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Monte Carlo estimation in plays a crucial role in stochastic reaction networks. However, reducing the statistical uncertainty of the corresponding estimators requires sampling a large number of trajectories. We propose control variates…
Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of simulated models and morphologies have exceeded the capacity of any…
Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living…
Model comparison for the purposes of selection, averaging and validation is a problem found throughout statistics. Within the Bayesian paradigm, these problems all require the calculation of the posterior probabilities of models within a…
Approximate Bayesian Computation is widely used to infer the parameters of discrete-state continuous-time Markov networks. In this work, we focus on models that are governed by the Chemical Master Equation (the CME). Whilst originally…
We apply the "weighted ensemble" (WE) simulation strategy, previously employed in the context of molecular dynamics simulations, to a series of systems-biology models that range in complexity from one-dimensional to a system with 354…
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
Analysis of large continuous-time stochastic systems is a computationally intensive task. In this work we focus on population models arising from chemical reaction networks (CRNs), which play a fundamental role in analysis and design of…
We study a class of Stochastic Differential Equations (SDEs) with jumps modeling multistage Michaelis--Menten enzyme kinetics, in which a substrate is sequentially transformed into a product via a cascade of intermediate complexes. These…
We show that discrete distributions on the $d$-dimensional non-negative integer lattice can be approximated arbitrarily well via the marginals of stationary distributions for various classes of stochastic chemical reaction networks. We…
We introduce a stochastic model that describes the quasi-static dynamics of an electric transmission network under perturbations introduced by random load fluctuations, random removing of system components from service, random repair times…
We address the problem of simulation and parameter inference for chemical reaction networks described by the chemical Langevin equation, a stochastic differential equation (SDE) representation of the dynamics of the chemical species. This…
While the analytical solution for the marginal distribution of a stochastic chemical reaction network has been extensively studied, its joint distribution, i.e. the solution of a high-dimensional chemical master equation, has received much…
The chemical master equation (CME), which describes the discrete and stochastic molecule number dynamics associated with biological processes like transcription, is difficult to solve analytically. It is particularly hard to solve for…
Several stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this paper, two commonly used SSAs are studied. The first SSA is an on-lattice…
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or…
The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of ordinary differential equations (ODEs). Alternative approaches based on formal calculi, often derived from process algebras or term…
We present a numerical algorithm that allows the approximation of optimal controls for stochastic reaction-diffusion equations with additive noise by first reducing the problem to controls of feedback form and then approximating the…
The past decade has seen a revived interest in the unavoidable or intrinsic noise in biochemical and genetic networks arising from the finite copy number of the participating species. That is, rather than modeling regulatory networks in…
The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They rely on knowledge of interevent probability density functions (PDFs) and on…