Related papers: Simulation of large deviation functions using popu…
We study the population profile in a simple discrete time model of population dynamics. Our model, which is closely related to certain ``bit-string'' models of evolution, incorporates competition for resources via a population dependent…
We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…
Mathematical models of interacting populations are often constructed as systems of differential equations, which describe how populations change with time. Below we study one such model connected to the nonlinear dynamics of a system of…
We consider the superposition of a symmetric simple exclusion dynamics, speeded-up in time, with a spin-flip dynamics in a one-dimensional interval with periodic boundary conditions. We prove the large deviations principle for the empirical…
Human mobility, enabled by diverse transportation modes, is fundamental to urban functionality. Studying these movements across scales-from microscopic to macroscopic-yields valuable insights into urban dynamics. Local adaptation and…
In this paper we propose a framework that enables the study of large deviations for point processes based on stationary sequences with regularly varying tails. This framework allows us to keep track not of the magnitude of the extreme…
We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…
High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear…
Understanding transport processes in complex nanoscale systems, like ionic conductivities in nanofluidic devices or heat conduction in low dimensional solids, poses the problem of examining fluctuations of currents within nonequilibrium…
Dynamical sampling deals with signals that evolve in time under the action of a linear operator. The purpose of the present paper is to analyze the performance of the basic dynamical sampling algorithms in the finite dimensional case and…
A method is presented which allows for a tremendous speed-up of computer simulations of statistical systems by orders of magnitude. This speed-up is achieved by means of a new observable, while the algorithm of the simulation remains…
Among the different computational approaches modelling the dynamics of isogenic cell populations, discrete stochastic models can describe with sufficient accuracy the evolution of small size populations. However, for a systematic and…
We study the large deviations of the time-integrated current for a driven diffusion on the circle, often used as a model of nonequilibrium systems. We obtain the large deviation functions describing the current fluctuations using a…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…
We propose a method for approximating the large deviation rate function of time-integrated observables of diffusion processes, used in statistical physics to characterize the fluctuations of nonequilibrium systems. The method is based on…
We describe a simple form of importance sampling designed to bound and compute large-deviation rate functions for time-extensive dynamical observables in continuous-time Markov chains. We start with a model, defined by a set of rates, and a…
Human mobility research concerns spatiotemporal individual and population movement. Accurate modeling and prediction of human mobility can provide opportunities to monitor, manage and optimize human movement for improved social-economic…
Traffic jams on roadways, echo chambers on social media, crowds of moving pedestrians, and opinion dynamics during elections are all complex social systems. These applications may seem disparate, but some of the questions that they motivate…
We study the optimal control of discrete time mean filed dynamical systems under partial observations. We express the global law of the filtered process as a controlled system with its own dynamics. Following a dynamic programming approach,…
The study of population dynamics originated with early sociological works but has since extended into many fields, including biology, epidemiology, evolutionary game theory, and economics. Most studies on population dynamics focus on the…