Showing papers in "Kybernetika in 1972"

A theory of biological pattern formation.

Abstract: One of the elementary processes in morphogenesis is the formation of a spatial pattern of tissue structures, starting from almost homogeneous tissue. It will be shown that relatively simple molecular mechanisms based on auto- and cross catalysis can account for a primary pattern of morphogens to determine pattern formation of the tissue. The theory is based on short range activation, long range inhibition, and a distinction between activator and inhibitor concentrations on one hand, and the densities of their sources on the other. While source density is expected to change slowly, e.g. as an effect of cell differentiation, the concentration of activators and inhibitors can change rapidly to establish the primary pattern; this results from auto- and cross catalytic effects on the sources, spreading by diffusion or other mechanisms, and degradation. Employing an approximative equation, a criterium is derived for models, which lead to a striking pattern, starting from an even distribution of morphogens, and assuming a shallow source gradient. The polarity of the pattern depends on the direction of the source gradient, but can be rather independent of other features of source distribution. Models are proposed which explain size regulation (constant proportion of the parts of the pattern irrespective of total size). Depending on the choice of constants, aperiodic patterns, implying a one-to-one correlation between morphogen concentration and position in the tissue, or nearly periodic patterns can be obtained. The theory can be applied not only to multicellular tissues, but also to intracellular differentiation, e.g. of polar cells. The theory permits various molecular interpretations. One of the simplest models involves bimolecular activation and monomolecular inhibition. Source gradients may be substituted by, or added to, sink gradients, e.g. of degrading enzymes. Inhibitors can be substituted by substances required for, and depleted by activation. Sources may be either synthesizing systems or particulate structures releasing activators and inhibitors. Calculations by computer are presented to exemplify the main features of the theory proposed. The theory is applied to quantitative data on hydra — a suitable one-dimensional model for pattern formation — and is shown to account for activation and inhibition of secondary head formation.

On a response characteristic of a mathematical neuron model.

Abstract: A mathematical neuron model in the form of a nonlinear difference equation is proposed and its response characteristic is investigated. If a sequence of pulses with a fixed frequency is applied to the neuron model as an input, and the amplitude of the input pulses is progressively decreased, the firing frequency of the neuron model, regarded as the output, also decreases. The relationship between them is quite complicated, but a mathematical investigation reveals that it takes the form of an extended Cantor's function. This result explains the “unusual and unsuspected” phenomenon which was found by L. D. Harmon in experimental studies with his transistor neuron models. Besides this, as an analogue of our mathematical neuron model, a very simple circuit composed of a delay line and a negative resistance element is presented and discussed.

Reversal time distribution in the perception of visual ambiguous stimuli.

Abstract: Reversal of perspective for ambiguous optical stimuli (Necker cube, Schroder staircase, honeycomb) has been studied, determining the statistical distribution of time intervals spent on each percept. The experimental distributions can be fitted with the gamma function, characterized by two parameters n, b. The two parameters are not independent, showing a correlatiomn ϱ = 0.74. Subsequent intervals appear to be largely independent; from the beta distribution for the fraction of time spent on a given percept, one can show that the subjects differ only in regard to the variance of this variable.

Neural Expectation: Cerebellar and Retinal Analogs of Cells Fired by Learnable or Unlearned Pattern Classes

Abstract: Neural networks are introduced which can be taught by classical or instrumental conditioning to fire in response to arbitrary learned classes of patterns. The filters of output cells are biased by presetting cells whose activation prepares the output cell to “expect” prescribed patterns. For example, an animal that learns to expect food in response to a lever press becomes frustrated if food does not follow the lever press. It's expectations are thereby modified, since frustration is negatively reinforcing. A neural analog with aspects of cerebellar circuitry is noted, including diffuse mossy fiber inputs feeding parallel fibers that end in Purkinje cell dendrites, climbing fiber inputs ending in Purkinje cell dendrites and giving off collaterals to nuclear cells, and inhibitory Purkinje cell outputs to nuclear cells. The networks are motivated by studying mechanisms of pattern discrimination that require no learning. The latter often use two successive layers of inhibition, analogous to horizontal and amacrine cell layers in vertebrate retinas. Cells exhibiting hue (in)constancy, brightness (in)constancy, or movement detection properties are included. These results are relevant to Land's retinex theory and to the existence of opponent- and nonopponent-type cell responses in retinal cells. Some adaptation mechanisms, and arousal mechanisms for crispening the pattern weights that can fire a given cell, are noted.

