Mathematics Colloquium
Bhargav Karamched
University of Houston
Title: From Individuals to Populations: How features and interactions of individuals shape population dynamics
Date: Friday, January 24, 2019
Place and Time: Room 101, Love Building, 3:35-4:25 pm
Refreshments: Room 204, Love Building, 3:00 pm
Abstract. The dynamics of multi-agent systems at the population level often depend sensitively upon the features and interactions of the agents that make up the population. In this talk, we will look at two examples of such systems. The first example is motivated by experimental findings in the synthetic biology laboratory. In spatially extended microfluidic traps, E. coli cells align orthogonally to the long side of the trap. We develop a stochastic lattice model that describes such emergent behavior and suggests that population level alignment is driven by a tug-of-war between local cell-cell interactions and boundary effects. The second example is motivated by the relevance of social networking in today's world and addresses optimal decision making in social settings. We generalize well-known Bayesian models of binary decision making to include exchange of social information. In the limit of large system sizes, we are able to perform asymptotic calculations and show that even if a large fraction of a population urges everyone to make a suboptimal decision, individuals can use the information available to them to ensure that overall the population can choose an optimal decision.