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## Neutral stability, rate propagation, and critical branching in feedforward networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 31/10/2012
Português

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Recent experimental and computational evidence suggests that several
dynamical properties may characterize the operating point of functioning neural
networks: critical branching, neutral stability, and production of a wide range
of firing patterns. We seek the simplest setting in which these properties
emerge, clarifying their origin and relationship in random, feedforward
networks of McCullochs-Pitts neurons. Two key parameters are the thresholds at
which neurons fire spikes, and the overall level of feedforward connectivity.
When neurons have low thresholds, we show that there is always a connectivity
for which the properties in question all occur: that is, these networks
preserve overall firing rates from layer to layer and produce broad
distributions of activity in each layer. This fails to occur, however, when
neurons have high thresholds. A key tool in explaining this difference is
eigenstructure of the resulting mean-field Markov chain, as this reveals which
activity modes will be preserved from layer to layer. We extend our analysis
from purely excitatory networks to more complex models that include inhibition
and 'local' noise, and find that both of these features extend the parameter
ranges over which networks produce the properties of interest.

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## Evolving networks in the human epileptic brain

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/09/2013
Português

Relevância na Pesquisa

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#Quantitative Biology - Neurons and Cognition#Physics - Data Analysis, Statistics and Probability#Physics - Medical Physics

Network theory provides novel concepts that promise an improved
characterization of interacting dynamical systems. Within this framework,
evolving networks can be considered as being composed of nodes, representing
systems, and of time-varying edges, representing interactions between these
systems. This approach is highly attractive to further our understanding of the
physiological and pathophysiological dynamics in human brain networks. Indeed,
there is growing evidence that the epileptic process can be regarded as a
large-scale network phenomenon. We here review methodologies for inferring
networks from empirical time series and for a characterization of these
evolving networks. We summarize recent findings derived from studies that
investigate human epileptic brain networks evolving on timescales ranging from
few seconds to weeks. We point to possible pitfalls and open issues, and
discuss future perspectives.; Comment: In press (Physica D)

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## An Analytical Approach to Connectivity in Regular Neuronal Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 28/10/2003
Português

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#Condensed Matter - Disordered Systems and Neural Networks#Quantitative Biology - Neurons and Cognition

This paper describes how realistic neuromorphic networks can have their
connectivity fully characterized in analytical fashion. By assuming that all
neurons have the same shape and are regularly distributed along the
two-dimensional orthogonal lattice with parameter $\Delta$, it is possible to
obtain the exact number of connections and cycles of any length from the
autoconvolution function as well as from the respective spectral density
derived from the adjacency matrix. It is shown that neuronal shape plays an
important role in defining the spatial distribution of synapses in neuronal
networks. In addition, we observe that neuromorphic networks typically exhibit
an interesting phenomenon where the pattern of connections is progressively
shifted along the spatial domain for increasing connection lengths. This is a
consequence of the fact that in neurons the axon reference point usually does
not coincide with the cell centre of mass. Morphological measurements for
characterization of the spatial distribution of connections, including the
adjacency matrix spectral density and the lacunarity of the connections, are
suggested and illustrated. We also show that Hopfield networks with
connectivity defined by different neuronal morphologies...

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## Synchronization is optimal in non-diagonalizable networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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#Condensed Matter - Disordered Systems and Neural Networks#Condensed Matter - Statistical Mechanics#Nonlinear Sciences - Adaptation and Self-Organizing Systems#Nonlinear Sciences - Chaotic Dynamics#Quantitative Biology - Neurons and Cognition

We consider the problem of maximizing the synchronizability of oscillator
networks by assigning weights and directions to the links of a given
interaction topology. We first extend the well-known master stability formalism
to the case of non-diagonalizable networks. We then show that, unless some
oscillator is connected to all the others, networks of maximum
synchronizability are necessarily non-diagonalizable and can always be obtained
by imposing unidirectional information flow with normalized input strengths.
The extension makes the formalism applicable to all possible network
structures, while the maximization results provide insights into hierarchical
structures observed in complex networks in which synchronization plays a
significant role.; Comment: 4 pages, 1 figure; minor revision

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## A biophysical observation model for field potentials of networks of leaky integrate-and-fire neurons