The estimation of the frequency response function of a mechanoreceptor

Abstract: Widespread use has been made of linear systems theory to describe the input-output relations of receptors. The frequency response function of an insect mechanoreceptor, the tactile spine of the cockroach, has been estimated by using deterministic inputs (sines and step functions), deterministic inputs added to a stochastic, auxiliary signal (band-limited white noise), and a stochastic input alone. When a stochastic input is used, spectral analysis provides methods for estimating the coherence function as well as the frequency response function. The coherence function of the tactile spine is low, suggesting that the linear frequency response function is not a good characterization of the input-output relation of the receptor. Two non-linearities, rectification and phase-locking are described. Rectification can reduce the absolute value of the frequency response measured using sine waves of all frequencies without changing its form. Phase-locking changes the form of the frequency response function at high frequencies. Use of a stochastic auxiliary signal linearizes the input-output relations of the receptor in the sense that the cycle histograms obtained with sinusoidal inputs are more sinusoidal and the form of the frequency response function agrees with that predicted from the step response over a wider range of frequencies.

Vestibular postural control model.

Abstract: Current models for physiological components and a posture control experiment conducted with three normal subjects form the basis for a model which seeks to describe quantitatively the control of body sway when only vestibular motion cues are used. Emphasis is placed on delineating the relative functional roles of the linear and the angular acceleration sensors and on modeling the functional interface between these sensors and the initiation of compensatory responses at the ankle joint.

Muscle spindles in muscle control

Abstract: Afferent discharges from single muscle spindles in the frog were recorded from the dorsal root ganglion in the reflexively active loop and in the same loop opened by cutting the dorsal roots. The closed loop response (i.e. pulse frequency) to muscle stretch was smooth and without “dead zones”, as compared to the response to the same stretch when the loop was open. The variations in gain between the open and closed loop modes of operation are shown to be small, both for muscle spindle afferent outflow and for muscle tension.

Muscle spindles in muscle control. 3. Analysis of adaptive system model.

Abstract: As an extension of a previous paper (Inbar, 1972/11) wherein the servo model of muscle control was analyzed and found insufficient in describing muscle control phenomena, an optimal adaptive model is proposed, where muscle spindles serve as the sensors of muscle dynamics. The concept of an adaptive system is defined and illustrated within the framework of an algorithmic adaptive, or "learning" scheme. A speculative attempt is made to correlate the various adaptive model components with the anatomical structures involved in muscle control. The paper concludes with a general discussion of the adaptive system approach to physiological systems.

[Feedback circuit of the knee tendon reflex in the walking-stick insect carausius morosus: reactions on passive movements of the tibia].

Abstract: 1. Passive flexion and extension of the femur-tibia-joint causes forces which are directed against the passive movements. Quantitative measurements of these forces are in accordance with the results obtained from step stimuli in open-loop-experiments (1965, 1972). Repetition of the experiments at the same joint often leads to different results: the animal is apparently able to change the amplification of the system. 2. If one brings the joint in a new position by hand, the tibia returns to its starting-point only very slowly. (Flexibilitas cerea). As a quantitative measure for Flexibilitas cerea the time interval is taken, during which a formerly fully extended joint returns to the 90°-position after a 30 sec flexion to 50° (t90) · t90 is not correllated with a quantitative measure of Thanatosis. Therefore it is not allowed to combine Thanatosis and Flexibilitas cerea to Katalepsis. — Legs whose receptor tendons were cut, show no Flexibilitas cerea. The behaviour of Flexibilitas cerea is explained by the attributes of the control system. 3. The reaction on very slow constant flexion and extension speeds (2,4°/sec – 0,3°/min) are described. Intact legs show a larger hysteresis at all speeds than legs with cut receptor tendons: it seems the control system reacts at those slow speeds. It responds only to the dynamic part of the movements, however not to the static one.

