Showing papers in "Kybernetika in 1970"

Ordnung und Orientierung der Elemente im Sehsystem der Fliege

Abstract: The neural elements in the visual ganglia of insects show an uncommonly high degree of order. The mapping of the array of sensory elements in the periphery (of sampling points in the visual space) onto four successive levels of the ganglionic chain can be quite precisely described, each neuron in the ganglia being related to a point, or a set of points, in the visual field. Also some of the fibers which connect neurons related to different visual-space-points are very precisely oriented. One of these sets of fibers oriented obliquely appear to match the interactions postulated on the basis of one of Gotz's (1968) models of movement perception in flies. Some embryological questions are also raised by the high degree of order and by the curious mirror symmetry with respect to the mid-sagittal plane on one hand and to the equatorial plane on the other, which pervades the whole system.

Linearizing: A method for analysing and synthesizing nonlinear systems

Abstract: Physical and especially biological systems behave many times in such a way that the methods of linear system analysis are not adequate, even when “small” signals are used.

Information processing in the vertebrate visual system. II

Abstract: In this paper it is tried to find a mathematical model for a number of mainly electrophysiological results concerning pattern recognition of mammals. The interpretations are essentially based on the experiments of Hubel and Wiesel in the visual system of the cat and the monkey. After a short introduction to the applied theory of linear nervous nets the investigations in the retina are interpreted. This part of the visual system can be considered as a bandpass-filter for space dependent oscillations. At the level of the geniculate body, a further filtering takes place which especially attenuates the low and the very high frequencies. The processes in the cortex regions 17, 18 and 19, where the further preprocessing of the pattern recognition takes place, can be interpreted by the theory of matched filters. In Area 17 the input pattern is reduced to the contour lines. In the two other areas the extraction of simple characteristic features such as line ends and corners takes place. By means of the present results it is not possible to draw complete conclusions on the structure of the recognition process.

Methodological and theoretical problems in the voluntary control of electroencephalographic occipital alpha by the subject.

Abstract: Twenty-one normal humans attempted to control the facilitation and inhibition of their EEG occipital alpha rhythm. They received auditory feedback which informed them whether or not alpha occurred. Most subjects learned to inhibit alpha, only four learned to facilitate it. Further training did not bring improved control of alpha. The results are presented to illustrate problems of method and interpretation which include the diversity of subjective attempts at control; day-to-day variability of the response; the control for alpha increase caused by habituation; and the feedback technique as an operant conditioning method. Descriptors: Autoregulation, alpha rhythm, feedback EEG, alpha training.

The possibilities of neural holographic processes within the brain.

Abstract: A theory of brain functioning is proposed based upon an analogy to optical holographic processes. There are many properties which holography potentially offers to neurophysiology. Chief among these is the property of distributedness, which is displayed only by holographic processes. This property, an attribute of certain types of holograms, permits any small portion of the hologram to reconstruct the entire original scene recorded by the hologram. Because of this fact and other supporting evidence, neural versions of the holographic processes appear as most promising candidates for the coding of sensory and memory processes. It is demonstrated that mathematical models based on known elementary neurophysiological processes can embrace “neural-holographic processes”. This is done in terms of equations from optical holography which are discretized in space and time and are suitably transformed to account for the substitution of neural-pulse waveforms in the place of the sinusoidal oscillations involved in optical holography. The possible or probable differences between optical and neural holographic processes are then examined in detail. The various types of holographic processes are considered as to their suitability as paradigms for the neural processes. Fourier-transform holography appears to be the most suitable type for initial neural holographic models. An exploration of the possible correspondences or isomorphisms between the state space of the holographic process and the plausible state spaces of the neural coding process has been initiated. The most probable pairing at the level of the hologram appears to be: first, the correspondence of the electromagnetic oscillation phase with the neural interspike interval; and second, the correspondence of amplitude with neural impulse height. If necessary, the impulse height at the neural hologram could be restricted to binary values of pulse-no pulse, still permitting a coding of the complete intensity scale of “grays” present in the reconstructed image of the original stimulus object. There is neurophysiological evidence indicating the possibility that the impulse height present in the stimulus object plane could be coded in terms of the impulse coherence-incoherence dimension, which would fit nicely into neural-holographic processes. Additional holographic properties are detailed and examined. When this is done collectively, it is concluded that: This hypothesis is discussed in terms of previously-formulated wave interference theories of brain functioning. It is pointed out that the holographic point of view is basic to a complete discussion of any waveinterference theory. Some psychophysical and neurophysiological evidence for this hypothesis is examined. The principal evidence for such a hypothesis comes from: 0) recordings of single cell activity from Area 17 of the monkey; 1) animal brain lesion work (this work presents some of the evidence that visual and auditory processes are “distributed” in at least one stage of the processing); 2) examination of brain-damaged human beings (it is pointed out that neural-holographic processes offer possible explanations formacular sparing andpolyopia); 3) general evidence for coherent pulse activity; and 4) some evidence of neural connectivity which would be suitable for neural holographic processes. Further approaches to experimental verification are suggested.

