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PubMed1996

Population networks: a large-scale framework for modelling cortical neural networks.

Artificial neural networks are usually built on rather few elements such as activation functions, learning rules, and the network topology. When modelling the more complex properties of realistic networks, however, a number of higher-level structural principles become important. In this paper we present a theoretical framework for modelling cortical networks at a high level of abstraction. Based on the notion of a population of neurons, this framework can accommodate the common features of cortical architecture, such as lamination, multiple areas and topographic maps, input segregation, and local variations of the frequency of different cell types (e.g., cytochrome oxidase blobs). The framework is meant primarily for the simulation of activation dynamics; it can also be used to model the neural environment of single cells in a multiscale approach.

Animals↗
PubMed1996

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 required perception of a relatively small number of significant stimulus components.

Action Potentials↗
PubMed1996

A mathematical model of activity-dependent, anatomical segregation induced by competition for neurotrophic support.

Mathematical or computational models of activity-dependent neural competition typically impose competition in anatomically fixed networks by the use of synaptic normalisation, for which there is very little experimental support. Recent experimental evidence, however, strongly implicates neurotrophic factors in neural plasticity and competition, in addition to their well-known potent effects on neurite outgrowth and synaptogenesis. We therefore present a simple, mathematical model of anatomical segregation induces by activity-dependent competition for a limited supply of a neurotrophic factor provided by target cells to afferents. We extract the behaviour of the model in various regimes, in which the neurotrophic factor is either in critical supply or in abundant supply, by a combination of analytical and numerical methods, and study the effects of correlations in afferent inputs on competition. We apply the model to three different systems: ocular dominance column formation; elimination of polyneuronal innervation at the vertebrate neuromuscular junction; trigeminal brain stem whisker-related structure formation. Several classes of related predictions emerge, including the prediction that kittens reared with strabismus should require a higher concentration of neurotrophic factor infusion into their primary visual cortex than normally reared cats in order to induce the anatomical desegregation of ocular dominance columns. We also speculate on the mechanisms of support of inhibitory rather than excitatory neurons, and suggest the existence of a separate, (Cl-)-mediated activity-dependent pathway for their neurotrophic support.

Animals↗
PubMed1996

Electrical activity of the sensory afferent pathway in the enteric nervous system.

In this paper we develop a mathematical model for the electrical activity of the afferent pathway, formed from the coupled primary and secondary sensory neurons. The primary sensory neuron possesses the electrical properties of AH neurons and morphological characteristics of Dogiel type II neurons; the secondary sensory neuron displays the tonic type of electrical behavior and has morphological features of Dogiel type III neurons. Free nerve endings of the mechanoreceptor form the receptive field of the pathway. Based on the general principles of the Hodgkin-Huxley description of excitable cells, the model simulates the following sequence of events: stretch of the receptive field initiates the dendritic potential at the mechanoreceptors; the excitation causes soma action potential development at the primary sensory neuron which is followed by soma action potential generation at the secondary sensory neuron. Numerical calculation have shown that the model is capable of reproducing different electrical patterns within the pathway under normal physiological conditions and after treatment with charybdotoxin, iberiotoxin, tetrodotoxin, omega-conotoxin GVIA, A1-A2 purinoceptor agonists, a protein kinase C activator, and a delta-opioid receptor agonist. Comparison of the computational results with the results of experiments conducted on the neurons of the submucous and myenteric plexi of the small bowel demonstrates their good qualitative and quantitative agreement.

Afferent Pathways↗
PubMed1996

A neural network simulation of the vestibular system: implications on the role of intervestibular nuclear coupling during vestibular compensation.

Previous neural network simulations of the vestibular system have been based loosely on known physiology. This research involved the use of a strongly physiologically based neural network model which was used to investigate the role of the vestibular commissure in restoring the bilateral symmetry of the resting rates of the vestibular nuclei during vestibular compensation following unilateral labyrinthectomy. It was found the readjustments in the gain of the vestibular commissure were not primarily responsible for vestibular compensation, as has previously been suggested, but rather that it was modifications in extralabyrinthine sources of tone which mediated the restoration of the central symmetry between the two nuclei.

Animals↗
PubMed1996

Numerical bifurcation analysis of distance-dependent on-center off-surround shunting neural networks.

