440 research outputs found
Reply to "Comment on 'Universal Behavior of Load Distribution in Scale-Free Networks'"
Reply to "Comment on 'Universal Behavior of Load Distribution in Scale-Free
Networks.'"Comment: 1 page, 1 figur
Velocity and hierarchical spread of epidemic outbreaks in scale-free networks
We study the effect of the connectivity pattern of complex networks on the
propagation dynamics of epidemics. The growth time scale of outbreaks is
inversely proportional to the network degree fluctuations, signaling that
epidemics spread almost instantaneously in networks with scale-free degree
distributions. This feature is associated with an epidemic propagation that
follows a precise hierarchical dynamics. Once the highly connected hubs are
reached, the infection pervades the network in a progressive cascade across
smaller degree classes. The present results are relevant for the development of
adaptive containment strategies.Comment: 4 pages, 4 figures, final versio
Co-evolution of density and topology in a simple model of city formation
We study the influence that population density and the road network have on
each others' growth and evolution. We use a simple model of formation and
evolution of city roads which reproduces the most important empirical features
of street networks in cities. Within this framework, we explicitely introduce
the topology of the road network and analyze how it evolves and interact with
the evolution of population density. We show that accessibility issues -pushing
individuals to get closer to high centrality nodes- lead to high density
regions and the appearance of densely populated centers. In particular, this
model reproduces the empirical fact that the density profile decreases
exponentially from a core district. In this simplified model, the size of the
core district depends on the relative importance of transportation and rent
costs.Comment: 13 pages, 13 figure
Optimal spatial transportation networks where link-costs are sublinear in link-capacity
Consider designing a transportation network on vertices in the plane,
with traffic demand uniform over all source-destination pairs. Suppose the cost
of a link of length and capacity scales as for fixed
. Under appropriate standardization, the cost of the minimum cost
Gilbert network grows essentially as , where on and on . This quantity is an upper bound in
the worst case (of vertex positions), and a lower bound under mild regularity
assumptions. Essentially the same bounds hold if we constrain the network to be
efficient in the sense that average route-length is only times
average straight line length. The transition at corresponds to
the dominant cost contribution changing from short links to long links. The
upper bounds arise in the following type of hierarchical networks, which are
therefore optimal in an order of magnitude sense. On the large scale, use a
sparse Poisson line process to provide long-range links. On the medium scale,
use hierachical routing on the square lattice. On the small scale, link
vertices directly to medium-grid points. We discuss one of many possible
variant models, in which links also have a designed maximum speed and the
cost becomes .Comment: 13 page
Patterns of dominant flows in the world trade web
The large-scale organization of the world economies is exhibiting
increasingly levels of local heterogeneity and global interdependency.
Understanding the relation between local and global features calls for
analytical tools able to uncover the global emerging organization of the
international trade network. Here we analyze the world network of bilateral
trade imbalances and characterize its overall flux organization, unraveling
local and global high-flux pathways that define the backbone of the trade
system. We develop a general procedure capable to progressively filter out in a
consistent and quantitative way the dominant trade channels. This procedure is
completely general and can be applied to any weighted network to detect the
underlying structure of transport flows. The trade fluxes properties of the
world trade web determines a ranking of trade partnerships that highlights
global interdependencies, providing information not accessible by simple local
analysis. The present work provides new quantitative tools for a dynamical
approach to the propagation of economic crises
On the theory of cavities with point-like perturbations. Part I: General theory
The theoretical interpretation of measurements of "wavefunctions" and spectra
in electromagnetic cavities excited by antennas is considered. Assuming that
the characteristic wavelength of the field inside the cavity is much larger
than the radius of the antenna, we describe antennas as "point-like
perturbations". This approach strongly simplifies the problem reducing the
whole information on the antenna to four effective constants. In the framework
of this approach we overcame the divergency of series of the phenomenological
scattering theory and justify assumptions lying at the heart of "wavefunction
