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In practice the relevant details of images exist only over a restricted range of scale. Hence it is important to study the dependence of image structure on the level of resolution. It seems clear enough that visual perception treats images on several levels of resolution simultaneously and that this fact must be important for the study of perception. However, no applicable mathematically formulated theory to deal with such problems appers to exist. In this paper it is shown that any image can be embedded in a one-parameter family of derived images (with resolution as the parameter) in essentially only one unique way if the constraint that no spurious detail should be generated when the resolution is diminished, is applied. The structure of this family is governed by the well known diffusion equation (a parabolic, linear, partial differential equation of the second order). As such the structure fits into existing theories that treat the front end of the visual system as a continuous tack of homogeneous layer, characterized by iterated local processing schemes. When resolution is decreased the images becomes less articulated because the extrem ('light and dark blobs') disappear one after the other. This erosion of structure is a simple process that is similar in every case. As a result any image can be described as a juxtaposed and nested set of light and dark blobs, wherein each blod has a limited range of resolution in which it manifests itself. The structure of the family of derived images permits a derivation of the sampling density required to sample the image at multiple scales of resolution. The natural scale along the resolution axis (leading to an informationally uniform sampling density) is logarithmic, thus the structure is apt for the description of size invariances. [ABSTRACT FROM AUTHOR]

In a psychophysical experiment the observer is given the task to detect a signal or to discriminate two signals; the performance of the observer in this task is to be determined as a function of the physical parameters of the stimuli presented. To increase efficiency of testing, one stimulus parameter is controlled in such a way that the task is made more difficult when the observer performs well and made easier when he doesn't. The observer then forms part of a feedback loop, a part that is characterized by stochastic behaviour. In a well-designed experiment the parameter under study will continually oscillate around its 'target value' (i.e., the threshold of detectability or of discriminability). This paper derives an expression for the equilibrium distribution of this parameter around the target point, valid for an extremely long experiment. The observer is described as a stochastic detector with stationary characteristics. In the experiment he is subjected to a number of trials with stimuli having constant parameters. A set of rules applied to the performance of the subject in a group of trials then determines in which direction the parameter under study is to be varied for the next group of trials. For a wide class of experimental designs the desired equilibrium distribution of this parameter can be found from a recurrence formula. The derivation of this formula is given. Examples of application of this theory are presented. Equilibrium distributions computed from the recurrence formula are found to be good predictors of results of experiments carried out with a finite length. This result allows a deeper study of what constitutes the best procedural design in a given case. It is finally shown how the class of usable procedures can be enlarged by judicious combination of different types of rules. [ABSTRACT FROM AUTHOR]

Discrete and continuous modes of visual pattern discrimination performance are analyzed using a model for the investigation of discrete internal pattern representations described in previous papers (Foster, 1980a, b). A simple quantitative criterion is derived to characterize the two kinds of visual discrimination performance. Values predicted by this criterion are then compared with values obtained from experimental data. [ABSTRACT FROM AUTHOR]

Planar arm trajectories are characterized by a segmentation of the hand velocity profile and by a coupling between shape and speed. The question addressed in this paper is whether such coupling, observed in two dimensions, still holds in three dimensions. This matter was investigated experimentally by recording three dimensional 'aimless' movements of the arm, particularly three dimensional scribbles, and the answer suggested by the experimental data is that only the 'bending' of the trajectory is coupled with speed, whereas the 'twisting' is independent of speed. The same behaviour was also found to characterize a computational model of trajectory formation which is based on the spatial composition of chains of planar strokes, overlapped in time. [ABSTRACT FROM AUTHOR]

Recently, a model for a pair of antogonistic muscles has been studied (Oğuztöreli and Stein, 1982). In the present paper we formulate and investigate the minimization of the costs associated with the time to complete the movement, the oscillation about the end-point, the energy costs to the muscles to complete the movement, the cost to the nervous system to supply the inputs, and the cost of reliability in the face of perturbing forces. To solve these optimization problems the maximum principle of Pontryagin is employed. In all of these optimization problems, except the energy optimal problem, the optimal controls (active states or nervous inputs) are of the bang-bang type. [ABSTRACT FROM AUTHOR]

Several simplified differential equations are derived from the Wilson and Cowan model describing the dynamics of excitatory and inhibitory neurons. It is shown, by expansions of the convolution integrals and the input-output functions, that the basic integrodifferential equations can be reduced to two coupled nonlinear partial differential equations of reaction-diffusion type. Further simplification leads to the coupled partial differential equations mathematically equivalent to the FitzHugh-Nagumo equations for the nerve impulse. Through a brief stability analysis in relation to the existing investigations on the bifurcation phenomena, an attempt is made to clarify the consequence due to the approximations introduced in this paper. [ABSTRACT FROM AUTHOR]

This paper proposes a computational model for different aspects of trajectory formation, from point-to-point movements to handwriting. The proposed model is based on a mechanism of composition of basic curve elements (strokes) which separates the spatial and the temporal aspects of trajectory formation. At the same time, the model suggests a method for storing and describing arm movements, as a list of stroke descriptors. Experimental trajectories were digitized and analyzed with regard to several types of movements: i) point-to-point trajectories, ii) closed trajectories, iii) trajectories with inflection points, iv) spiral-like trajectories, v) handwritten trajectories. Velocity and curvature profiles were computed for the trajectories and the model was fitted to the data. The implications of the model and its 'credibility' in the general context of motor control are discussed. [ABSTRACT FROM AUTHOR]

