Showing papers in "Kybernetika in 1974"

Model of brain rhythmic activity. The alpha-rhythm of the thalamus.

Abstract: 1. A model of a neuronal network has been set up in a digital computer based on histological and biophysical data experimentally obtained from the thalamus; the model includes two populations of neurons interconnected by means of negative feedback; in the model allowance is also made for other sort of interactions. 2. To test the hypothesis that the alpha-rhythm (8–13 Hz rhythmic activity characteristic of the EEG) is a filtered noise signal the simulated neuronal network was stimulated by random trains of pulses with a Poisson distribution. The density of pulses fired by the simulated neurons was computed as well as the oscillations of the mean membrane potential of the population of simulated neurons. The latter was found to be equivalent to the experimentally obtained alpha rhythms. 3. In order to test the hypothesis that several noise sources are responsible for thalamo-cortical coherences three simulated neuronal networks were coupled together using several noise sources as secondary inputs. It was shown that although all the networks produced simulated alpha signals with identical spectra they could have significantly different values of coherence depending on the relation between correlated and uncorrelated input signals. 4. The model was analysed by means of linear systems analysis after introducing the necessary simplifications and approximations. In this way it was possible to evaluate the influence of different physiological or histological parameters upon the statistical properties of the resulting rhythmic activity in an analytical form. 5. By changing the model parameters it was shown that a family of spectral curves could be obtained which simulated the development of the EEG as function of age from a predominantly low frequency to a clearly rhythmic type of signal. This was shown to depend mainly on the feedback coupling parameters.

A vector-magnitude model of contrast detection.

Abstract: A model of contrast detection is proposed in which the visibility of a low-contrast stimulus is determined by a non-Euclidean magnitude of the vector composed of the responses of a large number of independent channels. Although the vector-magnitude model is quite different from the probability-summation model which has been suggested previously, the contrast thresholds and psychometric functions predicted by the two models can be in agreement within 10% for up to 105 channels in the system. Presently available experimental evidence is insufficient to establish the correctness of either model, but the computational simplicity of the vector-magnitude model makes it interesting, if only as a useful approximation to the probability-summation model.

A method of statistical neurodynamics.

Abstract: A method of statistical neurodynamics is presented for treating ensembles of nets of randomly connected neuron-like elements. The concept of a macrostate plays a fundamental role in statistical neurodynamics and a criterion is given for ascertaining that given macroscopic quantities together constitute a macrostate. The activity of a nerve net is shown to be a macrostate and the equation of the dynamics of the activity is elucidated for various ensembles of random nerve nets. It is shown that the distance between two microstates can also be treated as a macrostate in a generalized sense. The equation of its dynamics represents how the distance between two states changes in the course of state transitions. The dynamics of distance reveals interesting microscopic properties of random nerve nets, such as the stability of state-transition, the transient lengths, etc.

Improved neuronal models for studying neural networks.

Abstract: Previous neuronal models used for the study of neural networks are considered. Equations are developed for a model which includes: 1) a normalized range of firing rates with decreased sensitivity at large excitatory or large inhibitory input levels, 2) a single rate constant for the increase in firing rate following step changes in the input, 3) one or more rate constants, as required to fit experimental data for the adaptation of firing rates to maintained inputs. Computed responses compare well with the types of neuronal responses observed experimentally. Depending on the parameters, overdamped increases and decreases, damped oscillatory or maintained oscillatory changes in firing rate are observed to step changes in the input. The integrodifferential equations describing the neuronal models can be represented by a set of first-order differential equations. Steady-state solutions for these equations can be obtained for constant inputs, as well as the stability of the solutions to small perturbations. The linear frequency response function is derived for sufficiently small time-varying inputs. The linear responses are also compared with the computed solutions for larger non-linear responses.

