4,385 research outputs found
Numerical assessment of the percolation threshold using complement networks
Models of percolation processes on networks currently assume locally
tree-like structures at low densities, and are derived exactly only in the
thermodynamic limit. Finite size effects and the presence of short loops in
real systems however cause a deviation between the empirical percolation
threshold and its model-predicted value . Here we show the
existence of an empirical linear relation between and across a
large number of real and model networks. Such a putatively universal relation
can then be used to correct the estimated value of . We further show how
to obtain a more precise relation using the concept of the complement graph, by
investigating on the connection between the percolation threshold of a network,
, and that of its complement,
Multiple structural transitions in interacting networks
Many real-world systems can be modeled as interconnected multilayer networks,
namely a set of networks interacting with each other. Here we present a
perturbative approach to study the properties of a general class of
interconnected networks as inter-network interactions are established. We
reveal multiple structural transitions for the algebraic connectivity of such
systems, between regimes in which each network layer keeps its independent
identity or drives diffusive processes over the whole system, thus generalizing
previous results reporting a single transition point. Furthermore we show that,
at first order in perturbation theory, the growth of the algebraic connectivity
of each layer depends only on the degree configuration of the interaction
network (projected on the respective Fiedler vector), and not on the actual
interaction topology. Our findings can have important implications in the
design of robust interconnected networked system, particularly in the presence
of network layers whose integrity is more crucial for the functioning of the
entire system. We finally show results of perturbation theory applied to the
adjacency matrix of the interconnected network, which can be useful to
characterize percolation processes on such systems
Fragility and anomalous susceptibility of weakly interacting networks
Percolation is a fundamental concept that brought new understanding on the
robustness properties of complex systems. Here we consider percolation on
weakly interacting networks, that is, network layers coupled together by much
less interlinks than the connections within each layer. For these kinds of
structures, both continuous and abrupt phase transition are observed in the
size of the giant component. The continuous (second-order) transition
corresponds to the formation of a giant cluster inside one layer, and has a
well defined percolation threshold. The abrupt transition instead corresponds
to the merger of coexisting giant clusters among different layers, and is
characterised by a remarkable uncertainty in the percolation threshold, which
in turns causes an anomalous trend in the observed susceptibility. We develop a
simple mathematical model able to describe this phenomenon and to estimate the
critical threshold for which the abrupt transition is more likely to occur.
Remarkably, finite-size scaling analysis in the abrupt region supports the
hypothesis of a genuine first-order phase transition
Rational Fair Consensus in the GOSSIP Model
The \emph{rational fair consensus problem} can be informally defined as
follows. Consider a network of (selfish) \emph{rational agents}, each of
them initially supporting a \emph{color} chosen from a finite set .
The goal is to design a protocol that leads the network to a stable
monochromatic configuration (i.e. a consensus) such that the probability that
the winning color is is equal to the fraction of the agents that initially
support , for any . Furthermore, this fairness property must
be guaranteed (with high probability) even in presence of any fixed
\emph{coalition} of rational agents that may deviate from the protocol in order
to increase the winning probability of their supported colors. A protocol
having this property, in presence of coalitions of size at most , is said to
be a \emph{whp\,--strong equilibrium}. We investigate, for the first time,
the rational fair consensus problem in the GOSSIP communication model where, at
every round, every agent can actively contact at most one neighbor via a
\emph{pushpull} operation. We provide a randomized GOSSIP protocol that,
starting from any initial color configuration of the complete graph, achieves
rational fair consensus within rounds using messages of
size, w.h.p. More in details, we prove that our protocol is a
whp\,--strong equilibrium for any and, moreover, it
tolerates worst-case permanent faults provided that the number of non-faulty
agents is . As far as we know, our protocol is the first solution
which avoids any all-to-all communication, thus resulting in message
complexity.Comment: Accepted at IPDPS'1
Photometric determination of the mass accretion rates of pre-main sequence stars. VI. The case of LH 95 in the Large Magellanic Cloud
We report on the accretion properties of low-mass stars in the LH95
association within the Large Magellanic Cloud (LMC). Using non-contemporaneous
wide-band and narrow-band photometry obtained with the HST, we identify 245
low-mass pre-main sequence (PMS) candidates showing H excess emission
above the 4 level. We derive their physical parameters, i.e. effective
temperatures, luminosities, masses (), ages, accretion luminosities,
and mass accretion rates (). We identify two different
stellar populations: younger than ~8Myr with median ~5.4x10/yr (and ~0.15-1.8) and older than
~8Myr with median ~4.8x10/yr (and
~0.6-1.2). We find that the younger PMS candidates are
assembled in groups around Be stars, while older PMS candidates are uniformly
distributed within the region without evidence of clustering. We find that
in LH95 decreases with time more slowly than what is
observed in Galactic star-forming regions (SFRs). This agrees with the recent
interpretation according to which higher metallicity limits the accretion
process both in rate and duration due to higher radiation pressure. The relationship shows different behaviour at different ages,
becoming progressively steeper at older ages, indicating that the effects of
mass and age on cannot be treated independently. With the
aim to identify reliable correlations between mass, age, and , we used for our PMS candidates a multivariate linear regression fit
between these parameters. The comparison between our results with those
obtained in other SFRs of our Galaxy and the MCs confirms the importance of the
metallicity for the study of the evolution in clusters with
different environmental conditions.Comment: Accepted for publication in ApJ; 26 pages, 12 pages, 3 tables;
abstract shortened. Fixed a typo in the name of a co-autho
Staggered fermions simulations on GPUs
We present our implementation of the RHMC algorithm for staggered fermions on
Graphics Processing Units using the NVIDIA CUDA programming language. While
previous studies exclusively deal with the Dirac matrix inversion problem, our
code performs the complete MD trajectory on the GPU. After pointing out the
main bottlenecks and how to circumvent them, we discuss the performance of our
code.Comment: Poster presented at the XXVIII International Symposium on Lattice
Field Theory, June 14-19, 2010, Villasimius, Sardinia Ital
Confinement: group case
The gauge group being centreless, gauge theory is a good laboratory for
studying the role of the centre of the group for colour confinement in
Yang-Mills gauge theories. In this paper, we investigate pure gauge
theory at finite temperature on the lattice. By studying the finite size
scaling of the plaquette, the Polyakov loop and their susceptibilities, we show
that a deconfinement phase transition takes place. The analysis of the
pseudocritical exponents give strong evidence of the deconfinement transition
being first order. Implications of our findings for scenarios of colour
confinement are discussed.Comment: 6 pages, 4 figures, Proceedings of the The XXV International
Symposium on Lattice Field Theory, Regensburg August 200
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