相关论文: A finite state projection algorithm for the statio…
We present an adaptive Finite State Projection (FSP) method for efficiently solving the Chemical Master Equation (CME) with rigorous error control. Our approach integrates time-stepping with dynamic state-space truncation, balancing…
The Finite State Projection (FSP) method approximates the Chemical Master Equation (CME) by restricting the dynamics to a finite subset of the (typically infinite) state space, enabling direct numerical solution with computable error…
Consider the standard stochastic reaction network model where the dynamics is given by a continuous-time Markov chain over a discrete lattice. For such models, estimation of parameter sensitivities is an important problem, but the existing…
Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space…
The probability distribution describing the state of a Stochastic Reaction Network evolves according to the Chemical Master Equation (CME). It is common to estimated its solution using Monte Carlo methods such as the Stochastic Simulation…
The stochastic nature of chemical reactions involving randomly fluctuating population sizes has lead to a growing research interest in discrete-state stochastic models and their analysis. A widely-used approach is the description of the…
The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space,…
The discrete chemical master equation (dCME) provides a fundamental framework for studying stochasticity in mesoscopic networks. Because of the multi-scale nature of many networks where reaction rates have large disparity, directly solving…
The stochastic dynamics of biochemical networks are usually modelled with the chemical master equation (CME). The stationary distributions of CMEs are seldom solvable analytically, and numerical methods typically produce estimates with…
Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells. These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not…
The Chemical Master Equation (CME) is well known to provide the highest resolution models of a biochemical reaction network. Unfortunately, even simulating the CME can be a challenging task. For this reason more simple approximations to the…
It is increasingly realized that taking stochastic effects into account is important in order to study biological cells. However, the corresponding mathematical formulation, the chemical master equation (CME), suffers from the curse of…
The Chemical Master Equation (CME) provides a highly accurate, yet extremely resource-intensive representation of a stochastic chemical reaction network and its kinetics due to the exponential scaling of its possible states with the number…
The chemical birth-death process, whose chemical master equation (CME) is exactly solvable, is a paradigmatic toy problem often used to get intuition for how stochasticity affects chemical kinetics. In a certain limit, it can be…
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…
Computing the stationary distributions of a continuous-time Markov chain (CTMC) involves solving a set of linear equations. In most cases of interest, the number of equations is infinite or too large, and the equations cannot be solved…
We introduce the exit time finite state projection (ETFSP) scheme, a truncation-based method that yields approximations to the exit distribution and occupation measure associated with the time of exit from a domain (i.e., the time of first…
The Cavity Master Equation (CME) is a closure scheme to the usual Master Equation representing the dynamics of discrete variables in continuous time. In this work we explore the CME for a ferromagnetic model in a random graph. We first…
The fixed-horizon constrained Markov Decision Process (C-MDP) is a well-known model for planning in stochastic environments under operating constraints. Chance-Constrained MDP (CC-MDP) is a variant that allows bounding the probability of…
The Chemical Master Equation (CME) is used to stochastically model biochemical reaction networks, under the Markovian assumption. The low-order statistical moments induced by the CME are often the key quantities that one is interested in.…