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PubMed1998

Analysis and modeling of the locomotor central pattern generator as a network of coupled oscillators.

The primary functions of spinal locomotor central pattern generators (CPGs) are to provide oscillatory motor commands to individual joints or segments and to control the precise timing of those commands across all joints or segments for efficient, coordinated locomotor behavior. Our ability to understand the neuronal mechanisms underlying intersegmental coordination has been hampered by the complexity of propriospinal interconnectivity and the paucity of quantitative data on the magnitude and timing of those connections. Theoretical approaches have therefore been employed to discover general rules by which CPG-like oscillator systems must be constructed to produce appropriate coordinated locomotor behavior; the locomotor CPG is represented as a network of oscillators, where each oscillator generates local motor output and interoscillator coupling provides intersegmental coordination. Mathematical analysis of such coupled oscillator systems has provided a number of experimentally testable predictions regarding the link between coupling and coordination. Application of these network-level predictions to the results of electrophysiological experiments has required data analysis methods that can relate the behavior of the in vitro spinal cord to the variables employed by the mathematical model. Hence, our most recent work has focused on developing analytic tools for quantifying the changes in locomotor output that result form experimental manipulations of the propriospinal system in terms of frequency, intersegmental phase, and intersegmental correlation. Results of recent experiments can now be used to put further constraints on the allowable kinds of intersegmental coupling provided by mathematical modeling of the system.

Animals↗
PubMed2006

Self-organization of spiking neural network that generates autonomous behavior in a real mobile robot.

In this paper, we propose self-organization algorithm of spiking neural network (SNN) applicable to autonomous robot for generation of adoptive and goal-directed behavior. First, we formulated a SNN model whose inputs and outputs were analog and the hidden unites are interconnected each other. Next, we implemented it into a miniature mobile robot Khepera. In order to see whether or not a solution(s) for the given task(s) exists with the SNN, the robot was evolved with the genetic algorithm in the environment. The robot acquired the obstacle avoidance and navigation task successfully, exhibiting the presence of the solution. After that, a self-organization algorithm based on a use-dependent synaptic potentiation and depotentiation at synapses of input layer to hidden layer and of hidden layer to output layer was formulated and implemented into the robot. In the environment, the robot incrementally organized the network and the given tasks were successfully performed. The time needed to acquire the desired adoptive and goal-directed behavior using the proposed self-organization method was much less than that with the genetic evolution, approximately one fifth.

Action Potentials↗
PubMed1994

Average case analysis of an Hebb-type rule that finds the network connectivity.

We describe an Hebb-type algorithm for learning unions of nonoverlapping perceptrons with binary weights. Two perceptrons are said to be nonoverlapping if they do not share any input variables. The learning algorithm is able to find both the network architecture and the weight values necessary to represent the target function. Moreover, the algorithm is local, homogeneous, and simple enough to be biologically plausible. We investigate the average behavior of this algorithm as a function of the size of the training set. We find that, as the size of the training set increases, the hypothesis network built by the algorithm "converges" to the target network, both in terms of the number of perceptrons and the connectivity. Moreover, the generalization rate converges exponentially to perfect generalization as a function of the number of training examples. The analytic expressions are in excellent agreement with the numerical simulations. To our knowledge, this is the first average case analysis of an algorithm that finds both the weight values and the network connectivity.

Algorithms↗
PubMed1996

A new type of self-organization associated with chaotic dynamics in neural networks.

A new type of self-organized dynamics is presented, in relation with chaos in neural networks. One is chaotic itinerancy and the other is chaos-driven contraction dynamics. The former is addressed as a universal behavior in high-dimensional dynamical systems. In particular, it can be viewed as one possible form of memory dynamics in brain. The latter gives rise to singular-continuous nowhere-differentiable attractors. These dynamics can be related to each other in the context of dimensionality and of chaotic information processings. Possible roles of these complex dynamics in brain are also discussed.

Animals↗
PubMed1999

Integrating neuromorphic action-oriented perceptual inputs to generate a navigation behaviour for a robot.

We use neural networks with pointer map architectures to provide simple attentional processing in a robotic task. A pointer map comprises a map of neurons that encode a stimulus. Besides global feedback inhibition, the map receives feedback excitation via a small group of pointer neurons that encode the location of a salient stimulus on the map as a vectorial representation. The pointer neurons are able to apply selective processing to a particular region of the network. The robot uses these properties to manoeuver in relation to an attended object. We implemented a controller composed of two pointer maps, and a motor map. The first pointer map reports the direction of a salient obstacle in a one-dimensional map of distance derived from infrared sensors. The second pointer map reports the direction to potential obstacles in a two-dimensional edge-enhanced image derived from a forward looking CCD-camera. These outputs are applied to a motor map, where they bias the motor control signals issued to the robots wheels, according to navigational intentions.

