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## Complexity without chaos: Plasticity within random recurrent networks generates robust timing and motor control

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 07/10/2012
Português

Relevância na Pesquisa

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#Nonlinear Sciences - Chaotic Dynamics#Condensed Matter - Disordered Systems and Neural Networks#Quantitative Biology - Neurons and Cognition

It is widely accepted that the complex dynamics characteristic of recurrent
neural circuits contributes in a fundamental manner to brain function. Progress
has been slow in understanding and exploiting the computational power of
recurrent dynamics for two main reasons: nonlinear recurrent networks often
exhibit chaotic behavior and most known learning rules do not work in robust
fashion in recurrent networks. Here we address both these problems by
demonstrating how random recurrent networks (RRN) that initially exhibit
chaotic dynamics can be tuned through a supervised learning rule to generate
locally stable neural patterns of activity that are both complex and robust to
noise. The outcome is a novel neural network regime that exhibits both
transiently stable and chaotic trajectories. We further show that the recurrent
learning rule dramatically increases the ability of RRNs to generate complex
spatiotemporal motor patterns, and accounts for recent experimental data
showing a decrease in neural variability in response to stimulus onset.

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## Coherent periodic activity in excitatory Erdos-Renyi neural networks:The role of network connectivity

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#Nonlinear Sciences - Chaotic Dynamics#Quantitative Biology - Neurons and Cognition

We consider an excitatory random network of leaky integrate-and-fire pulse
coupled neurons. The neurons are connected as in a directed Erd\"os-Renyi graph
with average connectivity $$ scaling as a power law with the number of
neurons in the network. The scaling is controlled by a parameter $\gamma$,
which allows to pass from massively connected to sparse networks and therefore
to modify the topology of the system. At a macroscopic level we observe two
distinct dynamical phases: an Asynchronous State (AS) corresponding to a
desynchronized dynamics of the neurons and a Partial Synchronization (PS)
regime associated with a coherent periodic activity of the network. At low
connectivity the system is in an AS, while PS emerges above a certain critical
average connectivity $_c$. For sufficiently large networks, $_c$
saturates to a constant value suggesting that a minimal average connectivity is
sufficient to observe coherent activity in systems of any size irrespectively
of the kind of considered network: sparse or massively connected. However, this
value depends on the nature of the synapses: reliable or unreliable. For
unreliable synapses the critical value required to observe the onset of
macroscopic behaviors is noticeably smaller than for reliable synaptic
transmission. Due to the disorder present in the system...

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## The Evolutionary Vaccination Dilemma in Complex Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

45.57%

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

In this work we analyze the evolution of voluntary vaccination in networked
populations by entangling the spreading dynamics of an influenza-like disease
with an evolutionary framework taking place at the end of each influenza season
so that individuals take or not the vaccine upon their previous experience. Our
framework thus put in competition two well-known dynamical properties of
scale-free networks: the fast propagation of diseases and the promotion of
cooperative behaviors. Our results show that when vaccine is perfect scale-free
networks enhance the vaccination behavior with respect to random graphs with
homogeneous connectivity patterns. However, when imperfection appears we find a
cross-over effect so that the number of infected (vaccinated) individuals
increases (decreases) with respect to homogeneous networks, thus showing up the
competition between the aforementioned properties of scale-free graphs.; Comment: 7 pages, 5 figures. Manuscript final version

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## Designing the Dynamics of Spiking Neural Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

45.57%

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

Precise timing of spikes and temporal locking are key elements of neural
computation. Here we demonstrate how even strongly heterogeneous, deterministic
neural networks with delayed interactions and complex topology can exhibit
periodic patterns of spikes that are precisely timed. We develop an analytical
method to find the set of all networks exhibiting a predefined pattern
dynamics. Such patterns may be arbitrarily long and of complicated temporal
structure. We point out that the same pattern can exist in very different
networks and have different stability properties.; Comment: 4 pages, 3 figures

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## Pattern formation in oscillatory complex networks consisting of excitable nodes

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

45.57%

Oscillatory dynamics of complex networks has recently attracted great
attention. In this paper we study pattern formation in oscillatory complex
networks consisting of excitable nodes. We find that there exist a few center
nodes and small skeletons for most oscillations. Complicated and seemingly
random oscillatory patterns can be viewed as well-organized target waves
propagating from center nodes along the shortest paths, and the shortest loops
passing through both the center nodes and their driver nodes play the role of
oscillation sources. Analyzing simple skeletons we are able to understand and
predict various essential properties of the oscillations and effectively
modulate the oscillations. These methods and results will give insights into
pattern formation in complex networks, and provide suggestive ideas for
studying and controlling oscillations in neural networks.; Comment: 15 pages, 7 figures, to appear in Phys. Rev. E