Vom femoralen Chordotonalorgan gesteuerte Reaktionen bei der Stabheuschrecke Carausius morosus: Messung der von der Tibia erzeugten Kraft im aktiven und inaktiven Tier

Abstract: In the Introduction (A) there is a list of unsolved problems concerning the role of the femoral chordotonal organ. A method to solve these problems by measuring the force at the distal end of the tibia during stimulation of the femoral chordotonal organ is described in (B). The step-response in inactive animals (C) is similar to that of the free-moving tibia. After an active movement caused by touching the abdomen the amplitude of the flexion-force is always higher than before. In (D) a method is described to measure the amplification of the control-system in intact animals. With this method it is verified, that the flexion-force produced by a distinct stimulus is higher after active movements caused by touching the abdomen. But this force is lower after spontaneous active movements caused by darkening the room (Fig. 2). Therefore one must assume, that there are two different types of activity: spontaneous activity and activity after a disturbance. In the frequency-response of the inactive animal (F) (Figs. 4 and 5) the amplitude of the force decreases with increasing frequency at a constant amplitude of stimulus. The phase-shift between reaction and stimulus is much smaller than with the free-moving tibia. Therefore, the large phase-shift as well as the strong decrease of the reaction-amplitude near 1 Hz observed in free-moving tibias (1972b) is mainly due to the mechanical attributes of the system. In Section (F) the receptor-apodeme is sinusoidally moved during active movements of intact and decerebrated animals. As with the free-moving tibia no reaction can be observed during active movements at that phase position for which the response occurs in inactive animals. Instead of this “inactive” response there is another response, called “active” with a phase-shift of about 180°. At the end of an active period the “active” and the “inactive” response can be observed simultaneously (Figs. 7 and 10). The amplitude of the “active” response decreases, and the amplitude of the “inactive” response increases from cycle to cycle. In decerebrated animals there are normally several minutes from the exclusively “active” response to the exclusively “inactive” response without a further increase in amplitude. In intact animals this transition takes only a few seconds. Step-stimuli during active movements (G) show, that in active animals stretching the chordotonal organ causes a flexion of the femor-tibia-joint. Releasing the chordotonal organ does not produce any reaction. Moving the receptor-apodeme in active animals influences the contralateral leg significantly only in middle legs (H). These legs tend to move within the same phase position as the stimulated leg. Moving the receptor-apodeme in a middle leg has no influence on the ipsilateral hind leg, but a weak influence on the ipsilateral front leg, which tends to move within the same phase position as the middle leg. In the discussion (I) a hypothesis is presented according to which the “active” response is a mechanism for adapting the leg movement to a surface which suddenly gives way (I 5). The influence on the contralateral middle leg seems to be a part of this mechanism (I 6). This reaction has nothing to do with the coordination of leg movements in walk (I 7). The feed-back systems which control the distance between the body and the walking surface may be inactive during walking (I 8), but those systems which control the forward movement of the body must be active. Since the feed-back system of the “Kniesehnen-reflex” controls predominantly the body-ground-distance it seems likely that it is normally inactive during walking.

Rigorous and extended application of information theory to the afferent visual system of the cat. I. Basic concepts.

Abstract: Information theory is applied to data from microelectrode recordings of the cat's afferent visual system in a manner more general than hitherto usual. It is shown that it is not necessary to know the particular neuronal code for information calculations by taking the signal itself as the symbols. Uncontrollable errors thus can be avoided. It is further shown that by this approach the dynamical behaviour of the system is fully considered for information transfer. Quantities are defined to exhibit the time course of transmitted information.

A model for repetitive firing in neurons

Abstract: This paper describes a model for the generation of repetitive firing patterns in single neurons to be used as a module in large-scale network simulation studies. The model is based on the combination of extended versions of Hill's model for accomodation and of Kernell's model for adaptation. Both digital computer and electronic circuit realizations of the model are presented. The model is shown to produce strength-duration curves for accomodation which are compatible with available data from real neurons. Both “high ceiling” and “low ceiling” cell types can be matched by adjusting parameters in the model. An equation relating steady-state firing rate to amplitude of applied steady current is presented which includes the accumulation of potassium conductance changes with repetitive firing. The occurence of phasic and tonic responses to step stimulation is mapped in the parameter space of the model. Several representative response patterns to irregular inputs are presented.

The role of rhythms in homeostasis.

