ALBERT

Notes: Zusammenfassung Anhand der Übertragungseigenschaften der einzelnen Glieder des sog. „inneren” Regelkreises der Willkürbewegung, Rezeptor-Rückenmark-Muskulatur, wurde der Übertragungsfaktor des gesamten Regelkreises aufgestellt. Ganz allgemein gilt danach für die Gliedmaßenbewegung, daß sie den Gesetzen eines Proportional-Integral-Regelsystems gehorcht. Ferner werden die Bedingungen für den Angriff der Führungs-und Störgrößen aus dem abgeleiteten Übertragungsfaktor diskutiert, insbesondere im Hinblick auf die Einspeisung der Führungsgröße an den Muskelspindeln oder in dem Rückenmark.

Notes: Summary Feedback mechanisms exist in all the periferal sense organs including the eye, which acts as a highly efficient position control servo system. Histological studies so far have not revealed the precise circuitry of the eye movement control system but some information about it can be obtained by a study of the sources of feedback. Existing theories have considered three types of feedback originating in the oculomotor tract, in the proprioceptive fibres of the extrinsic eye muscles and from retinal image displacement. In the present experiments an optical arrangement has been used to vary or eliminate the amount of information available from retinal image motion, and the response of the eye to simple harmonic displacement of a target has been recorded. The response curves of gain (eyeball movement divided by target motion) against frequency indicate that the system is lion linear when the image falls in the retinal region which is insensitive to position. Outside this area, retinal image position is used as negative feedback but the information from the oculomotor tract must be regenerative. There is also evidence for feedback proportional to the first derivative of eyeball position and this function is ascribed to the proprioceptive signals; this form of feedback appears to saturate for large amplitude movements, thus avoiding heavy damping of the flick movements. A schematic eye movement control system having the same characteristics as the eye is proposed. The transfer function of this system indicates that it should be unstable if the sign of the retinal image feedback loop is reversed. Experiments with this form of feedback show that steady fixation is impossible and the eye performs a pendular nystagmus.

Notes: Summary It is shown that the traditional antithesis of mind and matter stems from a grave misunderstanding or rather misarrangement of empirical facts. This oblique antithesis and numerous well-known contradictions connected with it are eliminated by careful analysis of the intricate situation from which they arose. The solution of the problem leads to a clear understanding of fundamental concepts upon which Cybernetics is founded, and of the achievements potentially within its reach.

Notes: Summary The level (=arithmetic average of all instantaneous values)of a self-sustained oscillation in general influences all properties of the oscillation, including period, amplitude and shape of the oscillation, and the rate of exchange of energy between the oscillator and its environment. Only when the non-linear damping factor does not depend on the instantaneous value of the oscillating function, but only on the amplitude of the oscillation, are the other properties independent of the average level. The differential equations describing self-sustained oscillations cannot be solved exactly, but methods of approximation are applicable. Numerical solutions to several different forms of the equations will be discussed. In the simplest case (van der Pol equation) all properties of the self-sustained oscillation (e.g. period, amplitude) are extreme when the level is zero. The oscillation continues only within a given range of levels (oscillating range); outside this range, the oscillation damps out. In other modifications of the equation, the oscillating function cannot assume a zero value. In all cases, the extent to which the average level influences the different properties depends on the factor ɛ, which describes the position of the oscillation within the range between harmonic and relaxation types of oscillation. In the elementary van der Pol equation, the correlation between level and frequency changes sign within the oscillating range; that is, the circadian rule, demanding an always positive correlation between level and frequency, cannot be fulfilled. Only with an additional non-linearity in the energy of recoil does the correlation remain unchanged in sign throughout the oscillating range. A stability condition demands a positive sign for this non-linearity, and hence, for the correlation (fulfilling the circadian rule); if the sign is negative (violating the circadian rule), the oscillation becomes unstable. With an additional term of the third order, the oscillation acquires a two-peaked shape typical of many circadian oscillations. A simple differential equation describing all general properties of the circadian periodicity must fulfil these conditions: the oscillation must be self-sustained and limited to positive values; and the energy of recoil must be non-linear with a positive coefficient to obtain the appropriate correlation between level and frequency. In the equations here developed the environment directly influences only one parameter of the oscillation, i.e. the level. In addition to the circadian periodicity, the differential equations here examined describe the behavior of several other biological oscillations.

Notes: Summary The Musculus sphincter pupillae of the toad Discoglossus pictus contracts when exposed to light, even if the iris with the muscle is cut out of the eye. Normally the size of the pupil is controlled by this photosensitivity and in addition by a nervous control mechanism. —Experiments are discribed in which the M. sphincter pupillae of the isolated iris was stimulated by various light programs. The contractile force was measured isometrically with a compensation system. It is shown that the response of the sphincter-muscle to changing light stimuli depends on the mean light intensity; i.e. the sphincter-muscle is an adapting system. The amplitude and phaseshift of the reactions to sinusoidal light stimuli were measured. When stimulus and response are both considered as functions of time, the transformation of stimulus in response by the muscle is linear, provided that the frequency of the sinusoidal light is high and its intensity and modulation degree are low. From this result the hypothesis is derived, that the transformation of stimulus into response is linear only when the level of adaptation does not change during contraction. From the response to sinusoidal light program it was possible to predict the reaction to square wave light programs. The time-course of the reaction to step up light stimuli are similar to the time-course of receptor potentials of phasic-tonic sense cells, showing a maximum, a minimum and a plateau. Within certain limits the amplitude of the reaction depends linearly on the tension of the muscle. Since in isometric experiments the reaction consists of an increase of muscle tension, the muscle becomes more sensitive during reaction and the contractile force increases for a long time, even when light intensity is held constant.

