ALBERT

Notes: Abstract Responses from neurons of the vestibular nuclei were recorded in N2O-anaesthetized cats. Most neurons in the rostral parts of the nuclei responded to bimodal visual-vestibular stimulation, following a trapezoidal velocity profile. Both combinations of the two stimuli were tested: rotation of the animal with stationary visual field and rotation with overtaking visual field, i.e. the visual pattern running in the same direction as the turntable with twice the velocity. Some correlation of physiological data with results in corresponding psychophysical experiments were found. As a possible biological function of visual-vestibular convergence a phylogenetic solution for discrimination of body and outer world movement is discussed.

Notes: Abstract The courtship tracking behaviour of male D. melanogaster was filmed in a range of visual mutants and in wild type flies under white and infra-red light. The absence of visual input severely restricts the velocity at which the female may be tracked but does not remove the male's ability to discriminate the female's abdomen from her head. Degradation of visual processing, such as occurs in certain visual mutants, leads mainly to disruption of the control of orientation in tracking. The gain control of translation may only be meaningfully assessed when vision is enabled. Courtship tracking does not depend upon the presence of a binocular field of vision; one eyed flies court with a lateral displacement of the body, and loose visual contact with the female readily when her image moves from the sighted towards the blind eye. The selection of the left or right wing for extension follows a distinct pattern with the male's position and orientation around the female; this may be controlled collateral to locomotor output and after interlateral comparison of sensory input.

Notes: Abstract We have studied the IMG functions associated with visual detection of targets moving across a background structure (Barbur and Ruddock, 1980a) in four subjects, each possessing a different visual abnormality. Results for subject J.F., a tritanope, show that the low-frequency IMG response associated with the blue-sensitive (π1) mechanism (Barbur and Ruddock, 1980b) is absent in his case, thus providing confirmation that it is π1 which gives rise to the low-frequency response. We establish that, for an albino subject, D.C., the low visual acuity for resolution of gratings arises post-receptorally and show that the IMG function is restricted to the same low spatial frequency range as the visual acuity data. Visual responses to moving targets can be elicited from the blind hemi-field of a hemianopic subject, G. Y., but there is no IMG function associated with these responses, which also exhibit very low spatial resolution. Finally, IMG functions, measured with longwavelength background gratings, are grossly abnormal for a subject, M. W., who possesses a central colour vision defect in detection of long-wavelength targets. On the basis of these experimental data, we argue that the IMG functions involve central response mechanisms, and we conclude that these functions provide a new method for the investigation of defective visual systems.

Notes: Abstract A quantitative hypothesis is presented modelling the neuromuscular subsystem which controls the walking movements of a single leg of an insect. The model shown how central and peripheral influences can act together to produce walking movements. The subsystem of one leg consists of a central part producing reference input for a negative feedback loop which controls the position of the leg. The means by which the peripheral signals influence the central part of the model is constructed so that intact sense organs play the decisive role in controlling the walking rhythm of the leg. However, the rhythm can be produced by the control part alone, acting as a safety device if sense organs are destroyed. Using this model a series of experimental results obtained by several authors can be described.

Notes: Abstract Steplike displacements of a striped pattern elicit biphasic optokinetic responses in the crab Carcinus maenas. Both the first fast phase and the second slow phase response are caused by interactions between adjacent ommatidia. The analysis of the influence of the pattern contrast revealed that both phases can only be identified by means of their time courses. On the basis of the correlation model for movement perception experiments are deviced to elicit both phases separately. For this purpose the presentation time of the pattern prior to and the duration of the interruption of the presentation during steplike displacement had to be varied, respectively, without changing the background illumination. The experimental results verified the assumption that two independent processes underlie the two phases of the response. The contribution of both subsystems to the response can be calculated according to the correlation model. Computer simulations of the step responses under closed loop conditions describe the experimental data well. The relation between step responses and responses to uniform motion of a striped pattern are discussed.

Notes: Abstract This paper introduces a theoretical framework for characterizing and classifying simple parallel algorithms and systems with many inputs, for example an array of photoreceptors. The polynomial representation (Taylor series development) of a large class of operators is introduced and its range of validity discussed. The problems involved in the polynomial approximation of systems are also briefly reviewed. Symmetry properties of the input-output map and their implications for the system structure (i.e. its kernels) are studied. Finally, the computational properties of polynomial mappings are characterized.

Notes: Abstract Recently, it was found that rhythmic movements (e.g. locomotion, swimmeret beating) are controlled by mutually coupled endogeneous neural oscillators (Kennedy and Davis, 1977; Pearson and Iles, 1973; Stein, 1974; Shik and Orlovsky, 1976; Grillner and Zangger, 1979). Meanwhile, it has been found out that the phase resetting experiment is useful to investigate the interaction of neural oscillators (Perkel et al., 1963; Stein, 1974). In the preceding paper (Yamanishi et al., 1979), we studied the functional interaction between the neural oscillator which is assumed to control finger tapping and the neural networks which control some tasks. The tasks were imposed on the subject as the perturbation of the phase resetting experiment. In this paper, we investigate the control mechanism of the coordinated finger tapping by both hands. First, the subjects were instructed to coordinate the finger tapping by both hands so as to keep the phase difference between two hands constant. The performance was evaluated by a systematic error and a standard deviation of phase differences. Second, we propose two coupled neural oscillators as a model for the coordinated finger tapping. Dynamical behavior of the model system is analyzed by using phase transition curves which were measured on one hand finger tapping in the previous experiment (Yamanishi et al., 1979). Prediction by the model is in good agreement with the results of the experiments. Therefore, it is suggested that the neural mechanism which controls the coordinated finger tapping may be composed of a coupled system of two neural oscillators each of which controls the right and the left finger tapping respectively.

Notes: Abstract This paper proposes a new correlation matrix network model of associative memory in brain. Each memorized pattern which consists of binary (+1 or-1) elements is preprocessed by a quantized Hadamard transform to increase selectivity. The association ability of a correlation matrix network model depends on the orthogonality between key patterns by which the corresponding memorized patterns are associatively recalled. In a brain model, however, it is rare that the key patterns are mutually orthogonal since they are memorized patterns themselves. The quantized Hadamard transform, presented in this paper, renders the memorized patterns approximately orthogonal. The model is tested by computer simulation.

Notes: Abstract Anatomical and physiological data from lower primates, and psychophysical data from humans, is used to construct a quantitative model of the local and global map structure (functional architecture) of human striate cortex. A series of successful estimates deriving from this model are reviewed, including a prediction for the width of human ocular dominance columns, which has recently been verified. A variety of perceptual phenomena are then discussed, from the point of view of cortical, rather than retinal, topography. It is suggested that the striate cortex may be viewed as a “cyclopean retina” whose non-linear map structure, summarized in terms of a concatenated complex logarithmic pattern, suggests insights into the nature of the Mackay complimentary image, the Frazer spiral, fortification illusions, and the relationship of the second order statistics of a visual stimulus to pre-attentive (textural) segmentation. Finally, the nature of neuronal representation is considered in the context of recent models of perceptual and cognitive function. It is suggested that anatomical re-mapping at successive stages of the CNS may provide a conceptual alternative to conventional single cell and connectionist models, and offers a viable approach towards a “field” theory of vision.

Notes: Abstract The statistical properties of background spike train activity recorded from a molluscan neurone are used to identify lengths of discharge which are produced by endogeneous pacemaker mechanisms. Such pacemaker discharge has an infinitely divisible interspike interval probability density function.

Notes: Abstract This paper presents a new analysis of the contrast flash data of Alpern et al. (1970a-d). It was prompted by the criticism of Wandell (1976) who pointed out that Alpern et al., main conclusion, i.e. that the inhibitory signal N *(ϕ) elicited by the contrast flash (ϕ) takes the form $$N^ * (\phi ) = \frac{\phi }{{\phi + \sigma }}$$ , would imply an unrealistic excitatory photo response. The present analysis shows the data to be consistent with an inhibitory signal of the form $$N^ * (\phi ) = \left( {\frac{\phi }{{\phi + \sigma }}} \right)^n $$ .

Notes: Abstract The multi-channel system of the segmental muscle stretch reflex arc is modelled as an arrangement of two or three parallel “component” loops coupled to each other at spinal and at muscle level. Such a model is thought to be more realistic than the usually adopted representation of the stretch reflex as a single negative feedback loop. Anatomical and physiological data were taken from the literature for an extensive simulation of the compound system with special reference to the problem of its stability. Particular emphasis was put on the question of which kind of central (spinal) connectivity is appropriate to best reduce the risk for instability which arises easily in certain system configurations. This paper describes the system and presents simple introductory computations apt to demonstrate the problems the physiological system has to cope with.

Notes: Abstract Visual processing in avian retina is interpreted by means of a layered model in which: a) outer layers provide with spatio temporal fast and retarded versions of the stimuli incident on the retina; a possibility is that horizontal cells are involved in isotropically generating the retarded version which is transversally translated; b) prominent specialization of ganglion cells is the result of local non-linear lateral interaction at the inner plexiform layer, mediated by amacrines which return, also isotropically, the translated retarded signals. Small though systematic deviations in the sites of the lateral interaction result in anisotropic but uniform receptive fields for some ganglion cells. A simple though general expressin for the model is derived which includes the various types of recorded avian ganglion retinal cells responses, which also permits a unified interpretation of visual processing in avian and cat's retinae.

