that the spectral gap need not decrease monotonically with respect to the decay rate or increase monotonically with respect to time. Our results highlight the importance of the interplay between the times that edges strengthen and decay in temporal networks.

"Topological Data Analysis of Task-Based fMRI Data from Experiments on Schizophrenia"

Another of my papers from an old project final came out in final form after a very long road. Here are some details.

Title: "Topological Data Analysis of Task-Based fMRI Data from Experiments on Schizophrenia"

Authors: Bernadette J. Stolz, Tegan Emerson, Satu Nahkuri, Mason A. Porter, and Heather A Harrington

Abstract: We use methods from computational algebraic topology to study functional brain networks in which nodes represent brain regions and weighted edges encode the similarity of functional magnetic resonance imaging (fMRI) time series from each region. With these tools, which allow one to characterize topological invariants such as loops in high-dimensional data, we are able to gain understanding of low-dimensional structures in networks in a way that complements traditional approaches that are based on pairwise interactions. In the present paper, we use persistent homology to analyze networks that we construct from task-based fMRI data from schizophrenia patients, healthy controls, and healthy siblings of schizophrenia patients. We thereby explore the persistence of topological structures such as loops at different scales in these networks. We use persistence landscapes and persistence images to represent the output of our persistent-homology calculations, and we study the persistence landscapes and persistence images using k-means clustering and community detection. Based on our analysis of persistence landscapes, we find that the members of the sibling cohort have topological features (specifically, their one-dimensional loops) that are distinct from the other two cohorts. From the persistence images, we are able to distinguish all three subject groups and to determine the brain regions in the loops (with four or more edges) that allow us to make these distinctions.

"Counterparty Credit Limits: The Impact of a Risk-Mitigation Measure on Everyday Trading"

A paper of mine (from an extremely old project) final came out in final form today. Here are some details.

Title: Counterparty Credit Limits: The Impact of a Risk-Mitigation Measure on Everyday Trading

Authors: Martin D. Gould, Nikolaus Hautsch, Sam D. Howison, and Mason A. Porter

Abstract: A counterparty credit limit (CCL) is a limit that is imposed by a financial institution to cap its maximum possible exposure to a specified counterparty. CCLs help institutions to mitigate counterparty credit risk via selective diversification of their exposures. In this paper, we analyse how CCLs impact the prices that institutions pay for their trades during everyday trading. We study a high-quality data set from a large electronic trading platform in the foreign exchange spot market that allows institutions to apply CCLs. We find empirically that CCLs had little impact on the vast majority of trades in this data set. We also study the impact of CCLs using a new model of trading. By simulating our model with different underlying CCL networks, we highlight that CCLs can have a major impact in some situations.

"Random-Graph Models and Characterization of Granular Networks"

A paper of mine from 2020 now has its final coordinates listed on the published file itself. Here are some details.

Title: Random-Graph Models and Characterization of Granular Networks

Authors: Silvia Nauer, Lucas Böttcher, and Mason A. Porter

Abstract: Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we examine a variety of common network measures and study their ability to characterize various two-dimensional and three-dimensional spatial random-graph models and empirical two-dimensional granular networks. We identify network measures that are able to distinguish between physically plausible and unphysical spatial network models. Our results also suggest that there are significant differences in the distributions of certain network measures in two and three dimensions, hinting at important differences that we also expect to arise in experimental granular networks.

"Nonlinear Localized Modes in Two-Dimensional Hexagonally-Packed Magnetic Lattices"

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

Title: Nonlinear Localized Modes in Two-Dimensional Hexagonally-Packed Magnetic Lattices

Authors: Christopher Chong, Yifan Wang, Donovan Maréchal, Efstathios G. Charalampidis, Miguel Molerón, Alejandro J. Martínez, Mason A. Porter, Panayotis G. Kevrekidis, and Chiara Daraio

