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

Laje, Rodrigo; Buonomano, Dean V.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 07/10/2012 Português
Relevância na Pesquisa
45.57%
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.

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

Tattini, Lorenzo; Olmi, Simona; Torcini, Alessandro
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.57%
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...

The Evolutionary Vaccination Dilemma in Complex Networks

Cardillo, Alessio; Reyes-Suárez, Catalina; Naranjo, Fernando; Gómez-Gardeñes, Jesús
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.57%
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

Designing the Dynamics of Spiking Neural Networks

Memmesheimer, Raoul-Martin; Timme, Marc
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.57%
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

Pattern formation in oscillatory complex networks consisting of excitable nodes

Xuhong, Liao; Qinzhi, Xia; Yu, Qian; Lisheng, Zhang; Gang, Hu; Yuanyuan, Mi
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

Model of Genetic Variation in Human Social Networks

Fowler, James H.; Dawes, Christopher T.; Christakis, Nicholas A.
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

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

Cardona, Gabriel; Llabres, Merce; Rossello, Francesc; Valiente, Gabriel
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

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

Perc, Matjaz
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/02/2009 Português
Relevância na Pesquisa
45.57%
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

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

Pei, Sen; Tang, Shaoting; Yan, Shu; Jiang, Shijin; Zhang, Xiao; Zheng, Zhiming
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

Rhythmogenic neuronal networks, pacemakers, and k-cores

Schwab, David J.; Bruinsma, Robijn F.; Levine, Alex J.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 05/12/2008 Português
Relevância na Pesquisa
45.57%
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

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

Vuksanović, Vesna; Hövel, Philipp
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 14/02/2013 Português
Relevância na Pesquisa
45.57%
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...

Signal Propagation in Feedforward Neuronal Networks with Unreliable Synapses

Guo, Daqing; Li, Chunguang
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 18/11/2011 Português
Relevância na Pesquisa
45.57%
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...

Transient and Equilibrium Synchronization in Complex Neuronal Networks

Costa, Luciano da Fontoura
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.57%
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...

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

Morita, Satoru
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/08/2015 Português
Relevância na Pesquisa
45.57%
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

Modeling of protein interaction networks

Vazquez, A.; Flammini, A.; Maritan, A.; Vespignani, A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 02/08/2001 Português
Relevância na Pesquisa
45.57%
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

Epidemic dynamics in finite size scale-free networks

Pastor-Satorras, Romualdo; Vespignani, Alessandro
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

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

Francis, Andrew R.; Steel, Mike
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.57%
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)

Cognitive computation with autonomously active neural networks: an emerging field

Gros, Claudius
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...

Deformation of crosslinked semiflexible polymer networks

Head, D. A.; Levine, A. J.; MacKintosh, F. C.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.57%
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

Self-Sustaining Oscillations in Complex Networks of Excitable Elements

McGraw, Patrick; Menzinger, Michael
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 02/09/2010 Português
Relevância na Pesquisa
45.57%
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