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## Constructing precisely computing networks with biophysical spiking neurons

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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While spike timing has been shown to carry detailed stimulus information at
the sensory periphery, its possible role in network computation is less clear.
Most models of computation by neural networks are based on population firing
rates. In equivalent spiking implementations, firing is assumed to be random
such that averaging across populations of neurons recovers the rate-based
approach. Recently, however, Den\'eve and colleagues have suggested that the
spiking behavior of neurons may be fundamental to how neuronal networks
compute, with precise spike timing determined by each neuron's contribution to
producing the desired output. By postulating that each neuron fires in order to
reduce the error in the network's output, it was demonstrated that linear
computations can be carried out by networks of integrate-and-fire neurons that
communicate through instantaneous synapses. This left open, however, the
possibility that realistic networks, with conductance-based neurons with
subthreshold nonlinearity and the slower timescales of biophysical synapses,
may not fit into this framework. Here, we show how the spike-based approach can
be extended to biophysically plausible networks. We then show that our network
reproduces a number of key features of cortical networks including irregular
and Poisson-like spike times and a tight balance between excitation and
inhibition. Lastly...

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## The spread of epidemic disease on networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/04/2002
Português

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#Condensed Matter - Statistical Mechanics#Condensed Matter - Disordered Systems and Neural Networks#Quantitative Biology

The study of social networks, and in particular the spread of disease on
networks, has attracted considerable recent attention in the physics community.
In this paper, we show that a large class of standard epidemiological models,
the so-called susceptible/infective/removed (SIR) models can be solved exactly
on a wide variety of networks. In addition to the standard but unrealistic case
of fixed infectiveness time and fixed and uncorrelated probability of
transmission between all pairs of individuals, we solve cases in which times
and probabilities are non-uniform and correlated. We also consider one simple
case of an epidemic in a structured population, that of a sexually transmitted
disease in a population divided into men and women. We confirm the correctness
of our exact solutions with numerical simulations of SIR epidemics on networks.; Comment: 12 pages, 3 figures

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## Exact deterministic representation of Markovian SIR epidemics on networks with and without loops

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 29/07/2013
Português

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#Mathematics - Probability#Mathematics - Dynamical Systems#Quantitative Biology - Populations and Evolution

In a previous paper Sharkey et al. [13] proved the exactness of closures at
the level of triples for Markovian SIR (susceptible-infected-removed) dynamics
on tree-like networks. This resulted in a deterministic representation of the
epidemic dynamics on the network that can be numerically evaluated. In this
paper, we extend this modelling framework to certain classes of networks
exhibiting loops. We show that closures where the loops are kept intact are
exact, and lead to a simplified and numerically solvable system of ODEs
(ordinary-differential-equations). The findings of the paper lead us to a
generalisation of closures that are based on partitioning the network around
nodes that are cut-vertices (i.e. the removal of such a node leads to the
network breaking down into at least two disjointed components or subnetworks).
Exploiting this structural property of the network yields some natural
closures, where the evolution of a particular state can typically be exactly
given in terms of the corresponding or projected sates on the subnetworks and
the cut-vertex. A byproduct of this analysis is an alternative probabilistic
proof of the exactness of the closures for tree-like networks presented in
Sharkey et al. [13]. In this paper we also elaborate on how the main result can
be applied to more realistic networks...

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## Resilience of human brain functional coactivation networks under thresholding

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 06/07/2014
Português

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#Computer Science - Social and Information Networks#Physics - Physics and Society#Quantitative Biology - Neurons and Cognition

Recent studies have demonstrated the existence of community structure and
rich club nodes, (i.e., highly interconnected, high degree hub nodes), in human
brain functional networks. The cognitive relevance of the detected modules and
hubs has also been demonstrated, for both task based and default mode networks,
suggesting that the brain self-organizes into patterns of co-activated sets of
regions for performing specific tasks or in resting state. In this paper, we
report studies on the resilience or robustness of this modular structure: under
systematic erosion of connectivity in the network under thresholding, how
resilient is the modularity and hub structure? The results show that the
network shows show strong resilience properties, with the modularity and hub
structure maintaining itself over a large range of connection strengths. Then,
at a certain critical threshold that falls very close to 0, the connectivity,
the modularity, and hub structure suddenly break down, showing a phase
transition like property. Additionally, the spatial and topological
organization of erosion of connectivity at all levels was found to be
homogenous rather than heterogenous; i.e., no "structural holes" of any
significant sizes were found, and no gradual increases in numbers of components
were detected. Any loss of connectivity is homogenously spread out across the
network. The results suggest that human task-based functional brain networks
are very resilient...

