"Ginzburg–Landau Functionals in the Large-Graph Limit"

Another of my papers has appeared in final form. Here are some details.

Title: Ginzburg–Landau Functionals in the Large-Graph Limit

Authors: Edith J. Zhang, James Scott, Qiang Du, and Mason A. Porter

Abstract: Ginzburg–Landau (GL) functionals on graphs, which are relaxations of graph-cut functionals on graphs, have yielded a variety of insights in image segmentation and graph clustering. In this paper, we study large-graph limits of GL functionals by taking a functional-analytic view of graphs as nonlocal kernels. For a graph W_n with n nodes, the corresponding graph GL functional GL_ϵ^{W_n} is an energy for functions on W_n. We minimize GL functionals on sequences of growing graphs that converge to functions called graphons. For such sequences of graphs, we show that the graph GL functional Γ-converges to a continuous and nonlocal functional that we call the graphon GL functional. We investigate the sharp-interface limits of the graph GL and graphon GL functionals, and we relate these limits to a nonlocal total-variation (TV) functional. We express the limiting GL functional in terms of Young measures and thereby obtain a probabilistic interpretation of the minimization problem in the large-graph limit. Finally, to develop intuition about graphon GL functionals, we determine the GL minimizer for several example families of graphons.

"Bounded-Confidence Opinion Models with Random-Time Interactions"

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

Title: Bounded-Confidence Opinion Models with Random-Time Interactions

Authors: Weiqi Chu and Mason A. Porter

Abstract: In models of opinion dynamics, agents interact with each other and can change their opinions as a result of those interactions. One type of opinion model is a bounded-confidence model (BCM), in which opinions take continuous values and interacting agents compromise their opinions with each other if their opinions are sufficiently similar. In studies of BCMs, researchers typically assume that interactions between agents occur at deterministic times. This assumption neglects an inherent element of randomness in social interactions, and it is desirable to account for it. In this paper, we study BCMs on networks and allow agents to interact at random times. To incorporate random-time interactions, we use renewal processes to determine social-interaction event times, which can follow arbitrary interevent-time distributions (ITDs). We establish connections between these random-time-interaction BCMs and deterministic-time-interaction BCMs. We analyze the quantitative impact of ITDs on the transient dynamics of BCMs and derive approximate governing equations for the time-dependent expectations of the BCM dynamics. We find that BCMs with Markovian ITDs have consistent statistical properties (in particular, they have the same expected time-dependent opinions) when the ITDs have the same mean but that the statistical properties of BCMs with non-Markovian ITDs depend on the type of ITD even when the ITDs have the same mean. We numerically examine the transient and steady-state dynamics of our BCMs with various ITDs on different networks, and we compare their expected order-parameter values and expected convergence times.

"Clustering-Induced Localization of Quantum Walks on Networks"

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

Title: Clustering-Induced Localization of Quantum Walks on Networks

Authors: Lucas Böttcher and Mason A. Porter

"Dynamical Processes on Metric Networks"

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

Title: Dynamical Processes on Metric Networks

Authors: Lucas Böttcher and Mason A. Porter

What Happens in Dresden Stays in Dresden (2025 Edition)

I'm heading to Dresden to give a colloquium at the Max Planck Institute for the Physics of Complex Systems.

"Perceived Community Alignment Increases Information Sharing"

One of my papers was published in final form today. Here are some details about it.

Title: Perceived Community Alignment Increases Information Sharing

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

Abstract: It has been proposed that information sharing, which is a ubiquitous and consequential behavior, plays a critical role in cultivating and maintaining a sense of shared reality. Across three studies, we test this theory by investigating whether or not people are especially likely to share information that they believe will be interpreted similarly by others in their social circles. Using neuroimaging data collected while people who live in the same residential community viewed brief film clips, we find that more similar neural responses across participants is associated with a greater likelihood to share content. We then test this relationship using two behavioral studies and find (1) that people are particularly likely to share content that they believe others in their social circles will interpret similarly and (2) that perceived similarity with others leads to increased sharing likelihood. In concert, our findings support the idea that people are driven to share information to create and reinforce shared understanding, which is critical to social connection.

What Happens in the Research Triangle Stays in the Research Triangle (2025 Edition)

I am flying over to the Research Triangle in North Carolina to give talks at NC State and UNC Chapel Hill and also to talk shop with some of my collaborators.

"Minimizing Congestion in Single-Source, Single-Sink Queuing Networks"

Another of my papers has appeared in final form. Here are some details about it.

Title: Minimizing Congestion in Single-Source, Single-Sink Queuing Networks

Authors: Fabian Ying, Alisdair O. G. Wallis, Mason A. Porter, Sam D. Howison, and Mariano Beguerisse-Díaz

Abstract: Motivated by the modeling of customer mobility and congestion in supermarkets, we study queueing networks with a single source and a single sink. We assume that walkers traverse a network according to an unbiased random walk, and we analyze how network topology affects the total mean queue size Q, which we use to measure congestion. We examine network topologies that minimize Q and provide proofs of optimality for some cases and numerical evidence of optimality for others. Finally, we present greedy algorithms that add edges to and delete edges from a network to reduce Q, and we apply these algorithms to a network that we construct using a supermarket store layout. We find that these greedy algorithms, which typically tend to add edges to the sink node, are able to significantly reduce Q. Our work helps improve understanding of how to design networks with low congestion and how to amend networks to reduce congestion.

"Recurrence Recovery in Heterogeneous Fermi–Pasta–Ulam–Tsingou Systems"

Another of my papers was published in final form today. Here are some details.

Title: Recurrence Recovery in Heterogeneous Fermi–Pasta–Ulam–Tsingou Systems

Authors: Zidu Li, Mason A. Porter, and Bhaskar Choubey

Abstract: The computational investigation of Fermi, Pasta, Ulam, and Tsingou (FPUT) of arrays of nonlinearly coupled oscillators has led to a wealth of studies in nonlinear dynamics. Most studies of oscillator arrays have considered homogeneous oscillators, even though there are inherent heterogeneities between individual oscillators in real-world arrays. Well-known FPUT phenomena, such as energy recurrence, can break down in such heterogeneous systems. In this paper, we present an approach—the use of structured heterogeneities—to recover recurrence in FPUT systems in the presence of oscillator heterogeneities. We examine oscillator variabilities in FPUT systems with cubic nonlinearities, and we demonstrate that centrosymmetry in oscillator arrays may be an important source of recurrence.

What Happens in Richland Stays in Richland

I'll soon be visiting Pacific Northwest National Laboratory as part of a Directory Advisory Committee.

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

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

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

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

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

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

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

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

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

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

"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.

"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.

"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 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).

"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.

"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.

"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.