1,130 research outputs found
Absence of epidemic threshold in scale-free networks with connectivity correlations
Random scale-free networks have the peculiar property of being prone to the
spreading of infections. Here we provide an exact result showing that a
scale-free connectivity distribution with diverging second moment is a
sufficient condition to have null epidemic threshold in unstructured networks
with either assortative or dissortative mixing. Connectivity correlations
result therefore ininfluential for the epidemic spreading picture in these
scale-free networks. The present result is related to the divergence of the
average nearest neighbors connectivity, enforced by the connectivity detailed
balance condition
Breaking of scale-invariance symmetry in adsorption processes
Standard models of sequential adsorption are implicitly formulated in a {\em
scale invariant} form, by assuming adsorption on an infinite surface, with no
characteristic length scales. In real situations, however, involving complex
surfaces, intrinsic length scales may be relevant. We present an analytic model
of continuous random sequential adsorption, in which the scale invariance
symmetry is explicitly broken. The characteristic length is imposed by a set of
scattered obstacles, previously adsorbed onto the surface. We show, by means of
analytic solutions and numerical simulations, the profound effects of the
symmetry breaking on both the jamming limit and the correlation function of the
adsorbed layer.Comment: 7 pages, 2 eps figures, EPL style. Europhys. Lett. (in press
Dipolar interactions induced order in assemblies of magnetic particles
We discuss the appareance of ordered structures in assemblies of magnetic
particles. The phenomenon occurs when dipolar interactions and the thermal
motion of the particles compete, and is mediated by screening and excluded
volume effects. It is observed irrespective of the dimensionality of the system
and the resulting structures, which may be regular or fractal, indicate that
new ordered phases may emerge in these system when dipolar interactions play a
significant role.Comment: 7 pages, 6 EPS figures. Journal of Magnetism and Magnetic Materials
(in press
Epidemic dynamics in finite size scale-free networks
Many real networks present a bounded scale-free behavior with a connectivity
cut-off due to physical constraints or a finite network size. We study epidemic
dynamics in bounded scale-free networks with soft and hard connectivity
cut-offs. The finite size effects introduced by the cut-off induce an epidemic
threshold that approaches zero at increasing sizes. The induced epidemic
threshold is very small even at a relatively small cut-off, showing that the
neglection of connectivity fluctuations in bounded scale-free networks leads to
a strong over-estimation of the epidemic threshold. We provide the expression
for the infection prevalence and discuss its finite size corrections. The
present work shows that the highly heterogeneous nature of scale-free networks
does not allow the use of homogeneous approximations even for systems of a
relatively small number of nodes.Comment: 4 pages, 2 eps figure
Percolation and Epidemic Thresholds in Clustered Networks
We develop a theoretical approach to percolation in random clustered
networks. We find that, although clustering in scale-free networks can strongly
affect some percolation properties, such as the size and the resilience of the
giant connected component, it cannot restore a finite percolation threshold. In
turn, this implies the absence of an epidemic threshold in this class of
networks extending, thus, this result to a wide variety of real scale-free
networks which shows a high level of transitivity. Our findings are in good
agreement with numerical simulations.Comment: 4 Pages and 3 Figures. Final version to appear in PR
The architecture of complex weighted networks
Networked structures arise in a wide array of different contexts such as
technological and transportation infrastructures, social phenomena, and
biological systems. These highly interconnected systems have recently been the
focus of a great deal of attention that has uncovered and characterized their
topological complexity. Along with a complex topological structure, real
networks display a large heterogeneity in the capacity and intensity of the
connections. These features, however, have mainly not been considered in past
studies where links are usually represented as binary states, i.e. either
present or absent. Here, we study the scientific collaboration network and the
world-wide air-transportation network, which are representative examples of
social and large infrastructure systems, respectively. In both cases it is
possible to assign to each edge of the graph a weight proportional to the
intensity or capacity of the connections among the various elements of the
network. We define new appropriate metrics combining weighted and topological
observables that enable us to characterize the complex statistical properties
and heterogeneity of the actual strength of edges and vertices. This
information allows us to investigate for the first time the correlations among
weighted quantities and the underlying topological structure of the network.
These results provide a better description of the hierarchies and
organizational principles at the basis of the architecture of weighted
networks
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