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## Interspecific competition underlying mutualistic networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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45.58%

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

The architecture of bipartite networks linking two classes of constituents is
affected by the interactions within each class. For the bipartite networks
representing the mutualistic relationship between pollinating animals and
plants, it has been known that their degree distributions are broad but often
deviate from power-law form, more significantly for plants than animals. Here
we consider a model for the evolution of the mutualistic networks and find that
their topology is strongly dependent on the asymmetry and non-linearity of the
preferential selection of mutualistic partners. Real-world mutualistic networks
analyzed in the framework of the model show that a new animal species
determines its partners not only by their attractiveness but also as a result
of the competition with pre-existing animals, which leads to the
stretched-exponential degree distributions of plant species.; Comment: 5 pages, 3 figures, accepted version in PRL

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## Extreme self-organization in networks constructed from gene expression data

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Condensed Matter - Soft Condensed Matter#Condensed Matter - Disordered Systems and Neural Networks#Quantitative Biology

We study networks constructed from gene expression data obtained from many
types of cancers. The networks are constructed by connecting vertices that
belong to each others' list of K-nearest-neighbors, with K being an a priori
selected non-negative integer. We introduce an order parameter for
characterizing the homogeneity of the networks. On minimizing the order
parameter with respect to K, degree distribution of the networks shows
power-law behavior in the tails with an exponent of unity. Analysis of the
eigenvalue spectrum of the networks confirms the presence of the power-law and
small-world behavior. We discuss the significance of these findings in the
context of evolutionary biological processes.; Comment: 4 pages including 3 eps figures, revtex. Revisions as in published
version

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## Self-sustained activity, bursts, and variability in recurrent networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 06/11/2013
Português

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There is consensus in the current literature that stable states of
asynchronous irregular spiking activity require (i) large networks of 10 000 or
more neurons and (ii) external background activity or pacemaker neurons. Yet
already in 1963, Griffith showed that networks of simple threshold elements can
be persistently active at intermediate rates. Here, we extend Griffith's work
and demonstrate that sparse networks of integrate-and-fire neurons assume
stable states of self-sustained asynchronous and irregular firing without
external input or pacemaker neurons. These states can be robustly induced by a
brief pulse to a small fraction of the neurons, or by short a period of
irregular input, and last for several minutes. Self-sustained activity states
emerge when a small fraction of the synapses is strong enough to significantly
influence the firing probability of a neuron, consistent with the recently
proposed long-tailed distribution of synaptic weights. During self-sustained
activity, each neuron exhibits highly irregular firing patterns, similar to
experimentally observed activity. Moreover, the interspike interval
distribution reveals that neurons switch between discrete states of high and
low firing rates. We find that self-sustained activity states can exist even in
small networks of only a thousand neurons. We investigated networks up to 100
000 neurons. Finally...

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## Bayesian Inference of Whole-Brain Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/02/2012
Português

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In structural brain networks the connections of interest consist of
white-matter fibre bundles between spatially segregated brain regions. The
presence, location and orientation of these white matter tracts can be derived
using diffusion MRI in combination with probabilistic tractography.
Unfortunately, as of yet no approaches have been suggested that provide an
undisputed way of inferring brain networks from tractography. In this paper, we
provide a computational framework which we refer to as Bayesian connectomics.
Rather than applying an arbitrary threshold to obtain a single network, we
consider the posterior distribution of networks that are supported by the data,
combined with an exponential random graph (ERGM) prior that captures a priori
knowledge concerning the graph-theoretical properties of whole-brain networks.
We show that, on simulated probabilistic tractography data, our approach is
able to reconstruct whole-brain networks. In addition, our approach directly
supports multi-model data fusion and group-level network inference.; Comment: 10 pages, 2 figures

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## Evolve Networks Towards Better Performance: a Compromise between Mutation and Selection

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 04/01/2009
Português

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#Condensed Matter - Statistical Mechanics#Physics - Physics and Society#Quantitative Biology - Populations and Evolution

