"Emergence of Polarization in a Sigmoidal Bounded-Confidence Model of Opinion Dynamics"

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

Title: Emergence of Polarization in a Sigmoidal Bounded-Confidence Model of Opinion Dynamics

Authors: Heather Z. Brooks, Philip S. Chodrow, and Mason A. Porter

Abstract: We study a nonlinear bounded-confidence model (BCM) of continuous-time opinion dynamics on networks with both persuadable individuals and zealots. The model is parameterized by a nonnegative scalar \gamma, which controls the steepness of a smooth influence function. This influence function encodes the relative weights that individuals place on the opinions of other individuals. When \gamma = 0, this influence function recovers Taylor's averaging model; when \gamma \rightarrow \infty, the influence function converges to that of a modified Hegselmann--Krause (HK) BCM. Unlike the classical HK model, however, our sigmoidal bounded-confidence model (SBCM) is smooth for any finite \gamma. We show that the set of steady states of our SBCM is qualitatively similar to that of the Taylor model when \gamma is small and that the set of steady states approaches a subset of the set of steady states of a modified HK model as \gamma \rightarrow \infty. For certain special graph topologies, we give analytical descriptions of important features of the space of steady states. A notable result is a closed-form relationship between graph topology and the stability of polarized states in a simple special case that models echo chambers in social networks. Because the influence function of our BCM is smooth, we are able to study it with linear stability analysis, which is difficult to employ with the usual discontinuous influence functions in BCMs.

"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.

"Social Network Analysis for Social Neuroscientists"

A paper of mine that was posted in advanced access more than a year ago has now finally been posted in final form. It is a survey and perspective article on social network analysis for social neuroscientists. Here are some details.

Title: Social Network Analysis for Social Neuroscientists

Authors: Elisa C. Baek, Mason A. Porter, and Carolyn Parkinson

Abstract: Although social neuroscience is concerned with understanding how the brain interacts with its social environment, prevailing research in the field has primarily considered the human brain in isolation, deprived of its rich social context. Emerging work in social neuroscience that leverages tools from network analysis has begun to advance knowledge of how the human brain influences and is influenced by the structures of its social environment. In this paper, we provide an overview of key theory and methods in network analysis (especially for social systems) as an introduction for social neuroscientists who are interested in relating individual cognition to the structures of an individual’s social environments. We also highlight some exciting new work as examples of how to productively use these tools to investigate questions of relevance to social neuroscientists. We include tutorials to help with practical implementations of the concepts that we discuss. We conclude by highlighting a broad range of exciting research opportunities for social neuroscientists who are interested in using network analysis to study social systems.

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

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

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

Authors: Yacoub H. Kureh and Mason A. Porter

Abstract: We investigate a nonlinear version of coevolving voter models, in which node states and network structure update as a coupled stochastic 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” with the nodes in its neighborhood. To explore this idea, we incorporate a local-survey parameter σ_i that encodes the fraction of neighbors of an updating node i that share its opinion state. In an update, with probability σ^q_i(for some nonlinearity parameter q), the updating node rewires; with complementary probability 1 − σ^q_i, the updating node adopts a new opinion state. We study this mechanism using three rewiring schemes: after an updating node deletes one of its discordant edges, 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 compar eour nonlinear coevolving voter model to several existing linear coevolving voter models on various network architectures. Relative to those models, we find in our model that initial network topology plays a larger role in the dynamics and that 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.

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

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

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

Authors: Heather Z. Brooks and Mason A. Porter

Abstract: 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 offline actions. 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 nonmedia 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 and the numbers of followers of those accounts. Using numerical computations, we find that the entrainment of the ideology of content that is spread by nonmedia 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.

"Who is the Most Important Character in Frozen? What Networks Can Tell Us about the World"

Petter Holme, Hiroki Sayama, and I decided to take on the challenge of writing a mathematics paper for Frontiers for Young Minds, a scientific journal for young readers. Only a handful of mathematics papers have been published among their many hundreds of articles. We decided to give an introduction to networks through the movie Frozen and calculation of centralities. Our paper came out today, and here are some details. You can take a look at our paper either at their website or in .pdf form.