Abstract: We conduct an extensive study of nonlinear localized modes (NLMs), which are temporally periodic and spatially localized structures, in a two-dimensional array of repelling magnets. In our experiments, we arrange a lattice in a hexagonal configuration with a light-mass defect, and we harmonically drive the center of the chain with a tunable excitation frequency, amplitude, and angle. We use a damped, driven variant of a vector Fermi–Pasta–Ulam–Tsingou lattice to model our experimental setup. Despite the idealized nature of this model, we obtain good qualitative agreement between theory and experiments for a variety of dynamical behaviors. We find that the spatial decay is direction-dependent and that drive amplitudes along fundamental displacement axes lead to nonlinear resonant peaks in frequency continuations that are similar to those that occur in one-dimensional damped, driven lattices. However, we observe numerically that driving along other directions results in asymmetric NLMs that bifurcate from the main solution branch, which consists of symmetric NLMs. We also demonstrate both experimentally and numerically that solutions that appear to be time-quasiperiodic bifurcate from the branch of symmetric time-periodic NLMs.

Some Academic Struggles and Survivorship Bias

Public Service Announcement: When you look at somebody's fancy CV (or fancy job or other hallmark of success), don't assume that they didn't have to go through major struggles — often many of them — before they got there.

PSA 2: Survivorship bias is a good thing to remember. pic.twitter.com/XaPk2Eoo0f

— Mason Porter (@masonporter) April 4, 2021

April Fooling: 2021 Edition

Well, the April 1st arXiv articles are out, and sure enough there are some of them that are in honor of April Fool's Day. For example, there is one about Taylor Swift and a paper that is "coauthored" by a cat in which the cat "analyzes" a laser pointer and a dot on a wall as a coupled dynamical system.

Update: Here are some other papers, although I don't think the one about procrastination qualifies. I saw that one in my own arXiv scouring, and in my opinion that one is more of the 'improbable research' style (something that first makes you laugh and then makes you think), rather than something that is simply a joke. (Tip of the cap to Celeste Labedz.)

Update (4/01/21): The article that I was thinking of — which concerns our poor estimation of how long things take — was indeed intended as a sort of a joke (based on the author's Twitter thread), but my own view of it is still as an example of 'improbable research'.

Update (4/01/21): Here is a joke about noodle knitting. (Tip of the cap to Katherine Seaton.)

Update (4/01/21): Some department websites also experienced a few changes. (Tip of the cap to Karen Daniels.)

Update (4/02/21): There is also now an article about various spoofs in physics and astronomy.

Update (4/02/21): The Santa Fe Institute finally created a web page for Dr. Ian Malcolm. Life finds a way, so to speak. (It has long been rumored that a certain SFI faculty member provided some inspiration for the fictional scientist. (As a subtle hint, think of The Power Law OF DOOM.)

Update (4/02/21): This fake rejection of Roxy Music fooled me.

"Twitter" in 1803: The Finger of Contempt

Twitter: 1803 style

Now where did I put my 👉Finger of Contempt? https://t.co/Y1yoNVLMtm

(h/t David Blau)

— Mason Porter (@masonporter) March 24, 2021

"Connecting the Dots: Discovering the “Shape” of Data"

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

Title: Connecting the Dots: Discovering the “Shape” of Data

Authors: Michelle Feng, Abighail Hickok, Yacoub H. Kureh, Mason A. Porter, and Chad M. Topaz

Abstract: Scientists use a mathematical subject called topology to study the shapes of objects. An important part of topology is counting the number of pieces and the number of holes in an object, and researchers use this information to group objects into different types. For example, a doughnut has the same number of holes and the same number of pieces as a teacup with one handle, but it is different from a ball. In studies that resemble activities like “connect-the-dots,” scientists use ideas from topology to study the “shape” of data. Ideas and methods from topology have been used to study the branching structures of veins in leaves, voting in elections, flight patterns in models of bird flocking, and more.

Here is my tweet, in case you want to share it on social media.

Our introduction to topological data analysis (TDA) for teenagers and preteens is finally out in final form in Frontiers for Young Minds: https://t.co/6KQF2yyJUn@michellehfeng, Abby Hickok, Yacoub Kureh, MAP, & @chadtopaz

(plus special guest appearances by several Pokémon)

— Mason Porter (@masonporter) March 18, 2021

2021 Abel Prize: László Lovász and Avi Wigderson

The 2021 Abel Prize goes to to mathematician László Lovász and computer scientist Avi Wigderson "for their foundational contributions to theoretical computer science and discrete mathematics, and their leading role in shaping them into central fields of modern mathematics."