On-center off-surround shunting neural networks are often applied as models for content-address-able memory (CAM), the equilibria being the stored memories. One important demand of biological plausible CAMs is that they function under a broad range of parameters, since several parameters vary due to postnatal maturation or learning. Ellias, Cohen and Grossberg have put much effort into showing the stability properties of several configurations of on-center off-surround shunting neural networks. In this article we present numerical bifurcation analysis of distance-dependent on-center off-surround shunting neural networks with fixed external input. We varied four parameters that may be subject to postnatal maturation: the range of both excitatory and inhibitory connections and the strength of both inhibitory and excitatory connections. These analyses show that fold bifurcations occur in the equilibrium behavior of the network by variation of all four parameters. The most important result is that the number of activation peaks in the equilibrium behavior varies from one to many if the range of inhibitory connections is decreased. Moreover, under a broad range of the parameters the stability of the network is maintained. The examined network is implemented in an ART network, Exact ART, where it functions as the classification layer F2. The stability of the ART network with the F2-field in different dynamic regimes is maintained and the behavior is functional in Exact ART. Through a bifurcation the learning behavior of Exact ART may even change from forming local representations to forming distributed representations.

Cybernetics↗
PubMed1997

Size principle and information theory.

The motor units of a skeletal muscle may be recruited according to different strategies. From all possible recruitment strategies nature selected the simplest one: in most actions of vertebrate skeletal muscles the recruitment of its motor units is by increasing size. This so-called size principle permits a high precision in muscle force generation since small muscle forces are produced exclusively by small motor units. Larger motor units are activated only if the total muscle force has already reached certain critical levels. We show that this recruitment by size is not only optimal in precision but also optimal in an information theoretical sense. We consider the motoneuron pool as an encoder generating a parallel binary code from a common input to that pool. The generated motoneuron code is sent down through the motoneuron axons to the muscle. We establish that an optimization of this motoneuron code with respect to its information content is equivalent to the recruitment of motor units by size. Moreover, maximal information content of the motoneuron code is equivalent to a minimal expected error in muscle force generation.

Animals↗
PubMed1997

Neural networks in higher levels of abstraction.

Existing artificial neural network models are not very successful in understanding or generating natural language texts. Therefore it is proposed to design novel neural network structures in higher levels of abstraction. This concept leads to a hierarchy of network layers which extract and store local details in every layer and transfer the remaining nonlocal context information to higher levels. At the same time data compression is provided from layer to layer. The use of the same network elements (meta-words) in higher levels for different word series in the basis level is introduced and discussed for grammatical identity or similarity. Thus text can be compressed to forms which are almost free of redundancy. Possible applications are storage, transmission, understanding, generating and translation of texts.

Cybernetics↗
PubMed1997

Colliding saccades evoked by frontal eye field stimulation: artifact or evidence for an oculomotor compensatory mechanism underlying double-step saccades?

What happens when the goal is changed before the movement is executed? Both the double-step and colliding saccade paradigms address this issue as they introduce a discrepancy between the retinal images of targets in space and the commands generated by the oculomotor system necessary to attain those targets. To maintain spatial accuracy under such conditions, transformations must update "retinal error' as eye position changes, and must also accommodate neural transmission delays in the system so that retinal and eye position information are temporally aligned. Different hypotheses have been suggested to account for these phenomena, based on observations of dissociable cortical and subcortical compensatory mechanisms. We now demonstrate how a single compensatory mechanism can be invoked to explain both double-step and colliding saccade paradigm results, based on the use of a damped signal of change in position that is used in both cases to update retinal error and, thereby, account for intervening movements. We conclude that the collision effect is not an artifact, but instead reveals a compensatory mechanism for saccades whose targets appear near the onset of a preceding saccade.

Brain Stem↗
PubMed1997

Two-arm trajectory planning in a manipulation task.

This paper addresses the trajectory planning problem for a task which requires positioning and orienting an object firmly grasped by two hands at a visually specified goal configuration in the horizontal plane. The motor task involves three degrees of freedom (two translational and one rotational), and the motions of the arms are constrained by the physical coupling through the held object. Experimentally measured trajectories of two arms in the coordinated positioning/orienting task are presented. The hypothesis that the rotational and translational components of motions are decoupled and independently planned is tested. Two explicit mathematical models to account for the kinematic features of the two-arm motions are formulated, and the predictions of the models are compared with the experimental data. Both models extend the minimum-jerk model to the two-arm coordinated motions case. The trajectories predicted by the models were found to be in qualitative agreement with the experimental data. However, neither model could account for the observed configuration dependence of the motions, nor for some of the properties of the measured velocity components of the motions. Our findings support the idea that the rotational and translational components of two-arm motions in the positioning/orienting task are independently planned in extra-personal space, and are further combined in a hierarchical fashion to produce the observed motions. The tested models may serve as a basis for further investigations of issues pertinent to the generation of two-arm trajectories.

