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PubMedDate not supplied

A generalized framework for network component analysis.

The authors recently introduced a framework, named Network Component Analysis (NCA), for the reconstruction of the dynamics of transcriptional regulators' activities from gene expression assays. The original formulation had certain shortcomings that limited NCA's application to a wide class of network dynamics reconstruction problems, either because of limitations in the sample size or because of the stringent requirements imposed by the set of identifiability conditions. In addition, the performance characteristics of the method for various levels of data noise or in the presence of model inaccuracies were never investigated. In this article, the following aspects of NCA have been addressed, resulting in a set of extensions to the original framework: 1) The sufficient conditions on the a priori connectivity information (required for successful reconstructions via NCA) are made less stringent, allowing easier verification of whether a network topology is identifiable, as well as extending the class of identifiable systems. Such a result is accomplished by introducing a set of identifiability requirements that can be directly tested on the regulatory architecture, rather than on specific instances of the system matrix. 2) The two-stage least square iterative procedure used in NCA is proven to identify stationary points of the likelihood function, under Gaussian noise assumption, thus reinforcing the statistical foundations of the method. 3) A framework for the simultaneous reconstruction of multiple regulatory subnetworks is introduced, thus overcoming one of the critical limitations of the original formulation of the decomposition, for example, occurring for poorly sampled data (typical of microarray experiments). A set of monte carlo simulations we conducted with synthetic data suggests that the approach is indeed capable of accurately reconstructing regulatory signals when these are the input of large-scale networks that satisfy the suggested identifiability criteria, even under fairly noisy conditions. The sensitivity of the reconstructed signals to inaccuracies in the hypothesized network topology is also investigated. We demonstrate the feasibility of our approach for the simultaneous reconstruction of multiple regulatory subnetworks from the same data set with a successful application of the technique to gene expression measurements of the bacterium Escherichia coli.

Algorithms↗
PubMed2004

Functional holography of recorded neuronal networks activity.

We present a new approach for analyzing multi-channel recordings, such as ECoG (electrocorticograph) recordings of cortical brain activity and of individual neuron dynamics, in cultured networks. The latter are used here to illustrate the method and its ability to discover hidden functional connectivity motifs in the recorded activity. The cultured networks are formed from dissociated mixtures of cortical neurons and glia-cells that are homogeneously spread over multi-electrode array for recording of the neuronal activity. Rich, spontaneous dynamical behavior is detected, marked by the formation of temporal sequences of synchronized bursting events (SBEs), partitioned into statistically distinguishable subgroups, each with its own characteristic spatio-temporal pattern of activity.In analogy with coherence connectivity networks for multi-location cortical recordings, we evaluated the inter-neuron correlation-matrix for each subgroup. Ordinarily such matrices are mapped onto a connectivity network between neuron positions in real space. In our functional holography, the correlations are normalized by the correlation distances Euclidian distances between the matrix columns. Then, we project the N-dimensional (for N channels) space spanned by the matrix of the normalized correlations, or correlation affinities, onto a corresponding 3D manifold (3D Cartesian space constructed by the three leading principal vectors of the principal component algorithm). The neurons are located by their principal eigenvalues and linked by their original (not normalized) correlations. By looking at these holograms, hidden causal motifs are revealed: each SBEs subgroup generates its characteristic connectivity diagram (network) in the 3D manifold, where the neuron locations and their links form simple structures. Moreover, the computed temporal ordering of neuron activity, when projected onto the connectivity diagrams, also exhibits simple patterns of causal propagation. We show that the method can expose functional connectivity motifs like the co-existence of subneuronal functional networks in the space of affinities. The method can be directly utilized to construct similar causal holograms for recorded brain activity. We expect that by doing so, hidden functional connectivity motifs with relevance to the understanding of brain activity might be discovered.

Animals↗
PubMed2004

Associative memory by recurrent neural networks with delay elements.

The synapses of real neural systems seem to have delays. Therefore, it is worthwhile to analyze associative memory models with delayed synapses. Thus, a sequential associative memory model with delayed synapses is discussed, where a discrete synchronous updating rule and a correlation learning rule are employed. Its dynamic properties are analyzed by the statistical neurodynamics. In this paper, we first re-derive the Yanai-Kim theory, which involves macrodynamical equations for the dynamics of the network with serial delay elements. Since their theory needs a computational complexity of O(L4t) to obtain the macroscopic state at time step t where L is the length of delay, it is intractable to discuss the macroscopic properties for a large L limit. Thus, we derive steady state equations using the discrete Fourier transformation, where the computational complexity does not formally depend on L. We show that the storage capacity alphaC is in proportion to the delay length L with a large L limit, and the proportion constant is 0.195, i.e. alphaC=0.195L. These results are supported by computer simulations.

