56,320 research outputs found
Analysis and perturbation of degree correlation in complex networks
Degree correlation is an important topological property common to many
real-world networks. In this paper, the statistical measures for characterizing
the degree correlation in networks are investigated analytically. We give an
exact proof of the consistency for the statistical measures, reveal the general
linear relation in the degree correlation, which provide a simple and
interesting perspective on the analysis of the degree correlation in complex
networks. By using the general linear analysis, we investigate the perturbation
of the degree correlation in complex networks caused by the addition of few
nodes and the rich club. The results show that the assortativity of homogeneous
networks such as the ER graphs is easily to be affected strongly by the simple
structural changes, while it has only slight variation for heterogeneous
networks with broad degree distribution such as the scale-free networks.
Clearly, the homogeneous networks are more sensitive for the perturbation than
the heterogeneous networks.Comment: 5 pages, 4 figure
Increased signaling entropy in cancer requires the scale-free property of protein interaction networks
One of the key characteristics of cancer cells is an increased phenotypic
plasticity, driven by underlying genetic and epigenetic perturbations. However,
at a systems-level it is unclear how these perturbations give rise to the
observed increased plasticity. Elucidating such systems-level principles is key
for an improved understanding of cancer. Recently, it has been shown that
signaling entropy, an overall measure of signaling pathway promiscuity, and
computable from integrating a sample's gene expression profile with a protein
interaction network, correlates with phenotypic plasticity and is increased in
cancer compared to normal tissue. Here we develop a computational framework for
studying the effects of network perturbations on signaling entropy. We
demonstrate that the increased signaling entropy of cancer is driven by two
factors: (i) the scale-free (or near scale-free) topology of the interaction
network, and (ii) a subtle positive correlation between differential gene
expression and node connectivity. Indeed, we show that if protein interaction
networks were random graphs, described by Poisson degree distributions, that
cancer would generally not exhibit an increased signaling entropy. In summary,
this work exposes a deep connection between cancer, signaling entropy and
interaction network topology.Comment: 20 pages, 5 figures. In Press in Sci Rep 201
Networks from gene expression time series: characterization of correlation patterns
This paper describes characteristic features of networks reconstructed from
gene expression time series data. Several null models are considered in order
to discriminate between informations embedded in the network that are related
to real data, and features that are due to the method used for network
reconstruction (time correlation).Comment: 10 pages, 3 BMP figures, 1 Table. To appear in Int. J. Bif. Chaos,
July 2007, Volume 17, Issue
The statistical mechanics of networks
We study the family of network models derived by requiring the expected
properties of a graph ensemble to match a given set of measurements of a
real-world network, while maximizing the entropy of the ensemble. Models of
this type play the same role in the study of networks as is played by the
Boltzmann distribution in classical statistical mechanics; they offer the best
prediction of network properties subject to the constraints imposed by a given
set of observations. We give exact solutions of models within this class that
incorporate arbitrary degree distributions and arbitrary but independent edge
probabilities. We also discuss some more complex examples with correlated edges
that can be solved approximately or exactly by adapting various familiar
methods, including mean-field theory, perturbation theory, and saddle-point
expansions.Comment: 15 pages, 4 figure
Self-organization of network dynamics into local quantized states
Self-organization and pattern formation in network-organized systems emerges
from the collective activation and interaction of many interconnected units. A
striking feature of these non-equilibrium structures is that they are often
localized and robust: only a small subset of the nodes, or cell assembly, is
activated. Understanding the role of cell assemblies as basic functional units
in neural networks and socio-technical systems emerges as a fundamental
challenge in network theory. A key open question is how these elementary
building blocks emerge, and how they operate, linking structure and function in
complex networks. Here we show that a network analogue of the Swift-Hohenberg
continuum model---a minimal-ingredients model of nodal activation and
interaction within a complex network---is able to produce a complex suite of
localized patterns. Hence, the spontaneous formation of robust operational cell
assemblies in complex networks can be explained as the result of
self-organization, even in the absence of synaptic reinforcements. Our results
show that these self-organized, local structures can provide robust functional
units to understand natural and socio-technical network-organized processes.Comment: 11 pages, 4 figure
Quantifying the connectivity of a network: The network correlation function method
Networks are useful for describing systems of interacting objects, where the
nodes represent the objects and the edges represent the interactions between
them. The applications include chemical and metabolic systems, food webs as
well as social networks. Lately, it was found that many of these networks
display some common topological features, such as high clustering, small
average path length (small world networks) and a power-law degree distribution
(scale free networks). The topological features of a network are commonly
related to the network's functionality. However, the topology alone does not
account for the nature of the interactions in the network and their strength.
Here we introduce a method for evaluating the correlations between pairs of
nodes in the network. These correlations depend both on the topology and on the
functionality of the network. A network with high connectivity displays strong
correlations between its interacting nodes and thus features small-world
functionality. We quantify the correlations between all pairs of nodes in the
network, and express them as matrix elements in the correlation matrix. From
this information one can plot the correlation function for the network and to
extract the correlation length. The connectivity of a network is then defined
as the ratio between this correlation length and the average path length of the
network. Using this method we distinguish between a topological small world and
a functional small world, where the latter is characterized by long range
correlations and high connectivity. Clearly, networks which share the same
topology, may have different connectivities, based on the nature and strength
of their interactions. The method is demonstrated on metabolic networks, but
can be readily generalized to other types of networks.Comment: 10 figure
Interregional synchrony of visuomotor tracking: perturbation effects and individual differences
The present study evaluated the neural and behavioural correlates associated with a visuomotor tracking task during which a sensory perturbation was introduced that created a directional bias between moving hand and cursor position. The results revealed that trajectory error increased as a result of the perturbation in conjunction with a dynamic neural reorganization of cluster patterns that reflected distinct processing. In particular, a negatively activated cluster, characterizing the degraded information processing due to the perturbation, involved both hemispheres as well as midline area. Conversely, a positively activated cluster, indicative of compensatory processing was strongly confined to the left (dominant) hemisphere. In addition, a brain-behavioural association of good vs. poor performing participants enabled to localize a neural circuit within the left hemisphere and midline area that linked with successful performance. Overall, these data reinforce the functional significance of interregional synchrony in defining response output and behavioural success
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