1,399 research outputs found
Dynamic rewiring in small world networks
We investigate equilibrium properties of small world networks, in which both
connectivity and spin variables are dynamic, using replicated transfer matrices
within the replica symmetric approximation. Population dynamics techniques
allow us to examine order parameters of our system at total equilibrium,
probing both spin- and graph-statistics. Of these, interestingly, the degree
distribution is found to acquire a Poisson-like form (both within and outside
the ordered phase). Comparison with Glauber simulations confirms our results
satisfactorily.Comment: 21 pages, 5 figure
A network-based threshold model for the spreading of fads in society and markets
We investigate the behavior of a threshold model for the spreading of fads
and similar phenomena in society. The model is giving the fad dynamics and is
intended to be confined to an underlying network structure. We investigate the
whole parameter space of the fad dynamics on three types of network models. The
dynamics we discover is rich and highly dependent on the underlying network
structure. For some range of the parameter space, for all types of substrate
networks, there are a great variety of sizes and life-lengths of the fads --
what one see in real-world social and economical systems
Quantum computing of delocalization in small-world networks
We study a quantum small-world network with disorder and show that the system
exhibits a delocalization transition. A quantum algorithm is built up which
simulates the evolution operator of the model in a polynomial number of gates
for exponential number of vertices in the network. The total computational gain
is shown to depend on the parameters of the network and a larger than quadratic
speed-up can be reached.
We also investigate the robustness of the algorithm in presence of
imperfections.Comment: 4 pages, 5 figures, research done at
http://www.quantware.ups-tlse.fr
CONTEST : a Controllable Test Matrix Toolbox for MATLAB
Large, sparse networks that describe complex interactions are a common feature across a number of disciplines, giving rise to many challenging matrix computational tasks. Several random graph models have been proposed that capture key properties of real-life networks. These models provide realistic, parametrized matrices for testing linear system and eigenvalue solvers. CONTEST (CONtrollable TEST matrices) is a random network toolbox for MATLAB that implements nine models. The models produce unweighted directed or undirected graphs; that is, symmetric or unsymmetric matrices with elements equal to zero or one. They have one or more parameters that affect features such as sparsity and characteristic pathlength and all can be of arbitrary dimension. Utility functions are supplied for rewiring, adding extra shortcuts and subsampling in order to create further classes of networks. Other utilities convert the adjacency matrices into real-valued coefficient matrices for naturally arising computational tasks that reduce to sparse linear system and eigenvalue problems
Optimization in task--completion networks
We discuss the collective behavior of a network of individuals that receive,
process and forward to each other tasks. Given costs they store those tasks in
buffers, choosing optimally the frequency at which to check and process the
buffer. The individual optimizing strategy of each node determines the
aggregate behavior of the network. We find that, under general assumptions, the
whole system exhibits coexistence of equilibria and hysteresis.Comment: 18 pages, 3 figures, submitted to JSTA
Information Horizons in Networks
We investigate and quantify the interplay between topology and ability to
send specific signals in complex networks. We find that in a majority of
investigated real-world networks the ability to communicate is favored by the
network topology on small distances, but disfavored at larger distances. We
further discuss how the ability to locate specific nodes can be improved if
information associated to the overall traffic in the network is available.Comment: Submitted top PR
Preferencial growth: exact solution of the time dependent distributions
We consider a preferential growth model where particles are added one by one
to the system consisting of clusters of particles. A new particle can either
form a new cluster (with probability q) or join an already existing cluster
with a probability proportional to the size thereof. We calculate exactly the
probability \Pm_i(k,t) that the size of the i-th cluster at time t is k. We
analyze the asymptotics, the scaling properties of the size distribution and of
the mean size as well as the relation of our system to recent network models.Comment: 8 pages, 4 figure
Epidemics and percolation in small-world networks
We study some simple models of disease transmission on small-world networks,
in which either the probability of infection by a disease or the probability of
its transmission is varied, or both. The resulting models display epidemic
behavior when the infection or transmission probability rises above the
threshold for site or bond percolation on the network, and we give exact
solutions for the position of this threshold in a variety of cases. We confirm
our analytic results by numerical simulation.Comment: 6 pages, including 3 postscript figure
Hawks and Doves on Small-World Networks
We explore the Hawk-Dove game on networks with topologies ranging from
regular lattices to random graphs with small-world networks in between. This is
done by means of computer simulations using several update rules for the
population evolutionary dynamics. We find the overall result that cooperation
is sometimes inhibited and sometimes enhanced in those network structures, with
respect to the mixing population case. The differences are due to different
update rules and depend on the gain-to-cost ratio. We analyse and qualitatively
explain this behavior by using local topological arguments.Comment: 12 pages, 8 figure
Asymptotic behavior of the Kleinberg model
We study Kleinberg navigation (the search of a target in a d-dimensional
lattice, where each site is connected to one other random site at distance r,
with probability proportional to r^{-a}) by means of an exact master equation
for the process. We show that the asymptotic scaling behavior for the delivery
time T to a target at distance L scales as (ln L)^2 when a=d, and otherwise as
L^x, with x=(d-a)/(d+1-a) for ad+1. These
values of x exceed the rigorous lower-bounds established by Kleinberg. We also
address the situation where there is a finite probability for the message to
get lost along its way and find short delivery times (conditioned upon arrival)
for a wide range of a's
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