A set of analytical and computational tools based on transition path theory (TPT) is proposed
to analyze flows in complex networks. Specifically, TPT is used to study the statistical …

We present an implementation of a scalable path deviation algorithm to find the k most
kinetically relevant paths in a transition network, where each path is distinguished on the …

The concept of metastability has caused a lot of interest in recent years. The spectral
decomposition of the generator matrix of a stochastic network exposes all of the transition …

We develop computational tools for spectral analysis of stochastic networks representing
energy landscapes of atomic and molecular clusters. Physical meaning and some properties …

Human rhinoviruses are causative agents of the common cold. In order to release their RNA
genome into the host during a viral infection, these small viruses must undergo …

Large continuous-time Markov chains with exponentially small transition rates arise in
modeling complex systems in physics, chemistry, and biology. We propose a constructive …

We consider stochastic networks with pairwise transition rates of the form where the
temperature T is a small parameter. Such networks arise in physics and chemistry and serve …

We consider a finite dimensional deterministic dynamical system with finitely many local
attractors Kι, each of which supports a unique ergodic probability measure Pι, perturbed by a …

In this paper we consider a finite state time discrete Markov chain that mimic the behaviour
of solutions of the stochastic differential equation X_ t^ ε (x)= x-∫ _0^ t U^ ′ (X_ s^ ε)\, d s+ …

Many real-world systems are well-modeled by Brownian particles subject to gradient
dynamics plus noise arising, eg, from the thermal fluctuations of a heat bath. Of central …