Stochastic Reaction Research Articles

An in situ, prepulse insensitive and comparatively accurate intensity measurement of ultra-strong lasers based on stochastic radiation reactions

An in situ, prepulse insensitive and comparatively accurate intensity measurement of ultra-strong lasers based on stochastic radiation reactions

Geometric Ergodicity of a Stochastic Reaction–Diffusion Tuberculosis Model with Varying Immunity Period

Geometric Ergodicity of a Stochastic Reaction–Diffusion Tuberculosis Model with Varying Immunity Period

Analysis of Singularly Perturbed Stochastic Chemical Reaction Networks Motivated by Applications to Epigenetic Cell Memory

Analysis of Singularly Perturbed Stochastic Chemical Reaction Networks Motivated by Applications to Epigenetic Cell Memory

Characterizing the nonmonotonic behavior of mutual information along biochemical reaction cascades.

Cells sense environmental signals and transmit information intracellularly through changes in the abundance of molecular components. Such molecular abundances can be measured in single cells and exhibit significant heterogeneity in clonal populations even in identical environments. Experimentally observed joint probability distributions can then be used to quantify the covariability and mutual information between molecular abundances along signaling cascades. However, because stationary state abundances along stochastic biochemical reaction cascades are not conditionally independent, their mutual information is not constrained by the data-processing inequality. Here, we report the conditions under which the mutual information between stationary state abundances increases along a cascade of biochemical reactions. This nonmonotonic behavior can be intuitively understood in terms of noise propagation and time-averaging stochastic fluctuations that are short-lived compared to an extrinsic signal. Our results reemphasize that mutual information measurements of stationary state distributions of cellular components may be of limited utility for characterizing cellular signaling processes because they do not measure information transfer.

Invariant Measures for Stochastic Reaction–Diffusion Problems on Unbounded Thin Domains Driven by Nonlinear Noise

Invariant Measures for Stochastic Reaction–Diffusion Problems on Unbounded Thin Domains Driven by Nonlinear Noise

A non-autonomous framework for climate change and extreme weather events increase in a stochastic energy balance model

We develop a three-timescale framework for modeling climate change and introduce a space-heterogeneous one-dimensional energy balance model. This model, addressing temperature fluctuations from rising carbon dioxide levels and the super-greenhouse effect in tropical regions, fits within the setting of stochastic reaction–diffusion equations. Our results show how both mean and variance of temperature increase, without the system going through a bifurcation point. This study aims to advance the conceptual understanding of the extreme weather events frequency increase due to climate change.

Novel solitary wave solutions for stochastic nonlinear reaction–diffusion equation with multiplicative noise

The primary objective of this paper is to explore solitary wave solutions within the context of the stochastic Reaction–Diffusion equation, a problem that has not been previously investigated with respect to multiplicative noise. This marks a novel aspect of the current study. To accomplish this goal, we utilize two distinct integration methods: the extended Kudryashov’s method and the G′G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left( \\frac{G'}{G}\\right) $$\\end{document}-expansion method. These methods are chosen for their efficacy in handling nonlinear differential equations and are applied in tandem to uncover new trigonometric and hyperbolic stochastic exact solutions. The employment of these methods is crucial in generating solutions that have not been previously identified in this particular context. Subsequently, to assess the validity and usefulness of these newly discovered solutions, we conduct numerical simulations. These simulations involve implementing the derived solutions across a variety of scenarios or samples, allowing for an evaluation of their performance and applicability. This paper represents a significant contribution to the field of stochastic Reaction–Diffusion equations by introducing a pioneering investigation into the effects of multiplicative noise on solitary wave solutions. Furthermore, it offers a fresh perspective on obtaining exact solutions in the presence of such noise, showcasing the potential of the integration methods in tackling complex nonlinear stochastic systems.

Dynamical behaviors of a stochastic multi-molecule biochemical reaction model with Ornstein-Uhlenbeck process

Dynamical behaviors of a stochastic multi-molecule biochemical reaction model with Ornstein-Uhlenbeck process

Large Deviations of Invariant Measures of Stochastic Reaction–Diffusion Equations on Unbounded Domains

This paper is concerned with the large deviation principle of invariant measures of the stochastic reaction–diffusion equation with polynomial drift driven by additive noise defined on the entire space Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^n$$\\end{document}. Since the standard Sobolev embeddings on Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^n$$\\end{document} are not compact and the spectrum of the Laplace operator on Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^n$$\\end{document} are not discrete, there are many issues for proving the large deviations of invariant measures in the case of unbounded domains, including the difficulties for proving the compactness of the level sets of rate functions, the uniform Dembo–Zeitouni large deviations on compact sets as well as the exponential tightness on compact sets. Currently, there is no result available in the literature on the large deviations of invariant measures for stochastic PDEs on unbounded domains, and this paper is the first one to deal with this issue. The non-compactness of the standard Sobolev embeddings on Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^n$$\\end{document} is circumvented by the idea of uniform tail-ends estimates together with the arguments of weighted spaces.