Abstract: Es wird allgemein angenommen, das biologische Rhythmen eine Rolle als Zeitgeber fur Systeme spielen. Zirkadische Rhythmen z.B. stellen die Beziehung zwischen dem hell-dunkel Zyklus der Umwelt und dem zeitlichen Ablauf interner Vorgange her. Schnellere Rhythmen sind wahrscheinlich auf Ein-/Ausschaltungen homeostatischer Regler zuruckzufuhren. Das hier beschriebene Modell besteht aus einem Ruckkopplungszweig, einem Ein-/Ausschalt-element und einem frequenzabhangigen Teil (Filter). Es reproduziert die wichtigsten Eigenschaften des lebenden Originals — exakte Regulierung, amplituden begrenzte spontane Schwingungen (Rhythmen) und das Synchronisieren dieser Schwingungen durch ausere periodische Storungen, die eine von der Frequenz abhangige Mindestamplitude uberschreiten.

Der Regelkreis des Kniesehnenreflexes bei der Stabheuschrecke Carausius morosus

Abstract: In Part B the tendon of the femoral chordotonal organ (receptor tendon) of a fixed leg is sinusoidally moved with different amplitudes and frequencies. This causes movements of the tibia. Figures 1–3 show the amplitudes of the tibia movements and the phase-shifts between tibia-movement and stimulus. As it is known, that a tibia-movement of about 13° corresponds to a movement of the receptor-tendon of 100 μm, a bode-plot can be constructed. Figure 4 is the first part of a three-dimensional bode-plot (amplitude ratio) which additionally shows the values of amplitudes and frequencies, at which a phase shift of 180° can be observed. The system is stable, if the gain of the system is smaller than 1 at these values. A gain equal or larger than 1 causes instability. As it can be seen in Fig. 4, the system is stable, but it is not very far from instability. In Part C an inert mass is coupled to the tibia in order to enlarge the phase-shift. After a disturbance, which causes a higher gain of the system, intact legs often show long lasting oscillations of small amplitude (Fig. 6a, b). During these oscillations the other legs are not moved. Sometimes active movements of all legs occur. Active movements of the tested legs have larger amplitudes and are always followed by small-amplitude-oscillations. Legs with cut receptor tendons and intact legs of decerebrated animals never show small-amplitude-oscillations but only active movements. Therefore it is probable that the small-amplitude-oscillations are oscillations of the feedback-system. In Part C 4 another possible explanation for these oscillations is discussed: The forces, produced by the muscles, might be represented by a noise of broad bandwidth from which the mechanical system selects only a small band given by its resonance frequency. In order to test this hypothesis, electrophysiological experiments are done (C5): During slow-amplitude-oscillations of legs with an inert mass added a spike-burst can be observed in the flexor tibiae during extension and in the extensor tibiae during flexion of the femur-tibia-joint. Sometimes no activity in the extensor can be observed. This means, that the activity in the muscles has a phase-shift of about 180° relative to the movement of the tibia: These supports the hypothesis, that the small-amplitude-oscillations are oscillations of the control system of the “Kniesehnenreflex”. In Part D it is discussed, whether the rocking-movements of the whole animal could be explained by oscillations of control systems. It is, deduced, that if this hypothesis is true, the control system in the coxa-trochanter-joint must be as near to instability as the control system of the “Kniesehnenreflex”.

Man and computer

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Properties of small neural networks.

Abstract: Networks containing neuronal models of the type considered in the previous paper can be described by a set of first order differential equations. Steady-state solutions and the stability of these solutions to small perturbations can be obtained. Networks of physiological interest which give rise to second, third and fourth order linear equations are analysed in detail. Conditions are derived under which such networks can be condensed into a single neuron of similar order. Simple mechanisms for memory storage, for the generation of oscillatory activity and for decision making in neural systems are suggested.

Growth with regulation in random environment.

Abstract: The diffusion model for a population subject to Malthusian growth is generalized to include regulation effects. This is done by incorporating a logarithmic term in the regulation function in a way to obtain, in the absence of noise, an S-shaped growth law retaining the qualitative features of the logistic growth curve. The growth phenomenon is modeled as a diffusion process whose transition p.d.f. is obtained in closed form. Its steady state behavior turns out to be described by the lognormal distribution. The expected values and the mode of the transition p.d.f. are calculated, and it is proved that their time course is also represented by monotonically increasing functions asymptotically approaching saturation values. The first passage time problem is then considered. The Laplace transform of the first passage time p.d.f. is obtained for arbitrary thresholds and is used to calculate the expected value of the first passage time. The inverse Laplace transform is then determined for a threshold equal to the saturation value attained by the population size in the absence of random components. The probability of absorption for an arbitrary barrier is finally calculated as the limit of the absorption probability in a two-barrier problem.

