Center for Applied Mathematics Colloquium
Biological aggregations such as bird flocks, fish schools, and insect swarms are striking examples of self-organization, and serve as the inspiration for 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 a field observation or numerical simulation. Interpreting this data to characterize the group's dynamics can be a challenge. To this end, we apply computational persistent homology — the workhorse of the field of topological data analysis — to the aggregation models of Vicsek et al (1995) and D’Orsogna et al. (2006). We assign a topological signature to each set of simulation data. This signature identifies dynamical events that traditional methods do not. Finally, we pose open questions related to topological signatures averaged over many simulations of stochastic models. This talk assumes no prior knowledge of topology.