Notes: Abstract The extensor tibiae muscle of Carausius is innervated by a fast (FETi), a slow (SETi) and a common inhibitor neuron (CI). Situation and shape of FETi and SETi in the ganglion correspond to Schistocerca mesothorax. In Extatosoma, a phasmid with visible cells in the ganglion, FETi does not project onto SETi. In Carausius the axons of all three neurons leave the ganglion within the same nerve (nl 3 ). FETi supplies the whole muscle except some fibres at the most distal end. SETi and CI project onto the most proximal end and the distal third.-The muscle can be divided into two parts: the proximal half being nearly exclusively FETi-innervated and the distal third being mostly triple innervated. From such preparations the time-course of the forces produced after stimulating the femoral chordotonal organ could be estimated for FETi and SETi separately. These time-courses do not correspond to those of the fast and slow channel of the previous simulation of the control-loop.-The nerve supplying the muscle is a mixed nerve, the largest sensory axons being as thick as the smaller motor axons. The conduction velocity of both types of neurons lies within the same range. The conduction time only creates a delay time of 2–5 ms in the femur-tibia-control system.

Notes: Abstract An important factor in trying to capture the complexity of many manipulation problems is the notion of Output Motor Impedance, i.e., the relationship between a set of disturbing forces and the resulting variation in arm configuration. The functional significance of such force/displacement characteristics is investigated, showing how several aspects of different manipulation tasks (holding against gravity, inserting, fast moving, and throwing) can be naturally described in terms of appropriate modulation of the impedance characteristics of the manipulator. For this reason, impedance modulation can be considered an integral part of motor control.

Notes: Abstract Electric current was injected into a rabbit's eye with white-noise modulations of the current amplitude. A variable D.C. bias was added to the whitenoise stimulus to study the effects of stimulus bias. For each bias level, the ERG response to the electrical stimulus was cross-correlated with the random stimulus to estimate first-and second-order Wiener kernels. The kernels indicated both linear and nonlinear characteristics of the Electrical ERG. The results for the zero biased stimulus are particularly relevant for clinical testing because the root mean square (RMS) level of the stimulus was less than 0.2 mA.

Notes: Abstract Identification of figural elements is based upon comparison of one of several formal pattern descriptions with subjective similarity judgements. The best description appears to contain figural elements which are heavily dependent on the visual domain chosen for the experiment. Generally those figural elements seem to be involved which distinguish optimally between the reference patterns used to mark off the visual domain. An algorithm is proposed for searching figural elements which are building stones of optimal descriptions. The present study indicates that grammars generating structures based upon features, higher order figures and rules of composition may be tools for visual research.

Notes: Abstract Previous results on the perception of motion indicate that perceived motion paths cannot be explained solely in terms of simple feature-specific analyzers. This is particularly true of apparent (phi) motion. In this paper we develop a dynamic network, with simple filtering and summation properties, which can predict the geometric paths of apparent motion in various spatio-temporal configurations. The network assumptions predict a non-Euclidean metric for the visual space-time of motion perception and we consider the implications of such distortions for various visual displays, including illusions.

Notes: Abstract The stimulus-event relation of single units in the auditory midbrain area, the torus semicircularis, of the anaesthetized grassfrog (Rana temporaria L.) during stimulation with a wide ensemble of natural stimuli, was analysed using first and second order statistical analysis techniques. The average stimulus preceding the occurrence of action potentials, in general, did not prove to give very informative results. The second order procedure consisted in the determination of the average dynamic power spectrum of the pre-event stimuli, following procedures as described elsewhere (Aertsen and Johannesma, 1980; Aertsen et al., 1980). The outcome of this analysis was filtered with the overall power spectrum of the complete stimulus ensemble in order to correct for its non-uniform spectral composition. The “stimulus-filtered” average pre-event dynamic spectrum gives a first indication of the “spectro-temporal receptive field” of a neuron under natural stimulus conditions. Results for a limited number of recordings are presented and, globally, compared to the outcome of an analogous analysis of experiments with tonal stimuli.

Notes: Abstract Saturation and hue perceived in monochromatic stimuli and in light mixtures were scaled psychophysically by a direct magnitude estimation method. The colors were of aperture mode and were presented against a dark background. As a result opponent-colors functions were obtained which show the hue sensations produced by the lights of the visible spectrum (under the observing conditions used). Compared to the opponent-colors functions of Hurwich and Jameson, obtained by a cancellation technique, the subjective hue sensation differed significantly. It may be concluded that these cancellation functions describe an earlier, probably a retinal level of data processing, while our results may be regarded as a description of the output of the color vision system.

Notes: Abstract A system of electronic analog neurons (neuromines) for modeling the activity in small neuronal networks is described. The system consists of sixteen analogs that simulate the integrative neuronal properties at the axon hillock and sixty-four analogs that serve to simulate synaptic interactions. The neuromime properties are based on a potential model incorporating the following properties: membrane potential, threshold, refractory period, adaption, post-inhibitory rebound, accommodation and pacemaker potential. Use of matrix switch boards provides for convenient interconnection of the neuromime elements, allowing the construction of even complex circuits.

Notes: Abstract This is a model of the steady-state influence of one pacemaker neuron upon another across a synapse with EPSP's. Its postulates require firstly the spontaneous regularity of both cells, whose intervals are E and N, respectively. In addition, they require a special shortening or negative “delay” of the interspike interval by one or more EPSP's, with a V-shaped dependence of the delay on the position or “phase” of the EPSP's in the interval; the minimum of the delay function corresponds to the earliest EPSP arrival phase (λ) that triggers a spike immediately. Finally, they impose on the variables certain bounds. The model's behavior has two main features. The first is a zig-zag relationship with an overall increasing trend between the steady-state pre- and post-synaptic discharge intensities (Fig. 7). The zig-zag is formed predominantly, if not exclusively, by segments with positive slopes that are rational fractions. Passage from one such segment to others is negatively-sloped (“paradoxical”), involving staggered positively-sloped segments whose details are unclear for weak presynaptic discharges and discontinuities for intense discharges. The same postsynaptic intensity may result from several presynaptic ones; the maximum postsynaptic intensity may reflect refractoriness, or the earliest instants of immediate triggering. The second main feature is the “locking” of the discharges in an invariant forward and backward temporal relation. With at most one EPSP per postsynaptic spike, locking is always present. If the presynaptic interval E is in the closed {rN+λ,(r+1)N} range, locking is 1:r+1, either stable at a greater-than-λ phase or unstable at a smaller one; arrivals at integral multiples of N do not affect the postsynaptic intensity. If E is in {rN, rN+λ} (r〉0), locking is at other ratios (e.g., 2:3) and less apparent. With more than one EPSP per spike, when E is below bounds that depend on the interspike interval and the point of earliest triggering, locking happens in the simple s′:1 ratio (s′=2,3, ...) and is stable; when E is above those bounds, there are E ranges where locking is in other ratios (e.g., 3:2) and ranges where behavior is unclear. The validity of any model is based jointly upon an a priori judgment as to whether postulates depart reasonably little from nature, and upon an a posteriori experimental comparison of modelled and real behaviors. The model's domain of applicability depends on the specific embodiment, each of the latter tolerating characteristically each departure. The present model will be evaluated in the crayfish stretch-receptor neuron (Diez-Martínez et al., in preparation). The model is applicable to any physical system that complies with its postulates, and evidence compatible with this notion is available in many disparate fields. It illustrates the modelling path to a scientific proposition, other paths being inference from experimentation, or deduction from premises acceptable at other approach levels (in this case, for example, from that of synaptic mechanisms). The periodicity postulates set this model within the category of those for oscillators. The notion of an oscillator has a far broader applicability than appears at first sight, since all physically realizable systems have some predominant output frequency, i.e., to a certain extent are oscillators.

Notes: Abstract The Culex circadian pacemaker's response to phase-resetting light signals was studied in the first 3 cycles of darkness following a 12h light exposure. (1) In both cycles 1 and 2 there is a clear change from “type 1” to “type 0” phase-resetting as the resetting signal is prologed (Fig. 2). (2) Mosquitoes in cycle 1 are about half as sensitive to phase-resetting as those in cycles 2 or 3 (the criterion being the minimum pulse duration required to produce type 0 phase-resetting) (Fig. 2). (3) Each cycle appears to have a corkscrew-shaped phaseresetting surface and a phase singularity (Figs. 4, 5, and 7). The hypothesis that the Culex pacemaker reaches a stable limit cycle within the first cycle leads to an economical explanation of the results.

Notes: Abstract An associative memory system is presented which does not require a “teacher” to provide the desired associations. For each input key it conducts a search for the output pattern which optimizes an external payoff or reinforcement signal. The associative search network (ASN) combines pattern recognition and function optimization capabilities in a simple and effective way. We define the associative search problem, discuss conditions under which the associative search network is capable of solving it, and present results from computer simulations. The synthesis of sensory-motor control surfaces is discussed as an example of the associative search problem.

Notes: Abstract The static discharge rate of Renshaw cells (studied in deafferented, intercollicularly decerebrate cats) has a nonlinear dependence on the frequency of trains of stimulus impulses to α-motor axons in the ventral root. This dependence is well described by a rectangular hyperbola that approaches saturation with increasing stimulus frequency. The tendency to saturate is independent of the number of motor axons exciting a Renshaw cell. On average, the stimulus frequency at which the discharge rate reaches half its saturation value lies between 10 and 15 Hz. The effect of Renshaw cell activity — measured as the antidromic inhibition of individual α-motoneurons — reflects the form of the static frequency characteristics. An electric circuit analog of the Renshaw cell membrane is presented which serves to explain the qualitative features of the static input-output relations; the nonlinearity is the result of synapses with linear properties acting together at the cell membrane.

