Related papers: Individual molecules dynamics in reaction network …

To study the dynamics of chemical processes, we often adopt rate equations to observe the change in chemical concentrations. However, when the number of the molecules is small, the fluctuations cannot be neglected. We often study the…

A protein undergoes conformational dynamics with multiple time scales, which results in fluctuating enzyme activities. Recent studies in single molecule enzymology have observe this "age-old" dynamic disorder phenomenon directly. However,…

We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…

Tracking the behaviour of stochastic systems is a crucial task in the statistical sciences. It has recently been shown that quantum models can faithfully simulate such processes whilst retaining less information about the past behaviour of…

Molecular dynamics simulations are widely used across chemistry, physics, and biology, providing quantitative insight into complex processes with atomic detail. However, their limited timescale of a few microseconds is a significant…

The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…

We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…

We formulate some simple conditions under which a Markov chain may be approximated by the solution to a differential equation, with quantifiable error probabilities. The role of a choice of coordinate functions for the Markov chain is…

In this paper we present a method to approximate optimal feedback controls for stochastic reaction-diffusion equations. We derive two approximation results providing the theoretical foundation of our approach and allowing for explicit error…

We extend the generating function technique for calculation of single molecule photon emission statistics [Y. Zheng and F. L. H. Brown, Phys. Rev. Lett., 90,238305 (2003)] to systems governed by multi-level quantum dynamics. This opens up…

We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…

The probability distribution describing the state of a Stochastic Reaction Network evolves according to the Chemical Master Equation (CME). It is common to estimated its solution using Monte Carlo methods such as the Stochastic Simulation…

We study a system of interacting particles that randomly react to form new particles. The reaction flux is the rescaled number of reactions that take place in a time interval. We prove a dynamic large-deviation principle for the reaction…

To forecast the time dynamics of an epidemic, we propose a discrete stochastic model that unifies and generalizes previous approaches to the subject. Viewing a given population of individuals or groups of individuals with given health state…

The transport and chemical reactions of solutes are modelled as a cellular automaton in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule. The model describes…

In this paper, a novel computational technique for finite discrete approximation of continuous dynamical systems suitable for a significant class of biochemical dynamical systems is introduced. The method is parameterized in order to affect…

In this thesis we present a mathematical model describing the population dynamics of molecules in an artificial chemistry where large molecules can be produced by successive ligation of pairs of smaller molecules. The chemistry contains a…

Statistical models provide a powerful and useful class of approximations for calculating reaction rates by bypassing the need for detailed, and often difficult, dynamical considerations. Such approaches invariably invoke specific…

Single-molecule stretching experiments are widely utilized within the fields of physics and chemistry to characterize the mechanics of individual bonds or molecules, as well as chemical reactions. Analytic relations describing these…

The paper analyses stochastic systems describing reacting molecular systems with a combination of two types of state spaces, a finite-dimensional, and an infinite dimenional part. As a typical situation consider the interaction of larger…