Information processing in the visual system of vertebrates. I

Abstract: : In the domain of form recognition the human visual system surpasses by far the capacity of actually existing technical devices designed to serve the same purpose. Therefore it appears advantageous to undertake a communication-theoretic function-description and structure-description of the biological system in order to gain suggestions for the solution of technical problems and in order to make possible the adaptation of technical apparatus to human beings. Over and above this an understanding of visual information processing will probably permit inferences to be drawn regarding the functioning of fairly large parts of the brain since the information picked up by the peripheral sense organs is processed in similarly structured networks in the cerebrum. The following investigation is based essentially on the electrophysiological studies of Hubel and Wiesel on the visual cortex of cats and monkeys. (Author)

The biologically relevant parameter in nerve impulse trains.

Abstract: An experiment is described, the results of which indicate that impulse rate is the information carrying parameter of impulse trains. The demodulation of such information occurs by low-pass filtering. This conceptual model is compatible with all the features of synaptic transmission. The implications of this model for the transmission of information in integrative neurons is discussed.

Probabilistic analysis of dendritic branching patterns of cortical neurons

Abstract: It is argued that the usual method of characterizing dendritic fields of nerve cells by enumerating the number of bifurcations and end points at various distances from the perikaryon, and the number of intersections of dendrites by virtual spheres around the centre is of limited value for an adequate description. Although these parameters give a reliable indication as to the spatial density of the dendritic material, one shortcoming is that the structural content of the plexus remains rather obscure because the topological and metrical aspects are represented in an intermingled way. A statistical theory is put forward that separates the two factors. As to the first factor, many experimental data can be described by assuming that the probability of bifurcation of a segment decreases geometrically with the order of that segment. As to the second factor, it is deduced that in most instances the terminal segments are, on the average, several times longer than the intermediary situated segments. Upon elaboration of the theory, in comparison with experimental findings reported in the literature, it seems profitable to evaluate these factors separately by measuring the distribution of the number of segments per order or generation, and the distribution of the lengths of the segments for each order. Emphasis is laid on the dynamic aspects of dendritic growth by analyzing data on changes in dendritic ramification patterns of cells in brains of animals of various ages, and reared under either normal or experimental conditions.

Context-dependent stuttering.

Abstract: An analysis of stuttering in the natural speech of Germans revealed the following facts: 1. Stuttered phonemes are frequently preceded or followed in the context by an identical phoneme defined as the inducing phoneme. 2. The inducing phoneme usually followed rather than preceded the stuttered phoneme. 3. The inducing phoneme occurred closer to the stuttered phoneme than would be expected by chance. 4. The stuttered and inducing phonemes were usually situated in identical syllabic positions. 5. Stuttered phonemes usually occurred in stressed syllables.

