Related papers: Interpretation of generalized Langevin equations
Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…
Stochastic modelling necessitates an interpretation of noise. In this paper, we describe the loss of deterministically stable behaviour in a fundamental fluid mechanics problem, conditional to whether noise is introduced in the sense of…
The usual Langevin approach to describe systems driven by noise fails to describe the long time behavior of systems with multiple attractors. The solution of the associated linear Fokker-Planck equation is always unique, even though it…
We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady-state by using joint probability distributions symmetries of different entropy production decompositions. The analytical approach is…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…
Modelling the evolution of a system using stochastic dynamics typically implies a greater subjective uncertainty in the adopted system coordinates as time progresses, and stochastic entropy production has been developed as a measure of this…
In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce…
Interpreting the noise in a stochastic differential equation, in particular the It\^o versus Stratonovich dilemma, is a problem that has generated a lot of debate in the physical literature. In the last decades, a third interpretation of…
The Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and are thus widely used to quantify random phenomena such as uncertainty propagation. For dynamical systems driven by non-Gaussian…
Traditionally, Probability theory was dealing with limit theorems where 'limit" means that time tends to infinity. Questions about finite time dynamics (evolution) were always considered as, although important for practical applications,…
Recent rapid advances in single particle tracking and supercomputing techniques resulted in an unprecedented abundance of diffusion data exhibiting complex behaviours, such the presence of power law tails of the msd and memory functions,…
We review the behaviour of the Gibbs' and conditional entropies in deterministic and stochastic systems and continue to a formulation appropriate for a stochastically perturbed system with delayed dynamics. The underlying question driving…
Response lags are generic to almost any physical system and often play a crucial role in the feedback loops present in artificial nanodevices and biological molecular machines. In this paper, we perform a comprehensive study of small…
We introduce ImitationFlow, a novel Deep generative model that allows learning complex globally stable, stochastic, nonlinear dynamics. Our approach extends the Normalizing Flows framework to learn stable Stochastic Differential Equations.…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…
A recent paper of Melbourne & Stuart, A note on diffusion limits of chaotic skew product flows, Nonlinearity 24 (2011) 1361-1367, gives a rigorous proof of convergence of a fast-slow deterministic system to a stochastic differential…
Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…