1,175 research outputs found
Local Rigidity in Sandpile Models
We address the problem of the role of the concept of local rigidity in the
family of sandpile systems. We define rigidity as the ratio between the
critical energy and the amplitude of the external perturbation and we show, in
the framework of the Dynamically Driven Renormalization Group (DDRG), that any
finite value of the rigidity in a generalized sandpile model renormalizes to an
infinite value at the fixed point, i.e. on a large scale. The fixed point value
of the rigidity allows then for a non ambiguous distinction between
sandpile-like systems and diffusive systems. Numerical simulations support our
analytical results.Comment: to be published in Phys. Rev.
Multi-layer model for the web graph
This paper studies stochastic graph models of the WebGraph. We present a new model that describes the WebGraph as an ensemble of different regions generated by independent stochastic processes (in the spirit of a recent paper by Dill et al. [VLDB 2001]). Models such as the Copying Model [17] and Evolving Networks Model [3] are simulated and compared on several relevant measures such as degree and clique distribution
An ensemble approach to the analysis of weighted networks
We present a new approach to the calculation of measures in weighted
networks, based on the translation of a weighted network into an ensemble of
edges. This leads to a straightforward generalization of any measure defined on
unweighted networks, such as the average degree of the nearest neighbours, the
clustering coefficient, the `betweenness', the distance between two nodes and
the diameter of a network. All these measures are well established for
unweighted networks but have hitherto proven difficult to define for weighted
networks. Further to introducing this approach we demonstrate its advantages by
applying the clustering coefficient constructed in this way to two real-world
weighted networks.Comment: 4 pages 3 figure
Supersymmetric gyratons in five dimensions
We obtain the gravitational and electromagnetic field of a spinning radiation
beam-pulse (a gyraton) in minimal five-dimensional gauged supergravity and show
under which conditions the solution preserves part of the supersymmetry. The
configurations represent generalizations of Lobatchevski waves on AdS with
nonzero angular momentum, and possess a Siklos-Virasoro reparametrization
invariance. We compute the holographic stress-energy tensor of the solutions
and show that it transforms without anomaly under these reparametrizations.
Furthermore, we present supersymmetric gyratons both in gauged and ungauged
five-dimensional supergravity coupled to an arbitrary number of vector
supermultiplets, which include gyratons on domain walls.Comment: 25 pages, no figures, uses JHEP3.cls. Final version to appear in CQ
Self-organized network evolution coupled to extremal dynamics
The interplay between topology and dynamics in complex networks is a
fundamental but widely unexplored problem. Here, we study this phenomenon on a
prototype model in which the network is shaped by a dynamical variable. We
couple the dynamics of the Bak-Sneppen evolution model with the rules of the
so-called fitness network model for establishing the topology of a network;
each vertex is assigned a fitness, and the vertex with minimum fitness and its
neighbours are updated in each iteration. At the same time, the links between
the updated vertices and all other vertices are drawn anew with a
fitness-dependent connection probability. We show analytically and numerically
that the system self-organizes to a non-trivial state that differs from what is
obtained when the two processes are decoupled. A power-law decay of dynamical
and topological quantities above a threshold emerges spontaneously, as well as
a feedback between different dynamical regimes and the underlying correlation
and percolation properties of the network.Comment: Accepted version. Supplementary information at
http://www.nature.com/nphys/journal/v3/n11/suppinfo/nphys729_S1.htm
Networks of equities in financial markets
We review the recent approach of correlation based networks of financial
equities. We investigate portfolio of stocks at different time horizons,
financial indices and volatility time series and we show that meaningful
economic information can be extracted from noise dressed correlation matrices.
We show that the method can be used to falsify widespread market models by
directly comparing the topological properties of networks of real and
artificial markets.Comment: 9 pages, 8 figures. Accepted for publication in EPJ
Statistical entropy of the Schwarzschild black hole
We derive the statistical entropy of the Schwarzschild black hole by
considering the asymptotic symmetry algebra near the boundary of
the spacetime at past null infinity. Using a two-dimensional description and
the Weyl invariance of black hole thermodynamics this symmetry algebra can be
mapped into the Virasoro algebra generating asymptotic symmetries of anti-de
Sitter spacetime. Using lagrangian methods we identify the stress-energy tensor
of the boundary conformal field theory and we calculate the central charge of
the Virasoro algebra. The Bekenstein-Hawking result for the black hole entropy
is regained using Cardy's formula. Our result strongly supports a non-local
realization of the holographic principleComment: 3 pages no figure
Hypergraph topological quantities for tagged social networks
Recent years have witnessed the emergence of a new class of social networks,
that require us to move beyond previously employed representations of complex
graph structures. A notable example is that of the folksonomy, an online
process where users collaboratively employ tags to resources to impart
structure to an otherwise undifferentiated database. In a recent paper[1] we
proposed a mathematical model that represents these structures as tripartite
hypergraphs and defined basic topological quantities of interest. In this paper
we extend our model by defining additional quantities such as edge
distributions, vertex similarity and correlations as well as clustering. We
then empirically measure these quantities on two real life folksonomies, the
popular online photo sharing site Flickr and the bookmarking site CiteULike. We
find that these systems share similar qualitative features with the majority of
complex networks that have been previously studied. We propose that the
quantities and methodology described here can be used as a standard tool in
measuring the structure of tagged networks.Comment: 8 pages, 9 figures, revte
Analysis of relative influence of nodes in directed networks
Many complex networks are described by directed links; in such networks, a
link represents, for example, the control of one node over the other node or
unidirectional information flows. Some centrality measures are used to
determine the relative importance of nodes specifically in directed networks.
We analyze such a centrality measure called the influence. The influence
represents the importance of nodes in various dynamics such as synchronization,
evolutionary dynamics, random walk, and social dynamics. We analytically
calculate the influence in various networks, including directed multipartite
networks and a directed version of the Watts-Strogatz small-world network. The
global properties of networks such as hierarchy and position of shortcuts,
rather than local properties of the nodes, such as the degree, are shown to be
the chief determinants of the influence of nodes in many cases. The developed
method is also applicable to the calculation of the PageRank. We also
numerically show that in a coupled oscillator system, the threshold for
entrainment by a pacemaker is low when the pacemaker is placed on influential
nodes. For a type of random network, the analytically derived threshold is
approximately equal to the inverse of the influence. We numerically show that
this relationship also holds true in a random scale-free network and a neural
network.Comment: 9 figure
The extremal limit of D-dimensional black holes
The extreme limit of a class of D-dimensional black holes is revisited. In
the static limit, it is shown that well defined extremal limiting procedure
exists and it leads to new solutions of the type AdS2 times constant curvature
symmetric spaces.Comment: 8 pages, proceedings of Londrina Conference, April 2000, Londrina,
Brazi
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