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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We present a biophysical approach for the coupling of neural network activity
as resulting from proper dipole currents of cortical pyramidal neurons to the
electric field in extracellular fluid. Starting from a reduced threecompartment
model of a single pyramidal neuron, we derive an observation model for
dendritic dipole currents in extracellular space and thereby for the dendritic
field potential that contributes to the local field potential of a neural
population. This work aligns and satisfies the widespread dipole assumption
that is motivated by the "open-field" configuration of the dendritic field
potential around cortical pyramidal cells. Our reduced three-compartment scheme
allows to derive networks of leaky integrate-and-fire models, which facilitates
comparison with existing neural network and observation models. In particular,
by means of numerical simulations we compare our approach with an ad hoc model
by Mazzoni et al. [Mazzoni, A., S. Panzeri, N. K. Logothetis, and N. Brunel
(2008). Encoding of naturalistic stimuli by local field potential spectra in
networks of excitatory and inhibitory neurons. PLoS Computational Biology 4
(12), e1000239], and conclude that our biophysically motivated approach yields
substantial improvement.; Comment: 31 pages...

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## eXamine: Exploring annotated modules in networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/07/2014
Português

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#Computer Science - Computational Engineering, Finance, and Science#Computer Science - Social and Information Networks#Quantitative Biology - Quantitative Methods

Background: Biological networks have a growing importance for the
interpretation of high-throughput omics data. Integrative network analysis
makes use of statistical and combinatorial methods to extract smaller
subnetwork modules, and performs enrichment analysis to annotate the modules
with ontology terms or other available knowledge. This process results in an
annotated module, which retains the original network structure and includes
enrichment information as a set system. A major bottleneck is a lack of tools
that allow exploring both network structure of extracted modules and its
annotations. Results:
Thispaperpresentsavisualanalysisapproachthattargetssmallmoduleswithmanyset-based
annotations, and which displays the annotations as contours on top of a
node-link diagram. We introduce an extension of self-organizing maps to lay out
nodes, links, and contours in a unified way. An implementation of this approach
is freely available as the Cytoscape app eXamine. Conclusions: eXamine
accurately conveys small and annotated modules consisting of several dozens of
proteins and annotations. We demonstrate that eXamine facilitates the
interpretation of integrative network analysis results in a guided case study.
This study has resulted in a novel biological insight regarding the
virally-encoded G-protein coupled receptor US28.; Comment: BioVis 2014 conference

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## Generation and analysis of networks with a prescribed degree sequence and subgraph family: Higher-order structure matters

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 25/11/2015
Português

Relevância na Pesquisa

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#Physics - Physics and Society#Computer Science - Social and Information Networks#Quantitative Biology - Populations and Evolution

Designing algorithms that generate networks with a given degree sequence
while varying both subgraph composition and distribution of subgraphs around
nodes is an important but challenging research problem. Current algorithms lack
control of key network parameters, the ability to specify to what subgraphs a
node belongs to, come at a considerable complexity cost or, critically, sample
from a limited ensemble of networks. To enable controlled investigations of the
impact and role of subgraphs, especially for epidemics, neuronal activity or
complex contagion, it is essential that the generation process be versatile and
the generated networks as diverse as possible. In this paper, we present two
new network generation algorithms that use subgraphs as building blocks to
construct networks preserving a given degree sequence. Additionally, these
algorithms provide control over clustering both at node and global level. In
both cases, we show that, despite being constrained by a degree sequence and
global clustering, generated networks have markedly different topologies as
evidenced by both subgraph prevalence and distribution around nodes, and
large-scale network structure metrics such as path length and betweenness
measures. Simulations of standard epidemic and complex contagion models on
those networks reveal that degree distribution and global clustering do not
always accurately predict the outcome of dynamical processes taking place on
them. We conclude by discussing the benefits and limitations of both methods.; Comment: 30 pages...

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## Optimal hierarchical modular topologies for producing limited sustained activation of neural networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/03/2010
Português

Relevância na Pesquisa

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#Quantitative Biology - Neurons and Cognition#Condensed Matter - Disordered Systems and Neural Networks#Physics - Physics and Society

An essential requirement for the representation of functional patterns in
complex neural networks, such as the mammalian cerebral cortex, is the
existence of stable regimes of network activation, typically arising from a
limited parameter range. In this range of limited sustained activity (LSA), the
activity of neural populations in the network persists between the extremes of
either quickly dying out or activating the whole network. Hierarchical modular
networks were previously found to show a wider parameter range for LSA than
random or small-world networks not possessing hierarchical organization or
multiple modules. Here we explored how variation in the number of hierarchical
levels and modules per level influenced network dynamics and occurrence of LSA.
We tested hierarchical configurations of different network sizes, approximating
the large-scale networks linking cortical columns in one hemisphere of the rat,
cat, or macaque monkey brain. Scaling of the network size affected the number
of hierarchical levels and modules in the optimal networks, also depending on
whether global edge density or the numbers of connections per node were kept
constant. For constant edge density, only few network configurations,
possessing an intermediate number of levels and a large number of modules...

