Related papers: Stochastic processes with distributed delays: chem…
We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the…
Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein.…
Stochastic models of biochemical reaction networks are widely used to capture intrinsic noise in cellular systems. The typical formulation of these models are based on Markov processes for which there is extensive research on efficient…
In spatially distributed cellular systems, it is often convenient to represent complicated auxiliary pathways and spatial transport by time-delayed reaction rates. Furthermore, many of the reactants appear in low numbers necessitating a…
It is well known that the kinetics of an intracellular biochemical network is stochastic. This is due to intrinsic noise arising from the random timing of biochemical reactions in the network as well as due to extrinsic noise stemming from…
Given a discrete stochastic process, for example a chemical reaction system or a birth and death process, we often want to find a continuous stochastic approximation so that the techniques of stochastic differential equations may be brought…
We used various analytical and numerical techniques to elucidate signal propagation in a small enzymatic cascade which is subjected to external and internal noise. The nonlinear character of catalytic reactions, which underlie protein…
A continuous approximation framework for non-linear stochastic as well as deterministic discrete maps is developed. For the stochastic map with uncorelated Gaussian noise, by successively applying the It\^o lemma, we obtain a Langevin type…
A new approach for the analysis of Langevin-type stochastic processes in the presence of strong measurement noise is presented. For the case of Gaussian distributed, exponentially correlated, measurement noise it is possible to extract the…
We develop a novel class of MCMC algorithms based on a stochastized Nesterov scheme. With an appropriate addition of noise, the result is a time-inhomogeneous underdamped Langevin equation, which we prove emits a specified target…
We solve the generalized Langevin equation driven by a stochastic force with power-law autocorrelation function. A stationary Markov process has been applied as a model of the noise. However, the resulting velocity variance does not…
We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive…
Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays traveling waves in its…
In many applied settings, the chemical Langevin equation and linear noise approximation are used in the simulation and data analysis of stochastic reaction networks. With the goal of exploring the sensitivities of reaction network paths to…
We propose here a method to estimate a delay from a time series taking advantage of analysis of random walks with delay. This method is applicable to a time series coming out of a system which is or can be approximated as a linear feedback…
Realistic networks display heterogeneous transmission delays. We analyze here the limits of large stochastic multi-populations networks with stochastic coupling and random interconnection delays. We show that depending on the nature of the…
Stochastic Chemical Reaction Networks are continuous time Markov chain models that describe the time evolution of the molecular counts of species interacting stochastically via discrete reactions. Such models are ubiquitous in systems and…
Time delay is ubiquitous in many experimental and real-world situations. It is often unclear whether time delay plays a significant role in observed phenomena, and if it does, how long the time lag really is. This would be invaluable…
We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…