Related papers: Mean-Field Semantics for a Process Calculus for Sp…
Several relevant aspects of quantum-field processes can be well described by semiclassical methods. In particular, the knowledge of non-trivial classical solutions of the field equations, and the thermal and quantum fluctuations around…
We derive the mean-field equations arising as the limit of a network of interacting spiking neurons, as the number of neurons goes to infinity. The neurons belong to a fixed number of populations and are represented either by the…
We propose a new approximation framework that unifies and generalizes a number of existing mean-field approximation methods for the SIS epidemic model on complex networks. We derive the framework, which we call the Universal Mean-Field…
We introduce a new type of Mean Field Game epidemiological models, in which subpopulations have different behavioral patterns: some are viewed as "highly rational" (choosing Nash-equilibrium long-term strategies) while others follow…
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 $\ell: \R_+ \to [0,\infty]$…
We study the random-field Ising model with long-range interactions and show the exactness of the mean-field theory under certain mild conditions. This is a generalization of the result of Mori for the non-random and spin-glass cases. To…
The proliferation of methods for modeling of human meaning-making constitutes a powerful class of instruments for the analysis of complex semiotic systems. However, the field lacks a general theoretical framework for describing these…
Multi-type birth-death processes underlie approaches for inferring evolutionary dynamics from phylogenetic trees across biological scales, ranging from deep-time species macroevolution to rapid viral evolution and somatic cellular…
Mechanisms are a fundamental concept in many areas of science. Nonetheless, there has been little effort to develop structures to represent mechanisms. We explore the issues in developing a basic semantic modeling framework for describing…
In this manuscript we present several possible ways of modeling human capital accumulation during the spread of a disease following an agent based approach, where agents behave maximizing their intertemporal utility. We assume that the…
We study analytically the effect of temperature cyclings in mean-field spin-glasses. In accordance with real experiments, we obtain a strong reinitialization of the dynamics on decreasing the temperature combined with memory effects when…
The paper describes and compares three approaches to modeling an epidemic spread. The first approach is a well-known system of SIR ordinary differential equations. The second is a mean-field model, in which an isolation strategy for each…
We present a resummed mean-field approximation for inferring the parameters of an Ising or a Potts model from empirical, noisy, one- and two-point correlation functions. Based on a resummation of a class of diagrams of the small correlation…
We give exact and explicit expressions of mean first-passage times for random walks in a rectangular domain, in both cases of reflecting boundary conditions and periodic boundary conditions. The situations with one or two absorbing targets…
This paper investigates the use of transformers to approximate the mean-field dynamics of interacting particle systems exhibiting collective behavior. Such systems are fundamental in modeling phenomena across physics, biology, and…
Modeling environmental ecosystems is critical for the sustainability of our planet, but is extremely challenging due to the complex underlying processes driven by interactions amongst a large number of physical variables. As many variables…
We use dialgebras, generalising both algebras and coalgebras, as a complement of the standard coalgebraic framework, aimed at describing the semantics of an interactive system by the means of reaction rules. In this model, interaction is…
We analyze the coalescing model where a `primary' colony grows and randomly emits secondary colonies that spread and eventually coalesce with it. This model describes population proliferation in theoretical ecology, tumor growth and is also…
The paper introduces a general framework for derivation of continuum equations governing meso-scale dynamics of large particle systems. The balance equations for spatial averages such as density, linear momentum, and energy were previously…
The Shape Calculus is a bio-inspired calculus for describing 3D shapes moving in a space. A shape forms a 3D process when combined with a behaviour. Behaviours are specified with a timed CCS-like process algebra using a notion of channel…