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PubMed1984

Geometrical structures determined by the functional order in nervous nets.

The functional order of a collection of neural elements may be defined as the order induced through the total of covariances of signals carried by the members of the collection. Thus functional order differs from geometrical order (e.g. somatotopy) in that geometrical order is only available to external observers, whereas functional order is available to the system itself. It has been shown before that the covariances can be used to construct a partially ordered set that explicitely represents the functional order. It is demonstrated that certain constraints, if satisfied, make this set isomorphic with certain geometrical entities such as triangulations. For instance there may exist a set of hyperspheres in a n-dimensional space with overlap relations that are described with the same partially ordered set as that which describes the simultaneous/successive order of signals in a nerve. Thus it is logically possible that the optic nerve carries (functionally) two-dimensional signals, quite apart from anatomical considerations (e.g. the geometrically two-dimensional structure of the retina which exists only to external observers). The dimension of the modality defined by a collection of nervous elements can in principle be obtained from a cross-correlation analysis of multi-unit recordings without any resort to geometrical data such as somatotopic mappings.

Animals↗
PubMed1984

Collective properties of neural networks: a statistical physics approach.

Among the various models proposed so far to account for the properties of neural networks, the one devised by Little and the one derived by Hopfield prove to be the most interesting because they allow the use of statistical mechanics techniques. The link between the Hopfield model and the statistical mechanics is provided by the existence of an extensive quantity. When the synaptic plasticity behaves according to a Hebbian procedure, the analogy with the classical spin glass models studied by Van Hemmen is complete. In particular exact solutions describing the steady states of noisy systems are found. On the other hand, the Little model introduces a Markovian dynamics. One shows that the evolution equation obeys the microreversibility principle if the synaptic efficiencies are symmetrical. Therefore, assuming that such a symmetry materializes, the Little model has to obey a Gibbs statistics. The corresponding Hamiltonian is derived accordingly. At last, using these results, both models are shown to display associative memory properties. In particular the storage capacity of neural networks working along with the Little dynamics is similar to the capacity of Hopfield neural networks. The conclusion drawn from the study of the Hopfield model can be extended to the Little model, which is certainly a more realistic description of the biological situation.

Action Potentials↗
PubMed1988

Coordinates transformation and learning control for visually-guided voluntary movement with iteration: a Newton-like method in a function space.

In order to control visually-guided voluntary movements, the central nervous system (CNS) must solve the following three computational problems at different levels: (1) determination of a desired trajectory in the visual coordinates, (2) transformation of the coordinates of the desired trajectory to the body coordinates and (3) generation of motor command. In this paper, the second and the third problems are treated at computational, representational and hardware levels of Marr. We first study the problems at the computational level, and then propose an iterative learning scheme as a possible algorithm. This is a trial and error type learning such as repetitive training of golf swing. The amount of motor command needed to coordinate activities of many muscles is not determined at once, but in a step-wise, trial and error fashion in the course of a set of repetitions. Actually, the motor command in the (n + 1)-th iteration is a sum of the motor command in the n-th iteration plus two modification terms which are, respectively, proportional to acceleration and speed errors between the desired trajectory and the realized trajectory in the n-th iteration. We mathematically formulate this iterative learning control as a Newton-like method in functional spaces and prove its convergence under appropriate mathematical conditions with use of dynamical system theory and functional analysis. Computer simulations of this iterative learning control of a robotic manipulator in the body or visual coordinates are shown. Finally, we propose that areas 2, 5, and 7 of the sensory association cortex are possible sites of this learning control. Further we propose neural network model which acquires transformation matrices from acceleration or velocity to motor command, which are used in these schemes.

Central Nervous System↗
PubMed1988

Properties of human visual memory for block patterns.

