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  • 1
    Electronic Resource
    Electronic Resource
    Sehen mit bewegten Augen (1978)
    Springer
    Naturwissenschaften 65 (1978), S. 96-103 
    Details
    ISSN: 1432-1904
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology , Natural Sciences in General
    Notes: Abstract Recent microelectrode studies of single neurons of the retina, lateral geniculate nucleus, superior colliculus, and visual and parietal cortex are related to the problems of visual stability, prevention of fading, control of eye movements, and visual attention.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00440547
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  • 2
    Electronic Resource
    Electronic Resource
    Eine mathematische Formulierung für Reiz-Reaktionsbeziehungen retinaler Ganglienzellen (1970)
    Springer
    Biological cybernetics 7 (1970), S. 160-166 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Summary 1. In order to describe stimulus-response relationships for retinal ganglion cells a mathematical formulation is presented on the basis of experimental data and some simple assumptions. This concept involves two mechanisms — an excitatory and an inhibitory one — both extending over the whole receptive field. 2. The following formula $$S\left( I \right) = \frac{{c{\text{ }}{I \mathord{\left/ {\vphantom {I {I_S - 1}}} \right. \kern-\nulldelimiterspace} {I_S - 1}}}}{{1 + a{\text{ }}a{I \mathord{\left/ {\vphantom {I {I_S + 1}}} \right. \kern-\nulldelimiterspace} {I_S + 1}}}}$$ is used for description of the excitatory responses (on-response for on-center neurones, off-response for off-center neurones). The value ofa depends on the area of light stimulation,c is a constant;I/I S designates the ratio of stimulus brightness to threshold brightness. 3. Thresholds and suprathreshold response curves for concentric stimuli are described quantitatively by the formula. The experimental data were obtained by computer counts of spike discharges during 200 and 500 ms following the exciting light increment or decrement. 4. Ricco's, Weber-Fechner's and Stevens's laws are included in our conception as approximations of neuronal summations. These relations are limited to certain stimulus ranges; in contrast the above response function saturates at certain maximum discharge rates, as found by the S-shaped experimental curves; thus the formula is valid over the whole range of stimulation from threshold to very high intensities. 5. Thresholds as well as excitatory and inhibitory effects depend on background illumination and stimulus parameters. Therefore, center and surround size depend on these factors. 6. The formulation is set up for stationary responses and consequently does not describe time dependent characteristics. 7. Within these limits on-center and off-center neurones appear to have identical stimulus-response functions for adequate stimuli. Since in our experiments light increments and decrements were not symmetrical with respect to background illumination, a factor of 2 had to be introduced corresponding to the lower discharge rates of off-center-neurones.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00571696
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  • 3
    Electronic Resource
    Electronic Resource
    The three-loop model: a neural network for the generation of saccadic reaction times (1995)
    Springer
    Biological cybernetics 72 (1995), S. 185-196 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract This paper presents a computer simulation of the three-loop model for the temporal aspects of the generation of visually guided saccadic eye movements. The intention is to reproduce complex experimental reaction time distributions by a simple neural network. The operating elements are artificial but realistic neurones. Four modules are constructed, each consisting of 16 neural elements. Within each module, the elements are connected in an all-to-all manner. The modules are working parallel and serial according to the anatomically and physiologically identified visuomotor pathways including the superior colliculus, the frontal eye fields, and the parietal cortex. Two transient-sustained input lines drive the network: one represents the visual activity produced by the onset of the saccade target, the other represents a central activity controlling the preparation of saccades, e.g. the end of active fixation. The model works completely deterministically; its stochastic output is a consequence of the stochastic properties of the input only. Simulations show how multimodal distributions of saccadic reaction times are produced as a natural consequence of the model structure. The gap effect on saccadic reaction times is correctly produced by the model: depending only on the gap duration (all model parameters unchanged) express, fast-regular, and slow-regular saccades are obtained in different numbers. In agreement with the experiments, bi- or trimodal distributions are produced only for medium gap durations (around 200 ms), while for shorter or longer gaps the express mode disappears and the distributions turn bi- or even unimodal. The effect of varying the strength of the transient-sustained components and the ongoing activity driving the hierarchically highest module are considered to account for the interindividual variability of the latency distributions obtained from different subjects, effects of different instructions to the same subject, and the observation of express makers (subjects who produce exclusively express saccades). How the model can be extended to describe the spatial aspects of the saccade system will be discussed as well as the effects of training and/or rapid adaptation to experimental conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00201483
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  • 4
    Electronic Resource
    Electronic Resource
    The three-loop model: a neural network for the generation of saccadic reaction times (1995)
    Springer