Notes: Abstract A sixth order nonlinear model for horizontal head rotations in humans is analyzed using an extended parameter sensitivity analysis and a global optimization algorithm. The sensitivity analysis is used in both the direct sense, as a model fitting tool, and in the indirect sense, as a guide to experimental design. Resolution is defined in terms of the sensitivity table, and is used to interpret the sensitivity results. Using sensitivity analyses, the head and eye movement systems are compared and contrasted. Controller signal parameters are the most influential. Their variations and effects on head movement trajectories and accelerations are investigated, and the conclusions are compared with clinical neurological findings. The global optimization algorithm, in addition to automating the fitting of various types of data, is combined with time optimality theory to give theoretical time-optimal inputs to the model.

Notes: Abstract The influence of exchanges of lipids and antioxidants (AO) between the cells on the cell proliferation is studied in the frame of the membrane model of the cell cycle. It is shown theoretically that the easy-oxidative lipids exchange favours the synchronization of cell division, while the AO exchange leads to desynchronization. The analytical consideration and some numerical estimations are carried out. The qualitative consequences accessible to experimental verification are discussed.

Notes: Abstract In this account fixation and the torque response to a transient moving stripe of flying femaleMusca domestica with monocular sight was tested. This was made by either covering one eye of the fly with opaque paint or by placing a screen in front of one side of the fly's visual field. A stripe was moved with constant speed once around the fly clockwise and, after a pause, counterclockwise. The torque response of the fly was measured during the motion of the stripe and shortly beforehand. The results demonstrated that the monocular torque response to progressive (from front to back) motion and regressive (from back to front) motion essentially do not differ from the binocular response, except for the region of bionocular overlap. The beginning of the response of a fly with monocular vision to progressive motion is 11 ° (on average) before the direction of flight (0°), which means that the maximal functional binocular overlap of femaleMusca domestica is stretched at least 15° to each side (3.1). In addition, the shape of the monocular torque response to a progressively moving stripe was determined (see Figs. 5Ia and 5IIb). In other experiments similar to the ones described above, a screen was placed on one side of the fly's visual field or then on the other, (instead of covering one eye) and the torque response to the moving stripe was measured. Using this method, a delay response of 90 ms was measured. We suggest that this is the delay of the direction-sensitive component of the torque response, and therefore an additional argument for the existence of two components for the optomotor torque response. Flies with a covered eye or with a screen placed in front of one side of the visual field were able to fixate a single narrow long black stripe. This, however, was possible only when an additional offset signal was added, in order to give the stripe a constant velocity component. As a result there was a shift of the fixation towards the unobscured eye. The shift was small for the monocular flies, and it was larger (13° on average) when the screen was on one side of the fly. A new type of laser torquethrust transducer was developed and is described.

Notes: Abstract The many indistinguishable texture pairs having identical second-, but different third- and higher-order statistics, led to the conjecture thatglobally the preattentive texture discrimination system cannot process statistical parameters of third- or higher-order. Thus in cases when iso-second-order textures yield discrimination this must be based onlocal conspicuous features calledtextons (Julesz, 1980). Here it is shown that globally even second-order statistical parameters, such as autocorrelation, cannot be processed by the textural system, and texture discrimination is solely the result of first-order statistics (density) of textons. It is also shown that the perceivable distance of statistical constraints (coherence distance) in densely packed stochastic textures is very short, four dots or less. As of now, only three texton classes were found: color, elongated blobs (line segments) of given width, orientation, and length, and the terminators (end-points) of these elongated blobs. The strength of these textons is demonstrated by several examples.

Notes: Abstract This communication compares the well known phenomenon of respiratory driving by the respiratory pump through the Breuer Hering reflex with a model (Segundo, 1979) of a neuronal pacemaker (i.e. regularly firing) interactions via IPSP's. The assumption involves a linear dependence (“delay function”) of the postsynaptic interval lengthening (or “delay”) produced by the IPSP's on the position (or “phase”) with respect to the preceding spike of the latter's arrival. Cats anesthetized and paralized with gallamine were artificially ventilated using a computer driven respirator. The pump period and the respiratory period (identified by the phrenic discharge) corresponded to the model's presynaptic pacemaker interval and to that of the post synaptic one, respectively. The delay of the respiratory period by an inflation was related linearly and in increasing manner to the latter's phase with respect to the inspiration onset. In the steady state, plots of average respiratory period versus pump period consisted in a succession of broad “paradoxical” segments with positive slopes 3, 2, 1, 1/2, 1/3 in which respiration was locked with the pump as predicted by the model. The locked condition were less easy to reach when FA CO 2increased or when level of anaesthesia decreased. The limits of paradoxical segments were different when measured using pump periods that increased or using periods that decreased. There was therefore a hysteresis as if the delay function parameters changed, a behavior that was not part of the model that assumed fixed characteristics. These modifications were related to dependency of each cycle on the preceding one. The model proposed for simple neuronal pacemaker interactions can thus be applied satisfactorily to the drive of the complex respiratory neuronal oscillator by the respiratory pump through Breuer Hering reflex, providing nevertheless some additonal assumptions concerning respiratory cycle interdependency are introduced to account for the hysteresis phenomenon. The Breuer Hering reflex could be considered as the equivalent of IPSP acting on the central respiratory oscillator. FA CO 2increase and anesthesia level decrease produced the same effect as the addition of noise to the model's presynaptic pacemaker, thus leading to the hypothesis that they act by adding noise (e.g., randomly distributed excitatory input) at the level of Breuer Hering reflex inhibition.

Notes: Abstract From recent theoretical work (Poggio and Reichardt, 1981), high frequency oscillations are expected in the angular trajectory of houseflies tracking a moving target if the target's retinal position controls the flight torque by means of a stronger optomotor response to progressive than to regressive motion. Experiments designed to test this conjecture have shown that (a) asymptotic non-decaying oscillations are found in the torque of female houseflies tracking targets moving at constant angular velocity; (b) the magnitude of the oscillations grows monotonically with mean retinal excentricity of the target; (c) the period of the oscillation is around 180–200 ms. The experimental findings are consistent with the hypothesis that a “progressive-regressive mechanism” plays a significant role in the tracking behaviour of female houseflies. From this phenomenological point of view a flicker mechanism that is active only for nonzero motion is equivalent to a progressive-regressive system. The relatively long period of the oscillation requires more complex reaction dynamics than a pure single dead-time delay. As a specific example we show that a model where the reaction to progressive motion is “sticky”, holding for a longish time after the ending of the stimulus, is consistent with the experimental data.

Notes: Abstract Using a very simple hypothesis concerning the length of the depolarized area during propagation of action potentials, distributions of latencies in bundles of myelinated axons have been derived. The internodal length, the number of nodes of Ranvier, the depolarized area and the variation in internodal length are the important parameters. To demonstrate the applicability of the derivation proposed here some examples taken from neurophysiological experiments are given.

Notes: Abstract The binary decision element described by the decision rule depending upon weight vector w is a model of neuron examined in this paper. The environment of the element is described by some unknown, stationary distribution p(x). The input signals x[n] of the element appear in each step n independently in accordance with the distribution p(x). During an unsupervised learning process the weight vector w[n] is changed on the base of the input vector x[n]. In the paper there are regarded two self-learning algorithms which are stochastic approximation type. For both algorithms the same rule of past experiences neglecting or the rule of weight decrease has been introduced. The first algorithm differs from the other one by a rule of weight increase. It has been proved that only one of these algorithms always leads to the same decision rule in a given environment p(x).

Notes: Abstract The model is based on the concept that non-linear lateral interaction at the inner plexiform layer accounts for most of the specialization and marked non-linearities in cat's retinal ganglion cell responses. The inputs to the lateral interaction processes are a spatio-temporal signal and its retarded, as suggested by the behaviour of simple ganglion cells. Lateral interaction in the model consists of lateral linear inhibition followed by local half wave rectification. The resulting signals are weighted and summated by the ganglion cell thereafter. A transparent and general expression is obtained for the response of the cell model which, albeit its simplicity, leads to most of known types of non-linear responses, including the rarely encountered specialized cells in cat's, retina, except colour coding units. For negligible lateral interaction, the model reduces to spatio-temporal linear models under the two paths hypothesis. A discussion of the possible role of anatomical units in these retinal processes in presented, where a general interpretation for visual processing in cat's retina evolves from.

Notes: Abstract In the present work we investigate the neuronal activities in a vertebrate retina by modelling and simulations using the results of (Oguztöreli, 1979). The basic retinal network considered here consists of interconnected five neurons: a receptor cell (rod or cone), a horizontal cell, a bipolar cell, an amacrine cell, and a retinal ganglion cell. The mathematical model for the basic network is a system of nonlinear ordinary integral differential difference equations. A number of simulations describing the dynamics of the neural activities in the basic network under different conditions are presented, actual and steady-state solutions are discussed. An algorithm is proposed for the determination of the system parameters experimentally.

Notes: Abstract Visual detection of targets moving against structured background fields has been studied with near-monochromatic stimuli, selected so as to isolate the different increment threshold spectral response mechanisms. It is shown that for foveal vision, the red-and green-sensitive mechanisms (π5 and π4 respectively) yield IMG functions (Barbur and Ruddock, 1980), similar to those found with white light. In contrast, the blue-sensitive (π1) mechanism yields a low-frequency IMG response quite unlike that found for the other mechanisms. There is also considerable variation between subjects in this case. Measurements taken 30° off-axis with low (1.4 log trolands) background illumination level, yield a low frequency response IMG function for both rod and cone spectral mechanisms, similar to those found with white light stimuli. At high illumination levels (〉2.2 log trolands), the IMG function for the π5-mechanism is shifted to higher spatial frequencies, as is also observed with white light stimuli. A wavelength-selective binocular interaction effect, manifested in the detection of moving targets, is also described, and it is suggested that this may be of value in the study of defective colour vision.

