Traveling-wave pattern generator controls movement and organization of sensory feedback in a spinal cord model

 A traveling wave in a two-dimensional spinal cord model constitutes a stable pattern generator for quadruped gaits. In the context of the somatotopic organization of the spinal cord, this pattern generator is sufficient to generate stable locomotive limb trajectories. The elastic properties of muscles alone, providing linear negative feedback, are sufficient to stabilize stance and locomotion in the presence of perturbative forces. We further show that such a pattern generator is capable of organizing sensory processing in the spinal cord. A single-layer perceptron was trained to associate the sensory feedback from the limb (coding force, length, and change of length for each muscle) with the two-dimensional activity profile of the traveling wave. This resulted in a well-defined spatial organization of the connections within the spinal network along a rostrocaudal axis. The spinal network driven by peripheral afferents alone supported autonomous locomotion in the positive feedback mode, whereas in the negative feedback mode stance was stabilized in response to perturbations. Systematic variation of a parameter representing the effect of gamma-motor neurons on muscle spindle activity in our model led to a corresponding shift of limb position during stance and locomotion, resulting in a systematic displacement alteration of foot positions. Received: 30 July 2001 / Accepted in revised form: 17 April 2002 Correspondence to: A. Kaske (e-mails: alexander.kaske@mtc.ki.se, alexander.kaske@vglab.com)     

Neuronal control of behavioral plasticity: the prepacemaker nucleus of weakly electric gymnotiform fish

 Gymnotiform fish of the genera Apteronotus and Eigenmannia provide an excellent vertebrate model system to study neural mechanisms controlling behavioral plasticity. These teleosts generate, by means of an electric organ, quasi-sinusoidal discharges of extremely stable frequency and waveform. Modulations consisting of transient rises in discharge frequency are produced during social encounters, and play an important role in communication. These so-called “chirps” exhibit a remarkable sexual dimorphism, as well as an enormous seasonal and individual variability. Chirping behavior is controlled by a subset of neurons in the complex of the central posterior/prepacemaker nucleus in the diencephalon. It is hypothesized that the plasticity in the performance of chirping behavior is, at least in part, governed by two mechanisms: first, by seasonally induced structural changes in dendritic morphology of neurons of the prepacemaker nucleus, thus leading to pronounced alterations in excitatory input. Second, by androgen-controlled changes in the innervation pattern of the prepacemaker nucleus by fibers expressing the neuropeptide substance P. In addition to these two dynamic processes, cells are generated continuously and at high number in the central posterior/prepacemaker nucleus during adulthood. This phenomenon may provide the basis for a “refreshment”, thus facilitating possible changes in the underlying neural network. Accepted: 17 September 1990     

Neural computations in the tiger salamander and mudpuppy outer retinae and an analysis of GABA action from horizontal cells

 A neural network architecture based on the neural anatomy and function of retinal neurons in tiger salamander and mudpuppy retinae is proposed to study basic aspects of early visual information processing. The model predictions for the main response characteristics of retinal neurons are found to be in agreement with neurophysiological data, including the antagonistic role of horizontal cells in the outer plexiform layer. The examination of possible γ-aminobutyric acid (GABA) action from horizontal cells suggests that GABA_A alone, GABA_B alone, or their weighted combination can generate the response characteristics observed in bipolar cells. Received: 25 June 2002 / Accepted: 28 January 2003 / Published online: 20 May 2003 Acknowledgements. The authors would like to thank an anonymous reviewer for valuable comments. Correspondence to: S. X. Yang (e-mail: syang@uoguelph.ca)     

A theory of hippocampal memory based on theta phase precession

 The neural dynamics of the hippocampal network for memory encoding of novel temporal sequences is proposed based on the theta rhythm modulated firing of place cells called theta phase precession. It is hypothesized that theta phase precession is generated at the entorhinal cortex by phase locking between local field theta oscillation and neural oscillators and that the hippocampal closed network with feedforward and backward projections employ theta phase precession to create selectivity in the associative connections needed for temporal sequence storage. Our analyses and computer experiments reveal that the phase precession generated by phase locking instantaneously endows stable phase relations among neural activities in the successively changing neural population. It is concluded that theta phase precession provides biologically plausible dynamics for the memory encoding of novel temporal sequences as episodic events. Received: 18 December 2002 / Accepted: 18 March 2003 / Published online: 20 May 2003 Correspondence to: Y. Yamaguchi (e-mail: yokoy@brain.riken.go.jp, Fax: +81-48-4676938) Acknowledgements. The author would like to express acknowledgement to Drs. McNaughton and Skaggs for their discussion and comment and to Dr. Amari for his continuous encouragement. Further thanks are given to Mr. Haga and Dr. Wu for their discussion and cooperation.     

