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At least 19 recordsLinked to original sources
PubMed2005

Conditions of activity bubble uniqueness in dynamic neural fields.

Dynamic neural fields (DNFs) offer a rich spectrum of dynamic properties like hysteresis, spatiotemporal information integration, and coexistence of multiple attractors. These properties make DNFs more and more popular in implementations of sensorimotor loops for autonomous systems. Applications often imply that DNFs should have only one compact region of firing neurons (activity bubble), whereas the rest of the field should not fire (e.g., if the field represents motor commands). In this article we prove the conditions of activity bubble uniqueness in the case of locally symmetric input bubbles. The qualitative condition on inhomogeneous inputs used in earlier work on DNFs is transfered to a quantitative condition of a balance between the internal dynamics and the input. The mathematical analysis is carried out for the two-dimensional case with methods that can be extended to more than two dimensions. The article concludes with an example of how our theoretical results facilitate the practical use of DNFs.

Action Potentials↗
PubMed2001

Toward an interpretation of dynamic neural activity in terms of chaotic dynamical systems.

Using the concepts of chaotic dynamical systems, we present an interpretation of dynamic neural activity found in cortical and subcortical areas. The discovery of chaotic itinerancy in high-dimensional dynamical systems with and without a noise term has motivated a new interpretation of this dynamic neural activity, cast in terms of the high-dimensional transitory dynamics among "exotic" attractors. This interpretation is quite different from the conventional one, cast in terms of simple behavior on low-dimensional attractors. Skarda and Freeman (1987) presented evidence in support of the conclusion that animals cannot memorize odor without chaotic activity of neuron populations. Following their work, we study the role of chaotic dynamics in biological information processing, perception, and memory. We propose a new coding scheme of information in chaos-driven contracting systems we refer to as Cantor coding. Since these systems are found in the hippocampal formation and also in the olfactory system, the proposed coding scheme should be of biological significance. Based on these intensive studies, a hypothesis regarding the formation of episodic memory is given.

Brain↗
PubMed2003

Global asymptotic stability of a class of dynamical neural networks.

The dynamics of cortical cognitive maps developed by self-organization must include the aspects of long and short-term memory. The behavior of the network is such characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural biologically relevant system. We present new stability conditions for analyzing the dynamics of a biological relevant system with different time scales based on the theory of flow invariance. We prove the existence and uniqueness of the equilibrium, and give a quadratic-type Lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables and thus prove the global stability of the equilibrium point.

Algorithms↗
PubMed2005

An efficient parameterization of dynamic neural networks for nonlinear system identification.

Dynamic neural networks (DNNs), which are also known as recurrent neural networks, are often used for nonlinear system identification. The main contribution of this letter is the introduction of an efficient parameterization of a class of DNNs. Having to adjust less parameters simplifies the training problem and leads to more parsimonious models. The parameterization is based on approximation theory dealing with the ability of a class of DNNs to approximate finite trajectories of nonautonomous systems. The use of the proposed parameterization is illustrated through a numerical example, using data from a nonlinear model of a magnetic levitation system.

Algorithms↗
PubMed2003

Intelligent optimal control with dynamic neural networks.

The application of neural networks technology to dynamic system control has been constrained by the non-dynamic nature of popular network architectures. Many of difficulties are-large network sizes (i.e. curse of dimensionality), long training times, etc. These problems can be overcome with dynamic neural networks (DNN). In this study, intelligent optimal control problem is considered as a nonlinear optimization with dynamic equality constraints, and DNN as a control trajectory priming system. The resulting algorithm operates as an auto-trainer for DNN (a self-learning structure) and generates optimal feed-forward control trajectories in a significantly smaller number of iterations. In this way, optimal control trajectories are encapsulated and generalized by DNN. The time varying optimal feedback gains are also generated along the trajectory as byproducts. Speeding up trajectory calculations opens up avenues for real-time intelligent optimal control with virtual global feedback. We used direct-descent-curvature algorithm with some modifications (we called modified-descend-controller-MDC algorithm) for the optimal control computations. The algorithm has generated numerically very robust solutions with respect to conjugate points. The adjoint theory has been used in the training of DNN which is considered as a quasi-linear dynamic system. The updating of weights (identification of parameters) are based on Broyden-Fletcher-Goldfarb-Shanno BFGS method. Simulation results are given for an intelligent optimal control system controlling a difficult nonlinear second-order system using fully connected three-neuron DNN.

