167 research outputs found
Quarantine generated phase transition in epidemic spreading
We study the critical effect of quarantine on the propagation of epidemics on
an adaptive network of social contacts. For this purpose, we analyze the
susceptible-infected-recovered (SIR) model in the presence of quarantine, where
susceptible individuals protect themselves by disconnecting their links to
infected neighbors with probability w, and reconnecting them to other
susceptible individuals chosen at random. Starting from a single infected
individual, we show by an analytical approach and simulations that there is a
phase transition at a critical rewiring (quarantine) threshold w_c separating a
phase (w<w_c) where the disease reaches a large fraction of the population,
from a phase (w >= w_c) where the disease does not spread out. We find that in
our model the topology of the network strongly affects the size of the
propagation, and that w_c increases with the mean degree and heterogeneity of
the network. We also find that w_c is reduced if we perform a preferential
rewiring, in which the rewiring probability is proportional to the degree of
infected nodes.Comment: 13 pages, 6 figure
Assortativity Decreases the Robustness of Interdependent Networks
It was recently recognized that interdependencies among different networks
can play a crucial role in triggering cascading failures and hence system-wide
disasters. A recent model shows how pairs of interdependent networks can
exhibit an abrupt percolation transition as failures accumulate. We report on
the effects of topology on failure propagation for a model system consisting of
two interdependent networks. We find that the internal node correlations in
each of the two interdependent networks significantly changes the critical
density of failures that triggers the total disruption of the two-network
system. Specifically, we find that the assortativity (i.e. the likelihood of
nodes with similar degree to be connected) within a single network decreases
the robustness of the entire system. The results of this study on the influence
of assortativity may provide insights into ways of improving the robustness of
network architecture, and thus enhances the level of protection of critical
infrastructures
Dynamics at a smeared phase transition
We investigate the effects of rare regions on the dynamics of Ising magnets
with planar defects, i.e., disorder perfectly correlated in two dimensions. In
these systems, the magnetic phase transition is smeared because static
long-range order can develop on isolated rare regions. We first study an
infinite-range model by numerically solving local dynamic mean-field equations.
Then we use extremal statistics and scaling arguments to discuss the dynamics
beyond mean-field theory. In the tail region of the smeared transition the
dynamics is even slower than in a conventional Griffiths phase: the spin
autocorrelation function decays like a stretched exponential at intermediate
times before approaching the exponentially small equilibrium value following a
power law at late times.Comment: 10 pages, 8eps figures included, final version as publishe
Epidemics in partially overlapped multiplex networks
Many real networks exhibit a layered structure in which links in each layer
reflect the function of nodes on different environments. These multiple types
of links are usually represented by a multiplex network in which each layer has
a different topology. In real-world networks, however, not all nodes are
present on every layer. To generate a more realistic scenario, we use a
generalized multiplex network and assume that only a fraction of the nodes
are shared by the layers. We develop a theoretical framework for a branching
process to describe the spread of an epidemic on these partially overlapped
multiplex networks. This allows us to obtain the fraction of infected
individuals as a function of the effective probability that the disease will be
transmitted . We also theoretically determine the dependence of the epidemic
threshold on the fraction of shared nodes in a system composed of two
layers. We find that in the limit of the threshold is dominated by
the layer with the smaller isolated threshold. Although a system of two
completely isolated networks is nearly indistinguishable from a system of two
networks that share just a few nodes, we find that the presence of these few
shared nodes causes the epidemic threshold of the isolated network with the
lower propagating capacity to change discontinuously and to acquire the
threshold of the other network.Comment: 13 pages, 4 figure
The physics of spreading processes in multilayer networks
The study of networks plays a crucial role in investigating the structure,
dynamics, and function of a wide variety of complex systems in myriad
disciplines. Despite the success of traditional network analysis, standard
networks provide a limited representation of complex systems, which often
include different types of relationships (i.e., "multiplexity") among their
constituent components and/or multiple interacting subsystems. Such structural
complexity has a significant effect on both dynamics and function. Throwing
away or aggregating available structural information can generate misleading
results and be a major obstacle towards attempts to understand complex systems.
