Adi Rangan, CIMS

Abstract:

The study of dynamics on networks is becoming increasingly more relevant within biology. An important subclass of biological networks are `pulse-coupled' networks, such as neuronal networks. An important question is: what is the relationship (or map) between a pulse-coupled network's architecture and any given statistical feature of its dynamics? In many circumstances this question cannot be answered easily, and theorists and modelers often resort to simulations in order to probe the properties of this map. I will present a framework which takes a first step towards answering this question. By expressing the desired statistical feature of the network's dynamics in terms of an appropriate integral of the equilibrium distribution of system paths in state-space (i.e., a projection of the system's filtration), one can derive a systematic expansion (in terms of coupling strength) of any desired projection of the network's dynamics. After motivating the derivation, I will present a few examples illustrating the utility of this new method.