Association Learning↗
PubMed1998

The neural network approach to a parallel decentralized network routing.

With the progress of high-speed optical transmission and packet switching, a large capacity packet-based multi-media communication network is expected to spread rapidly. One of the key issues in these networks is the network routing that chooses the route to the destination for packet transmission in the network. In most previous work, the whole network is mapped to a large size-Hopfield-type neural network. Hence, the network routing by this method is not beyond the centralized control. In this paper, a parallel decentralized Network Routing method is presented. The model comprises an interconnection of groups of an intraconnected network, which is fully connected, and resides at each node of the communication network. Since the dynamics of each neuron in the whole system follows a unique state equation, we can see easily how the update of a neuron maps to real world network routing problems. Most important, becauase of the dynamics of the neurons with such a high speed of convergence, the model has the ability to achieve a sub-optimum routing solution in a real-time application. Finally, simulation results validate the proposed method.

Journal Article↗
PubMed1986

Associative recognition and storage in a model network of physiological neurons.

We consider a neural network model in which the single neurons are chosen to closely resemble known physiological properties. The neurons are assumed to be linked by synapses which change their strength according to Hebbian rules on a short time scale (100 ms). The dynamics of the network--the time evolution of the cell potentials and the synapses--is investigated by computer simulation. As in more abstract network models (Cooper 1973; Hopfield 1982; Kohonen 1984) it is found that the local dynamics of the cell potentials and the synaptic strengths result in global cooperative properties of the network and enable the network to process an incoming flux of information and to learn and store patterns associatively. A trained net can associate missing details of a pattern, can correct wrong details and can suppress noise in a pattern. The network can further abstract the prototype from a series of patterns with variations. A suitable coupling constant connecting the dynamics of the cell potentials with the synaptic strengths is derived by a mean field approximation. This coupling constant controls the neural sensitivity and thereby avoids both extremes of the network state, the state of permanent inactivity and the state of epileptic hyperactivity.

Animals↗
PubMed2004

Global asymptotic stability of Hopfield neural network involving distributed delays.

In the paper, we study dynamical behaviors of Hopfield neural networks system with distributed delays. Some new criteria ensuring the existence and uniqueness, and the global asymptotic stability (GAS) of equilibrium point are derived. In the results, we do not assume that the signal propagation functions satisfy the Lipschitz condition and do not require them to be bounded, differentiable or strictly increasing. Moreover, the symmetry of the connection matrix is not also necessary. Thus, we improve some previous works of other researchers. These conditions are presented in terms of system parameters and have importance leading significance in designs and applications of the GAS for Hopfield neural networks system with distributed delays. Two examples are also worked out to demonstrate the advantages of our results.

Computer Simulation↗
PubMed2006

When response variability increases neural network robustness to synaptic noise.

Cortical sensory neurons are known to be highly variable, in the sense that responses evoked by identical stimuli often change dramatically from trial to trial. The origin of this variability is uncertain, but it is usually interpreted as detrimental noise that reduces the computational accuracy of neural circuits. Here we investigate the possibility that such response variability might in fact be beneficial, because it may partially compensate for a decrease in accuracy due to stochastic changes in the synaptic strengths of a network. We study the interplay between two kinds of noise, response (or neuronal) noise and synaptic noise, by analyzing their joint influence on the accuracy of neural networks trained to perform various tasks. We find an interesting, generic interaction: when fluctuations in the synaptic connections are proportional to their strengths (multiplicative noise), a certain amount of response noise in the input neurons can significantly improve network performance, compared to the same network without response noise. Performance is enhanced because response noise and multiplicative synaptic noise are in some ways equivalent. So if the algorithm used to find the optimal synaptic weights can take into account the variability of the model neurons, it can also take into account the variability of the synapses. Thus, the connection patterns generated with response noise are typically more resistant to synaptic degradation than those obtained without response noise. As a consequence of this interplay, if multiplicative synaptic noise is present, it is better to have response noise in the network than not to have it. These results are demonstrated analytically for the most basic network consisting of two input neurons and one output neuron performing a simple classification task, but computer simulations show that the phenomenon persists in a wide range of architectures, including recurrent (attractor) networks and sensorimotor networks that perform coordinate transformations. The results suggest that response variability could play an important dynamic role in networks that continuously learn.