Der „Kniesehnenreflex” bei Carausius morosus: Übergangsfunktion und Frequenzgang

Abstract: Stretching and releasing the femoral chordotonal organ caused by a movement of the tendon of the organ gives rise to a movement of the tibia. This reaction is called “Kniesehnenreflex” (knee-tendon-reflex). Its step response can be described in the following manner: After a certain reaction-time (at flexion 0.02–0.06 sec, at extension 0.06–0.2 sec) the tibia moves with a maximum speed between 150°/sec and 1000°/sec at extension and between 20°/sec and 450°/sec at flexion. The amplitude of the movement and the maximum speed of tibia movement are correlated. After reaching the extreme position the tibia returnes nearly to its starting-point with half lifes of 3–58 sec after a flexion and 7–232 sec after an extension. — The frequency response shows a strong decrease of the amplitude of the tibia at about 1 Hz. Above 2 Hz the amplitude is only a few degrees. The phase shift between stimulus and reaction increases with increasing frequency. Big individual differences are observed. A step stimulus, which is given in addition to a sinoidal stimulus causes a response at all frequencies. — Slow stretching and releasing the chordotonal organ with constant speeds causes movements of the tibia even at stimulus speeds of 0.002 mm/min. — It is discussed: the significance of the results for the theory of the control mechanism at walk, the stability of the control system in connection with the rocking-movements of the animal and the control of Flexibilitas cerea.

A study of the time and frequency characteristics of the potentials evoked in the acoustical cortex

Abstract: Evoked potentials in the auditory cortex of the cat are measured by applying auditory stimulations in the form of tone bursts of 700 Hz. Transient evoked potentials obtained in this way are transformed to the frequency domain using a Laplace Transform. The amplitude frequency characteristic obtained with this semi-empirical method depicts maxima of EEG-amplitude in frequency ranges of 10–13 Hz and 60–80 Hz. The correlation between the time course of evoked potentials and spontaneous activity of the brain and the efficiency of the method used are pointed out.

Analysis and simulation of networks of mutually inhibiting neurons.

Abstract: Networks of mutually inhibiting neurons are analyzed and simulated on a digital computer. In the analysis and simulation a continuous-variable model of the neuron is used as the basic element. It consists of a many-input adder, a first-order low-pass filter and a diode-type nonlinearity. A mutually inhibiting network is formed by connecting the output of every element to inputs of the other elements through weight-coefficient setting units. Each element of the network is assumed to receive a certain number of constant inputs from elements of other networks.

The influence of the retinal inhomogeneity on the perception of spatial patterns.

Abstract: From the fact that the retina is rather inhomogeneous, it can be inferred that the perception of spatial patterns of appreciable extent will be dependent on the retinal location. Anatomical, electrophysiological and psychophysical findings substantiate the claim that the retina is very inhomogeneous of composition. In order to investigate the influence of this inhomogeneity on the perception of patterns, a model of spatiotemporal signal processing in the retina was developed on the basis of a paradigm for the Weber type adaptation. Such “scaling-ensembles” proved successful in the prediction of spatiotemporal modulation transfer in the human fovea (Koenderink et al., 1971). One prediction of the present model is that certain spatial patterns are optimally detected at well defined retinal locations, dependent on the spatial frequency content of the stimulus. A confrontation of the model's predictions with measurements published by Bryngdahl (1966) enabled us to estimate some of the relevant parameters of the retinal receptive fields as a function of the eccentricity. We obtained estimates that compare reasonably well with previously known values; for instance with values of acuity and anatomical measurements. The present discussion bears relevance on the question of whether the retina is composed of independently tuned spatial frequency filters at any retinal location, or whether the tuning is with respect to the eccentricity.