Notes: Summary Recently it was shown (Reichardt 1961) that lateral neural inhibition, such as was found in the lateral eye of Limulus polyphemus by Hartline and Ratliff, can in principle compensate for the dioptric apparatus of the eye. The model of lateral inhibition in Limulus developed there is here considered further, with emphasis on the changes in the effective structure of the nerve network (and the associated vector transformation) resulting from the forced inactivity of fibers whose inhibition exceeds their excitation. The stability of the network model as a function of the inhibition coefficients is studied and two theorems regarding the stability are proven. The dependence of the properties of the network on the pattern of receptor excitation are investigated and it is shown by examples that the network could be used for form discrimination. This model's relationship to previously known pattern recognition systems is discussed and its possible application in computer technology is mentioned.

Notes: Summary The recognition of misalignment in a pair of lines positioned end-to-end, as when setting a vernier scale, presents a simple problem in the detection of self-congruence. The accuracy with which this task can be performed has been measured both in normal vision and in the absence of retinal image motion; it is found that in the latter case the precision of the setting is decreased when the gap between the ends of the lines is small, but that the reduction in accuracy is not significant when the separation of the lines is increased to 30 min. arc. A search has been made for eye movements generating patterns of scanning activity designed to test the self-congruence of the vernier lines but without success, the distribution of spontaneous eye movements appears to be a function of the subject and not of the target lie is viewing. The reduction of vernier acuity in stabilized vision indicates that when retinal image motion is absent, the resultant pattern of neural activity is less well defined, this is ascribed to the loss of dynamic lateral inhibition effects but the reduction which occurs as the gap between the lines increases can be attributed to random neural events becoming confused with the stimulus; this hypothesis has been tested by the introduction of visual “noise” which is also found to reduce acuity.

Notes: Abstract An electric analogue model of the neuron is described. The model neuron is composed of the active units which simulate the electric behaviors of the active loci of the membrane of a neuron. The active units include the model axon and the model synapses of six different types (the ordinary, incremental and decremental onse each having the excitatory and the inhibitory types). The properties of the models are described.

Notes: Summary The human ear shows a fine pitch discrimination combined with a short transient time; the product of bandwidth and transient time is smaller than 1. According to the investigations of G. v. Békésy the mechanism of this frequency discrimination cannot be located in the inner ear; it must be searched in the cochlear nerve or in the brain. New nonlinear devices for frequency discrimination are described, having small bandwidth and short transient time. The properties of such “coincidence-filters” are discussed. These circuits may serve as a first model of pitch discrimination in the cochlear nerve. Investigations on combinations of several coincidence-filters have been carried out. A function-model of the cochlear nerve is described, consisting of two coincidence-filters connected in cascade. It is working at a frequency of 1 kcps and has a bandwidth of 3 cps; th3 transienttime is 3 msec.

Notes: Abstract Whenever the eye views a spatially-varying gradient of luminance, the Mach bands arise, causing a subjective distribution different from the luminance distribution of the field of view. This phenomenon has been used for the determination of the contrast-transfer function of the visual system when working under normal viewing conditions, i.e., operating in a region where both luminance and detail size are well above threshold. The Mach bands have been measured by making subjective photometric comparisons and the data have been analyzed under the assumption of linearity of response to input. The hypothesis that the visual system may be treated as an approximately linear link in the imaging chain is satisfied best when the luminances are plotted logarithmically. The possibility of this type of investigation is discussed. The result found is compared with apparent subjective contrast measurements of a sine-wave spatial luminance distribution.

