Topological Data Analysis of Biological Aggregation Models
Speaker: Chad Topaz, Macalester College
Date & Time:
3:30 PM - 4:30 PM
Owens Science Hall (OWS) 250
Abstract: Biological aggregations are groups such as bird flocks, fish schools, and insect swarms in which organisms interact socially. These groups are striking examples of emergent self-organization, and simultaneously, they have served as inspiration for the development of algorithms in robotics, computer science, applied mathematics, and other fields. Aggregations give rise to massive amounts of data, for instance, the position and velocity of each group member at each moment in time during an observation. Interpreting this data to characterize the group's dynamics can be a challenge. To this end, we apply techniques of topological data analysis to two influential aggregation models. We construe position and velocity data from numerical simulations as point clouds of data varying over time. Using a method called persistent homology, we identify topological features that persist over multiple spatial scales, and see that the topological analysis detects dynamical events that are invisible to more commonly used methods. This talk aims to explain persistent homology in nontechnical terms and assumes no prior knowledge of topology.
Biosketch: Chad Topaz is a Professor of Mathematics at Macalester College. He received his Ph.D. in applied mathematics from Northwestern University. His research on complex and nonlinear systems has been supported continuously by the National Science Foundation since 2006. A versatile investigator, Chad examines problems in biology, chemistry, physics, and the social sciences through several lenses, including data science, modeling, analysis, topology, geometric dynamical systems, numerical simulation, and experiment... all with an eye towards understanding and predicting complex behavior. Chad has received several fellowships and other honors for his research as well as recognition for his excellent teaching.