Several characteristics of human short-term visual memory (STVM) were specified through a series of experiments, by using block patterns (BPs) of varying complexity and matrix size (n-by-n). For each matrix size, BPs with high and low complexity were formed (i.e. n-by-n-H and n-by-n-L). In experiment I, the characteristics of the acquisition process were examined through a recall task. The recall rate for a single glance (exposure time less than 0.3 s) is more than 90% for 3-by-3 and 4-by-4-L BPs. For 4-by-4-H BPs, an improvement in recall rate was not found even when exposure time was increased to 2.4s. The recall rate for 6-by-6-H, 7-by-7, and 8-by-8 BPs did not change even when the exposure time was increased to 9s. In experiment II, the characteristics of the STVM decay process were examined using a recall task. Though a difference between the 4-by-4-L and 4-by-4-H acquisition rates was found, no difference was found in the forgetting rates. No decay was found for 6-by-6 BPs. Furthermore, the information obtained during a short duration was not forgotten for 4-by-4, and 6-by-6 BPs. It was concluded from these results that: 1) The acquisition rate into STVM depends upon figural complexity. 2) The decay rate does not depend upon figural complexity. 3) The limit of STVM was between 4-by-4-L, and 4-by-4-H BPs.(ABSTRACT TRUNCATED AT 250 WORDS)

Cybernetics↗
PubMed1988

Maximum likelihood analysis of spike trains of interacting nerve cells.

Suppose that a neuron is firing spontaneously or that it is firing under the influence of other neurons. Suppose that the data available are the firing times of the neurons present. An "integrate several inputs and fire" model is developed and studied empirically. For the model a neuron's firing occurs when an internal state variable crosses a random threshold. This conceptual model leads to maximum likelihood estimates of internal quantities, such as the postsynaptic potentials of the measured influencing neurons, the membrane potential, the absolute threshold and also estimates of derived quantities such as the strength-duration curve and the recovery process of the threshold. The model's validity is examined via an estimate of the conditional firing probability. The approach appears useful for estimating biologically meaningful parameters, for examining hypotheses re these parameters, for understanding the connections present in neural networks and for aiding description and classification of neurons and synapses. Analyses are presented for a number of data sets collected for the sea hare, Aplysia californica, by J. P. Segundo. Both excitatory and inhibitory examples are provided. The computations were carried out via the Glim statistical package. An example of a Glim program realizing the work is presented in the Appendix.

Animals↗
PubMed1988

Analysis of the activity of single neurons in stochastic settings.

This paper presents a new way of modeling the activity of single neurons in stochastic settings. It incorporates in a natural way many physiological mechanisms not usually found in stochastic models, such as spatial integration, non-linear membrane characteristics and non-linear interactions between excitation and inhibition. The model is based on the fact that most of the neuronal inputs have a finite lifetime. Thus, the stochastic input can be modeled as a simple finite markov chain, and the membrane potential becomes a function of the state of this chain. Firing occurs at states whose membrane potential is above threshold. The main mathematical results of the model are: (i) the input-output firing rate curve is convex at low firing rates and is saturated at high firing rates, and (ii) at low firing rates, firing usually occurs when there is synchronous convergence of many excitatory events.

Action Potentials↗
PubMed1986

A self-similar stack model for human and machine vision.

A new model is proposed that not only exhibits the major properties of primate spatial vision but also has a structure that can be implemented efficiently in a machine vision system. The model is based on a self-similar stack structure with a spatial resolution that varies with eccentricity. It correctly reproduces the visual cortical mapping function, yet it has the important attribute that it can produce invariant responses to local changes in the size and position of image features. By proposing a novel purpose for cortical "bar-detectors", the model can also produce invariance to more general distortions. The structure of the model allows efficient hierarchical search to be made and it naturally embraces the concept of "attention area". Exploitation of this model has already confirmed these properties and has also revealed its robust ability to control the focus and gain of machine vision systems.

Cybernetics↗
PubMed1987

A model of handwriting.

The research reported here is concerned with hand trajectory planning for the class of movements involved in handwriting. Previous studies show that the kinematics of human two-joint arm movements in the horizontal plane can be described by a model which is based on dynamic minimization of the square of the third derivative of hand position (jerk), integrated over the entire movement. We extend this approach to both the analysis and the synthesis of the trajectories occurring in the generation of handwritten characters. Several basic strokes are identified and possible stroke concatenation rules are suggested. Given a concise symbolic representation of a stroke shape, a simple algorithm computes the complete kinematic specification of the corresponding trajectory. A handwriting generation model based on a kinematics from shape principle and on dynamic optimization is formulated and tested. Good qualitative and quantitative agreement was found between subject recordings and trajectories generated by the model. The simple symbolic representation of hand motion suggested here may permit the central nervous system to learn, store and modify motor action plans for writing in an efficient manner.