Notes: Summary The functional properties of the processing of visual information by the complex eye of Limulus was studied. The spatial distribution of activity that results in the optic nerve when the Limulus eye is exposed to a stationary optical pattern depends upon the transfer characteristics of two subsystems: the dioptric apparatus and the nervous interactions comprising the lateral inhibition system. — The transfer characteristic of the dioptric apparatus is determined by the sensitivity distribution function of single ommatidia. This distribution was measured and found to be approximately of Gauss-function type. The sensitivity falls off to 1/e at a distance of one ommatidium; thus the visual fields of adjacent ommatidia strongly overlap. As a consequence of the overlap, amplitudes of the spatial Fourier components, of which the brightness distribution of the optical surround is made up, are more and more reduced with increasing frequency in the intensity distribution on the receptor mosaic. The amplitude of the spatial frequency 1/λ=0,25 (λ in units of interommatidial distance) is reduced to half of the maximum value, which is attained at zero frequency. It is shown that the amplitude frequency characteristic of the sensitivity distribution function has no zeros, which means that no loss of optical information results from overlap of visual fields. Thus the resolving power of the dioptric apparatus is limited only by the number of receptors per unit area. — The transfer characteristic of the lateral inhibition system in the Limulus eye depends on the distribution of the inhibitory coefficients around the individual receptors. This distribution function was determined from excitatory responses in the optic nerve elicited by a spatial light intensity step function on the receptor mosaic. It is found that this distribution is also Gaussian in form, but decays to 1/e at a distance of eight to nine ommatidia along the major axis of the eye. The average value of the inhibitory coefficients between adjacent ommatidia was found to be 0,025. The amplitude frequency response of the inhibitory system is constant for high spatial frequencies down to 1/λ=0,1 while amplitudes of lower frequency sinusoids are reduced down to nearly half of the maximum value at frequency zero. The amplitude frequency characteristic of the inhibitory system ensures a one to one correspondence between the intensity distribution on the receptor mosaic and the excitation distribution in the optic nerve. The overall transfer characteristic of the eye is derived from the transfer characteristics of the dioptric apparatus and the inhibitory system. This characteristic is of bandpass type with a maximum amplitude response at a frequency of 1/λ=0,07. The overall transfer characteristic was independently confirmed in a separate experiment. The nature of the overall transfer characteristic shows that the inhibitory system does not exactly correct for the overlap of the visual fields of single ommatidia, which in principal the system could do if the distributions of inhibitory coefficients and ommatidia sensitivity were equal. The overall transfer characteristic of the Limulus eye garantees a one to one correspondence between patterns in the optical surround and excitation distributions in the optic nerve. — The average values of the inhibitory coefficients derived from these experiments are at least a factor ten smaller than those determined directly by other investigators. Possible explanations of this discrepency are discussed. — In a separate chapter the overall transfer characteristic for eyes submerged in water is described. It was found that this characteristic does not differ from that determined in air for the eye region which was investigated in the experiments. This result is explained by two properties of the eye which are dependent on the refractive index of the surround medium and whose influences cancel each other: the visual fields of ommatidia are reduced under water, while the divergence angles between the optical axes of adjacent ommatidia also diminish.

Notes: Summary Lashley's suggestion that serial behavior has a dual organization, central facilitation of the entire sequence plus scanning of the individual movements, is taken as the starting point for the construction of a model to illustrate in more detail how the nervous system might work during such behavior. Two stages in the learning of a sequence are distinguished: 1. immediate reproduction of a presented sample, and 2. reproduction of habitual responses by association, without the necessity of recent access to the original sample. The model is primarily concerned with performances of the first type. Neurons of a scanning chain, which always fire one another in the same order, acquire temporary connections with the movements to be recalled. The connections fade rapidly with disuse so that the same scanning chain can be used again with different combinations of movements. The same mechanism will also permit the recall of sequences of words, or other habitual movement complexes, as if they were individual movements. It is assumed that such habitual motor patterns as words are under the control of higher-order cell assemblies which regulate the sequences of movements within the response, and thus substitute for the general scanning mechanism. This leaves the scanner free to form temporary associations with the higher-order cell assemblies for the words. It is suggested that the scanning mechanism is actuated only by unpredictable inputs so that the elements within a habitual series do not acquire unnecessary connections with the scanning neurons. The arousal system is known to have this characteristic of not being disturbed by the expected, and it seems likely that the two systems are intimately related.

Notes: Summary Due to the manner in which the English language is used, words exhibit strong internal constraints on letters, but some additional constraint may be imposed by the context in which words appear. In order to estimate the internal constraints of words and the overall effect of context, an experiment was carried out using 225 human subjects who predicted letters in each of the first four positions within words, both with and without context prior to the words. It was found that as more letters at the beginning of words are given, prediction of the following letters increases monotonically, but the increase is not smooth. Prediction of the third letter of words given the first two letters is only a little better than prediction of the second letter given only the first. This effect may be explained by the probable combinations of vowels and consonants at the beginning of words. Letters in the first two positions show no improvement due to long context but prediction of later letters is increased by such context so that prediction rises smoothly from the initial letter to the fourth letter. Also, the type of word in which the letters are to be predicted affects the prediction, function words showing more constraint on letters than content words. The difference between function and content words does not take effect, however, until the first two letters of the word are given. Using the prediction data from words preceded by long context, extrapolations of constraint out to the tenth letter were obtained. From the values of constraint at the first ten letter positions it was possible to estimate the maximum unilateral sequential constraint in English. A value of about 48% was obtained which compares with previous estimates of 50%. A further evaluation of the overall effect of context indicates that about 81% of the constraint in English is contained within the words themselves, and the other 19% is due to any additional context.

Notes: Summary 1. A brief outline of the evolution of neuron modeling is given and an argument is presented for studying neural behavior by “black-box” logical equivalence. 2. An electronic circuit incorporating many of the digital and analog properties of neurons is described. Having such properties as variable threshold, summation, all-or-none output, absolute and relative refractoriness, and inhibition, it exhibits a considerable amount of functional equivalence to biological structures. 3. Properties of the model are described in detail and relevance to biological neuron measurements are shown. Such behavior as time-intensity trade, repetitive firing and temporal summation are readily achieved and are shown to approximate in vivo behavior. 4. The model is sufficiently flexible so that with simple parameter changes and external circuit configurations, a wide variety of neurological phenomena can be exhibited and studied closely. By adding stimulus-derived inhibition for example, accommodation and adaptation are obtained. 5. Experiments with the model have suggested new relationships which nervous structures may exhibit. A linear dependence of burst pulse number on accommodation time constant, and a summation-division phenomenon are examples of such findings. 6. Models of this sort have utility not only for studying single unit properties but also for investigating group interactions. Such studies may be relevant to elucidation of neural network behavior.