Algorithms↗
PubMed2005

iVici: Interrelational Visualization and Correlation Interface.

We have developed an application, iVici, to analyze cellular networks represented as addressable symmetric or asymmetric two-dimensional matrices. iVici was designed to permit simultaneous visualization and correlation of multiple datasets, representing any relationship between a set of genes, mRNAs, or proteins. Visual overlay of datasets and addressable access to gene annotations permits comparison of networks of different types (for example protein-protein interactions and genetic networks) or investigation of the dynamic reorganization of a particular network.

Computational Biology↗
PubMedDate not supplied

On the neural correlates of visual perception.

Neurological findings suggest that the human striate cortex (V1) is an indispensable component of a neural substratum subserving static achromatic form perception in its own right and not simply as a central distributor of retinally derived information to extrastriate visual areas. This view is further supported by physiological evidence in primates that the finest-grained conjoined representation of spatial detail and retinotopic localization that underlies phenomenal visual experience for local brightness discriminations is selectively represented at cortical levels by the activity of certain neurons in V1. However, at first glance, support for these ideas would appear to be undermined by incontrovertible neurological evidence (visual hemineglect and the simultanagnosias) and recent psychophysical results on 'crowding' that confirm that activation of neurons in V1 may, at times, be insufficient to generate a percept. Moreover, a recent proposal suggests that neural correlates of visual awareness must project directly to those in executive space, thus automatically excluding V1 from a related perceptual space because V1 lacks such direct projections. Both sets of concerns are, however, resolved within the context of adaptive resonance theories. Recursive loops, linking the dorsal lateral geniculate nucleus (LGN) through successive cortical visual areas to the temporal lobe by means of a series of ascending and descending pathways, provide a neuronal substratum at each level within a modular framework for mutually consistent descriptions of sensory data. At steady state, such networks obviate the necessity that neural correlates of visual experience project directly to those in executive space because a neural phenomenal perceptual space subserving form vision is continuously updated by information from an object recognition space equivalent to that destined to reach executive space. Within this framework, activity in V1 may engender percepts that accompany figure-ground segregations only when dynamic incongruities are resolved both within and between ascending and descending streams. Synchronous neuronal activity on a short timescale within and across cortical areas, proposed and sometimes observed as perceptual correlates, may also serve as a marker that a steady state has been achieved, which, in turn, may be a requirement for the longer time constants that accompany the emergence and stability of perceptual states compared to the faster dynamics of adapting networks and the still faster dynamics of individual action potentials. Finally, the same consensus of neuronal activity across ascending and descending pathways linking multiple cortical areas that in anatomic sequence subserve phenomenal visual experiences and object recognition may underlie the normal unity of conscious experience.

Adaptation, Physiological↗
PubMed2006

Neuronal networks and synaptic plasticity: understanding complex system dynamics by interfacing neurons with silicon technologies.

Information processing in the central nervous system is primarily mediated through synaptic connections between neurons. This connectivity in turn defines how large ensembles of neurons may coordinate network output to execute complex sensory and motor functions including learning and memory. The synaptic connectivity between any given pair of neurons is not hard-wired; rather it exhibits a high degree of plasticity, which in turn forms the basis for learning and memory. While there has been extensive research to define the cellular and molecular basis of synaptic plasticity, at the level of either pairs of neurons or smaller networks, analysis of larger neuronal ensembles has proved technically challenging. The ability to monitor the activities of larger neuronal networks simultaneously and non-invasively is a necessary prerequisite to understanding how neuronal networks function at the systems level. Here we describe recent breakthroughs in the area of various bionic hybrids whereby neuronal networks have been successfully interfaced with silicon devices to monitor the output of synaptically connected neurons. These technologies hold tremendous potential for future research not only in the area of synaptic plasticity but also for the development of strategies that will enable implantation of electronic devices in live animals during various memory tasks.

Animals↗
PubMed2005

Generating Boolean networks with a prescribed attractor structure.

