1,347 research outputs found
Multi-species grandcanonical models for networks with reciprocity
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
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
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
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
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
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 bosons produced in proton-proton collisions at TeV with the ATLAS detector
This paper presents measurements of the and 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