Title: Who is the Most Important Character in Frozen? What Networks Can Tell Us about the World

Authors: Petter Holme, Mason A. Porter, and Hiroki Sayama

Abstract: How do we determine the important characters in a movie like Frozen? We can watch it, of course, but there are also other ways—using mathematics and computers—to see who is important in the social network of a story. The idea is to compute numbers called centralities, which are ways of measuring who is important in social networks. In this paper, we talk about how different types of centralities measure importance in different ways. We also discuss how people use centralities to study many kinds of networks, not just social ones. Scientists are now developing centrality measures that also consider changes over time and different types of relationships.

"Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction"

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

Title: Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction

Authors: Baichuan Yuan, Hao Li, Andrea L. Bertozzi, P. Jeffrey Brantingham, and Mason A. Porter

Abstract: There is often latent network structure in spatial and temporal data, and the tools of network analysis can yield fascinating insights into such data. In this paper, we develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. In contrast to prior work on network reconstruction with point-process models, which has often focused on exclusively temporal information, our approach uses both temporal and spatial information and does not assume a specific parametric form of network dynamics. This leads to an effective way of recovering an underlying network. We illustrate our approach using both synthetic networks and networks that we construct from real-world data sets (a location-based social-media network, a narrative of crime events, and violent gang crimes). Our results demonstrate that, in comparison to using only temporal data, our spatiotemporal approach yields improved network reconstruction, providing a basis for meaningful subsequent analysis—such as examinations of community structure and motifs—of the reconstructed networks.

"The Use of Multilayer Network Analysis in Animal Behaviour"

One of my articles came out in final form today. Here are some details.

Title: The Use of Multilayer Network Analysis in Animal Behaviour

Authors: Kelly R. Finn, Matthew J. Silk, Mason A. Porter, and Noa Pinter-Wollman

Abstract: Network analysis has driven key developments in research on animal behaviour by providing quantitative methods to study the social structures of animal groups and populations. A recent formalism, known as multilayer network analysis, has advanced the study of multifaceted networked systems in many disciplines. It offers novel ways to study and quantify animal behaviour through connected ‘layers’ of interactions. In this article, we review common questions in animal behaviour that can be studied using a multilayer approach, and we link these questions to specific analyses. We outline the types of behavioural data and questions that may be suitable to study using multilayer network analysis. We detail several multilayer methods, which can provide new insights into questions about animal sociality at individual, group, population and evolutionary levels of organization. We give examples for how to implement multilayer methods to demonstrate how taking a multilayer approach can alter inferences about social structure and the positions of individuals within such a structure. Finally, we discuss caveats to undertaking multilayer network analysis in the study of animal social networks, and we call attention to methodological challenges for the application of these approaches. Our aim is to instigate the study of new questions about animal sociality using the new toolbox of multilayer network analysis.


P.S. There is an easter egg in the paper. Let me know when you find it!

A Wassermanian–Faustian Bargain

Earlier today, I was looking for 'balance' in "Social Network Analysis" by Wasserman & Faust, but instead I found the 'beast'.

(I suppose that social network analysis is sometimes a Wassermanian–Faustian bargain.) pic.twitter.com/cm4jZiupeW

— Mason Porter (@masonporter) August 13, 2018

"Message-Passing Methods for Complex Contagions"

Here is the published version of a the chapter that James Gleeson and I wrote for the book Complex Spreading Phenomena in Social Systems, which was edited by Sune Lehmann and YY Ahn. You can also find preprint versions of many chapters available for free on this website.

"Can Multilayer Networks Advance Animal Behavior Research?"

The final version of a new paper of mine now has its final coordinates in a journal. Here are some details.

Title: Can Multilayer Networks Advance Animal Behavior Research?

