"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.

"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 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!

Videos of Two of My Talks

In February 2013, I gave a talk on Cascades and Social Influence on Networks at Cornell University. I was giving the Center for Applied Mathematics colloquium (i.e., the colloquium in the program from which I got my PhD). This was my first visit to Cornell since I graduated in 2002. During the past few days, I gave updated versions of this talk at Simon Fraser University and University of British Columbia.

In December 2011, I gave a plenary talk on Social Structure of Facebook Networks at a conference in Henley.


Enjoy!

The Onion Wins. Again.

Tomorrow and Monday I am giving talks about cascades and social influence on networks, and (thanks to The Onion) I just picked up a new slide for the introduction. Sweet!

Tales From the ArXiv: "The BS Model"

I have decided that naming a model after yourself is slightly forgivable if your initials and author order mean that it will called "the BS model", which is what happened in this paper. :)

"Multi-Stage Complex Contagions"

I just blogged about my new paper on billiards, which just got published in final form today in Chaos. Well, the very next article in the journal, which was (unsurprisingly, given these statements) also published today, is my new paper on modelling social influence. Here are the details for that paper.

Title: Multi-Stage Complex Contagions

Authors: Sergey Melnik, Jonathan A. Ward, James P. Gleeson, and Mason A. Porter

Abstract: The spread of ideas across a social network can be studied using complex contagion models, in which agents are activated by contact with multiple activated neighbors. The investigation of complex contagions can provide crucial insights into social influence and behavior-adoption cascades on networks. In this paper, we introduce a model of a multi-stage complex contagion on networks. Agents at different stages --- which could, for example, represent differing levels of support for a social movement or differing levels of commitment to a certain product or idea --- exert different amounts of influence on their neighbors. We demonstrate that the presence of even one additional stage introduces novel dynamical behavior, including interplay between multiple cascades, which cannot occur in single-stage contagion models. We find that cascades—and hence collective action—can be driven not only by high-stage influencers but also by low-stage influencers.


Fun Fact: This might be the first published mathematics paper that uses the word "hipster". You should click on the link and see how we use it. :)