1,114 research outputs found
A framework for evaluating statistical dependencies and rank correlations in power law graphs
We analyze dependencies in power law graph data (Web sample, Wikipedia sample and a preferential attachment graph) using statistical inference for multivariate regular variation. To the best of our knowledge, this is the first attempt to apply the well developed theory of regular variation to graph data. The new insights this yields are striking: the three above-mentioned data sets are shown to have a totally different dependence structure between different graph parameters, such as in-degree and PageRank. Based on the proposed methodology, we suggest a new measure for rank correlations. Unlike most known methods, this measure is especially sensitive to rank permutations for topranked nodes. Using this method, we demonstrate that the PageRank ranking is not sensitive to moderate changes in the damping factor
Degree-degree correlations in random graphs with heavy-tailed degrees
Mixing patterns in large self-organizing networks, such as the Internet, the
World Wide Web, social and biological networks are often characterized by
degree-degree {dependencies} between neighbouring nodes. One of the problems
with the commonly used Pearson's correlation coefficient (termed as the
assortativity coefficient) is that {in disassortative networks its magnitude
decreases} with the network size. This makes it impossible to compare mixing
patterns, for example, in two web crawls of different size.
We start with a simple model of two heavy-tailed highly correlated random
variable and , and show that the sample correlation coefficient
converges in distribution either to a proper random variable on , or to
zero, and if then the limit is non-negative. We next show that it is
non-negative in the large graph limit when the degree distribution has an
infinite third moment. We consider the alternative degree-degree dependency
measure, based on the Spearman's rho, and prove that it converges to an
appropriate limit under very general conditions. We verify that these
conditions hold in common network models, such as configuration model and
Preferential Attachment model. We conclude that rank correlations provide a
suitable and informative method for uncovering network mixing patterns
The frustrated Brownian motion of nonlocal solitary waves
We investigate the evolution of solitary waves in a nonlocal medium in the
presence of disorder. By using a perturbational approach, we show that an
increasing degree of nonlocality may largely hamper the Brownian motion of
self-trapped wave-packets. The result is valid for any kind of nonlocality and
in the presence of non-paraxial effects. Analytical predictions are compared
with numerical simulations based on stochastic partial differential equationComment: 4 pages, 3 figures
Stability of two-dimensional spatial solitons in nonlocal nonlinear media
We discuss existence and stability of two-dimensional solitons in media with
spatially nonlocal nonlinear response. We show that such systems, which include
thermal nonlinearity and dipolar Bose Einstein condensates, may support a
variety of stationary localized structures - including rotating spatial
solitons. We also demonstrate that the stability of these structures critically
depends on the spatial profile of the nonlocal response function.Comment: 8 pages, 9 figure
Remarks on the Central Limit Theorem for Non-Convex Bodies
In this note, we study possible extensions of the Central Limit Theorem for
non-convex bodies. First, we prove a Berry-Esseen type theorem for a certain
class of unconditional bodies that are not necessarily convex. Then, we
consider a widely-known class of non-convex bodies, the so-called p-convex
bodies, and construct a counter-example for this class
TAC 2011 MultiLing pilot overview
The Text Analysis Conference MultiLing Pilot of 2011 posed a multi-lingual summarization task to the summarization community, aiming to quantify and measure the performance of multi-lingual, multi-document summarization systems. The task was to create a 240–250 word summary from 10 news texts, describing a given topic. The texts of each topic were provided in seven languages (Arabic, Czech, English, French, Greek, Hebrew, Hindi) and each participant generated summaries for at least 2 languages. The evaluation of the summaries was performed using automatic (AutoSummENG, Rouge) and manual processes (Overall Responsiveness score). The participating systems were 8, some of which providing summaries across all languages. This paper provides a brief description for the collection of the data, the evaluation methodology, the problems and challenges faced, and an overview of participation and corresponding results
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