This paper presents a method for the calculation of the information transfer, or transinformation, in multiple input/single output neuronal systems. Our approach is an extension of an approach introduced by Eckhorn and Poepel in 1974. These authors computed the transinformation in single input/single output neuronal channels by regarding the spike (or stimulus) trains involved as finite Markov chains. The expressions for multiple input systems presented here are derived in close analogy to formulae in linear systems theory which show explicity the correlations between the different input channels. A number of equivalent forms for the transinformation are discussed. [ABSTRACT FROM AUTHOR]

In a previous paper we defined the associative search problem and presented a system capable of solving it under certain conditions. In this paper we interpret a spatial learning problem as an associative search task and describe the behavior of an adaptive network capable of solving it. This example shows how naturally the associative search problem can arise and permits the search, association, and generalization properties of the adaptive network to bee clearly illustrated. [ABSTRACT FROM AUTHOR]

This paper forms a preface and introduction to a new method for the estimation of evoked potentials: a posteriori time-varying filtering. A simple evoked potential model, consisting of a transient signal and additive noise, is discussed and the underlying assumptions explicitly formulated. Assuming this model, the problem of estimating the signal from an ensemble is considered from the statistical and communication engineering point of view, along with a brief survey of the pertinent literature. It is explained why ensemble averaging, in general, does not provide the best estimate in the mean-square error sense. After a summary of the controversial aspects of timeinvariant ' a posteriori 'Wiener' filtering', it is indicated how that method can be generalized to a time-varying counterpart, which is able to handle the essentially transient character of evoked potential waveforms. Finally, the new method is presented on a conceptual level and its application illustrated by examples. [ABSTRACT FROM AUTHOR]

In this paper, we report on two experiments concerning the effect of the visual field of fovea on the subjective estimation of angular velocity. Experiment 1 investigates the effect of a slow moving target on the perception of self motion. The result of this experiment can be summarized as follows: a slow moving target seen in the visual field of fovea by a stationary person generates in this person a sensation of self rotation in the same direction as the motion of the target. This phenomenon will be called foveal induced ego motion. Experiment 2 investigates the latency for the detection of a self angular acceleration when the person focusses his fovea on a slowly moving target. From the results of this experiment we conclude that the latency for detection of a small self angular acceleration is shorter if the person sees a small foveal target moving with respect to the person in the direction of self rotation than if that small foveal target is moving (with respect to the person) in the opposite direction. The results of these experiments help us in refining existing models of visual-vestibular interaction, by providing a model which accounts for the phenomenon of oculogyral illusion. [ABSTRACT FROM AUTHOR]

The study of the orientation behavior of flies requires the consideration of a few simple control systems for fixation and tracking. In this paper two such control systems are analyzed, in terms of the corresponding difference and differential equations. The first control system corrects with a delay ɛ the angular trajectory proportionally to the error angle ψ; the second control system also corrects proportionally to the error angle ψ but only when the absolute value of ψ is increasing. The differential equations are and u[ ] being the step function ( u[ x]=1 if x>0, otherwise u[ x]=0). Under suitable restrictions on the parameters it is proved (a) that the difference equations and which can be associated to Eqs. (0) and (*), are 'asymptotically equivalent' (for large n) if the time scale is 'smoothed' over two time units and (b) that the second equation, with 0<α<2, always converge to a set of oscillating solutions of period 2 for arbitrary initial conditions. Numerical simulations show that the delay-differential equations behave in a similar way. We have also demonstrated with computer simulations that both control systems can satisfactorily predict the 3- D trajectory of a fly chasing another fly. The main biological implications of the analysis are: (1) The two control systems are practically equivalent descriptions of the fly's control of flight on a 'coarse' time scale (2 times the fly's delay), consistently with an earlier more general derivation of Eq. (0) (Poggio and Reichardt, 1973). (2) On a fine time scale the second control system is characterized by an asymptotic oscillation with period twice the fly's delay. It is conjectured that a wide range of control systems of the same general type must have a similar oscillatory behavior. Finally, we predict the existence of asymptotic oscillations in the angular trajectory and the torque of tracking flies (if a control system of the second type is involved to a significant extent). Such oscillations should have a basic period of twice the effective reaction delay, and should be best detectable outside the binocular region. Closed loop experiments and the analysis of free flight trajectories may provide critical tests of this prediction. [ABSTRACT FROM AUTHOR]

This paper continues the investigation of a three-loop representation of the segmental muscle stretch reflex system introduced in a preceding communication. Frequency response characteristics were computed for open-loop conditions, control and disturbance signal inputs under a variety of conditions: (i) 'in parallel' and 'in series' peripheral arrangements of muscle compartments, (ii) various patterns of central connectivity, (iii) various recruitment levels of motor units, (iv) various overall reflex gains, (v) absence or presence of muscle spindle accleration sensitivity. These computations disclosed a number of mechanisms by which the nervous system might improve system stability and behaviour. These mechanisms are discussed with regard to physiological data. [ABSTRACT FROM AUTHOR]

