arXiv subjects

Mason A. Porter

Publications and source records attributed to Mason A. Porter.

At least 91 records · Page 5Linked to original sources

arXiv2020

A unified framework for equivalences in social networks

A key concern in network analysis is the study of social positions and roles of actors in a network. The notion of "position" refers to an equivalence class of nodes that have similar ties to other nodes, whereas a "role" is an equivalence class of compound relations that connect the same pairs of nodes. An open question in network science is whether it is possible to simultaneously perform role and positional analysis. Motivated by the principle of functoriality in category theory we propose a new method that allows to tie role and positional analysis together. We illustrate our methods on two well-studied data sets in network science.

cs.SI↗

arXiv2020

Spatial Applications of Topological Data Analysis: Cities, Snowflakes, Random Structures, and Spiders Spinning Under the Influence

Spatial networks are ubiquitous in social, geographical, physical, and biological applications. To understand the large-scale structure of networks, it is important to develop methods that allow one to directly probe the effects of space on structure and dynamics. Historically, algebraic topology has provided one framework for rigorously and quantitatively describing the global structure of a space, and recent advances in topological data analysis (TDA) have given scholars a new lens for analyzing network data. In this paper, we study a variety of spatial networks -- including both synthetic and natural ones -- using novel topological methods that we recently developed for analyzing spatial networks. We demonstrate that our methods are able to capture meaningful quantities, with specifics that depend on context, in spatial networks and thereby provide useful insights into the structure of those networks, including a novel approach for characterizing them based on their topological structures. We illustrate these ideas with examples of synthetic networks and dynamics on them, street networks in cities, snowflakes, and webs spun by spiders under the influence of various psychotropic substances.

cs.SI↗

arXiv2020

Migration Networks: Applications of Network Analysis to Macroscale Migration Patterns

An emerging area of research is the study of macroscale migration patterns as a network of nodes that represent places (e.g., countries, cities, and rural areas) and edges that encode migration ties that connect those places. In this chapter, we first review advances in the study of migration networks and recent work that has employed network analysis to examine such networks at different geographical scales. In our discussion, we focus in particular on global scale migration networks. We then propose ways to leverage network analysis in concert with digital technologies and online geolocated data to examine the structure and dynamics of migration networks. The implementation of such approaches for studying migration networks faces many challenges, including ethical ones, methodological ones, socio-technological ones (e.g., data availability and reuse), and research reproducibility. We detail these challenges, and we then consider possible ways of linking digital geolocated data to administrative and survey data as a way of harnessing new technologies to construct increasingly realistic migration networks (e.g., using multiplex networks). We also briefly discuss new methods (e.g., multilayer network analysis) in network analysis and adjacent fields (e.g., machine learning) that can help advance understanding of macroscale patterns of migration.

cs.SI↗

arXiv2020

Random walks and diffusion on networks

Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can be used to extract information about important entities or dense groups of entities in a network. Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures. In the present article, we survey the theory and applications of random walks on networks, restricting ourselves to simple cases of single and non-adaptive random walkers. We distinguish three main types of random walks: discrete-time random walks, node-centric continuous-time random walks, and edge-centric continuous-time random walks. We first briefly survey random walks on a line, and then we consider random walks on various types of networks. We extensively discuss applications of random walks, including ranking of nodes (e.g., PageRank), community detection, respondent-driven sampling, and opinion models such as voter models.

physics.soc-ph↗

arXiv2020

Spatial Strength Centrality and the Effect of Spatial Embeddings on Network Architecture

For many networks, it is useful to think of their nodes as being embedded in a latent space, and such embeddings can affect the probabilities for nodes to be adjacent to each other. In this paper, we extend existing models of synthetic networks to spatial network models by first embedding nodes in Euclidean space and then modifying the models so that progressively longer edges occur with progressively smaller probabilities. We start by extending a geographical fitness model by employing Gaussian-distributed fitnesses, and we then develop spatial versions of preferential attachment and configuration models. We define a notion of "spatial strength centrality" to help characterize how strongly a spatial embedding affects network structure, and we examine spatial strength centrality on a variety of real and synthetic networks.