Avoidance Learning↗
PubMed2006

Are sparse-coding simple cell receptive field models physiologically plausible?

Olshausen and Field (1996) developed a simple cell receptive field model for natural scene processing in V1, based on unsupervised learning and non-orthogonal basis function optimization of an overcomplete representation of visual space. The model was originally tested with an ensemble of whitened natural scenes, simulating pre-cortical filtering in the retinal ganglia and lateral geniculate nucleus, and the basis functions qualitatively resembled the orientation-specific responses of V1 simple cells in the spatial domain. In this study, the quantitative tuning responses of the basis functions in the spectral domain are estimated using a Gaussian model, to determine their goodness-of-fit to the known bandwidths of simple cells in primate V1. Five simulation experiments which examined key features of the model are reported: changing the size of the basis functions; using a complete versus over-complete representation; changing the sparseness factor; using a variable learning rate; and mapping the basis functions with a whitening spatial function. The key finding of this study is that across all image themes, basis function sizes, number of basis functions, sparseness factors and learning rates, the spatial-frequency tuning did not closely resemble that of primate area 17 -- the model results more closely resembled the unclassified cat neurones of area 19 with a single exception, and not area 17 as predicted.

Action Potentials↗
PubMed2003

Timing of network synchronization by refractory mechanisms.

Even without active pacemaker mechanisms, temporally patterned synchronization of neural network activity can emerge spontaneously and is involved in neural development and information processing. Generation of spontaneous synchronization is thought to arise as an alternating sequence between a state of elevated excitation followed by a period of quiescence associated with neuronal and/or synaptic refractoriness. However, the cellular factors controlling recruitment and timing of synchronized events have remained difficult to specify, although the specific temporal pattern of spontaneous rhythmogenesis determines its impact on developmental processes. We studied spontaneous synchronization in a model of 600-1,000 integrate-and-fire neurons interconnected with a probability of 5-30%. One-third of neurons generated spontaneous discharges and provided a background of intrinsic activity to the network. The heterogeneity and random coupling of these neurons maintained this background activity asynchronous. Refractoriness was modeled either by use-dependent synaptic depression or by cellular afterhyperpolarization. In both cases, the recruitment of neurons into spontaneous synchronized discharges was determined by the interplay of refractory mechanisms with stochastic fluctuations in background activity. Subgroups of easily recruitable neurons served as amplifiers of these fluctuations, thereby initiating a cascade-like recruitment of neurons ("avalanche effect"). In contrast, timing depended on the precise implementation of neuronal refractoriness and synaptic connectivity. With synaptic depression, neuronal synchronization always occurred stochastically, whereas with cellular afterhyperpolarization, stochastic turned into periodic behavior with increasing synaptic strength. These results associate the type of refractory mechanism with the temporal statistics and the mechanism of synchronization, thereby providing a framework for differentiating between cellular mechanisms of spontaneous rhythmogenesis.

Action Potentials↗
PubMed2006

Dynamical characteristics common to neuronal competition models.

Models implementing neuronal competition by reciprocally inhibitory populations are widely used to characterize bistable phenomena such as binocular rivalry. We find common dynamical behavior in several models of this general type, which differ in their architecture in the form of their gain functions, and in how they implement the slow process that underlies alternating dominance. We focus on examining the effect of the input strength on the rate (and existence) of oscillations. In spite of their differences, all considered models possess similar qualitative features, some of which we report here for the first time. Experimentally, dominance durations have been reported to decrease monotonically with increasing stimulus strength (such as Levelt's "Proposition IV"). The models predict this behavior; however, they also predict that at a lower range of input strength dominance durations increase with increasing stimulus strength. The nonmonotonic dependency of duration on stimulus strength is common to both deterministic and stochastic models. We conclude that additional experimental tests of Levelt's Proposition IV are needed to reconcile models and perception.

Action Potentials↗
PubMed2003

Lack of monosynaptic corticomotoneuronal EPSPs in rats: disynaptic EPSPs mediated via reticulospinal neurons and polysynaptic EPSPs via segmental interneurons.

In the rat, some findings have been taken to suggest the existence of monosynaptic corticomotoneuronal (CM) connections. Because this connection is believed to be largely responsible for the ability to make independent digit movements in primates and man, it has been inferred that the monosynaptic CM connection in the rat is likewise important for skilled prehension. Comparison of intra- and extracellular recordings from forelimb motoneurons in anesthetized rats, revealed no monosynaptic CM excitatory postsynaptic potentials (EPSPs). The fastest descending excitation in forelimb motoneurons was disynaptically mediated via a corticoreticulospinal pathway and slowly conducted excitation via corticospinal fibers and segmental interneurons. The findings stress the importance of di- and trisynaptic excitatory corticofugal pathways to forelimb motoneurons in the control of skillful digit movements.