In this paper we propose a model of visual perception in which a positive feedback mechanism can reproduce the pattern stimulus on a neurons screen. The pattern stimulus reproduction is based on informations coming from the spatial derivatives of visual pattern. This information together with the response of the feature extractors provides to the reproduction of the visual pattern as neuron screen electric activity. We simulate several input patterns and prove that the model reproduces the percept. [ABSTRACT FROM AUTHOR]

In order to investigate the spectro-temporal selectivity of single auditory neurons in the auditory midbrain of the grassfrog under different stimulus conditions a stimulus ensemble consisting of tonal and natural stimuli has been constructed. The selection of characteristics of the tonal stimuli was inspired by the general properties of vocalizations of the male grassfrog. The natural stimuli contained a variety of vocalizations of various anuran species and other sounds, taken from the natural environment of the grassfrog (i.e. its biotope). The main point of interest in the present paper is the spectro-temporal characterization of acoustic stimuli. For narrowband signals a parametric description in terms of instantaneous amplitude and instantaneous frequency appears to be attractive. A more general approach, also covering wideband signals, is a description by means of the dynamic power spectrum. Both types of analysis are described. Mathematically they can be based on the theory of analytic signals. The basic principles of this theory are summarized. [ABSTRACT FROM AUTHOR]

As in the preceding paper stick insects walk on a treadwheel and different legs are put on platforms fixed relative to the insect's body. The movement of the walking legs is recorded in addition to the force oscillations of the standing legs. The coordination between the different legs depends upon the number and arrangement of the walking legs and the legs standing on platforms. In most experimental situations one finds a coordination which is different from that of a normal walking animal. [ABSTRACT FROM AUTHOR]

An elementary model of neuronal activity involves temporal and spatial summation of postsynaptic currents that are elicited by presynaptic spikes and that, in turn, elicit postsynaptic potentials at a trigger zone; when the potential at the trigger zone exceeds a 'threshold' level, a postsynaptic spike is generated. This paper describes three methods of estimating the 'summation function', that is, the function of time that converts the synaptic current into potential at the trigger zone: namely, maximum likelihood, cross-correlation analysis and cross-spectral analysis. All three methods, when applied to input-output data collected on various neurons of Aplysia californica, give comparable results. As estimated, the summation function involved in the explored cells has an early positive-going swing that is large and brief. In the cell L5, but not in R2, there was also a late negative-going swing of longer duration. [ABSTRACT FROM AUTHOR]

The visual system of the fly performs various computations on photoreceptor outputs. The detection and measurement of movement is based on simple nonlinear multiplication-like interactions between adjacent pairs and groups of photoreceptors. The position of a small contrasted object against a uniform background is measured, at least in part, by (formally) 1-input nonlinear flicker detectors. A fly can also detect and discriminate a figure that moves relative to a ground texture. This computation of relative movement relies on a more complex algorithm, one which detects discontinuities in the movement field. The experiments described in this paper indicate that the outputs of neighbouring movement detectors interact in a multiplication-like fashion and then in turn inhibit locally the flicker detectors. The following main characteristic properties (partly a direct consequence of the algorithm's structure) have been established experimentally: a) Coherent motion of figure and ground inhibit the position detectors whereas incoherent motion fails to produce inhibition near the edges of the moving figure (provided the textures of figure and ground are similar). b) The movement detectors underlying this particular computation are direction-insensitive at input frequencies (at the photoreceptor level) above 2.3 Hz. They become increasingly direction-sensitive for lower input frequencies. c) At higher input frequencies the fly cannot discriminate an object against a texture oscillating at the same frequency and amplitude at 0° and 180° phase, whereas 90° or 270° phase shift between figure and ground oscillations yields maximum discrimination. d) Under conditions of coherent movement, strong spatial incoherence is detected by the same mechanism. The algorithm underlying the relative movement computation is further discussed as an example of a coherence measuring process, operating on the outputs of an array of movement detectors. Possible neural correlates are also mentioned. [ABSTRACT FROM AUTHOR]

In this paper the visual masking effect is interpreted on the basis of the transient characteristic in two dimensional neuronal networks. The study investigates the suitability of the effect for use as a measurement method. It is shown that the stimulus distribution in space can be scanned at different points in time and that various dynamic characteristic values of the system can be measured. [ABSTRACT FROM AUTHOR]

The Shannon's information theory in multiway channels (Shannon, 1961) is applied to multi-input-output relations of the stochastic automaton models for interaction of excitatory and inhibitory impulse sequences proposed in the previous papers (Tsukada et al., 1977). In these models, the output spike train depends upon several statistical characteristics (mean frequency, standard deviation, form, order-dependence or order-independence, etc.) of the excitatory and inhibitory input spike trains. By the use of the multiple-access channel in information theory, some stochastic properties of temporal pattern discrimination in neurons are analyzed and discussed with biological systems. [ABSTRACT FROM AUTHOR]