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## Comparing Poiseuille with 1D Navier-Stokes Flow in Rigid and Distensible Tubes and Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 11/05/2013
Português

Relevância na Pesquisa

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A comparison is made between the Hagen-Poiseuille flow in rigid tubes and
networks on one side and the time-independent one-dimensional Navier-Stokes
flow in elastic tubes and networks on the other. Analytical relations, a
Poiseuille network flow model and two finite element Navier-Stokes
one-dimensional flow models have been developed and used in this investigation.
The comparison highlights the differences between Poiseuille and
one-dimensional Navier-Stokes flow models which may have been unjustifiably
treated as equivalent in some studies.; Comment: 26 pages, 6 figures

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## Distributed simulation of polychronous and plastic spiking neural networks: strong and weak scaling of a representative mini-application benchmark executed on a small-scale commodity cluster

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

45.59%

#Computer Science - Distributed, Parallel, and Cluster Computing#Quantitative Biology - Neurons and Cognition#C.2.4#C.1.4

We introduce a natively distributed mini-application benchmark representative
of plastic spiking neural network simulators. It can be used to measure
performances of existing computing platforms and to drive the development of
future parallel/distributed computing systems dedicated to the simulation of
plastic spiking networks. The mini-application is designed to generate spiking
behaviors and synaptic connectivity that do not change when the number of
hardware processing nodes is varied, simplifying the quantitative study of
scalability on commodity and custom architectures. Here, we present the strong
and weak scaling and the profiling of the computational/communication
components of the DPSNN-STDP benchmark (Distributed Simulation of Polychronous
Spiking Neural Network with synaptic Spike-Timing Dependent Plasticity). In
this first test, we used the benchmark to exercise a small-scale cluster of
commodity processors (varying the number of used physical cores from 1 to 128).
The cluster was interconnected through a commodity network. Bidimensional grids
of columns composed of Izhikevich neurons projected synapses locally and toward
first, second and third neighboring columns. The size of the simulated network
varied from 6.6 Giga synapses down to 200 K synapses. The code demonstrated to
be fast and scalable: 10 wall clock seconds were required to simulate one
second of activity and plasticity (per Hertz of average firing rate) of a
network composed by 3.2 G synapses running on 128 hardware cores clocked @ 2.4
GHz. The mini-application has been designed to be easily interfaced with
standard and custom software and hardware communication interfaces. It has been
designed from its foundation to be natively distributed and parallel...

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## Dynamics of Boolean Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/07/2013
Português

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Boolean networks are special types of finite state time-discrete dynamical
systems. A Boolean network can be described by a function from an n-dimensional
vector space over the field of two elements to itself. A fundamental problem in
studying these dynamical systems is to link their long term behaviors to the
structures of the functions that define them. In this paper, a method for
deriving a Boolean network's dynamical information via its disjunctive normal
form is explained. For a given Boolean network, a matrix with entries 0 and 1
is associated with the polynomial function that represents the network, then
the information on the fixed points and the limit cycles is derived by
analyzing the matrix. The described method provides an algorithm for the
determination of the fixed points from the polynomial expression of a Boolean
network. The method can also be used to construct Boolean networks with
prescribed limit cycles and fixed points. Examples are provided to explain the
algorithm.

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## Correlated fluctuations in strongly-coupled binary networks beyond equilibrium

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/12/2015
Português

Relevância na Pesquisa

45.59%

#Condensed Matter - Disordered Systems and Neural Networks#Quantitative Biology - Neurons and Cognition

Randomly coupled Ising spins constitute the classical model of collective
phenomena in disordered systems, with applications covering ferromagnetism,
combinatorial optimization, protein folding, stock market dynamics, and social
dynamics. The phase diagram of these systems is obtained in the thermodynamic
limit by averaging over the quenched randomness of the couplings. However, many
applications require the statistics of activity for a single realization of the
possibly asymmetric couplings in finite-sized networks. Examples include
reconstruction of couplings from the observed dynamics, learning in the central
nervous system by correlation-sensitive synaptic plasticity, and representation
of probability distributions for sampling-based inference. The systematic
cumulant expansion for kinetic binary (Ising) threshold units with strong,
random and asymmetric couplings presented here goes beyond mean-field theory
and is applicable outside thermodynamic equilibrium; a system of approximate
non-linear equations predicts average activities and pairwise covariances in
quantitative agreement with full simulations down to hundreds of units. The
linearized theory yields an expansion of the correlation- and response
functions in collective eigenmodes...