My Top-5 Emoji: The Power of Positive Thinking

😱🙄🤔🙀🤢

Yup. My top-5 emoji certainly do appear to be my aesthetic.

Because I believe in the power of positive thinking. https://t.co/XizplVRldD

— Mason Porter (@masonporter) March 16, 2021

An Ancient Roman d20

This is very cool!

1st to 3rd century Roman dice. pic.twitter.com/R8ZsgmCJ1S

— The French History Podcast (@FrenchHist) March 15, 2021

Previously, I blogged about an ancient Roman dice tower and an ancient Egyptian d20.

(Tip of the cap to Chris Klausmeier.)

Pro Tip: Life is Short. Be Cat 3.

life is short, be cat3 https://t.co/JmpPWMiQ81

— @jeffbigham (@jeffbigham) March 14, 2021

(Tip of the cap to Yisong Yue.)

An Epic Figure Caption

Wow. Just wow.

Clearly, it needs a figure to go with it.

(Tip of the cap to Jesús Cuevas Maraver, who retweeted this tweet.)

"The Waiting-Time Paradox"

Another of our papers for teens and pre-teens came out in final form today. Here are some details.

Title: The Waiting-Time Paradox

Authors: Naoki Masuda and Mason A. Porter

Abstract: Suppose that you are going to school and arrive at a bus stop. How long do you have to wait before the next bus arrives? Surprisingly, it is longer—possibly much longer—than what you might guess from looking at a bus schedule. This phenomenon, which is called the waiting-time paradox, has a purely mathematical origin. In this article, we explore the waiting-time paradox, explain why it occurs, and discuss some of its implications (beyond the possibility of being late for school).

RIP Dame Fiona Caldicott (1941–2021)

Today I once again have woken up to awful news: Dame Fiona Caldicott, who I know from her role as Principal of Somerville College, died today.

A tribute has been posted on the UK government page.

Here is her Wikipedia entry.

"Disease Detectives: Using Mathematics to Forecast the Spread of Infectious Diseases"

Our article for teens and preteens about modeling the spread of infectious diseases just came out in final form. Here are some details.

Title: Disease Detectives: Using Mathematics to Forecast the Spread of Infectious Diseases

Authors: Heather Z. Brooks, Unchitta Kanjanasaratool, Yacoub H. Kureh, and Mason A. Porter

Abstract: The COVID-19 pandemic has led to significant changes in how people are currently living their lives. To determine how to best reduce the effects of the pandemic and start reopening communities, governments have used mathematical models of the spread of infectious diseases. In this article, we introduce a popular type of mathematical model of disease spread. We discuss how the results of analyzing mathematical models can influence government policies and human behavior, such as encouraging mask wearing and physical distancing to help slow the spread of a disease.

Dodgers Sign Trevor Bauer!

The Dodgers have signed free-agent pitcher Trevor Bauer!

"Models of Continuous-Time Networks with Tie Decay, Diffusion, and Convection"

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

Title: Models of Continuous-Time Networks with Tie Decay, Diffusion, and Convection

Authors: Xinzhe Zuo and Mason A. Porter

Abstract: The study of temporal networks in discrete time has yielded numerous insights into time-dependent networked systems in a wide variety of applications. However, for many complex systems, it is useful to develop continuous-time models of networks and to compare them to associated discrete models. In this paper, we study several continuous-time network models and examine discrete approximations of them both numerically and analytically. To consider continuous-time networks, we associate each edge in a graph with a time-dependent tie strength that can take continuous non-negative values and decays in time after the most recent interaction. We investigate how the moments of the tie strength evolve with time in several models, and we explore—both numerically and analytically—criteria for the emergence of a giant connected component in some of these models. We also briefly examine the effects of the interaction patterns of continuous-time networks on the contagion dynamics of a susceptible–infected–recovered model of an infectious disease.

"Persistent Homology of Geospatial Data: A Case Study with Voting"

A new paper of mine is out in final form today. Here are some details.