This paper extends recent analyses (Roberts and Hartline, 1975; Oğuztöreli and Stein, 1977) of optimal linear filters for separating neural signals from more than one electrode site. Roberts and Hartline's result, using a matched filter criterion, represents one of a class of optimal filters with different, but symmetrical, output waveforms derived by Oğuztöreli and Stein (1977). Another narrow bandwidth filter of this class will give the optimal results according to an energy criterion, but may be less useful in practical situations. [ABSTRACT FROM AUTHOR]

Mammalian primary muscle spindle endings receive two inputs from fusimotor fibers and length changes of their extrafusal environment. Both inputs are also powerful noise sources disturbing the discharge patterns of the receptors. In this paper emphasis is laid on the extrafusal component. It is shown that extrafusal muscle activity can be viewed as a stochastic process which, acting as a common source, can correlate discharge patterns of adjacent muscle spindles. Some quantitative characteristics of these correlations and their relation to the underlying mechanical events are investigated in some detail in order to provide data for more theoretical considerations on their possible physiological importance. [ABSTRACT FROM AUTHOR]

This paper presents theoretical considerations on the possibility of topographically ordered signal transmission in the control system of the muscle stretch reflex. It is investigated how correlations between Ia fibres from primary muscle spindle endings in conjunction with an appropriate connectivity of Ia fibres and motoneurones enable the stretch reflex system to trace local routes through the spinal cord. The complex data processing capabilities of the motoneuronal soma-dendritic membrane system are fully taken into account, and it is argued that correlations between inputs to this system may play an important role for signal transmission through the spinal cord. [ABSTRACT FROM AUTHOR]

Many methods for the analysis of nonlinear systems rely on a Volterra system-representation in terms of integral kernels. This paper considers two questions: 1) whether Volterra-like representations are possible for all smooth systems (i.e. analytic operators),-2) which classes of systems can be approximated by some interesting subclasses of the smooth systems, e.g. Volterra systems with separable kernels and 'sandwich systems' (cascades of linear systems and nomemory nonlinearities). Whereas the answer to question 1 is positive, the answer to question 2 depends on the type of approximation, i.e. topology, that is used. [ABSTRACT FROM AUTHOR]

Multi-unit neural recordings often occur in neurophysiological studies, and a wide variety of techniques have been proposed to separate the multi-unit activity. In this paper we propose a method for evaluating the power of various multi-unit sorting techniques. The analysis can also be applied to a data set to determine whether a given multi-unit isolation technique can isolate a given set of wavelets to a specified statistical standard. The apparent separation matrix described in the paper is then used to evaluate the ability of four multi-unit isolation techniques to resolve a population of 8 units simultaneously recorded in the medial articular nerve of the cat. [ABSTRACT FROM AUTHOR]

A self-learning neuronal network called MACSIM (Mathematical Analyzer and Composer of Simple Melodies) for music pattern recognition is proposed. As universal network elements the D-neurons defined in the previous paper (Fedor and Majernik, 1977) are used. MACSIM is intended to model, at the level of elementar neuronal circuits, the processing of simple melodies which takes place in the human brain auditory system. Melody composing and music itself are considered in this study in order to verify the principles of design and functioning of the proposed basic D-neuronal networks (organs) of MACSIM, only. Two kinds of neuronal organs are incorporated in MACSIM, namely the so-called analyzers and the so-called neuro-effectors. The first ones carry out predicting, learning and decoding of the input sequences of tones. An analyzer consists of several neuronal trees that have the ability to specialize and respecialize so that every melody repeated several times can be recognized after a corresponding learning period. Such a self-learning process runs without structural changes within the mentioned networks. A melody which has been memorized in an analyzer can be memorized later in a neuro-effector, namely in a form suitable for its recall at the output of MACSIM. The neuronal organization of the neuro-effectors is similar, to a certain extent, to that of the cerebellar cortex. With the help of the staggered arrangement of D-neurons set up on the lines of the organization of Purkinje cells in the cerebellar cortex, a new reliable memory storage mechanism is proposed. This paper is not self-contained; the reader is assumed to be familiar with the above-mentioned paper. [ABSTRACT FROM AUTHOR]

The present paper looks for possible neural mechanism underlying such high-level brain functioning as association and concept-formation. Primitive neural models of association and concept-formation are presented, which will elucidate the distributed and multiply superposed manner of retaining knowledge in the brain. The models are subject to two rules of self-organization of synaptic weights, orthogonal and covariance learning. The convergence of self-organization is proved, and the characteristics of these learning rules are shown. The performances, especially the noise immunity, of the association net and concept-formation net are analyzed. [ABSTRACT FROM AUTHOR]

A mathematical model of the neuron, socalled D-neuron, is proposed on the basis of some new conceptions concerning the molecular mechanism of the synaptical memory. According to these conceptions, the receptors of the neuron reception surface are divided into functional independent fields of receptors. The receptors of any field belong to corresponding membrane protein complex which contains moreover Na-channels, K-channels and eventually other protein subunits. Three processes are supposed to take place in any complex by its interaction with chemical transmitters: i cooperative transitions of the subunits, ii time-controlled transport of ions and iii changes of concentrations of the protein complex subunits. These processes correspond to the following information processings: i recording in the memory, ii discrimination and iii accomodation. In this paper they all are described by an idealized system of algebraic and differential equations. The proposed neuron model can account for the short- and long-term memory mechanism on the level of a single neuron as well as for the control of the neuron networks by the hormones. finally, the neuron model is presented as a universal unit of self-learning networks. [ABSTRACT FROM AUTHOR]