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## Model of Genetic Variation in Human Social Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

45.57%

Social networks exhibit strikingly systematic patterns across a wide range of
human contexts. While genetic variation accounts for a significant portion of
the variation in many complex social behaviors, the heritability of egocentric
social network attributes is unknown. Here we show that three of these
attributes (in-degree, transitivity, and centrality) are heritable. We then
develop a "mirror network" method to test extant network models and show that
none accounts for observed genetic variation in human social networks. We
propose an alternative "Attract and Introduce" model with two simple forms of
heterogeneity that generates significant heritability as well as other
important network features. We show that the model is well suited to real
social networks in humans. These results suggest that natural selection may
have played a role in the evolution of social networks. They also suggest that
modeling intrinsic variation in network attributes may be important for
understanding the way genes affect human behaviors and the way these behaviors
spread from person to person.; Comment: Additional materials related to the paper are available at
http://jhfowler.ucsd.edu

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## The comparison of tree-sibling time consistent phylogenetic networks is graph isomorphism-complete

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/02/2009
Português

Relevância na Pesquisa

45.57%

In a previous work, we gave a metric on the class of semibinary tree-sibling
time consistent phylogenetic networks that is computable in polynomial time; in
particular, the problem of deciding if two networks of this kind are isomorphic
is in P. In this paper, we show that if we remove the semibinarity condition
above, then the problem becomes much harder. More precisely, we proof that the
isomorphism problem for generic tree-sibling time consistent phylogenetic
networks is polynomially equivalent to the graph isomorphism problem. Since the
latter is believed to be neither in P nor NP-complete, the chances are that it
is impossible to define a metric on the class of all tree-sibling time
consistent phylogenetic networks that can be computed in polynomial time.; Comment: 10 pages, 3 figures

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## Evolution of cooperation on scale-free networks subject to error and attack

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/02/2009
Português

Relevância na Pesquisa

45.57%

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

We study the evolution of cooperation in the prisoner's dilemma and the
snowdrift game on scale-free networks that are subjected to intentional and
random removal of vertices. We show that, irrespective of the game type,
cooperation on scale-free networks is extremely robust against random deletion
of vertices, but declines fast if vertices with the maximal degree are
targeted. In particular, attack tolerance is lowest if the temptation to defect
is largest, whereby a small fraction of removed vertices suffices to decimate
cooperators. The decline of cooperation can be directly linked to the decrease
of heterogeneity of scale-free networks that sets in due to the removal of high
degree vertices. We conclude that the evolution of cooperation is characterized
by similar attack and error tolerance as was previously reported for
information readiness and spread of viruses on scale-free networks.; Comment: 9 pages, 3 figures; accepted for publication in New Journal of
Physics

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## How to enhance the dynamic range of excitatory-inhibitory excitable networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/12/2013
Português

Relevância na Pesquisa

45.57%

We investigate the collective dynamics of excitatory-inhibitory excitable
networks in response to external stimuli. How to enhance dynamic range, which
represents the ability of networks to encode external stimuli, is crucial to
many applications. We regard the system as a two-layer network (E-Layer and
I-Layer) and explore the criticality and dynamic range on diverse networks.
Interestingly, we find that phase transition occurs when the dominant
eigenvalue of E-layer's weighted adjacency matrix is exactly one, which is only
determined by the topology of E-Layer. Meanwhile, it is shown that dynamic
range is maximized at critical state. Based on theoretical analysis, we propose
an inhibitory factor for each excitatory node. We suggest that if nodes with
high inhibitory factors are cut out from I-Layer, dynamic range could be
further enhanced. However, because of the sparseness of networks and passive
function of inhibitory nodes, the improvement is relatively small compared
tooriginal dynamic range. Even so, this provides a strategy to enhance dynamic
range.; Comment: 7 pages, 9 figures

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## Rhythmogenic neuronal networks, pacemakers, and k-cores

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/12/2008
Português

Relevância na Pesquisa

45.57%

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

Neuronal networks are controlled by a combination of the dynamics of
individual neurons and the connectivity of the network that links them
together. We study a minimal model of the preBotzinger complex, a small
neuronal network that controls the breathing rhythm of mammals through periodic
firing bursts. We show that the properties of a such a randomly connected
network of identical excitatory neurons are fundamentally different from those
of uniformly connected neuronal networks as described by mean-field theory. We
show that (i) the connectivity properties of the networks determines the
location of emergent pacemakers that trigger the firing bursts and (ii) that
the collective desensitization that terminates the firing bursts is determined
again by the network connectivity, through k-core clusters of neurons.; Comment: 4+ pages, 4 figures, submitted to Phys. Rev. Lett

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## Large-scale neural network model for functional networks of the human cortex