A second order mechanical model of muscle spindle primary endings

Abstract: With reference to experimental data and the failure of earlier proposed first order linear models of mammalian muscle spindles, a second order mechanical model of de-efferented primary endings is studied. The model takes into account the presence of two different types of intrafusal muscle fibres in a complete spindle organ. It further allows the incorporation of different gain of the mechano-electric conversion into a depolarization of the sensory terminals innervating the two types of fibres. It is shown that a closer approximation to the behaviour of the biological prototype is obtained if the transducer gain of the branch corresponding to the nuclear bag intrafusal fibres is chosen significantly higher than that corresponding to the nuclear chain branch. The marked nonlinear behaviour of muscle spindle primary endings as recently reported by Matthews and Stein (1968, 1969) is interpreted as a saturation effect of the high gain mechano-electric transducer of the nuclear bag branch. The saturation is considered to reflect a condition of complete depolarization of these sensory terminals. If a higher transducer gain actually is present, a complete depolarization of these terminals would occur at a lower degree of mechanical deformation than for the nuclear chain terminals. The mechano-electric transducer system of the nuclear chain fibres might thus behave approximately linearly within a larger range of input amplitudes. The greatly reduced gain of the primary endings at large emplitudes of imposed muscle vibrations as observed experimentally (Matthews and Stein, 1968, 1969) may thus be accounted for by the transducer gain of the nuclear chain fibres alone.

Feedback regulation of the alpha electroencephalogram activity through control of the internal and external parameters

Abstract: Experiments with feedback stimulation triggered from the subject’s electroencephalogram result in changing the sequential time series of intervals of occipital alpha and intervals of little or no alpha EEG activity. The rate of recurrence of alpha and no-alpha EEG can be changed by regulating the external feedback stimuli or by asking the subject to change his internal state. Four different paradigms were investigated and the results interpreted in terms of the hypothesis that oculomotor functions regulate the occurrence and nonoccurrence of alpha.

Models of retinal signal processing at high luminances.

Abstract: In psychophysics the relation between the threshold luminance increment and the background luminance for visual increment detection, is known to become linear for high luminances. This so called Weber-law means that at high luminances the threshold is caused by the detection apparatus, and not by the quantum noise of the stimulus itself. A simple machine implementing the Weber-law is discussed. This machine obviates the need for an internal noise source (or dark light). It is the combined result of an apparatus that reduces the output event rate by causing the quantum to spike ratio to follow the input intensity, and a detection criterion that needs a constant number of extra output events to generate a positive response. The dynamic properties of the machine are described by the solutions of a simple though nonlinear differential equation. The supra threshold properties prove to mimic several of the responses known to occur at ganglion cell level in the cat's retina. A tentative model of an on-center receptive field is presented, and results obtained by simulating this model on a digital cumputer are compared with some recent electrophysiological findings. Finally a possible extension of the model to a full on-center/off-surround receptive field model is discussed.

A feature extractor for curvilinear patterns: a design suggested by the mammalian visual system.

Abstract: A feature extractor for a pattern recognizer which can effectively process curvilinear drawings has been synthesized and simulated on a digital computer. The design of the network was suggested by the visual system of higher animals — especially the structure of the receptive fields of cortical neurons. This feature extractor is a multilayered parallel network composed of “analog threshold elements”. It consists of six layers in cascade. The first layer is a two-dimensional array of photoreceptors. The second layer is a contrast-detecting layer, each element of which has an “on”-center-type receptive field. The third one is a line-detecting layer. An element of this layer corresponds to a “simple” cortical cell, and responds to lines whose orientation is proper for the element. Each element has a receptive field consisting of an elongated excitatory region flanked on either side by inhibitory regions. The fourth layer is also a line-detecting layer, but each element, which corresponds to a “complex” cell, is not sensitive to the exact position of the line. An element of the fifth layer, which may correspond to a “hypercomplex” cell, responds when the line detected in the preceeding layer is curved. In the final layer, the curvature of the line is detected regardless of the orientation of the line, that is, an element of this layer gives an output approximately proportional to the curvature of the line presented in its receptive field.