A generalization of an earlier paper (Capocelli and Ricciardi, 1971), dealing with a diffusion approximation for a neuron subject to one excitatory and one inhibitory Poisson input, is provided by not imposing any restrictions on number and magnitude if synaptic inputs. An equation for the neuron's transition p.d.f. is derived, use of which is made to determine the moments of the membrane potential. It is finally shown that a diffusion approximation is possible and that the resulting diffusion process is characterized by constant infinitesimal variance and linear drift. [ABSTRACT FROM AUTHOR]

In this article we treat purely metrical properties of the visual image, e.g. the time changes of the relative positions and orientations of image details. Self-induced movements of an observer relative to rigid bodies in his environment generate charactertistic motion parallax fields. The observer may regard those fields as proprioceptive and interprete the geometrical invariants of the fields as indicators of solid shape. In this way his perceptions become object-oriented, which is the normal case as the many constancy-phenomena show. Similar arguments apply to the disparity field of binocular vision. In this paper we treat the qualitative nature of such fields. [In this case the qualitative nature is basic. Compare the case of an equation with a single unknown. Often one is interested primarily in the qualitative solution (are there roots? How many?), and only slightly in the quantitative information (the numerical value of a root).] The qualitative nature of the fields is fixed if their singularities are known. It is shown that the singularities are of two types: isolated points (so-called specular points) and line-singularities (so-called folds, cusps and T-junctions). It is shown that for most vantage points that an observer can occupy, the topological structure of the set of singularities does not change if the observer performs small exploratory movements. That is most vantage points are stable. At an unstable vantage point the set of singularities changes and the observer experiences an event. Because certain properties of the set of singularities are shown to be preserved, only a few simple types of event are possible. A complete list is presented. The occurrence of an event is shown to be simply related to the solid shape of the objects of vision. Our geometrical theory enables us to understand the structure of the observer's internal models of external bodies. [ABSTRACT FROM AUTHOR]

The Wiener filtration of average evoked potentials supplies the estimate of evoked response with the least square error. However, this error is dependent on the choice of interstimulating intervals. This dependence was not considered in hitherto applications of the Wiener filter. In this paper the Wiener filter with respect to the concrete choice of interstimulating intervals is derived. [ABSTRACT FROM AUTHOR]

Part I of this paper describes a model for the parallel development and adult coding of neural feature detectors. It shows how any set of arbitrary spatial patterns can be recoded, or transformed, into any other spatial patterns (universal recoding), if there are sufficiently many cells in the network's cortex. This code is, however, unstable through time if arbitrarily many patterns can perturb a fixed number of cortical cells. This paper shows how to stabilize the code in the general case using feedback between cellular sites. A biochemically defined critical period is not necessary to stabilize the code, nor is it sufficient to ensure useful coding properties. We ask how short term memory can be reset in response to temporal sequences of spatial patterns. This leads to a context-dependent code in which no feature detector need uniquely characterize an input pattern; yet unique classification by the pattern of activity across feature detectors is possible. This property uses learned expectation mechanisms whereby unexpected patterns are temporarily suppressed and/or activate nonspecific arousal. The simplest case describes reciprocal interactions via trainable synaptic pathways (long term memory traces) between two recurrent on-center off-surround networks undergoing mass action (shunting) interactions. This unit can establish an adaptive resonance, or reverberation, between two regions if their coded patterns match, and can suppress the reverberation if their patterns do not match. This concept yields a model of olfactory coding within the olfactory bulb and prepyriform cortex. The resonance idea also includes the establishment of reverberation between conditioned reinforcers and generators of contingent negative variation if presently avialable sensory cues are compatible with the network's drive requirements at that time; and a search and lock mechanism whereby the disparity between two patterns can be minimized and the minimal disparity images locked into position. Stabilizing the code uses attentional mechanisms, in particular nonspecific arousal as a tuning and search device. We suggest that arousal is gated by a chemical transmitter system-for example, norepinephrine-whose relative states of accumulation at antagonistic pairs of on-cells and off-cells through time can shift the spatial pattern of STM activity across a field of feature detectors. For example, a sudden arousal increment in response to an un-expected pattern can reverse, or rebound, these relative activities, thereby suppressing incorrectly classified populations. The rebound mechanism has formal properties analogous to negative afterimages and spatial frequency adaptation. [ABSTRACT FROM AUTHOR]