Title: Persistent Homology of Geospatial Data: A Case Study with Voting

Authors: Michelle Feng and Mason A. Porter

Abstract: A crucial step in the analysis of persistent homology is the transformation of data into an appropriate topological object (which, in our case, is a simplicial complex). Software packages for computing persistent homology typically construct Vietoris–Rips or other distance-based simplicial complexes on point clouds because they are relatively easy to compute. We investigate alternative methods of constructing simplicial complexes and the effects of making associated choices during simplicial-complex construction on the output of persistent-homology algorithms. We present two new methods for constructing simplicial complexes from two-dimensional geospatial data (such as maps). We apply these methods to a California precinct-level voting data set, and we thereby demonstrate that our new constructions can capture geometric characteristics that are missed by distancebased constructions. Our new constructions can thus yield more interpretable persistence modules and barcodes for geospatial data. In particular, they are able to distinguish short-persistence features that occur only for a narrow range of distance scales (e.g., voting patterns in densely populated cities) from short-persistence noise by incorporating information about other spatial relationships between regions.

The Baseball Hall of Fame Throws a Shutout

There will be no new 2021 Hall of Famers for Major League Baseball. (Curt Schilling would have made it—and his playing career is clearly of Hall of Fame caliber—but he's a collossal dipshit.) None of the "Veterans Committees" met because of the COVID-19 pandemic, so the 2021 induction ceremony will honor the 2020 inductees (along with the broadcasters and writers, who get particular awards).

Here is a tabulation of the 2021 ballot's winners and losers. As usual, I have been following things very closely on the Hall of Fame tracker, so I already had a very good idea of what was going to transpire (with very good estimates of final vote percentages). Now we also have the precise voting outcomes.

Scott Rolen, Todd Helton, Bill Wagner, Andruw Jones, and Gary Sheffield all mae very large strides.

Players who will debut on the ballot in 2022 include Alex Rodriguez and David Ortiz.

Update (1/27/21): Here is Jay Jaffe's roundup of how each candidate performed in the voting, as well as their prospects for future enshrinement in the Hall of Fame.

Update (1/27/21): Dan Haren has a fantastic sense of humor. Also check out his Twitter handle, which is an homage to the speed of his "fastball". I love it! (Tip of the cap to Jay Jaffe.)

Update (2/01/21): Here are Jay Jaffe's forecasts of the Hall of Fame voting for the next few years.

"Tunable Eigenvector-Based Centralities for Multiplex and Temporal Networks"

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

Title: Tunable Eigenvector-Based Centralities for Multiplex and Temporal Networks

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

RIP Hank Aaron (1934–2021)

Baseball has lost yet another giant: Hank Aaron died this morning, becoming the third baseball Hall of Famer to die this year already. (Baseball lost quite a few Hall of Famers last year, and we're off to a horrible start this year.) You can read about Hank Aaron's many accomplishments in his Wikipedia entry.

(Tip of the cap to Gregg Schneider.)

RIP Don Sutton (1945–2021)

We have lost yet another Hall-of-Fame Dodger: pitcher Don Sutton has died.

(Tip of the cap to Gregg Schneider.)

RIP Tommy Lasorda (1927–2021)

Dodger great and Hall of Fame manager Tommy Lasorda has died. He died late last night. Tommy was a lifelong Dodger, "bleeding Dodger blue", with 71 years in the organization. I'm glad that he lived to see us ("us" = The Dodgers) finally win another World Series. He was also great in The Baseball Bunch, which I watched as a kid.

To read some things about Lasorda, in addition to his Wikipedia entry above, here is some reactions from around the sports world (including the brilliant video of an infamous fight that he had with the Phillie Phanatic), and some lovely stories from Tim Kurkjian.

Naturally, no obituary of Tommy Lasorda would be complete without a montage of some of his classical meltdowns.

It's a sad day in the Dodger World. RIP, Tommy.

(Tip of the cap to Gregg Schneider.)

Update: This article in The Los Angeles Times has some memorable quotes by Lasorda.

Brilliant Headstones

There are some brilliant epitaphs on these tombstones. I have seen a few of them before (such as "I Told You I Was Sick", which is a favorite), but there are a lot of great ones I hadn't yet seen.

RIP Phil Niekro (1939–2020)

The great knuckleballer and Hall of Fame pitcher Phil Niekro died in his sleep last night.

Yet another great baseball player has left us this year.

