715 research outputs found
Directionality reduces the impact of epidemics in multilayer networks
The study of how diseases spread has greatly benefited from advances in
network modeling. Recently, a class of networks known as multilayer graphs has
been shown to describe more accurately many real systems, making it possible to
address more complex scenarios in epidemiology such as the interaction between
different pathogens or multiple strains of the same disease. In this work, we
study in depth a class of networks that have gone unnoticed up to now, despite
of its relevance for spreading dynamics. Specifically, we focus on directed
multilayer networks, characterized by the existence of directed links, either
within the layers or across layers. Using the generating function approach and
numerical simulations of a stochastic susceptible-infected-susceptible (SIS)
model, we calculate the epidemic threshold for these networks for different
degree distributions of the networks. Our results show that the main feature
that determines the value of the epidemic threshold is the directionality of
the links connecting different layers, regardless of the degree distribution
chosen. Our findings are of utmost interest given the ubiquitous presence of
directed multilayer networks and the widespread use of disease-like spreading
processes in a broad range of phenomena such as diffusion processes in social
and transportation systems.Comment: 20 pages including 7 figures. Submitted for publicatio
A network approach for power grid robustness against cascading failures
Cascading failures are one of the main reasons for blackouts in electrical
power grids. Stable power supply requires a robust design of the power grid
topology. Currently, the impact of the grid structure on the grid robustness is
mainly assessed by purely topological metrics, that fail to capture the
fundamental properties of the electrical power grids such as power flow
allocation according to Kirchhoff's laws. This paper deploys the effective
graph resistance as a metric to relate the topology of a grid to its robustness
against cascading failures. Specifically, the effective graph resistance is
deployed as a metric for network expansions (by means of transmission line
additions) of an existing power grid. Four strategies based on network
properties are investigated to optimize the effective graph resistance,
accordingly to improve the robustness, of a given power grid at a low
computational complexity. Experimental results suggest the existence of
Braess's paradox in power grids: bringing an additional line into the system
occasionally results in decrease of the grid robustness. This paper further
investigates the impact of the topology on the Braess's paradox, and identifies
specific sub-structures whose existence results in Braess's paradox. Careful
assessment of the design and expansion choices of grid topologies incorporating
the insights provided by this paper optimizes the robustness of a power grid,
while avoiding the Braess's paradox in the system.Comment: 7 pages, 13 figures conferenc
Structural transition in interdependent networks with regular interconnections
Networks are often made up of several layers that exhibit diverse degrees of
interdependencies. A multilayer interdependent network consists of a set of
graphs that are interconnected through a weighted interconnection matrix , where the weight of each inter-graph link is a non-negative real number . Various dynamical processes, such as synchronization, cascading failures
in power grids, and diffusion processes, are described by the Laplacian matrix
characterizing the whole system. For the case in which the multilayer
graph is a multiplex, where the number of nodes in each layer is the same and
the interconnection matrix , being the identity matrix, it has
been shown that there exists a structural transition at some critical coupling,
. This transition is such that dynamical processes are separated into
two regimes: if , the network acts as a whole; whereas when , the network operates as if the graphs encoding the layers were isolated. In
this paper, we extend and generalize the structural transition threshold to a regular interconnection matrix (constant row and column sum).
Specifically, we provide upper and lower bounds for the transition threshold in interdependent networks with a regular interconnection matrix
and derive the exact transition threshold for special scenarios using the
formalism of quotient graphs. Additionally, we discuss the physical meaning of
the transition threshold in terms of the minimum cut and show, through
a counter-example, that the structural transition does not always exist. Our
results are one step forward on the characterization of more realistic
multilayer networks and might be relevant for systems that deviate from the
topological constrains imposed by multiplex networks.Comment: 13 pages, APS format. Submitted for publicatio
Adaptive Sparse Array Beamformer Design by Regularized Complementary Antenna Switching
In this work, we propose a novel strategy of adaptive sparse array beamformer
design, referred to as regularized complementary antenna switching (RCAS), to
swiftly adapt both array configuration and excitation weights in accordance to
the dynamic environment for enhancing interference suppression. In order to
achieve an implementable design of array reconfiguration, the RCAS is conducted
in the framework of regularized antenna switching, whereby the full array
aperture is collectively divided into separate groups and only one antenna in
each group is switched on to connect with the processing channel. A set of
deterministic complementary sparse arrays with good quiescent beampatterns is
first designed by RCAS and full array data is collected by switching among them
while maintaining resilient interference suppression. Subsequently, adaptive
sparse array tailored for the specific environment is calculated and
reconfigured based on the information extracted from the full array data. The
RCAS is devised as an exclusive cardinality-constrained optimization, which is
reformulated by introducing an auxiliary variable combined with a piece-wise
linear function to approximate the -norm function. A regularization
formulation is proposed to solve the problem iteratively and eliminate the
requirement of feasible initial search point. A rigorous theoretical analysis
is conducted, which proves that the proposed algorithm is essentially an
equivalent transformation of the original cardinality-constrained optimization.
Simulation results validate the effectiveness of the proposed RCAS strategy
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