Related papers: A Fast Algorithm for High-Dimensional Markov Proce…
The problem of appropriately matching items subject to compatibility constraints arises in a number of important applications. While most of the literature on matching theory focuses on a static setting with a fixed number of items, several…
A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition…
The goal of this work is to formally abstract a Markov process evolving in discrete time over a general state space as a finite-state Markov chain, with the objective of precisely approximating its state probability distribution in time,…
We report new statistical time-series analysis tools providing significant improvements in the rapid, precision extraction of discrete state dynamics from large databases of experimental observations of molecular machines. By building…
A properly designed controller can help improve the quality of experimental measurements or force a dynamical system to follow a completely new time-evolution path. Recent developments in deep reinforcement learning have made steep advances…
We develop and analyze an asynchronous algorithm for distributed convex optimization when the objective writes a sum of smooth functions, local to each worker, and a non-smooth function. Unlike many existing methods, our distributed…
Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
Nowadays, algorithms with fast convergence, small memory footprints, and low per-iteration complexity are particularly favorable for artificial intelligence applications. In this paper, we propose a doubly stochastic algorithm with a novel…
The reduction of a continuous Markov process with multiple metastable states to a discrete rate process is investigated in the presence of slow time dependent parameters such as periodic external forces or slowly fluctuating barrier…
We propose score dynamics (SD), a general framework for learning accelerated evolution operators with large timesteps from molecular-dynamics simulations. SD is centered around scores, or derivatives of the transition log-probability with…
This paper examines a discrete-time queuing system with applications to telecommunications traffic. The arrival process is a particular Markov modulated process which belongs to the class of discrete batched Markovian arrival processes. The…
In the paper we consider some piecewise deterministic Markov process whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson process. The associated Markov chain describes the states of…
The use of stochastic models, in effect piecewise deterministic Markov processes (PDMP), has become increasingly popular especially for the modeling of chemical reactions and cell biophysics. Yet, exact simulation methods, for the…
This paper formed part of a preliminary research report for a risk consultancy and academic research. Stochastic Programming models provide a powerful paradigm for decision making under uncertainty. In these models the uncertainties are…
Strong and weak simulation relations have been proposed for Markov chains, while strong simulation and strong probabilistic simulation relations have been proposed for probabilistic automata. However, decision algorithms for strong and weak…
The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by its Kolmogorov equations, which is a system of linear ODEs…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
We consider Piecewise Deterministic Markov Processes (PDMPs) with a finite set of discrete states. In the regime of fast jumps between discrete states, we prove a law of large number and a large deviation principle. In the regime of fast…
In order to develop systems capable of artificial evolution, we need to identify which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical…
For rare events described in terms of Markov processes, truly unbiased estimation of the rare event probability generally requires the avoidance of numerical approximations of the Markov process. Recent work in the exact and…