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PubMed1992

Distributed processing of sensory information in the leech. III. A dynamical neural network model of the local bending reflex.

The subpopulation of identified interneurons in the local bending reflex receive multiple inputs from dorsal and ventral mechanoreceptors and have outputs to dorsal and ventral motor neurons. Their connections suggest a distributed processing mechanism in which withdrawal from dorsal, ventral, or lateral stimuli is controlled by a single population of approximately 40 multifunctional interneurons, but it is unclear whether additional interneurons dedicated to particular inputs are needed to account for each kind of bend. We therefore asked whether a model could be constructed that reproduced all behaviors without dedicated interneurons. Interneurons in the model were constrained to receive both dorsal and ventral inputs. Connection strengths were adjusted by gradient descent optimization until the model reproduced the amplitude and time course of motor neuron synaptic potentials in intracellular recordings of the response to many different stimuli. After optimization, the similarity between model and identified interneurons showed that additional dedicated interneurons are not necessary to produce all forms of the behavior. Successful optimization of networks with many fewer interneurons showed that the 40-interneuron network is redundant, raising the possibility that the interneurons have additional functions. Finally, optimizing networks with additional constraints produced better matches to some of the identified interneurons and showed that local bending can be produced by two populations of interneurons: one with outputs consistent with dorsal bending, the other with ventral bending. This suggests a simple model in which two principal types of interneurons produce many different behaviors and predicts the type of interneuron that remains to be identified.

Animals↗
PubMed1989

Muscle afferents and the neural dynamics of limb position and velocity sensations.

Today muscle spindles are thought to be the primary receptor responsible for limb position and velocity. A mathematical model describing the muscle spindle's complex dynamical behavior was developed recently by Hasan. Other researchers have observed neuronal firing in the cortex of primates when muscles surrounding a joint have been passively stretched by joint movement. The purpose of this paper is to apply the muscle spindle model to a "two-muscle joint" and quantitate the resultant firing rates for various joint positions and velocities. With this information insights into the required neuronal dynamics for extracting position and velocity information from muscle spindles can be gained.

Afferent Pathways↗
PubMed1995

Human-like dynamic programming neural networks for dynamic time warping speech recognition.

This paper presents a human-like dynamic programming neural network method for speech recognition using dynamic time warping. The networks are configured, much like human's, such that the minimum states of the network's energy function represent the near-best correlation between test and reference patterns. The dynamics and properties of the neural networks are analytically explained. Simulations for classifying speaker-dependent isolated words, consisting of 0 to 9 and A to Z, show that the method is better than conventional methods. The hardware implementation of this method is also presented.

Humans↗
PubMed2000

Précis of Neural organization: structure, function, and dynamics.

NEURAL ORGANIZATION: Structure, function, and dynamics shows how theory and experiment can supplement each other in an integrated, evolving account of the brain's structure, function, and dynamics. (1) STRUCTURE: Studies of brain function and dynamics build on and contribute to an understanding of many brain regions, the neural circuits that constitute them, and their spatial relations. We emphasize Szentágothai's modular architectonics principle, but also stress the importance of the microcomplexes of cerebellar circuitry and the lamellae of hippocampus. (2) FUNCTION: Control of eye movements, reaching and grasping, cognitive maps, and the roles of vision receive a functional decomposition in terms of schemas. Hypotheses as to how each schema is implemented through the interaction of specific brain regions provide the basis for modeling the overall function by neural networks constrained by neural data. Synthetic PET integrates modeling of primate circuitry with data from human brain imaging. (3) DYNAMICS: Dynamic system theory analyzes spatiotemporal neural phenomena, such as oscillatory and chaotic activity in both single neurons and (often synchronized) neural networks, the self-organizing development and plasticity of ordered neural structures, and learning and memory phenomena associated with synaptic modification. Rhythm generation involves multiple levels of analysis, from intrinsic cellular processes to loops involving multiple brain regions. A variety of rhythms are related to memory functions. The Précis presents a multifaceted case study of the hippocampus. We conclude with the claim that language and other cognitive processes can be fruitfully studied within the framework of neural organization that the authors have charted with John Szentágothai.

