Related papers: Model reduction methods for classical stochastic s…

We study a model ecosystem by means of dynamical techniques from disordered systems theory. The model describes a set of species subject to competitive interactions through a background of resources, which they feed upon. Additionally…

We propose a model to characterize how a diffusing population adapts under a time periodic selection, while its environment undergoes shifts and size changes, leading to significant differences with classical results on fixed domains. After…

We study the stability of non-conservative deterministic cross diffusion models and prove that they are approximated by stochastic population models when the populations become locally large. In this model, the individuals of two species…

Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…

Biochemical processes typically involve many chemical species, some in abundance and some in low molecule numbers. Here we first identify the rate constant limits under which the concentrations of a given set of species will tend to…

The paper analyses stochastic systems describing reacting molecular systems with a combination of two types of state spaces, a finite-dimensional, and an infinite dimenional part. As a typical situation consider the interaction of larger…

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…

It is a well established result that, in classical dynamical systems with sufficient time-scale separation, the fast chaotic degrees of freedom are well modeled by (Gaussian) white noise. In this paper, we present the stochastic dynamical…

Stochastic differential equations characterized by uncertainty are effective in modelling virus dynamics and provide an alternative to traditional deterministic models. Epidemic models are inevitably subjected to the randomness within the…

Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…

We consider continuous time Markovian processes where populations of individual agents interact stochastically according to kinetic rules. Despite the increasing prominence of such models in fields ranging from biology to smart cities,…

It is well-established that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic…

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…

Stochastic diffusion is the noisy and uncertain process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. Understanding these processes is becoming increasingly important as we attempt to…

Stochastic models of biochemical reaction networks are widely used to capture intrinsic noise in cellular systems. The typical formulation of these models are based on Markov processes for which there is extensive research on efficient…

We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…

The behavior of interacting populations typically displays irregular temporal and spatial patterns that are difficult to reconcile with an underlying deterministic dynamics. A classical example is the heterogeneous distribution of plankton…

When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…

The training of modern machine learning models often consists in solving high-dimensional non-convex optimisation problems that are subject to large-scale data. In this context, momentum-based stochastic optimisation algorithms have become…

We propose a method to reduce the relaxation time towards equilibrium in stochastic sampling of complex energy landscapes in statistical systems with discrete degrees of freedom by generalizing the platform previously developed for…