Notes: Abstract A model is described to account for damped oscillatory activity of two interacting neural populations, pyramidal cells and interneurons. This network in the hippocampus is treated as a lumped system with tine delays between elements. The physiological mechanism underlying the oscillatory activity appears to involve neural population interaction and cannot be described in terms of a network composed of but two neurons, a single pyramidal cell and a single interneuron. An unusual aspect of the model is the explicit incorporation of an ongoing background input to raise the mean level of activity of the pyramidal cell population. This model has evolved from a series of studies previously performed on cats. To test the model experiments were performed on rabbits. The data showing oscillatory activity following fornix stimulation in the rabbit indicate that the model can be applied not only to the cat but also to the rabbit. In additions, for commissural stimulation oscillatory potentials of neural populations and individual pyramidal cells were evoked as predicted by the model.

Notes: Abstract Using the experimental results of Cruse and Saxler (1980a, b) and other authors (Graham, 1972; Pearson, 1972; Bässler, 1977, 1979) a quantitative model is developed in order to describe the behaviour of the systems controlling the leg movements of a walking insect. The whole model consists of six subsystems each of which controls the movement of an individual leg. The single subsystem (Fig. 1) consists of a central part which can assume two modes (protraction, retraction) the transition between which can be controlled by sensory influence. The central part produces the reference input for a feedback loop which controls the leg position. The reference input is however also determined by influences from other subsystems. Four different types of such connections are assumed to exist between the subsystems. Two of these produce alternating (t1, t3), two others “in phase” coupling (t2, t4) between the subsystems to be connected. These connections can transfer information originating from the central part as well as from the periphery of other subsystems. The model is capable of describing either quantitatively or qualitatively the experimental results of Cruse and Saxler (1980a, b) (see Figs. 3 and 4). In addition it is capable of describing the results of other authors, e.g. the temporal leg coordination of the free walking animal (Graham, 1972).

Notes: Abstract A method is proposed for the interpretation of the signals in sensory nerve fibres. It is applicable to systems in which the transfer function between the input to a sense organ and the action potential firing frequency is known. In the present case, the chelonian muscle spindle is considered since its output to ramphold-relase and sinusoidal stretches can be rather accurately simulated.

Notes: Abstract A model is introduced for the motor program which controls final position. The first part of the model relates the biomechanical properties of the muscles to the EMG activities of the extensor and flexor muscles and thereby generates quatitative predictions for the relationships between the EMGs, final position, external forces, muscle stiffness, and muscle tension. To the extent that comparable data exist, the model is shown to give correct quantitative predictions. When only qualitative comparisons can be made, the model is consistent with the data in the literature. The model is complete and can be tested quantitatively in detail in the future. An equivalent circuit for the neural network that innervates the muscles is given. It is shown to have the advantages of making the programming of final position simple to either compute or lookup in a table. In addition, new situations, such as adapting to a force, or an unusual viewing angle, lead to very simple changes in the basic program in terms of the equivalent circuit.

Notes: Abstract Low calcium increases the excitability of neurones and can induce autorhythmicity in excitable cells. Numerical solutions of the Hodgkin-Huxley membrane equations, and numerical evaluations of the small-signal impedance and admittance are used to illustrate the increase in resonance produced by low [Ca2+]0. The resonant frequency may be located either by the peak of the amplitude of the impedance, or by the frequency at which the phase angle is zero for 1:1 entrained action potentials. Autorhythmicity is produced by any mechanism which increases the resonant peak of the amplitude of the membrane impedance.

Notes: Abstract In a recent work (Oguztöreli, 1980) a mathematical model for studying the neutral activities in a vertebrate retina has been investigated, where the basic retinal network involves interconnected five neurons of different kind. This model is general enough to cover a great variety of neurons in the same retina as well as in the retinas of different species. In the present work we deal with an extension of the basic network considered in (Oguztöreli, 1980). This extended model contains interconnected twelve neurons: three receptor cells, two horizontal cells, two bipolar cells, two amacrine cells and three ganglion cells. The performance of the model under different conditions, and, the experimental determination of the system parameters are discussed. The background of the modelling and simulations can be found in (Oguztöreli, 1979, 1980).

Notes: Abstract A network of reciprocally inhibitory motorneurons has been previously postulated to account for the firing patterns of motor units during dipteran flight. Possible activity patterns of such a network were analyzed by means of appropriately interconnected neuromimes. This theoretical analysis showed that the proposed network can account for many aspects of dipteran motor unit activity patterns including firing in specific sequences, stability, and resetting of the firing pattern by antidromic spikes. In addition, the analysis showed that one aspect of physiological activity, motor unit phase locking, can not be explained simply on the basis of network properties alone; evidently specific membrane properties of the dipteran motor units also play an essential role in establishing the activity pattern.

Notes: Abstract In a recent work (Oğuztöreli, 1980) a mathematical model for studying the neural activities in a vertebrate retina has been investigated, where the basic network contains five interconnected neurons: a receptor cell, a bipolar cell, a horizontal cell, an amacrine cell, and a retinal ganglion cell. More recently, in (Oğuztöreli and O'Mara, 1980) the basic network has been extended to a larger network containing twelve neurons. In both of these works, the performances of the basic and extended models were discussed under different structural and processing conditions with constant inputs by using the results of one of our earlier work (Oğuztöreli, 1979). In the present paper we investigate by simulations the responses of the basic retinal network to piecewise constant and periodic inputs. The step and frequency responses of the extended retinal network will be discussed in a forthcoming paper.

Notes: Abstract A model of human muscle action is presented for a maximally fast, large-amplitude forearm movement to target. the inputs to the model are approximately the biceps and triceps EMG envelopes over a single movement. The model's output gives the corresponding displacement angle of the forearm about a fixed elbow position as a function of time. The idea of the model is to conceive of both EMG input drives as successions of millisecond input pulses, with each pulse resulting in a muscle tension twitch. Every twitch is amplitude-scaled, parametrically-shaped, and duration-limited as a function of the muscle's contractile history thus far in the movement. The muscle tension at any time t is the sum of the residual tension levels of all twitches begun before t. The model was developed and tested with special reference to two subjects: one, according to the model dynamics, was a comparatively slow-twitch type, and the other modelled as a fast-twitch type. Good agreement was found between model output and subject response data whenever the subject's EMG's were “synchronous”. The model can be used to characterize each subject's responses by a suite of twitch characteristics. This will enable us to check the accepted but now suspect correlation between muscle biopsy-and performance-determined muscle twitch type.

Notes: Abstract Static and dynamic components of mechanical impedance of human forearm were evaluated by applying two kinds of perturbations: 1) large viscoelastic loads, and 2) small pseudo-random perturbations. When the task involved the active resistance of the perturbations, both stiffness and viscosity increased relatively to their values in the passive task, the increment in stiffness being larger than that in viscosity. The time course of such changes was investigated during the transition between the two operating points defined by the instructions “do not resist” and “resist” the applied perturbations. The changes in stiffness and viscosity were relatively slow, those in the latter lagging behind those in the former.

Notes: Abstract The feed back mechanism subserving the regulation of the body-substrate-distance in the stick insect Carausius morosus has been investigated by means of step-like stimuli. Based on the results obtained in open-loop experiments a model is developed which describes the results obtained under closed loop conditions. When the experimental animal is pushed or pulled in dorso-ventral direction an initial fast and a subsequent very slow change of the body height z over the substrate are observed. The late slow response is a nearly linear function of time and can last for more than one hour if the animal is pulled with moderate forces. It withstands less effectively if pushed. During the slow phase of the response sudden changes of z and of the slope of the z(t)-curves occur, presumably due to corresponding changes of the amplification within the feed back loop.

Notes: Abstract LGN Y-cells in 3 anaesthetized (N2O/O2) and paralyzed rhesus monkeys were investigated with stimuli, intensity modulated by gaussian white noise, and with moving and counterphase modulated spatial sine wave gratings. The results support the model, postulated on the base of electrophysiological recordings in the retina of cat and mudpuppy, which consists of a linear centre and surround mechanism whose responses are modified in a frequency-selective multiplicative way by a nonlinear mechanism in the receptive field. This nonlinear mechanism is also held responsible for the second-order harmonic responses, which are the defining characteristic of Y-cells. The temporal and spatial characteristics of these mechanisms were determined. The responses obtained with the GWN stimulation and with modulated spatial sine wave gratings both indicate that the optimal temporal frequency of the linear mechanisms is near 7 Hz at 70 td and near 5 Hz for the nonlinear mechanism. The optimal spatial frequency for the linear mechanism is between 0.5–2 cycles/deg and between 6–12 cycles/deg for the nonlinear mechanism.

Notes: Abstract A new association scheme which can still recall appropriate data when some key elements are missing (blank) is presented. The traditional associative memory models are designed to deal with complete (memorized) keys, but in the real world, key elements are often missing due to error, equipment failure, observation difficulty, etc. The traditional models, in this case, can not have an optimal association except for special cases. When an incomplete key containing blanks is given, we wish to get the same data, as nearly as possible, as would be obtained with the complete key. In this paper, the optimal associative memory model which operates with partly missing keys is proposed. The model is constructed on the basis of the theory of the pseudoinverse of matrices. Even from the incomplete keys which contain a large percentage of blanks, the model recalls the appropriate data optimally under the MSE criterion. From the results of computer simulations, we can show that the model has the expected ability.