Artificial Intelligence↗
PubMed1999

Identification of hemifield single trial PVEP on the basis of generalized dynamic neural network classifiers.

This paper is concerned with the application of generalized dynamic neural networks for the identification of hemifield pattern-reversal visual evoked potentials. The identification process is performed by different networks with time-varying weights using signals from different electrode positions as external inputs. Since dynamic neural networks are able to process time-varying signals, the identification of the stimulated hemiretinae is performed without feature extraction. The performance of the method presented is compared with a reference method based on the values of instantaneous frequency at the occipital electrode positions at P100 latency.

Adult↗
PubMed2006

Some new stability properties of dynamic neural networks with different time-scales.

Dynamic neural networks with different time-scales include the aspects of fast and slow phenomenons. Some applications require that the equilibrium points of these networks to be stable. The main contribution of the paper is that Lyapunov function and singularly perturbed technique are combined to access several new stable properties of different time-scales neural networks. Exponential stability and asymptotic stability are obtained by sector and bound conditions. Compared to other papers, these conditions are simpler. Numerical examples are given to demonstrate the effectiveness of the theoretical results.

Mathematics↗
PubMed2002

Estimation of neural dynamics from MEG/EEG cortical current density maps: application to the reconstruction of large-scale cortical synchrony.

There is a growing interest in elucidating the role of specific patterns of neural dynamics--such as transient synchronization between distant cell assemblies--in brain functions. Magnetoencephalography (MEG)/electroencephalography (EEG) recordings consist in the spatial integration of the activity from large and multiple remotely located populations of neurons. Massive diffusive effects and poor signal-to-noise ratio (SNR) preclude the proper estimation of indices related to cortical dynamics from nonaveraged MEG/EEG surface recordings. Source localization from MEG/EEG surface recordings with its excellent time resolution could contribute to a better understanding of the working brain. We propose a robust and original approach to the MEG/EEG distributed inverse problem to better estimate neural dynamics of cortical sources. For this, the surrogate data method is introduced in the MEG/EEG inverse problem framework. We apply this approach on nonaveraged data with poor SNR using the minimum norm estimator and find source localization results weakly sensitive to noise. Surrogates allow the reduction of the source space in order to reconstruct MEG/EEG data with reduced biases in both source localization and time-series dynamics. Monte Carlo simulations and results obtained from real MEG data indicate it is possible to estimate non invasively an important part of cortical source locations and dynamic and, therefore, to reveal brain functional networks.

Action Potentials↗
PubMed2003

The dynamic neural filter: a binary model of spatiotemporal coding.

We describe and discuss the properties of a binary neural network that can serve as a dynamic neural filter (DNF), which maps regions of input space into spatiotemporal sequences of neuronal activity. Both deterministic and stochastic dynamics are studied, allowing the investigation of the stability of spatiotemporal sequences under noisy conditions. We define a measure of the coding capacity of a DNF and develop an algorithm for constructing a DNF that can serve as a source of given codes. On the basis of this algorithm, we suggest using a minimal DNF capable of generating observed sequences as a measure of complexity of spatiotemporal data. This measure is applied to experimental observations in the locust olfactory system, whose reverberating local field potential provides a natural temporal scale allowing the use of a binary DNF. For random synaptic matrices, a DNF can generate very large cycles, thus becoming an efficient tool for producing spatiotemporal codes. The latter can be stabilized by applying to the parameters of the DNF a learning algorithm with suitable margins.

Algorithms↗
PubMed1989

Dynamical neural network organization of the visual pursuit system.

The central nervous system is a parallel dynamical system which connects sensory input with motor output for the performance of visual tracking. This paper applies elementary control system tools to extend dynamical neural network models to the visual smooth pursuit system. Observed eye position responses to target motions and characteristics of the plant (eye muscles and orbital mechanics) place dynamical constraints on the interposed neural network controller. In the process of constructing a model for the controller, we show two previous pursuit system models, using efference copy and feedforward compensation, are equivalent from an input-output standpoint. We introduce a controller model possessing a potentially highly parallel implementation and offer an example with supporting neural firing rate data. Changes in time delays or other system dynamics are expected to lead to compensatory adaptive changes in the controller. A scheme to noninvasively simulate such changes in system dynamics was developed. Actual physiologic data of adaptive responses to increased time delay is presented as an example of the utility of this parallel controller. Compensatory changes in our parallel controller model are easily predicted. These results suggest a productive interaction between neural network modeling, neurophysiology, and control systems engineering.

