Friday, December 31, 2021

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.

Thursday, December 30, 2021

"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.

Thursday, December 23, 2021

"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.

Tuesday, December 14, 2021

"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.

Friday, December 10, 2021

"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.

Tuesday, December 07, 2021

Sunday, December 05, 2021

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.

Wednesday, December 01, 2021

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!

Saturday, November 27, 2021

"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.

Monday, November 22, 2021

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.

Thursday, November 18, 2021

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.

Wednesday, November 17, 2021

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.

Tuesday, November 16, 2021

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.

Monday, November 15, 2021

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.

Wednesday, November 10, 2021

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.

Friday, November 05, 2021

"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.

Friday, October 15, 2021

"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.

Thursday, October 14, 2021

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.

Wednesday, October 06, 2021

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.

Sunday, October 03, 2021

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).

Wednesday, September 15, 2021

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

“Math Prof”

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

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

What did she say?

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

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?

Oh that hurts! I don’t know!

Oh, shut up. Think faster. Now go!
I am your math prof

Goodness gracious!

And I enjoy the career that I picked

Really love it

I am your math prof

Proving theorems

And I get off on the pain I inflict

Really love it

I thrill when I ask a tough question

Tough question
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!


Say mu!


Say nu!


Now prove it!

Thursday, September 09, 2021

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).

Thursday, August 26, 2021

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.

Friday, August 06, 2021

"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.

Friday, July 30, 2021

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".

Tuesday, July 27, 2021

XKCD and Flawed Data

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

Friday, July 16, 2021

My Current Mathematics Genealogy

Here is my current mathematics genealogy.

Thursday, July 08, 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.

Monday, June 28, 2021

"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.

Thursday, May 20, 2021

"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.

Tuesday, May 18, 2021

"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.

Friday, May 07, 2021

"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.

Tuesday, April 06, 2021

"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.

Sunday, April 04, 2021

Some Academic Struggles and Survivorship Bias

Wednesday, March 31, 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.

Wednesday, March 24, 2021

"Twitter" in 1803: The Finger of Contempt

Wednesday, March 17, 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.

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."

Tuesday, March 16, 2021

My Top-5 Emoji: The Power of Positive Thinking

Monday, March 15, 2021

An Ancient Roman d20

This is very cool!

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

(Tip of the cap to Chris Klausmeier.)

Saturday, March 13, 2021

Pro Tip: Life is Short. Be Cat 3.

(Tip of the cap to Yisong Yue.)

Tuesday, March 09, 2021

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.)

Thursday, February 25, 2021

"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).

Monday, February 15, 2021

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.

Tuesday, February 09, 2021

"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.

Friday, February 05, 2021

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.

Thursday, February 04, 2021

"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.

Tuesday, January 26, 2021

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.

Sunday, January 24, 2021

"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

Friday, January 22, 2021

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.)

Tuesday, January 19, 2021

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.)

Friday, January 08, 2021

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.