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## Spontaneous coordinated activity in cultured networks: Analysis of multiple ignition sites, primary circuits, burst phase delay distributions and functional structures

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 12/04/2010
Português

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All higher order central nervous systems exhibit spontaneous neural activity,
though the purpose and mechanistic origin of such activity remains poorly
understood. We explore the ignition and spread of collective spontaneous
electrophysiological burst activity in networks of cultured cortical neurons
growing on microelectrode arrays using information theory and
first-spike-in-burst analysis methods. We show the presence of burst leader
neurons, which form a mono-synaptically connected primary circuit, and initiate
a majority of network bursts. Leader/follower firing delay times form
temporally stable positively skewed distributions. Blocking inhibitory synapses
usually results in shorter delay times with reduced variance. These
distributions are generalized characterizations of internal network dynamics
and provide estimates of pair-wise synaptic distances. We show that mutual
information between neural nodes is a function of distance, which is maintained
under disinhibition. The resulting analysis produces specific quantitative
constraints and insights into the activation patterns of collective neuronal
activity in self-organized cortical networks, which may prove useful for models
emulating spontaneously active systems.; Comment: 4 pages...

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## Surrogate-assisted analysis of weighted functional brain networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/08/2014
Português

Relevância na Pesquisa

45.59%

Graph-theoretical analyses of complex brain networks is a rapidly evolving
field with a strong impact for neuroscientific and related clinical research.
Due to a number of confounding variables, however, a reliable and meaningful
characterization of particularly functional brain networks is a major
challenge. Addressing this problem, we present an analysis approach for
weighted networks that makes use of surrogate networks with preserved edge
weights or vertex strengths. We first investigate whether characteristics of
weighted networks are influenced by trivial properties of the edge weights or
vertex strengths (e.g., their standard deviations). If so, these influences are
then effectively segregated with an appropriate surrogate normalization of the
respective network characteristic. We demonstrate this approach by
re-examining, in a time-resolved manner, weighted functional brain networks of
epilepsy patients and control subjects derived from simultaneous EEG/MEG
recordings during different behavioral states. We show that this
surrogate-assisted analysis approach reveals complementary information about
these networks, can aid with their interpretation, and thus can prevent
deriving inappropriate conclusions.

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## Quantitative analysis of a Schaffer collateral model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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Advances in techniques for the formal analysis of neural networks have
introduced the possibility of detailed quantitative analyses of brain
circuitry. This paper applies a method for calculating mutual information to
the analysis of the Schaffer collateral connections between regions CA3 and CA1
of the hippocampus. Attention is given to the introduction of further details
of anatomy and physiology to the calculation: in particular, the distribution
of the number of connections that CA1 neurons receive from CA3, and the graded
nature of the firing-rate distribution in region CA3.; Comment: Revised version. 16 pages LaTeX, 5 figs. To be published in Baddeley
et al (Eds) Information Theory and the Brain, Cambridge Univ. Press 1998

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## Statistics of Dynamic Random Networks: A Depth Function Approach

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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#Condensed Matter - Disordered Systems and Neural Networks#Condensed Matter - Statistical Mechanics#Physics - Data Analysis, Statistics and Probability#Quantitative Biology - Quantitative Methods#Statistics - Methodology#G.3#E.1#J.2#I.5

The study of random graphs and networks had an explosive development in the
last couple of decades. Meanwhile, statistical analysis of graph sequences is
less developed. In this paper we focus on graphs with a fixed number of labeled
nodes and study some statistical problems in a nonparametric framework. We
introduce natural notions of center and a depth function for graphs that evolve
in time. This allows us to develop several statistical techniques including
testing, supervised and unsupervised classification, and a notion of principal
component sets in the space of graphs. Some examples and asymptotic results are
given, as well as a real data example.; Comment: 20 pages, 6 figures. Real data example added

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## Structure and Recognition of 3,4-leaf Powers of Galled Phylogenetic Networks in Polynomial Time