Notes: Summary The resolving power of the human eye and the apposition eye in insects is discussed on the basis of Fraunhofer's diffraction theory. It is then shown that diffraction does not play an important role in the Limulus facet eye. In spite of this the visual fields of neighboured ommatidia overlap strongly as Waterman has shown. A mathematical relation which describes the process of imaging the optical surroundings onto the generator potentials of the excentric cells of the receptors is presented. This relation takes into account the overlap of the visual fields and the logarithmic relation between light intensity and generator potential (MacNichol, Fuortes). On the basis of Hartline and Ratliff's reports on lateral inhibition in the Limulus eye it is shown that this process corrects the overlap and therefore increases the resolving power of the eye. The functional mechanism of lateral inhibition is in principle able to create an image of the optical surroundings in the optic nerve. It therefore can compensate for the dioptric apparatus in front of the receptor mosaic. The correction process in the Limulus eye is studied quantitatively and other cases of principle interest are investigated by means of an analog computer. The results are discussed and other inhibitory processes in the visual and auditory system etc. are mentioned.

Notes: Summary 1. Artificial neurons (neuromimes) are used to simulate the external spiral innervation of the cochlea. 2. On the basis of the experimental observations the proposition is advanced that the spiral innervation serves to extend the dynamic range of the ear. Dynamic range extension follows from elementary considerations of the refractory and summing properties of nerve fibers. 3. Experiments with different neuromime densities, supported with psychophysical observations reported in the literature, lead to the hypothesis that dynamic range and growth of sensation are related to the innervation density in the area of sensory tissue under consideration (e.g., skin). The spiral nerves are considered as a special case of a more general sensory nerve, branching in binary fashion. 4. The pathological phenomenon of “loudness recruitment” is explained as a “thinning” of cochlear innervation density, giving rise to smaller dynamic range and faster growth of loudness.

Notes: Summary 1. A simple model is described which establishes a relationship between physiological and psychophysical flicker-fusion data. The three components of the model are a transducer, a filter and a flicker-detector. The model is consistent with the view that fusion is purely retinal. 2. An electronic analog is used to realize the model. Its essential elements are a source of generator pot1ential, a low-pass filter, and a simulated ganglion cell. 3. The model was originally designed to reproduce the psychophysical results obtained by de Lange. Special importance is attached to the envelope of his curves; the model reproduces this envelope. His low-intensity results are duplicated accurately, while the high-intensity, high-frequency data are derived somewhat less accurately. The high-intensity low-frequency data are attributed to a mechanism not included in the model. 4. In the simulation of physiological data obtained by Enroth, close resemblance to the firing characteristics of retinal ganglia in cat is shown by the model. Firing occurs for bursts lasting for at most half the period of the alternating stimulus, the number of spikes per burst diminishing to unity as “fusion” is approached. 5. The phase lags and latencies of responses in the model satisfy neurophysiological evidence. Both off-latency and inhibition-latency are satisfactorily reproduced. 6. The model has been used to simulate two-component flicker data. The “flicker-detector” employed leads to results very similar to those obtained psychophysically. The phase characteristics of the assumed filter agree less well.

Notes: Summary Nonlinear properties of the human pupillary light reflex have been studied using binocular light stimuli of sinusoidally varying intensity. As reported earlier, the pupil responds with a net contraction to the modulation of the light intensity within a wide range of modulation frequencies. Results of the present experiments show that the net contraction does not depend upon the relative phase difference of the binocular light stimuli. However in the lower frequency range, where the in-phase stimuli result in a periodic light reflex, the out-of-phase stimuli fail to do so. These results allow certain conclusions to be drawn regarding the localisation within the photopupil reflex arc of the nonlinearities involved.

Notes: Summary The activity of single units of the optic tract, lateral geniculate body, optic radiations and striate cortex was recorded in cats (encephale isolé preparations) by means of microelectrodes. The optic nerves or radiations were stimulated with electrical shocks (0.3–1400 per sec). In other experiments binocular light stimuli were used. 1. When 50–200 msec trains of stimuli were applied, the maximal impulse rate transmitted by optic nerve or radiation fibers was found to be between 350 and 1100 per sec. Above these values fiber discharges followed successive stimuli in 1∶2 or 1∶3 ratios. The transmission through a geniculate or cortical synapse reduced this maximal impulse rate to 30–50 percent of that of the fibers. 2. Presynaptic stimulation frequencies above 100–400 per sec were observed to block impulse transmission through the synaptic stations about 10–120 msec after onset of electrical stimulation. Within a small range of stimulation frequency, just below that eliciting blocking, 1∶2, 1∶3 or 1∶4 transmission occured through cortical or geniculate synapses. 3. The maximal impulse frequency transmitted through a neuronal chain decreased as the number of neurons in the chain increased. 4. The information capacity of one afferent channel can be estimated to be 20–120 bit/sec. The information given by a neuronal impulse is not comparable to that of a binary digital unit pulse. Neuronal information can be understood as result of the operation of a system having a pulse frequency modulation code with considerable statistical fluctuation. These considerations do not take in account the added margin of information which is made possible by the spatial and temporal relationships of activity between different channels. 5. The information capacity af the afferent visual system is limited by the frequency properties of synaptic transmission and not by those of afferent fibers. 6. In single cortical units that could be activated by electrical stimulation of either optic nerve, the statistical conditions for “both” — or “either-or” — responses could be demonstrated using bilateral optic nerve stimuli separated by different intervals. 7. With binocular light stimuli summation of excitatory and inhibitory processes were found at the level of cortical neurons. 8. Some neurons in the visual cortex had the capacity of “measuring” the time difference between two light stimuli, one applied to the ipsilateral eye and the other to the contralateral one. 9. The results are compared with the findings of Kuepfmuellee and Jenik regarding transmission and processing of information by an electronic model neuron.

