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Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…

Machine Learning · Computer Science 2021-09-30 Lukas Köhs , Bastian Alt , Heinz Koeppl

This work investigates variational frameworks for modeling stochastic dynamics in incompressible fluids, focusing on large-scale fluid behavior alongside small-scale stochastic processes. The authors aim to develop a coupled system of…

Fluid Dynamics · Physics 2025-03-21 Arnaud Debussche , Etienne Mémin

This paper investigates optimal fluctuations for chemical reaction systems with N species, M reactions, and general rate law. In the limit of large volume, large fluctuations for such models occur with overwhelming probability in the…

Probability · Mathematics 2025-06-10 Feng Zhao , Jinjie Zhu , Yang Li , Xianbin Liu , Dongping Jin

Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small population sizes. This makes it necessary to favor…

Probability · Mathematics 2022-02-28 Daniele Cappelletti , Badal Joshi

Exploring the intersection of deterministic and stochastic dynamics, this paper delves into Lagrangian discovery for conservative and non-conservative systems under stochastic excitation. Traditional Lagrangian frameworks, adept at…

Dynamical Systems · Mathematics 2024-02-28 Tapas Tripura , Satyam Panda , Budhaditya Hazra , Souvik Chakraborty

Stochasticity plays important roles in reaction systems. Vector fields of probability flux and velocity characterize time-varying and steady-state properties of these systems, including high probability paths, barriers, checkpoints among…

Molecular Networks · Quantitative Biology 2018-12-05 Anna Terebus , Chun Liu , Jie Liang

Dynamical phase transitions (DPTs) arise from qualitative changes in the long-time behavior of stochastic trajectories, often observed in systems with kinetic constraints or driven out of equilibrium. Here we demonstrate that first-order…

Statistical Mechanics · Physics 2024-07-29 Takahiro Kanazawa , Kyogo Kawaguchi , Kyosuke Adachi

In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…

Adaptation and Self-Organizing Systems · Physics 2013-03-18 Hong Qian

Within a fully microscopic setting, we derive a variational principle for the non-equilibrium steady states of chemical reaction networks, valid for time-scales over which chemical potentials can be taken to be slowly varying: at…

Molecular Networks · Quantitative Biology 2015-06-05 Andrea De Martino , Daniele De Martino , Roberto Mulet , Guido Uguzzoni

A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…

Probability · Mathematics 2007-05-23 Karen Ball , Thomas G. Kurtz , Lea Popovic , Greg Rempala

We establish a large deviation principle for the empirical measure process associated with a general class of finite-state mean field interacting particle systems with Lipschitz continuous transition rates that satisfy a certain ergodicity…

Probability · Mathematics 2016-01-26 Paul Dupuis , Kavita Ramanan , Wei Wu

One-dimensional run-and-tumble processes may converge towards some localized non-equilibrium steady state when the two velocities and/or the two switching rates are space-dependent. A long dynamical trajectory can be then analyzed via the…

Statistical Mechanics · Physics 2021-08-23 Cecile Monthus

We consider multiscale stochastic spatial gene networks involving chemical reactions and diffusions. The model is Markovian and the transitions are driven by Poisson random clocks. We consider a case where there are two different spatial…

Probability · Mathematics 2020-07-10 Arnaud Debussche , Mac Jugal Nguepedja Nankep

We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…

Probability · Mathematics 2007-05-23 Samuel Herrmann , Peter Imkeller , Dierk Peithmann

External flows of energy, entropy, and matter can cause sudden transitions in the stability of biological and industrial systems, fundamentally altering their dynamical function. How might we control and design these transitions in chemical…

Molecular Networks · Quantitative Biology 2023-06-19 Zachary G. Nicolaou , Schuyler B. Nicholson , Adilson E. Motter , Jason R. Green

Dynamical phase transitions are defined as non-analytic points of the large deviation function of current fluctuations. We show that for boundary driven systems, many dynamical phase transitions can be identified using the geometrical…

Statistical Mechanics · Physics 2017-12-13 Ohad Shpielberg

We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…

Probability · Mathematics 2022-11-03 Zachary Bezemek , Konstantinos Spiliopoulos

We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behaviour, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the…

Probability · Mathematics 2017-02-17 Francesco Cordoni , Luca Di Persio

Key features of biological activity can often be captured by transitions between a finite number of semi-stable states that correspond to behaviors or decisions. We present here a broad class of dynamical systems that are ideal for modeling…

Dynamical Systems · Mathematics 2022-12-14 Megan Morrison , Lai-Sang Young

We give a new proof of the large deviation principle from the hydrodynamic limit for the Ginzberg-Landau model studied in Donsker and Varadhan (1989) using techniques from the theory of stochastic control and weak convergence methods. The…

Probability · Mathematics 2018-03-28 Sayan Banerjee , Amarjit Budhiraja , Michael Perlmutter