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We consider Markov models of large-scale networks where nodes are characterized by their local behavior and by a mobility model over a two-dimensional lattice. By assuming random walk, we prove convergence to a system of partial…
Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…
We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as…
We introduce the concept of {\it mean-field optimal control} which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional…
The processes of interplant competition within a field are still poorly understood. However, they explain a large part of the heterogeneity in a field and may have longer-term consequences, especially in mixed stands. Modeling can help to…
Understanding quantum many-body systems with long-range or infinite-range interactions is of relevance across a broad set of physical disciplines, including quantum optics, nuclear magnetic resonance and nuclear physics. From a theoretical…
We develop a continuum limit and mean-field theory for interacting particle systems (IPS) on self-similar networks, a new class of discrete models whose large-scale behavior gives rise to nonlocal evolution equations on fractal domains.…
We study in this paper the large-time asymptotics of the empirical vector associated with a family of finite-state mean-field systems with multi-classes. The empirical vector is composed of local empirical measures characterizing the…
Rich out of equilibrium collective dynamics of strongly interacting large assemblies emerge in many areas of science. Some intriguing and not fully understood examples are the glassy arrest in atomic, molecular or colloidal systems,…
We deal with the problem of bridging the gap between two scales in neuronal modeling. At the first (microscopic) scale, neurons are considered individually and their behavior described by stochastic differential equations that govern the…
In many stochastic games stemming from financial models, the environment evolves with latent factors and there may be common noise across agents' states. Two classic examples are: (i) multi-agent trading on electronic exchanges, and (ii)…
In this paper, we address the problem of modeling the traffic flow of a heritage city whose streets are represented by a network. We consider a mean field approach where the standard forward backward system of equations is also intertwined…
Most epidemic processes on networks can be modelled by a compartmental model, that specifies the spread of a disease in a population. The corresponding compartmental graph describes how the viral state of the nodes (individuals) changes…
We investigate the dynamics of large heterogeneous network dynamical systems composed of nonlocally coupled chaotic maps. We show that the mean-field limit of such systems is governed by a suitably defined Self-Consistent Transfer Operator…
Many natural phenomena are effectively described by interacting particle systems, which can be modeled using either deterministic or stochastic differential equations (SDEs). In this study, we specifically investigate particle systems…
Simple elastic models of spin-crossover compounds are known empirically to exhibit classical critical behavior. We demonstrate how the long-ranged interactions responsible for this behavior arise naturally upon integrating out mechanical…
Recent advances in metagenomics have revealed macroecological patterns or "laws" describing robust statistical regularities across microbial communities. Stochastic logistic models (SLMs), which treat species as independent -- akin to ideal…
The mean-field analysis of a multi-population agent-based model is performed. The model couples a particle dynamics driven by a nonlocal velocity with a Markow-type jump process on the probability that each agent has of belonging to a given…
Localized perturbations in a real-world network have the potential to trigger cascade failures at the whole system level, hindering its operations and functions. Standard approaches analytically tackling this problem are mostly based either…
We present an exact solution of percolation in a generalized class of Watts-Strogatz graphs defined on a 1-dimensional underlying lattice. We find a non-classical critical point in the limit of the number of long-range bonds in the system…