Notes: Summary Two semi-linear models for lateral inhibition are discussed. The interaction between “receptor units” is assumed to be linear, as demonstrated by Hartline and Ratliff in the eye of the horseshoe crab Limulus polyphemus. Yet a model of such an inhibitory system must be nonlinear, since the output values correspond to nerve activities, which cannot be negativ. Models with forward inhibition were used often to describe contrast phenomena in the human nervous system. However, in order to simulate the input-output relation in systems similar to the eye of Limulus, a model with backward inhibition must be constructed. Two important properties of backward inhibition not shared by forward inhibition are: (1) Inhibition in a receptor unit has an influence upon its excitation, as well as upon its ability to inhibit other units (Disinhibition). (2) The range of interaction between sensory units is not necessarily the same as the range of direct cross connections. It is shown in this paper, that also forward inhibition may possess these two properties, provided that it is repeated on subsequent levels. Some properties of systems with backward and forward inhibition are studied and compared in models consisting of three units. The input-output relation for large systems with backward inhibition was calculated under special assumptions concerning the inhibitory coefficients. If the inhibitory coefficients in a system with backward inhibition decrease like a power series, as a function of the distance between receptor units, only neighboring receptors have an effect upon each other. That is, in an equivalent system with forward inhibition the inhibitory interaction is confined to neighbouring receptors. Conversely, when backward inhibition exists only between neighbouring receptors, the inhibitory coefficients in an equivalent system with forward inhibition are described, as a function of the distance between the receptor units, by a power series with alternating sign.

Notes: summary The dynamic response of a simple ganglionic photoreceptor has been studied. It exemplifies the general processes of sensory reception and transmission of sensory information in the form of trains of nerve impulses. The experimental basis of the defining linear transfer function is presented. This transfer function is composed of a second order lag and a transport delay. The ventral nerve cord conduction time does not contribute to the transport delay. Nonlinear discrepancies from the linear model are evaluated and discussed.

Notes: Summary The construction of an element of thinking machine is described, as studied by E. R. Caianiello, in analogy with brain functions. This element is made of two parts: one simulates the operation of a neuron, and the other the connection between neurons. The possibility of a memory is inserted in the latter. Operating data are also given.

Notes: Summary 1. Information received by the sense organs is transmitted into the central nervous system by means of different discharge patterns of the neurons in the afferent pathways. As demonstrated in a previous paper these discharge patterns show in the visual system a remarkable random fluctuation in response to peripheral stimuli of constant characteristic. 2. The information capacity of a single nerve cell in an afferent sensory pathway is assumed to be $$I = \frac{1}{{t_i }}ld(t_i \cdot F_{max} ) bit \cdot sec^{ - 1} .$$ t i is the “summation interval” determined by the time constant of the central integrating process (15–80 msec), F max is the maximal impulse rate (per sec) of a given nerve cell within the interval t i . 3. The consequences of this equation are discussed and a three dimensional graphical representation of the equation is given. It is believed that F max and t i are different in different populations of neurons. 4. t i probably depends upon chemical processes in the CNS related to the synaptic transmission. A change of t i results in a change of the amount of information which can be transmitted by a nerve cell without changing the maximal impulse rate of the nerve cell.

Notes: Zusammenfassung Frühere Arbeiten liefen darauf hinaus, ein Nervenelement (das künstliche Neuron) qualitativ zu simulieren. Im folgenden werden die Ergebnisse der weiteren Entwicklungsstufe beschrieben — die Simulierung eines Neuronenanalogons, dessen Zeitbasis mit der der Aplysia identisch ist und dessen Spannungsamplitude(n) sich voneinander um einen Maßstabsfaktor unterscheiden. Dieses künstliche Neuron, das aus einem einzigen Operationsverstärker mit parallelverlaufenden linearen und nichtlinearen Rückkopplungsleitungen besteht, weist nicht nur eine quantitative Beziehung zu dem natürlichen auf; es ist auch in der Arbeitsweise und dem Schaltschema nach viel einfacher. Die Verhaltenscharakteristiken des Analogous, mit bzw. ohne Rückkopplung, werden beschrieben. Einige von den dargestellten und im Text erläuterten Charakteristiken sind: Ansetzen eines Wirkungspotentials durch depolarisierende Eingänge, Anodendurchschlagsspannung, Wiederpolarisation, gegen Totzeit aufgetragene Impulsstärke, Akkommodation, Adaptation und wiederholte Erzeugung des Wirkungspotentials durch andauerndes depolarisierendes Reizen.

Notes: Summary By means of an electronic averaging technique, it is possible to measure the evoked responses to acoustic stimuli on the outside of the human scalp, in spite of a signal-to-noise ratio of about 1∶20. The normal information flow gathered in the periphery by all sense organs, is reduced nearly for 10−7 on its way to higher storage centres. This diminution is caused partially by the so called “optimizing function” of the central nervous system, which is supposed to contribute most of the limited capacity of the higher parts of the information channel to that sensory system, which just contains the most (essential for the living organism) information. Based probably on the “unspecific pathway” the “optimizing function” is common to all sensory channels. Results of our experiments on the influence of the optimizing function and on multisensory stimulation give some view in information processing in man.