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/02/2013
Português

Relevância na Pesquisa

45.57%

#Quantitative Biology - Neurons and Cognition#Nonlinear Sciences - Adaptation and Self-Organizing Systems

We investigate the influence of indirect connections, interregional distance
and collective effects on the large-scale functional networks of the human
cortex. We study topologies of empirically derived resting state networks
(RSNs), extracted from fMRI data, and model dynamics on the obtained networks.
The RSNs are calculated from mean time-series of blood-oxygen-level-dependent
(BOLD) activity of distinct cortical regions via Pearson correlation
coefficients. We compare functional-connectivity networks of simulated BOLD
activity as a function of coupling strength and correlation threshold. Neural
network dynamics underpinning the BOLD signal fluctuations are modelled as
excitable FitzHugh-Nagumo oscillators subject to uncorrelated white Gaussian
noise and time-delayed interactions to account for the finite speed of the
signal propagation along the axons. We discuss the functional connectivity of
simulated BOLD activity in dependence on the signal speed and correlation
threshold and compare it to the empirical data.; Comment: To appear in A. Pelster and G. Wunner (Editors): Proceedings of the
International Symposium Selforganization in Complex Systems: The Past,
Present, and Future of Synergetics; Hanse Institute of Advanced Studies...

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## Signal Propagation in Feedforward Neuronal Networks with Unreliable Synapses

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 18/11/2011
Português

Relevância na Pesquisa

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In this paper, we systematically investigate both the synfire propagation and
firing rate propagation in feedforward neuronal network coupled in an
all-to-all fashion. In contrast to most earlier work, where only reliable
synaptic connections are considered, we mainly examine the effects of
unreliable synapses on both types of neural activity propagation in this work.
We first study networks composed of purely excitatory neurons. Our results show
that both the successful transmission probability and excitatory synaptic
strength largely influence the propagation of these two types of neural
activities, and better tuning of these synaptic parameters makes the considered
network support stable signal propagation. It is also found that noise has
significant but different impacts on these two types of propagation. The
additive Gaussian white noise has the tendency to reduce the precision of the
synfire activity, whereas noise with appropriate intensity can enhance the
performance of firing rate propagation. Further simulations indicate that the
propagation dynamics of the considered neuronal network is not simply
determined by the average amount of received neurotransmitter for each neuron
in a time instant, but also largely influenced by the stochastic effect of
neurotransmitter release. Second...

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## Transient and Equilibrium Synchronization in Complex Neuronal Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

45.57%

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

Transient and equilibrium synchronizations in complex neuronal networks as a
consequence of dynamics induced by having sources placed at specific neurons
are investigated. The basic integrate-and-fire neuron is adopted, and the
dynamics is estimated computationally so as to obtain the activation at each
node along each instant of time. In the transient case, the dynamics is
implemented so as to conserve the total activation entering the system. In our
equilibrium investigations, the internally stored activation is limited to the
value of the respective threshold. The synchronization of the activation of the
network is then quantified in terms of its normalized entropy. The equilibrium
investigations involve the application of a number of complementary
characterization methods, including spectra and Principal Component Analysis,
as well as of an equivalent model capable of reproducing both the transient and
equilibrium dynamics. The potential of such concepts and measurements is
explored with respect to several theoretical models, as well as for the
neuronal network of \emph{C. elegans}. A series of interesting results are
obtained and discussed, including the fact that all models led to a transient
period of synchronization, whose specific features depend on the topological
structures of the networks. The investigations of the equilibrium dynamics
revealed a series of remarkable insights...

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## Six Susceptible-Infected-Susceptible Models on Scale-free Networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/08/2015
Português

Relevância na Pesquisa

45.57%

#Physics - Physics and Society#Condensed Matter - Statistical Mechanics#Computer Science - Social and Information Networks#Nonlinear Sciences - Adaptation and Self-Organizing Systems#Quantitative Biology - Populations and Evolution

Spreading phenomena are ubiquitous in nature and society. For example,
disease, rumor, and information spread over underlying social and information
networks. It is well known that there is no threshold for epidemic models on
scale-free networks; this suggests that disease can spread on such networks,
regardless of how low the contact rate may be. In this paper, I consider six
models with different contact and propagation mechanisms. Each model is
analyzed by degree-based mean-field theory. I show that the presence or absence
of an outbreak threshold depends on the contact and propagation mechanism.; Comment: 6 pages, 1 figure

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## Modeling of protein interaction networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/08/2001
Português

