1,347 research outputs found

    Multi-species grandcanonical models for networks with reciprocity

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    Reciprocity is a second-order correlation that has been recently detected in all real directed networks and shown to have a crucial effect on the dynamical processes taking place on them. However, no current theoretical model generates networks with this nontrivial property. Here we propose a grandcanonical class of models reproducing the observed patterns of reciprocity by regarding single and double links as Fermi particles of different `chemical species' governed by the corresponding chemical potentials. Within this framework we find interesting special cases such as the extensions of random graphs, the configuration model and hidden-variable models. Our theoretical predictions are also in excellent agreement with the empirical results for networks with well studied reciprocity.Comment: 4 pages, 1 figur

    Generalized Bose-Fermi statistics and structural correlations in weighted networks

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    We derive a class of generalized statistics, unifying the Bose and Fermi ones, that describe any system where the first-occupation energies or probabilities are different from subsequent ones, as in presence of thresholds, saturation, or aging. The statistics completely describe the structural correlations of weighted networks, which turn out to be stronger than expected and to determine significant topological biases. Our results show that the null behavior of weighted networks is different from what previously believed, and that a systematic redefinition of weighted properties is necessary.Comment: Final version accepted for publication on Physical Review Letter

    Detecting spatial homogeneity in the world trade web with Detrended Fluctuation Analysis

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    In a spatially embedded network, that is a network where nodes can be uniquely determined in a system of coordinates, links' weights might be affected by metric distances coupling every pair of nodes (dyads). In order to assess to what extent metric distances affect relationships (link's weights) in a spatially embedded network, we propose a methodology based on DFA (Detrended Fluctuation Analysis). DFA is a well developed methodology to evaluate autocorrelations and estimate long-range behaviour in time series. We argue it can be further extended to spatially ordered series in order to assess autocorrelations in values. A scaling exponent of 0.5 (uncorrelated data) would thereby signal a perfect homogeneous space embedding the network. We apply the proposed methodology to the World Trade Web (WTW) during the years 1949-2000 and we find, in some contrast with predictions of gravity models, a declining influence of distances on trading relationships.Comment: 15 pages, 7 figure

    Effects of network topology on wealth distributions

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    We focus on the problem of how wealth is distributed among the units of a networked economic system. We first review the empirical results documenting that in many economies the wealth distribution is described by a combination of log--normal and power--law behaviours. We then focus on the Bouchaud--M\'ezard model of wealth exchange, describing an economy of interacting agents connected through an exchange network. We report analytical and numerical results showing that the system self--organises towards a stationary state whose associated wealth distribution depends crucially on the underlying interaction network. In particular we show that if the network displays a homogeneous density of links, the wealth distribution displays either the log--normal or the power--law form. This means that the first--order topological properties alone (such as the scale--free property) are not enough to explain the emergence of the empirically observed \emph{mixed} form of the wealth distribution. In order to reproduce this nontrivial pattern, the network has to be heterogeneously divided into regions with variable density of links. We show new results detailing how this effect is related to the higher--order correlation properties of the underlying network. In particular, we analyse assortativity by degree and the pairwise wealth correlations, and discuss the effects that these properties have on each other.Comment: References adde

    Fitness-dependent topological properties of the World Trade Web

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    Among the proposed network models, the hidden variable (or good get richer) one is particularly interesting, even if an explicit empirical test of its hypotheses has not yet been performed on a real network. Here we provide the first empirical test of this mechanism on the world trade web, the network defined by the trade relationships between world countries. We find that the power-law distributed gross domestic product can be successfully identified with the hidden variable (or fitness) determining the topology of the world trade web: all previously studied properties up to third-order correlation structure (degree distribution, degree correlations and hierarchy) are found to be in excellent agreement with the predictions of the model. The choice of the connection probability is such that all realizations of the network with the same degree sequence are equiprobable.Comment: 4 Pages, 4 Figures. Final version accepted for publication on Physical Review Letter

    Patterns of link reciprocity in directed networks

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    We address the problem of link reciprocity, the non-random presence of two mutual links between pairs of vertices. We propose a new measure of reciprocity that allows the ordering of networks according to their actual degree of correlation between mutual links. We find that real networks are always either correlated or anticorrelated, and that networks of the same type (economic, social, cellular, financial, ecological, etc.) display similar values of the reciprocity. The observed patterns are not reproduced by current models. This leads us to introduce a more general framework where mutual links occur with a conditional connection probability. In some of the studied networks we discuss the form of the conditional connection probability and the size dependence of the reciprocity.Comment: Final version accepted for publication on Physical Review Letter

    Measurement of the cross-section and charge asymmetry of WW bosons produced in proton-proton collisions at s=8\sqrt{s}=8 TeV with the ATLAS detector

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    This paper presents measurements of the W+μ+νW^+ \rightarrow \mu^+\nu and WμνW^- \rightarrow \mu^-\nu cross-sections and the associated charge asymmetry as a function of the absolute pseudorapidity of the decay muon. The data were collected in proton--proton collisions at a centre-of-mass energy of 8 TeV with the ATLAS experiment at the LHC and correspond to a total integrated luminosity of 20.2~\mbox{fb^{-1}}. The precision of the cross-section measurements varies between 0.8% to 1.5% as a function of the pseudorapidity, excluding the 1.9% uncertainty on the integrated luminosity. The charge asymmetry is measured with an uncertainty between 0.002 and 0.003. The results are compared with predictions based on next-to-next-to-leading-order calculations with various parton distribution functions and have the sensitivity to discriminate between them.Comment: 38 pages in total, author list starting page 22, 5 figures, 4 tables, submitted to EPJC. All figures including auxiliary figures are available at https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/STDM-2017-13

    Search for direct stau production in events with two hadronic tau-leptons in root s=13 TeV pp collisions with the ATLAS detector