11,948 research outputs found
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
The non-linear q-voter model
We introduce a non-linear variant of the voter model, the q-voter model, in
which q neighbors (with possible repetition) are consulted for a voter to
change opinion. If the q neighbors agree, the voter takes their opinion; if
they do not have an unanimous opinion, still a voter can flip its state with
probability . We solve the model on a fully connected network (i.e.
in mean-field) and compute the exit probability as well as the average time to
reach consensus. We analyze the results in the perspective of a recently
proposed Langevin equation aimed at describing generic phase transitions in
systems with two ( symmetric) absorbing states. We find that in mean-field
the q-voter model exhibits a disordered phase for high and an
ordered one for low with three possible ways to go from one to the
other: (i) a unique (generalized voter-like) transition, (ii) a series of two
consecutive Ising-like and directed percolation transition, and (iii) a series
of two transitions, including an intermediate regime in which the final state
depends on initial conditions. This third (so far unexplored) scenario, in
which a new type of ordering dynamics emerges, is rationalized and found to be
specific of mean-field, i.e. fluctuations are explicitly shown to wash it out
in spatially extended systems.Comment: 9 pages, 7 figure
Square-free class sizes in products of groups
We obtain some structural properties of a factorised group , given
that the conjugacy class sizes of certain elements in are not
divisible by , for some prime . The case when is a mutually
permutable product is especially considered
Quasi-chemical approximation for polyatomic mixtures
The statistical thermodynamics of binary mixtures of polyatomic species was
developed on a generalization in the spirit of the lattice-gas model and the
quasi-chemical approximation (QCA). The new theoretical framework is obtained
by combining: (i) the exact analytical expression for the partition function of
non-interacting mixtures of linear -mers and -mers (species occupying
sites and sites, respectively) adsorbed in one dimension, and its extension
to higher dimensions; and (ii) a generalization of the classical QCA for
multicomponent adsorbates and multisite-occupancy adsorption. The process is
analyzed through the partial adsorption isotherms corresponding to both species
of the mixture. Comparisons with analytical data from Bragg-Williams
approximation (BWA) and Monte Carlo simulations are performed in order to test
the validity of the theoretical model. Even though a good fitting is obtained
from BWA, it is found that QCA provides a more accurate description of the
phenomenon of adsorption of interacting polyatomic mixtures.Comment: 27 pages, 8 figure
Mean-field diffusive dynamics on weighted networks
Diffusion is a key element of a large set of phenomena occurring on natural
and social systems modeled in terms of complex weighted networks. Here, we
introduce a general formalism that allows to easily write down mean-field
equations for any diffusive dynamics on weighted networks. We also propose the
concept of annealed weighted networks, in which such equations become exact. We
show the validity of our approach addressing the problem of the random walk
process, pointing out a strong departure of the behavior observed in quenched
real scale-free networks from the mean-field predictions. Additionally, we show
how to employ our formalism for more complex dynamics. Our work sheds light on
mean-field theory on weighted networks and on its range of validity, and warns
about the reliability of mean-field results for complex dynamics.Comment: 8 pages, 3 figure
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
Typical medium theory of Anderson localization: A local order parameter approach to strong disorder effects
We present a self-consistent theory of Anderson localization that yields a
simple algorithm to obtain \emph{typical local density of states} as an order
parameter, thereby reproducing the essential features of a phase-diagram of
localization-delocalization quantum phase transition in the standard lattice
models of disordered electron problem. Due to the local character of our
theory, it can easily be combined with dynamical mean-field approaches to
strongly correlated electrons, thus opening an attractive avenue for a genuine
{\em non-perturbative} treatment of the interplay of strong interactions and
strong disorder.Comment: 7 pages, 4 EPS figures, revised version to appear in Europhysics
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