Related papers: Maximal Spread of Coherent Distributions: a Geomet…

Let ($X,Y)$ be a random vector with distribution function $F(x,y),$ and $(X_{1},Y_{1}),(X_{2},Y_{2}),...,(X_{n},Y_{n})$ are independent copies of ($X,Y).$ Let $X_{i:n}$ be the $i$th order statistics constructed from the sample…

The problem of an electromagnetic wave scattered from a random medium layer with rough boundaries is formulated using integral equations which involve two kinds of Green functions. The first one describes the wave scattered by the random…

We introduce and validate a theoretical framework for coherent control of multichannel scattering of linear waves to route waves through complex geometries with multiple scattering. We show that steady-state perfect routing solutions are…

Let $G$ be a finite connected graph on two or more vertices and $G^{[N,k]}$ the distance $k$-graph of the $N$-fold Cartesian power of $G$. For a fixed $k\ge1$, we obtain explicitly the large $N$ limit of the spectral distribution (the…

In algebraic statistics, the maximum likelihood degree of a statistical model refers to the number of solutions (counted with multiplicity) of the score equations over the complex field. In this paper, the maximum likelihood degree of the…

Coherent transport promises to be the basis for an emerging new technology. Notwithstanding, a mechanistic understanding of the fundamental principles behind optimal scattering media is still missing. Here, complex network analysis is…

This paper presents a novel pairwise constraint propagation approach by decomposing the challenging constraint propagation problem into a set of independent semi-supervised learning subproblems which can be solved in quadratic time using…

The spread of a graph $G$ is the difference between the largest and smallest eigenvalues of the adjacency matrix of $G$. In this paper, we consider the family of graphs which contain no $K_{2,t}$-minor. We show that for any $t\geq 2$, there…

We provide optimal rates of convergence to the asymptotic distribution of the (properly scaled) degree of a fixed vertex in two preferential attachment random graph models. Our approach is to show that these distributions are unique fixed…

Recent advances in dynamic graph processing have enabled the analysis of highly dynamic graphs with change at rates as high as millions of edge changes per second. Solutions in this domain, however, have been demonstrated only for…

Probabilistic graphical models are a powerful concept for modeling high-dimensional distributions. Besides modeling distributions, probabilistic graphical models also provide an elegant framework for performing statistical inference;…

An $(\alpha,\beta)$-ruling set of a graph $G=(V,E)$ is a set $R\subseteq V$ such that for any node $v\in V$ there is a node $u\in R$ in distance at most $\beta$ from $v$ and such that any two nodes in $R$ are at distance at least $\alpha$…

This paper is motivated by two applications, namely i) generalizations of cuckoo hashing, a computationally simple approach to assigning keys to objects, and ii) load balancing in content distribution networks, where one is interested in…

Let $G$ be an $r$-partite graph such that the edge density between any two parts is at least $\alpha$. How large does $\alpha$ need to be to guarantee that $G$ contains a connected transversal, that is, a tree on $r$ vertices meeting each…

This paper introduces a declarative framework to specify and reason about distributions of data over computing nodes in a distributed setting. More specifically, it proposes distribution constraints which are tuple and equality generating…

Let $\Delta_{k;n}$ be the maximum number of common neighbors of a set of $k$ vertices in $G(n,p)$. In this paper, we find $a_n$ and $\sigma_n$ such that $\frac{\Delta_{k;n}-a_n}{\sigma_n}$ converges in distribution to a random variable…

We resolve a long standing question regarding the suitable effective diffusion coefficient of the spherically-symmetric transport equation, which is valid at long times. To that end, we generalize a transport solution in three dimensions…

The spread of a graph $G$ is the difference between the largest and smallest eigenvalue of the adjacency matrix of $G$. Gotshall, O'Brien and Tait conjectured that for sufficiently large $n$, the $n$-vertex outerplanar graph with maximum…

Epidemic spreading phenomena are ubiquitous in nature and society. Examples include the spreading of diseases, information, and computer viruses. Epidemics can spread by local spreading, where infected nodes can only infect a limited set of…

We consider upward-planar layered drawings of directed graphs, i.e., crossing-free drawings in which each edge is drawn as a y-monotone curve going upward from its tail to its head, and the y-coordinates of the vertices are integers. The…