28,993 research outputs found
A simple asymmetric evolving random network
We introduce a new oriented evolving graph model inspired by biological
networks. A node is added at each time step and is connected to the rest of the
graph by random oriented edges emerging from older nodes. This leads to a
statistical asymmetry between incoming and outgoing edges. We show that the
model exhibits a percolation transition and discuss its universality. Below the
threshold, the distribution of component sizes decreases algebraically with a
continuously varying exponent depending on the average connectivity. We prove
that the transition is of infinite order by deriving the exact asymptotic
formula for the size of the giant component close to the threshold. We also
present a thorough analysis of aging properties. We compute local-in-time
profiles for the components of finite size and for the giant component, showing
in particular that the giant component is always dense among the oldest nodes
but invades only an exponentially small fraction of the young nodes close to
the threshold.Comment: 33 pages, 3 figures, to appear in J. Stat. Phy
Transport on complex networks: Flow, jamming and optimization
Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we address this question by using numerical models in which both structure and dynamics are controlled systematically. We consider the traffic of information packets that include driving, searching and queuing. We present the results of extensive simulations on two classes of networks; a correlated cyclic scale-free network and an uncorrelated homogeneous weakly clustered network. By measuring different dynamical variables in the free flow regime we show how the global statistical properties of the transport are related to the temporal fluctuations at individual nodes (the traffic noise) and the links (the traffic flow). We then demonstrate that these two network classes appear as representative topologies for optimal traffic flow in the regimes of low density and high density traffic, respectively. We also determine statistical indicators of the pre-jamming regime on different network geometries and discuss the role of queuing and dynamical betweenness for the traffic congestion. The transition to the jammed traffic regime at a critical posting rate on different network topologies is studied as a phase transition with an appropriate order parameter. We also address several open theoretical problems related to the network dynamics
Optimal Resource Allocation in Random Networks with Transportation Bandwidths
We apply statistical physics to study the task of resource allocation in
random sparse networks with limited bandwidths for the transportation of
resources along the links. Useful algorithms are obtained from recursive
relations. Bottlenecks emerge when the bandwidths are small, causing an
increase in the fraction of idle links. For a given total bandwidth per node,
the efficiency of allocation increases with the network connectivity. In the
high connectivity limit, we find a phase transition at a critical bandwidth,
above which clusters of balanced nodes appear, characterised by a profile of
homogenized resource allocation similar to the Maxwell's construction.Comment: 28 pages, 11 figure
The spectral dimension of random trees
We present a simple yet rigorous approach to the determination of the
spectral dimension of random trees, based on the study of the massless limit of
the Gaussian model on such trees. As a byproduct, we obtain evidence in favor
of a new scaling hypothesis for the Gaussian model on generic bounded graphs
and in favor of a previously conjectured exact relation between spectral and
connectivity dimensions on more general tree-like structures.Comment: 14 pages, 2 eps figures, revtex4. Revised version: changes in section
I
The Organization and Control of an Evolving Interdependent Population
Starting with Darwin, biologists have asked how populations evolve from a low
fitness state that is evolutionarily stable to a high fitness state that is
not. Specifically of interest is the emergence of cooperation and
multicellularity where the fitness of individuals often appears in conflict
with that of the population. Theories of social evolution and evolutionary game
theory have produced a number of fruitful results employing two-state two-body
frameworks. In this study we depart from this tradition and instead consider a
multi-player, multi-state evolutionary game, in which the fitness of an agent
is determined by its relationship to an arbitrary number of other agents. We
show that populations organize themselves in one of four distinct phases of
interdependence depending on one parameter, selection strength. Some of these
phases involve the formation of specialized large-scale structures. We then
describe how the evolution of independence can be manipulated through various
external perturbations.Comment: To download simulation code cf. article in Proceedings of the Royal
Society, Interfac
Modeling of the Acute Toxicity of Benzene Derivatives by Complementary QSAR Methods
A data set containing acute toxicity values (96-h LC50) of 69 substituted benzenes for
fathead minnow (Pimephales promelas) was investigated with two Quantitative Structure-
Activity Relationship (QSAR) models, either using or not using molecular descriptors,
respectively. Recursive Neural Networks (RNN) derive a QSAR by direct treatment of the
molecular structure, described through an appropriate graphical tool (variable-size labeled
rooted ordered trees) by defining suitable representation rules. The input trees are encoded by
an adaptive process able to learn, by tuning its free parameters, from a given set of structureactivity
training examples. Owing to the use of a flexible encoding approach, the model is
target invariant and does not need a priori definition of molecular descriptors. The results
obtained in this study were analyzed together with those of a model based on molecular
descriptors, i.e. a Multiple Linear Regression (MLR) model using CROatian MultiRegression
selection of descriptors (CROMRsel). The comparison revealed interesting similarities that
could lead to the development of a combined approach, exploiting the complementary
characteristics of the two approaches
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