The interior of a living cell is a crowded, heterogenuous, fluctuating environment. Hence, a
major challenge in modeling intracellular transport is to analyze stochastic processes within …

There has been a resurgence of interest in non-equilibrium stochastic processes in recent
years, driven in part by the observation that the number of molecules (genes, mRNA …

One of the major challenges in modern biology is to understand how the molecular
components of a living cell operate in a highly noisy environment. What are the specific …

This is a book on mathematical neuroscience, in which the unifying theme is wavelike
phenomena at multiple spatial and temporal scales. There are already several excellent …

Neurons exhibit complex geometry in their branched networks of neurites which is essential
to the function of individual neuron but also brings challenges to transport a wide variety of …

We construct a path-integral representation of solutions to a stochastic hybrid system,
consisting of one or more continuous variables evolving according to a piecewise …

In this chapter, neural field theory is used to model binocular rivalry waves. During binocular
rivalry, visual perception switches back and forth between different images presented to the …

The intracellular transport process plays an important role in delivering essential materials
throughout branched geometries of neurons for their survival and function. Many …

We develop a dynamical system model for the transport of neurofilaments in axons, inspired
by Brown's “stop-and-go” model for slow axonal transport. We use fast/slow time-scale …

We analyze a piecewise deterministic PDE consisting of the diffusion equation on a finite
interval Ω with randomly switching boundary conditions and diffusion coefficient. We …