Friday,
April 20, 12:00 p.m. GWC 487
Shev Mac
MIT
Master Equations with Time-Dependent Rates, with Application in Immunolog
Abstract
Stochastic models for competing clonotypes of T cells by multivariate,
continuous-time, discrete state, Markov processes have recently been
proposed in the literature. A stochastic modelling framework is
important because of rare events associated with small populations of
some critical cell types. Computational techniques for studying these
processes are described, including Krylov methods for evolving the
matrix exponential, Finite State Projection methods for handling high
dimensional state spaces, and Magnus expansions for time-dependent
Master Equations. Computational challenges include handling widely
varying spectra that may arise in time-dependent descriptions of the
way the immune system ages. An interesting aspect is the different
scales of the life times of the clonotypes being modelled, interpreted
via quasi-stationary distributions that in some cases last for an
extraordinarily long time. It is a subtle effect but important in an
immunological setting because this is what maintains diversity and
strength in the immune system, in a process known as T cell
homeostasis.