Gollum's Cover of "Nothing Compares 2 U"

This deepfake of Gollum covering the song "Nothing Compares 2 U" is wrong on many, many levels. It's also glorious.

Witness the power of deepfakes! If I ever again speak at a workshop about deepfakes, I am whipping out this video.

(This cover needs to be used as a Ride chaser.)

(Tip of the cap to Jennifer Ouellette.)

RIP Peter Neumann (1940–2020)

This morning, I saw the terrible news that my former Oxford colleague Peter Neumann died today, supposedly due to complications from COVID-19 (although I can't verify if that is the known cause of death). Here is is Peter's Wikipedia entry.

I had the chance to interact with Peter quite a few times at Oxford. When I knew him, he was concentrating on mathematics history, and I contacted him with a query about some mathematical linguistics (concerning, for example, the use of "topological" only versus both "geometric" and "geometrical"). I knew that Peter was the right person to approach when I wanted to dive deeper than what I was able to do via Google. Here is my 2013 blog entry about that.

Peter was one of the people in Oxford who was always so kind and supportive of me (and, from what I can tell, of many others as well). When I got some pointed negative teaching evaluations, Peter invited me to The Queen's College to dinner to chat about things (and to give gentle advice and so on). But if I am getting rewarded with a dinner like that for messing up, it does create strange incentives. My students in my courses now are certainly benefiting from advice Peter gave me over the years. He also supported me in various fights on committees (we were on Teaching Committee together) and particularly in efforts that I made against "We've always done it this way." comments to try to change things in Oxford's Mathematical Institute.

(Tip of the cap to Card Colm Mulcahy.)

"Inference of Edge Correlations in Multilayer Networks"

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

Title: Inference of Edge Correlations in Multilayer Networks

Authors: A. Roxana Pamfil, Sam D. Howison, and Mason A. Porter

Abstract: Many recent developments in network analysis have focused on multilayer networks, which one can use toencode time-dependent interactions, multiple types of interactions, and other complications that arise in complexsystems. Like their monolayer counterparts, multilayer networks in applications often have mesoscale features,such as community structure. A prominent approach for inferring such structures is the employment of multilayerstochastic block models (SBMs). A common (but potentially inadequate) assumption of these models is thesampling of edges in different layers independently, conditioned on the community labels of the nodes. In thispaper, we relax this assumption of independence by incorporating edge correlations into an SBM-like model. Wederive maximum-likelihood estimates of the key parameters of our model, and we propose a measure of layercorrelation that reflects the similarity between the connectivity patterns in different layers. Finally, we explainhow to use correlated models for edge “prediction” (i.e., inference) in multilayer networks. By incorporating edgecorrelations, we find that prediction accuracy improves both in synthetic networks and in a temporal network ofshoppers who are connected to previously purchased grocery products.

The Cleveland Baseball Team

The Major League Baseball team that is situated in Cleveland will no longer be called the Indians. Finally! This is long past due. Hopefully, the Atlanta Braves will eventually follow suit.

Tales from the ArXiv: "A Nudge Framework"

A new paper that just appeared on arXiv this evening is called "Steering the aggregative behavior of noncooperative agents: a nudge framework". I come from a Jewish family, so I am very familiar with this strategy.

RIP Jean-Paul Revel (1931–2020)

Cellular biologist Jean-Paul Revel, who was Caltech's Dean of Students for several years (including during some of my undergraduate time), died a few days ago.

À bientôt, Dean Revel.

Update (12/09/20): I am aware of what "À bientôt" means. I used that line because Dean Revel ended all of his articles with it. (So, in case you were worrying about me, there is no need to worry!)

What Happens on Zoom Stays on Zoom

I'm not traveling these days, so I figure this is how this type of post needs to go nowadays.

XKCD: Linguists (and Probably How My Coauthors Feel)

I deeply understand today's XKCD about linguists. Also, given my linguistic tendencies, I think the person in the hole probably has feelings that are similar to those of my coauthors. ;)

And don't forget to read the mouseover text.

A Visual Illusion: Game-and-Watch Style

Here is a visual illusion (in game-and-watch style) for you. The illusion is of the forward motion. It arises from a border of about 1 pixel that lags/leads the dominant color.