Notes: Zusammenfassung Dieser Bericht enthält die Ergebnisse einer Untersuchung des Farbensehens der Wirbeltiere, dargestellt in einem theoretischen Modell, das, obgleich es nur einen Receptor besitzt, auch auf mehrere Receptoren erweitert werden kann. Es wird angenommen 1., daß die Zeitkonstante der Veränderung des Receptor-Potentials die Farbeninformation des Lichtreizes überträgt, während die Potentialgröße mit der Intensität des Lichtreizes zusammenhängt, und 2., daß eine Gruppe von Zellen, die vorläufig als Ganglionzellen angenommen werden, mit jedem Receptorfeld assoziiert sind. Diese Zellen werden nur dann aktiviert, wenn die Zeitkonstante in einen bestimmten Bereich fällt. Demgemäß kann das visuelle Spektrum in Bereiche eingeteilt werden, die die Information aus diesem Bereich an das Zentralnervensystem weiterleiten. Die Unterscheidung der Wellenlängen in dem theoretischen Modell erreicht man durch ein Teilmodell der Retina, das differentiell beeinflußt wird. Ein Analogrechner wurde bei dieser Voruntersuchung verwandt. Es wurde besonders darauf geachtet, daß das Modell mit dem heutigen Stand des Wissens der Anatomie und Physiologie übereinstimmt. Die Ergebnisse ähneln den Verläufen von Granits Spektralempfindlichkeit und Kellys Amplitudenempfindlichkeit. Das Modell, das „Subjektive Farben-Erscheinungen” bei passenden Frequenzen voraussagt, wirft Fragen auf, die psychophysiologischen Methoden zugänglich sind.

Notes: Summary Binary sequences, whose statistical properties follow some law can be predicted with an accuracy depending on their statistical law. The conditional cumulative entropy is a measure of predictability and can be measured in a relatively simple way by using suitable methods. A binary predictor can be realized by the learning matrix for binary signals due to K. Steinbuch. The predictor system depends on the order of the statistical interdependence of the binary digits, which can be expressed in terms of cumulative redundancy. Binary sequences randomly generated by subjects show statistical interdependence between even three preceding digits. Experiments with 121 such binary sequences with 700 digits each have shown that on the average 73% of the digits can be predicted.

Notes: Summary It has been demonstrated that by functional error correction of translator circuits according to the definitions of part 1 a) it is possible to obtain the correct response in spite of a limited number of failing hardware elements; b) failing hardware elements can be located quickly and without large expense c) the cost of this method is insignificantly higher, eventually even lower than conventional diode circuitery (see fig. 14) d) the probability of failure of these circuits is by some magnitudes lower than that of conventional circuits (see fig. 13) e) the number of corrigible circuit failures can be increased under certain conditions (see part 3) likewise by subdivision of the correcting matrix (see table II). In this case the number of hardware elements or the cost of the self-correcting circuits resp. (see fig. 5 and table 2) is reduced further. f) The code redundancy of the non-binary code of the similarity matrix can be fully utilized by multiple discrimination and processing by several correcting matrices (see eq. 12).

Notes: Summary Using the physical and mathematical basis given in two foregoing papers, a differential equation is proposed for a model of the biological 24-hour-periodicity. This oscillation equation contains two characteristic non-linearities describing the self-sustaining property and the “circadian rule”. The right side of the equation (“external force”) represents the controlling environmental conditions, mainly the intensity of illumination. Solutions were obtained for different environmental conditions using a digital computer. Under “constant conditions” the solution of the equation describes oscillations self-sustained within a certain range of environmental conditions. In this range the oscillations fulfil the circadian rule, e.g. for light-active organisms: The frequency and the mean value of the oscillation increase with increasing light intensity; with an additional (arbitrary) threshold separating activity time and rest time for describing an activity rhythm, the α∶ρ (activity time ∶ rest time) ratio and the total amount of activity also increase. Under periodically changing environmental conditions five properties of the “Zeitgeber” used (two distinct intensities with twilight transitions) are variable and varied: The range of oscillation of the Zeitgeber, its frequency, its mean value, its L ∶ D ratio (time relation of light time and dark time), and the duration of the twilights. The most important of the examined properties was the phase angle difference between the (forced) oscillation and the (forcing) Zeitgeber. The general result for light-active organisms was: The phase of the oscillation advances relative to the Zeitgeber (in sofar as the oscillation is synchronized) if the period of the Zeitgeber, or its mean value, or its L∶D ratio, or the duration of the twilights increase. In dark-active organisms, the relation between phase angle difference and the mean value or the L∶D ratio is reversed. Exceptions to this general rule exist in the relation between phase angle difference and L ∶ D ratio if the “free running” period of the oscillation deviates too much from the period of a “weak” Zeitgeber (mainly in dark-active organisms) or if the duration of the twilights is too short (especially if the transitions are rectangular). Single exposures to light (or darkness) during constant conditions result in phase shifts depending in direction and amount on the phase of the oscillation at which the disturbance occured. The resulting response curves depend in range and form on the one hand on the time of measuring the phase shifts (either immediately or after several periods — in the steady state — following the disturbance) and, on the other hand, on the intensity of the initial illumination, on the duration, and on the intensity of the exposures, each in a different manner. Moreover, response curves effective in LD conditions deviate from those measured under constant conditions; the reason being the difference in the energy state of the oscillations in the two conditions. Therefore, it is impossible to derive the phase angle difference between the oscillation and a Zeitgeber in self-sustained oscillations from the measurement of response curves alone. The oscillation equation used contains only one free parameter, the frequency coefficient. If this coefficient is changed, the equation describes other biological rhythms. For instance, with a high value it describes the behaviour of single nerve cells, and that not only in cases of spontaneous rhythmicity (e.g. receptor cells) but also in cases of reactions to single or rhythmic stimuli. Moreover, the derived characteristics of the equation — especially the non-linearities — seem to be significant for other biological problems such as control mechanisms.

