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Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…

We consider cooperative reactions and we study the effects of the interaction strength among the system components on the reaction rate, hence realizing a connection between microscopic and macroscopic observables. Our approach is based on…

The possibility to apply phase-space methods to many-body interacting systems might provide accurate descriptions of correlations with a reduced numerical cost. For instance, the so--called stochastic mean-field phase-space approach, where…

Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural…

In microscopic mechanical systems interactions between elastic structures are often mediated by the hydrodynamics of a solvent fluid. At microscopic scales the elastic structures are also subject to thermal fluctuations. Stochastic…

Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…

For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…

Interacting particle systems are known for their ability to generate large-scale self-organized structures from simple local interaction rules between each agent and its neighbors. In addition to studying their emergent behavior, a main…

This work introduces a geometric framework and a novel network architecture for creating correspondences between samples of different conditions. Under this formalism, the latent space is a fiber bundle stratified into a base space encoding…

Machine learning algorithms relying on deep neural networks recently allowed a great leap forward in artificial intelligence. Despite the popularity of their applications, the efficiency of these algorithms remains largely unexplained from…

Realistic effective interparticle interactions of quantum many-body systems are widely seen as being short-range. However, the rigorous mathematical analysis of this type of model turns out to be extremely difficult, in general, with many…

The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations comprised of $N$ stochastic excitable units each is performed by studying an approximate system, obtained by…

We study a model of interacting neurons. The structure of this neural system is composed of two layers of neurons such that the neurons of the first layer send their spikes to the neurons of the second one: if $N$ is the number of neurons…

The brain's activity is characterized by the interaction of a very large number of neurons that are strongly affected by noise. However, signals often arise at macroscopic scales integrating the effect of many neurons into a reliable…

We study a subclass of the May-Leonard stochastic model with an arbitrary, even number of species, leading to the arising of two competing partnerships where individuals are indistinguishable. By carrying out a series of accurate numerical…

In the stochastic mean-field approach, an ensemble of initial conditions is considered to incorporate correlations beyond the mean-field. Then each starting pont is propagated separately using the Time-Dependent Hartree-Fock equation of…

There has been recent progress on the problem of inferring the structure of interactions in complex networks when they are in stationary states satisfying detailed balance, but little has been done for non-equilibrium systems. Here we…

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…

Oscillator networks with an asymmetric bipolar distribution of natural frequencies are useful representations of power grids. We propose a mean-field model that captures the onset, form and linear stability of frequency synchronization in…

Mean-field models have the ability to predict grain size distribution evolution occurring through thermomechanical solicitations. This article focuses on a comparison of mean-field models under grain growth conditions. Different…