Project Report

EAPSI: Multiple interactions in a network facilitates its threshold cascades Viral marketing, instant fads, the spread of bank defaults—these cascades of changes in people, companies and financial institutions increasingly pervade modern life, with important and sometimes dire consequences. This has motivated the study of simple models of cascades in a network of individuals connected to one another. A commonly studied rule (the so-called Watts model) is that people buy a new product, say, if a sufficiently large fraction of their friends have (because friends recommend it and because its utility increases as more people use the product). By considering lending rather than friendships, this model can also describe spreading default among banks. Most studies so far consider just one kind of interaction among the system’s constituents, such as friendships in a social network. But often people, banks, countries and others interact in many different ways. For instance, friends and work colleagues exhibit different influence on a person’s decision to buy a new smartphone app. Banks also interact in many ways—through balance sheet claims, derivatives contracts and reliance on common credit lines—which collectively cause cascades. This motivates studying multiple kinds of interactions. On an NSF EAPSI fellowship in Seoul, South Korea, in collaboration with Prof. Kwang-Il Goh and his PhD student Kyu-Min Lee at Korea University, we generalized the Watts model to multiple kinds of interactions. Namely, we studied the rule that a person joins a growing movement, say, if a sufficiently large fraction of friends in any of her social spheres have joined it. What we found is that considering multiple kinds of interactions facilitates cascades—and in nontrivial ways. It is easier to get an enormous cascade when people (or banks) interact in multiple ways. What this suggests is that advertising may become more effective with every new medium, while banks may grow more vulnerable with every new lending mechanism. Prof. Goh, PhD student Kyu-Min Lee and I continue to collaborate across the Pacific after the summer concluded. We intend to publish more papers on cascades in networks with multiple kinds of interaction, both in theoretical models and using empirical datasets. In addition to this research, the NSF EAPSI fellowship offered me the opportunity to visit other research groups in South Korea (at Seoul National University, Korea Institute for Advanced Studies and KAIST) to give a talk on my previous research and to meet other students and professors in my field. These Korean contacts will undoubtedly prove useful in future conferences, job searches and cross-Pacific collaboration. The summer also provided a healthy dose of Korean culture. I ate so much kimchi that I grew to crave it. When Korean lab-mates and I weren’t hiking the mountains in Seoul (see photo), we were exploring new culinary territory by going out to lunch at a different restaurant every day (see photo). Chatting over lunch about matters Korean and American, scientific and frivolous provided an invaluable window into Korean culture. Journal publication: C. D. Brummitt, K.-M. Lee, K.-I. Goh. Multiplexity-facilitated cascades in networks. arXiv:1112.0093. Submitted.

National Science Foundation (NSF)
Office of International and Integrative Activities (IIA)
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Carter Kimsey
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Brummitt Charles D
United States
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