Brain↗
PubMed2005

Dynamics of a neural system with a multiscale architecture.

The architecture of the brain is characterized by a modular organization repeated across a hierarchy of spatial scales-neurons, minicolumns, cortical columns, functional brain regions, and so on. It is important to consider that the processes governing neural dynamics at any given scale are not only determined by the behaviour of other neural structures at that scale, but also by the emergent behaviour of smaller scales, and the constraining influence of activity at larger scales. In this paper, we introduce a theoretical framework for neural systems in which the dynamics are nested within a multiscale architecture. In essence, the dynamics at each scale are determined by a coupled ensemble of nonlinear oscillators, which embody the principle scale-specific neurobiological processes. The dynamics at larger scales are 'slaved' to the emergent behaviour of smaller scales through a coupling function that depends on a multiscale wavelet decomposition. The approach is first explicated mathematically. Numerical examples are then given to illustrate phenomena such as between-scale bifurcations, and how synchronization in small-scale structures influences the dynamics in larger structures in an intuitive manner that cannot be captured by existing modelling approaches. A framework for relating the dynamical behaviour of the system to measured observables is presented and further extensions to capture wave phenomena and mode coupling are suggested.

Brain↗
PubMed2005

Dynamics of neural networks with variable coefficients and time-varying delays.

This paper studies the general neural networks dynamical systems with variable coefficients and time-varying delays. By applying the Young inequality technique, Dini derivative and introducing many real parameters, and estimating the upper bound of solutions of the system, a series of new and useful criteria on the boundedness, global exponential stability and the existence and global exponential stability of the periodic solutions are established. Particularly, when the system degenerates into the autonomous case, the new criteria on the existence, uniqueness and global exponential stability of the equilibrium points are obtained. The results obtained in this paper extend and generalize the corresponding results existing in previous literature.

Computer Simulation↗
PubMed1999

On redundancy in neural architecture: dynamics of a simple module-based neural network and initial-state independence.

This article discusses the relationship between redundancy in neural architecture and activity (cell output or internal state) dynamics with a simple module-based neural network. In the network, a single neural cell with self-feedback is employed as a module sub-network, and all module sub-networks are connected via inter-module connections. In general, the activity dynamics of a single neural cell with positive self-feedback may have two minima in its energy surface, and the minimum the cell state converges to depends on the initial states. However, in the module-based network with all the same intra-module connections, an independence from initial states becomes conspicuous as the number of modules increases due to the architectural redundancy. Simulation and analytical studies on the network dynamics illustrate that the cell states always converge to a global minimum irrelevantly of the initial cell-states, and they never go to a local minimum when a sufficient number of modules are employed.

Journal Article↗
PubMed2004

Connectivity and dynamics of neural information processing.

In this article, we systematically review the current literature on neural connectivity and dynamics, or equivalently, structure and function. In particular, we discuss how changes in the connectivity of a neural network affect the spatiotemporal network dynamics qualitatively. The three major criteria of comparison are, first, the local dynamics at the network nodes which includes fixed point dynamics, oscillatory and chaotic dynamics; second, the presence of time delays via propagation along connecting pathways; and third, the properties of the connectivity matrix such as its statistics, symmetry, and translational invariance. Since the connection topology changes when anatomical scales are traversed, so will the corresponding network dynamics change. As a consequence different types of networks are encountered on different levels of neural organization.

Animals↗
PubMed1994

On the classification capability of a dynamic threshold neural network.

This paper proposes a new type of neural network called the Dynamic Threshold Neural Network (DTNN) which is theoretically and experimentally superior to a conventional sigmoidal multilayer neural network in classification capability. Given a training set containing 4k + 1 patterns in Rn, to successfully learn this training set, the upper bound on the number of free parameters for a DTNN is (k + 1)(n + 2) + 2(k + 1), while the upper bound for a sigmoidal network is 2k(n + 1) + (2k + 1). We also derive a learning algorithm for the DTNN in a similar way to the derivation of the backprop learning algorithm. In simulations on learning the Two-Spirals problems, our DTNN with 30 neurons in one hidden layer takes only 3200 epochs on average to successfully learn the whole training set, while the single-hidden-layer feedforward sigmoidal neural networks have never been reported to successfully learn the given training set even though more hidden neurons are used.