The interaction between natural selection and random mutation is frequently
debated in recent years. Does similar dilemma also exist in the evolution of
real networks such as biological networks? In this paper, we try to discuss
this issue by a simple model system, in which the topological structure of
networks is repeatedly modified and selected in order to make them have better
performance in dynamical processes. Interestingly, when the networks with
optimal performance deviate from the steady state networks under pure
mutations, we find the evolution behaves as a balance between mutation and
selection. Furthermore, when the timescales of mutations and dynamical
processes are comparable with each other, the steady state of evolution is
mainly determined by mutation. On the opposite side, when the timescale of
mutations is much longer than that of dynamical processes, selection dominates
the evolution and the steady-state networks turn to have much improved
performance and highly heterogeneous structures. Despite the simplicity of our
model system, this finding could give useful indication to detect the
underlying mechanisms that rein the evolution of real systems.; Comment: 27 pages 15 figures

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## Probabilistic Regulatory Networks: Modeling Genetic Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/06/2006
Português

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We describe here the new concept of $\epsilon$-Homomorphisms of Probabilistic
Regulatory Gene Networks(PRN). The $\epsilon$-homomorphisms are special
mappings between two probabilistic networks, that consider the algebraic action
of the iteration of functions and the probabilistic dynamic of the two
networks. It is proved here that the class of PRN, together with the
homomorphisms, form a category with products and coproducts. Projections are
special homomorphisms, induced by invariant subnetworks. Here, it is proved
that an $\epsilon$-homomorphism for 0 <$\epsilon$< 1 produces simultaneous
Markov Chains in both networks, that permit to introduce the concepts of
$\epsilon$-isomorphism of Markov Chains, and similar networks.; Comment: 8 pages, 2 figures, International Congress of Matematicians, to be
published in Proceedings of the Fifth International Conference on Engineering
Computational Technology, 2006, Las Palmas, Gran Canaria

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## Excitable Scale Free Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Quantitative Biology - Neurons and Cognition#Condensed Matter - Disordered Systems and Neural Networks#Nonlinear Sciences - Cellular Automata and Lattice Gases#Physics - Biological Physics

When a simple excitable system is continuously stimulated by a Poissonian
external source, the response function (mean activity versus stimulus rate)
generally shows a linear saturating shape. This is experimentally verified in
some classes of sensory neurons, which accordingly present a small dynamic
range (defined as the interval of stimulus intensity which can be appropriately
coded by the mean activity of the excitable element), usually about one or two
decades only. The brain, on the other hand, can handle a significantly broader
range of stimulus intensity, and a collective phenomenon involving the
interaction among excitable neurons has been suggested to account for the
enhancement of the dynamic range. Since the role of the pattern of such
interactions is still unclear, here we investigate the performance of a
scale-free (SF) network topology in this dynamic range problem. Specifically,
we study the transfer function of disordered SF networks of excitable
Greenberg-Hastings cellular automata. We observe that the dynamic range is
maximum when the coupling among the elements is critical, corroborating a
general reasoning recently proposed. Although the maximum dynamic range yielded
by general SF networks is slightly worse than that of random networks...

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## The functional structure of cortical neuronal networks grown in vitro

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 07/03/2007
Português

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

We apply an information theoretic treatment of action potential time series
measured with microelectrode arrays to estimate the connectivity of mammalian
neuronal cell assemblies grown {\it in vitro}. We infer connectivity between
two neurons via the measurement of the mutual information between their spike
trains. In addition we measure higher point multi-informations between any two
spike trains conditional on the activity of a third cell, as a means to
identify and distinguish classes of functional connectivity among three
neurons. The use of a conditional three-cell measure removes some
interpretational shortcomings of the pairwise mutual information and sheds
light into the functional connectivity arrangements of any three cells. We
analyze the resultant connectivity graphs in light of other complex networks
and demonstrate that, despite their {\it ex vivo} development, the connectivity
maps derived from cultured neural assemblies are similar to other biological
networks and display nontrivial structure in clustering coefficient, network
diameter and assortative mixing. Specifically we show that these networks are
weakly disassortative small world graphs, which differ significantly in their
structure from randomized graphs with the same degree. We expect our analysis
to be useful in identifying the computational motifs of a wide variety of
complex networks...

