Related papers: Mean-field Modeling of Social Interactions Using C…
We typically interact in groups, not just in pairs. For this reason, it has recently been proposed that the spread of information, opinion or disease should be modelled over a hypergraph rather than a standard graph. The use of hyperedges…
Heider balance theory provides a fundamental framework for understanding the formation of friendly and hostile relations in social networks. Existing stochastic formulations typically assume a uniform social temperature, implying that all…
A density functional theory is developed for fermions in one dimension, interacting via a delta-function. Such systems provide a natural testing ground for questions of principle, as the local density approximation should work well for…
A dynamical model of an ecological community is analyzed within a "mean-field approximation" in which one of the species interacts with the combination of all of the other species in the community. Within this approximation the model may be…
The aim of this work is to implement a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. A class of simple mean field discrete models is introduced and discussed both from the theoretical…
We study the interactions between two negatively charged macroscopic surfaces confining positive counterions. A density-functional approach is introduced which, besides the usual mean-field interactions, takes into account the correlations…
In models of $N$ interacting particles in $\R^d$ as in Density Functional Theory or crowd motion, the repulsive cost is usually described by a two-point function $c_\e(x,y) =\ell\Big(\frac{|x-y|}{\e}\Big)$ where $\ell: \R_+ \to [0,\infty]$…
Active systems, which are driven out of equilibrium by local non-conservative forces, exhibit unique behaviors and structures with potential utility for the design of novel materials. An important and difficult challenge along the path…
The spread of an epidemic disease and the population's collective behavioural response are deeply intertwined, influencing each other's evolution. Such a co-evolution typically has been overlooked in mathematical models, limiting their…
The primitive model describes ions by point charges with an additional hard-core interaction. In classical density-functional theory the mean-field electrostatic contribution can be obtained from the first order of a functional perturbation…
We propose a class of mean-field models for the isostatic transition of systems of soft spheres, in which the contact network is modeled as a random graph and each contact is associated to $d$ degrees of freedom. We study such models in the…
Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…
We develop a unified theory that encompasses the macroscopic dynamics of recurrent interactions of binary units within arbitrary network architectures. Using the martingale theory, our mathematical analysis provides a complete description…
Quite recently I have proposed a nonperturbative dynamical effective field model (DEFM) to quantitatively describe the dynamics of interacting ferrofluids. Its predictions compare very well with the results from simulations. In this paper I…
We consider a multi-population epidemic model with one or more (almost) isolated communities and one mobile community. Each of the isolated communities has contact within itself and, in addition, contact with the outside world but only…
We present a density functional theory (DFT) for lattice models with local electron-electron (e-e) and electron-phonon (e-ph) interactions. Exchange-correlation potentials are derived via dynamical mean field theory for the…
A general expansion scheme based on the concept of linked cluster expansion from the theory of classical spin systems is constructed for models of interacting electrons. It is shown that with a suitable variational formulation of mean-field…
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…