Notes: Abstract The formalism of photoreceptor optics, developed in an earlier paper, is applied to a system consisting of a small receptor, supporting a few waveguide modes, which is excited by light focussed onto it by a lens. The effects of various lens parameters on the angular and absolute sensitivities of this system are described. Receptor variations in the form of caps and tapers are introduced and their effects on the excitation process evaluated. The results obtained are also related to the approach to vision research based on the receptor as a sampling element. Finally, an analysis is presented of the deduction of receptor properties by means of reverse light path observations. The emphasis is on results and graphs are presented so that trends and magnitudes are readily appreciated.

Notes: Abstract Nonlinearities present in the motor output response of biceps and triceps muscles in normal human subjects to applied torque perturbations were evaluated quantitatively. When the applied perturbations were relatively continuous, consisting of a pseudo-random train of pulses, the identified nonlinearities were small, never exceeding 20% of the amplitude of the linear component of the response and usually being much less.

Notes: Abstract When an observer moves in a 3D world, optical flow fields are generated on his retina. We argue that such an observer can in principle compute the parameters of his egomotion, and following this, the relative depth map of the stationary environment solely from the instantaneous positional velocity fields (IPVF). Moreover, we argue that in the stationary world, this analysis can be done locally, and is not dependent on global properties of the optical flow under the imposed constraints (smoothness of the egomotion path, rigidity of objects, temporal continuity of perception). To investigate the method, and to analyze its performance, a computer model has been constructed which simulates an observer moving through a 3D world of stationary rectangular planes at different depths and orientations. The results suggest that the method offers a reasonable and computationally feasible means of extracting information about egomotion and surface layout from optical flows, under certain circumstances. We discuss some issues related to extending the analysis to the case of a rigid world of moving objects, and some issues related to the status of information extractable from optical flows with respect to other sources of information.

Notes: Abstract In the experiments presented here adult stick insects (Carausius morosus) walk on a treadwheel with various legs standing on platforms fixed relative to the body of the insect. These standing legs produce large forees directed towards the rear which are modulated in the rhythm of the walking legs. Neighbouring legs which both stand on a platform often oscillate “in phase”. Possible reasons for the occurrence of the force oscillations are discussed.

Notes: Abstract The objective of the paper is to determine in abstract terms the algorithms used by the cat detecting simple patterns and to quantify the contributions of the visual areas 17, 18, 19 for this task. The data incorporated in the algorithm are collected from behavioral experiments where the animals had to distinguish between two patterns. The patterns were superimposed with gaussian noise and the detection probability was measured. The resulting model describes pattern recognition in two steps: first extraction of features and second classification. The test of the validity of the model system was to predict the outcome of similar experiments but with different patterns. With the help of the model it is possible to deccribe the effect of a lesion in parametric form. This in turn gives some hints about the functions of the visual areas 17, 18, 19 for the specific fask, tested in the experiments.

Notes: Abstract Beck (1972, 1973) hypothesized that textural segmentation occurs strongly on the basis of simple properties such as brightness, color, size, and the slopes of contours and lines of the elemental descriptors of a texture or textural elements. The experiment reported supports the hypothesis that specific stimulus features, rather than second-order statistics, account for textural segmentation. The results agree with Julesz (1981a, b) who has reported evidence disproving his original conjecture of the importance of second-order statistics. Julesz (1981a, b) now hypothesizes textural segmentation to be a function of local features which he called textons. Textons are features that give textural segmentation when textures have identical second-order statistics. The two hypotheses are to date in complete agreement on the stimulus features producing textural segmentation, and the experiment reported is consistent with both.

Notes: Abstract A model for monocular line perception by humanSs is based on three basic assumptions: (a) the line's inclination is coded by the maximally excited orientation detector's number; (b) the inclination of the perceived line is equivocally determined by the excitation vector in the subjective space; (c) the analyzer has a maximum differential sensitivity over the whole range of the line inclinations. This simple model for the line inclination analyzer, taking into account the optimization of its sensitivity, provides incomplex explanations for a wide range of psychophysical and neurophysiological data obtained from human and animal experiments.

Notes: Abstract It is often reported in the early literature that insects walk with the legs protacting in diagonal pairs rather than the triplet of three legs associated with the tripod step pattern. The diagonal pattern implies that legs of the same segment have a phase relationship significantly different from 0.5. Such a pattern of leg recovery has been demonstrated quantitatively for the stick insect (Graham, 1972). Such patterns occur in several insects and systematic asymmetry can even be detected in the earliest quantitative study on cockroaches (Hughes, 1957) when the animals are walking slowly. More recently Spirito and Mushrush (1979) have reported systematic deviations from a phase of 0.5 similar to those observed in stick insects. Asymmetry has also been quantitatively demonstrated in Katydids (Graham, 1978) and has recently been observed in Mantid walking (Thomson, personal communication). This phenomenon seems to be a general characteristic of slow walking coordination in insects. In stick insects asymmetry only becomes obvious in gait II at slow speeds although there can be systematic differences in ipsilateral coordination on right and left sides even at the highest speeds in this gait (Graham, 1972).

Notes: Abstract 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.

Notes: Abstract Interactions between pacemaker cells in a chain were calculated according to a “phase-reset” model. It is based on effects of action potentials in the cells on the cycle lengths of neighbouring cells. These effects were defined for each cell by a latency-phase curve (LPC), giving the latency time (L) until the onset of the next action potential in that cell, as a function of the phase (ø) at which a neighbour cell fired an action potential. Neighbour cells with simultaneous action potentials did not influence each others cycle length. We investigated how stable synchronization depends on the shape of the LPC's of the pacemaker cells and on chain length. Three types of interactive behaviour were distinguished. First, anti-phase synchrony, in which neighbouring cells fired with large phase differences with respect to the synchronized periodP s .Second, asynchrony, in which the periods of the cells did not become equal and constant. Third, in-phase synchrony, in which the phase differences between the neighbouring cells were zero or much smaller than the synchronized periodP s ,depending on the differences between the intrinsic periods. Asynchrony and antiphase synchrony may be seen as cardiophysiological arrhythmias, while in-phase synchrony represents the physiological type of synchrony in the heart. In-phase synchrony appeared to be strongly favoured by LPC's, which have a no-effect (refractory) part at early phases, a lengthened latency (or phase delay) part at intermediate phases and a shortened latency (or phase advance) part at late phases in the cycle. Such LPC-shapes are commonly found in preparations of cardiac pacemaker cells. When the pacemaker cells were identical, the synchronized periodP s during in-phase synchrony was equal to their intrinsic periodP * i . For different intrinsic periods,P s was equal to the intrinsic period of the fastest cell if the LPC's contained a sufficiently long initial no-effect period at early phases and a shorteried latency part at late phases. When, on the other hand, such cell chains had a linear gradient in their intrinsic periods, “action potentials” started from the fast end and traveled along the chain. The propagation of an action potential wave slowed down as it reached the slower cells. When the gradient in the intrinsic periods was too steep, only the intrinsically fast end of the chain developed synchrony. Surprisingly, by making the intrinsic gradient some-what irregular such a chain of cells could be made to exhibit areas of cells that were locally synchronized at different frequencies. These model results show that the concept of phase resetting provides a useful framework to understand interactions between pacemaker cells by action potential effects.

Notes: Abstract Humans can overcome the 150 ms time delay of the smooth pursuit eye movement system and track smoothly moving visual targets with zero-latency. Our target-selective adaptive control model can also overcome an inherent time delay and produce zero-latency tracking. No other model or man-made system can do this. Our model is physically realizable and physiologically realistic. The technique used in our model should be useful for analyzing other time-delay systems, such as man-machine systems and robots.

Notes: Abstract A multi-layered neural assembly is developed which has the capability of learning arbitrary Boolean functions. Though the model neuron is more powerful than those previously considered, assemblies of neurons are needed to detect non-linearly separable patterns. Algorithms for learning at the neuron and assembly level are described. The model permits multiple output systems to share a common memory. Learned evaluation allows sequences of actions to be organized. Computer simulations demonstrate the capabilities of the model.

Notes: Abstract Binocular rivalry is an interesting phenomenon observed in the human vision. It occurs when the right and left eyes are given different stimuli (pictures). This paper describes a mathematical model which explains the mechanism of binocular rivalry. Our basic assumption is that binocular rivalry is elicited by the mutual inhibition between the right and left visual neuron systems. The mutual inhibition between two neurons is first discussed in detail, where a special emphasis is put on a fatigue effect of neurons, and then its results are applied to a simulation model of binocular rivalry.

Notes: Abstract The quantitative dynamics of a biochemical control circuit that regulates enzyme or protein synthesis by end-product feedback is analyzed. We first study a simplified repressible system, which is known to exhibit either a steady state or an oscillatory solution. By showing the analogy of thisn-dimensional system with a time-delay equation for a single variable the mechanism of the self-sustained oscillations becomes transparent. In a more sophisticated system we will find as well either steady state or oscillatory solutions. We determine the role of the parameters with respect to stability and frequency. The most general case will be treated by means of the concept of Lyapunov exponents.

Notes: Abstract 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.