Notes: Summary In this paper a mathematical model for the fluctuation in excitability of nerve fibres is presented. The model is based on the concept of a threshold subject to noise-like variations. Emphasis is laid on the rate of fluctuation of these disturbances.

Notes: Summary The mean diameter of the human pupil was measured during stimulation of the eye with light of sinusoidally varying intensity and during stationary illumination with the corresponding average intensity. Continuous records of the pupil diameter were obtained using an electronic pupillometer. The light stimuli were electronically controlled by utilizing the Faraday effect and applied under “open loop” conditions. The pupil responded with a net contraction to modulation of the light intensity within a range of modulation frequencies up to 30 c/sec. The net contraction was maximal between 1 and 3 c/sec, but remained significant at high frequencies, which did not result in a periodic light reflex any more. The higher the modulation degree and the average intensity, the larger the net contraction. The dependence of the net contraction upon the modulation frequency is very similar to that of the subjective brightness (Brücke effect), although certain difficulties are encountered in attempting a direct comparison of the two phenomena.

Notes: Summary The optical properties of the compound eye of Drosophila have been analysed using the optomotor reactions of flies with normal and mutant eye pigmentation. The stimulus was provided by cylindrical patterns with different periodic intensity distributions rotating at different speeds. The response consists of a torque about the vertical axis and was recorded under conditions of fixed flight. (Maximum reaction is about 0.04 dyn · cm). The transfer characteristics of the optical system are determined by the inter-ommatidial angle Δϕ, influencing the resolving power and by the width of the visual field of single ommatidia Δρ, influencing the response at high spatial frequencies. The values Δϕ = 4.6° and Δρ= 3.5° are obtained from stimulus-response experiments with Drosophila. They are independent of the presence of screening pigments. Differences in the response of flies with strong (+, se), weak (w a), and missing (w) pigmentation can be explained by the increased amount of scattered light in the pigment-deficient eyes. The overall intensities in the equally illuminated receptors are expected to be in the ratio 1∶1∶8∶25, respectively. The perception of motion depends only on the temporal, not on the spatial phase relations between periodic intensity variations in neighbouring ommatidia. Therefore the inhomogeneous distribution of the inter-ommatidial angle Δϕ changes the resolving power in different parts of the eye without changing the response to motion. Different simultaneous stimuli of equal strength in different parts of the eye are averaged in the perceptive system of Drosophila according to the number of ommatidia in these parts.

Notes: Zusammenfassung Die „Lernmatrix”d ist eine Schaltungsstruktur, welche „Bedingte Reflexe” so zusammenfaßt, daß Lernvorgänge verwirklicht werden können. Im Verhalten der Lernmatrix sind zwei Phasen zu unterscheiden, nämlich: Die Lernphase, während welcher der Lernmatrix gleichzeitig Sätze von Signalen (Eigenschaften) {e} und den zugehörigen Bedeutungen b angeboten werden und sich demzufolge die Bedingten Reflexe bilden, und die Kannphase, während der sich nach Eingabe der Sätze Eigenschaften {e} die Bedeutung b oder nach Eingabe der Bedeutung b die Sätze Eigenschaften {e} ergeben. Die Lernmatrix kann beispielsweise mit Strukturspeichern (z.B. ferromagnetischen Ringkernen oder Transfluxoren) verwirklicht werden. Hierbei muß stufenweise eingeschrieben und nichtzerstörend abgelesen werden. Außerdem kann die Lernmatrix durch elektro-chemische Reaktionen verwirklicht werden. Wichtige Anwendungen der Lernmatrix werden sein: Automatische Zeichenerkennung, automatische Spracherkennung, allgemein Decodierung erlernter und eventuell gestörter Zeichen, Wiederauffinden von Informationen (Information Retrieval). Schließlich scheint die Lernmatrix ein nützliches Modell für die semantische Informationstheorie und für das Verständnis der Nachrichtenverarbeitung im Menschen zu sein.

Notes: Summary Hitherto it was assumed that the input signals to a learning matrix are digital, especially binary. In this paper the properties of learning matrices capable of learning and processing accordingly patterns of non-digital nature are investigated. It is shown that the recognition of patterns by means of such non-digital learning matrices offers extraordinary possibilities for the formation of invariants. For the description of the learning process a formal “perceptor” is defined, the properties of which are characteristic of both organic and technological perceptors. In addition, it is shown how the technological realization of non-digital learning matrices can be accomplished.

Notes: Summary The problem of finding metric strategies for decisions in which it is not possible to define mathematically the risks connected with the decision is a methodical problem. We must first know something about the laws of probability governing actual decisions of a big group of individuals. A theoretical basis for empirical tests is given in this paper. In the first part the structure of a probability-automaton is defined, which besides the applicability to decision processes may have also applications to formal neuron theory. The second part shows the use of the automaton for decision processes.

