Reduction of a stochastic model of gene expression: Lagrangian dynamics gives access to basins of attraction as cell types and metastabilty.

Differentiation is the process whereby a cell acquires a specific phenotype, by differential gene expression as a function of time. This is thought to result from the dynamical functioning of an underlying Gene Regulatory Network (GRN). The precise path from the stochastic GRN behavior to the resulting cell state is still an open question.

On a new class of score functions to estimate tail probabilities of some stochastic processes with adaptive multilevel splitting.

We investigate the application of the adaptive multilevel splitting algorithm for the estimation of tail probabilities of solutions of stochastic differential equations evaluated at a given time and of associated temporal averages. We introduce a new, very general, and effective family of score functions that is designed for these problems. We illustrate its behavior in a series of numerical experiments.