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. Received: 21 May 2002 / Accepted in revised form: 3 December 2002 / Published online: 7 March 2003 Correspondence to: P. Kudela (e-mail: pkudela@jhmi.edu) Acknowledgements. This research was supported by NIH grant NS 38958.     

Visual depth encoding in populations of neurons with localized receptive fields

 Stereopsis is the ability to perceive three-dimensional structure from disparities between the two-dimensional retinal images. Although disparity-sensitive neurons have been proposed as a neural representation of this ability many years ago, it is still difficult to link all qualities of stereopsis to properties of the neural correlate of binocular disparities. The present study wants to support efforts directed at closing the gap between electrophysiology and psychophysics. Populations of disparity-sensitive neurons in V1 were simulated using the energy-neuron model. Responses to different types of stimuli were evaluated with an efficient statistical estimator and related to psychophysical findings. The representation of disparity in simulated population responses appeared to be very robust. Small populations allowed good depth discrimination. Two types of energy neurons (phase- and position-type models) that are discussed as possible neural implementations of disparity-selectivity could be compared to each other. Phase-type coding was more robust and could explain a tendency towards zero disparity in degenerated stimuli and, for high-pass stimuli, exhibited the breakdown of disparity discrimination at a maximum disparity value. Contrast-inverted stereograms led to high variances in disparity representation, which is a possible explanation of the absence of depth percepts in large contrast-inverted stimuli. Our study suggests that nonlocal interactions destroy depth percepts in large contrast-inverted stereograms, although these percepts occur for smaller stimuli of the same class. Received: 21 December 2001 / Accepted: 29 April 2002 RID="*" ID="*" Present address: Bayer AG BTS-PT-MVT-MKM, Geb. K9, 51368 Leverkusen, Germany Acknowledgement. This work was supported by a scholarship from the Studienstiftung des deutschen Volkes to J.L. Correspondence to: J. Lippert (e-mail: joerg.lippert.jl@bayer-ag.de)     

Simulation of plasticity in the adult visual cortex

 Retinal plasticity has been shown in the adult visual nervous system in mammals. Following a retinal lesion (scotoma) there is a reorganization of the cortical receptive field distribution: cortical neurons selective to visual stimuli in the area of the visual field corresponding to the retinal lesion, become selective to other parts of the visual field. In this work, we study this effect with a self-organizing neural network. In a first stage, the network reaches a pattern of connectivity that represents normal development of neuronal selectivity. The scotoma is simulated by perturbing accordingly the properties of a region of the input layer representing the retina. The system evolves to a new receptive field distribution mainly by means of the reorganization of the intra cortical connectivity. No major change of the geniculo cortical connectivity is detected. This may explain the surprisingly short time scale of the event. Received: 6 June 2000 / Accepted in revised form: 16 October 2000     

Binding and segmentation of multiple objects through neural oscillators inhibited by contour information

 Temporal correlation of neuronal activity has been suggested as a criterion for multiple object recognition. In this work, a two-dimensional network of simplified Wilson-Cowan oscillators is used to manage the binding and segmentation problem of a visual scene according to the connectedness Gestalt criterion. Binding is achieved via original coupling terms that link excitatory units to both excitatory and inhibitory units of adjacent neurons. These local coupling terms are time independent, i.e., they do not require Hebbian learning during the simulations. Segmentation is realized by a two-layer processing of the visual image. The first layer extracts all object contours from the image by means of “retinal cells” with an “on-center” receptive field. Information on contour is used to selectively inhibit Wilson-Cowan oscillators in the second layer, thus realizing a strong separation among neurons in different objects. Accidental synchronism between oscillations in different objects is prevented with the use of a global inhibitor, i.e., a global neuron that computes the overall activity in the Wilson-Cowan network and sends back an inhibitory signal. Simulations performed in a 50×50 neural grid with 21 different visual scenes (containing up to eight objects + background) with random initial conditions demonstrate that the network can correctly segment objects in almost 100% of cases using a single set of parameters, i.e., without the need to adjust parameters from one visual scene to the next. The network is robust with reference to dynamical noise superimposed on oscillatory neurons. Moreover, the network can segment both black objects on white background and vice versa and is able to deal with the problem of “fragmentation.” The main limitation of the network is its sensitivity to static noise superimposed on the objects. Overcoming this problem requires implementation of more robust mechanisms for contour enhancement in the first layer in agreement with mechanisms actually realized in the visual cortex. Received: 25 October 2001 / Accepted: 26 February 2003 / Published online: 20 May 2003 Correspondence to: Mauro Ursino (e-mail: mursino@deis.unibo.it, Tel.: +39-051-2093008, Fax: +39-051-2093073)     