Animals↗
PubMed2005

Drosophila CAKI/CMG protein, a homolog of human CASK, is essential for regulation of neurotransmitter vesicle release.

Vertebrate CASK is a member of the membrane-associated guanylate kinase (MAGUK) family of proteins. CASK is present in the nervous system where it binds to neurexin, a transmembrane protein localized in the presynaptic membrane. The Drosophila homologue of CASK is CAKI or CAMGUK. CAKI is expressed in the nervous system of larvae and adult flies. In adult flies, the expression of caki is particularly evident in the visual brain regions. To elucidate the functional role of CASK, we employed a caki null mutant in the model organism Drosophila melanogaster. By means of electrophysiological methods, we analyzed, in adult flies, the spontaneous and evoked neurotransmitter release at the neuromuscular junction (NMJ) as well as the functional status of the giant fiber pathway and of the visual system. We found that in caki mutants, when synaptic activity is modified, the spontaneous neurotransmitter release of the indirect flight muscle NMJ was increased, the response of the giant fiber pathway to continuous stimulation was impaired, and electroretinographic responses to single and continuous repetitive stimuli were altered and optomotor behavior was abnormal. These results support the involvement of CAKI in neurotransmitter release and nervous system function.

Animals↗
PubMed1994

Synchronization properties of spindle oscillations in a thalamic reticular nucleus model.

1. We address the hypothesis of Steriade and colleagues that the thalamic reticular nucleus (RE) is a pacemaker for thalamocortical spindle oscillations by developing and analyzing a model of a large population of all-to-all coupled inhibitory RE neurons. 2. Each RE neuron has three ionic currents: a low-threshold T-type Ca2+ current (ICa-T), a calcium-activated potassium current (IAHP) and a leakage current (IL). ICa-T underlies a cell's postinhibitory rebound properties, whereas IAHP hyperpolarizes the neuron after a burst. Each neuron, which is a conditional oscillator, is coupled to all other RE neurons via fast gamma-aminobutyric acid-A (GABAA) and slow GABAB synapses. 3. For generating network oscillations IAHP may not be necessary. Synaptic inhibition can provide the hyperpolarization for deinactivating ICa-T that causes bursting if the reversal potentials for GABAA and GABAB synapses are sufficiently negative. 4. If model neurons display sufficiently powerful rebound excitability, an isolated RE network of such neurons oscillates with partial but typically not full synchrony. The neurons spontaneously segregate themselves into several macroscopic clusters. The neurons within a cluster follow the same time course, but the clusters oscillate differently from one another. In addition to activity patterns in which clusters burst sequentially (e.g., 2 or 3 clusters bursting alternately), a two-cluster state may occur with one cluster active and one quiescent. Because the neurons are all-to-all coupled, the cluster states do not have any spatial structure. 5. We have explored the sensitivity of such partially synchronized patterns to heterogeneity in cells' intrinsic properties and to simulated neuroelectric noise. Although either precludes precise clustering, modest levels of heterogeneity or noise lead to approximate clustering of active cells. The population-averaged voltage may oscillate almost regularly but individual cells burst at nearly every second cycle or less frequently. The active-quiescent state is not robust at all to heterogeneity or noise. Total asynchrony is observed when heterogeneity or noise is too large, e.g., even at 25% heterogeneity for our reference set of parameter values. 6. The fast GABAA inhibition (with a reversal potential more negative than, say, -65 mV) favors the cluster states and prevents full synchrony. Our simulation results suggest two mechanisms that can fully synchronize the isolated RE network model. With GABAA removed or almost totally blocked, GABAB inhibition (because it is slow) can lead to full synchrony, which is partially robust to heterogeneity and noise.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗
PubMed2003

A simple and stable numerical solution for the population density equation.

A population density description of large populations of neurons has generated considerable interest recently. The evolution in time of the population density is determined by a partial differential equation (PDE). Most of the algorithms proposed to solve this PDE have used finite difference schemes. Here, I use the method of characteristics to reduce the PDE to a set of ordinary differential equations, which are easy to solve. The method is applied to leaky-integrate-and-fire neurons and produces an algorithm that is efficient and yields a stable and manifestly nonnegative density. Contrary to algorithms based directly on finite difference schemes, this algorithm is insensitive to large density gradients, which may occur during evolution of the density.

