相关论文: Vlasov Equations on Directed Hypergraph Measures

Hypergraphs are a generalization of graphs in which edges can connect any number of vertices. They allow the modeling of complex networks with higher-order interactions, and their spectral theory studies the qualitative properties that can…

Due to the advantages of hypergraphs in modeling high-order relationships in complex systems, they have been applied to higher-order clustering, hypergraph neural networks and computer vision. These applications rely heavily on access to…

Graph generation is a crucial task in many fields, including network science and bioinformatics, as it enables the creation of synthetic graphs that mimic the properties of real-world networks for various applications. Graph Generative…

Simulations with an explicit description of intermolecular forces using electronic structure methods are still not feasible for many systems of interest. As a result, empirical methods such as force fields (FF) have become an established…

We establish the convergence of the deep Galerkin method (DGM), a deep learning-based scheme for solving high-dimensional nonlinear PDEs, for Hamilton-Jacobi-Bellman (HJB) equations that arise from the study of mean field control problems…

We analyse a reduced 1D Vlasov--Maxwell system introduced recently in the physical literature for studying laser-plasma interaction. This system can be seen as a standard Vlasov equation in which the field is split in two terms: an…

Recently, Vision Graph Neural Network (ViG) has gained considerable attention in computer vision. Despite its groundbreaking innovation, Vision Graph Neural Network encounters key issues including the quadratic computational complexity…

The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular,…

Dynamical mean field theory (DMFT) combined with the local density approximation (LDA) is widely used in solids to predict properties of correlated systems. In this paper, its application to one of the simplest strongly correlated systems,…

We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…

This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field.…

We present a generalization of Vlasov-Maxwell kinetic theory that accounts for intense electromagnetic fields. A strongly-radiating, possibly optically-thick plasma is decomposed into fragments, each comprising a charged particle together…

We establish the local asymptotic normality (LAN) property for estimating a multidimensional parameter in the drift of a system of $N$ interacting particles observed over a fixed time horizon in a mean-field regime $N \rightarrow \infty$.…

The $\boldsymbol{\beta}$-model for random graphs is commonly used for representing pairwise interactions in a network with degree heterogeneity. Going beyond pairwise interactions, Stasi et al. (2014) introduced the hypergraph…

The mean field approximation to the Ising model is a canonical variational tool that is used for analysis and inference in Ising models. We provide a simple and optimal bound for the KL error of the mean field approximation for Ising models…

We consider the number of crossings in a random embedding of a graph, $G$, with vertices in convex position. We give explicit formulas for the mean and variance of the number of crossings as a function of various subgraph counts of $G$.…

We consider the graphon mean-field system introduced in the work of Bayraktar, Chakraborty, and Wu. It is the large-population limit of a heterogeneously interacting diffusive particle system, where the interaction is of mean-field type…

Many physical systems -- such as optical waveguide lattices and dense neuronal or vascular networks -- can be modeled by metric graphs, where slender "wires" (edges) support wave or diffusion equations subject to Kirchhoff conditions at the…

The study of hypergraphs has received a lot of attention over the past few years, however up until recently there has been no interest in systems where higher order interactions are not undirected. In this article we introduce the notion of…

The dynamical mean field theory (DMFT) has become a standard technique for the study of strongly correlated models and materials overcoming some of the limitations of density functional approaches based on local approximations. An important…