Related papers: A Diffusion-Based Embedding of the Stochastic Simu…
Simulation of stochastic spatially-extended systems is a challenging problem. The fundamental quantities in these models are individual entities such as molecules, cells, or animals, which move and react in a random manner. In big systems,…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…
Diffusion models have gained attention for their success in modeling complex distributions, achieving impressive perceptual quality in SR tasks. However, existing diffusion-based SR methods often suffer from high computational costs,…
A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge of stochastic simulations is assumed. The methods are explained using illustrative examples. The article starts with the…
We describe a new algorithm for simulating complex Markoff-processes. We have used a reaction-cell method in order to simulate arbitrary reactions. It can be used for any kind of RDS on arbitrary topologies, including fractal dimensions or…
Models of reaction chemistry based on the stochastic simulation algorithm (SSA) have become a crucial tool for simulating complicated biological reaction networks due to their ability to handle extremely complicated reaction networks and to…
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…
We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are…
A class of Brownian dynamics algorithms for stochastic reaction-diffusion models which include reversible bimolecular reactions is presented and analyzed. The method is a generalization of the $\lambda$--$\newrho$ model for irreversible…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
Up to now, it is not possible to obtain analytical solutions for complex molecular association processes (e.g. Molecule recognition in Signaling or catalysis). Instead Brownian Dynamics (BD) simulations are commonly used to estimate the…
A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…
Two algorithms that combine Brownian dynamics (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the…
Several different methods exist for efficient approximation of paths in multiscale stochastic chemical systems. Another approach is to use bursts of stochastic simulation to estimate the parameters of a stochastic differential equation…
We present a highly efficient and accurate hybrid stochastic simulation algorithm (HSSA) for the purpose of simulating a subset of biochemical reactions of large gene regulatory networks (GRN). The algorithm relies on the separability of a…
Stochastic differential equations (SDEs) or diffusions are continuous-valued continuous-time stochastic processes widely used in the applied and mathematical sciences. Simulating paths from these processes is usually an intractable problem,…
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic…
Brownian Dynamics algorithms are widely used for simulating soft-matter and biochemical systems. In recent times, their application has been extended to the simulation of coarse-grained models of cellular networks in simple organisms. In…
Biochemical reactions typically occur at low copy numbers, but at once in crowded and diverse environments. Space and stochasticity therefore play an essential role in biochemical networks. Spatial-stochastic simulations have become a…