The hippocampal EEG-activity and a systems analytical interpretation of averaged evoked potentials of the brain

Abstract: Evoked Potentials in the hippocampus dorsalis are measured using chronically implanted and freely moving cats in applying auditory stimulations in the form of tone bursts of 3000 Hz. The hippocampal evoked potentials are characterized by 3 positive (I, III, V) and 3 negative peaks (II, IV, VI). Peaks I to VI have latencies of about 10, 28, 50, 75, 95 and 125 msec. These responses are then analyzed with a Laplace transform in order to obtain the hippocampal frequency characteristics. The amplitude frequency characteristic depicts resonance maxima of EEG-amplitude in theta (3–8 Hz) and beta (18–32 Hz) frequency ranges. A resonance in the frequencies of 3–8 Hz was expected because of the spontaneous hippocampal theta activity. Therefore this finding emphasize the reliability of the mathematical method used. On the other hand the existence of a hippocampal beta selectivity is highly remarkable and apparently the hippocampal activity is regulated at least by two different systems. The use of the mathematical method (Laplace transform) indicates that the simple knowledge of the latencies and the number of potential waves(usuallydenoted as P 1, P 2, ..., N 1, N 2 ...) cannot allow exact statements on mechanisms causing the formation of these peaks. Rather the slope and slope changes of the waves are determining. Different waves in the transient evoked response can be generated from a mechanism having only one resonant maximum in the frequency domain.

Die Sehfelder der zentralen Ommatidien in den Appositionsaugen von Apis mellifica und Cataglyphis bicolor (Apidae, Formicidae; Hymenoptera)

Abstract: Experimental equipment has been developed to make possible continuous recordings of intensity distribution curves as a function of angle of incidence of light in single ommatidia of arthropod compound eyes. — As preliminary experiment, the visual fields of ommatidia in Limulus, Apis and Cataglyphis have been ascertained without a light measuring instrument. A point source was moved through the visual field and the angular position of the light source on both sides of the visual field at which the rhabdome in the cut-off eye viewed from proximal turned dark was determined. In the dorsal part of the Limulus eye, the cranio-caudal width of the visual field is 42.6±0.3°. The width of the visual field of central ommatidia in Apis is 6.68±0.14° in the dorsoventral plane and 7.42±0.24° in the cranio-caudal direction, in Cataglyphis 15.5±0.5° and 12.5±0.4° respectively.— Similar Gaussian curves for light and dark adapted ommatidia resulted from the continuous recordings of intensity distribution curves in Apis. The rotatory symmetric curve of the worker bee has a half-width of Δρ=2.57°. The standardized curve of amplitude one may be approximated by the function y=exp (-0.41 [degree−2]ϕ2). In Cataglyphis, the half-width of the intensity distribution curve is Δρ=8.8° in the dorso-ventral plane and Δρ=6.8° in the cranio-caudal plane. Near the axis, the functions y=exp(-0.04 [degree−2]ϕ2) and y=exp(-0.06 [degree−2]ϕ2) approximate the standardized curves. — Knowledge of intensity distributions in connection with interommatidial angles Δρ allows estimation of contrast transfer and resolving power of the array of the dioptric systems. Correlations with behavioural findings are attempted.

Cyclic modes in artificial neural nets

Abstract: Artificial neural nets constructed of dicrete populations of 200–1000 formal neurons have been studied through computer simulation. Among the basic assumptions of operation of these nets are the following: a) Each neuron fires at times which are integral multiples of the synaptic delay τ. b) It produces the appropriate PSP's after τ. c) All the neurons have the same refractory period and d) temporal summation occurs without decrement, for a period less than the synaptic delay. The nets were specified by a number of parameters: fraction of inhibitory neurons in the population, average number of connections to each cell, threshold for cell firing. These parameters did not determine the detailed “microscopical” structures of nets which was established separately on a random basis.