Animals↗
PubMed2006

The dynamic neural field approach to cognitive robotics.

This tutorial presents an architecture for autonomous robots to generate behavior in joint action tasks. To efficiently interact with another agent in solving a mutual task, a robot should be endowed with cognitive skills such as memory, decision making, action understanding and prediction. The proposed architecture is strongly inspired by our current understanding of the processing principles and the neuronal circuitry underlying these functionalities in the primate brain. As a mathematical framework, we use a coupled system of dynamic neural fields, each representing the basic functionality of neuronal populations in different brain areas. It implements goal-directed behavior in joint action as a continuous process that builds on the interpretation of observed movements in terms of the partner's action goal. We validate the architecture in two experimental paradigms: (1) a joint search task; (2) a reproduction of an observed or inferred end state of a grasping-placing sequence. We also review some of the mathematical results about dynamic neural fields that are important for the implementation work.

Animals↗
PubMed2004

Neural dynamics in human imitation revealed by ERP surface topography.

To clarify the neural dynamics in human motor imitation, we examined event-related potentials (ERP) for a reaction time task that required responses to an actor's finger motions with identical motions. Compared with a control task (reaction to an LED illumination), the ERP surface topography in the imitative reaction was differentiated at around 120-200 ms post-cueing, showing an early sensitivity to the response hand over the pre-central region. This result suggested that activities around the motor areas were facilitated in the imitative reaction, which is consistent with recent neuroimaging studies. However, taken together with that there were no differences in reaction times, the early ERP latency of conditional divergence indicated that neural activities related to imitation are visual responses and do not directly lead to motor acceleration.

Adult↗
PubMed1996

Temporal segmentation in a neural dynamic system.

Oscillatory attractor neural networks can perform temporal segmentation, i.e., separate the joint inputs they receive, through the formation of staggered oscillations. This property, which may be basic to many perceptual functions, is investigated here in the context of a symmetric dynamic system. The fully segmented mode is one type of limit cycle that this system can develop. It can be sustained for only a limited number n of oscillators. This limitation to a small number of segments is a basic phenomenon in such systems. Within our model we can explain it in terms of the limited range of narrow subharmonic solutions of the single nonlinear oscillator. Moreover, this point of view allows us to understand the dominance of three leading amplitudes in solutions of partial segmentation, which are obtained for high n. The latter are also abundant when we replace the common input with a graded one, allowing for different inputs to different oscillators. Switching to an input with fluctuating components, we obtain segmentation dominance for small systems and quite irregular waveforms for large systems.

Electrophysiology↗
PubMed1989

Analysis of neural dynamics and memory organization.

We analysed neural network dynamics by a Caianiello type of equation with special reference to memory organization and the corresponding synaptic connection matrix. Global analysis of the dynamics yielded only stable equilibrium configurations and no periodic solutions.

Animals↗
PubMed1996

Neural dynamics in cortex-striatum co-cultures--II. Spatiotemporal characteristics of neuronal activity.

Neural dynamics in organotypic cortex-striatum co-cultures grown for three to six weeks under conditions of dopamine deficiency are described. Single neuron activities were recorded intra- and extracellularly, and spatiotemporal spreading of population activity was mapped using voltage-sensitive dyes. The temporal properties of spike firing were characterized by interspike interval histograms, autocorrelation and crosscorrelation. Cortical pyramidal neurons (n = 40) showed irregular firing with a weak tendency to burst or to oscillate. Crosscorrelations revealed strong near-coincident firing and synaptic interactions. Disinhibition was a notable feature in a strongly firing cortical interneuron. Cortical activity spread in the co-culture, thus inducing an overall, homogeneous depolarization in the striatal part. Striatal cells were divided into principal cells and type I and II secondary cells. Principal cells (n = 40) were similar to those reported previously in vivo. Spiking activity ranged from irregular spiking at very low rates to episodic bursting, with an average burst duration of 1 s. Interspike intervals were single-peaked. Intracellular recordings revealed characteristic, long-lasting subthreshold depolarizations ("enabled state") that were shortened by local muscarinic receptor blockade. During prolonged time periods in the "enabled state", locally applied bicuculline induced strong firing in most principal neurons. Striatal secondary type I neurons (n = 25) showed high spiking rates, single- and double-peaked interval histograms and low-threshold, short-lasting stereotyped bursting activity and occasional rhythmic bursting. The firing of these neurons was increased by bicuculline. Crosscorrelations showed synchronization of these cells with principal cell activity. Secondary type II neurons (n = 15) revealed tonic, irregular firing patterns similar to cortical neurons, except with occasional firing in doublet spikes. We conclude that under conditions of dopamine deficiency in corticostriatal co-cultures (i) the cortex induces the "enabled" state and typical bursting mode in striatal principal neurons; (ii) principal neurons are strongly inhibited during the "enabled" state; (iii) muscarinic activity, presumably from tonically active striatal cholinergic interneurons, stabilizes the "enabled" state; (iv) striatal GABAergic interneurons receives synaptic inhibition and take part in synchronized activity among striatal principal cells. Our results favor the view of the striatum as a lateral inhibition network.