Authors: Matthew J. Silk, Kelly R. Finn, Mason A. Porter, and Noa Pinter-Wollman

Abstract: Interactions among individual animals — and between these individuals and their environment — yield complex, multifaceted systems. The development of multilayer network analysis offers a promising new approach for studying animal social behavior and its relation to eco-evolutionary dynamics.

"Neither Global nor Local: Heterogeneous Connectivity in Spatial Network Structures of World Migration"

One of my papers, which has had a DOI for about half a year, finally has its final publication coordinates. Notably, this is my first paper in a sociology journal. Here are some details.

Title: Neither Global nor Local: Heterogeneous Connectivity in Spatial Network Structures of World Migration

Authors: Valentin Danchev and Mason A. Porterc

Abstract: For a long time, geographic regions were considered the dominant spatial arbiter of international migration of people. However, since the late 1970s, many scholars have argued that movements reach beyond contiguous regions to connect distant, dispersed, and previously disconnected countries across the globe. The precise structure of world migration, however, remains an open question. We apply network analysis that incorporates spatial information to international migration-stock data to examine what multilateral structures of world migration have emerged from the interplay of regional concentration (local cohesion)and global interconnectedness (global cohesion) for the period 1960–2000. In the world migration network (WMN), nodes represent countries located in geographic space, and edges represent migrants froman origin country who live in a destination country during each decade. We characterize the large-scale structure and evolution of the WMN by algorithmically detecting international migration communities (i.e., sets of countries that are densely connected via migration) using a generalized modularity function for spatial, temporal, and directed networks. Our findings for the whole network suggest that movements in the WMN deviate significantly from the regional boundaries of the world and that international migration communities have become globally interconnected over time. However, we observe a strong variability in the distribution of strengths, neighborhood overlaps, and lengths of migration edges in the WMN. This manifests as three types of communities: global, local, and glocal. We find that long-distance movements in global communities bridge multiple non-contiguous countries, whereas local (and, to a lesser extent, glocal) communities remain trapped in contiguous geographic regions (or neighboring regions) for almost the whole period, contributing to a spatially fragmented WMN. Our findings demonstrate that world migration is neither regionally concentrated nor globally interconnected, but instead exhibits a heterogeneous connectivity pattern that channels unequal migration opportunities across the world.

United States Senators and Social Licking Among Cows

I am amused by this 2002 paper by Faust and Skvoretz, called Comparing Networks Across Space and Time, Size and Species.

Here is a choice quote: "The model of social licking among cows best predicts, as a target, cosponsorship among U.S. senators in the Ninety-Third Congress."

Note: The sentence is highly amusing, and I understand it in the context of the paper, but (1) the term "predicts" is misleading with respect to the analysis performed, and (2) one of course has to ask how the result changes if a different sample of networks is used. There has, of course, been a bunch of work (including by my collaborators and me) in the last decade and a half on examining similarities among networks.

(Tip of the cap to Brian Keegan.)

Congratulations to Dr. Valentin Danchev!

The D.Phil. thesis of my student Valentin Danchev (now a postdoc in the Knowledge Lab at University of Chicago) has now been officially approved. Valentin's other supervisor was Michael Keith of COMPAS (Centre on Migration, Policy, and Society) at University of Oxford.

Valentin is a sociologist and was a D.Phil. student in University of Oxford's International Migration Institute. His thesis is called Spatial Network Structures of World Migration: Heterogeneity of Global and Local Connectivity, and we have a joint paper on the topic in progress. We plan to submit that paper to a sociology journal.

"Structure of Triadic Relations in Multiplex Networks"

One of my papers, which my collaborators and I first posted on the arXiv and submitted to a journal two years ago, has finally been published in final form. Here are the details.