Signal transmission in random spike trains with applications to the statocyst neurons of the lobster

Abstract: The power spectral density of a modulated Poisson point process is derived, the results showing that modulation of the rate of the process introduces power only at those frequencies contained in the modulation, unlike the case of very “regular” carriers.

Models of the processing of quantum signals by the human peripheral retina.

Abstract: The retinal rods are usually assumed to function, at least under certain stimulus conditions, as single-photon-detectors. Thus the problem arises how a stream of events (the elementary photon responses) with Poisson statistics, but in general with a modulated mean, can be processed. Since the human visual system has a dynamic range of some 10 decades and optic nerve fibers cannot carry higher event rates than, say, 400–1,000 events/sec, “event rate reduction” seems to be necessary. Event rate reduction of modulated Poisson processes is possible with K-scalers (devices that only pass the K-th event following the previous output event). In view of the enormous dynamic range mentioned above, adaptation of the scaling factor is necessary. An adapting scaler that implements the Weber-law proves to furnish an interesting receptor model. Such a Weber-machine can function as a single-event detector at low input intensities and as an event rate differentiator at high intensities. Absolute threshold measurements have led to the idea that at least 2–12 photons have to be absorbed in a retinal sampling-unit within some coincidence interval T in order to perceive a flash. Such a coincidence detection can be combined with the idea of adapting scalers in a “deVries-Rose machine” or “square-root-coincidence scaler” (van de Grind and Bouman, 1968). Placing the deVries-Rose machines as centres of convergence at the bipolar level and the Weber machines at the receptor level, we get a model that makes understandable both absolute threshold phenomena and increment threshold data for the scotopic as well as the photopic range of luminances. The incorporation of adaptation phenomena by the creation of “adaptation pools” is possible if the horizontal cells are postulated to regulate the scaling factors of the receptors (Weber machines) and the amacrine cells those of the bipolars (deVries-Rose machines). The stepresponses of the two types of machines as displayed in P.S.T.-histograms can be directly compared with those of many visual (and auditory) cells as reported in the literature. This greatly reinforces our trust in the present approach.

On the asymptotic rate of non-ergodic information sources.

Abstract: Before proceeding to the formulation of the problem we are treating in this paper, we shall remind some simple facts upon which the concepts given in the sequel are based. Let us imagine such a situation when a receiver is expecting one of the messages z belonging to a finite set Z of messages which are possible to come under the given situation. The uncertainty of the situation described is evidently the greater, the larger is the number of all a priori possible messages; let us denote the latter number, i.e. the number of messages in Z, by \z\. Originally the quantity of information which is needed to remove this uncertainty, is numerically expressed by the number log \z\, where the logarithm.is taken to the base 2; in other words, log \z\ represents the quantity of information expressed in bits which is contained in any message z in Z reaching the receiver. Consequently, the number log \Z\ as a measure of uncertainty may be called the logarithmic uncertainty of the set Z.

Synthesis of reverberating neural networks.

Abstract: In the first Part explicit methods are given, following the work of Refs. [1–3], for the design of networks whose reverberations cannot exceed prefixed periods no matter how coefficients are changed, as well as of networks obeying pre-assigned constants of motion. In the second Part the role of coupling strengths in determining cyclic behaviors is investigated and shown to lead to new methods for the design of reverberating networks.