Optomotor responses of the fly Musca domestica to transient stimuli of edges and stripes.

Abstract: The fly's optomotor response to transient stimuli was studied under open loop conditions The stimuli used were moving edges and stripes A comparison of the fly's responses to these stimuli bends to the result that progressive moving patterns (from front to back with respect to the fly) elicit stronger responses than regressive moving ones (from back to front) Edges followed by darkness elicit a stronger response than those followed by light A narrow, bright or dark stripe and a single edge evoke a similar response, whereas a broad stripe elicitis a stronger response than a single edge

An application of the cross-correlation coefficient to pattern recognition of honey bees

Abstract: 1. In training experiments with honey bees, the discrimination of 6-pointed stars of different form and contrast is measured. The following assumptions allow a quantitative description of these results. 2. The bee computes the two-dimensional cross correlation coefficient r xy between the two shapes to be discriminated (the rewarded shape and the one seen at present). This presupposes, that the rewarded shape is stored in the memory point by point. 3. In addition to the cross correlation coefficient, the shapes are discriminated by means of their contour length and their contrast. 4. A noise is superimposed on the values stored in the memory. Because of this noise, the accuracy of detecting the outline of the stored shape depends on the value of the contrast. The lower the contrast, the less accurately is the outline detectable. The exactness of the stored value of the contrast itself is also diminished by the noise. 5. Although the results of these and of most previously published experiments can be described quantitatively by this model, some other results (Anderson, 1972; Mazochin-Porshnyakov, 1969) can certainly not be described in this way. In such cases, it seems more probable that bees use abstract parameters to discriminate the shapes because of the particular experimental method.

Variations in the output impedance of the human motor system.

Abstract: The hypothesis that the properties of the stretch reflex could be changed dependent on the appointed task of the motor system was tested by measuring the mechanical output impedance of the hand of a human subject. Small disturbing torques were exerted on the hand rotating in the wrist joint in palmar and dorsal direction. The angular position, velocity and acceleration were recorded during 180 msec after the start of the disturbing torque. Within the linear range differences were found between the situations that (1) the subject kept his hand in a fixed position (posture) and (2) the subject tracked a simple and slow moving target (tracking). A simple model of the peripheral part of the motor system with the spinal reflex mechanism was made to analyse the responses. With the help of this model the changes in the reflex sensors were distinguished from changes in the mechanical system of the hand with the muscles attached to it and from changes in the effect of an activation of the muscle. During posture the responses were affected by the attention of the subject. An important part of these changes was a shift in the delay time of the reflex. During tracking the responses changed markely dependent on the velocity of the hand. When this velocity is larger than about 0.05 rad.sec−1 then the strength of the reflex is approximately suppressed to about a half of the value during posture. Above this velocity the mechanical system of the hand with the muscles attached to it appeared to be less damped. The suppression of the reflex is caused by a decrease of the gain of the feedback sensors to about a third and an increase in the gain of the system of muscles with their load to about one and a half. It was concluded that the gain of the feedback sensors is controlled by signals from supraspinal levels.

Reliability of pattern separation by the cerebellar mossy fiber--granule cell system.

Abstract: As a simple example of a neuronal network in which synaptic connectivity among neurons is probabilistic, Marr's model for the granular layer of cat cerebellar cortex is examined. The mean and variance are computed for the fraction of granule cells activated, and for the extent of pattern separation by granule cells, for various mossy fiber inputs and various values of connectivity and electrical parameters of the network structure. Results suggest different functions for the network, and different optimal ranges for its parameters, depending on whether Golgi cells are present or absent. The model network does not perform the functions originally prescribed for it with high reliability.

Computer simulation of rhythmic oscillations in neuron pools

Abstract: This paper describes computer simulation of 100 artificial neurons interconnected in mutually exciting random pools. The individual neuromimes include accommodation according to an extended version of Hill's model and adaptation according to an extended version of Kernell's model. The main finding is that the constituent cells of the pools tend to fire in coordinated bursts and that these bursts recur rhythmically. The rate of burst recurrence depends primarily on the time constant of recovery of the after-hyperpolarization conductance change although it may be slightly altered by the average level of random background activity. It does not seem possible to attribute the salient slow rhythm observed in the rat mesencephalic reticular formation to this mechanism, as matching the data requires absurdly large values of the conductance change recovery time constant.