Arm↗
PubMed1997

Examination of the gamma equilibrium point hypothesis when applied to single degree of freedom movements performed with different inertial loads.

One of the theories of human motor control is the gamma Equilibrium Point Hypothesis. It is an attractive theory since it offers an easy control scheme where the planned trajectory shifts monotionically from an initial to a final equilibrium state. The feasibility of this model was tested by reconstructing the virtual trajectory and the stiffness profiles for movements performed with different inertial loads and examining them. Three types of movements were tested: passive movements, targeted movements, and repetitive movements. Each of the movements was performed with five different inertial loads. Plausible virtual trajectories and stiffness profiles were reconstructed based on the gamma Equilibrium Point Hypothesis for the three different types of movements performed with different inertial loads. However, the simple control strategy supported by the model, where the planned trajectory shifts monotonically from an initial to a final equilibrium state, could not be supported for targeted movements performed with added inertial load. To test the feasibility of the model further we must examine the probability that the human motor control system would choose a trajectory more complicated than the actual trajectory to control.

Adult↗
PubMed1997

Coherency and connectivity in oscillating neural networks: linear partialization analysis.

This paper studies the relation between the functional synaptic connections between two artificial neural networks and the correlation of their spiking activities. The model neurons had realistic non-oscillatory dynamic properties and the networks showed oscillatory behavior as a result of their internal synaptic connectivity. We found that both excitation and inhibition cause phase locking of the oscillating activities. When the two networks excite each other the oscillations synchronize with zero phase lag, whereas mutual inhibition between the networks resulted in an anti-phase (half period phase difference) synchronization. Correlations between the activities of the two networks can also be caused by correlated external inputs driving the systems (common input). Our analysis shows that when the networks exhibit oscillatory behavior and the rate of the common input is smaller than a characteristic network oscillator frequency, the cross-correlation functions between the activities of two systems still carry information about the mutual synaptic connectivity. This information can be retrieved with linear partialization, removing the influence of the common input. We further explored the network responses to periodic external input. We found that when the input is of a frequency smaller than a certain threshold, the network responds with bursts at the same frequency as the input. Above the threshold, the network responds with a fraction of the input frequency. This frequency threshold, characterizing the oscillatory properties of the network, is also found to determine the limit to which linear partialization works.

Computer Simulation↗
PubMed1997

Classification of protein families and detection of the determinant residues with an improved self-organizing map.

Using a SOM (self-organizing map) we can classify sequences within a protein family into subgroups that generally correspond to biological subcategories. These maps tend to show sequence similarity as proximity in the map. Combining maps generated at different levels of resolution, the structure of relations in protein families can be captured that could not otherwise be represented in a single map. The underlying representation of maps enables us to retrieve characteristic sequence patterns for individual subgroups of sequences. Such patterns tend to correspond to functionally important regions. We present a modified SOM algorithm that includes a convergence test that dynamically controls the learning parameters to adapt them to the learning set instead of being fixed and externally optimized by trial and error. Given the variability of protein family size and distribution, the addition of this features is necessary. The method is successfully tested with a number of families. The rab family of small GTPases is used to illustrate the performance of the method.

Algorithms↗
PubMed1997

The role of retinal bipolar cell in early vision: an implication with analogue networks and regularization theory.

A linear analogue network model is proposed to describe the neuronal circuit of the outer retina consisting of cones, horizontal cells, and bipolar cells. The model reflects previous physiological findings on the spatial response properties of these neurons to dim illumination and is expressed by physiological mechanisms, i.e., membrane conductances, gap-junctional conductances, and strengths of chemical synaptic interactions. Using the model, we characterized the spatial filtering properties of the bipolar cell receptive field with the standard regularization theory, in which the early vision problems are attributed to minimization of a cost function. The cost function accompanying the present characterization is derived from the linear analogue network model, and one can gain intuitive insights on how physiological mechanisms contribute to the spatial filtering properties of the bipolar cell receptive field. We also elucidated a quantitative relation between the Laplacian of Gaussian operator and the bipolar cell receptive field. From the computational point of view, the dopaminergic modulation of the gap-junctional conductance between horizontal cells is inferred to be a suitable neural adaptation mechanism for transition between photopic and mesopic vision.

Animals↗
PubMed1997

A model for learning human reaching movements.