This may be the strongest optical illusion I’ve ever seen.pic.twitter.com/J8fCqbQUJ1

— Siqi Chen (@blader) November 22, 2020

(Tip of the cap to Sydney Padua.)

Revenge of the Oxford Comma: 2020 Edition

Truth is stranger than fiction. Always.

Update your lesson plans, we have a new perfect example for Oxford commas. https://t.co/gm1K8IHkGv

— Laura Ansley (@lmansley) November 14, 2020

(Tip of the cap to Jan van den Heuvel.)

2020 Most Valuable Player Awards

Major League Baseball's 2020 Most Valuable Player (MVP) awards were announced today. José Abreu of the Chicago White Sox has been named the American League MVP, and Freddie Freeman of the Atlanta Braves was named the National League MVP. These two were the winners that I expected.

The top-10 vote-getters in each league are available at the above hyperlinks, and the entire list of vote-getters is available at this web page.

2020 Cy Young Awards

Baseball's 2020 Cy Young Awards have now been announced. Unsurprisingly, Shane Bieber of the Cleveland Indians was the unanimous winner in the American League. Free agent Trevor Bauer (who spent 2020 with the Cincinnati Reds) won the National League Cy Young Award over Yu Darvish (of the Cubs) and Jacob deGrom (of the Mets).

2020 Managers of the Year

Baseball's 2020 Managers of the Year have been announced, and both winners are the expected ones: Kevin Cash of the Tampa Bay Rays in the American League and Don Mattingly of the Miami Marlins in the National League. Cash received 22 of the 30 first-place votes, and Mattingly received 20 of the 30 first-place votes. (I expected Mattingly to win unanimously.)

2020 Rookies of the Year

This year's American League Rookie of the Year is Mariners outfielder Kyle Lewis (who won unanimously), and this year's National League Rookie of the Year is Brewers reliever Devin Williams.

Update: The above page about the NL award doesn't (yet) include the vote totals; you can find them on this page.

RIP Alex Trebek (1940–2020)

Alex Trebek, the longtime host of the game show Jeopardy!, died earlier today.

2020 Gold Glove Winners

The winners of the 2020 Gold Glove Awards were announced today.

"Forecasting Elections Using Compartmental Models of Infection"

One of my particularly exciting papers just came out in final form. Here are some details (and a convenient tweet for you to spread it on social media).

Title: Forecasting Elections Using Compartmental Models of Infection

Authors: Alexandria Volkening, Daniel F. Linder, Mason A. Porter, and Grzegorz A. Rempala

Abstract: Forecasting elections---a challenging, high-stakes problem---is the subject of much uncertainty, subjectivity, and media scrutiny. To shed light on this process, we develop a method for forecasting elections from the perspective of dynamical systems. Our model borrows ideas from epidemiology, and we use polling data from United States elections to determine its parameters. Surprisingly, our model performs as well as popular forecasters for the 2012 and 2016 U.S. presidential, senatorial, and gubernatorial races. Although contagion and voting dynamics differ, our work suggests a valuable approach for elucidating how elections are related across states. It also illustrates the effect of accounting for uncertainty in different ways, provides an example of data-driven forecasting using dynamical systems, and suggests avenues for future research on political elections. We conclude with our forecasts for the senatorial and gubernatorial races on 6 November 2018 (which we posted on 5 November 2018).

The published version of our paper on forecasting elections using dynamical systems (with compartmental models of infection) is now live: https://t.co/t2IXPBiXSG

On my webpage: https://t.co/YVfya7jbjy

2020 election forecasts: https://t.co/UQ9MXqAJLh

[cc @al_volkening] pic.twitter.com/CKBbrzt8Vj

— Mason Porter (@masonporter) October 28, 2020

2020* World Champion Los Angeles Dodgers!!!

The Los Angeles Dodgers have won the World Series! 

 Of course, the whole year gets an asterisk (not just the Baseball season). 

 I have been waiting for 32 years, but under the dumpster-fire circumstances of everything, I am much less excited than I would normally be. I'm still very happy about it, but the excitement is less than it would be in normal times. Still, it's great! 

 Let's do this again next year when I can enjoy it more! 

