Related papers: Stochastic modelling of reaction-diffusion process…
When the output of an atomistic simulation (such as the Gillespie stochastic simulation algorithm, SSA) can be approximated as a diffusion process, we may be interested in the dynamic features of the deterministic (drift) component of this…
We introduce a new class of cellular automata to model reaction-diffusion systems in a quantitatively correct way. The construction of the CA from the reaction-diffusion equation relies on a moving average procedure to implement diffusion,…
Stochastic simulators are ubiquitous in many fields of applied sciences and engineering. In the context of uncertainty quantification and optimization, a large number of simulations is usually necessary, which becomes intractable for…
Stochastic models of reaction-diffusion systems are important for the study of biochemical reaction networks where species are present in low copy numbers or if reactions are highly diffusion limited. In living cells many such systems…
Mathematical models of transport and reactions in biological systems have been traditionally written in terms of partial differential equations (PDEs) that describe the time evolution of population-level variables. In recent years, the use…
This paper is concerned with classes of models of stochastic reaction dynamics with time-scales separation. We demonstrate that the existence of the time-scale separation naturally leads to the application of the averaging principle and…
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…
Stochastic approximation (SA) algorithms are widely used in system optimization problems when only noisy measurements of the system are available. This paper studies two types of SA algorithms in a multivariate Kiefer-Wolfowitz setting:…
This paper investigates the problem of distributed stochastic approximation in multi-agent systems. The algorithm under study consists of two steps: a local stochastic approximation step and a diffusion step which drives the network to a…
We have developed a coarse-grained formulation for modeling the dynamic behavior of cells quantitatively, based on stochasticity and heterogeneity, rather than on biochemical reactions. We treat each reaction as a continuous-time stochastic…
Open biochemical systems of interacting molecules are ubiquitous in life-related processes. However, established computational methodologies, like molecular dynamics, are still mostly constrained to closed systems and timescales too small…
We consider the problem of efficiently simulating stochastic models of chemical kinetics. The Gillespie Stochastic Simulation algorithm (SSA) is often used to simulate these models, however, in many scenarios of interest, the computational…
The multi-level method for discrete state systems, first introduced by Anderson and Higham [Multiscale Model. Simul. 10:146--179, 2012], is a highly efficient simulation technique that can be used to elucidate statistical characteristics of…
Reaction-diffusion models are widely used to study spatially-extended chemical reaction systems. In order to understand how the dynamics of a reaction-diffusion model are affected by changes in its input parameters, efficient methods for…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
The simulation of stochastic reaction-diffusion systems using fine-grained representations can become computationally prohibitive when particle numbers become large. If particle numbers are sufficiently high then it may be possible to…
We present and analyse a model for cell signalling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces, and both inter- and intracellular signalling. Using techniques from the theory of…
In this paper, we study the distributed adaptive estimation problem of continuous-time stochastic dynamic systems over sensor networks where each agent can only communicate with its local neighbors. A distributed least squares (LS)…
In biochemical networks, reactions often occur on disparate timescales and can be characterized as either "fast" or "slow." The quasi-steady state approximation (QSSA) utilizes timescale separation to project models of biochemical networks…
Traditional stochastic modeling of reactive systems limits the domain of applicability of the associated path thermodynamics to systems involving a single elementary reaction at the origin of each observed change in composition. An…