Steady-state and limit cycle activity of mass of neurons forming simple feedback loops (I): lumped circuit model.

Abstract: The neurons in the mammalian olfactory bulb sustain two types of synaptic feedback. The periglomerular cells excite each other and form a positive feedback loop. The mitral-tufted cells are excited by periglomerular neurons, and they excite granule cells and are inhibited by them. The last two neural populations form a negative feedback loop. This work contains mathematical proofs for the existence of steady state unvarying activity in periglomerular neurons, and of steady state oscillatory activity of mitral-tufted and granule cells, which is manifested in the EEG. The following predictions are made. 1) The level of mean ongoing pulse activity of the periglomerular population is determined by peripheral sensory and centrifugal input. 2) The interaction of mitral and granule populations determines a limit cycle detectable in the EEG. 3) The frequency of the limit cycle is determined by periglomerular and centrifugal input. 4) The steady and oscillatory pulse rates are stable, and if they are perturbed, they return to the levels preceding perturbation.

On some properties of stochastic information processes in neurons and neuron populations - Mathematical model approach

Abstract: The information in the nervous spike trains and its processing by neural units are discussed. In these problems, our attention is focused on the stochastic properties of neurons and neuron populations. There are three subjects in this paper, which are the spontaneous type neuron, the forced type neuron and the reciprocal inhibitory pairs. 1. The spontaneous type neuron produces spikes without excitatory inputs. The mathematical model has the following assumptions. The neuron potential (NP) has the fluctuation and obeys the Ornstein-Uhlenbeck process, because the N P is not so perfectly random as that of the Wiener process but has an attraction to the rest value. The threshold varies exponentially and the NP has the constant lower limit. When the NP reaches the threshold, the neuron fires and the NP is reset to a certain position. After a firing, an absolute refractory period exists. In discussing the stochastic properties of neurons, the transition probability density function and the first passage time density function are the important quantities, which are governed by the Kolmogorov's equations. Although they can be set up easily, we can rarely obtain the analytical solutions in time domain. Moreover, they cover only simple properties. Hence the numerical analysis is performed and a good deal of fair results are obtained and discussed. 2. The forced type neuron has input pulse trains which are assumed to be based on the Poisson process. Other assumptions and methods are almost the same as above except the diffusion approximation of the stochastic process. In this case, we encounter the inhomogeneous process due to the pulse-frequency-modulation, whose first passage time density reveals the multimodal distribution. The numerical analysis is also tried, and the output spike interval density is further discussed in the case of the periodic modulation. 3. Two types of reciprocal inhibitory pairs are discussed. The first type has two excitatory driving inputs which are mutually independent. The second type has one common excitatory input but it advances in two ways, one of which has a time lag. The neuron dynamics is the same as that of the forced type neuron and each neuron has an identical structure. The inputs are assumed to be based on the Poisson process and the inhibition occurs when the companion neuron fires. In this case, the equations of the probability density functions are not obtained. Hence the computer simulation is tried and it is observed that the stochastic rhythm emerges in spite of the temporally homogeneous inputs. Furthermore, the case of inhomogeneous inputs is discussed.

Vibrotaktile Informationsübertragung mit Folgen binärer Zeichen

Abstract: Results of experiments in transmitting information by the aid of the sense of touch are presented. The patterns are limited sequences of binary signals, presented as vibrotactile pulses at the forearm. The information, transmitted by a signal decreases with the length of the sequence and the serial number of the signal within the sequence. With increasing difficulty in pattern recognition the information transmitted by the whole pattern exceeds the sum of the information transmitted by the signals. It is shown, that the process during a sequence is not stationary. Finally it is shown, how the recognition of signals is correlated to the adjoining signals in the sequence.

A model of a neural network with recurrent inhibition.