MOTIVATION: Dynamical modeling of gene regulation via network models constitutes a key problem for genomics. The long-run characteristics of a dynamical system are critical and their determination is a primary aspect of system analysis. In the other direction, system synthesis involves constructing a network possessing a given set of properties. This constitutes the inverse problem. Generally, the inverse problem is ill-posed, meaning there will be many networks, or perhaps none, possessing the desired properties. Relative to long-run behavior, we may wish to construct networks possessing a desirable steady-state distribution. This paper addresses the long-run inverse problem pertaining to Boolean networks (BNs). RESULTS: The long-run behavior of a BN is characterized by its attractors. The rest of the state transition diagram is partitioned into level sets, the j-th level set being composed of all states that transition to one of the attractor states in exactly j transitions. We present two algorithms for the attractor inverse problem. The attractors are specified, and the sizes of the predictor sets and the number of levels are constrained. Algorithm complexity and performance are analyzed. The algorithmic solutions have immediate application. Under the assumption that sampling is from the steady state, a basic criterion for checking the validity of a designed network is that there should be concordance between the attractor states of the model and the data states. This criterion can be used to test a design algorithm: randomly select a set of states to be used as data states; generate a BN possessing the selected states as attractors, perhaps with some added requirements such as constraints on the number of predictors and the level structure; apply the design algorithm; and check the concordance between the attractor states of the designed network and the data states. AVAILABILITY: The software and supplementary material is available at http://gsp.tamu.edu/Publications/BNs/bn.htm

Algorithms↗
PubMed2007

Modelling memory functions with recurrent neural networks consisting of input compensation units: II. Dynamic situations.

Modelling the cognitive abilities of humans or animals or building agents that are supposed to behave cognitively requires modelling a memory system that is able to store and retrieve various contents. The content to be stored is assumed to comprise information about more or less invariant environmental objects as well as information about movements. A combination of information about both objects and movements may be called a situation model. Here we focus, in part, on models storing dynamic patterns. In particular, two abilities of humans in representing dynamical systems receive special focus: the capability of representing the acceleration of objects, as can be found in the movement of a pendulum or freely falling objects, and the capability of representing actions of transfer, i.e. motion from one point to another, have been modelled using recurrent networks consisting of input compensation units. In addition, possibilities of combining static and dynamic properties within a single model are studied.

Cognition↗
PubMed2001

Spatially structured metapopulation models: global and local assessment of metapopulation capacity.

We model metapopulation dynamics in finite networks of discrete habitat patches with given areas and spatial locations. We define and analyze two simple and ecologically intuitive measures of the capacity of the habitat patch network to support a viable metapopulation. Metapopulation persistence capacity lambda(M) defines the threshold condition for long-term metapopulation persistence as lambda(M)>delta, where delta is defined by the extinction and colonization rate parameters of the focal species. Metapopulation invasion capacity lambda(I) sets the condition for successful invasion of an empty network from one small local population as lambda(I)>delta. The metapopulation capacities lambda(M) and lambda(I) are defined as the leading eigenvalue or a comparable quantity of an appropriate "landscape" matrix. Based on these definitions, we present a classification of a very general class of deterministic, continuous-time and discrete-time metapopulation models. Two specific models are analyzed in greater detail: a spatially realistic version of the continuous-time Levins model and the discrete-time incidence function model with propagule size-dependent colonization rate and a rescue effect. In both models we assume that the extinction rate increases with decreasing patch area and that the colonization rate increases with patch connectivity. In the spatially realistic Levins model, the two types of metapopulation capacities coincide, whereas the incidence function model possesses a strong Allee effect characterized by lambda(I)=0. For these two models, we show that the metapopulation capacities can be considered as simple sums of contributions from individual habitat patches, given by the elements of the leading eigenvector or comparable quantities. We may therefore assess the significance of particular habitat patches, including new patches that might be added to the network, for the metapopulation capacities of the network as a whole. We derive useful approximations for both the threshold conditions and the equilibrium states in the two models. The metapopulation capacities and the measures of the dynamic significance of particular patches can be calculated for real patch networks for applications in metapopulation ecology, landscape ecology, and conservation biology.

Animals↗
PubMed2003

Detecting functional interactions in a gene and signaling network by time-resolved somatic complementation analysis.

Somatic complementation by fusion of two mutant cells and mixing of their cytoplasms occurs when the genetic defect of one fusion partner is cured by the functional gene product provided by the other. We have found that complementation of mutational defects in the network mediating stimulus-induced commitment and sporulation of Physarum polycephalum may reflect time-dependent changes in the signaling state of its molecular building blocks. Network perturbation by fusion of mutant plasmodial cells in different states of activation, and the time-resolved analysis of somatic complementation effects can be used to systematically probe network structure and dynamics. Time-resolved somatic complementation quantitatively detects regulatory interactions between the functional modules of a network, independent of their biochemical composition or subcellular localization, and without being limited to direct physical interactions.