measurements". This selfconsistent approach allowed us to go beyond the
one-pole approximation, in particular, to treat the experiments with
degenerated states. The central idea of the approach is to introduce
``renormalized'' Green function, which contains the information on boundary
reflections and has no singularity inside the cavity.Comment: 23 pages, 6 figure
Gravity model in the Korean highway
We investigate the traffic flows of the Korean highway system, which contains
both public and private transportation information. We find that the traffic
flow T(ij) between city i and j forms a gravity model, the metaphor of physical
gravity as described in Newton's law of gravity, P(i)P(j)/r(ij)^2, where P(i)
represents the population of city i and r(ij) the distance between cities i and
j. It is also shown that the highway network has a heavy tail even though the
road network is a rather uniform and homogeneous one. Compared to the highway
network, air and public ground transportation establish inhomogeneous systems
and have power-law behaviors.Comment: 13 page
A universal model for mobility and migration patterns
Introduced in its contemporary form by George Kingsley Zipf in 1946, but with
roots that go back to the work of Gaspard Monge in the 18th century, the
gravity law is the prevailing framework to predict population movement, cargo
shipping volume, inter-city phone calls, as well as bilateral trade flows
between nations. Despite its widespread use, it relies on adjustable parameters
that vary from region to region and suffers from known analytic
inconsistencies. Here we introduce a stochastic process capturing local
mobility decisions that helps us analytically derive commuting and mobility
fluxes that require as input only information on the population distribution.
The resulting radiation model predicts mobility patterns in good agreement with
mobility and transport patterns observed in a wide range of phenomena, from
long-term migration patterns to communication volume between different regions.
Given its parameter-free nature, the model can be applied in areas where we
lack previous mobility measurements, significantly improving the predictive
accuracy of most of phenomena affected by mobility and transport processes.Comment: Main text and supplementary informatio
Two-dimensional SIR epidemics with long range infection
We extend a recent study of susceptible-infected-removed epidemic processes
with long range infection (referred to as I in the following) from
1-dimensional lattices to lattices in two dimensions. As in I we use hashing to
simulate very large lattices for which finite size effects can be neglected, in
spite of the assumed power law for the
probability that a site can infect another site a distance vector
apart. As in I we present detailed results for the critical case, for the
supercritical case with , and for the supercritical case with . For the latter we verify the stretched exponential growth of the
infected cluster with time predicted by M. Biskup. For we find
generic power laws with dependent exponents in the supercritical
phase, but no Kosterlitz-Thouless (KT) like critical point as in 1-d. Instead
of diverging exponentially with the distance from the critical point, the
correlation length increases with an inverse power, as in an ordinary critical
point. Finally we study the dependence of the critical exponents on in
the regime , and compare with field theoretic predictions. In
particular we discuss in detail whether the critical behavior for
slightly less than 2 is in the short range universality class, as conjectured
recently by F. Linder {\it et al.}. As in I we also consider a modified version
of the model where only some of the contacts are long range, the others being
between nearest neighbors. If the number of the latter reaches the percolation
threshold, the critical behavior is changed but the supercritical behavior
stays qualitatively the same.Comment: 14 pages, including 29 figure
Optimal Traffic Networks
Inspired by studies on the airports' network and the physical Internet, we
propose a general model of weighted networks via an optimization principle. The
topology of the optimal network turns out to be a spanning tree that minimizes
a combination of topological and metric quantities. It is characterized by a
strongly heterogeneous traffic, non-trivial correlations between distance and
traffic and a broadly distributed centrality. A clear spatial hierarchical
organization, with local hubs distributing traffic in smaller regions, emerges
as a result of the optimization. Varying the parameters of the cost function,
different classes of trees are recovered, including in particular the minimum
spanning tree and the shortest path tree. These results suggest that a
variational approach represents an alternative and possibly very meaningful
path to the study of the structure of complex weighted networks.Comment: 4 pages, 4 figures, final revised versio
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