Zur Beeinflussung der Bewegungsweise eines Beines von Carausius morosus durch Amputation anderer Beine

Abstract: Amputation of a leg alters the amplitude of the adjacent ipsilateral legs during walking: Amputation of a middle leg encreases the amplitude of the foreleg especially by changing the rear extreme position. Amputation of a foreleg reduces the amplitude of the middle leg especially by changing the front extreme position. There is no significant influence observable on contralateral legs.

[Using the Fick's shifting hypothesis to explain dyschromatopsia in a model computation for data processing of disordered colored vision in man].

Abstract: Nach der von Fick postulierten Verschiebungshypothese entstehen die dichromatischen Systeme aus dem normaltrichromatischen System dadurch, das die spektrale Erregbarkeitskurve einer der Komponenten mit der einer anderen identisch geworden ist, das aber die betreffende Komponente mit ihren spezifischen Sinnesempfindungen an sich erhalten ist. Die anomalen Farbensysteme ergeben sich nach dieser Hypothese daraus, das die Verlagerung der spektralen Erregbarkeitskurve einer Komponente nur in Richtung zu der benachbarten hin erfolgt, nicht aber mit dieser identisch wird.

Markov Process of Maintained Impulse Activity in Central Single Neurons

Abstract: To clarify the stochast properties of the maintained impulse activity of the central nervous system, we proposed a measure of statistical dependency on the basis of Shannon's entropy. This measure could provide the Markov properties of the neural impulse sequences, representing the necessary and sufficient condition for the statistical dependence. The order of Markov process of the sequence is determined by the conditional entropy which is derived from the joint entropy. Here the joint entropy in the case of Gaussian process is directly related with the covariance matrix which is substituted for the matrix of the serial correlation coefficients. Therefore the condition to determine the order of Markov process is obtained by the equation of the matrices of the serial correlation coefficients. The order of Markov process of the neural impulse sequences recorded from the mesencephalic reticular formation (MRF), red nucleus (RN), and lateral geniculate nucleus (LGN) neurons has been estimated. The maintained impulse activity of the MRF and RN neurons had from the 2-nd to 4-th order Markov property, while that of the LGN had no Markov property, in the consecutive impulse sequences.

Opponent color coding: A mechanistic model and a new metric for color space.

Abstract: A mechanistic model of opponent color coding in the human retina is described. This description is based on the concept of the scaling-ensemble (Koenderink et al., 1971). All receptors that are a member of the same scaling-ensemble adapt together, regardless of their type. If the adaptation is the Weber-type adaptation, then it is shown that the sum of the outputs of receptors of an ensemble displays typical on-cell characteristics. In contradistinction with the phasic response of the sum signal, difference signals are of a typical tonic type. With three kinds of cones, one can essentially form two opponent signals and one non-opponent signal. The responses of the opponent and the non-opponent channels to spatiotemporal modulations of the input signal are entirely different. In this model the interaction betweenthe opponent and the non-opponent channels is such that even large intensity modulations do not disturb the opponent responses very much. The opponent signals carry almost entirely information about the spectral distribution of the input signal. The results of computer simulation studies of the proposed model are compared to electrophysiologically determined responses of cells in the monkeys lateral geniculate body. In the second part of this paper we make use of the line element approach in order to be able to confront the model's predictions with psychophysical measurements. This line element is closely related to those proposed earlier by Helmholtz (1896) and Schrodinger (1920). It introduces a hyperbolic geometry in perceptual color space. This specific metric leads to the vector model for brightness addition. In addition it is possible to regard the Bezold-Brucke hue shift as the direct result of the curvature of color space, induced by our metric.

State space approach to discrete linear control

Abstract: The state space approach to the synthesis of a class of discrete linear control systems is given. Both time-optimal and quadratic-cost problems are considered and a comparison to classical methods is made via the technique of pole assignment.

Nonstationary power spectrum analysis of the photic alpha blocking.

