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  • 1
    Electronic Resource
    Electronic Resource
    Identification of MGB cells by Volterra kernels (1987)
    Springer
    Biological cybernetics 56 (1987), S. 261-268 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract Neuronal systems can be described by their transfer functions, which can be represented by a Volterra series expansion. While the high level of abstraction which characterizes this representation enables a global description, it is problematic, to some extent, in the context of linking the formal representation of the system to its actual structure. The formal representation is unique, yet there are multiple physical realizations of this representation. Separating the system's output into its logical components (linear, cross-linear, and self nonlinear, in this study), and inspecting the relative contribution of these components, might provide a key towards a linkage between the formal and actual representations. Based on results drawn from identification of MGB cells of the squirrel monkey, it is shown that the relative contributions can be described in neurobiological terms such as excitation and inhibition and thus be attributed to actual sybsystems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00365221
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Analysis of recall and recognition in a certain class of adaptive networks (1979)
    Springer
    Biological cybernetics 32 (1979), S. 35-40 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract A general model of adaptive networks which perform recall is analyzed in view of qualitative psychological findings. The assumptions underlying the basic model are few and general in the sense that no specifications of structure or mechanisms of adaptation are imposed. The analysis of the model is towards the addition of various features drawn from the global input-output relations expected from the networks. The memorizing process of recognition is found to be intrinsic to the model, and four of the most prominent relations between the performance of recall and recognition are shown to either exist in model or to be realizable by means of few additional plausible features.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00337449
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Identification of MGB cells by Volterra kernels (1985)
    Springer
    Biological cybernetics 51 (1985), S. 383-390 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract The function of CNS sites is frequently explored by an analysis of its input-output relationships. However, such research are often confined to a qualitative and subjective inspection of raw data. System Identification methods can be used to formalize the stimulus-response relations, and one of them, the Volterra approach, is employed here in order to define these relations in the MGB of the squirrel monkey, natural vocalizations being the stimuli. In order to validate the formal representation of the system under study, the predictibility power of the model is tested. Having the distances between responses (PSTH) and predicted response quantified, it is found that the predictions made by the model are, in general, “closer” to the actual responses then some arbitrarily chosen responses. It is concluded that there are cells in the MGB that can be characterized by their Volterra kernels, and further research on the cell's functional role can be based on these kernels.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00350778
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  • 4
    Electronic Resource
    Electronic Resource
    Prediction of linear and non-linear responses of MGB neurons by system identification methods
    Amsterdam : Elsevier
    Bulletin of Mathematical Biology 51 (1989), S. 337-346 
    Details
    ISSN: 0092-8240
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1016/S0092-8240(89)80080-1
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Prediction of linear and non-linear responses of MGB neurons by system identification methods
    Amsterdam : Elsevier
    Bulletin of Mathematical Biology 51 (1989), S. 337-346 
    Details
    ISSN: 0092-8240
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1016/S0092-8240(89)80080-1
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Discrete stochastic models for firing of a neuron
    Amsterdam : Elsevier
    Journal of Theoretical Biology 34 (1972), S. 155-184 
    Details
    ISSN: 0022-5193
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1016/0022-5193(72)90061-6
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  • 7
    Electronic Resource
    Electronic Resource
    On the extinction of a colonizing species
    Amsterdam : Elsevier
    Theoretical Population Biology 3 (1972), S. 406-433 
    Details
    ISSN: 0040-5809
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1016/0040-5809(72)90014-7
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Prediction of linear and non-linear responses of MGB neurons by system identification methods (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 337-346 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In sensory physiology, various System Identification methods are implemented to formalized stimulus-response relationships. We applied the Volterra approach for characterizing input-output relationships of cells in the medial geniculate body (MGB) of an awake squirrel monkey. Intraspecific communication calls comprised the inputs and the corresponding cellular evoked responses—the outputs. A set of vocalization was used to calculate the kernels of the transformation, and these kernels subserved to predict the responses of the cell to a different set of vocalizations. It was found that it is possible to predict the response (PSTH) of MGB cells to natural vocalizations, based on envelopes of the spectral components of the vocalization. Some of the responses could be predicted by assuming a linear transformation function, whereas other responses could be predicted by non-linear (second order) kernels. These two modes of transformation, which are also reflected by a distinct spatial distribution of the linearvis-à-vis non-linear responding cells, apparently representa new revelation of parallel processing of auditory information.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460112
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  • 9
    Electronic Resource
    Electronic Resource
    Identification of MGB cells by volterra kernels (1987)
    Springer
    Biological cybernetics 56 (1987), S. 203-208 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract System Identification methods can be implemented in sensory physiology to formalize stimulus-response relationships. We apply the Volterra approach in order to define input-output relations of Medial Geniculate Body (MGB) cells in the awake squirrel monkey. The transfer functions (kernels) of MGB cells are computed using input output pairs. The inputs are intraspecific communication sounds, represented by their spectral components at a 1 or 1/3 octave resolution, yielding thus a multi input system. The outputs are represented by the responses of single neurons expressed as the smoothed Peri Stimulus Time Histograms (PSTHs). The kernels are computed for various combinations of the model: linear and quadratic Volterra expansions respectively 1 and 1/3 octave resolution of the input. Judging by the predictions of these models, it can be concluded that the model predictibility power is systematically improved as the order of the model and its spectral resolution are increased. An analysis of the predicted responses reveals that in certain cases, the quality of the predictions might be related primarily to either the order of the model, or alternatively to the spectral resolution of the input. The quality of the predictions, and their “Linearity”, are associated with the spatial location of the cells within the MGB. Cells located at the medial aspect of the nucleus exhibit more “linear” responses, which are also better predicted, compared with most other cells.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00317995
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  • 10
    Electronic Resource
    Electronic Resource
    Variational Principles and Sobolev-Type Estimates for Generalized Interpolation on a Riemannian Manifold (1999)
    Springer
    Constructive approximation 15 (1999), S. 175-208 
    Details
    ISSN: 1432-0940
    Keywords: Key words. Approximation order, Positive definite kernels, Sobolev spaces, Riemannian manifolds. AMS Classification. Primary: 41A05, 42A82, 42C10; Secondary: 42A10.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. The purpose of this paper is to study certain variational principles and Sobolev-type estimates for the approximation order resulting from using strictly positive definite kernels to do generalized Hermite interpolation on a closed (i.e., no boundary), compact, connected, orientable, m -dimensional C ∞ Riemannian manifold $ \cal M $ , with C ∞ metric g ij . The rate of approximation can be more fully analyzed with rates of approximation given in terms of Sobolev norms. Estimates on the rate of convergence for generalized Hermite and other distributional interpolants can be obtained in certain circumstances and, finally, the constants appearing in the approximation order inequalities are explicit. Our focus in this paper will be on approximation rates in the cases of the circle, other tori, and the 2 -sphere.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s003659900104
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