On the efficiency of data representation on the modeling and characterization of complex networks

Specific choices about how to represent complex networks can have a substantial impact on the execution time required for the respective construction and analysis of those structures. In this work we report a comparison of the effects of representing complex networks statically by adjacency matrices or dynamically by adjacency lists. Three theoretical models of complex networks are considered: two types of Erdos-Renyi as well as the Barabasi-Albert model. We investigated the effect of the different representations with respect to the construction and measurement of several topological properties (i.e. degree, clustering coefficient, shortest path length, and betweenness centrality). We found that different forms of representation generally have a substantial effect on the execution time, with the sparse representation frequently resulting in remarkably superior performance. (C) 2011 Elsevier B.V. All rights reserved.

Trigger and aperture of the surface detector array of the Pierre Auger Observatory

The surface detector array of the Pierre Auger Observatory consists of 1600 water-Cherenkov detectors, for the study of extensive air showers (EAS) generated by ultra-high-energy cosmic rays. We describe the trigger hierarchy, from the identification of candidate showers at the level of a single detector, amongst a large background (mainly random single cosmic ray muons), up to the selection of real events and the rejection of random coincidences. Such trigger makes the surface detector array fully efficient for the detection of EAS with energy above 3 x 10(18) eV, for all zenith angles between 0 degrees and 60 degrees, independently of the position of the impact point and of the mass of the primary particle. In these range of energies and angles, the exposure of the surface array can be determined purely on the basis of the geometrical acceptance. (C) 2009 Elsevier B.V. All rights reserved.

Atmospheric effects on extensive air showers observed with the surface detector of the Pierre Auger observatory

Atmospheric parameters, Such as pressure (P), temperature (T) and density (rho proportional to P/T), affect the development of extensive air showers initiated by energetic cosmic rays. We have Studied the impact of atmospheric variations on extensive air showers by means of the surface detector of the Pierre Auger Observatory. The rate of events shows a similar to 10% seasonal modulation and similar to 2% diurnal one. We find that the observed behaviour is explained by a model including the effects associated with the variations of P and rho. The former affects the longitudinal development of air showers while the latter influences the Moliere radius and hence the lateral distribution of the shower particles. The model is validated with full simulations of extensive air showers using atmospheric profiles measured at the site of the Pierre Auger Observatory. (C) 2009 Elsevier B.V. All rights reserved.

Upper limit on the cosmic-ray photon fraction at EeV energies from the Pierre Auger Observatory

From direct observations of the longitudinal development of ultra-high energy air showers performed with the Pierre Auger Observatory, upper limits of 3.8%, 2.4%, 3.5% and 11.7% (at 95% c.l.) are obtained on the fraction of cosmic-ray photons above 2, 3, 5 and 10 EeV (1 EeV equivalent to 10(18) eV), respectively. These are the first experimental limits on ultra-high energy photons at energies below 10 EeV. The results complement previous constraints on top-down models from array data and they reduce systematic uncertainties in the interpretation of shower data in terms of primary flux, nuclear composition and proton-air cross-section. (C) 2009 Elsevier B.V. All rights reserved.

Anisotropy and chemical composition of ultra-high energy cosmic rays using arrival directions measured by the Pierre Auger Observatory

The Pierre Auger Collaboration has reported. evidence for anisotropy in the distribution of arrival directions of the cosmic rays with energies E > E(th) = 5.5 x 10(19) eV. These show a correlation with the distribution of nearby extragalactic objects, including an apparent excess around the direction of Centaurus A. If the particles responsible for these excesses at E > E(th) are heavy nuclei with charge Z, the proton component of the sources should lead to excesses in the same regions at energies E/Z. We here report the lack of anisotropies in these directions at energies above E(th)/Z (for illustrative values of Z = 6, 13, 26). If the anisotropies above E(th) are due to nuclei with charge Z, and under reasonable assumptions about the acceleration process, these observations imply stringent constraints on the allowed proton fraction at the lower energies.

