On the independence and chromatic numbers of random regular graphs

AbstractLet Gr denote a random r-regular graph with vertex set {1, 2, …, n} and α(Gr) and χ(Gr) denote respectively its independence and chromatic numbers. We show that with probability going to 1 as n → ∞ respectively |δ(Gr) − 2nr(logr − log logr + 1 − log 2)|⩽γnr and |χ(Gr) − r2 log r − 8r log logr(log)2| ⩽ 8r log log r(log r)2 provided r = o(nθ), θ < 13, 0 < ε < 1, are constants, and r ≥ rε, where rε depends on ε only

Vertex similarity in networks

We consider methods for quantifying the similarity of vertices in networks. We propose a measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar. This leads to a self-consistent matrix formulation of similarity that can be evaluated iteratively using only a knowledge of the adjacency matrix of the network. We test our similarity measure on computer-generated networks for which the expected results are known, and on a number of real-world networks

Finding community structure in networks using the eigenvectors of matrices

We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as "modularity" over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.Comment: 22 pages, 8 figures, minor corrections in this versio

Resolving the infinitude controversy

A simple inductive argument shows natural languages to have infinitly many sentences, but workers in the field have uncovered clear evidence of a diverse group of ‘exceptional’ languages from Proto-Uralic to Dyirbal and most recently, Pirahã, that appear to lack recursive devices entirely. We argue that in an information-theoretic setting non-recursive natural languages appear neither exceptional nor functionally inferior to the recursive majority

On noise treatment in radio measurements of cosmic ray air showers

Precise measurements of the radio emission by cosmic ray air showers require an adequate treatment of noise. Unlike to usual experiments in particle physics, where noise always adds to the signal, radio noise can in principle decrease or increase the signal if it interferes by chance destructively or constructively. Consequently, noise cannot simply be subtracted from the signal, and its influence on amplitude and time measurement of radio pulses must be studied with care. First, noise has to be determined consistently with the definition of the radio signal which typically is the maximum field strength of the radio pulse. Second, the average impact of noise on radio pulse measurements at individual antennas is studied for LOPES. It is shown that a correct treatment of noise is especially important at low signal-to-noise ratios: noise can be the dominant source of uncertainty for pulse height and time measurements, and it can systematically flatten the slope of lateral distributions. The presented method can also be transfered to other experiments in radio and acoustic detection of cosmic rays and neutrinos.Comment: 4 pages, 6 figures, submitted to NIM A, Proceedings of ARENA 2010, Nantes, Franc

A Probabilistic Bound on the Basic Role Mining Problem and Its Applications

Abstract In this paper we describe a new probabilistic approach to the role engineering process for RBAC. In particular, we address the issue of minimizing the number of roles, problem known in literature as the Basic Role Mining Problem (basicRMP). We leverage the equivalence of the above issue with the vertex coloring problem. Our main result is the proof that the minimum number of roles is sharply concentrated around its expected value. A further contribution is to show how this result can be applied as a stop condition when striving to find out an approximation for the basicRMP. We also show that the proposal can be used to decide whether it is advisable to undertake the efforts to renew an RBAC state. Note that both these applications can result in a substantial saving of resources. A thorough analysis using advanced probabilistic tools supports our results. Finally, further relevant research directions are also highlighted.

KASCADE-Grande Limits on the Isotropic Diffuse Gamma-Ray Flux between 100 TeV and 1 EeV

KASCADE and KASCADE-Grande were multi-detector installations to measure individual air showers of cosmic rays at ultra-high energy. Based on data sets measured by KASCADE and KASCADE-Grande, 90% C.L. upper limits to the flux of gamma-rays in the primary cosmic ray flux are determined in an energy range of ${10}^{14} - {10}^{18}$ eV. The analysis is performed by selecting air showers with a low muon content as expected for gamma-ray-induced showers compared to air showers induced by energetic nuclei. The best upper limit of the fraction of gamma-rays to the total cosmic ray flux is obtained at $3.7 \times {10}^{15}$ eV with $1.1 \times {10}^{-5}$. Translated to an absolute gamma-ray flux this sets constraints on some fundamental astrophysical models, such as the distance of sources for at least one of the IceCube neutrino excess models.Comment: Published in The Astrophysical Journal, Volume 848, Number 1. Posted on: October 5, 201

The LOPES experiment - recent results, status and perspectives

The LOPES experiment at the Karlsruhe Institute of Technology has been taking radio data in the frequency range from 40 to 80 MHz in coincidence with the KASCADE-Grande air shower detector since 2003. Various experimental configurations have been employed to study aspects such as the energy scaling, geomagnetic dependence, lateral distribution, and polarization of the radio emission from cosmic rays. The high quality per-event air shower information provided by KASCADE-Grande has been the key to many of these studies and has even allowed us to perform detailed per-event comparisons with simulations of the radio emission. In this article, we give an overview of results obtained by LOPES, and present the status and perspectives of the ever-evolving experiment.Comment: Proceedings of the ARENA2010 conference, Nantes, Franc