This paper describes an approach to the analysis of the inputoutput relationships present in a neuron pool that receives a number of inputs. These inputs consist of primary inputs to the neuron pool and inputs resulting from feedback of information from the neuron pool as well. Multiple input-output relationships are obtained in terms of the synaptic weightings of the inputs, the membrane response characteristics of the neurons and the conduction delays on the feedback pathways. y=(I+MHD) ·MFx is the explicit representation of the cell pool behavior assuming quasi-linear conditions, where y is the output vector of cell responses, I is the identity matrix, M is the response matrix of the cells, H is the feedback synaptic weighting matrix, D is the delay matrix, F is the input weighting matrix, and x is the input vector. It is shown that a solution to this formulation exists, is unique, is stable, and can be computed by specified algorithms. An insight gained from this formulation suggests that the output of each cell in the pool is related to virtually all of the inputs to the pool and the outputs of all cells in the pool. [ABSTRACT FROM AUTHOR]

This paper presents psychological and physical experiments carried out by using a vibrometer as an acoustical calibration apparatus. This study has shown the relationship between the vibratory sensibility and the electric signal generated in a living body. The threshold curve for square wave vibration is lower by 12.3 dB than that for sine wave vibration near 30 Hz. The stimulus level is taken as the horizontal axis, and potential variation and strengh evaluation are plotted on the vertical axis, the former has a nearly rectiliner relation with the latter. [ABSTRACT FROM AUTHOR]

An analysis has been made of the spontaneous firing of neurons from the posterior motor cortex of the rabbit. Extracellular recordings were made by means of glass capillary micro-electrodes. The recorded neural activity was processed with a general purpose computer and an adapted data processing system. The impulse interval series were analysed by means of a statistical time series analysis. In the first part of the paper, the first order properties of the neutral activity are examined. Using a mathematical model for data reduction, an overall picture of the first order properties of the activity of the set of recorded neurons are obtained. In the second part of the paper, the second order properties of this activity are examined. Using another simple mathematical model completing the first one, the principal aspect of the second order properties are summarized. Nous avons analysé l'activité unitaire spontanée des cellules nerveuses du cortex moteur postérieur du lapin. Les enregistrements extra-cellulaires sont effectués à l'aide de micropipettes de verre. Les trains d'impulsions sont traités avec un ordinateur universel et un système de traitement de données adapté. Les séries d'intervalles sont analysées en utilisant l'analyse statistique des séries temporelles d'évènements. Dans une première partie nous étudions les propriétés du premier ordre de l'activité des neurones. En utilisant un modèle mathématique pour réduire les données, nous obtenons un aperçu général des propriétés de l'activité de l'ensemble des neurones enregistrés. Dans une seconde partie, nous avons étudié les propriétés du second ordre de cette activité. En utilisant un autre model mathématique simple qui complète le premier, nous avons résumé l'aspect principal des propriétés de second ordre. [ABSTRACT FROM AUTHOR]

This paper deals with information transfer from the environment and 'self'-organization in open, nonlinear systems far from thermodynamic equilibrium - in the presence of either non-stationary phase jitter noise, or amplitude stationary noise. By 'self'-organization we mean here the progressive formation within the system of sequential, ordered (coherent) relationships between appropriate dynamical variables-like for example, the phase differences between the oscillating components of the system. We take up (in Section II) the classical Laser as a specific example and examine in detail the influence of phase jitter noise in the mode (phase) locking process. We find-as expected-that phase fluctuations in the cavity cause degradation of the coherent behaviour (i.e. increase the entropy) of the system - which, however, levels off, or saturates with time. Further (in Section III) we examine systems where the number of self-sustained oscillating components may vary with time in such a way that the maximum entropy of the system increases faster than the overall instantaneous entropy. We put forth the hypothesis that in such cases - because of the increase of the redundancy - the system gets organized not just in spite of, but merely because of the presence of Noise. Possible applications in biological systems (especially concerning a model of cerebral organization) are briefly discussed. It is understood here, that the system has to display some preliminary dynamical structure before the organizing procedure takes over. What happens afterwards is the subject of this paper. [ABSTRACT FROM AUTHOR]

This paper discusses a neuronal model based on a model of Coleman and Gastwirth (1969). It is assumed that the excitatory input forms a Poisson process while the inhibitory input forms a stationary renewal process. The proposed interaction scheme is as follows: an inhibitor deletes at most N consecutive excitatory inputs and a response only occurs after the cummalative storage of M excitatory inputs. The Laplace transform of the probability density function (p.d.f.) of the inter-response intervals is derived together with results of the numerical inversions. [ABSTRACT FROM AUTHOR]

Abstract. This paper presents a handwriting generation model that takes advantage of the asymptotic impulse response of neuromuscular networks to produce and control complex two-dimensional synergistic movements. A parametric definition of a ballistic stroke in the context of the kinematic theory of rapid human movements is given. Two types of parameters are used: command and system parameters. The first group provides a representation of the action plan while the second takes into account the temporal properties of the neuromuscular systems executing that plan. Handwriting is described as the time superimposition of basic discontinuous strokes that results in a continuous summation of delta-lognormal velocity vectors. The model leads to trajectory reconstruction, both in the spatial and in the kinematic domain. According to this new paradigm, the angular velocity does not have to be controlled independently and continuously; it naturally emerges from the vectorial summation process. Several psychophysical phenomena related to two-dimensional movements are explained and analyzed in the context of the model: the speed/accuracy tradeoffs, spatial scaling, the isochrony principle, the two-thirds power law, effector independence, etc. The overall approach also shows how basic handwriting characteristics (dimension, slant, baseline, shape, etc.) are affected and controlled using an action plan made up of virtual targets fed into a neuromuscular synergy that is governed by a delta-lognormal law. [ABSTRACT FROM AUTHOR]