Cybernetics↗
PubMed1987

Recognition of hierarchically encoded images by technical and biological systems.

All the contours and regions of objects can be mapped to code-trees of the Hierarchical Structure Code (HSC). Invariant features like structure classes, shape descriptions, or relations between structures and components may be easily extracted from the HSC. HSC-based pattern recognition provides a straightforward transition between the signal-space of the image and the space of its symbolic representation. Physiological data are well predicted and do not exclude an implementation of an HSC-based system within the visual cortex.

Cybernetics↗
PubMed1987

The human arm as a redundant manipulator: the control of path and joint angles.

The movements studied involved moving the tip of a pointer attached to the hand from a given starting point to a given end point in a horizontal plane. Three joints--the shoulder, elbow and wrist--were free to move. Thus the system represented a redundant manipulator. The coordination of the movements of the three joints was recorded and analyzed. The study concerned how the joints are controlled during a movement. The results are used to evaluate several current hypotheses for motor control. Basically, the incremental changes are calculated so as to move the tip of the manipulator along a straight line in the workspace. The values of the individual joints seem to be determined as follows. Starting from the initial values the incremental changes in the three joint angles represent a compromise between two criteria: 1) the amount of the angular change should be about the same in the three joints, and 2) the angular changes should minimize the total cost of the arm position as determined by cost functions defined for each joint as a function of angle. By itself, this mechanism would produce strongly curved trajectories in joint space which could include additional acceleration and deceleration in a joint. These are reduced by the influence of a third criterion which fits with the mass-spring hypothesis. Thus the path is calculated as a compromise between a straight line in workspace and a straight line in joint space. The latter can produce curved paths in the workspace such as were actually found in the experiments. A model calculation shows that these hypotheses can qualitatively describe the experimental findings.

Arm↗
PubMed1987

Muscle dynamics: dependence of muscle length on changes in external load.

A phenomenological theory of muscle dynamics has been elaborated on the basis of data obtained in experiments on hind limb extensor muscles of narcotized cat. Functional dependence of muscle length on external load was explored in conditions of a constant frequency of the efferent stimulation. It was shown that the system under study could be presented for a rather wide class of input signals as a system with nonlinear statics and linear dynamics. The nonlinear statics was shown to be determined mainly by the hysteretical effects of muscle contraction, whereas dynamic element was described by the first order linear differential equation corresponding to the traditional three-component mechanical model of the muscle. A hypothesis was proposed to explain the hysteresis in active muscle on the basis of functioning of the troponin-tropomyosin regulatory complex. Elaborated mathematical model of muscle dynamics can be used to predict and evaluate changes in the muscle length evoked by arbitrary changes in the external load.

Animals↗
PubMed1987

On visual orientation of dot patterns.

Two-dimensional normally distributed random dot patterns were used in two experiments on visual orientation estimation. In the first experiment the patterns differed in their sample correlation and in dot number. In the second one the number of dots was maintained constant but the patterns were generated as a superposition of two normally distributed orthogonal sets composed of different number of dots. In both experiments the estimated orientation depended on stimuli correlation - with increasing correlation the estimated orientation gets closer to the orientation of the least square distance axis of the pattern. Even at very low unsignificant correlations there still remained a hint about stimulus orientation which was not estimated at random. Equalizing consecutively the number of dots in the two orthogonal dot patterns during the second experiment did not result in chance performance either. The bimodal angular distributions of the obtained responses permitted to approach the problem of orientation ambiguity. The results are discussed in terms of optimization processes taking place in the visual system.

Cybernetics↗
PubMed1983

Four neural circuit models and their role in the organization of voluntary movement.