Algorithms↗
PubMed2003

Localization of function via lesion analysis.

This article presents a general approach for employing lesion analysis to address the fundamental challenge of localizing functions in a neural system. We describe functional contribution analysis (FCA), which assigns contribution values to the elements of the network such that the ability to predict the network's performance in response to multilesions is maximized. The approach is thoroughly examined on neurocontroller networks of evolved autonomous agents. The FCA portrays a stable set of neuronal contributions and accurate multilesion predictions that are significantly better than those obtained based on the classical single lesion approach. It is also used for a detailed synaptic analysis of the neurocontroller connectivity network, delineating its main functional backbone. The FCA provides a quantitative way of measuring how the network functions are localized and distributed among its elements. Our results question the adequacy of the classical single lesion analysis traditionally used in neuroscience and show that using lesioning experiments to decipher even simple neuronal systems requires a more rigorous multilesion analysis.

Algorithms↗
PubMed2003

The time-organized map algorithm: extending the self-organizing map to spatiotemporal signals.

The new time-organized map (TOM) is presented for a better understanding of the self-organization and geometric structure of cortical signal representations. The algorithm extends the common self-organizing map (SOM) from the processing of purely spatial signals to the processing of spatiotemporal signals. The main additional idea of the TOM compared with the SOM is the functionally reasonable transfer of temporal signal distances into spatial signal distances in topographic neural representations. This is achieved by neural dynamics of propagating waves, allowing current and former signals to interact spatiotemporally in the neural network. Within a biologically plausible framework, the TOM algorithm (1) reveals how dynamic neural networks can self-organize to embed spatial signals in temporal context in order to realize functional meaningful invariances, (2) predicts time-organized representational structures in cortical areas representing signals with systematic temporal relation, and (3) suggests that the strength with which signals interact in the cortex determines the type of signal topology realized in topographic maps (e.g., spatially or temporally defined signal topology). Moreover, the TOM algorithm supports the explanation of topographic reorganizations based on time-to-space transformations (Wiemer, Spengler, Joublin, Stagge, & Wacquant, 2000).

Algorithms↗
PubMed2003

New conditions on global stability of Cohen-Grossberg neural networks.

In this letter, we discuss the dynamics of the Cohen-Grossberg neural networks. We provide a new and relaxed set of sufficient conditions for the Cohen-Grossberg networks to be absolutely stable and exponentially stable globally. We also provide an estimate of the rate of convergence.

Neural Networks, Computer↗
PubMed2004

Investigation of possible neural architectures underlying information-geometric measures.

A novel analytical method based on information geometry was recently proposed, and this method may provide useful insights into the statistical interactions within neural groups. The link between informationgeometric measures and the structure of neural interactions has not yet been elucidated, however, because of the ill-posed nature of the problem. Here, possible neural architectures underlying information-geometric measures are investigated using an isolated pair and an isolated triplet of model neurons. By assuming the existence of equilibrium states, we derive analytically the relationship between the information-geometric parameters and these simple neural architectures. For symmetric networks, the first- and second-order information-geometric parameters represent, respectively, the external input and the underlying connections between the neurons provided that the number of neurons used in the parameter estimation in the log-linear model and the number of neurons in the network are the same. For asymmetric networks, however, these parameters are dependent on both the intrinsic connections and the external inputs to each neuron. In addition, we derive the relation between the information-geometric parameter corresponding to the two-neuron interaction and a conventional cross-correlation measure. We also show that the information-geometric parameters vary depending on the number of neurons assumed for parameter estimation in the log-linear model. This finding suggests a need to examine the information-geometric method carefully. A possible criterion for choosing an appropriate orthogonal coordinate is also discussed. This article points out the importance of a model-based approach and sheds light on the possible neural structure underlying the application of information geometry to neural network analysis.

Action Potentials↗
PubMed2005

Analysis of cyclic dynamics for networks of linear threshold neurons.

The network of neurons with linear threshold (LT) transfer functions is a prominent model to emulate the behavior of cortical neurons. The analysis of dynamic properties for LT networks has attracted growing interest, such as multistability and boundedness. However, not much is known about how the connection strength and external inputs are related to oscillatory behaviors. Periodic oscillation is an important characteristic that relates to nondivergence, which shows that the network is still bounded although unstable modes exist. By concentrating on a general parameterized two-cell network, theoretical results for geometrical properties and existence of periodic orbits are presented. Although it is restricted to two-dimensional systems, the analysis can provide a useful contribution to analyze cyclic dynamics of some specific LT networks of high dimension. As an application, it is extended to an important class of biologically motivated networks of large scale: the winner-take-all model using local excitation and global inhibition.

Action Potentials↗