Notes: Summary The biological 24-hour-periodicity is based upon an endogenous (self-sustained) oscillation which is synchronized with the earth's rotation by periodically changing factors of the environment, primarily by the alternation of light and dark. These external „Zeitgebers” affect the phase of the endogenous oscillation. Theoretically, there are four different simple types of phase-control; all complicated types are combinations of these four types. In model experiments the behaviour of an oscillation in each of the four cases of phase-control is clearly demonstrated. The comparison of model experiments and biological experiments suggests that in organisms a specific combination-type of phase-control occurs. In this combination-type, a change in frequency is always positively correlated with a change in average level of the oscillation. Both parameters of the oscillation increase in light-active organisms and decrease in dark-active organisms with increasing light-intensity (“circadian rule”). In organisms both parameters are coupled by means of non-linear elements. The differential equation describing the 24-hour-periodcity is characterized by certain non-linearities. One of these makes the oscillation self-sustained and simultaneously couples the frequency of the oscillation to the average level, in the sense postulated by the circadian rule. The magnitude of the non-linearity is such that the resulting oscillation is intermediated between a harmonic and a relaxation type of oscillation, but has more characteristics of a harmonic oscillation. A second non-linearity which also couples frequency and level positively concerns the energy of recoil. All general properties of the biological 24-hour-periodicity can be reproduced by the described oscillator model. Some special properties (e.g. “pattern”) are more easily understood by the assumption of two coupled oscillators; the second oscillator, following the same general laws described above, is controlled by the first one. The oscillator hypothesis can be applied to biological periodicities with other frequencies; in general, the higher the frequency of a system the more the oscillation tends towards a relaxation type of oscillation.

Notes: Zusammenfassung/Summary 1. The activity of single nerve cells in the visual system of cats (curarized or encéphale isolé preparations) was investigated. Records were sampled from units in the optic tract, the lateral geniculate body, and the striate cortex. The non-sequential interval distribution and the mean discharge rate of spontaneous activity and of that during stimulation of the retina with continuous light was analysed over long periods. An interval analyser was used. 2. The mean discharge rate of spontaneous activity is highest in the optic tract and decreases significantly towards the visual cortex. The mean values are: 35.5 per sec in the optic tract (13 units), 14.0 per sec in the lateral geniculate (24 units) and 5.7 per sec in the visual cortex (145 units). 3. The variety of possible interval distributions was reduced to 3 characteristic types. As belonging to type I those distributions were classified which showed exponential form. Only the frequency of short intervals was reduced, so that the distribution had a peak at 8–10 msec. The joint interval histogram showed that the successive single discharges were independent from each other. From this it could be assumed that spike generation in these cells occurs according to a Poisson-type process. The initial dead time can be explained by the excitability cycle of the units or by recurrent or collateral synaptic interactions. — Bi- or trimodal interval distributions were labelled as type II. The different peaks were attributed to different activity determining factors. A third group (type III) is found by those distributions which show transitional characteristics between the other two. Only one peak of short intervals is distinguishable and flanked by a wide and unsystematic distribution of longer intervals. 4. In the optic tract mainly type I, in the lateral geniculate mainly type II and in the visual cortex almost always type III distributions were found. 5. The interval distribution from each unit in darkness remained essentially the same under continuous illumination, even though the average discharge rate of optic nerve fibers was considerably changed by stimulation. In cortical cells only little changes of discharge rate were induced by continuous illumination of the retina.

Notes: Summary This paper is concerned with the learning matrix for non-binary signals (LMn) as a classifying network. It can be shown that the properties of a LMn are determined by five parameters. One of these parameters corresponds to a criterion of similarity as the basis of the classification process. Two types of LMn, incorporating different criteria of similarity are investigated and compared as far as the accuracy and the invariance of classification are concerned. The second part of the paper deals with the technical realization of both types of the LMn. There the main problem is the storage of non-binary information in the connecting elements of the LMn. This difficulty can be met by the application of control techniques. Finally some results of investigations on transfluxors are reported which show that transfluxors are suitable connecting elements of a LMn.

Notes: Summary The torque exerted by the housefly Musca domestica during fixed flight was used as a measure of the optomotor reaction of the insect elicited by the rotation of cylindrical patterns with periodic distributions of surface brightness. Measurements were made of the dependence of the reaction on the wave length, speed of rotation, contrast, and mean brightness of the stimulus patterns. The effect on the reaction of modulation of the light illuminating the stimulus pattern was examined. Further experiments indicated that stimulation of only one of the two complex eyes is sufficient to elicit an optomotor reaction, and that there is overlap between the visual fields of neighboring photoreceptor units in the complex eye. Estimates of the rates of absorption of light quanta by individual ommatidia in the complex eye indicated that these rates are low enough that the Poisson statistics of the light quanta results in a significant level of noise in the light signals received by the photoreceptors, when the brightness of the stimulus pattern is low but still sufficient to elicit a measurable reaction. The contrast that is required of a rotating stimulus pattern in order to elicit a just-measurable reaction was found to depend upon the mean brightness of the pattern in a manner that is consistent with the hypothesis that the noise due to the statistics of the light quanta absorbed by the photoreceptors in the complex eye is a principle cause of the breakdown of the optomotor reaction at low values of the contrast and mean brightness of the stimulus pattern.