Friday, December 31, 2021
Thursday, December 30, 2021
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
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
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
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
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
Saturday, November 27, 2021
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
Thursday, November 18, 2021
Wednesday, November 17, 2021
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
As with the Rookies of the Year, neither winner is surprising.
Monday, November 15, 2021
Neither choice is surprising.
Wednesday, November 10, 2021
Friday, November 05, 2021
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"
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
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
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
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
(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
And I enjoy the career that I picked
Really love it
I am your math prof
And I get off on the pain I inflict
Really love it
I thrill when I ask a 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
'Cause I'm a math prof and a success
Now prove it!
Thursday, September 09, 2021
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
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
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
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
Friday, July 16, 2021
My current Mathematics Genealogy (with doctoral students only): https://t.co/EAOiY0tasi— Mason Porter (@masonporter) July 16, 2021
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
Thursday, July 08, 2021
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
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
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
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
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
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
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.— Mason Porter (@masonporter) April 4, 2021
PSA 2: Survivorship bias is a good thing to remember. pic.twitter.com/XaPk2Eoo0f
Wednesday, March 31, 2021
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
Wednesday, March 17, 2021
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— Mason Porter (@masonporter) March 18, 2021
(plus special guest appearances by several Pokémon)
Tuesday, March 16, 2021
😱🙄🤔🙀🤢— Mason Porter (@masonporter) March 16, 2021
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
Monday, March 15, 2021
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.)
Saturday, March 13, 2021
Tuesday, March 09, 2021
Thursday, February 25, 2021
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
A tribute has been posted on the UK government page.
Here is her Wikipedia entry.
Tuesday, February 09, 2021
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
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
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
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
Title: Tunable Eigenvector-Based Centralities for Multiplex and Temporal Networks
Authors: Dane Taylor, Mason A. Porter, and Peter J. Mucha
Friday, January 22, 2021
(Tip of the cap to Gregg Schneider.)
Tuesday, January 19, 2021
Friday, January 08, 2021
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.