Animals↗
PubMed2003

Changing excitation and inhibition in simulated neural networks: effects on induced bursting behavior.

The development of synchronous bursting in neuronal ensembles represents an important change in network behavior. To determine the influences on development of such synchronous bursting behavior we study the dynamics of small networks of sparsely connected excitatory and inhibitory neurons using numerical simulations. The synchronized bursting activities in networks evoked by background spikes are investigated. Specifically, patterns of bursting activity are examined when the balance between excitation and inhibition on neuronal inputs is varied and the fraction of inhibitory neurons in the network is changed. For quantitative comparison of bursting activities in networks, measures of the degree of synchrony are used. We demonstrate how changes in the strength of excitation on inputs of neurons can be compensated by changes in the strength of inhibition without changing the degree of synchrony in the network. The effects of changing several network parameters on the network activity are analyzed and discussed. These changes may underlie the transition of network activity from normal to potentially pathologic (e.g., epileptic) states.

Action Potentials↗
PubMed2001

Interfacing a silicon chip to pairs of snail neurons connected by electrical synapses.

Future hybrid neuron-semiconductor chips will consist of complex neural networks that are directly interfaced to electronic integrated circuits. They will help us to understand the dynamics of neuronal networks and may lead to novel computational facilities. Here we report on an elementary step towards such neurochips. We designed and fabricated a silicon chip for multiple two-way interfacing, and cultured on it pairs of neurons from the pedal ganglia of the snail Lymnaea stagnalis. These neurons were joined to each other by an electrical synapse, and to the chip by a capacitive stimulator and a recording transistor. We obtained a set of neuroelectronic units with sequential and parallel signal transmission through the neuron-silicon interface and the synapse, with a bidirectionally interfaced neuron-pair and with a signal path from the chip through a synaptically connected neuron pair back to the chip. The prospects for assembling more involved hybrid networks on the basis of these neuroelectronic units are considered.

Animals↗
PubMed2004

LGL: creating a map of protein function with an algorithm for visualizing very large biological networks.

Networks are proving to be central to the study of gene function, protein-protein interaction, and biochemical pathway data. Visualization of networks is important for their study, but visualization tools are often inadequate for working with very large biological networks. Here, we present an algorithm, called large graph layout (LGL), which can be used to dynamically visualize large networks on the order of hundreds of thousands of vertices and millions of edges. LGL applies a force-directed iterative layout guided by a minimal spanning tree of the network in order to generate coordinates for the vertices in two or three dimensions, which are subsequently visualized and interactively navigated with companion programs. We demonstrate the use of LGL in visualizing an extensive protein map summarizing the results of approximately 21 billion sequence comparisons between 145579 proteins from 50 genomes. Proteins are positioned in the map according to sequence homology and gene fusions, with the map ultimately serving as a theoretical framework that integrates inferences about gene function derived from sequence homology, remote homology, gene fusions, and higher-order fusions. We confirm that protein neighbors in the resulting map are functionally related, and that distinct map regions correspond to distinct cellular systems, enabling a computational strategy for discovering proteins' functions on the basis of the proteins' map positions. Using the map produced by LGL, we infer general functions for 23 uncharacterized protein families.

Algorithms↗
PubMed2004

Non-linear filtering of ultrasonic signals using neural networks.

Structure noise from inhomogeneous micro-structures makes the detection of flaws present in highly scattering materials difficult. Several techniques have been applied to improve the signal-to-noise ratio (SNR) in order to make flaw detection easier. Linear filtering does not provide good results because both structure noise and flaw signal concentrate energy in the same frequency band. Non-linear filtering can be used to reduce the structure noise of ultrasonic signals. Therefore, neural networks are applied in this work for this purpose. In order to use neural networks for non-linear filtering, dynamic structures must be applied. The easiest way to implement a neural network with the capability of processing temporal patterns is to consider them spatial ones, applying the signal into a tapped delay line of finite extension, that is the input of a static neural network (for example, a multi-layer perceptron). In this work, a dynamic neural network has been built to filter ultrasonic signals with structure noise, and has been trained with the real-time back-propagation algorithm, using as inputs 3000 synthetic ultrasonic signals of 896 samples each. Target signals for training are the same as the ones used as inputs but without noise. The neural network is trained in order to generate as output the target signal when the noisy input one is applied. For testing the performance of the non-linear filter, a new set of 500 noisy signals has been used. The SNR improvement is about 6 dB average. The results show that this non-linear filtering method is quite useful as pre-processing stage in flaw detection systems.

Algorithms↗