On the Amount of Information Contained in a Sequence of Independent Observations

Abstract: In the present paper basic properties of a Chernoff bound established previously are summarized and new ones are derived. The Chernoff bound is figuring as an asymptotic parameter in a formula for Shannon's information contained in a sequence of independent observations concerning a discrete parameter. By 9 we denote a random variable taking on a finite number of values 1, 2,... and by £ another random variable with a sample measurable space (X, S£). By £, U E, 2 ,... subsequent realizations of £, will be denoted; they are supposed to be mutually independent for any given value of 9. Finally, 1(9, £ lt ..., £ \") will denote the Shannon's information contained in (£ l5 <* 2 , ..., £, \") concerning 9. The information 1(9, tf x ,..., £ \") can serve as an important numerical characteristic of the following statistical problem: the statistician is interested in the value of 9 which is not directly observable but he can observe the values of the value of 9 can be uniquely determined with probability 1. (Remark that the first equality holds iff 9 and £ are independent whereas the second equality holds iff there exists a deterministic relation between 9 and £.) It can be relatively very easily shown (cf. Th. 1 in [1]) that* (1) J(0,f 1) ...,g«JJ(0)-exp(-nJj), where D e [0, + 00] depends on a conditional distribution P^ g of £ only. The parameter D has been independently evaluated by A. Renyi [2] and by the author (cf. Th. 2 in [l]); it was shown that D is the Chernoff bound [3] corresponding to a Bayes testing of the simple hypotheses Jf ; : 0 = i, i = 1, 2 on the basis of (£, u £ 2 ,... » We write anxa~ X\" instead of an = aX n+oW , n = 1, 2,...

Eine mathematische Formulierung für Reiz-Reaktionsbeziehungen retinaler Ganglienzellen

Abstract: 1. In order to describe stimulus-response relationships for retinal ganglion cells a mathematical formulation is presented on the basis of experimental data and some simple assumptions. This concept involves two mechanisms — an excitatory and an inhibitory one — both extending over the whole receptive field. 2. The following formula $$S\left( I \right) = \frac{{c{\text{ }}{I \mathord{\left/ {\vphantom {I {I_S - 1}}} \right. \kern- ulldelimiterspace} {I_S - 1}}}}{{1 + a{\text{ }}a{I \mathord{\left/ {\vphantom {I {I_S + 1}}} \right. \kern- ulldelimiterspace} {I_S + 1}}}}$$ is used for description of the excitatory responses (on-response for on-center neurones, off-response for off-center neurones). The value ofa depends on the area of light stimulation,c is a constant;I/ISdesignates the ratio of stimulus brightness to threshold brightness. 3. Thresholds and suprathreshold response curves for concentric stimuli are described quantitatively by the formula. The experimental data were obtained by computer counts of spike discharges during 200 and 500 ms following the exciting light increment or decrement. 4. Ricco's, Weber-Fechner's and Stevens's laws are included in our conception as approximations of neuronal summations. These relations are limited to certain stimulus ranges; in contrast the above response function saturates at certain maximum discharge rates, as found by the S-shaped experimental curves; thus the formula is valid over the whole range of stimulation from threshold to very high intensities. 5. Thresholds as well as excitatory and inhibitory effects depend on background illumination and stimulus parameters. Therefore, center and surround size depend on these factors. 6. The formulation is set up for stationary responses and consequently does not describe time dependent characteristics. 7. Within these limits on-center and off-center neurones appear to have identical stimulus-response functions for adequate stimuli. Since in our experiments light increments and decrements were not symmetrical with respect to background illumination, a factor of 2 had to be introduced corresponding to the lower discharge rates of off-center-neurones.

Signal stabilization and noise suppression in neural systems

Abstract: Neural activity is viewed as a stochastic point process, in which information resides in the modulation of a background of spontaneous activity. Characteristic features of the spatial and temporal mapping of sensory signals are discussed. One of the puzzling aspects of neural functioning is the integrity of the signal in its passage toward higher brain centers, in view of the fundamentally noisy response of the individual neuron. It is shown, that a process, we call image stabilization, is a direct consequence of the particular mapping function exemplified by lateral inhibition and adaptation.

A mechanical model of the secondary endings of mammalian muscle spindles

Abstract: A mechano-electric model of the secondary endings of the mammalian muscle spindle receptors has been developed. The model involves a mechanical system with second order transfer dynamics connected to a zero order mechano-electric transducer with constant gain.