Animals↗
PubMed2006

Dynamic and interactive generation of object handling behaviors by a small humanoid robot using a dynamic neural network model.

This study presents experiments on the learning of object handling behaviors by a small humanoid robot using a dynamic neural network model, the recurrent neural network with parametric bias (RNNPB). The first experiment showed that after the robot learned different types of ball handling behaviors using human direct teaching, the robot was able to generate adequate ball handling motor sequences situated to the relative position between the robot's hands and the ball. The same scheme was applied to a block handling learning task where it was shown that the robot can switch among learned different block handling sequences, situated to the ways of interaction by human supporters. Our analysis showed that entrainment of the internal memory structures of the RNNPB through the interactions of the objects and the human supporters are the essential mechanisms for those observed situated behaviors of the robot.

Algorithms↗
PubMed2006

Neural dynamics in monkey parietal reach region reflect context-specific sensorimotor transformations.

We investigated the neural dynamics of sensorimotor transformations in the parietal reach region (PRR) of monkeys. To dissociate sensory from motor goal representations, we used a memory-guided anti-reach task. The monkeys had to reach either to a visually instructed, memorized peripheral target position (pro-reach) or to a diametrically opposed position (anti) while keeping central ocular fixation. Pro- and anti-reaches were randomly interleaved and indicated by a color instruction from the beginning of each trial. We analyzed spatiotemporal single-cell tuning and performed time-resolved population decoding to quantify the dynamic representation of the spatial visual cue, the reach goal, and the currently valid task rule (pro/anti mapping). Sensory information regarding the visual cue position was represented weakly during a short period of cue visibility. PRR predominantly encoded the reach goal from the end of the cue period on. The representation of the reach goal in the memory task evolves later for the anti- compared with pro-reaches, consistent with a 40-50 ms difference in reaction time between the two task rules. The task rule could be decoded before the appearance of the spatial cue, which indicates that abstract rule information is present in PRR that is independent of spatial cue or motor goal representations. Our findings support the hypothesis that PRR immediately translates current sensory information into reach movement plans, rather than storing the memorized cue location in the instructed-delay task. This finding indicates that PRR represents integrated knowledge on spatial sensory information combined with abstract behavioral rules to encode the desired movement goal.

Action Potentials↗
PubMed1994

Supervised training of dynamical neural networks for associative memory design and identification of nonlinear maps.

Complexity of implementation has been a major difficulty in the development of gradient descent learning algorithms for dynamical neural networks with feedback and recurrent connections. Some insights from the stability properties of the equilibrium points of the network, which suggest an appropriate tailoring of the sigmoidal nonlinear functions, can however be utilized in obtaining simplified learning rules, as demonstrated in this paper. An analytical proof of convergence of the learning scheme under specific conditions is given and some upper bounds on the adaptation parameters for an efficient implementation of the training procedure are developed. The performance features of the learning algorithm are illustrated by applying it to two problems of importance, viz., design of associative memories and nonlinear input-output mapping. For the first application, a systematic procedure is given for training a network to store multiple memory vectors as its stable equilibrium points, whereas for the second application, specific training rules are developed for a three-layer network architecture comprising a dynamical hidden layer for the identification of nonlinear input-output maps. A comparison with the performance of a standard backpropagation network provides an illustration of the capabilities of the present network architecture and the learning algorithm.

Algorithms↗