Title: Structure of Triadic Relations in Multiplex Networks

Authors: Emanuele Cozzo, Mikko Kivelä, Manlio De Domenico, Albert Solé-Ribalta, Alex Arenas, Sergio Gómez, Mason A Porter, and Yamir Moreno

Abstract: Recent advances in the study of networked systems have highlighted that our interconnected world is composed of networks that are coupled to each other through different 'layers' that each represent one of many possible subsystems or types of interactions. Nevertheless, it is traditional to aggregate multilayer networks into a single weighted network in order to take advantage of existing tools. This is admittedly convenient, but it is also extremely problematic, as important information can be lost as a result. It is therefore important to develop multilayer generalizations of network concepts. In this paper, we analyze triadic relations and generalize the idea of transitivity to multiplex networks. By focusing on triadic relations, which yield the simplest type of transitivity, we generalize the concept and computation of clustering coefficients to multiplex networks. We show how the layered structure of such networks introduces a new degree of freedom that has a fundamental effect on transitivity. We compute multiplex clustering coefficients for several real multiplex networks and illustrate why one must take great care when generalizing standard network concepts to multiplex networks. We also derive analytical expressions for our clustering coefficients for ensemble averages of networks in a family of random multiplex networks. Our analysis illustrates that social networks have a strong tendency to promote redundancy by closing triads at every layer and that they thereby have a different type of multiplex transitivity from transportation networks, which do not exhibit such a tendency. These insights are invisible if one only studies aggregated networks.

"Topological Data Analysis of Contagion Maps for Examining Spreading Processes on Networks"

Our Nature Communications paper just came out today! Here are the details.

Title: Topological Data Analysis of Contagion Maps for Examining Spreading Processes on Networks

Authors: Dane Taylor, Florian Klimm, Heather A. Harrington, Miroslav Kramár, Konstantin Mischaikow, Mason A. Porter, and Peter J. Mucha

Abstract: Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth’s surface; however, in modern contagions long-range edges––for example, due to airline transportation or communication media––allow clusters of a contagion to appear in distant locations. Here we study the spread of contagions on networks through a methodology grounded in topological data analysis and nonlinear dimension reduction. We construct 'contagion maps' that use multiple contagions on a network to map the nodes as a point cloud. By analysing the topology, geometry and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modelling, forecast and control of spreading processes. Our approach highlights contagion maps also as a viable tool for inferring low-dimensional structure in networks.


Instead of trying to explain our work in layperson's terms here, I'll point you to the press release from University of Oxford.

You can also download our data and our code.

What Happens in Brighton Stays in Brighton

Tomorrow afternoon, I'll be heading on the train to "Bright"on to attend the "Sun"belt conference on social network analysis! As you can see from the program, I helped organize a three-part session on multilayer networks.

Time to hang out with some of my sociologist peeps!

Here is an appropriate theme song for my trip.

Video of My Seminar: "Cascades and Social Influence on Networks"

Here is a video of a seminar on cascades and social influence on networks that I presented at UNAM last October.

The associated slides (or at least a set of slides that are almost exactly the same) are available on Slideshare.

Thanks to my UNAM host Carlos Gershenson for posting the video.

What Happens in Goleta Stays in Goleta

I flew into Santa Barbara yesterday to give a talk called Cascades and Social Influence on Networks at UCSB yesterday. It's been a fun visit!

What Happens in Silwood Park Stays in Silwood Park

This evening, I'll be taking the train (and, apparently, replacement bus service) to Ascot to get myself over to Imperial College's Silwood Park campus for environmental fluctuations, recovery, and resilience of biological networks, which is part of their program on Grand Challenges in the Ecosystem and the Environment (GCEE).

Take a look at a a map of the local area, which covers Silwood, Windsor Park, and Maidenhead. Based on the names of some of the places on this map, it looks like I'm going to be pretty close to a Hellmouth. Also, this map is a great example of how awesome the Brits can be sometimes with their naming conventions. It would be pretty damn awesome, for example, if "Cheapside" has evolved to be a posh, expensive location filled with luxurious mansions. ("Unfortunately, I can't afford to live in Cheapside.")

Update: I have reached the center for population biology that Imperial College has at their Silkwood Park campus, and there are rabbits all over the place here. There is something right with the world.