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 …

When I am called upon to teach fluid mechanics, I always show students a copy of Newton's
Principia. I do this for a number of reasons, not least of which is the connection I hope they …

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 …

We consider stochastically modeled chemical reaction systems with mass-action kinetics
and prove that a product-form stationary distribution exists for each closed, irreducible …

This paper is concerned with the dynamical properties of deterministically modeled chemical
reaction systems. Specifically, this paper provides a proof of the Global Attractor Conjecture …

Persistence and permanence are properties of dynamical systems that describe the long-
term behavior of the solutions and in particular specify whether positive solutions approach …

The global attractor conjecture says that toric dynamical systems (ie, a class of polynomial
dynamical systems on the positive orthant) have a globally attracting point within each …

This paper introduces the class of strongly endotactic networks, a subclass of the endotactic
networks introduced by Craciun, Nazarov, and Pantea. The main result states that the global …

We model the dynamics of self-organized robot aggregation inspired by a study on the
aggregation of gregarious arthropods. In swarms of German cockroaches, aggregation into …

This paper concerns the long-term behavior of population systems, and in particular of
chemical reaction systems, modeled by deterministic mass-action kinetics. We approach two …