physics.soc-ph↗

arXiv2020

Social Network Analysis for Social Neuroscientists

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 pursue this issue, advancing 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 implementation 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.

cs.SI↗

arXiv2020

Fitting In and Breaking Up: A Nonlinear Version of Coevolving Voter Models

We investigate a nonlinear version of coevolving voter models, in which node states and network structure update as a coupled stochastic dynamical process. Most prior work on coevolving voter models has focused on linear update rules with fixed and homogeneous rewiring and adopting probabilities. By contrast, in our nonlinear version, the probability that a node rewires or adopts is a function of how well it "fits in" within its neighborhood. To explore this idea, we incorporate a parameter $σ$ that represents the fraction of neighbors of an updating node that share its opinion state. In an update, with probability $σ^q$ (for some nonlinearity parameter $q$), the updating node rewires; with complementary probability $1-σ^q$, the updating node adopts a new opinion state. We study this mechanism using three rewiring schemes: after an updating node deletes a discordant edge, it then either (1) "rewires-to-random" by choosing a new neighbor in a random process; (2) "rewires-to-same" by choosing a new neighbor in a random process from nodes that share its state; or (3) "rewires-to-none" by not rewiring at all (akin to "unfriending" on social media). We compare our nonlinear coevolving model to several existing linear models, and we find in our model that initial network topology plays a larger role in the dynamics and the choice of rewiring mechanism plays a smaller role. A particularly interesting feature of our model is that, under certain conditions, the opinion state that is held initially by a minority of the nodes can effectively spread to almost every node in a network if the minority nodes view themselves as the majority. In light of this observation, we relate our results to recent work on the majority illusion in social networks.

physics.soc-ph↗

arXiv2020

Pull out all the stops: Textual analysis via punctuation sequences

Whether enjoying the lucid prose of a favorite 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 marvelously 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)?

cs.CL↗

arXiv2020

A Model for the Influence of Media on the Ideology of Content in Online Social Networks

Many people rely on online social networks as sources of news and information, and the spread of media content with ideologies across the political spectrum influences online discussions and impacts actions offline. To examine the impact of media in online social networks, we generalize bounded-confidence models of opinion dynamics by incorporating media accounts as influencers in a network. We quantify partisanship of content with a continuous parameter on an interval, and we formulate higher-dimensional generalizations to incorporate content quality and increasingly nuanced political positions. We simulate our model with one and two ideological dimensions, and we use the results of our simulations to quantify the "entrainment" of content from non-media accounts to the ideologies of media accounts in a network. We maximize media impact in a social network by tuning the number of media accounts that promote the content and the number of followers of the accounts. Using numerical computations, we find that the entrainment of the ideology of content spread by non-media accounts to media ideology depends on a network's structural features, including its size, the mean number of followers of its nodes, and the receptiveness of its nodes to different opinions. We then introduce content quality --- a key novel contribution of our work --- into our model. We incorporate multiple media sources with ideological biases and quality-level estimates that we draw from real media sources and demonstrate that our model can produce distinct communities ("echo chambers") that are polarized in both ideology and quality. Our model provides a step toward understanding content quality and ideology in spreading dynamics, with ramifications for how to mitigate the spread of undesired content and promote the spread of desired content.

physics.soc-ph↗

arXiv2019

A Framework for the Construction of Generative Models for Mesoscale Structure in Multilayer Networks