Probabilistic models for determining the input-output relationship in formalized neurons. I. A theoretical approach.

Abstract: In order to investigate under which assumptions one can expect to determine the probabilistic response of a neural unit to an incoming stochastic excitation, we propose a model that endows the neuron with a variable threshold. It is shown that a fairly complete statistical description of the input-output relationships can be obtained when the input is Poisson, non-homogeneous Poisson and, finally, any stationary continuous stochastic process.

The transformation induced by light stimulus on the retinal discharge: study of the interval distribution at high frequencies of sinusoidal stimulation.

Abstract: A further step in the analysis of the relationship between light stimulus and cat retinal ganglion cell discharge is presented, which completes the study of the transformation induced by light stimulus on the distribution of the interpulse intervals. The interval distribution is shown to be invariant under a change of the light stimulus, if the following change of variable is performed on the intervals: $$\theta = \mathop {\int r }\limits_{t_1 }^{t_2 } (t)dt.$$ t 1 and t 2 being the times of occurrence of the impulses of the interval, and r(t) the average number of cell impulses per unit time.

A mode control model of a neuron's axon and dendrites.

Abstract: The ability of a neuron network to process information depends upon the ability of the individual neurons to transport impulses and to control the signal transport process in other neurons. The transport process for the action potential seen at the axon depends upon the excitable characteristic of the neural membrane. Propagation of signals in the dendrites, where synaptic imputs are most likely processed, is not clearly understood. Extracellular recordings of dendritic systems indicate that the dendrites are partially excitable and can conduct spikes. Further, electrical stimulation of the reticular formation or specific thalamic nuclei suggest that the conduction process can be modified in the dendrites of cortical cells. A Mode Control model is described which demonstrates many of the observed transport and control properties of dendrite and axon membrane. The model is based upon a simple extension of Fitzhugh's BVP model. Lateral transport over the membrane has been introduced by applying Kirchhoff's laws. Reinterpreting the variables, the influence of membrane potential, pH, and calcium ions can be identified. Modification of the voltage-current characteristic of the membrane model can change the axon model to a dendrite model. The dendrite model possesses a diffusion equation mode, a wave equation mode and a pulse mode. Signals are transferred in the wave and pulse mode and blocked in the diffusion mode. The dendrite's mode is controlled by the “resting” depolarization level. Experimental evidence tends to confirm these phenomena.

A hypothetical synaptic-neural-behavioral model of operant learning.

Abstract: 1. General biological theories of learning are mentioned. The importance of developing more specific formulations is argued. 2. A neural-behavioral model of operant learning is presented. The model shows hypothesized, functional connections among various neurons and the muscles which control behavior. The operation and role of various neurons are described in detail. This model demonstrates the necessary condition that the physiological changes which result from an organism's reinforcement and feedback reaction to its response are able to account for the increased probability of correct response observed behaviorally when an organism is retested following training. Proposed changes occur only at those neurons which are instrumental in establishing response. Therefore fortuitous changes are avoided. 3. A synaptic-neural model is proposed as part of the neural-behavioral model in order to explain how changes in learning may be physically realized. This model involves the interaction of transmitter molecules but only to a significant extent when two adjacent synapses of the neural-behavioral model are concurrently highly active. The suggested result of the transmitter interaction is a blockage of postsynaptic receptor sites. A kinetic description is proposed for these reactions and solved numerically by computer techniques. With suitably selected values for the rate constants, this model is shown to yield a formulation consistent with the requirements of the neural-behavioral model. 4. The features and assumptions of the model presented and of several other biological models are discussed. More experimental investigations into the interaction of presynaptic terminals on the same neuron during paired excitation are encouraged. Some predictions about behavior are derived from the model. Comparison with behavioral data is made. The goals of hypothetical modeling are stated.