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Stochastic reaction networks (SRNs) provide models of many real-world networks. Examples include networks in epidemiology, pharmacology, genetics, ecology, chemistry, and social sciences. Here, we model stochastic reaction networks by…

Probability · Mathematics 2023-01-26 Carsten Wiuf , Chuang Xu

We consider Markov processes, which describe e.g. queueing network processes, in a random environment which influences the network by determining random breakdown of nodes, and the necessity of repair thereafter. Starting from an explicit…

Probability · Mathematics 2015-03-03 H. Daduna , R. Szekli

We consider steady states of dynamics that have an underlying network structure. We study how a steady state responds to small perturbations in the network parameters and how this sensitivity is connected to the network structure. We…

Molecular Networks · Quantitative Biology 2023-03-20 Robin Chemnitz

Reaction networks are mathematical models of interacting chemical species that are primarily used in biochemistry. There are two modeling regimes that are typically used, one of which is deterministic and one that is stochastic. In…

Molecular Networks · Quantitative Biology 2018-09-14 David Anderson , Daniele Cappelletti

Background: Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state…

Quantitative Methods · Quantitative Biology 2012-07-10 Steffen Waldherr , Bernard Haasdonk

Based on the theory of stochastic chemical kinetics, the inherent randomness and stochasticity of biochemical reaction networks can be accurately described by discrete-state continuous-time Markov chains. The analysis of such processes is,…

Numerical Analysis · Mathematics 2014-10-14 Andreychenko Alexander , Mikeev Linar , Wolf Verena

The importance of considering contextual probabilities in shaping response patterns within psychological testing is underscored, despite the ubiquitous nature of order effects discussed extensively in methodological literature. Drawing from…

Methodology · Statistics 2024-03-28 Andrea Bosco

In this paper we study a class of stochastic chemical reaction networks (CRNs) for which chemical species are created by a sequence of chain reactions. We prove that under some convenient conditions on the initial state, some of these…

Probability · Mathematics 2024-06-19 Lucie Laurence , Philippe Robert

A chemical reaction network (CRN) is composed of reactions that can be seen as interactions among entities called species, which exist within the system. Endowed with kinetics, CRN has a corresponding set of ordinary differential equations…

Dynamical Systems · Mathematics 2021-04-20 Bryan S. Hernandez , Ralph John L. De la Cruz

The stochastic kinetics of BRN are described by a chemical master equation (CME) and the underlying laws of mass action. The CME must be usually solved numerically by generating enough traces of random reaction events. The resulting…

Molecular Networks · Quantitative Biology 2023-06-21 Pavel Loskot

Stochastic chemical reaction networks (SRNs) in cellular systems are commonly modeled as continuous-time Markov chains (CTMCs) describing the dynamics of molecular copy numbers. The exact evaluation of transient copy number statistics is,…

Quantitative Methods · Quantitative Biology 2026-04-07 Takeyuki Iwasaki , Yutaka Hori

This paper contributes an in-depth study of properties of continuous time Markov chains (CTMCs) on non-negative integer lattices $\N_0^d$, with particular interest in one-dimensional CTMCs with polynomial transitions rates. Such stochastic…

Probability · Mathematics 2020-06-22 Chuang Xu , Mads Christian Hansen , Carsten Wiuf

We address a fundamental question: under which conditions do the dynamics and thermodynamics of open chemical reaction networks (CRNs), grounded on the notion of idealized chemostats that exchange selected species, emerge from underlying…

Statistical Mechanics · Physics 2026-04-17 Benedikt Remlein , Massimiliano Esposito , Francesco Avanzini

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…

Molecular Networks · Quantitative Biology 2025-12-03 Thomas P. Steele , David J. Warne

Kinetic theory and thermodynamics of reaction networks are extended to the out-of-equilibrium dynamics of continuous-flow stirred tank reactors (CSTR) and serial transfers. On the basis of their stoichiometry matrix, the conservation laws…

Statistical Mechanics · Physics 2018-04-24 Alex Blokhuis , David Lacoste , Pierre Gaspard

Stochastic models for chemical reaction networks have become very popular in recent years. For such models, the estimation of parameter sensitivities is an important and challenging problem. Sensitivity values help in analyzing the network,…

Probability · Mathematics 2013-10-08 Ankit Gupta , Mustafa Khammash

Chemical reaction networks (CRNs) model the behavior of molecules in a well-mixed system. The emerging field of molecular programming uses CRNs not only as a descriptive tool, but as a programming language for chemical computation.…

Computational Complexity · Computer Science 2015-09-04 Adam Case , Jack H. Lutz , D. M. Stull

We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…

Dynamical Systems · Mathematics 2019-12-03 Daniele Cappelletti , Abhishek Pal Majumder , Carsten Wiuf

Inferring chemical reaction networks (CRN) from concentration time series is a challenge encouragedby the growing availability of quantitative temporal data at the cellular level. This motivates thedesign of algorithms to infer the…

Quantitative Methods · Quantitative Biology 2023-02-09 Julien Martinelli , Jeremy Grignard , Sylvain Soliman , Annabelle Ballesta , François Fages

We study chemical reaction networks with discrete state spaces, such as the standard continuous time Markov chain model, and present sufficient conditions on the structure of the network that guarantee the system exhibits an extinction…

Dynamical Systems · Mathematics 2017-01-11 Matthew D. Johnston , David F. Anderson , Gheorghe Craciun , Robert Brijder