The recent "multilayer" approach for modeling networked systems explicitly
allows the incorporation of multiplexity and other features of realistic
systems. On one hand, it allows one to couple different structural
relationships by encoding them in a convenient mathematical object. On the
other hand, it also allows one to couple different dynamical processes on top
of such interconnected structures. The resulting framework plays a crucial role
in helping achieve a thorough, accurate understanding of complex systems. The
study of multilayer networks has also revealed new physical phenomena that
remain hidden when using ordinary graphs, the traditional network
representation. Here we survey progress towards attaining a deeper
understanding of spreading processes on multilayer networks, and we highlight
some of the physical phenomena related to spreading processes that emerge from
multilayer structure.Comment: 25 pages, 4 figure
Rare region effects at classical, quantum, and non-equilibrium phase transitions
Rare regions, i.e., rare large spatial disorder fluctuations, can
dramatically change the properties of a phase transition in a quenched
disordered system. In generic classical equilibrium systems, they lead to an
essential singularity, the so-called Griffiths singularity, of the free energy
in the vicinity of the phase transition. Stronger effects can be observed at
zero-temperature quantum phase transitions, at nonequilibrium phase
transitions, and in systems with correlated disorder. In some cases, rare
regions can actually completely destroy the sharp phase transition by smearing.
This topical review presents a unifying framework for rare region effects at
weakly disordered classical, quantum, and nonequilibrium phase transitions
based on the effective dimensionality of the rare regions. Explicit examples
include disordered classical Ising and Heisenberg models, insulating and
metallic random quantum magnets, and the disordered contact process.Comment: Topical review, 68 pages, 14 figures, final version as publishe
The State of the Art in Multilayer Network Visualization
Modelling relationships between entities in real-world systems with a simple
graph is a standard approach. However, reality is better embraced as several
interdependent subsystems (or layers). Recently the concept of a multilayer
network model has emerged from the field of complex systems. This model can be
applied to a wide range of real-world datasets. Examples of multilayer networks
can be found in the domains of life sciences, sociology, digital humanities and
more. Within the domain of graph visualization there are many systems which
visualize datasets having many characteristics of multilayer graphs. This
report provides a state of the art and a structured analysis of contemporary
multilayer network visualization, not only for researchers in visualization,
but also for those who aim to visualize multilayer networks in the domain of
complex systems, as well as those developing systems across application
domains. We have explored the visualization literature to survey visualization
techniques suitable for multilayer graph visualization, as well as tools,
tasks, and analytic techniques from within application domains. This report
also identifies the outstanding challenges for multilayer graph visualization
and suggests future research directions for addressing them
Effects of temporal correlations in social multiplex networks
Multi-layered networks represent a major advance in the description of natural complex systems, and their study has shed light on new physical phenomena. Despite its importance, however, the role of the temporal dimension in their structure and function has not been investigated in much detail so far. Here we study the temporal correlations between layers exhibited by real social multiplex networks. At a basic level, the presence of such correlations implies a certain degree of predictability in the contact pattern, as we quantify by an extension of the entropy and mutual information analyses proposed for the single-layer case. At a different level, we demonstrate that temporal correlations are a signature of a ‘multitasking’ behavior of network agents, characterized by a higher level of switching between different social activities than expected in a uncorrelated pattern. Moreover, temporal correlations significantly affect the dynamics of coupled epidemic processes unfolding on the network. Our work opens the way for the systematic study of temporal multiplex networks and we anticipate it will be of interest to researchers in a broad array of fields
Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment
In this paper, we review theoretical and experimental research on rare region
effects at quantum phase transitions in disordered itinerant electron systems.
After summarizing a few basic concepts about phase transitions in the presence
of quenched randomness, we introduce the idea of rare regions and discuss their
importance. We then analyze in detail the different phenomena that can arise at
magnetic quantum phase transitions in disordered metals, including quantum
Griffiths singularities, smeared phase transitions, and cluster-glass
formation. For each scenario, we discuss the resulting phase diagram and
summarize the behavior of various observables. We then review several recent
experiments that provide examples of these rare region phenomena. We conclude
by discussing limitations of current approaches and open questions.Comment: 31 pages, 7 eps figures included, v2: discussion of the dissipative
Ising chain fixed, references added, v3: final version as publishe
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