Abstract. A model for the development of spatiotemporal receptive fields of simple cells in the visual cortex is proposed. The model is based on the 1990 hypothesis of Saul and Humphrey that the convergence of four types of input onto a cortical cell, viz. non-lagged ON and OFF inputs and lagged ON and OFF inputs, underlies the spatial and temporal structure of the receptive fields. It therefore explains both orientation and direction selectivity of simple cells. The response properties of the four types of input are described by the product of linear spatial and temporal response functions. Extending the 1994 model of one of the authors (K.D. Miller), we describe the development of spatiotemporal receptive fields as a Hebbian learning process taking into account not only spatial but also temporal correlations between the different inputs. We derive the correlation functions that drive the development both for the period before and after eye-opening and demonstrate how the joint development of orientation and direction selectivity can be understood in the framework of correlation-based learning. Our investigation is split into two parts that are presented in two papers, in the first, the model for the response properties and for the development of direction-selective receptive fields is presented, in the second paper we present simulation results that are compared with experimental data, and also provide a first analysis of our model. [ABSTRACT FROM AUTHOR]

Abstract. Presented in this paper is a neural network model that can be used to investigate the possible sell-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 vive. [ABSTRACT FROM AUTHOR]

Abstract. In recent papers we demonstrated by means of a modeling study that the smoothness of hand paths and the bell-shaped character of hand velocity profiles which have been experimentally observed in point-to-point arm movements can be largely attributed to the biomechanical properties of the arm rather than to specific planning by the central nervous system. In this paper we present a study of the robustness of our earlier results comprising two goals: (i) the determination of the range of model parameters for which such observations remain valid, (ii) the identification of possible relationships between model parameters and kinematic variables. The results of this study imply three conclusions: (i) the valid range of the tested model parameters (namely the main muscle parameters) is large, (ii) the modeled phenomena are well behaved in that parametric changes do not give rise to bifurcations or other behavioral discontinuities in the analyzed ranges, (iii) there exist precise relationships between certain muscle parameters and the time course of the hand velocity. These results point out that the phenomena observed in our previous work are indeed robust and can lead to useful insights into the mechanisms comprising the regulatory action of the central nervous system as well as into the design principles for biologically inspired artificial arms. [ABSTRACT FROM AUTHOR]

Abstract. Many tasks require the arm to move from its initial position to a specified target position, but leave us free to choose the trajectory between them. This paper presents and tests the hypothesis that trajectories are chosen to minimize metabolic energy costs. Costs are calculated for the range of possible trajectories, for movements between the end points used in previously published experiments. Calculated energy minimizing trajectories for a model with biarticular elbow muscles agree well with observed trajectories for fast movements. Good agreement is also obtained for slow movements if they are assumed to be performed by slower muscles. A model in which all muscles are uniarticular is less successful in predicting observed trajectories. The effects of loads and of reversing the direction of movement are investigated. [ABSTRACT FROM AUTHOR]

It is shown in this paper that electrical bursting and the oscillations in the intracellular calcium concentration, [Ca[sup 2+] ][sub i] , observed in excitable cells such as pancreatic β-cells and R-15 cells of the mollusk Aplysia may be driven by a slow oscillation of the calcium concentration in the lumen of the endoplasmic reticulum, [Ca[sup 2+] ][sub lum] . This hypothesis follows from the inclusion of the dynamic changes of [Ca[sup 2+] ][sub lum] in the Chay bursting model. This extended model provides answers to some puzzling phenomena, such as why isolated single pancreatic β-cells burst with a low frequency while intact β-cells in an islet burst with a much higher frequency. Verification of the model prediction that [Ca[sup 2+] ][sub lum] is a primary oscillator which drives electrical bursting and [Ca[sup 2+] ][sub i] oscillations in these cells awaits experimental testing. Experiments using fluorescent dyes such as mag-fura-2-AM or aequorin could provide relevant information. [ABSTRACT FROM AUTHOR]

Diffusion processes have been extensively used to describe membrane potential behavior. In this approach the interspike interval has a theoretical counterpart in the first-passage-time of the diffusion model employed. Since the mathematical complexity of the first-passage-time problem increases with attempts to make the models more realistic it seems useful to compare the features of different models in order to highlight their relative performance. In this paper we compare the Feller and Ornstein-Uhlenbeck models under three different criteria derived from the level of information available about their parameters. We conclude that the Feller model is preferable when complete knowledge of the characterizing parameters is assumed. On the other hand, when only limited information about the parameters is available, such as the mean firing time and the histogram shape, no advantage arises from using this more complex model. [ABSTRACT FROM AUTHOR]