Time representing cortical activities: two models inspired by prefrontal persistent activity

 Timing information in the range of seconds is significantly correlated with our behavior. There is growing interest in the cognitive behaviors that rely on perception, comparison, or generation of timing. However, little is known about the neural mechanisms underlying such behaviors. Here we model two different neural mechanisms to represent timing information in the range of seconds. In one model, a recurrent network of bistable spiking neurons shows a quasistable state that is initiated by a brief input and typically lasts for a few to several seconds. The duration of this quasistable activity may be regarded as the neural representation of internal time obeying a psychophysical law of time recognition. Another model uses synfire chains to provide the timing information necessary for predicting the times of anticipated events. In this model, the neurons projected to by multiple synfire chains are conditioned to fire synchronously at the times when an external event (GO signal) is expected. The conditioning is accomplished by spike-timing-dependent plasticity. The two models are inspired by the prefrontal activities of the monkeys engaging in different timing-information-related tasks. Thus, this cortical region may provide the timing information required for organizing various behaviors. Received: 12 March 2002 / Accepted in revised form: 26 November 2002 / Published online: 28 March 2003 Correspondence to: T. Fukai (e-mail: tfukai@eng.tamagawa.ac.jp, Tel.: +81-42-7398434, Fax: +81-42-7397135) Acknowledgements. K. Kitano was supported by Japan Society for the Promotion of Science.     

Passive bipedal walking with phasic muscle contraction

The existence of self-organizing walking patterns is often considered the result of a mechanical system interacting with the environment and a (neural) oscillating unit. The pattern generators might be thought of as an indispensable component for the existence of limit cycle behavior. This paper shows that this is not a necessity for the existence of a self-organizing bipedal walking pattern. Stable walking cycles emerge from a simple passive bipedal structure, with an energy source inevitably present to sustain the oscillation. In this work the energy source is chosen to be phasic muscle contraction. A two-dimensional model is composed of two legs and a hip mass, symbolizing the trunk. The stance leg stiffness is generated by two muscles. The hip stiffness is generated by four muscles. Muscle activation is caused by two reflex-like trigger signals, without feedback control. Human equivalent model parameters such as geometry and mass distribution were assumed. With return map analysis, the model is analyzed on periodic behavior. Stable walking cycles were found and could be manipulated during walking by varying the muscle or reflex parameters, forcing the oscillation to converge to a new attractor. Received: 5 November 1998 / Accepted in revised form: 26 March 1999     

Object segmentation model: analytical results and biological implications

 A simple, biologically motivated neural network for segmentation of a moving object from a visual scene is presented. The model consists of two parts: an object selection model which employs a scaling approach for receptive field sizes, and a subsequent network implementing a spotlight by means of multiplicative synapses. The network selects one object out of several, segments the rough contour of the object, and encodes the winner object's position with high accuracy. Analytical equations for the performance level of the network, e.g., for the critical distance of two objects above which they are perceived as separate, are derived. The network preferentially chooses the object with the largest angular velocity and the largest angular width. An equation for the velocity and width preferences is presented. Additionally it is shown that for certain neurons of the model, flat receptive fields are more favourable than Gaussian ones. The network exhibits performances similar to those known from amphibians. Various electrophysiological and behavioral results – e.g., the distribution of the diameters of the receptive fields of tectal neurons, of the tongue-projecting salamander Hydromantes italicus and the range of optimal prey velocities for prey catching – can be understood on the basis of the model. Received: 7 December 2000 / Accepted: 13 February 2001     

A neural model for generating and learning a rapid movement sequence

 In this article, a neural model for generating and learning a rapid ballistic movement sequence in two-dimensional (2D) space is presented and evaluated in the light of some considerations about handwriting generation. The model is based on a central nucleus (called a planning space) consisting of a fully connected grid of leaky integrators simulating neurons, and reading an input vector Ξ (t) which represents the external movement of the end effector. The movement sequencing results in a succession of motor strokes whose instantiation is controlled by the global activation of the planning space as defined by a competitive interaction between the neurons of the grid. Constraints such as spatial accuracy and movement time are exploited for the correct synchronization of the impulse commands. These commands are then fed into a neuromuscular synergy whose output is governed by a delta lognormal equation. Each movement sequence is memorized originally as a symbolic engram representing the sequence of the principal reference points of the 2D movement. These points, called virtual targets, correspond to the targets of each single rapid motor stroke composing the movement sequence. The task during the learning phase is to detect the engram corresponding to a new observed movement; the process is controlled by the dynamics of the neural grid. Received: 16 March 1995/Accepted in revised form: 25 July 1995     

