The mean weight of a cycle in an edge-weighted graph is the sum of the cycle’s edge weights divided by the cycle’s length. We study the minimum mean-weight cycle on the complete graph on n vertices, with random i.i.d. edge weights drawn from an exponential distribution with mean 1. We show that the probability of the min meanweight being at most c/n tends to a limiting function of c which is an...

We propose a slightly revised Miller-Hagberg (MH) algorithm that efficiently generates a random network from a given expected degree sequence. The revision was to replace the approximated edge probability between a pair of nodes with a combinatorically calculated edge probability that better captures the likelihood of edge presence especially where edges are dense. The computational complexity ...

O. Sotolongo-Costa and G. J. Rodgers Department of Theoretical Physics, Havana University, 10400 Havana,Cuba Department of Mathematical Sciences, Brunel University, Uxbridge, Middlesex UB8 3PH, U.K. and 3 Henri Poincare Chair of Complex Systems, Havana University. Abstract We consider the phenomenon of Bose-Einstein condensation in a random growing directed network. The network grows by the add...

This paper presents a novel wavelet-based image denoising algorithm under overcomplete expansion. In order to optimize the denoising performance, we make a systematic study of both signal and noise characteristics under overcomplete expansion. Highband coefficients are viewed as the mixture of non-edge class and edge class observing different probability models. Based on improved statistical mo...

In this paper, we propose an edge detection technique based on some local smoothing of the image followed by a statistical hypothesis testing on the gradient. An edge point being defined as a zero-crossing of the Laplacian, it is said to be a significant edge point if the gradient at this point is larger than a threshold s(ε) defined by: if the image I is pure noise, then the probability of ‖∇I...

By extending Heider’s and Cartwright-Harary’s theory of balance in deterministic social structures, we study the problem of balance in social structures where relations between individuals are random. An appropriate model for representing such structures is the so called random signed graphs Gn,p,q defined as follows. Given a set of n vertices and fixed numbers p and q, 0 < p+ q < 1, then, betw...

We consider random paths on a square lattice which take a left or a right turn at every vertex. The possible turns are taken with equal probability, except at a vertex which has been visited before. In such case the vertex is left via the unused edge. When the initial edge is reached the path is considered completed. We also consider families of such paths which together cover every edge of the...

We formulate edge detection as statistical inference. This statistical edge detection is data driven, unlike standard methods for edge detection which are model based. For any set of edge detection filters (implementing local edge cues), we use presegmented images to learn the probability distributions of filter responses conditioned on whether they are evaluated on or off an edge. Edge detecti...

let $g$ be a simple graph of order $n$ and size $m$.the edge covering of $g$ is a set of edges such that every vertex of $g$ is incident to at least one edge of the set. the edge cover polynomial of $g$ is the polynomial$e(g,x)=sum_{i=rho(g)}^{m} e(g,i) x^{i}$,where $e(g,i)$ is the number of edge coverings of $g$ of size $i$, and$rho(g)$ is the edge covering number of $g$. in this paper we stud...

let g=(v,e) be a simple graph. an edge labeling f:e to {0,1} induces a vertex labeling f^+:v to z_2 defined by $f^+(v)equiv sumlimits_{uvin e} f(uv)pmod{2}$ for each $v in v$, where z_2={0,1} is the additive group of order 2. for $iin{0,1}$, let e_f(i)=|f^{-1}(i)| and v_f(i)=|(f^+)^{-1}(i)|. a labeling f is called edge-friendly if $|e_f(1)-e_f(0)|le 1$. i_f(g)=v_f(1)-v_f(0) is called the edge-f...