2,818 research outputs found
Statics and dynamics of selfish interactions in distributed service systems
We study a class of games which model the competition among agents to access
some service provided by distributed service units and which exhibit congestion
and frustration phenomena when service units have limited capacity. We propose
a technique, based on the cavity method of statistical physics, to characterize
the full spectrum of Nash equilibria of the game. The analysis reveals a large
variety of equilibria, with very different statistical properties. Natural
selfish dynamics, such as best-response, usually tend to large-utility
equilibria, even though those of smaller utility are exponentially more
numerous. Interestingly, the latter actually can be reached by selecting the
initial conditions of the best-response dynamics close to the saturation limit
of the service unit capacities. We also study a more realistic stochastic
variant of the game by means of a simple and effective approximation of the
average over the random parameters, showing that the properties of the
average-case Nash equilibria are qualitatively similar to the deterministic
ones.Comment: 30 pages, 10 figure
Directed percolation depinning models: Evolution equations
We present the microscopic equation for the growing interface with quenched
noise for the model first presented by Buldyrev et al. [Phys. Rev. A 45, R8313
(1992)]. The evolution equation for the height, the mean height, and the
roughness are reached in a simple way. The microscopic equation allows us to
express these equations in two contributions: the contact and the local one. We
compare this two contributions with the ones obtained for the Tang and
Leschhorn model [Phys. Rev A 45, R8309 (1992)] by Braunstein et al. [Physica A
266, 308 (1999)]. Even when the microscopic mechanisms are quiet different in
both model, the two contribution are qualitatively similar. An interesting
result is that the diffusion contribution, in the Tang and Leschhorn model, and
the contact one, in the Buldyrev model, leads to an increase of the roughness
near the criticality.Comment: 10 pages and 4 figures. To be published in Phys. Rev.
Failure-recovery model with competition between failures in complex networks: a dynamical approach
Real systems are usually composed by units or nodes whose activity can be
interrupted and restored intermittently due to complex interactions not only
with the environment, but also with the same system. Majdand\v{z}i\'c
[Nature Physics 10, 34 (2014)] proposed a model to study systems in which
active nodes fail and recover spontaneously in a complex network and found that
in the steady state the density of active nodes can exhibit an abrupt
transition and hysteresis depending on the values of the parameters. Here we
investigate a model of recovery-failure from a dynamical point of view. Using
an effective degree approach we find that the systems can exhibit a temporal
sharp decrease in the fraction of active nodes. Moreover we show that,
depending on the values of the parameters, the fraction of active nodes has an
oscillatory regime which we explain as a competition between different failure
processes. We also find that in the non-oscillatory regime, the critical
fraction of active nodes presents a discontinuous drop which can be related to
a "targeted" k-core percolation process. Finally, using mean field equations we
analyze the space of parameters at which hysteresis and oscillatory regimes can
be found
Social distancing strategies against disease spreading
The recurrent infectious diseases and their increasing impact on the society
has promoted the study of strategies to slow down the epidemic spreading. In
this review we outline the applications of percolation theory to describe
strategies against epidemic spreading on complex networks. We give a general
outlook of the relation between link percolation and the
susceptible-infected-recovered model, and introduce the node void percolation
process to describe the dilution of the network composed by healthy individual,
, the network that sustain the functionality of a society. Then, we survey
two strategies: the quenched disorder strategy where an heterogeneous
distribution of contact intensities is induced in society, and the intermittent
social distancing strategy where health individuals are persuaded to avoid
contact with their neighbors for intermittent periods of time. Using
percolation tools, we show that both strategies may halt the epidemic
spreading. Finally, we discuss the role of the transmissibility, , the
effective probability to transmit a disease, on the performance of the
strategies to slow down the epidemic spreading.Comment: to be published in "Perspectives and Challenges in Statistical
Physics and Complex Systems for the Next Decade", Word Scientific Pres
Squeezing as an irreducible resource
We show that squeezing is an irreducible resource which remains invariant
under transformations by linear optical elements. In particular, we give a
decomposition of any optical circuit with linear input-output relations into a
linear multiport interferometer followed by a unique set of single mode
squeezers and then another multiport interferometer. Using this decomposition
we derive a no-go theorem for superpositions of macroscopically distinct states
from single-photon detection. Further, we demonstrate the equivalence between
several schemes for randomly creating polarization-entangled states. Finally,
we derive minimal quantum optical circuits for ideal quantum non-demolition
coupling of quadrature-phase amplitudes.Comment: 4 pages, 3 figures, new title, removed the fat
Large deviations of cascade processes on graphs
Simple models of irreversible dynamical processes such as Bootstrap
Percolation have been successfully applied to describe cascade processes in a
large variety of different contexts. However, the problem of analyzing
non-typical trajectories, which can be crucial for the understanding of the
out-of-equilibrium phenomena, is still considered to be intractable in most
cases. Here we introduce an efficient method to find and analyze optimized
trajectories of cascade processes. We show that for a wide class of
irreversible dynamical rules, this problem can be solved efficiently on
large-scale systems
Epidemic Model with Isolation in Multilayer Networks
The Susceptible-Infected-Recovered (SIR) model has successfully mimicked the
propagation of such airborne diseases as influenza A (H1N1). Although the SIR
model has recently been studied in a multilayer networks configuration, in
almost all the research the isolation of infected individuals is disregarded.
Hence we focus our study in an epidemic model in a two-layer network, and we
use an isolation parameter to measure the effect of isolating infected
individuals from both layers during an isolation period. We call this process
the Susceptible-Infected-Isolated-Recovered () model. The isolation
reduces the transmission of the disease because the time in which infection can
spread is reduced. In this scenario we find that the epidemic threshold
increases with the isolation period and the isolation parameter. When the
isolation period is maximum there is a threshold for the isolation parameter
above which the disease never becomes an epidemic. We also find that epidemic
models, like overestimate the theoretical risk of infection. Finally, our
model may provide a foundation for future research to study the temporal
evolution of the disease calibrating our model with real data.Comment: 18 pages, 5 figures.Accepted in Scientific Report
The influence of persuasion in opinion formation and polarization
We present a model that explores the influence of persuasion in a population
of agents with positive and negative opinion orientations. The opinion of each
agent is represented by an integer number that expresses its level of
agreement on a given issue, from totally against to totally in favor
. Same-orientation agents persuade each other with probability ,
becoming more extreme, while opposite-orientation agents become more moderate
as they reach a compromise with probability . The population initially
evolves to (a) a polarized state for , where opinions' distribution is
peaked at the extreme values , or (b) a centralized state for ,
with most opinions around . When , polarization lasts for a
time that diverges as , where is the population's size. Finally,
an extremist consensus ( or ) is reached in a time that scales as
for
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