Search for first harmonic modulation in the right ascension distribution of cosmic rays detected at the Pierre Auger Observatory

We present the results of searches for dipolar-type anisotropies in different energy ranges above 2.5 x 10(17) eV with the surface detector array of the Pierre Auger Observatory, reporting on both the phase and the amplitude measurements of the first harmonic modulation in the right-ascension distribution. Upper limits on the amplitudes are obtained, which provide the most stringent bounds at present, being below 2% at 99% C.L. for EeV energies. We also compare our results to those of previous experiments as well as with some theoretical expectations. (C) 2011 Elsevier B.V. All rights reserved.

The Pierre Auger Observatory scaler mode for the study of solar activity modulation of galactic cosmic rays

Since data-taking began in January 2004, the Pierre Auger Observatory has been recording the count rates of low energy secondary cosmic ray particles for the self-calibration of the ground detectors of its surface detector array. After correcting for atmospheric effects, modulations of galactic cosmic rays due to solar activity and transient events are observed. Temporal variations related with the activity of the heliosphere can be determined with high accuracy due to the high total count rates. In this study, the available data are presented together with an analysis focused on the observation of Forbush decreases, where a strong correlation with neutron monitor data is found.

The exposure of the hybrid detector of the Pierre Auger Observatory

The Pierre Auger Observatory is a detector for ultra-high energy cosmic rays. It consists of a surface array to measure secondary particles at ground level and a fluorescence detector to measure the development of air showers in the atmosphere above the array. The ""hybrid"" detection mode combines the information from the two subsystems. We describe the determination of the hybrid exposure for events observed by the fluorescence telescopes in coincidence with at least one water-Cherenkov detector of the surface array. A detailed knowledge of the time dependence of the detection operations is crucial for an accurate evaluation of the exposure. We discuss the relevance of monitoring data collected during operations, such as the status of the fluorescence detector, background light and atmospheric conditions, that are used in both simulation and reconstruction. (C) 2010 Elsevier B.V. All rights reserved.

Update on the correlation of the highest energy cosmic rays with nearby extragalactic matter

Data collected by the Pierre Auger Observatory through 31 August 2007 showed evidence for anisotropy in the arrival directions of cosmic rays above the Greisen-Zatsepin-Kuz`min energy threshold, 6 x 10(19) eV. The anisotropy was measured by the fraction of arrival directions that are less than 3.1 degrees from the position of an active galactic nucleus within 75 Mpc (using the Veron-Cetty and Veron 12th catalog). An updated measurement of this fraction is reported here using the arrival directions of cosmic rays recorded above the same energy threshold through 31 December 2009. The number of arrival directions has increased from 27 to 69, allowing a more precise measurement. The correlating fraction is (38(-6)(+7))%, compared with 21% expected for isotropic cosmic rays. This is down from the early estimate of (69-(+11)(13))%. The enlarged set of arrival directions is examined also in relation to other populations of nearby extragalactic objects: galaxies in the 2 Microns All Sky Survey and active galactic nuclei detected in hard X-rays by the Swift Burst Alert Telescope. A celestial region around the position of the radiogalaxy Cen A has the largest excess of arrival directions relative to isotropic expectations. The 2-point autocorrelation function is shown for the enlarged set of arrival directions and compared to the isotropic expectation. (C) 2010 Elsevier B.V. All rights reserved.

The fluorescence detector of the Pierre Auger Observatory

The Pierre Auger Observatory is a hybrid detector for ultra-high energy cosmic rays. It combines a surface array to measure secondary particles at ground level together with a fluorescence detector to measure the development of air showers in the atmosphere above the array. The fluorescence detector comprises 24 large telescopes specialized for measuring the nitrogen fluorescence caused by charged particles of cosmic ray air showers. In this paper we describe the components of the fluorescence detector including its optical system, the design of the camera, the electronics, and the systems for relative and absolute calibration. We also discuss the operation and the monitoring of the detector. Finally, we evaluate the detector performance and precision of shower reconstructions. (C) 2010 Elsevier B.V All rights reserved.

