Thursday, February 9, 2012, 3pm

***Note special location: Johnson Center, Room B

Juan G. Restrepo
Department of Mathematics
University of Colorado, Boulder

Criticality and Dynamic Range in Network Cascading Processes

I will present recent work on the effect of network topology on cascading processes. The motivation for our work is a series of recent experiments on cascades of excitation in rat cortical tissue cultures, where it is found that these neural networks maximize their dynamic range (the range of stimulus intensities resulting in distinguishable network responses). We develop a theoretical framework to study the effect of network topology on the response to a stochastic stimulus, and find that the dynamic range is maximized when the largest eigenvalue of the transmission probability matrix is one. In the critical regime with maximum dynamic range, the response of the network is characterized by excitation avalanches with power-law distributions of size and duration. We find that these experimental signatures of criticality are robust to the underlying network structure. Using our theory, we characterize the network topologies that can achieve the largest dynamic range. I will discuss potential applications of these results to other networked systems.