Related papers: Quantifying Rare Events in Stochastic Reaction-Dif…
We consider stochastic reaction-diffusion equations on a finite network represented by a finite graph. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given supplemented by a…
A variety of simulation methodologies have been used for modeling reaction-diffusion dynamics -- including approaches based on Differential Equations (DE), the Stochastic Simulation Algorithm (SSA), Brownian Dynamics (BD), Green's Function…
Various kinetic Monte Carlo algorithms become inefficient when some of the population sizes in a system are large, which gives rise to a large number of reaction events per unit time. Here, we present a new acceleration algorithm based on…
A macroscopic mesoscopic, deterministic stochastic coupling strategy is proposed to accelerate the direct simulation Monte Carlo (DSMC) method for chemical reaction. First, a macroscopic synthetic equation is formulated by integrating…
In this work, we consider a differential description of the evolution of the state of a reaction-diffusion system under environmental fluctuations. We are interested in estimating the state of the system when only partial observations are…
In this paper we introduce a general stochastic representation for an important class of processes with resetting. It allows to describe any stochastic process intermittently terminated and restarted from a predefined random or non-random…
Extreme weather events epitomize high cost: to society through their physical impacts, and to computer servers that simulate them to assess risk and advance physical understanding. It costs hundreds of simulation years to sample a few…
Chemical reaction networks can undergo nonequilibrium phase transitions upon variation of external control parameters like the chemical potential of a species. We investigate the flux in the associated chemostats that is proportional to the…
We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the…
Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via…
In these lecture notes, we explore the mathematical preliminaries and foundational concepts that connect stochastic processes with partial differential equations. We begin by investigating Brownian motion, which serves as a model for random…
We apply tensor networks to counting statistics for the stochastic particle transport in an out-of-equilibrium diffusive system. This system is composed of a one-dimensional channel in contact with two particle reservoirs at the ends. Two…
In the present Short Note an idea is proposed to explain the emergence and the observation of processes in complex media that are driven by fractional non-Markovian master equations. Particle trajectories are assumed to be solely Markovian…
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…
We consider chemical reaction networks modeled by a discrete state and continuous in time Markov process for the vector copy number of the species and provide a novel particle filter method for state and parameter estimation based on exact…
The stochastic reaction network in which chemical species evolve through a set of reactions is widely used to model stochastic processes in physics, chemistry and biology. To characterize the evolving joint probability distribution in the…
In this work, we consider the numerical estimation of the probability for a stochastic process to hit a set B before reaching another set A. This event is assumed to be rare. We consider reactive trajectories of the stochastic Allen-Cahn…
Computational systems biology has provided plenty of insights into cell biology. Early on, the focus was on reaction networks between molecular species. Spatial distribution only began to be considered mostly within the last decade.…
Diffusion with stochastic resetting, instantaneous returns of a diffusing particle to a reference point, creates a stationary probability distribution. The paradigm is extended here to a doubly stochastic protocol in which the resetting…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…