7,243 research outputs found
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
Letter
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
Glassy behavior of electrons near metal-insulator transitions
The emergence of glassy behavior of electrons is investigated for systems
close to the disorder and/or interaction-driven metal-insulator transitions.
Our results indicate that Anderson localization effects strongly stabilize such
glassy behavior, while Mott localization tends to suppress it. We predict the
emergence of an intermediate metallic glassy phase separating the insulator
from the normal metal. This effect is expected to be most pronounced for
sufficiently disordered systems, in agreement with recent experimental
observations.Comment: Final version as published in Physical Review Letter
Statistical significance of communities in networks
Nodes in real-world networks are usually organized in local modules. These
groups, called communities, are intuitively defined as sub-graphs with a larger
density of internal connections than of external links. In this work, we
introduce a new measure aimed at quantifying the statistical significance of
single communities. Extreme and Order Statistics are used to predict the
statistics associated with individual clusters in random graphs. These
distributions allows us to define one community significance as the probability
that a generic clustering algorithm finds such a group in a random graph. The
method is successfully applied in the case of real-world networks for the
evaluation of the significance of their communities.Comment: 9 pages, 8 figures, 2 tables. The software to calculate the C-score
can be found at http://filrad.homelinux.org/cscor
Interdependent networks with correlated degrees of mutually dependent nodes
We study a problem of failure of two interdependent networks in the case of
correlated degrees of mutually dependent nodes. We assume that both networks (A
and B) have the same number of nodes connected by the bidirectional
dependency links establishing a one-to-one correspondence between the nodes of
the two networks in a such a way that the mutually dependent nodes have the
same number of connectivity links, i.e. their degrees coincide. This implies
that both networks have the same degree distribution . We call such
networks correspondently coupled networks (CCN). We assume that the nodes in
each network are randomly connected. We define the mutually connected clusters
and the mutual giant component as in earlier works on randomly coupled
interdependent networks and assume that only the nodes which belong to the
mutual giant component remain functional. We assume that initially a
fraction of nodes are randomly removed due to an attack or failure and find
analytically, for an arbitrary , the fraction of nodes which
belong to the mutual giant component. We find that the system undergoes a
percolation transition at certain fraction which is always smaller than
the for randomly coupled networks with the same . We also find that
the system undergoes a first order transition at if has a finite
second moment. For the case of scale free networks with , the
transition becomes a second order transition. Moreover, if we find
as in percolation of a single network. For we find an exact
analytical expression for . Finally, we find that the robustness of CCN
increases with the broadness of their degree distribution.Comment: 18 pages, 3 figure
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Smarter than humans: rationality reflected in primate neuronal reward signals
Rational choice, in all its definitions by various disciplines, allows agents to maximize utility. Formal axioms and simple choice designs are suitable for assessing rationality in monkeys. Their economic preferences are complete and transitive; the dopamine signal follows transitivity. Dopamine signals also satisfy first-order stochastic dominance that unequivocally defines the better option. Neurons in orbitofrontal cortex (OFC) reflect the unchanged preferences when an irrelevant option is removed from the option set, thus satisfying Arrow’s Weak Axiom of Revealed Preference (WARP) concerning the Independence of Irrelevant Alternatives (IIA). While monkeys, with their reward neurons, may not be more rational than humans, the constraints of controlled experiments seem to allow them to behave rationally within their informational, cognitive and temporal bounds
Voter models on weighted networks
We study the dynamics of the voter and Moran processes running on top of
complex network substrates where each edge has a weight depending on the degree
of the nodes it connects. For each elementary dynamical step the first node is
chosen at random and the second is selected with probability proportional to
the weight of the connecting edge. We present a heterogeneous mean-field
approach allowing to identify conservation laws and to calculate exit
probabilities along with consensus times. In the specific case when the weight
is given by the product of nodes' degree raised to a power theta, we derive a
rich phase-diagram, with the consensus time exhibiting various scaling laws
depending on theta and on the exponent of the degree distribution gamma.
Numerical simulations give very good agreement for small values of |theta|. An
additional analytical treatment (heterogeneous pair approximation) improves the
agreement with numerics, but the theoretical understanding of the behavior in
the limit of large |theta| remains an open challenge.Comment: 21 double-spaced pages, 6 figure
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Determination of biomembrane bending moduli in fully atomistic simulations.
The bilayer bending modulus (Kc) is one of the most important physical constants characterizing lipid membranes, but precisely measuring it is a challenge, both experimentally and computationally. Experimental measurements on chemically identical bilayers often differ depending upon the techniques employed, and robust simulation results have previously been limited to coarse-grained models (at varying levels of resolution). This Communication demonstrates the extraction of Kc from fully atomistic molecular dynamics simulations for three different single-component lipid bilayers (DPPC, DOPC, and DOPE). The results agree quantitatively with experiments that measure thermal shape fluctuations in giant unilamellar vesicles. Lipid tilt, twist, and compression moduli are also reported
Corrections to scaling in the forest-fire model
We present a systematic study of corrections to scaling in the self-organized
critical forest-fire model. The analysis of the steady-state condition for the
density of trees allows us to pinpoint the presence of these corrections, which
take the form of subdominant exponents modifying the standard finite-size
scaling form. Applying an extended version of the moment analysis technique, we
find the scaling region of the model and compute the first non-trivial
corrections to scaling.Comment: RevTeX, 7 pages, 7 eps figure
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