Algorithms↗
PubMed1995

Dynamical recurrent neural networks--towards environmental time series prediction.

Dynamical Recurrent Neural Networks (DRNN) (Aussem 1995a) are a class of fully recurrent networks obtained by modeling synapses as autoregressive filters. By virtue of their internal dynamic, these networks approximate the underlying law governing the time series by a system of nonlinear difference equations of internal variables. They therefore provide history-sensitive forecasts without having to be explicitly fed with external memory. The model is trained by a local and recursive error propagation algorithm called temporal-recurrent-backpropagation. The efficiency of the procedure benefits from the exponential decay of the gradient terms backpropagated through the adjoint network. We assess the predictive ability of the DRNN model with meterological and astronomical time series recorded around the candidate observation sites for the future VLT telescope. The hope is that reliable environmental forecasts provided with the model will allow the modern telescopes to be preset, a few hours in advance, in the most suited instrumental mode. In this perspective, the model is first appraised on precipitation measurements with traditional nonlinear AR and ARMA techniques using feedforward networks. Then we tackle a complex problem, namely the prediction of astronomical seeing, known to be a very erratic time series. A fuzzy coding approach is used to reduce the complexity of the underlying laws governing the seeing. Then, a fuzzy correspondence analysis is carried out to explore the internal relationships in the data. Based on a carefully selected set of meteorological variables at the same time-point, a nonlinear multiple regression, termed nowcasting (Murtagh et al. 1993, 1995), is carried out on the fuzzily coded seeing records. The DRNN is shown to outperform the fuzzy k-nearest neighbors method.

Environmental Monitoring↗
PubMed1993

Identification of coding regions in genomic DNA sequences: an application of dynamic programming and neural networks.

Dynamic programming (DP) is applied to the problem of precisely identifying internal exons and introns in genomic DNA sequences. The program GeneParser first scores the sequence of interest for splice sites and for these intron- and exon-specific content measures: codon usage, local compositional complexity, 6-tuple frequency, length distribution and periodic asymmetry. This information is then organized for interpretation by DP. GeneParser employs the DP algorithm to enforce the constraints that introns and exons must be adjacent and non-overlapping and finds the highest scoring combination of introns and exons subject to these constraints. Weights for the various classification procedures are determined by training a simple feed-forward neural network to maximize the number of correct predictions. In a pilot study, the system has been trained on a set of 56 human gene fragments containing 150 internal exons in a total of 158,691 bps of genomic sequence. When tested against the training data, GeneParser precisely identifies 75% of the exons and correctly predicts 86% of coding nucleotides as coding while only 13% of non-exon bps were predicted to be coding. This corresponds to a correlation coefficient for exon prediction of 0.85. Because of the simplicity of the network weighting scheme, generalization performance is nearly as good as with the training set.

Algorithms↗
PubMed2002

A dynamically coupled neural oscillator network for image segmentation.

We propose a dynamically coupled neural oscillator network for image segmentation. Instead of pair-wise coupling, an ensemble of oscillators coupled in a local region is used for grouping. We introduce a set of neighborhoods to generate dynamical coupling structures associated with a specific oscillator. Based on the proximity and similarity principles, two grouping rules are proposed to explicitly consider the distinct cases of whether an oscillator is inside a homogeneous image region or near a boundary between different regions. The use of dynamical coupling makes our segmentation network robust to noise on an image, and unlike image processing algorithms no iterative operation is needed for noise removal. For fast computation, a segmentation algorithm is abstracted from the underlying oscillatory dynamics, and has been applied to synthetic and real images. Simulation results demonstrate the effectiveness of our oscillator network in image segmentation.

Algorithms↗