Stochastic Analysis

An asymptotic framework for optimal control of multiclass stochastic processing networks, using formal diffusion approximations under suitable temporal and spatial scaling, by Brownian control problems (BCP) and their equivalent workload formulations (EWF), has been developed by Harrison (1988). This framework has been implemented in many works for constructing asymptotically optimal control policies for a broad range of stochastic network models.

It has recently been shown that structural conditions on the reaction network, rather than a ‘fine-tuning’ of system parameters, often suffice to impart ‘absolute concentration robustness’ on a wide class of biologically relevant, deterministically modeled mass-action systems [Shinar and Feinberg, Science, 2010].

In this talk I will discuss some problems involving persistence computation with a highlight on two particular cases. The first example looks at the problem of approximating relative persistent homology by extending the results on the stability of persistence modules. The second example will look at how to compute persistence with bounds on the memory usage using a spectral sequence approach. I will discuss how we encounter similar problems in both examples.

Many gene regulatory networks are modeled at the mesoscopic scale, where
chemical populations change according to a discrete state (jump)
Markov process. The chemical master equation for such a process is
typically infinite dimensional and unlikely to be computationally
tractable without reduction. The recently proposed Finite State
Projection technique allows for a bulk reduction of the CME while
explicitly keeping track of its own approximation error. We show how a
projection approach can be used to directly determine the