There was some late-breaking news right after the game, and it turns out that Justin Turner was removed from today's game because of a positive COVID-19 test. 

So far, I have received two congratulatory e-mails from undergraduate students of mine and one from a friend. Corey Seager is the World Series; he was also the NLCS MVP. 

Clayton Kershaw has exorcised his demons a bit, and he now has more strikeouts than any other pitcher in postseason history. Obviously, he has benefited from playoffs with many more rounds than used to be the case. 

I need to get a plush COVID-19 with a Dodger cap.

"Songs and Lyrics by Tom Lehrer"

Here's some great news!

Tom Lehrer has released, into the public domain, the lyrics of his songs (also including sheet music for some), including many that you've probably never heard of!!!

There are also alternative lyrics for several songs.

Go here: https://t.co/VKtRztNu1Q

— Mason Porter (@masonporter) October 19, 2020

The Dodgers are Heading to the World Series! (2020 Edition)

The Dodgers have come from behind from a deficit of 3 games to 1 to defeat the Atlanta Braves in game 7 of the National League Championship Series. We're heading to the World Series! 

(It hasn't been announced yet as I write this, but I assume that Corey Seager is going to be named the Most Valuable Player of the NLCS.)

Update: As expected, Seager has been named the MVP.

"Stochastic Block Models are a Discrete Surface Tension"

A paper of mine that was published in advanced access in spring 2019 has finally received its final journal coordinates, so I am blogging about it now (even though it is old news). Here are some details.

  

Title: Stochastic Block Models are a Discrete Surface Tension

Authors: Zachary M. Boyd, Mason A. Porter, and Andrea L. Bertozzi 

Abstract: Networks, which represent agents and interactions between them, arise in myriad applications throughout the sciences, engineering, and even the humanities. To understand large-scale structure in a network, a common task is to cluster a network’s nodes into sets called “communities,” such that there are dense connections within communities but sparse connections between them. A popular and statistically principled method to perform such clustering is to use a family of generative models known as stochastic block models (SBMs). In this paper, we show that maximum-likelihood estimation in an SBM is a network analog of a well-known continuum surface-tension problem that arises from an application in metallurgy. To illustrate the utility of this relationship, we implement network analogs of three surface-tension algorithms, with which we successfully recover planted community structure in synthetic networks and which yield fascinating insights on empirical networks that we construct from hyperspectral videos.

"The Multiplex Nature of Global Financial Contagions"

Our new article came out today. Here are some details.

Title: "The multiplex nature of global financial contagions"

Authors: R. Maria del Rio-Chanona, Yevgeniya Korniyenko, Manasa Patnam, and Mason A. Porter

Abstract: As illustrated by the 2008 global financial crisis, the financial distress of one country can trigger financial distress in other countries. We examine the problem of identifying such “systemically important” countries (i.e., countries whose financial distress can trigger further distress), which is important for assessing global financial stability. Using data on bilateral financial positions that are split by asset type, we build a multiplex global financial network in which nodes represent countries, edges encode cross-country financial assets of various types, and layers represent asset types. We examine the temporal evolution of a measure of node importance known as MultiRank centrality, and we find that several major European countries decrease in rank and that several major Asian countries increase in rank since 2008. We then develop a multiplex threshold model of financial contagions in which a shock can propagate either within a layer or between layers. We find that the number of systemically important countries can be twice as large when we take into account the heterogeneity of financial exposures (i.e., when using a multiplex network) than in a contagion on an associated aggregate global financial network (i.e., on a monolayer network), as is often examined in other studies. We also study the extent to which buffers can reduce the propagation of financial distress. Our analysis suggests that accounting for both intralayer and interlayer propagation of contagions in a multiplex structure of financial assets is important for understanding interconnected financial systems of countries.

RIP Joe Morgan (1943–2020)

The baseball world has lost another great one. Second baseman Joe Morgan died today. We have lost a lot of Hall of Famers in the past few weeks (most recently Whitey Ford, before today).

Dodgers Advance to the National League Championship Series!

The Dodgers have just finished sweeping the San Diego Padres in their National League Division Series matchup and are heading to the National League Championship Series, where they will face (and hopefully defeat) the Atlanta Braves.