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## Statistical Properties of Avalanches in Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 17/04/2012
Português

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45.58%

#Condensed Matter - Disordered Systems and Neural Networks#Nonlinear Sciences - Cellular Automata and Lattice Gases#Physics - Physics and Society#Quantitative Biology - Neurons and Cognition

We characterize the distributions of size and duration of avalanches
propagating in complex networks. By an avalanche we mean the sequence of events
initiated by the externally stimulated `excitation' of a network node, which
may, with some probability, then stimulate subsequent firings of the nodes to
which it is connected, resulting in a cascade of firings. This type of process
is relevant to a wide variety of situations, including neuroscience, cascading
failures on electrical power grids, and epidemology. We find that the
statistics of avalanches can be characterized in terms of the largest
eigenvalue and corresponding eigenvector of an appropriate adjacency matrix
which encodes the structure of the network. By using mean-field analyses,
previous studies of avalanches in networks have not considered the effect of
network structure on the distribution of size and duration of avalanches. Our
results apply to individual networks (rather than network ensembles) and
provide expressions for the distributions of size and duration of avalanches
starting at particular nodes in the network. These findings might find
application in the analysis of branching processes in networks, such as
cascading power grid failures and critical brain dynamics. In particular...

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## Scale-free brain functional networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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45.58%

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

Functional magnetic resonance imaging (fMRI) is used to extract {\em
functional networks} connecting correlated human brain sites. Analysis of the
resulting networks in different tasks shows that: (a) the distribution of
functional connections, and the probability of finding a link vs. distance are
both scale-free, (b) the characteristic path length is small and comparable
with those of equivalent random networks, and (c) the clustering coefficient is
orders of magnitude larger than those of equivalent random networks. All these
properties, typical of scale-free small world networks, reflect important
functional information about brain states.; Comment: 4 pages, 5 figures, 2 tables

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## Epidemics in partially overlapped multiplex networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

45.58%

Many real networks exhibit a layered structure in which links in each layer
reflect the function of nodes on different environments. These multiple types
of links are usually represented by a multiplex network in which each layer has
a different topology. In real-world networks, however, not all nodes are
present on every layer. To generate a more realistic scenario, we use a
generalized multiplex network and assume that only a fraction $q$ of the nodes
are shared by the layers. We develop a theoretical framework for a branching
process to describe the spread of an epidemic on these partially overlapped
multiplex networks. This allows us to obtain the fraction of infected
individuals as a function of the effective probability that the disease will be
transmitted $T$. We also theoretically determine the dependence of the epidemic
threshold on the fraction $q > 0$ of shared nodes in a system composed of two
layers. We find that in the limit of $q \to 0$ the threshold is dominated by
the layer with the smaller isolated threshold. Although a system of two
completely isolated networks is nearly indistinguishable from a system of two
networks that share just a few nodes, we find that the presence of these few
shared nodes causes the epidemic threshold of the isolated network with the
lower propagating capacity to change discontinuously and to acquire the
threshold of the other network.; Comment: 13 pages...

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## Training recurrent neural networks with sparse, delayed rewards for flexible decision tasks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

45.58%

Recurrent neural networks in the chaotic regime exhibit complex dynamics
reminiscent of high-level cortical activity during behavioral tasks. However,
existing training methods for such networks are either biologically
implausible, or require a real-time continuous error signal to guide the
learning process. This is in contrast with most behavioral tasks, which only
provide time-sparse, delayed rewards. Here we show that a biologically
plausible reward-modulated Hebbian learning algorithm, previously used in
feedforward models of birdsong learning, can train recurrent networks based
solely on delayed, phasic reward signals at the end of each trial. The method
requires no dedicated feedback or readout networks: the whole network
connectivity is subject to learning, and the network output is read from one
arbitrarily chosen network cell. We use this method to successfully train a
network on a delayed nonmatch to sample task (which requires memory, flexible
associations, and non-linear mixed selectivities). Using decoding techniques,
we show that the resulting networks exhibit dynamic coding of task-relevant
information, with neural encodings of various task features fluctuating widely
over the course of a trial. Furthermore, network activity moves from a
stimulus-specific representation to a response-specific representation during
response time...

