2,572 research outputs found
Congestion-gradient driven transport on complex networks
We present a study of transport on complex networks with routing based on
local information. Particles hop from one node of the network to another
according to a set of routing rules with different degrees of congestion
awareness, ranging from random diffusion to rigid congestion-gradient driven
flow. Each node can be either source or destination for particles and all nodes
have the same routing capacity, which are features of ad-hoc wireless networks.
It is shown that the transport capacity increases when a small amount of
congestion awareness is present in the routing rules, and that it then
decreases as the routing rules become too rigid when the flow becomes strictly
congestion-gradient driven. Therefore, an optimum value of the congestion
awareness exists in the routing rules. It is also shown that, in the limit of a
large number of nodes, networks using routing based on local information jam at
any nonzero load. Finally, we study the correlation between congestion at node
level and a betweenness centrality measure.Comment: 11 pages, 8 figure
Optimal routing on complex networks
We present a novel heuristic algorithm for routing optimization on complex
networks. Previously proposed routing optimization algorithms aim at avoiding
or reducing link overload. Our algorithm balances traffic on a network by
minimizing the maximum node betweenness with as little path lengthening as
possible, thus being useful in cases when networks are jamming due to queuing
overload. By using the resulting routing table, a network can sustain
significantly higher traffic without jamming than in the case of traditional
shortest path routing.Comment: 4 pages, 5 figure
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 complete devil's staircase in the Falicov-Kimball model
We consider the neutral, one-dimensional Falicov-Kimball model at zero
temperature in the limit of a large electron--ion attractive potential, U. By
calculating the general n-ion interaction terms to leading order in 1/U we
argue that the ground-state of the model exhibits the behavior of a complete
devil's staircase.Comment: 6 pages, RevTeX, 3 Postscript figure
Canalization in the Critical States of Highly Connected Networks of Competing Boolean Nodes
Canalization is a classic concept in Developmental Biology that is thought to
be an important feature of evolving systems. In a Boolean network it is a form
of network robustness in which a subset of the input signals control the
behavior of a node regardless of the remaining input. It has been shown that
Boolean networks can become canalized if they evolve through a frustrated
competition between nodes. This was demonstrated for large networks in which
each node had K=3 inputs. Those networks evolve to a critical steady-state at
the boarder of two phases of dynamical behavior. Moreover, the evolution of
these networks was shown to be associated with the symmetry of the evolutionary
dynamics. We extend these results to the more highly connected K>3 cases and
show that similar canalized critical steady states emerge with the same
associated dynamical symmetry, but only if the evolutionary dynamics is biased
toward homogeneous Boolean functions.Comment: 8 pages, 5 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.
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