Time: Tuesday, September 15, 2:00pm

Speaker: Professor Maria Cameron (University of Maryland)

Title: Methods for spectral analysis of stochastic networks

Abstract: Stochastic networks (continuous-time Markov chains) with pairwise transition rates containing a small parameter arise in modeling natural processes. Time-reversible processes include the dynamics of clusters of interacting particles, conformal changes in molecules, and protein folding, while time-irreversible ones are exemplified e.g. by walks of molecular motors. The spectral decomposition of the generator matrix of the stochastic network gives a key to understanding its dynamics, the extraction of quasi-invariant sets, and building coarse-grained models. However, its direct calculation is exceedingly difficult if the matrix is large and its entries vary by tens of orders of magnitude. I will introduce a single-sweep algorithm for computing the asymptotic spectral decomposition and discuss continuation techniques. This approach allows us to easily interpret the results and largely avoid the issues associated with the floating point arithmetic. An application to the Lennard-Jones cluster of 75 atoms will be discussed.