Notes: Abstract The righting maneuver of a freely falling cat was filmed at 1000 pictures per second, and the head position about the roll axis was digitized from each film frame using a graphics input tablet. The head angular velocity and acceleration were computed from the roll axis position trajectory. Head acceleration trajectories approximated two periods of a damped sinusoid at a frequency of 26 Hz. Head acceleration peak amplitudes exceeded 120,000 deg/s2. These trajectories were used as stimuli for the horizontal semicircular canals in a computer simulation of first-order afferent responses during the fall. Linear system afferent response dynamics, characterized in a previous study of the cat horizontal canal using pseudorandom rotations, provided the basis for linear predictions of falling cat afferent responses. Results showed predicted single afferent firing rates that exceeded physiological values; and variations in afferent sensitivities and phase were predicted among different neurons. Fast head movement information could be carried by ensemble populations of vestibular neurons, and a phase-locking encoding hypothesis is proposed which accomplishes this. Implications for central program versus peripheral vestibular feedback strategies for motor control during falling are presented and discussed.

Notes: Abstract Two classes of amacrine cells are simulated, small-field and large-field. Small-field amacrine cells are formed by input from a single bipolar cell, while large-field amacrine cell is formed by inputs from same 7 bipolar cells that form the ganglion cell. Only tonic amacrine cells are studied with both chromatic and luminosity types as well as double-and single-opponent receptive fields. Amacrine cells are used in both feedforward to ganglion cells and feedback to bipolar and horizontal cells. Feedback to bipolar cells or feedfoward to ganglion cells affected steady state levels in a predictable fashion. Negative feedback to bipolar cells and positive feedfoward to ganglion cells does not introduce transients to ganglion cells while negative feedback to horizontal cells and negative feedfoward does. Feedback to horizontal cells produces complex effects on bipolar, amacrine and ganglion cells dependent on such factors as center-surround field balance and negative feedback from luminosity type of horizontal cell to cones.

Notes: Abstract An algorithm for the estimation of stochastic processes in a neural system is presented. This process is defined here as the continuous stochastic process reflecting the dynamics of the neural system which has some inputs and generates output spike trains. The algorithm proposed here is to identify the system parameters and then estimate the stochastic process called neural system process here. These procedures carried out on the basis of the output spike trains which are supposed to be the data observed in the randomly missing way by the threshold time function in the neural system. The algorithm is constructed with the well-known Kalman filters and realizes the estimation of the neural system process by cooperating with the algorithm for the parameter estimation of the threshold time function presented previously (Nakao et al., 1983). The performance of the algorithm is examined by applying it to the various spike trains simulated by some artificial models and also to the neural spike trains recorded in cat's optic tract fibers. The results in these applications are thought to prove the effectiveness of the algorithm proposed here to some extent. Such attempts, we think, will serve to improve the characterizing and modelling techniques of the stochastic neural systems.

Notes: Abstract The validness of a model describing the relation between mean saccadic latency and stimulus asynchrony based on facilitation instead of suppression was tested experimentally. As a result, suppression of signals generated by the onset of a peripheral stimulus due to fixation of another target, giving rise to an increase of mean saccadic latency, does not seem very likely. The influence of the intensity of the fixation target on the latency of visually evoked saccades was studied. According to the facilitation model, the offset of the fixation target induces after an afferent delay, a transition of the state of the facilitation mechanism from the unfacilitated condition into a mode of maximal facilitation. The time-period during which this change is accomplished is called Facilitation-Rise-Time (FRT). An interpretation within the context of the facilitation model of gap-overlap latency data for different values of the intensity of the fixation stimulus suggests, in combination with computer-computations of the model, that lowering of this intensity causes an increase in FRT. The results in normal subjects of step stimulus experiments with a dim fixation point substantiate the hypothesis of a facilitation mechanism, which is triggerable not only by an external signal such as the offset of the fixation point, but also by some internal stimulus independent signal. Moreover, data for tracking by an amblyopic eye seem to support this conclusion. The findings of increased saccadic latencies in amblyopic and Optic Neuritis (ON) eyes suggest a slowing of processing of visual information in the sensory pathways from the central retina, subsequently utilized by the oculomotor system in the generation of saccades. Increased saccadic latencies in amblyopic and ON eyes can, within the context of the facilitation model, be explained by an increase in FRT and an increase in afferent foveal transport time.

Notes: Abstract Using the mathematical model of the pacemaker neuron formulated by Chay, we have investigated the conditions in which a neuron can generate chaotic signals in response to variation in temperature, ionic compositions, chemicals, and the strength of applied depolarizing current.

Notes: Abstract This paper presents the approximate expression of the recollection probability of a three-dimensional correlation matrix autoassociative memory, in which each memorized pattern consists of binary (+1 or-1) elements, and discusses the recollection ability in comparison with that of the conventional two-dimensional correlation matrix associative memory. An associative memory using the correlation properties between memorized patterns desires the condition that the memorized patterns are mutually orthogonal or approximately orthogonal. The three-dimensional correlation matrix associative memory that inscribes the third order correlation of a memorized pattern heightens the recollection ability even though the above condition is not satisfied.

Notes: Abstract A special class of stochastic processes with optimization (SPO) is considered and their long-run behaviour is investigated. At each step of the process {X h} h ≧0 (where X h is a discrete random variable) a loss function expressing the distance with respect to the moments in the previous step is minimized. The transformation leading from a certain probability distribution F k (step k) to the next probability distribution F k+1 (step k+1) is accomplished by means of an optimization operator, or simply optimator, that is, a nonlinear operator performing an optimization. The constraints involved by the optimator are typically regarded as a message conveying the information needed for the stepwise evolution of the system. In other words, the behaviour of the system is expressed by an ordered set of events (actions) to be realized with given probabilities and minimum losses, while the message is viewed as a set of constraints providing an inferior bound for that probabilities, hence, ensuring that the required actions are performed. Besides, in order to account for some relaxation phenomena taking place in higher systems each active step (active optimator) is followed by a relaxation step (recovery optimator). Under these conditions it is shown that repeated presentation of a stimulus pattern leads to a convergent process, so that the action is finally performed with minimum minimorum losses. This reveals some fundamental relations between optimization and learning in higher systems, highlighting also the key role of the relaxation processes. Further the behaviour of the system is described in terms of a special class of Non-Markovian processes termed stochastic processes with optimization and relaxation (SPORs). It is shown that two basic subclasses of SPORs exist, namely the monoergodic and the biergodic SPORs. Sufficient conditions for both monoergodicity and biergodicity are given. Finally, a particular feature of the optimators, the so-called nonredundancy is shown to be relevant with respect to the influence of the past on the current evolution of the system.

Notes: Abstract This paper attempts to combine (and thereby briefly review) various sets of physiological data in order to outline a qualitative model of the different states of stochastic neural activity underlying different forms of physiological tremor. Particular emphasis in put on spatial distributions of the properties of neural elements and their interconnexions, and on discharge characteristics of motor units and muscle spindle afferents including so-called “early discharges” and nonlinearities. It is argued that the wide variety of internal anatomical and functional structures of skeletal muscles and of their reflex organization must be considered when dealing with stability problems. Computer simulations of stochastic population models of the involved neuromuscular elements are advocated as means to investigate the relative importance of the many factors possibly contributing to stabilizing or de-stabilizing neuromuscular systems.

Notes: Abstract The spontaneous discharges which recorded extracellularly from cells in the lateral geniculate nucleus (LGN) of a cat were classified into the following 3 main groups depending upon the shapes of their interval histograms and autocorrelation functions: the gamma type whose interval histogram is fitted by a gamma distribution function and whose autocorrelation function has some periodic property which damps down within about several 10 ms, the burst type whose interval histogram has a peak in the first bin (less than 8 ms) and whose autocorrelation function has a large positive peak within several msec, and the multimodal type whose interval histogram has a complex shape with three or more peaks and whose autocorrelation function has a periodic property. Each type of spontaneous discharge seems to be inherent at scotopic and mesopic backgrounds, and the cells whose spontaneous discharges are the gamma type, the burst type, and the multimodal type are called here a gamma cell, burst cell, and the multimodal cell, respectively. Gamma cells are subdivided into X- and Y-cells (gamma-X and gamma-Y cells), but burst cells are all Y-cells and multimodal cells observed up to now are all X-cells. It is clear that these various types of cells are distributed significantly differently in each lamina. All the cells that we found up to now in lamina A were either burst cells or multimodal cells, but every type of cell was found in lamina A1. The majority of cells in lamina C were the gamma type. In most cases, the peak values of the PST histograms of gamma-Y cells (especially, on-center cells) are larger than those of burst cells. These results suggest that Y-cells projecting to area 17 from laminae A and A1 are the burst type, and Y-cells projecting to area 18 from laminae C and A1 are the gamma-Y type.

Notes: Abstract Electronic simulation of generalized vertebrate cone retina consists of 43x41 grid of red-, green-, and blue-sensitive cones. Each retinal element is simulated by a linear summator in series with a leaky integrator and spatial-temporal properties are developed by spatial organization of cone mosaic into unit hexagons and interplay of antagonistic inputs of differing time courses. Model has full compliments of horizontal and bipolar cells including color- and noncolor coding as well as single- and double-opponent receptive fields for bipolar cells. Electronic simulation also has negative feedback from L-horizontal cells to cones. Ganglion cells are formed by convergence of 7 bipolar cells, either all same and thus homogeneous, or else with a central-DPBC (or HPBC) and 6 surround-HPBCs (or DPBCs) and thus non-homogeneous. Responses of color- and non-color-coded ganglion cells as well as single- and double-opponents are investigated with stationary and moving light spots using white and colored lights. While responses to stationary light spots are predictable from digital models, responses to moving spots are complicated by differing time lags of components involved in total response. Therefore, responses to moving stimuli are more readily simulated by analogue models.