Some Notable American Physical Society Spring 2021 Prizes

The American Physical Society (APS) has announced its Spring 2021 prizes. It includes some awards to some great people in topics of interest to me. Here are ones that I want to highlight.

2021 Dannie Heineman Prize for Mathematical Physics

Joel L. Lebowitz, Rutgers University

For seminal contributions to nonequilibrium and equilibrium statistical mechanics, in particular, studies of large deviations in nonequilibrium steady states and rigorous analysis of Gibbs equilibrium ensembles.

2021 Leo P. Kadanoff Prize

Sidney Redner, Santa Fe Institute

For leadership in transcending traditional disciplinary boundaries by applying and advancing deep concepts and methods of statistical physics to gain novel insights into diverse real-world phenomena.

2021 Lars Onsager Prize

Lev P. Pitaevskii, INO-CNR BEC Center, University of Trento; Kapitza Institute for Physical Problems, Russian Academy of Sciences

For originating the Gross-Pitaevskii theory of non-uniform Bose-Einstein condensates and subsequent extensive contributions to the theory of quantum fluids, especially as applied to ultracold atomic gases.

2021 Early Career Award for Soft Matter Research

Eleni Katifori, University of Pennsylvania

For the seminal use of physical principles in understanding living transport networks.

2020 Nobel Prize in Physics

The 2020 Nobel Prize in Physics was announced today.

The first thing that I noticed was that my Mathematical Institute (Unversity of Oxford) colleague Roger Penrose got half the prize. Additionally, Andrea Ghez from UCLA's physics department shared the other half of the prize with Reinhard Genzel. Ghez also got a Ph.D. from Caltech in 1992, so several of my institutions (and my former home department at Oxford!) did very well today. Congratulations!

Here is the terse citation: 

The Royal Swedish Academy of Sciences has decided to award the Nobel Prize in Physics 2020 with one half to Roger Penrose "for the discovery that black hole formation is a robust prediction of the general theory of relativity" and and the other half jointly to Reinhard Genzel and Andrea Ghez "for the discovery of a supermassive compact object at the centre of our galaxy".

Some other websites to look at are the popular blurb and more advanced information from the Nobel page. Additionally, here are UCLA's press release and a blurb from University of Oxford's Mathematical Institute.

RIP Bob Gibson (1935–2020)

Baseball has lost yet another immortal. Hall of Fame pitcher Bob Gibson died today at the age of 84. (Tip of the cap to Gregg Schneider.)

Dodgers Advance to the Division Series!

Clayton Kershaw had his most dominant performance of 2020, advancing the Dodgers over the Brewers in their "Wild Card Series". This advances us to a Division Series against the winner of the Cardinals–Padres series. The Padres are a more dangerous team, but they're also a more interesting one, so I hope that we play them.

RIP Jay Johnstone (1945–2020)

Baseball player and noted prankster Jay Johnstone died today. Here is ESPN's article about it.

Also, read his books. They're hilarious.

Personal Dice

Thanks very much to @chadtopaz for designing these dice for me!

It was awesome to wake up to these designs on social media.

I need to get these made in physical form. I especially want something in d20 form. pic.twitter.com/20gx0Vy6fq

— Mason Porter (@masonporter) September 27, 2020

2020 Ig Nobel Laureates

This year's Ig Nobel laureates were announced in today's ceremony. 

 I have some fondness for the Physics prize (for exciting Faraday-like waves in earthworms), given that nonlinear dynamics and pattern formation are involved, and several of the other ones are also very amusing, but I think that my favorite one this year is the one in Management:

(奚广安) Xi Guang-An, (莫天祥) Mo Tian-Xiang, (杨康生) Yang Kang-Sheng, (杨广生) Yang Guang-Sheng, and (凌显四) Ling Xian Si, five professional hitmen in Guangxi, China, who managed a contract for a hit job (a murder performed for money) in the following way: After accepting payment to perform the murder, Xi Guang-An then instead subcontracted the task to Mo Tian-Xiang, who then instead subcontracted the task to Yang Kang-Sheng, who then instead subcontracted the task to Yang Guang-Sheng, who then instead subcontracted the task to Ling Xian-Si, with each subsequently enlisted hitman receiving a smaller percentage of the fee, and nobody actually performing a murder.