Related papers: Mean-field Modeling of Social Interactions Using C…
In this paper we derive and analyse mean-field models for the dynamics of groups of individuals undergoing a random walk. The random motion of individuals is only influenced by the perceived densities of the different groups present as well…
We study binary state dynamics on a network where each node acts in response to the average state of its neighborhood. Allowing varying amounts of stochasticity in both the network and node responses, we find different outcomes in random…
In some systems, the behavior of the constituent units can create a `context' that modifies the direct interactions among them. This mechanism of indirect modification inspired us to develop a minimal model of context-dependent spreading.…
This is a brief "proof of concept" article that shows nonlocal diffusion is well suited to the study of pattern formation and the particular application of public sentiment. We use a nonlocal reaction-diffusion equation to model the…
We propose a data-driven framework to learn interaction kernels in stochastic multi-agent systems. Our approach aims at identifying the functional form of nonlocal interaction and diffusion terms directly from trajectory data, without any a…
An annealed version of the quenched mean-field model for epidemic spread is introduced and investigated analytically and assisted by numerical calculations. The interaction between individuals follows a prescription that is used to generate…
The propagation of chaos property for a system of interacting particles, describing the spatial evolution of a network of interacting filaments is studied. The creation of a network of mycelium is analyzed as representative case, and the…
Mean-field theory is an approximation replacing an extended system by a few variables. For depinning of elastic manifolds, these are the position of its center of mass $u$, and the statistics of the forces $F(u)$. There are two proposals to…
We introduce a new class of exchange-correlation potentials for a static and time-dependent Density Functional Theory of strongly correlated systems in 3D. The potentials are obtained via Dynamical Mean Field Theory and, for strong enough…
We introduce a mean-field framework for the study of systems of interacting particles sharing a conserved quantity. The work generalises and unites the existing fields of asset-exchange models, often applied to socio-economic systems, and…
We introduce a fiber bundle model where the interaction among fibers is modeled by an adjustable stress-transfer function which can interpolate between the two limiting cases of load redistribution, the global and the local load sharing…
A three-phase contact line in a three-phase fluid system is modeled by a mean-field density functional theory. We use a variational approach to find the Euler-Lagrange equations. Analytic solutions are obtained in the two-phase regions at…
Complex contagion models that involve contagion along higher-order structures, such as simplicial complexes and hypergraphs, yield new classes of mean-field models. Interestingly, the differential equations arising from many such models…
We introduce the first analytical model of asymmetric community dynamics to yield Hubbell's neutral theory in the limit of functional equivalence among all species. Our focus centers on an asymmetric extension of Hubbell's local community…
Two versions of the susceptible-infected-susceptible epidemic model, which have different transmission rules, are analysed. Both models are considered on a weighted network to simulate a mitigation in the connection between the individuals.…
This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on…
We discuss a non-equilibrium dynamical mean-field framework for simulating inhomogeneous Hubbard models with local disorders. Our approach treats electron interactions and disorders on equal footing, by considering only local dynamical…
Recent advances in experimental techniques enable the simultaneous recording of activity from thousands of neurons in the brain, presenting both an opportunity and a challenge: to build meaningful, scalable models of large neural…
We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in…
We employ Statistical Field Theory techniques for coarse-graining the steady-state properties of Active Ornstein-Uhlenbeck particles. The computation is carried on in the framework of the Unified Colored Noise approximation that allows an…