Notes: Abstract Recording of simultaneous but separated activity of neural populations overwhelms the experimenter with a large amount of information. A clearly structured display technique the “Neurochrome” is introduced, usable on-line and real-time. It shows neural activity patterns while preserving neural identity by employing a color code. The Neurochrome assists the experimenter in generating and verifying hypotheses about neural correlations and stimulus-event relations already during the experiment. In auditory research single neurons are characterized by their spectro-temporal sensitivity to auditory stimuli. A straightforward generalization of this concept, applicable to neural populations, is proposed leading to a global indication of a populations' activity to stimuli: the Multi-Unit Spectro-Temporal Sensitivity. This approach is inversely related to the Neurochrome, the latter however containing more information. The combination of both approaches seems quite powerful in the investigation of neural assemblies. The procedures are illustrated with examples of extracellular multiunit recordings from the auditory midbrain of the grassfrog (Rana temporaria L.).

Notes: Abstract The paper deals with the initiation of visually guided saccades, in order to break down the saccadic reaction time into functionally different periods of time. It takes into account that spatial processing of information is so basic that modelling of saccadic control properties should include spatio-temporal arrangements. The output signal of the saccadic system was measured in response to visual stimuli in which the time between the appearance of a visual stimulus in the peripheral field and the disappearance of the central fixation point was varied. The variation of the mean saccadic latency time, measured with respect to the onset of the peripheral stimulus, as a function of stimulus asynchrony was highly significant. This variation may be represented by a so-called gap-overlap curve, which is characterized here by means of five parameters. A facilitation model is introduced to fit the results of the gap-overlap experiments. The facilitation model for the initiation of visually evoked saccades incorporates a mechanism which governs the efficiency of processing of signals that arise from a stimulus presented at a particular position in space. It explains how visual information may be affected by other sensory information before it is used to command further saccades. It allows determination of saccadic system parameters, such as the peripheral and the foveal afferent processing time, the central processing time for a saccade and the degree of facilitation. These quantities were found to be characteristic for the given test subjects, and where these data could be compared with neurophysiological data, the agreement was within the experimental error.

Notes: Abstract Population growth is modelled by means of diffusion processes originating from fluctuation equations of a new type. These equations are obtained in the customary way by inserting random fluctuations into first order non linear differential equations. However, differently from the cases so far considered in the literature, equations possessing two non trivial fixed points are taken into account. The underlying deterministic models depict the regulated growth of a population whose size cannot decrease below some preassigned lower threshold naturally acting as an absorbing boundary. A fairly comprehensive mathematical description of these models is provided.

Notes: Abstract We have previously proposed that electrocortical activity (EEG) arises as a manifestation of linear waves generated by resonance among telencephalic neurones, and that this activity is controlled in part by ascending neurones from the brain-steim, which regulate the damping of each resonance. The presentexperiments focus on a specific class of ascending neurones, the mesotelencephalic dopaminergic cells, because these cells are thought to mediate important psychological effects, and are conveniently subject to selective lesion. A critical test of the theory is undertaken, by performing selective unilateral lesion, assessing the changes in the power spectrum of the EEG attributable to lesion, and determining whether the changes in phase of the EEG correspond to that predicted from the changes in power. Results support the theory, although the model order applicable in these experiments is inadequate. The consequences of these findings for automata theory, linear network theory and their application to mammalian brains are briefly discussed.

Notes: Abstract An electrical analogue model for the recurrent lateral inhibition system formed by the omega neurons in the cricket's auditory pathway is described (Fig. 1A). The two reciprocally coupled inhibitory neurons are mimicked by the action of two inverting operational amplifiers in circuit with RLC combinations. The oscillatory properties of this reciprocal arrangement introduce a time delay in action of the feedback in the circuit, which corresponds to half the period of the characteristic frequency of the two-cell resonator. Varying degrees of coupling between the two “inhibitory” arms of the model produce a family of resonance curves (Fig. 4A) for frequency dependent contrast enhancement which allows the compromises observed in the physiological circuit to be discussed. In psychophysical experiments using the model circuit as an input stage for the human auditory pathway, frequency dependent lateral inhibition markedly improved identification of the apparent location of the sound source when the frequency of the input signals matched the resonant frequency of the circuit.

Notes: Abstract In any realization of an autoregressive time series there exist a few observations having a noticeable feature: they express the useful properties of the time series and, therefore, they represent the entire process. Such representative observations (or, simply, representatives) can be determined by an optimization procedure, provided that the absolute value criterion is used instead of the customary least squares. To achieve this, a special kind of optimization operator (optimator) which generate the parameters of the time series is considered. The concepts of strong and weak similarity of the time series are defined in terms of the representatives and sufficient conditions for both strong and weak similarity are derived. It is shown that there exists a subclass of strongly similar processes, say X, such that ordinary addition is a binary operation in X. An analogous result is shown to hold for weakly similar autoregressive processes. Some examples illustrating these results are given.

Notes: Abstract 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.

Notes: Abstract The spatial information capacity of the human eye for photopic vision has been determined taking into account the intensity response function of the photoreceptor. It has been found that spatial information capacity increases with the mean luminance upto a certain value of mean luminance and after that it starts decreasing. The decrement occurs below the damage threshold. These results are in agreement with the reported experimental observations. It has been concluded that the limited number of Na+ channels in the photoreceptor outer segment and the photon noise are responsible for the fall in the information capacity below the damage threshold.

Notes: Abstract Nonlinear interactions in the human visual system were studied using visual evoked potentials (VEPs). In one experiment (superimposed condition), all segments of a dartboard pattern were contrast reversed in time by a sum of two sinusoidal signals. In a second experiment (lateral condition), segments in some regions of the dartboard pattern were contrast reversed by a single sinusoid of one frequency, while segments in other (contiguous) regions of the pattern were contrast reversed by a single sinusoid of another frequency. An identical set of ten frequency pairs was used in each experiment. The frequency pairs were chosen such that the difference between frequencies in each pair was 2 Hz. Amplitudes and phases of the sum and difference frequency components of the VEP (intermodulation terms) were retrieved by Fourier analysis and served as measures of nonlinear interactions. The use of input pairs with a fixed separation in frequency enabled the estimation of the temporal characteristics of the visual pathways prior to a second linear stage. The use of superimposed and lateral conditions revealed antagonistic contributions to the VEP, possibly reflecting direct-through excitatory and lateral inhibitory pathways, respectively.

Notes: Abstract In consideration of the generation of bursts of nerve impulses (that is, rhythmic oscillation in impulse density) in the ring neural network, a synaptic modification algorithm is newly proposed. Rhythmic oscillation generally occurs in the regular ring network with feedback inhibition and in fact such signals can be observed in the real nervous system. Since, however, various additional connections can cause a disturbance which easily extinguishes the rhythmic oscillation in the network, some function for maintaining the rhythmic oscillation is to be expected to exist in the synapses if such signals play an important part in the nervous system. Our preliminary investigation into the rhythmic oscillation in the regular ring network has led to the selection of the parameters, that is, the average membrane potential (AMP) and the average impulse density (AID) in the synaptic modification algorithm, where the decrease of synaptic strength is supposed to be essential. This synaptic modification algorithm using AMP and AID enables both the rhythmic oscillation and the non-oscillatory state to be dealt with in the algorithm without distinction. Simulation demonstrates cases in which the algorithm catches and holds the rhythmic oscillation in the disturbed ring network where the rhythmic oscillation was previously extinguished.

Notes: Abstract Goal directed movements, executed by means of a manipulator with various dynamics, were investigated in order to establish to what extent the loading affects the executed movement. The desired movement concept, together with a describing function model for goal directed movements, was applied to parameterize the movements. Analysis of the results showed that the position trajectories, when scaled by means of a fundamental scale property, with respect to the maximum velocity of the desired movements, were invariant under variation of the manipulator dynamics. From this invariance in the phasing of the movements, it was concluded that the subjects fully adapted to the applied loads.

Notes: Abstract The altered feedback technique is very suited to display nonlinearities of the human smooth pursuit system. In fact, when the gain of the retinal feedback path is raised, for the horizontal channel, above its normal unitary negative value, a threshold is met beyond which sustained horizontal self-excited smooth oscillations of the eye can be observed, which point out the existence of a stable limit cycle. Furthermore, the characterizing features of both the transient and steady state show a well defined dependence on the total feedback factor K. In particular, the analytical dependence on K of the amplitude and frequency of limit cycle oscillations can be derived. Implications of the experiment with respect to the mathematical modelling of the system are discussed.

Notes: Abstract Drift of the retinal images of the surroundings elicits optomotor responses of flight control in the fruitfly, Drosophila melanogaster, and in the housefly, Musca domestica. The present investigation deals with the responses of tethered flies in still air. The responses were elicited by continuous movement of striped patterns in front of the eyes, and characterized by the magnitude and elevation of the resulting force of flight which is the average of the forces produced during a wingbeat cycle. The force of flight is resolved into the upward directed lift and the forward directed thrust. In either species, pattern movement acts upon the magnitude, but not upon the elevation of the force of flight. The elevation relative to the longitudinal body axis is almost invariably 24° in Drosophila, and 29° in Musca. The lift/thrust ratio in still air is fixed accordingly, and can be changed only by variation of the body angle. Keeping an angle of minimum body drag does not contribute significantly to the efficiency of insect flight at very low Reynolds numbers (Re). Control of the lift/thrust ratio by variation of the body angle is, therefore, less surprising in Drosophila where Re is in the order of 102, than in Musca, where Re is in the order of 103. Control of this ratio without variation of the body angle is actually established in insects flying at even higher Re. Covariance of lift and thrust in the investigated flies is achieved by control of wingbeat amplitude or wingbeat frequency, but not by control of wing pitch or stroke plane. A change in the latter parameters would have deflected the force of flight and is, therefore, inconsistent with the constant elevation found in the present experiments. The results obtained, so far, do not exclude active deflections of the force vector during occasional bouts of aerobatics, or passive deflections of this vector during flight at non-zero airspeed.