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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A graph is a $k$-leaf power of a tree $T$ if its vertices are leaves of $T$
and two vertices are adjacent in $T$ if and only if their distance in $T$ is at
most $k$. Then $T$ is a $k$-leaf root of $G$. This notion was introduced by
Nishimura, Ragde, and Thilikos [2002] motivated by the search for underlying
phylogenetic trees. We study here an extension of the $k$-leaf power graph
recognition problem. This extension is motivated by a new biological question
for the evaluation of the latteral gene transfer on a population of viruses. We
allow the host graph to slightly differs from a tree and allow some cycles. In
fact we study phylogenetic galled networks in which cycles are pairwise vertex
disjoint. We show some structural results and propose polynomial algorithms for
the cases $k=3$ and $k=4$. As a consequence, squares of galled networks can
also be recognized in polynomial time.

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## Self-sustained asynchronous irregular states and Up/Down states in thalamic, cortical and thalamocortical networks of nonlinear integrate-and-fire neurons

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

45.59%

Randomly-connected networks of integrate-and-fire (IF) neurons are known to
display asynchronous irregular (AI) activity states, which resemble the
discharge activity recorded in the cerebral cortex of awake animals. However,
it is not clear whether such activity states are specific to simple IF models,
or if they also exist in networks where neurons are endowed with complex
intrinsic properties similar to electrophysiological measurements. Here, we
investigate the occurrence of AI states in networks of nonlinear IF neurons,
such as the adaptive exponential IF (Brette-Gerstner-Izhikevich) model. This
model can display intrinsic properties such as low-threshold spike (LTS),
regular spiking (RS) or fast-spiking (FS). We successively investigate the
oscillatory and AI dynamics of thalamic, cortical and thalamocortical networks
using such models. AI states can be found in each case, sometimes with
surprisingly small network size of the order of a few tens of neurons. We show
that the presence of LTS neurons in cortex or in thalamus, explains the robust
emergence of AI states for relatively small network sizes. Finally, we
investigate the role of spike-frequency adaptation (SFA). In cortical networks
with strong SFA in RS cells, the AI state is transient...

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## Statistically validated networks in bipartite complex systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/08/2010
Português

Relevância na Pesquisa

45.59%

Many complex systems present an intrinsic bipartite nature and are often
described and modeled in terms of networks [1-5]. Examples include movies and
actors [1, 2, 4], authors and scientific papers [6-9], email accounts and
emails [10], plants and animals that pollinate them [11, 12]. Bipartite
networks are often very heterogeneous in the number of relationships that the
elements of one set establish with the elements of the other set. When one
constructs a projected network with nodes from only one set, the system
heterogeneity makes it very difficult to identify preferential links between
the elements. Here we introduce an unsupervised method to statistically
validate each link of the projected network against a null hypothesis taking
into account the heterogeneity of the system. We apply our method to three
different systems, namely the set of clusters of orthologous genes (COG) in
completely sequenced genomes [13, 14], a set of daily returns of 500 US
financial stocks, and the set of world movies of the IMDb database [15]. In all
these systems, both different in size and level of heterogeneity, we find that
our method is able to detect network structures which are informative about the
system and are not simply expression of its heterogeneity. Specifically...

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## Probabilistic Gene Regulatory Networks, isomorphisms of Markov Chains

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/03/2006
Português

Relevância na Pesquisa

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#Mathematics - Dynamical Systems#Mathematics - Probability#Quantitative Biology - Genomics#03C60#00A71#05C20#68Q01

In this paper we study homomorphisms of Probabilistic Regulatory Gene
Networks(PRN) introduced in arXiv:math.DS/0603289 v1 13 Mar 2006. The model PRN
is a natural generalization of the Probabilistic Boolean Networks (PBN),
introduced by I. Shmulevich, E. Dougherty, and W. Zhang in 2001, that has been
using to describe genetic networks and has therapeutic applications. In this
paper, our main objectives are to apply the concept of homomorphism and
$\epsilon$-homomorphism of probabilistic regulatory networks to the dynamic of
the networks. The meaning of $\epsilon$ is that these homomorphic networks have
similar distributions and the distance between the distributions is upper
bounded by $\epsilon$. Additionally, we prove that the class of PRN together
with the homomorphisms form a category with products and coproducts.
Projections are special homomorphisms, and they always induce invariant
subnetworks that contain all the cycles and steady states in the network. Here,
it is proved that the $\epsilon$-homomorphism for $0<\epsilon<1$ produce
simultaneous Markov Chains in both networks, that permit to introduce the
concept of $\epsilon$-isomorphism of Markov Chains, and similar networks.

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