Competition in the temporal domain among neural activities phase-locked to subthreshold oscillations

 In the presence of a subthreshold membrane oscillation, analog information may be encoded in the timing of spike generation phase-locked to the oscillation. With this spike timing neural code, a competitive network of inhibitory spiking neurons was shown to achieve a novel timing mechanism of neural activity selection: the neurons had higher probabilities of becoming winners if they were stimulated earlier in each oscillatory cycle. Here the timing mechanism and its robustness are studied both numerically and analytically, and the conditions to yield a given number of winners (the inhibitory neurons that remain active after the competition) are investigated. The analysis revealed that activity selection with a small number of winners is ensured for broad ranges of values of the parameters such as the strength and time constant of inhibition. In particular, the number of winners is almost unchanged for various timing differences between stimuli to different neurons. This implies that the timing mechanism is useful for such biological information processing as requires perception of a relatively small number of significant stimulus components. Received: 24 January 1996 / Accepted in revised form: 24 July 1996     

An associative memory that can form hypotheses: a phase-coded neural network

 Nonlinear associative memories as realized, e.g., by Hopfield nets are characterized by attractor-type dynamics. When fed with a starting pattern, they converge to exactly one of the stored patterns which is supposed to be most similar. These systems cannot render hypotheses of classification, i.e., render several possible answers to a given classification problem. Inspired by von der Malsburg’s correlation theory of brain function, we extend conventional neural network architectures by introducing additional dynamical variables. Assuming an oscillatory time structure of neural firing, i.e., the existence of neural clocks, we assign a so-called phase to each formal neuron. The phases explicitly describe detailed correlations of neural activities neglected in conventional neural network architectures. Implementing this extension into a simple self-organizing network based on a feature map, we present an associative memory that actually is capable of forming hypotheses of classification. Received: 6 December 1993/Accepted in revised form: 14 July 1994     

Self-organizing effects of spontaneous neural activity on the development of spinal locomotor circuits in vertebrates

Presented in this paper is a neural network model that can be used to investigate the possible self-organizing mechanisms occurring during the early ontogeny of spinal neural circuits in the vertebrate motor system. The neural circuit is composed of multiple types of neurons which correspond to motorneurons, Renshaw cells and a hypothetical class of interneurons. While the connectivity of this circuit is genetically predetermined, the efficacies of these connections – the synaptic s trengths – evolve in accordance with activity-dependent mechanisms which are initiated by the intrinsic, autonomous activity present in the developing spinal cord. Using Oja's rule, a modified Hebbian learning scheme for adjusting the values of the connections, the network stably self-organizes developing, in the process, reciprocally activated motorneuron pools analogous to those which exist in vivo. Received: 30 December 1996 / Accepted in revised form: 20 June 1997     

Deriving physical connectivity from neuronal morphology

 A model is presented that allows prediction of the probability for the formation of appositions between the axons and dendrites of any two neurons based only on their morphological statistics and relative separation. Statistics of axonal and dendritic morphologies of single neurons are obtained from 3D reconstructions of biocytin-filled cells, and a statistical representation of the same cell type is obtained by averaging across neurons according to the model. A simple mathematical formulation is applied to the axonal and dendritic statistical representations to yield the probability for close appositions. The model is validated by a mathematical proof and by comparison of predicted appositions made by layer 5 pyramidal neurons in the rat somatosensory cortex with real anatomical data. The model could be useful for studying microcircuit connectivity and for designing artificial neural networks. Received: 11 February 2002 / Accepted: 5 November 2002 / Published online: 20 February 2003 Correspondence to: H. Markram (e-mail: Henry.Markram@epfl.ch Tel.: +41-21-6939537, Fax: +41-21-6935350) Acknowledgements. This study was supported by the National Alliance for Autism Research, the Minerva Foundation, the US Navy, the Ebner Center for Biomedical Research, and the Edith Blum Foundation.     

