Related papers: Coupling and Tensorization of Kinetic Theory and G…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint…
We study the problem of coupling a stochastic block model with a planted bisection to a uniform random graph having the same average degree. Focusing on the regime where the average degree is a constant relative to the number of vertices…
We present a comprehensive study exploring the relationship between transport properties and measures of quantum entanglement in the Einstein-Maxwell-Axion-Horndeski theory. By using holographic duality, we study the entanglement measures,…
Kinetic theory of dissipative particle dynamics is developed in terms of a Boltzmann pair collision theory. The kinetic transport coefficients are computed from explicit collision integrals and compared favourably with detailed simulations.…
This paper studies multi-agent systems with nonlinear consensus protocols, i.e., only nonlinear measurements of the states are available to agents. The solutions of these systems are understood in Filippov sense since the possible…
In this paper, we present new results on consensus for continuous-time multi- agent systems. We introduce the assumptions of persistent connectivity of the interaction graph and of slow divergence of reciprocal interaction weights.…
This work considers the distributed computation of the one-to-one vertex correspondences between two undirected and connected graphs, which is called \textit{graph matching}, over multi-agent networks. Given two \textit{isomorphic} and…
Recent work has introduced sparse exchangeable graphs and the associated graphex framework, as a generalization of dense exchangeable graphs and the associated graphon framework. The development of this subject involves the interplay…
The driven transport of plastic systems in various disordered backgrounds is studied within mean field theory. Plasticity is modeled using non-convex interparticle potentials that allow for phase slips. This theory most naturally describes…
Numerical simulations are used to test the kinetic theory constitutive relations of inertial granular shear flow. These predictions are shown to be accurate in the dilute regime, where only binary collisions are relevant, but underestimate…
This article considers a class of disordered mean-field combinatorial optimization problems. We focus on the Gibbs measure, where the inverse temperature does not vary with the size of the graph and the edge weights are sampled from a…
We derive an upper bound on the maximum balanced bipartite entanglement entropy of ground states of many-body Hamiltonians defined on a graph, agnostic to any particular model, that possesses a nontrivial automorphism group. We show that…
Action convergence provides a limit theory for linear bounded operators $A_n:L^{\infty}(\Omega_n)\longrightarrow L^1(\Omega_n)$ where $\Omega_n$ are potentially different probability spaces. This notion of convergence emerged in graph…
We define a range of new coarse geometric invariants based on various graph-theoretic measures of complexity for finite graphs, including: treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these…
We use the recently developed probabilistic analysis of mean field games with finitely many states in the weak formulation, to set-up a principal / agent contract theory model where the principal faces a large population of agents…
We consider the number of edge crossings in a random graph drawing generated by projecting a random geometric graph on some compact convex set $W\subset \mathbb{R}^d$, $d\geq 3$, onto a plane. The positions of these crossings form the…
In this review we survey the literature on mean-field coupled maps. We start with the early works from the physics literature, arriving to some recent results from ergodic theory studying the thermodynamic limit of globally coupled maps and…
A graph theoretic framework recently has been proposed to stabilize interconnected multiagent systems in a distributed fashion, while systematically capturing the architectural aspect of cyber-physical systems with separate agent or…
We consider the problem of tensor completion with graphs serving as side information to represent interrelationships among variables. Existing approaches suffer from several limitations: (1) they are often task-specific and lack generality…