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Constructing precisely computing networks with biophysical spiking neurons

Schwemmer, Michael A.; Fairhall, Adrienne L.; Denéve, Sophie; Shea-Brown, Eric T.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.58%
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...

The spread of epidemic disease on networks

Newman, M. E. J.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/04/2002 Português
Relevância na Pesquisa
45.58%
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

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

Kiss, Istvan Z.; Morris, Charles G.; Sélley, Fanni; Simon, Péter L.; Wilkinson, Robert R.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 29/07/2013 Português
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45.58%
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...

Resilience of human brain functional coactivation networks under thresholding

Sarkar, S.; Chawla, S.; Weng, H.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 06/07/2014 Português
Relevância na Pesquisa
45.58%
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...

Interspecific competition underlying mutualistic networks

Maeng, Seong Eun; Lee, Jae Woo; Lee, Deok-Sun
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.58%
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

Extreme self-organization in networks constructed from gene expression data

Agrawal, Himanshu
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.58%
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

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

Gewaltig, Marc-Oliver
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 06/11/2013 Português
Relevância na Pesquisa
45.58%
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...

Bayesian Inference of Whole-Brain Networks

Hinne, M.; Heskes, T.; van Gerven, M. A. J.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 08/02/2012 Português
Relevância na Pesquisa
45.58%
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

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

Shao, Zhen; Zhou, Hai-jun
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 04/01/2009 Português
Relevância na Pesquisa
45.58%
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

Probabilistic Regulatory Networks: Modeling Genetic Networks

Avino-Diaz, Maria A.; Moreno, Oscar
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 22/06/2006 Português
Relevância na Pesquisa
45.58%
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

Excitable Scale Free Networks

Copelli, Mauro; Campos, Paulo R. A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.58%
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...

The functional structure of cortical neuronal networks grown in vitro

Bettencourt, Luis M. A.; Stephens, Greg J.; Ham, Michael I.; Gross, Guenter W.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 07/03/2007 Português
Relevância na Pesquisa
45.58%
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...

Statistical Properties of Avalanches in Networks

Larremore, Daniel B.; Carpenter, Marshall Y.; Ott, Edward; Restrepo, Juan G.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 17/04/2012 Português
Relevância na Pesquisa
45.58%
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...

Scale-free brain functional networks

Eguiluz, Victor M.; Chialvo, Dante R.; Cecchi, Guillermo A.; Baliki, Marwan; Apkarian, A. Vania
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.58%
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

Epidemics in partially overlapped multiplex networks

Buono, C.; Zuzek, L. G. Alvarez; Macri, P. A.; Braunstein, L. A.
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...

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

Miconi, Thomas
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...

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

Franco, Leonardo
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/11/2001 Português
Relevância na Pesquisa
45.58%
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...

Connectivity Distribution of Spatial Networks

Herrmann, Carl; Barthelemy, Marc; Provero, Paolo
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/02/2003 Português
Relevância na Pesquisa
45.58%
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

Phase Diagram of Spiking Neural Networks

Seyed-allaei, Hamed
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
45.58%
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...

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

Amancio, Diego R.; Oliveira Jr., Osvaldo N.; Costa, Luciano da F.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 24/09/2012 Português
Relevância na Pesquisa
45.58%
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...