Neural network mosaic model for pupillary responses to spatial stimuli

A neural network mosaic model was developed to investigate the spatial-temporal properties of the human pupillary control system. It was based on the double-layer neural network model developed by Cannon and Robinson and the pupillary dual-path model developed by Sun and Stark. The neural network portion of the model received its input from a sensor array and consisted of a retina-like two-dimensional neuronal layer. The dual-path portion of the model was composed of interconnections of the neurons that formed a mosaic of AC transient and DC sustained paths. The spatial aggregates of the AC and DC signals were input to the AC and DC summing neurons, respectively. Finally, the weighted sum of the aggregate AC and DC signals provided the output for driving the pupillary response. An important property of the model was that it could adaptively learn from training samples by adjustment of the weights. The neural network mosaic model showed excellent performance in simulating both the traditional pupillary phenomena and the new spatial stimulation findings such as responses to change in stimulus pattern and shift of light spot. Moreover, the model could also be used for the diagnosis of clinical deficits and image processing in machine vision. Received: 12 December 1997 / Accepted in revised form: 22 April 1998     

A rotation and translation invariant discrete saliency network

 We describe a neural network that enhances and completes salient closed contours in images. Our work is different from all previous work in three important ways. First, like the input provided to primary visual cortex (V1) by the lateral geniculate nucleus (LGN), the input to our computation is isotropic. That is, it is composed of spots, not edges. Second, our network computes a well-defined function of the input based on a distribution of closed contours characterized by a random process. Third, even though our computation is implemented in a discrete network, its output is invariant to continuous rotations and translations of the input image. Received: 11 July 2002 / Accepted in revised form: 25 October 2002 Acknowledgements. L.R.W. was supported in part by Los Alamos National Laboratory. J.W.Z. was supported in part by the Albuquerque High Performance Computing Center. We wish to thank Jonas August and Steve Zucker for their insightful comments. Correspondence to: L.R. Williams (e-mail: Williams@cs.unm.edu)     

A biologically motivated and analytically soluble model of collective oscillations in the cortex

. Feature linking and pattern separation are shown to be performed as simultaneous processes by a highly connected auto-associative network of spiking neurons (spike response model). In principle, many (e.g., with nine) patterns can be separated, but with a biological set of parameters the number is limited to four. The patterns have been learned by an asymmetric hebbian rule that can handle a low activity which may vary from pattern to pattern (in a range between 4% and 7%). Spikes are generated by a threshold process and – with some delay – transmitted to postsynaptic neurons. There they evoke an excitatory or inhibitory postsynaptic potential (EPSP or IPSP). Spike emission is followed by an absolute refractory period (1 ms) and activates an inhibitory delay loop that prevents continuous firing. Three different network topologies are discussed, i.e., a structureless fully connected system, a network composed of two ‘hemispheres’, and finally a hierarchical network with four subsystems that represent different ‘functions’ and interact via feedforward and feedback connections. Functional feedback turns out to be essential for context-sensitive binding. The coherence between the two hemispheres is dependent on the interhemispheric delays. If these are on average too large, the two hemispheres oscillate coherently by themselves but phase-shifted by half a period with respect to each other. Received: 16 June 1993/Accepted in revised form: 24 March 1994     

A generalized locomotion CPG architecture based on oscillatory building blocks

 Neural oscillation is one of the most extensively investigated topics of artificial neural networks. Scientific approaches to the functionalities of both natural and artificial intelligences are strongly related to mechanisms underlying oscillatory activities. This paper concerns itself with the assumption of the existence of central pattern generators (CPGs), which are the plausible neural architectures with oscillatory capabilities, and presents a discrete and generalized approach to the functionality of locomotor CPGs of legged animals. Based on scheduling by multiple edge reversal (SMER), a primitive and deterministic distributed algorithm, it is shown how oscillatory building block (OBB) modules can be created and, hence, how OBB-based networks can be formulated as asymmetric Hopfield-like neural networks for the generation of complex coordinated rhythmic patterns observed among pairs of biological motor neurons working during different gait patterns. It is also shown that the resulting Hopfield-like network possesses the property of reproducing the whole spectrum of different gaits intrinsic to the target locomotor CPGs. Although the new approach is not restricted to the understanding of the neurolocomotor system of any particular animal, hexapodal and quadrupedal gait patterns are chosen as illustrations given the wide interest expressed by the ongoing research in the area. Received: 14 June 2002 / Accepted: 18 February 2003 / Published online: 20 May 2003 Correspondence to: Z. Yang (e-mail: zhijun.yang@ed.ac.uk) Acknowledgements. This work was partially supported by CNPq, the Brazilian Research Agency, under support number 143032/96-8. We are grateful for the helpful discussions with Prof. V.C. Barbosa, Dr. A.E. Xavier, Dr. M.S. Dutra, and Dr. A.F.R. Araújo. The donations of FPGA hardware and software from XILINX Incorporation under the order No. XUP2930 and XUP3576 are also highly appreciated.