## Monday, January 17, 2022

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

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

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

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

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

## Sunday, January 16, 2022

### The PrickRank' Algorithm

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

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

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

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

## Sunday, January 09, 2022

### The Donkey Kong Visual Illusion

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

## Thursday, January 06, 2022

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

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

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

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

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

## 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.