Measurement of the energy spectrum of cosmic rays above 10(18) eV using the Pierre Auger Observatory

We report a measurement of the flux of cosmic rays with unprecedented precision and Statistics using the Pierre Auger Observatory Based on fluorescence observations in coincidence with at least one Surface detector we derive a spectrum for energies above 10(18) eV We also update the previously published energy spectrum obtained with the surface detector array The two spectra are combined addressing the systematic uncertainties and, in particular. the influence of the energy resolution on the spectral shape The spectrum can be described by a broken power law E(-gamma) with index gamma = 3 3 below the ankle which is measured at log(10)(E(ankle)/eV) = 18 6 Above the ankle the spectrum is described by a power law with index 2 6 followed by a flux suppression, above about log(10)(E/eV) = 19 5, detected with high statistical significance (C) 2010 Elsevier B V All rights reserved

A study of the effect of molecular and aerosol conditions in the atmosphere on air fluorescence measurements at the Pierre Auger Observatory

The air fluorescence detector of the Pierre Auger Observatory is designed to perforin calorimetric measurements of extensive air showers created by Cosmic rays of above 10(18) eV. To correct these measurements for the effects introduced by atmospheric fluctuations, the Observatory contains a group Of monitoring instruments to record atmospheric conditions across the detector site, ail area exceeding 3000 km(2). The atmospheric data are used extensively in the reconstruction of air showers, and are particularly important for the correct determination of shower energies and the depths of shower maxima. This paper contains a summary of the molecular and aerosol conditions measured at the Pierre Auger Observatory since the start of regular operations in 2004, and includes a discussion of the impact of these measurements oil air shower reconstructions. Between 10(18) and 10(20) eV, the systematic Uncertainties due to all atmospheric effects increase from 4% to 8% in measurements of shower energy, and 4 g cm(-2) to 8 g cm(-2) in measurements of the shower maximum. (C) 2010 Elsevier B.V. All rights reserved.

Sparse partition universal graphs for graphs of bounded degree

In 1983, Chvatal, Trotter and the two senior authors proved that for any Delta there exists a constant B such that, for any n, any 2-colouring of the edges of the complete graph K(N) with N >= Bn vertices yields a monochromatic copy of any graph H that has n vertices and maximum degree Delta. We prove that the complete graph may be replaced by a sparser graph G that has N vertices and O(N(2-1/Delta)log(1/Delta)N) edges, with N = [B`n] for some constant B` that depends only on Delta. Consequently, the so-called size-Ramsey number of any H with n vertices and maximum degree Delta is O(n(2-1/Delta)log(1/Delta)n) Our approach is based on random graphs; in fact, we show that the classical Erdos-Renyi random graph with the numerical parameters above satisfies a stronger partition property with high probability, namely, that any 2-colouring of its edges contains a monochromatic universal graph for the class of graphs on n vertices and maximum degree Delta. The main tool in our proof is the regularity method, adapted to a suitable sparse setting. The novel ingredient developed here is an embedding strategy that allows one to embed bounded degree graphs of linear order in certain pseudorandom graphs. Crucial to our proof is the fact that regularity is typically inherited at a scale that is much finer than the scale at which it is assumed. (C) 2011 Elsevier Inc. All rights reserved.

The 3-colored Ramsey number of even cycles

Denote by R(L, L, L) the minimum integer N such that any 3-coloring of the edges of the complete graph on N vertices contains a monochromatic copy of a graph L. Bondy and Erdos conjectured that when L is the cycle C(n) on n vertices, R(C(n), C(n), C(n)) = 4n - 3 for every odd n > 3. Luczak proved that if n is odd, then R(C(n), C(n), C(n)) = 4n + o(n), as n -> infinity, and Kohayakawa, Simonovits and Skokan confirmed the Bondy-Erdos conjecture for all sufficiently large values of n. Figaj and Luczak determined an asymptotic result for the `complementary` case where the cycles are even: they showed that for even n, we have R(C(n), C(n), C(n)) = 2n + o(n), as n -> infinity. In this paper, we prove that there exists n I such that for every even n >= n(1), R(C(n), C(n), C(n)) = 2n. (C) 2009 Elsevier Inc. All rights reserved.

Conjectures and theorems in the theory of entire functions

Motivated by the recent solution of Karlin's conjecture, properties of functions in the Laguerre-Polya class are investigated. The main result of this paper establishes new moment inequalities fur a class of entire functions represented by Fourier transforms. The paper concludes with several conjectures and open problems involving the Laguerre-Polya class and the Riemann xi -function.