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## A measure for the complexity of Boolean functions related to their implementation in neural networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/11/2001
Português

Relevância na Pesquisa

45.58%

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

We define a measure for the complexity of Boolean functions related to their
implementation in neural networks, and in particular close related to the
generalization ability that could be obtained through the learning process. The
measure is computed through the calculus of the number of neighbor examples
that differ in their output value. Pairs of these examples have been previously
shown to be part of the minimum size training set needed to obtain perfect
generalization in feedforward neural networks.
The main advantage of the proposed measure, in comparison to existing ones,
is the way in which the measure is evaluated, as it can be computed from the
definition of the function itself, independently of its implementation. The
validity of the proposal is analyzed through numerical simulations performed on
different feedforward neural networks architectures, and a good agreement is
obtained between the predicted complexity and the generalization ability for
different classes of functions.
Also an interesting analogy was found between the proposed complexity measure
and the energy function of ferromagnetic systems, that could be exploited, by
use of the existing results and mathematical tools developed within a
statistical mechanics framework...

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## Connectivity Distribution of Spatial Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/02/2003
Português

Relevância na Pesquisa

45.58%

#Condensed Matter - Disordered Systems and Neural Networks#Condensed Matter - Statistical Mechanics#Quantitative Biology - Genomics

We study spatial networks constructed by randomly placing nodes on a manifold
and joining two nodes with an edge whenever their distance is less than a
certain cutoff. We derive the general expression for the connectivity
distribution of such networks as a functional of the distribution of the nodes.
We show that for regular spatial densities, the corresponding spatial network
has a connectivity distribution decreasing faster than an exponential. In
contrast, we also show that scale-free networks with a power law decreasing
connectivity distribution are obtained when a certain information measure of
the node distribution (integral of higher powers of the distribution) diverges.
We illustrate our results on a simple example for which we present simulation
results. Finally, we speculate on the role played by the limiting case P(k)=1/k
which appears empirically to be relevant to spatial networks of biological
origin such as the ones constructed from gene expression data.; Comment: 6 pages, 1 figure

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## Phase Diagram of Spiking Neural Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

45.58%

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

In computer simulations of spiking neural networks, often it is assumed that
every two neurons of the network are connected by a probability of 2\%, 20\% of
neurons are inhibitory and 80\% are excitatory. These common values are based
on experiments, observations, and trials and errors, but here, I take a
different perspective, inspired by evolution, I systematically simulate many
networks, each with a different set of parameters, and then I try to figure out
what makes the common values desirable. I stimulate networks with pulses and
then measure their: dynamic range, dominant frequency of population activities,
total duration of activities, maximum rate of population and the occurrence
time of maximum rate. The results are organized in phase diagram. This phase
diagram gives an insight into the space of parameters -- excitatory to
inhibitory ratio, sparseness of connections and synaptic weights. This phase
diagram can be used to decide the parameters of a model. The phase diagrams
show that networks which are configured according to the common values, have a
good dynamic range in response to an impulse and their dynamic range is robust
in respect to synaptic weights, and for some synaptic weights they oscillate in
$\alpha$ or $\beta$ frequencies...

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## A decaying factor accounts for contained activity in neuronal networks with no need of hierarchical or modular organization

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 24/09/2012
Português

Relevância na Pesquisa

45.58%

#Physics - Biological Physics#Physics - Physics and Society#Quantitative Biology - Neurons and Cognition

The mechanisms responsible for contention of activity in systems represented
by networks are crucial in various phenomena, as in diseases such as epilepsy
that affects the neuronal networks, and for information dissemination in social
networks. The first models to account for contained activity included
triggering and inhibition processes, but they cannot be applied to social
networks where inhibition is clearly absent. A recent model showed that
contained activity can be achieved with no need of inhibition processes
provided that the network is subdivided in modules (communities). In this
paper, we introduce a new concept inspired in the Hebbian theory through which
activity contention is reached by incorporating a dynamics based on a decaying
activity in a random walk mechanism preferential to the node activity. Upon
selecting the decay coefficient within a proper range, we observed sustained
activity in all the networks tested, viz. random, Barabasi-Albert and
geographical networks. The generality of this finding was confirmed by showing
that modularity is no longer needed if the dynamics based on the
integrate-and-fire dynamics incorporated the decay factor. Taken together,
these results provide a proof of principle that persistent...

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