Multilayer networks allow one to represent diverse and coupled connectivity patterns --- e.g., time-dependence, multiple subsystems, or both --- that arise in many applications and which are difficult or awkward to incorporate into standard network representations. In the study of multilayer networks, it is important to investigate mesoscale (i.e., intermediate-scale) structures, such as dense sets of nodes known as communities, to discover network features that are not apparent at the microscale or the macroscale. The ill-defined nature of mesoscale structure and its ubiquity in empirical networks make it crucial to develop generative models that can produce the features that one encounters in empirical networks. Key purposes of such generative models include generating synthetic networks with empirical properties of interest, benchmarking mesoscale-detection methods and algorithms, and inferring structure in empirical multilayer networks. In this paper, we introduce a framework for the construction of generative models for mesoscale structures in multilayer networks. Our framework provides a standardized set of generative models, together with an associated set of principles from which they are derived, for studies of mesoscale structures in multilayer networks. It unifies and generalizes many existing models for mesoscale structures in fully-ordered (e.g., temporal) and unordered (e.g., multiplex) multilayer networks. One can also use it to construct generative models for mesoscale structures in partially-ordered multilayer networks (e.g., networks that are both temporal and multiplex). Our framework has the ability to produce many features of empirical multilayer networks, and it explicitly incorporates a user-specified dependency structure between layers.

cs.SI↗

arXiv2019

Nonlinearity + Networks: A 2020 Vision

I briefly survey several fascinating topics in networks and nonlinearity. I highlight a few methods and ideas, including several of personal interest, that I anticipate to be especially important during the next several years. These topics include temporal networks (in which the entities and/or their interactions change in time), stochastic and deterministic dynamical processes on networks, adaptive networks (in which a dynamical process on a network is coupled to dynamics of network structure), and network structure and dynamics that include "higher-order" interactions (which involve three or more entities in a network). I draw examples from a variety of scenarios, including contagion dynamics, opinion models, waves, and coupled oscillators.

cs.SI↗

arXiv2019

Dominance, Sharing, and Assessment in an Iterated Hawk--Dove Game

Animals use a wide variety of strategies to reduce or avoid aggression in conflicts over resources. These strategies range from sharing resources without outward signs of conflict to the development of dominance hierarchies, in which initial fighting is followed by the submission of subordinates. Although models have been developed to analyze specific strategies for resolving conflicts over resources, little work has focused on trying to understand why particular strategies are more likely to arise in certain situations. In this paper, we use a model based on an iterated Hawk--Dove game to analyze how resource holding potentials (RHPs) and other factors affect whether sharing, dominance relationships, or other behaviours are evolutionarily stable. We find through extensive numerical simulations that sharing is stable only when the cost of fighting is low and the animals in a contest have similar RHPs, whereas dominance relationships are stable in most other situations. We also explore what happens when animals are unable to assess each other's RHPs without fighting, and we compare a range of strategies for this problem using simulations. We find (1) that the most successful strategies involve a limited period of assessment followed by a stable relationship in which fights are avoided and (2) that the duration of assessment depends both on the costliness of fighting and on the difference between the animals' RHPs. Along with our direct work on modeling and simulations, we develop extensive software to facilitate further testing; it is available at \url{https://bitbucket.org/CameronLHall/dominancesharingassessmentmatlab/}.

q-bio.PE↗

arXiv2019

Random-Graph Models and Characterization of Granular Networks

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.

cond-mat.soft↗

arXiv2019

Online reactions to the 2017 'Unite the Right' rally in Charlottesville: Measuring polarization in Twitter networks using media followership

We study the Twitter conversation following the August 2017 `Unite the Right' rally in Charlottesville, Virginia, using tools from network analysis and data science. We use media followership on Twitter and principal component analysis (PCA) to compute a `Left'/`Right' media score on a one-dimensional axis to characterize nodes. We then use these scores, in concert with retweet relationships, to examine the structure of a retweet network of approximately 300,000 accounts that communicated with the #Charlottesville hashtag. The retweet network is sharply polarized, with an assortativity coefficient of 0.8 with respect to the sign of the media PCA score. Community detection using two approaches, a Louvain method and InfoMap, yields largely homogeneous communities in terms of Left/Right node composition. When comparing tweet content, we find that tweets about `Trump' were widespread in both the Left and Right, though the accompanying language was unsurprisingly different. Nodes with large degrees in communities on the Left include accounts that are associated with disparate areas, including activism, business, arts and entertainment, media, and politics. Support of Donald Trump was a common thread among the Right communities, connecting communities with accounts that reference white-supremacist hate symbols, communities with influential personalities in the alt-right, and the largest Right community (which includes the Twitter account FoxNews).