Efficient generation of barrier crossing trajectories using approximate Brownian bridges.

We examine continuous random walks that are conditioned to reach one region before another. These conditioned processes are used to generate stochastic trajectories for barrier crossing events, which are generally rare and difficult to sample. The processes are generated using a Brownian bridge technique, resulting in near perfect sampling efficiency without accruing error in the conditional statistics of the process. The construction requires the hitting probability or committer function, which is a solution to the backward Fokker-Planck equation, a partial-differential equationthat can be difficult to solve through general means. Therefore, we derive a one-dimensional approximation through asymptotic methods for barrier crossing trajectories. We show that this approximation has a simple analytical representation and approaches the true solution as the barrier height increases. Brownian bridge trajectories generated with this approximate solution are then shown to result in accurate conditional statistics when used in conjunction with importance sampling, even in the case when potential energy barriers are not large. We show this idea's effectiveness by simulating rare events in a stochastic chemical reaction network (Schögl reaction) with multiple steady states. This methodology shows great promise for future implementation to simulate rare barrier crossing events for a wide variety of physical processes.

A topological mechanism for robust and efficient global oscillations in biological networks

Long and stable timescales are often observed in complex biochemical networks, such as in emergent oscillations. How these robust dynamics persist remains unclear, given the many stochastic reactions and shorter time scales demonstrated by underlying components. We propose a topological model that produces long oscillations around the network boundary, reducing the system dynamics to a lower-dimensional current in a robust manner. Using this to model KaiC, which regulates the circadian rhythm in cyanobacteria, we compare the coherence of oscillations to that in other KaiC models. Our topological model localizes currents on the system edge, with an efficient regime of simultaneously increased precision and decreased cost. Further, we introduce a new predictor of coherence from the analysis of spectral gaps, and show that our model saturates a global thermodynamic bound. Our work presents a new mechanism and parsimonious description for robust emergent oscillations in complex biological networks.

Event horizon kinetic Monte Carlo.

In this study, we present a novel approach for modeling the dynamics of stochastic processes. The fundamental concept involves constructing a stochastic Markov chain comprising states separated by more than one stochastic event. Initially, the method explores the network of neighboring states connected by stochastic events. This exploration results in a "horizon" of events leading to a set of "boundary" states at the periphery of each local network. Subsequently, the next member in the Markov chain is selected from the "boundary" states based on the probability of reaching each of the "boundary" states for the first time. Meanwhile, the simulation clock is updated according to the time required to reach the boundary for the first time. This can be achieved using an analytical approach, where the probability of reaching each boundary state for the first time is estimated using absorbing conditions for all boundary states in the analytical solution of a master equation describing the local network of states around each current state. The proposed method is demonstrated in modeling the dynamics in networks of stochastic reactions but can be easily applied in any stochastic system whose dynamics can be expressed via the solution of a master equation. It is expected to enhance the efficiency of event-driven Monte Carlo simulations, originally introduced by Gillespie and widely regarded as the gold standard in the field, especially in cases where the presence of events is characterized by different timescales.

Macroscopic limit for stochastic chemical reactions involving diffusion and spatial heterogeneity

To model bio-chemical reaction systems with diffusion one can either use stochastic, microscopic reaction–diffusion master equations or deterministic, macroscopic reaction–diffusion system. The connection between these two models is not only theoretically important but also plays an essential role in applications. This paper considers the macroscopic limits of the chemical reaction–diffusion master equation for first-order chemical reaction systems in highly heterogeneous environments. More precisely, the diffusion coefficients as well as the reaction rates are spatially inhomogeneous and the reaction rates may also be discontinuous. By carefully discretizing these heterogeneities within a reaction–diffusion master equation model, we show that in the limit we recover the macroscopic reaction–diffusion system with inhomogeneous diffusion and reaction rates.

