Related papers: Maximal Spread of Coherent Distributions: a Geomet…
Structures with heavy-tailed distributions of disorder occur widely in nature. The evolution of such systems, as in foraging for food or the occurrence of earthquakes is generally analyzed in terms of an incoherent series of events. But the…
We examine maximum vertex coloring of random geometric graphs, in an arbitrary but fixed dimension, with a constant number of colors. Since this problem is neither scale-invariant nor smooth, the usual methodology to obtain limit laws…
We focus on belief propagation for the assignment problem, also known as the maximum weight bipartite matching problem. We provide a constructive proof that the well-known upper bound on the number of iterations (Bayati, Shah, Sharma 2008)…
A very popular class of models for networks posits that each node is represented by a point in a continuous latent space, and that the probability of an edge between nodes is a decreasing function of the distance between them in this latent…
Motivated by constructions from applied topology, there has been recent interest in the homological algebra of linear representations of posets, particularly in the context of homological algebra relative to non-standard exact structures. A…
We present a general framework to construct symmetric, well-conditioned, cross-element compatible nodal distributions that can be used for high-order and high-dimensional finite elements. Starting from the inherent symmetries of an element…
We view hyper-graphs as incidence graphs, i.e. bipartite graphs with a set of nodes representing vertices and a set of nodes representing hyper-edges, with two nodes being adjacent if the corresponding vertex belongs to the corresponding…
We study the coherent propagation and incoherent diffusion of in-plane elastic waves in a two dimensional continuum populated by many, randomly placed and oriented, edge dislocations. Because of the Peierls-Nabarro force the dislocations…
We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their…
By prior work, there is a distributed algorithm that finds a maximal fractional matching (maximal edge packing) in $O(\Delta)$ rounds, where $\Delta$ is the maximum degree of the graph. We show that this is optimal: there is no distributed…
We show that the probability of appearance of synchronisation in chaotic coupled map lattices is related to the distribution of the maximum of a certain observable evaluated along almost all orbit. We show that such distribution belongs to…
A detailed analysis of the propagation of laser gaussian beams at critical angles shows in which conditions it is possible to maximize the breaking of symmetry in the angular distribution and for which values of the laser wavelength and…
Coboundary and cosystolic expansion are notions of expansion that generalize the Cheeger constant or edge expansion of a graph to higher dimensions. The classical Cheeger inequality implies that for graphs edge expansion is equivalent to…
The asymptotic normality of the maximum likelihood estimator (MLE) under regularity conditions is a cornerstone of statistical theory. In this paper, we give explicit upper bounds on the distributional distance between the distribution of…
Motivated by very large-scale communication networks, we newly introduce exponentiation of graphs. Using the exponential operation on graphs, we can construct various graphs of multi-exponential order with logarithmic diameter. We show that…
We study stochastic graph optimization problems in a novel distributed setting. As in the standard centralized setting, a random subgraph $G^*$ of a known base graph $G$ is realized by including each edge $e$ independently with a known…
A length-$n$ random sequence $X_1,\ldots,X_n$ in a space $S$ is finitely exchangeable if its distribution is invariant under all $n!$ permutations of coordinates. Given $N > n$, we study the extendibility problem: when is it the case that…
Statistical properties of coherent radiation propagating in a quasi - 1D random media is studied in the framework of random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission…
The binding number $b(G)$ of a graph, introduced by Woodall [J. Combin. Theory, Ser. B, 1973], is a central topic of both structural and extremal graph theory. It is closely related to fundamental combinatorial and structural properties of…
We solve a problem of Krivelevich, Kwan and Sudakov [SIAM Journal on Discrete Mathematics 31 (2017), 155-171] concerning the threshold for the containment of all bounded degree spanning trees in the model of randomly perturbed dense graphs.…