cs.SI↗

arXiv2019

Customer mobility and congestion in supermarkets

The analysis and characterization of human mobility using population-level mobility models is important for numerous applications, ranging from the estimation of commuter flows in cities to modeling trade flows between countries. However, almost all of these applications have focused on large spatial scales, which typically range between intra-city scales to inter-country scales. In this paper, we investigate population-level human mobility models on a much smaller spatial scale by using them to estimate customer mobility flow between supermarket zones. We use anonymized, ordered customer-basket data to infer empirical mobility flow in supermarkets, and we apply variants of the gravity and intervening-opportunities models to fit this mobility flow and estimate the flow on unseen data. We find that a doubly-constrained gravity model and an extended radiation model (which is a type of intervening-opportunities model) can successfully estimate 65--70\% of the flow inside supermarkets. Using a gravity model as a case study, we then investigate how to reduce congestion in supermarkets using mobility models. We model each supermarket zone as a queue, and we use a gravity model to identify store layouts with low congestion, which we measure either by the maximum number of visits to a zone or by the total mean queue size. We then use a simulated-annealing algorithm to find store layouts with lower congestion than a supermarket's original layout. In these optimized store layouts, we find that popular zones are often in the perimeter of a store. Our research gives insight both into how customers move in supermarkets and into how retailers can arrange stores to reduce congestion. It also provides a case study of human mobility on small spatial scales.

physics.soc-ph↗

arXiv2019

Supracentrality Analysis of Temporal Networks with Directed Interlayer Coupling

We describe centralities in temporal networks using a supracentrality framework to study centrality trajectories, which characterize how the importances of nodes change in time. We study supracentrality generalizations of eigenvector-based centralities, a family of centrality measures for time-independent networks that includes PageRank, hub and authority scores, and eigenvector centrality. We start with a sequence of adjacency matrices, each of which represents a time layer of a network at a different point or interval of time. Coupling centrality matrices across time layers with weighted interlayer edges yields a \emph{supracentrality matrix} $\mathbb{C}(ω)$, where $ω$ controls the extent to which centrality trajectories change over time. We can flexibly tune the weight and topology of the interlayer coupling to cater to different scientific applications. The entries of the dominant eigenvector of $\mathbb{C}(ω)$ represent \emph{joint centralities}, which simultaneously quantify the importance of every node in every time layer. Inspired by probability theory, we also compute \emph{marginal} and \emph{conditional centralities}. We illustrate how to adjust the coupling between time layers to tune the extent to which nodes' centrality trajectories are influenced by the oldest and newest time layers. We support our findings by analysis in the limits of small and large $ω$.

cs.SI↗

arXiv2019

Persistent Homology of Geospatial Data: A Case Study with Voting

A crucial step in the analysis of persistent homology is the transformation of data into an appropriate topological object (in our case, a simplicial complex). Modern packages for persistent homology often 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 these 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, demonstrating that our new constructions can capture geometric characteristics that are missed by distance-based 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 behaviors in densely populated cities) from short-persistence noise by incorporating information about other spatial relationships between precincts.

cs.CG↗

arXiv2019

A two-patch epidemic model with nonlinear reinfection

The propagation of infectious diseases and its impact on individuals play a major role in disease dynamics, and it is important to incorporate population heterogeneity into efforts to study diseases. As a simplistic but illustrative example, we examine interactions between urban and rural populations in the dynamics of disease spreading. Using a compartmental framework of susceptible--infected--susceptible ($\mathrm{SI\widetilde{S}}$) dynamics with some level of immunity, we formulate a model that allows nonlinear reinfection. We investigate the effects of population movement in the simplest scenario: a case with two patches, which allows us to model movement between urban and rural areas. To study the dynamics of the system, we compute a basic reproduction number for each population (urban and rural). We also compute steady states, determine the local stability of the disease-free steady state, and identify conditions for the existence of endemic steady states. From our analysis and computational experiments, we illustrate that population movement plays an important role in disease dynamics. In some cases, it can be rather beneficial, as it can enlarge the region of stability of a disease-free steady state.

q-bio.PE↗