Four neural circuit models and their role in the organization of voluntary movement are presented here. These circuits collectively control a ballistic type biped voluntary movement. The structure of each circuit, and its function is discussed. Three of the circuits are central and contribute to the construction of two classes of inputs, analogous to the alpha signals and gamma signals in biological systems. The fourth circuit plays a role in stabilization of the movement, and in compensation for the receptors. Digital computer simulations are undertaken to demonstrate the construction of all the intermediate signals and the response of a two link biped to these efferent signals.

Animals↗
PubMed1983

A neural network model for cognitive activity.

A consideration of the storage of information as an energized neuronal state leads to the development of a new type of neural network model which is capable of pattern recognition, concept formation and recognition of patterns of events in time. The network consists of several layers of cells, each cell representing by connections from the lower levels some combination of features or concepts. Information travels toward higher layers by such connections during an association phase, and then reverses during a recognition phase, where higher-order concepts can redirect the flow to more appropriate elements, revising the perception of the environment. This permits a more efficient method of distinguishing closely-related patterns and also permits the formation of negative associations, which is a likely requirement for formation of "abstract" concepts.

Association Learning↗
PubMed1983

A model of binocular brightness and binaural loudness perception in humans with general applications to nonlinear summation of sensory inputs.

A single neural model is proposed to account for how responses of the two eyes and two ears combine to form the perception of binocular brightness and binaural loudness respectively. It involves nonlinear reciprocal feedback inhibition between left and right channels, followed by linear summation between the channels. Local circuit synaptic interactions are an important source of nonlinearity. The model combines inputs in a manner that approximates vector magnitude models in general. This suggests that the model can be applied to a variety of circumstances beyond the visual and auditory data discussed here.

Auditory Perception↗
PubMed1983

Peripheral vision and perceived visual direction.

Experiments are described in which the subjects had to localize brief light stimuli presented up to 10 degrees from the fixation center. The localization was performed relative to a continuously illuminated scale with numbered or lettered divisions. Systematic errors were obtained, the stimuli being mislocated nearer the fixation point than they were actually presented. The angular size of errors increased with the increase of stimulus eccentricity. It appeared to be a characteristic of the stimulated retinal locus, independent of the viewing distance and the scale element corresponding to this locus. It is concluded that despite the presence of a visible background frame of reference, subjects prefer to base their reports on the perceived egocentric direction of the stimulus which does not coincide with the physical direction of the stimulus. A parallel is drawn between this study and the studies on serial position function for letter identification.

Cybernetics↗
PubMed1983

A proposed neural network for the integrator of the oculomotor system.

Single-unit recordings, stimulation studies, and eye movement measurements all indicate that the firing patterns of many oculomotor neurons in the brain stem encode eye-velocity commands in premotor circuits while the firing patterns of extraocular motoneurons contain both eye-velocity and eye-position components. It is necessary to propose that the eye-position component is generated from the eye-velocity signal by a leaky hold element or temporal integrator. Prior models of this integrator suffer from two important problems. Since cells appear to have a steady, background signal when eye position and velocity are zero, how does the integrator avoid integrating this background rate? Most models employ some form of lumped, positive feedback the gain of which must be kept within totally unreasonable limits for proper operation. We propose a lateral inhibitory network of homogeneous neurons as a model for the neural integrator that solves both problems. Parameter sensitivity studies and lesion simulations are presented to demonstrate robustness of the model with respect to both the choice of parameter values and the consequences of pathological changes in a portion of the neural integrator pool.

Animals↗
PubMed1985

Entrainment of two coupled van der Pol oscillators by an external oscillation. As a base of "holonic control".

A system composed of two coupled internal oscillators and an external oscillation is studied as a model of biological control systems. The type of interaction between the internal oscillators is a mutual and dissipative one. Three macroscopic states of the internal oscillators are demonstrated in the absence of the external oscillation. Strict and loose entrainment regions of the internal oscillators by the external oscillation are shown in respect to the intensity of the mutual interaction, the intrinsic frequency difference of the internal oscillations, and the magnitude and frequency of the external oscillation. On the other hand, an idea of "holonic system" is introduced and the fundamental properties of the model as a holonic system are elucidated.

Animals↗