    Biological cybernetics 72 (1995), S. 185-196 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract.  This paper presents a computer simulation of the three-loop model for the temporal aspects of the generation of visually guided saccadic eye movements. The intention is to reproduce complex experimental reaction time distributions by a simple neural network. The operating elements are artificial but realistic neurones. Four modules are constructed, each consisting of 16 neural elements. Within each module, the elements are connected in an all-to-all manner. The modules are working parallel and serial according to the anatomically and physiologically identified visuomotor pathways including the superior colliculus, the frontal eye fields, and the parietal cortex. Two transient-sustained input lines drive the network: one represents the visual activity produced by the onset of the saccade target, the other represents a central activity controlling the preparation of saccades, e.g. the end of active fixation. The model works completely deterministically; its stochastic output is a consequence of the stochastic properties of the input only. Simulations show how multimodal distributions of saccadic reaction times are produced as a natural consequence of the model structure. The gap effect on saccadic reaction times is correctly produced by the model: depending only on the gap duration (all model parameters unchanged) express, fast-regular, and slow-regular saccades are obtained in different numbers. In agreement with the experiments, bi- or trimodal distributions are produced only for medium gap durations (around 200 ms), while for shorter or longer gaps the express mode disappears and the distributions turn bi- or even unimodal. The effect of varying the strength of the transient-sustained components and the ongoing activity driving the hierarchically highest module are considered to account for the interindividual variability of the latency distributions obtained from different subjects, effects of different instructions to the same subject, and the observation of express makers (subjects who produce exclusively express saccades). How the model can be extended to describe the spatial aspects of the saccade system will be discussed as well as the effects of training and/or rapid adaptation to experimental conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004220050123
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  • 5
    Electronic Resource
    Electronic Resource
    Mathematical principles in afferent visual neurons: Differentiation, integration and transient proportionality related to receptive fields and shift-effect (1976)
    Springer
    Bulletin of mathematical biology 38 (1976), S. 253-267 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The dual reciprocal and antagonistic organization of B- and D-neurons of the afferent visual system is obtained using differentiation and integration as mathematical equivalents of visual information processing by an impulse frequency code. The spatial and temporal derivatives lead to the transient responses. A constant and a time-dependent term proportional to the luminance distribution describe the sustained response components and the shift-effect of retinal on- and off-center ganglion cells. Receptive field properties of lateral geniculate cells and their antagonistic shift-effect are obtained by passing the retinal output, i.e. the difference between B- and D-neurons' activity, once again through the same operations. However, the factor of proportionality is applied to the retina alone. The surprisingly small difference between retinal and geniculate receptive field properties on the one hand and the dramatic change from a synergistic to an antagonistic shift-effect on the other hand are thereby explained. The theory offers an understanding of a a possible functional significance of the shift-effect as a mechanism of transientrestoration of visual information, which prevents the system from total fading by means of shifts of the retinal image, normally produced by eye movements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459558
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  • 6
    Electronic Resource
    Electronic Resource
    A neuron field theory: Mathematical approaches to the problem of large numbers of interacting nerve cells (1973)
    Springer
    Bulletin of mathematical biology 35 (1973), S. 345-357 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A field theoretical approach to the problem of continuously distributed and simultaneously active nerve cells is presented, starting with a differential-integral field equation of the form $$\frac{\partial }{{\partial t}}\psi (r,t) = H\psi (r,t) + F(r,t)$$ which relates the field ψ to its inhibitory and excitatory sourcesF by means of the field operatorH. General solutions are represented with the aid of Green's functions. The Green's function, giving the response of the system to a very short point stimulation, is calculated in the absence of interaction between neurons and for a special case of non-local interaction. Possible applications of the theory are demonstrated for receptive fields and neuronal mechanisms in the vertebrate retina.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458342
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  • 7
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    Eine mathematische Formulierung f�r Reiz-Reaktionsbeziehungen retinaler Ganglienzellen (1970)
    Springer
    Details
    Publication Date: 1970-09-01
    Print ISSN: 0340-1200
    Electronic ISSN: 1432-0770
    Topics: Biology , Computer Science , Physics
    Published by Springer
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  • 8
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    The three-loop model: a neural network for the generation of saccadic reaction times (1995)
    Springer
    Details
    Publication Date: 1995-02-01
    Print ISSN: 0340-1200
    Electronic ISSN: 1432-0770
    Topics: Biology , Computer Science , Physics
    Published by Springer
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  • 9
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    The three-loop model: a neural network for the generation of saccadic reaction times (1995)
    Springer
    Details
    Publication Date: 1995-02-01
    Print ISSN: 0340-1200
    Electronic ISSN: 1432-0770
    Topics: Biology , Computer Science , Physics
    Published by Springer
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  • 10
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    Sehen mit bewegten Augen (1978)
    Springer
    Details
    Publication Date: 1978-02-01
    Print ISSN: 0028-1042
    Electronic ISSN: 1432-1904
    Topics: Biology , Chemistry and Pharmacology , Natural Sciences in General
    Published by Springer
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