Abstract: The dynamics of the EEG activity under light stimulation was investigated in terms of the nonstationary power spectrum method. The alpha wave was blocked by light stimulation, however the blocking was temporary, and the alpha activity recovered to that of the resting state even though under light. Moreover the alpha rhythm was also blocked by light off. The frequencies of the preand post-blocked activity were different. The frequency of the post-blocked wave shifted gradually downward and became stable after 3–4 sec.

Versuch einer quantitativen Beschreibung des Formensehens der Honigbiene

Abstract: 1. Form discrimination by honeybees can be measured when individuals are trained to select a rewarded shape in preference to other, unrewarded ones (Table 2). In these experiments, the values of discrimination for some pairs of shapes depend upon which of the pair is rewarded (“symmetrical, asymmetrical discrimination”, Table 3, 4). 2. Two groups of possible mechanisms of form discrimination will be discussed. Experimental findings preclude the exclusive use by the bees of any one of those mechanisms. The following discrimination function, however, describes the present as well as previously reported results: $$U = \left| {C_{\text{1}} \frac{{R^ + + R^ - }}{G}F^ + + C_2 {\text{(log}}K^ + {\text{ - log}}K^ - {\text{)}}} \right|$$ (Figs. 4, 5, 7, 8, 9, 10). R+, R−, G and F+ are parts of areas (Fig. 1), K+ and K− contour lengths of the shapes to be compared. 3. The weighting factors, C1 and C2, are apparently given different values by the bee for different shape combinations. Some results might support Mazochin-Porshnyakov's (1969) hypothesis that bees can also recognize other features of the shapes, according to the problem to be solved (Sect. D).

Holographic aspects of temporal memory and optomotor responses.

Abstract: A mathematical analogy between the holographic models of temporal memory and Reichardt's optomotor theory is stressed. It is pointed out that the sequence of operations which is essential to any holographic model of brain function. ing is actually carried out by a nervous structure in the opto- motor behaviour. Some implications in both the optomotor theory and the hypothesis of neural holographic processes are further sug- gested.

Dynamische Eigenschaften von Nervennetzen im visuellen System

Abstract: The preprocessing of optical information in the visual system takes place in the two-dimensional homogeneous nervous nets of the retina and the geniculate body. These networks can be considered as band-pass filters for space-dependent oscillations if the input stimuli are independent of time. If the synapses of the neurons have timefrequency dependent properties the performance of the system in the space domain, which is important for pattern recognition, is determined by the time dependence of input signal. For a description of these networks in this investigation the space spectrum for various values of the time frequency ω is used. The answers of real nervous nets can be interpreted by the model when the two-dimensional input signals are switched, flickered or moved. For this reason these dynamic stimuli are necessary for an analysis of the cortex. The theoretical combination of space- and time-dependent filtering is essential for an understanding of cortical transformations.

Methods for comparison of the efficiency of biological and technical systems

Abstract: In this work the methods of the communication theory for binary detection, multiple detection and extraction are applied to biological systems. It is the objective of this investigation to compare the performance of optimal and biological systems in receiving signals superimposed by noise. The required mathematical relations and methods of measurements are derived. In the second part of this work pattern recognition experiments (multiple detection) at the human visual system with stationary and time variant patterns are described. The comparison of the performance between optimal and biological system shows that the human visual system acts in a suboptimal way. From some other detection experiments it can be concluded that the recognition process is describable by spatial cross-correlation.

Localized EEG alpha feedback training: a possible technique for mapping subjective, conscious, and behavioral experiences.

Abstract: Subjects who received EEG alpha feedback recorded from two homologous scalp areas (central-temporal) were trained to have ON-OFF control over the left and right sides. The partial success in demonstrating localized control suggests that subjects may be trained for very specific control. Localized training may be used to partition the subjective, conscious and behavioral experiences associated with selected EEG patterns and to develop an independent subjective physiological language. Applications to medicine and altered states of consciousness are discussed.