Relevância na Pesquisa

45.57%

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

We introduce a graph generating model aimed at representing the evolution of
protein interaction networks. The model is based on the hypotesis of evolution
by duplications and divergence of the genes which produce proteins. The
obtained graphs shows multifractal properties recovering the absence of a
characteristic connectivity as found in real data of protein interaction
networks. The error tolerance of the model to random or targeted damage is in
very good agreement with the behavior obtained in real protein networks
analysis. The proposed model is a first step in the identification of the
evolutionary dynamics leading to the development of protein functions and
interactions.; Comment: 9 pages, 3 figures

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## Epidemic dynamics in finite size scale-free networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 18/02/2002
Português

Relevância na Pesquisa

45.57%

Many real networks present a bounded scale-free behavior with a connectivity
cut-off due to physical constraints or a finite network size. We study epidemic
dynamics in bounded scale-free networks with soft and hard connectivity
cut-offs. The finite size effects introduced by the cut-off induce an epidemic
threshold that approaches zero at increasing sizes. The induced epidemic
threshold is very small even at a relatively small cut-off, showing that the
neglection of connectivity fluctuations in bounded scale-free networks leads to
a strong over-estimation of the epidemic threshold. We provide the expression
for the infection prevalence and discuss its finite size corrections. The
present work shows that the highly heterogeneous nature of scale-free networks
does not allow the use of homogeneous approximations even for systems of a
relatively small number of nodes.; Comment: 4 pages, 2 eps figures

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## Tree-like Reticulation Networks - When Do Tree-like Distances Also Support Reticulate Evolution?

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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Hybrid evolution and horizontal gene transfer (HGT) are processes where
evolutionary relationships may more accurately be described by a reticulated
network than by a tree. In such a network, there will often be several paths
between any two extant species, reflecting the possible pathways that genetic
material may have been passed down from a common ancestor to these species.
These paths will typically have different lengths but an `average distance' can
still be calculated between any two taxa. In this article, we ask whether this
average distance is able to distinguish reticulate evolution from pure
tree-like evolution. We consider two types of reticulation networks:
hybridization networks and HGT networks. For the former, we establish a general
result which shows that average distances between extant taxa can appear
tree-like, but only under a single hybridization event near the root; in all
other cases, the two forms of evolution can be distinguished by average
distances. For HGT networks, we demonstrate some analogous but more intricate
results.; Comment: 19 pages, 9 figures. Revised version includes clarification in proof
of Theorem 2, and a new figure (Fig 9)

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## Cognitive computation with autonomously active neural networks: an emerging field

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/01/2009
Português

Relevância na Pesquisa

45.57%

The human brain is autonomously active. To understand the functional role of
this self-sustained neural activity, and its interplay with the sensory data
input stream, is an important question in cognitive system research and we
review here the present state of theoretical modelling.
This review will start with a brief overview of the experimental efforts,
together with a discussion of transient vs. self-sustained neural activity in
the framework of reservoir computing. The main emphasis will be then on two
paradigmal neural network architectures showing continuously ongoing
transient-state dynamics: saddle point networks and networks of attractor
relics.
Self-active neural networks are confronted with two seemingly contrasting
demands: a stable internal dynamical state and sensitivity to incoming stimuli.
We show, that this dilemma can be solved by networks of attractor relics based
on competitive neural dynamics, where the attractor relics compete on one side
with each other for transient dominance, and on the other side with the
dynamical influence of the input signals. Unsupervised and local Hebbian-style
online learning then allows the system to build up correlations between the
internal dynamical transient states and the sensory input stream. An emergent
cognitive capability results from this set-up. The system performs online...

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## Deformation of crosslinked semiflexible polymer networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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Networks of filamentous proteins play a crucial role in cell mechanics. These
cytoskeletal networks, together with various crosslinking and other associated
proteins largely determine the (visco)elastic response of cells. In this letter
we study a model system of crosslinked, stiff filaments in order to explore the
connection between the microstructure under strain and the macroscopic response
of cytoskeletal networks. We find two distinct regimes as a function primarily
of crosslink density and filament rigidity: one characterized by affine
deformation and one by non-affine deformation. We characterize the crossover
between these two.; Comment: Typos fixed and some technical details clarified. To appear in Phys.
Rev. Lett

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## Self-Sustaining Oscillations in Complex Networks of Excitable Elements

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/09/2010
Português

Relevância na Pesquisa

45.57%

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

Random networks of symmetrically coupled, excitable elements can
self-organize into coherently oscillating states if the networks contain loops
(indeed loops are abundant in random networks) and if the initial conditions
are sufficiently random. In the oscillating state, signals propagate in a
single direction and one or a few network loops are selected as driving loops
in which the excitation circulates periodically. We analyze the mechanism,
describe the oscillating states, identify the pacemaker loops and explain key
features of their distribution. This mechanism may play a role in epileptic
seizures.; Comment: 5 pages, 4 figures included, submitted to Phys. Rev. Lett

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