Reaching movement is a fast movement towards a given target. The main characteristics of such a movement are straight path and a bell-shaped speed profile. In this work a mathematical model for the control of the human arm during ballistic reaching movements is presented. The model of the arm contains a 2 degrees of freedom planar manipulator, and a Hill-type, non-linear mechanical model of six muscles. The arm model is taken from the literature with minor changes. The nervous system is modeled as an adjustable pattern generator that creates the control signals to the muscles. The control signals in this model are rectangular pulses activated at various amplitudes and timings, that are determined according to the given target. These amplitudes and timings are the parameters that should be related to each target and initial conditions in the work-space. The model of the nervous system consists of an artificial neural net that maps any given target to the parameter space of the pattern generator. In order to train this net, the nervous system model includes a sensitivity model that transforms the error from the arm end-point coordinates to the parameter coordinates. The error is assessed only at the termination of the movement from knowledge of the results. The role of the non-linearity in the muscle model and the performance of the learning scheme are analysed, illustrated in simulations and discussed. The results of the present study demonstrate the central nervous system's (CNS) ability to generate typical reaching movements with a simple feedforward controller that controls only the timing and amplitude of rectangular excitation pulses to the muscles and adjusts these parameters based on knowledge of the results. In this scheme, which is based on the adjustment of only a few parameters instead of the whole trajectory, the dimension of the control problem is reduced significantly. It is shown that the non-linear properties of the muscles are essential to achieve this simple control. This conclusion agrees with the general concept that motor control is the result of an interaction between the nervous system and the musculoskeletal dynamics.

Algorithms↗
PubMed1997

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 strengths--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.

Animals↗
PubMed1997

Learned changes in the complexity of movement organization during multijoint, standing pulls.

This paper tests the hypothesis that the central nervous system (CNS) learns to organize multijoint movements during a multijoint 'bouncing pull' task such that, after practice, motion of the anterior-posterior center of mass (CMAP) more closely resembles that of a conservative, one degree of freedom (DF), inverted pendulum model. The task requires standing human subjects to produce precise peak pulling forces on a handle while maintaining balance-goals that can be easily accomplished if movement is organized as in the model. Ten freely standing subjects practiced making brief, bouncing pulls in the horizontal direction to target forces (20-80% of maximum) for 5 days. Pulling force, body kinematic and force plate data were recorded. An eight-segment analysis determined sagittal-plane CM motion. We compared the effects of practice on the regression-based fit between actual and model-simulated CMAP trajectories, and on measures of CMAP phase plane symmetry and parameter constancy that the model predicts. If the CNS learns to organize movements like the inverted pendulum model, then model fit should improve and all other measures should approach zero after practice. The fit between modeled and actual CMAP motion did not improve significantly with practice, except for moderate force pulls. Nor did practice increase phase plane symmetry or parameter constancy. Specifically, practice did not decrease the differences between the pre-impact and rebound positions or speeds of the CMAP, although speed difference increased with pulling force. CMAP at the end of the movement was anterior to its initial position; the anterior shift increased after practice. Differences between the pre-pull and balance-recovery ankle torque (TA) impulses were greater on day 5 and correlated with the anterior shift in CMAP. These results suggest that practice separately influenced the force production and balance recovery phases. A modified model with damping could not explain the observed behaviors. A modified model using the actual time-varying TA profiles improved fit at lower force levels, but did not explain the increased postural shift after practice. We conclude that the CNS does not learn to organize movements like the conservative, inverted pendulum model, but rather learned a more complex form of organization that capitalized on more time-varying controls and more intersegmental dynamics. We hypothesize that at least one additional DF and at least one time-varying parameter will be needed to explain fully how the CNS learns to organize multijoint, bouncing pulls made while standing.

Adult↗
PubMed1997

Fast cortical selection: a principle of neuronal self-organization for perception?

It is commonly accepted that larger visual objects are represented in the cerebral cortex by specific spatial patterns of neuronal activity. Self-organization is a key concept in the different explanations of such neuronal representations. We here propose as a hypothesis that fast cortical selection (FCS) is an intrinsic functional element of cortical self-organization during perception. Selection is a central concept in theoretical biology which has proved its explanatory power in different fields of our natural and cultural world. The central element in the cortical selection process is the pyramidal cell with its two types of excitatory input. In primary cortical areas one of these inputs comes from any of the sensory organs, determining the topological and typological receptive field properties of the cell and also driving it directly. The other type of input connects reciprocally neighbouring pyramidal cells by axon collaterals and only facilitates the driving input. These two functionally different inputs constitute the elementary selection system working by iterative mutual facilitation as a biological algorithm. A short simulation, based entirely on such biological facts, illustrates the dynamic of this selection process: the activity of cells responding better to the external stimulus 'grow and survive' the stimulation, whereas less responsive cells decrease their activity due to competition.

Algorithms↗