Math Modeling Seminar: Complex networks with complex nodes

Math Modeling Seminar
Complex networks with complex nodes

Dr. Raissa D'Souza
Department of Computer Science
Department of Mechanical and Aerospace Engineering
Graduate Group in Applied Math
Graduate Group in Physics
Complexity Sciences Center
University of California, Davis

You may attend this lecture in person at 2305 Gosnell Hall or virtually via Zoom.
If you’d like to attend virtually, you may register here for Zoom link.

Abstract:
Real world networks -- from brain networks to social networks to critical infrastructure networks -- are composed of nodes with nonlinear behaviors coupled together via highly non-trivial network structures. Approaches from statistical physics study how behaviors arise in collections of simple elements connected together in complex structures such as modular or scale-free networks. They provide understanding about massive networks, revealing implications that network structure can have on network function and resilience. In contrast, approaches from dynamical systems and control theory typically study small systems of nonlinear nodes connected together in simple networks. This talk presents recent work bridging the gap of complex networks with complex nodes. First is considering nonlinear phase-amplitude oscillators coupled together by simple ring networks and how the interplay of nodal dynamics and coupling structure gives rise to emergent long-range order and its stability properties. Next is increasing the structural complexity from dyadic networks to hypergraphs to capture higher-order interactions and study cluster synchronization. The focus will then turn to social networks, starting from modeling humans as nodes with underlying attributes coupled in complete graphs, and moving on to real-world multiplex social networks in macaque monkey societies. We reveal the tensions between the forces of homophily and social balance, as well as developing a meaningful multiplex ranking method that takes into account the heterogeneous characteristics and functions of the distinct layers in the multiplex.

Speaker Bio:
Dr. Raissa D'Souza is Professor of Computer Science and of Mechanical Engineering at the University of California, Davis, as well as an External Professor at the Santa Fe Institute. She uses the tools of statistical physics and applied mathematics to develop models capturing the interplay between the structure and function of networks. The general principles derived provide insights into the behaviors of real-world networks such as infrastructure networks and social networks, and opportunities to identify small interventions to control the self-organizing, collective behaviors displayed in these systems. She is a Fellow of the American Physical Society, a Fellow of the Network Science Society, and has received several honors such as the inaugural Euler Award of the Network Science Society and the 2018 ACM Test-of-Time award. She is currently Lead Editor at Physical Review Research and on the Board of Reviewing Editors at Science. She was a member of the World Economic Forum's Global Agenda Council on Complex Systems and served as President of the Network Science Society, 2015-18.
Read more here.

Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.

The Math Modeling Seminar will recur each week throughout the semester on the same day and time. Find out more about upcoming speakers on the Mathematical Modeling Seminar Series webpage.
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