Stochastic filtering of reaction networks partially observed in time snapshots

Stochastic reaction network models arise in intracellular chemical reactions, epidemiological models and other population process models, and are a class of continuous time Markov chains which have the nonnegative integer lattice as state space. We consider the problem of estimating the conditional probability distribution of a stochastic reaction network given exact partial state observations in time snapshots. We propose a particle filtering method called the targeting method. Our approach takes into account that the reaction counts in between two observation snapshots satisfy linear constraints and also uses inhomogeneous Poisson processes as proposals for the reaction counts to facilitate exact interpolation. We provide rigorous analysis as well as numerical examples to illustrate our method and compare it with other alternatives.

Efficient and scalable prediction of stochastic reaction–diffusion processes using graph neural networks

The dynamics of locally interacting particles that are distributed in space give rise to a multitude of complex behaviours. However the simulation of reaction–diffusion processes which model such systems is highly computationally expensive, the cost increasing rapidly with the size of space. Here, we devise a graph neural network based approach that uses cheap Monte Carlo simulations of reaction–diffusion processes in a small space to cast predictions of the dynamics of the same processes in a much larger and complex space, including spaces modelled by networks with heterogeneous topology. By applying the method to two biological examples, we show that it leads to accurate results in a small fraction of the computation time of standard stochastic simulation methods. The scalability and accuracy of the method suggest it is a promising approach for studying reaction–diffusion processes in complex spatial domains such as those modelling biochemical reactions, population evolution and epidemic spreading.

Large Deviation Principle for Stochastic Reaction–Diffusion Equations with Superlinear Drift on $$\mathbb {R}$$ Driven by Space–Time White Noise

Large Deviation Principle for Stochastic Reaction–Diffusion Equations with Superlinear Drift on $$\mathbb {R}$$ Driven by Space–Time White Noise

Persistence and extinction of a reaction–diffusion vegetation-water system with time–space white noise

This study considers an ecosystem subjected to stochastic fluctuations, and presents a stochastic reaction–diffusion vegetation-water model with time–space noise. Using a truncation and stop time method, this paper gives several properties important to the mild solution such as existence uniqueness, positivity, and continuity with respect to initial values. Sufficient conditions for persistence and extinction of vegetation are derived. Theoretical results are demonstrated using numerical simulations.

Long-term dynamics of fractional stochastic delay reaction–diffusion equations on unbounded domains

Long-term dynamics of fractional stochastic delay reaction–diffusion equations on unbounded domains

Synchronization of delayed stochastic reaction–diffusion Hopfield neural networks via sliding mode control

Synchronization of stochastic reaction–diffusion Hopfield neural networks with s-delays via sliding mode control is investigated in this article. To begin with, we choose suitable functional space for state variables, then the system is transformed into a functional differential equation in an infinite-dimensional Hilbert space by using appropriate functional analysis technique. Based on above preliminary preparation, sliding mode control (SMC) is constructed to drive the error trajectory into the designed switching surface. Specifically, the switching surface is constructed as linear combination of state variables, which is related to control gains. Then novel SMC law is designed which involving delay, reaction diffusion term, and reaching law. Furthermore, the criterion of mean-square exponential synchronization for stochastic delayed reaction–diffusion Hopfield neural networks with s-delays is given in the form of matrix form. This criterion is less restrictive and easy to check in computer. Meanwhile, a different novel Lyapunov–Krasovskii functional (LKF) mixed with Itô’s formula, Young inequality, Hanalay inequality is employed in this proof procedure. At last, a numerical example is presented to validate the availability of theoretical result. The simulation is based on the finite difference method, and numerical result coincides with the theoretical result proposed.

Surface-Initiated Polymerization with an Initiator Gradient: A Monte Carlo Simulation.

Due to the difficulty of accurately characterizing properties such as the molecular weight (Mn) and grafting density (σ) of gradient brushes (GBs), these properties are traditionally assumed to be uniform in space to simplify analysis. Applying a stochastic reaction model (SRM) developed for heterogeneous polymerizations, we explored surface-initiated polymerizations (SIPs) with initiator gradients in lattice Monte Carlo simulations to examine this assumption. An initial exploration of SIPs with 'homogeneously' distributed initiators revealed that increasing σ slows down the polymerization process, resulting in polymers with lower molecular weight and larger dispersity (Đ) for a given reaction time. In SIPs with an initiator gradient, we observed that the properties of the polymers are position-dependent, with lower Mn and larger Đ in regions of higher σ, indicating the non-uniform properties of polymers in GBs. The results reveal a significant deviation in the scaling behavior of brush height with σ compared to experimental data and theoretical predictions, and this deviation is attributed to the non-uniform Mn and Đ.