Abstract: A model of a neural network with recurrent inhibition has been studied The model is intended as a possible description of the cerebral cortex, although this interpretation is not necessary Using the corresponding neuroanatomical concepts, it can be described in the following way The network consists of pyramidal cells and stellate cells These are assumed to be of excitatory and inhibitory type, respectively The input consists of excitatory signals and so-called unspecified signals Both types of input are connected to the pyramidal cells The output of the model is similarly formed by the output of these cells However, the pyramidal cell output is also connected to the stellate cells These are in their turn connected to the pyramidal cells, thus completing a closed circuit All connections between cells are of random character It is assumed that synapses can be facilitated as a result of simultaneous presynaptic and postsynaptic activity This gives the model a capability of associative learning The model's ability to retrieve information is investigated by studying the output in the absence of unspecified signals It is shown that, under suitable conditions, the output pattern will become composed of just one major component even if the excitatory input pattern is a mixture of several patterns that were present during learning This major component is a part of the specific output pattern that during learning became associated with the input pattern corresponding to the largest component of the pattern mixture This behavior is obtained through a dynamic process in which the pattern separation properties of the feedback link play an important role The model's operation can be viewed as pattern recognition and this aspect as well as some physiological and psychological interpretations are discussed

Dynamics of the electroencephalogram during performance of a mental task.

Abstract: Dynamics of the EEG activity — during the performance of a mental task — was investigated by the nonstationary power spectrum method. The performance of the mental arithmetic is associated with suppression of the alpha wave. The suppression of the alpha wave is not as marked as the alpha blocking accompanying opening of the eyes. Alpha wave suppression during the mental task was nonsymmetric around the center frequency of the alpha wave, and lower frequency components were suppressed more than high frequency components. An explanation of these observations is proposed in terms of decrease in the periods of alpha prevalence during performance of mental tasks.

Statistical inference on markov process of neuronal impulse sequences.

Abstract: To clarify the stochastic properties of the neuronal impulse sequences, we have proposed a measure of statistical dependency di(T=τ) and an equation ɛm of the matrices of the serial correlation coefficients. Markov properties of the interval sequences could be provided with di(T=τ) and ɛm, which represent the necessary and sufficient condition for the statistical dependence. A method to estimate the order of Markov process with the use of di(T=τ) and ɛm was found to be useful in practice. This was proved by the interval sequences of the 0-th, 1-st, and 2nd order semi-Markov process generated by computer. It was also found that the order of Markov process of neuronal impulse sequence is an important parameter representing the pattern of the sequence. This was proved with computer simulation by semi-Markov model of impulse sequence.

Information and entropy of countable measurable partitions. I

Abstract: In ergodic theory, the notions of information and entropy are separated from each other. In the existing literature, it is usual to assume the additive nature of information. In this paper, we have proposed a general definition of information in § 2 and studied its properties extensively in § 3. In § 4, information and entropy of countable measurable partitions of a Lebesgue probability space have been defined.

Response characteristics of a neuron model to a periodic input.

Abstract: A mathematical neuron model defined by a difference equation was investigated when it was exposed to an environment of a periodic input stimulus. It is shown that pulse sequences constructed in advance by a particular method are actually realizable as the output of the system and the condition for the output sequence is also obtained with respect to the magnitude of the input. The results are interesting from a point of view of number theory.

Model of a plausible learning scheme for CA3 Hippocampus

Abstract: There is ample evidence that mammalian Hippocampus, defined as ammon's horn sectors 1 through 4, can learn. In particular, sector CA3 is presumed able to learn to produce a wide range of appropriate output patterns in response to extrinsic inputs arriving over the mossy fiber, temporo-ammonic, septo-hippocampal, and commissural systems. The neuroanatomy and neurophysiology of CA3 have been studied extensively, but the information conveyed by its signals and the way its circuit actions represent decisionary and memory functions remain elusive. Several roles have been posited for the Hippocampus in the guidance of animal behavior, but they are not inter-related in any clear way, and seem separated by several levels of abstraction from the circuit actions which actually embody decisionary and memory functions. We present a plastic circuit model of the CA3 sector and discuss its computer simulation as a caricature of developmental and neurophysiological processes. In particular, we concentrate on plausible ways in which excitatory and inhibitory interneurons can learn to properly influence articulate pyramidal cell output patterns under the guidance of only diffuse positive or negative reinforcement. Statistical learning in interneuronal-to-pyramidal synapses is posited to occur in one cell cluster after another until the overall circuit matures. A kind of intra-pyramidal Markovian learning is also posited and simulated, with quite remarkable results. A list of critical assumptions each of which is testable in principle is given, so the model can be thoroughly tested. The effect of each assumption is documented by computer simulation data.