Notes: Abstract A rule for environmentally dependent modification of the neuronal state is examined. Under the rule, the neuron selects a trigger feature that matches either a particular pattern in the stimulus set, or the most common pattern component, depending on a certain parameter. Thus a neuron may evolve to respond to its stimulus environment in one of two capacities, namely specification or generalization. Neurons of the former variety are labelled “S-cells”; and those of the latter, “G-cells”. In the model, synaptic modification is modulated by two postsynaptic mechanisms which act antagonistically to strengthen or weaken the synaptic connectivities. The functional dependence of these mechanisms on the postsynaptic activity is shown to determine whether the neuron acts as an S-cell or a G-cell. A circuit is proposed for a module that consists of a G-cell and several S-cells sharing a common set of inputs. By inhibiting the G-cells, the S-cell acts as a contrast-enhancing element, increasing their specificities for individual patterns in the stimulus set. The output from the module is a recoded representation of the environment with respect to its general and distinctive features.

Notes: Abstract An analysis is presented of the optical factors influencing photoreceptor excitation. Small receptors are considered and the incident light is focussed onto them by a lens. The theoretical principles involved are outlined and explained in simple terms and by using analogies, so that they are also accessible to the nontheoretician. System parameters relevant to the fly are used as a basis for study. The theory is used to discuss the choice of lens parameters, the effects of defocussing and chromatic aberration. The emphasis is on results and in all cases graphs are presented so that magnitudes and trends are readily appreciated.

Notes: Abstract Based on recent physiological observations, a new hypothesis for the algorithm for synaptic modification is proposed: an interactive process between postsynaptic competition and presynaptic regulation controls the synaptic modification, and both functions obey the same competitive rule. A fundamental algorithm for the competitive rule is proposed and analysed. The interactive process is decomposed into two procedures. The first one is a postsynaptic competition, in which all synapses making contact with the same postsynaptic cell compete for their terminal sites, and the postsynaptic cell makes demands for synaptic modification upon the presynaptic cells. The second one is a presynaptic regulation, in which the presynaptic cell regulates the postsynaptic demands and determines the net amount of the modification for each synapse originating from it. The performance of the algorithm has been simulated on a digital computer. The initial structure of the simulated neural network consists of randomly-connected presynaptic and postsynaptic cells, with no other structures assumed. After repetitive presentations of a uniform stimulus, the basic configurations of neural connections (one-to-one, one-to-many, many-to-one and many-to-many connections) are organized in dependence on the parameters of the algorithm.

Notes: Abstract A mechanism for impulse encoding is advanced for those neurones whose impulse trigger zone membrane is more excitable than the general axonal membrane. Electrical communication between an electrotonically small patch of highly excitable membrane and neighboring membrane places the control of membrane potential — in varying degree — to the larger membrane area throughout the interspike intervals. That control is relinquished to the trigger membrane near the time of action potential initiation in a natural fashion. Model calculations demonstrate that this mechanism can lead to a dramatic lowering of the minimum stable firing frequency of tonic neurons, and, additionally influence the shape of the stimulus —versus — impulse frequency curve. The results are compared with the behavior of the slowly adapting stretch receptor neuron of the crayfish.

Notes: Abstract In the setting of a kinetic approach to neural systems a more refined model is proposed. The subsequent kinetic equations are subjected to numerical investigation. The results show that the model retains the most evident properties of transmission of information of the natural neural systems.

Notes: Abstract The human system of pattern recognition is explored. This system utilizes the method of syntactic feature comparison, activation of the patterns containing the feature, and sorting among the activated patterns. Both the pattern recognition process without thinking and with thinking are discussed, and examples are given. Contrary to the usual concept, the more complicated pattern has a better chance to be recognized correctly.

Notes: Abstract Because of the enormous complexity which characterizes the activity of the brain a special effort has been made toward the development of neural models. These models are necessarily based on fundamental simplification of neural structures, and neural mechanisms. It is however necessary that any assumed mechanism be based on acceptable physiological criteria. We have developed such a model in the past (Anninos, 1969; Anninos et al., 1970) and in this paper we elaborate on it and attempt to incorporate in it a mechanism which will give rise to α-rhythm activity.

Notes: Abstract The reaction of color sensitive neural networks to intensity and color steps on logarithmic transformation of the input signals is calculated mathematically. The networks consist of opponent-color cells respectively with (duple system 1) or without a surround (duple system 2) or of double opponent-color cells (quadruple system). The output signals are independent of the intensity level. Both duple systems are able to code the color of homogeneous areas on a dichromatic level. The hue corresponds to the sign, the saturation to the absolute value of the output signal. The coding of saturation becomes incorrect at intensity borders only with duple system 1 (due to a Mach band response) at color borders however with duple system 1 and 2 (due to low-pass properties). The quadruple system (like duple system 2) is insensitive to intensity differences. It only responds to color differences, which are transferred according to a band-pass filter. The system therefore is able to function as a detector of color borders. The results are used in a new model for the processing of color and color borders. A linear transformation has been found to be less suited for color coding.

Notes: Abstract In a previous experiment the author has shown how perceived rotations, in the kinetic depth effect, decrease as a function of temporal frequency. It was argued that many of the ambiguous motion effects, and the temporally limited nature of the phenomenon, are due to the inability to discriminate curvature and torsion information as well as the finite time required to extract these latter sequentially dependent image parameters. In this paper we extend the investigation to consider the perception of rotations and rigidity as a function of complexity, including amplitude and phase differences between image elements. Results indicate that perceived rigidity is specifically a function of phase information, or relative motion components, and that rotations decrease as a function of complexity. In this way the curvature and torsion extraction processes are integrated with the sinusoidal nature of the image motion.

Notes: Abstract It is shown how field potentials due to neuronal membrane processes can be computed by means of a digital computer system. The essence of the method consists in evaluating a discrete expression for the field potential as a function of membrane potentials. This expression is considered as a threedimensional convolution. In the computer system this convolution is performed by multiplication in the spatial Fourier domain. Introduction of a density function provides the possibility of evaluating in an easy way the field potential of a population of neurons. To demonstrate the applicability of the system, field potentials of different membrane potential configurations in the brain have been computed.

Notes: Abstract Published observations of the dynamic properties of lateral and self-inhibition in the Limulus retina lead to a non-linear integral equation for the response of ommatidia located near the center of a uniformly illuminated region. Coleman and Renninger (1976, 1978) showed that when the excitation is constant in time and the sum of the inhibitory coefficients for the illuminated region exceeds a critical value, the integral equation has a stable periodic solution describing a sustained, spatially synchronized, oscillatory response in which bursts of activity alternate with silent periods. Such spatially synchronized “bursting” has been observed in the Limulus retina in situ by Barlow and Fraioli (1978), using the preparation of Barlow and Kaplan (1971). Employing experimental data on the temporal dependence of lateral and self-inhibition, which were then available only for the excised eye, Coleman and Renninger calculated a value of 0.34 s for the period p of the bursting response, which is significantly above the range, 0.11–0.20 s, of values of p observed for the Limulus eye in situ. Brodie et al. (1978) have recently published measurements of the temporal dependence of lateral and self-inhibition for the in situ preparation. Here we show that when the kernel functions in Coleman and Renninger's integral equation are chosen in accord with these new data, the periodic solutions of the equation have a period of approximately 0.13s, which is in the range (0.11–0.20 s) required for agreement with experiment. Other properties of the periodic solutions, i.e., their general form and the threshold levels of inhibition required for their existence, are also in accord with published observations of the behavior of the retina in situ.

Notes: Abstract Response characteristics of human operators in manual pursuit tracking with auditory input are investigated. The human operator hears in his left ear a sound whose frequency varies in proportion to an external random signal. At the same time, he hears in his right ear another sound whose frequency varies in proportion to the angle of a control lever of a potentiometer. The operator controls the angle of the lever so that the frequencies of the sounds in both ears remain as close as possible. The dynamics of the human operator is studied by assuming a “manmachine system” whose input is the external signal and whose output is the voltage of the potentiometer. A learning identification method proposed by one of the authors is used to calculate the weighting function of the man-machine system, which is displayed on a CRT screen in real time. During the tracking task, the skin potential activity (SPA) is measured as an index of arousal of the operator.

Notes: Abstract Peripheral sensory and motor systems may be characterized by models consisting of multiple parallel convergent pathways, each described by the same set of equations, but having different parameter values in each path. Such models, although deterministic, are best analyzed using a statistical approach, which is illustrated here by analysis of several simple multipath models composed of linear dynamic elements and static non-linear elements. Relationships between instantaneous means of signals at different points in such systems are used to show that a multipath system can exhibit behaviour which would not be expected from observations of individual pathways. Mechanisms for linearization of static non-linearities are briefly described. Important implications for neurophysiologists are discussed.