We have previously proposed an optimal trajectory and control theory for continuous movements, such as reaching or cursive handwriting. According to Marr's three-level description of brain function, our theory can be summarized as follows: (1) The computational theory is the minimum torque-change model; (2) the intermediate representation of a pattern is given as a set of via-points extracted from an example pattern; and (3) algorithm and hardware are provided by FIRM, a neural network that can generate and control minimum torque-change trajectories. In this paper, we propose a computational theory for movement pattern recognition that is based on our theory for optimal movement pattern generation. The three levels of the description of brain function in the recognition theory are tightly coupled with those for pattern generation. In recognition, the generation process and the recognition process are actually two flows of information in opposite directions within a single functional unit. In our theory, if the input movement trajectory data are identical to the optimal movement pattern reconstructed from an intermediate representation of some symbol, the input data are recognized as that symbol. If an error exists between the movement trajectory data and the generated trajectory, the putative symbol is corrected, and the generation is repeated. In particular, we present concrete computational procedures for the recognition of connected cursive handwritten characters, as well as for the estimation of phonemic timing in natural speech. Our most important contribution is to demonstrate the computational realizability for the 'motor theory of movement pattern perception': the movement-pattern recognition process can be realized by actively recruiting the movementpattern formation process. The way in which the formation process is utilized in pattern recognition in our theory suggests a duality between movement pattern formation and movement pattern perception. [ABSTRACT FROM AUTHOR]

The focus of this paper is the study of stability and point-to-point movement of a one-link arm. The sagittal arm has two musculotendon actuators, two neural oscillators that generate burst signals as motoneuron inputs, and spindles and Golgi tendon organs for extrinsic reflex feedbacks. It is shown that coactivation leads to intrinsic position and velocity feedback, and that the tendons introduce intrinsic force and rate of force feedback. In addition, the integrating effects of the tendons are studied when the actuator is constructed from a large number of identical fibers that are excited by alpha signals whose arrival times at the fiber are randomly distributed. Each of the musculotendon actuators receives two input signals - a burst signal analogous to alpha inputs and a conventional analogue signal that represents fusimotor input to the spindles. The process of combining burst signals and conventional analogue signals is studied. Simulation results show that the movement of the system with burst signals as inputs has overshoot and speed similar to the system with analogue signals. [ABSTRACT FROM AUTHOR]

The application of a discrete Hopfield-type neural network to solving the NP-Hard optimization problem - the N-Queens Problem (NQP) - is presented. The applied network is binary, and at every moment each neuron potential is equal to either 0 or 1. The network can be implemented in the asynchronous mode as well as in the synchronous one with n parallel running processors. In both cases the convergence rate is up to 100%, and the experimental estimate of the average computational complexity is polynomial. Based on the computer simulation results and the theoretical analysis, the proper network parameters are established. The behaviour of the network is explained. [ABSTRACT FROM AUTHOR]

A correction to this paper has been published: https://doi.org/10.1007/s00422-021-00869-7 [ABSTRACT FROM AUTHOR]

In internally coupled ears (ICE), the displacement of one eardrum creates pressure waves that propagate through air-filled passages in the skull, causing a displacement of the opposing eardrum and vice versa. In this review, a thorough mathematical analysis of the membranes, passages, and propagating pressure waves reveals how internally coupled ears generate unique amplitude and temporal cues for sound localization. The magnitudes of both of these cues are directionally dependent. On the basis of the geometry of the interaural cavity and the elastic properties of the two eardrums confining it at both ends, the present paper reviews the mathematical theory underlying hearing through ICE and derives analytical expressions for eardrum vibrations as well as the pressures inside the internal passages, which ultimately lead to the emergence of highly directional hearing cues. The derived expressions enable one to explicitly see the influence of different parts of the system, e.g., the interaural cavity and the eardrum, on the internal coupling, and the frequency dependence of the coupling. The tympanic fundamental frequency segregates a low-frequency regime with constant time-difference magnification (time dilation factor) from a high-frequency domain with considerable amplitude magnification. By exploiting the physical properties of the coupling, we describe a concrete method to numerically estimate the eardrum's fundamental frequency and damping solely through measurements taken from a live animal. [ABSTRACT FROM AUTHOR]

The peripheral auditory system of lizards has been extensively studied, because of its remarkable directionality. In this paper, we review the research that has been performed on this system using a biorobotic approach. The various robotic implementations developed to date, both wheeled and legged, of the auditory model exhibit strong phonotactic performance for two types of steering mechanisms-a simple threshold decision model and Braitenberg sensorimotor cross-couplings. The Braitenberg approach removed the need for a decision model, but produced relatively inefficient robot trajectories. Introducing various asymmetries in the auditory model reduced the efficiency of the robot trajectories, but successful phonotaxis was maintained. Relatively loud noise distractors degraded the trajectory efficiency and above-threshold noise resulted in unsuccessful phonotaxis. Machine learning techniques were applied to successfully compensate for asymmetries as well as noise distractors. Such techniques were also successfully used to construct a representation of auditory space, which is crucial for sound localisation while remaining stationary as opposed to phonotaxis-based localisation. The peripheral auditory model was furthermore found to adhere to an auditory scaling law governing the variation in frequency response with respect to physical ear separation. Overall, the research to date paves the way towards investigating the more fundamental topic of auditory metres versus auditory maps, and the existing robotic implementations can act as tools to compare the two approaches. [ABSTRACT FROM AUTHOR]