2,212 research outputs found
Local heuristics and the emergence of spanning subgraphs in complex networks
We study the use of local heuristics to determine spanning subgraphs for use
in the dissemination of information in complex networks. We introduce two
different heuristics and analyze their behavior in giving rise to spanning
subgraphs that perform well in terms of allowing every node of the network to
be reached, of requiring relatively few messages and small node bandwidth for
information dissemination, and also of stretching paths with respect to the
underlying network only modestly. We contribute a detailed mathematical
analysis of one of the heuristics and provide extensive simulation results on
random graphs for both of them. These results indicate that, within certain
limits, spanning subgraphs are indeed expected to emerge that perform well in
respect to all requirements. We also discuss the spanning subgraphs' inherent
resilience to failures and adaptability to topological changes
Probabilistic heuristics for disseminating information in networks
We study the problem of disseminating a piece of information through all the
nodes of a network, given that it is known originally only to a single node. In
the absence of any structural knowledge on the network other than the nodes'
neighborhoods, this problem is traditionally solved by flooding all the
network's edges. We analyze a recently introduced probabilistic algorithm for
flooding and give an alternative probabilistic heuristic that can lead to some
cost-effective improvements, like better trade-offs between the message and
time complexities involved. We analyze the two algorithms both mathematically
and by means of simulations, always within a random-graph framework and
considering relevant node-degree distributions
Nonmonotonic External Field Dependence of the Magnetization in a Finite Ising Model: Theory and MC Simulation
Using field theory and Monte Carlo (MC) simulation we investigate
the finite-size effects of the magnetization for the three-dimensional
Ising model in a finite cubic geometry with periodic boundary conditions. The
field theory with infinite cutoff gives a scaling form of the equation of state
where
is the reduced temperature, is the external field and
is the size of system. Below and at the theory predicts a
nonmonotonic dependence of with respect to at fixed and a crossover
from nonmonotonic to monotonic behaviour when is further increased. These
results are confirmed by MC simulation. The scaling function obtained
from the field theory is in good quantitative agreement with the finite-size MC
data. Good agreement is also found for the bulk value at .Comment: LaTex, 12 page
Percolation transition in networks with degree-degree correlation
We introduce an exponential random graph model for networks with a fixed
degree distribution and with a tunable degree-degree correlation. We then
investigate the nature of a percolation transition in the correlated network
with the Poisson degree distribution. It is found that negative correlation is
irrelevant in that the percolation transition in the disassortative network
belongs to the same universality class of the uncorrelated network. Positive
correlation turns out to be relevant. The percolation transition in the
assortative network is characterized by the non-diverging mean size of finite
clusters and power-law scalings of the density of the largest cluster and the
cluster size distribution in the non-percolating phase as well as at the
critical point. Our results suggest that the unusual type percolation
transition in the growing network models reported recently may be inherited
from the assortative degree-degree correlation.Comment: 7 pages, 11 figur
Number of spanning clusters at the high-dimensional percolation thresholds
A scaling theory is used to derive the dependence of the average number
of spanning clusters at threshold on the lattice size L. This number should
become independent of L for dimensions d<6, and vary as log L at d=6. The
predictions for d>6 depend on the boundary conditions, and the results there
may vary between L^{d-6} and L^0. While simulations in six dimensions are
consistent with this prediction (after including corrections of order loglog
L), in five dimensions the average number of spanning clusters still increases
as log L even up to L = 201. However, the histogram P(k) of the spanning
cluster multiplicity does scale as a function of kX(L), with X(L)=1+const/L,
indicating that for sufficiently large L the average will approach a finite
value: a fit of the 5D multiplicity data with a constant plus a simple linear
correction to scaling reproduces the data very well. Numerical simulations for
d>6 and for d=4 are also presented.Comment: 8 pages, 11 figures. Final version to appear on Physical Review
Colloids with key-lock interactions: non-exponential relaxation, aging and anomalous diffusion
The dynamics of particles interacting by key-lock binding of attached
biomolecules are studied theoretically. Experimental realizations of such
systems include colloids grafted with complementary single-stranded DNA
(ssDNA), and particles grafted with antibodies to cell-membrane proteins.
Depending on the coverage of the functional groups, we predict two distinct
regimes. In the low coverage localized regime, there is an exponential
distribution of departure times. As the coverage is increased the system enters
a diffusive regime resulting from the interplay of particle desorption and
diffusion. This interplay leads to much longer bound state lifetimes, a
phenomenon qualitatively similar to aging in glassy systems. The diffusion
behavior is analogous to dispersive transport in disordered semiconductors:
depending on the interaction parameters it may range from a finite
renormalization of the diffusion coefficient to anomalous, subdiffusive
behavior. We make connections to recent experiments and discuss the
implications for future studies.Comment: v2: substantially revised version, new treatment of localized regime,
19 pages, 10 figure
Model for Anisotropic Directed Percolation
We propose a simulation model to study the properties of directed percolation
in two-dimensional (2D) anisotropic random media. The degree of anisotropy in
the model is given by the ratio between the axes of a semi-ellipse
enclosing the bonds that promote percolation in one direction. At percolation,
this simple model shows that the average number of bonds per site in 2D is an
invariant equal to 2.8 independently of . This result suggests that
Sinai's theorem proposed originally for isotropic percolation is also valid for
anisotropic directed percolation problems. The new invariant also yields a
constant fractal dimension for all , which is the same
value found in isotropic directed percolation (i.e., ).Comment: RevTeX, 9 pages, 3 figures. To appear in Phys.Rev.
Crossover transition in bag-like models
We formulate a simple model for a gas of extended hadrons at zero chemical
potential by taking inspiration from the compressible bag model. We show that a
crossover transition qualitatively similar to lattice QCD can be reproduced by
such a system by including some appropriate additional dynamics. Under certain
conditions, at high temperature, the system consist of a finite number of
infinitely extended bags, which occupy the entire space. In this situation the
system behaves as an ideal gas of quarks and gluons.Comment: Corresponds to the published version. Added few references and
changed the titl
Distribution of averages in a correlated Gaussian medium as a tool for the estimation of the cluster distribution on size
Calculation of the distribution of the average value of a Gaussian random
field in a finite domain is carried out for different cases. The results of the
calculation demonstrate a strong dependence of the width of the distribution on
the spatial correlations of the field. Comparison with the simulation results
for the distribution of the size of the cluster indicates that the distribution
of an average field could serve as a useful tool for the estimation of the
asymptotic behavior of the distribution of the size of the clusters for "deep"
clusters where value of the field on each site is much greater than the rms
disorder.Comment: 15 pages, 6 figures, RevTe
Scaling of cluster heterogeneity in percolation transitions
We investigate a critical scaling law for the cluster heterogeneity in
site and bond percolations in -dimensional lattices with . The
cluster heterogeneity is defined as the number of distinct cluster sizes. As an
occupation probability increases, the cluster size distribution evolves
from a monodisperse distribution to a polydisperse one in the subcritical
phase, and back to a monodisperse one in the supercritical phase. We show
analytically that diverges algebraically approaching the percolation
critical point as with the critical exponent
associated with the characteristic cluster size. Interestingly, its
finite-size-scaling behavior is governed by a new exponent where is the fractal dimension of the critical percolating
cluster and is the correlation length exponent. The corresponding scaling
variable defines a singular path to the critical point. All results are
confirmed by numerical simulations.Comment: 4 pages, 4 figure
- …