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We propose a simple discrete stochastic model for calcium dynamics in living cells. Specifically, the calcium concentration distribution is assumed to give rise to a set of probabilities for the opening/closing of channels which release…

patt-sol · Physics 2009-10-31 Markus Baer , Martin Falcke , Herbert Levine , Lev S. Tsimring

Population dynamics are often affected by sudden environmental perturbations. Parameters of stochastic models are often imprecise due to various uncertainties. In this paper, we formulate a stochastic multimolecular biochemical reaction…

Probability · Mathematics 2020-04-30 Fei Sun

An effective macroscopic model for a stochastic microscopic system is derived. The original microscopic system is modeled by a stochastic partial differential equation defined on a domain perforated with small holes or heterogeneities. The…

Analysis of PDEs · Mathematics 2007-05-23 Wei Wang , Daomin Cao , Jinqiao Duan

Despite the growing interest in diffusion models, gaining a deep understanding of the model class remains an elusive endeavour, particularly for the uninitiated in non-equilibrium statistical physics. Thanks to the rapid rate of progress in…

Machine Learning · Computer Science 2025-05-23 Fabio De Sousa Ribeiro , Ben Glocker

Physically motivated stochastic dynamics are often used to sample from high-dimensional distributions. However such dynamics often get stuck in specific regions of their state space and mix very slowly to the desired stationary state. This…

Machine Learning · Statistics 2025-05-13 Abhijith Jayakumar , Andrey Y. Lokhov , Sidhant Misra , Marc Vuffray

A stochastic Lie system on a manifold $M$ is a stochastic differential equation whose dynamics is described by a linear combination with functions depending on $\mathbb{R}^\ell$-valued semi-martigales of vector fields on $M$ spanning a…

Probability · Mathematics 2025-12-02 Javier de Lucas , Marcin Zając

We present a model for the dynamics of a population of bacteria with a continuum of traits, who compete for resources and exchange horizontally (transfer) an otherwise vertically inherited trait with possible mutations. Competition…

Probability · Mathematics 2017-07-27 Sylvain Billiard , Pierre Collet , Régis Ferrière , Sylvie Méléard , Viet Chi Tran

We revisit the modeling of the diauxic growth of a pure microorganism on two distinct sugars which was first described by Monod. Most available models are deterministic and make the assumption that all cells of the microbial ecosystem…

Populations and Evolution · Quantitative Biology 2020-05-19 Carl Graham , Jérôme Harmand , Sylvie Méléard , Josué Tchouanti

Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…

Machine Learning · Statistics 2021-03-17 Joseph Bakarji , Daniel M. Tartakovsky

Angiogenesis is the formation of new blood vessels from pre-existing ones in response to chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a mesoscopic lattice-based model of angiogenesis, in which…

Tissues and Organs · Quantitative Biology 2016-03-02 Fabian Spill , Pilar Guerrero , Tomas Alarcon , Philip K. Maini , Helen M. Byrne

We investigate the static and dynamic properties of a celebrated model of social segregation, providing a complete explanation of the mechanisms leading to segregation both in one- and two-dimensional systems. Standard statistical physics…

Physics and Society · Physics 2009-11-13 Luca Dall'Asta , Claudio Castellano , Matteo Marsili

Stochastic mechanics---the study of classical stochastic systems governed by things like master equations and Fokker-Planck equations---exhibits striking mathematical parallels to quantum mechanics. In this article, we make those parallels…

Statistical Mechanics · Physics 2019-10-01 John J. Vastola , William R. Holmes

The central goal of a dynamical theory of evolution is to abstract the mean evolutionary trajectory in the trait space by considering ecological processes at the level of the individual. In this work, we develop such a theory for a new…

Populations and Evolution · Quantitative Biology 2020-03-25 Vaibhav Madhok

Stochastic simulation is a widely used method for estimating quantities in models of chemical reaction networks where uncertainty plays a crucial role. However, reducing the statistical uncertainty of the corresponding estimators requires…

Quantitative Methods · Quantitative Biology 2019-06-13 Michael Backenköhler , Luca Bortolussi , Verena Wolf

We consider the problem of selecting deterministic or stochastic models for a biological, ecological, or environmental dynamical process. In most cases, one prefers either deterministic or stochastic models as candidate models based on…

Applications · Statistics 2015-10-26 Libo Sun , Chihoon Lee , Jennifer A. Hoeting

Biological living systems in general exhibit complex and diverse dynamics. The latter, in particular, is essential, since diversification increases the odds of survival of an organism while reducing the risk of extinction of the population.…

Probability · Mathematics 2022-08-19 Sandesh Athni Hiremath

Biomolecular condensates play a central role in the spatial organization of living matter. Their formation is now well understood as a form of liquid-liquid phase separation that occurs very far from equilibrium. For instance, they can be…

Soft Condensed Matter · Physics 2024-10-14 Roxanne Berthin , Jacques Fries , Marie Jardat , Vincent Dahirel , Pierre Illien

Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…

Machine Learning · Computer Science 2025-09-03 Andrea Montanari

Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…

Machine Learning · Computer Science 2025-11-07 Yuansan Liu , Sudanthi Wijewickrema , Dongting Hu , Christofer Bester , Stephen O'Leary , James Bailey

We address the reachability problem for continuous-time stochastic dynamic systems. Our objective is to present a unified framework that characterizes the reachable set of a dynamic system in the presence of both stochastic disturbances and…

Systems and Control · Electrical Eng. & Systems 2024-09-04 Saber Jafarpour , Zishun Liu , Yongxin Chen