2,009 research outputs found
Transport optimization on complex networks
We present a comparative study of the application of a recently introduced
heuristic algorithm to the optimization of transport on three major types of
complex networks. The algorithm balances network traffic iteratively by
minimizing the maximum node betweenness with as little path lengthening as
possible. We show that by using this optimal routing, a network can sustain
significantly higher traffic without jamming than in the case of shortest path
routing. A formula is proved that allows quick computation of the average
number of hops along the path and of the average travel times once the
betweennesses of the nodes are computed. Using this formula, we show that
routing optimization preserves the small-world character exhibited by networks
under shortest path routing, and that it significantly reduces the average
travel time on congested networks with only a negligible increase in the
average travel time at low loads. Finally, we study the correlation between the
weights of the links in the case of optimal routing and the betweennesses of
the nodes connected by them.Comment: 19 pages, 7 figure
Optimal transport on wireless networks
We present a study of the application of a variant of a recently introduced
heuristic algorithm for the optimization of transport routes on complex
networks to the problem of finding the optimal routes of communication between
nodes on wireless networks. Our algorithm iteratively balances network traffic
by minimizing the maximum node betweenness on the network. The variant we
consider specifically accounts for the broadcast restrictions imposed by
wireless communication by using a different betweenness measure. We compare the
performance of our algorithm to two other known algorithms and find that our
algorithm achieves the highest transport capacity both for minimum node degree
geometric networks, which are directed geometric networks that model wireless
communication networks, and for configuration model networks that are
uncorrelated scale-free networks.Comment: 5 pages, 4 figure
A stochastic spectral analysis of transcriptional regulatory cascades
The past decade has seen great advances in our understanding of the role of
noise in gene regulation and the physical limits to signaling in biological
networks. Here we introduce the spectral method for computation of the joint
probability distribution over all species in a biological network. The spectral
method exploits the natural eigenfunctions of the master equation of
birth-death processes to solve for the joint distribution of modules within the
network, which then inform each other and facilitate calculation of the entire
joint distribution. We illustrate the method on a ubiquitous case in nature:
linear regulatory cascades. The efficiency of the method makes possible
numerical optimization of the input and regulatory parameters, revealing design
properties of, e.g., the most informative cascades. We find, for threshold
regulation, that a cascade of strong regulations converts a unimodal input to a
bimodal output, that multimodal inputs are no more informative than bimodal
inputs, and that a chain of up-regulations outperforms a chain of
down-regulations. We anticipate that this numerical approach may be useful for
modeling noise in a variety of small network topologies in biology
Canalization and Symmetry in Boolean Models for Genetic Regulatory Networks
Canalization of genetic regulatory networks has been argued to be favored by
evolutionary processes due to the stability that it can confer to phenotype
expression. We explore whether a significant amount of canalization and partial
canalization can arise in purely random networks in the absence of evolutionary
pressures. We use a mapping of the Boolean functions in the Kauffman N-K model
for genetic regulatory networks onto a k-dimensional Ising hypercube to show
that the functions can be divided into different classes strictly due to
geometrical constraints. The classes can be counted and their properties
determined using results from group theory and isomer chemistry. We demonstrate
that partially canalized functions completely dominate all possible Boolean
functions, particularly for higher k. This indicates that partial canalization
is extremely common, even in randomly chosen networks, and has implications for
how much information can be obtained in experiments on native state genetic
regulatory networks.Comment: 14 pages, 4 figures; version to appear in J. Phys.
Mean-Field Analysis and Monte Carlo Study of an Interacting Two-Species Catalytic Surface Reaction Model
We study the phase diagram and critical behavior of an interacting one
dimensional two species monomer-monomer catalytic surface reaction model with a
reactive phase as well as two equivalent adsorbing phase where one of the
species saturates the system. A mean field analysis including correlations up
to triplets of sites fails to reproduce the phase diagram found by Monte Carlo
simulations. The three phases coexist at a bicritical point whose critical
behavior is described by the even branching annihilating random walk
universality class. This work confirms the hypothesis that the conservation
modulo 2 of the domain walls under the dynamics at the bicritical point is the
essential feature in producing critical behavior different from directed
percolation. The interfacial fluctuations show the same universal behavior seen
at the bicritical point in a three-species model, supporting the conjecture
that these fluctuations are a new universal characteristic of the model.Comment: 11 pages using RevTeX, plus 4 Postscript figures. Uses psfig.st
Interacting Monomer-Dimer Model with Infinitely Many Absorbing States
We study a modified version of the interacting monomer-dimer (IMD) model that
has infinitely many absorbing (IMA) states. Unlike all other previously studied
models with IMA states, the absorbing states can be divided into two equivalent
groups which are dynamically separated infinitely far apart. Monte Carlo
simulations show that this model belongs to the directed Ising universality
class like the ordinary IMD model with two equivalent absorbing states. This
model is the first model with IMA states which does not belong to the directed
percolation (DP) universality class. The DP universality class can be restored
in two ways, i.e., by connecting the two equivalent groups dynamically or by
introducing a symmetry-breaking field between the two groups.Comment: 5 pages, 5 figure
Braided Rivers and Superconducting Vortex Avalanches
Magnetic vortices intermittently flow through preferred channels when they
are forced in or out of a superconductor. We study this behavior using a
cellular model, and find that the vortex flow can make braided rivers
strikingly similar to aerial photographs of braided fluvial rivers, such as the
Brahmaputra. By developing an analysis technique suitable for characterizing a
self-affine (multi)fractal, the scaling properties of the braided vortex rivers
in the model are compared with those of braided fluvial rivers. We suggest that
avalanche dynamics leads to braiding in both cases.Comment: 4 pages, 3 figures. To appear in PR
Dynamics-dependent criticality in models with q absorbing states
We study a one-dimensional, nonequilibrium Potts-like model which has
symmetric absorbing states. For , as expected, the model belongs to the
parity conserving universality class. For the critical behaviour depends
on the dynamics of the model. Under a certain dynamics it remains generically
in the active phase, which is also the feature of some other models with three
absorbing states. However, a modified dynamics induces a parity conserving
phase transition. Relations with branching-annihilating random walk models are
discussed in order to explain such a behaviour.Comment: 5 pages, 5 eps figures included, Phys.Rev.E (accepted
Damage spreading for one-dimensional, non-equilibrium models with parity conserving phase transitions
The damage spreading (DS) transitions of two one-dimensional stochastic
cellular automata suggested by Grassberger (A and B) and the kinetic Ising
model of Menyh\'ard (NEKIM) have been investigated on the level of kinks and
spins. On the level of spins the parity conservation is not satisfied and
therefore studying these models provides a convenient tool to understand the
dependence of DS properties on symmetries. For the model B the critical point
and the DS transition point is well separated and directed percolation damage
spreading transition universality was found for spin damage as well as for kink
damage in spite of the conservation of damage variables modulo 2 in the latter
case. For the A stochastic cellular automaton, and the NEKIM model the two
transition points coincide with drastic effects on the damage of spin and kink
variables showing different time dependent behaviours. While the kink DS
transition is continuous and shows regular PC class universality, the spin
damage exhibits a discontinuous phase transition with compact clusters and PC
like dynamical scaling (), () and () exponents whereas
the static exponents determined by FSS are consistent with that of the spins of
the NEKIM model at the PC transition point. The generalised hyper-scaling law
is satisfied.Comment: 11 pages, 20 figures embedded in the text, minor changes in the text,
a new table and new references are adde
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