Abstract

Stochastic process and statistics has a glorious history in physics, chemistry and biology. Due to the advance of experimental techniques at single-molecule and single-cell levels, stochastic modeling and statistics become more and more useful and popular in chemistry and biology recently. I will talk about three short stories, including cycle symmetry of nearest-neighbor random walks and general diffusion processes on a circle, the fluctuating-rate model as well as the rate formula for the phenotype transition in an intermediate scenario of a single cell, and inference of dynamic network via repeated cross-sectional data such as single-cell transcriptome data.