584 research outputs found
Universal behavior of optimal paths in weighted networks with general disorder
We study the statistics of the optimal path in both random and scale free
networks, where weights are taken from a general distribution . We
find that different types of disorder lead to the same universal behavior.
Specifically, we find that a single parameter ( for
-dimensional lattices, and for random networks)
determines the distributions of the optimal path length, including both strong
and weak disorder regimes. Here is the percolation connectivity exponent,
and depends on the percolation threshold and . For uniform,
Poisson or Gaussian the crossover from weak to strong does not occur, and only
weak disorder exists.Comment: Accepted by PR
Scaling theory of transport in complex networks
Transport is an important function in many network systems and understanding
its behavior on biological, social, and technological networks is crucial for a
wide range of applications. However, it is a property that is not
well-understood in these systems and this is probably due to the lack of a
general theoretical framework. Here, based on the finding that renormalization
can be applied to bio-networks, we develop a scaling theory of transport in
self-similar networks. We demonstrate the networks invariance under length
scale renormalization and we show that the problem of transport can be
characterized in terms of a set of critical exponents. The scaling theory
allows us to determine the influence of the modular structure on transport. We
also generalize our theory by presenting and verifying scaling arguments for
the dependence of transport on microscopic features, such as the degree of the
nodes and the distance between them. Using transport concepts such as diffusion
and resistance we exploit this invariance and we are able to explain, based on
the topology of the network, recent experimental results on the broad flow
distribution in metabolic networks.Comment: 8 pages, 6 figure
Finite Size Scaling Analysis of Biased Diffusion on Fractals
Diffusion on a T fractal lattice under the influence of topological biasing
fields is studied by finite size scaling methods. This allows to avoid
proliferation and singularities which would arise in a renormalization group
approach on infinite system as a consequence of logarithmic diffusion. Within
the scheme, logarithmic diffusion is proved on the basis of an analysis of
various temporal scales such as first passage time moments and survival
probability characteristic time. This confirms and puts on firmer basis
previous renormalization group results. A careful study of the asymptotic
occupation probabilities of different kinds of lattice points allows to
elucidate the mechanism of trapping into dangling ends, which is responsible
of the logarithmic time dependence of average displacement.Comment: 17 pages TeX, 3 Postscript figure
Dynamics of Surface Roughening with Quenched Disorder
We study the dynamical exponent for the directed percolation depinning
(DPD) class of models for surface roughening in the presence of quenched
disorder. We argue that for dimensions is equal to the exponent
characterizing the shortest path between two sites in an
isotropic percolation cluster in dimensions. To test the argument, we
perform simulations and calculate for DPD, and for
percolation, from to .Comment: RevTex manuscript 3 pages + 6 figures (obtained upon request via
email [email protected]
Recovery of Interdependent Networks
Recent network research has focused on the cascading failures in a system of
interdependent networks and the necessary preconditions for system collapse. An
important question that has not been addressed is how to repair a failing
system before it suffers total breakdown. Here we introduce a recovery strategy
of nodes and develop an analytic and numerical framework for studying the
concurrent failure and recovery of a system of interdependent networks based on
an efficient and practically reasonable strategy. Our strategy consists of
repairing a fraction of failed nodes, with probability of recovery ,
that are neighbors of the largest connected component of each constituent
network. We find that, for a given initial failure of a fraction of
nodes, there is a critical probability of recovery above which the cascade is
halted and the system fully restores to its initial state and below which the
system abruptly collapses. As a consequence we find in the plane of
the phase diagram three distinct phases. A phase in which the system never
collapses without being restored, another phase in which the recovery strategy
avoids the breakdown, and a phase in which even the repairing process cannot
avoid the system collapse
Worldwide spreading of economic crisis
We model the spreading of a crisis by constructing a global economic network
and applying the Susceptible-Infected-Recovered (SIR) epidemic model with a
variable probability of infection. The probability of infection depends on the
strength of economic relations between the pair of countries, and the strength
of the target country. It is expected that a crisis which originates in a large
country, such as the USA, has the potential to spread globally, like the recent
crisis. Surprisingly we show that also countries with much lower GDP, such as
Belgium, are able to initiate a global crisis. Using the {\it k}-shell
decomposition method to quantify the spreading power (of a node), we obtain a
measure of ``centrality'' as a spreader of each country in the economic
network. We thus rank the different countries according to the shell they
belong to, and find the 12 most central countries. These countries are the most
likely to spread a crisis globally. Of these 12 only six are large economies,
while the other six are medium/small ones, a result that could not have been
otherwise anticipated. Furthermore, we use our model to predict the crisis
spreading potential of countries belonging to different shells according to the
crisis magnitude.Comment: 13 pages, 4 figures and Supplementary Materia
Directed Polymer -- Directed Percolation Transition
We study the relation between the directed polymer and the directed
percolation models, for the case of a disordered energy landscape where the
energies are taken from bimodal distribution. We find that at the critical
concentration of the directed percolation, the directed polymer undergoes a
transition from the directed polymer universality class to the directed
percolation universality class. We also find that directed percolation clusters
affect the characterisrics of the directed polymer below the critical
concentration.Comment: LaTeX 2e; 12 pages, 5 figures; in press, will be published in
Europhys. Let
Efficient Immunization Strategies for Computer Networks and Populations
We present an effective immunization strategy for computer networks and
populations with broad and, in particular, scale-free degree distributions. The
proposed strategy, acquaintance immunization, calls for the immunization of
random acquaintances of random nodes (individuals). The strategy requires no
knowledge of the node degrees or any other global knowledge, as do targeted
immunization strategies. We study analytically the critical threshold for
complete immunization. We also study the strategy with respect to the
susceptible-infected-removed epidemiological model. We show that the
immunization threshold is dramatically reduced with the suggested strategy, for
all studied cases.Comment: Revtex, 5 pages, 4 ps fig
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