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  • 1
    Electronic Resource
    Electronic Resource
    Nonlinear autoregressive analysis of the 3/s ictal electroencephalogram: implications for underlying dynamics (1995)
    Springer
    Biological cybernetics 72 (1995), S. 527-532 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract.  In a previous study, nonlinear autoregressive (NLAR) models applied to ictal electroencephalogram (EEG) recordings in six patients revealed nonlinear signal interactions that correlated with seizure type and clinical diagnosis. Here we interpret these models from a theoretical viewpoint. Extended models with multiple nonlinear terms are employed to demonstrate the independence of nonlinear dynamical interactions identified in the ‘NLAR fingerprint’ of patients with 3/s seizure discharges. Analysis of the role of periodicity in the EEG signal reveals that the fingerprints reflect the dynamics not only of the periodic discharge itself, but also of the fluctuations of each cycle about an average waveform. A stability analysis is used to make qualitative inferences concerning the network properties of the ictal generators. Finally, the NLAR fingerprint is analyzed in the context of Volterra-Weiner theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004220050155
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  • 2
    Electronic Resource
    Electronic Resource
    Characteristic nonlinearities of the 3/s ictal electroencephalogram identified by nonlinear autoregressive analysis (1995)
    Springer
    Biological cybernetics 72 (1995), S. 519-526 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract We describe a method for the characterization of electroencephalographic (EEG) signals based on a model which features nonlinear feedback. The characteristic EEG ‘fingerprints’ obtained through this approach display the time-course of nonlinear interactions, rather than aspects susceptible to standard spectral analysis. Fingerprints of seizure discharges in six patients (five with typical absence seizures, one with complex partial seizures) revealed significant nonlinear interactions. The timing and pattern of these interactions correlated closely with the seizure type. Nonlinear autoregressive (NLAR) analysis is compared with other nonlinear dynamical measures that have been applied to the EEG.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00199894
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  • 3
    Electronic Resource
    Electronic Resource
    Characteristic nonlinearities of the 3/s ictal electroencephalogram identified by nonlinear autoregressive analysis (1995)
    Springer
    Biological cybernetics 72 (1995), S. 519-526 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract.  We describe a method for the characterization of electroencephalographic (EEG) signals based on a model which features nonlinear feedback. The characteristic EEG ‘fingerprints’ obtained through this approach display the time-course of nonlinear interactions, rather than aspects susceptible to standard spectral analysis. Fingerprints of seizure discharges in six patients (five with typical absence seizures, one with complex partial seizures) revealed significant nonlinear interactions. The timing and pattern of these interactions correlated closely with the seizure type. Nonlinear autoregressive (NLAR) analysis is compared with other nonlinear dynamical measures that have been applied to the EEG.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004220050154
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  • 4
    Electronic Resource
    Electronic Resource
    Discriminable textures with identical buffon needle statistics (1978)
    Springer
    Biological cybernetics 31 (1978), S. 231-234 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract A method is presented for generating pairs of textures for which the statistics of intersection with any collinear set of points placed at random on either texture are the same. The constraint that such “Buffon needle statistics” be identical is stronger than identity of second-order statistics. Nonetheless, many such texture pairs are effortlessly distinguishable. An example is given of such a texture pair, whose components are composed of either congruent ellipses or circles of various radii. The discriminability of such texture pairs implies that adequate models for human texture preception must contain local nonlinearities which receive input from non-collinear points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00337094
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  • 5
    Electronic Resource
    Electronic Resource
    Nonlinear autoregressive analysis of the 3/s ictal electroencephalogram: implications for underlying dynamics (1995)
    Springer
    Biological cybernetics 72 (1995), S. 527-532 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract In a previous study, nonlinear autoregressive (NLAR) models applied to ictal electroencephalogram (EEG) recordings in six patients revealed nonlinear signal interactions that correlated with seizure type and clinical diagnosis. Here we interpret these models from a theoretical viewpoint. Extended models with multiple nonlinear terms are employed to demonstrate the independence of nonlinear dynamical interactions identified in the ‘NLAR fingerprint’ of patients with 3/s seizure discharges. Analysis of the role of periodicity in the EEG signal reveals that the fingerprints reflect the dynamics not only of the periodic discharge itself, but also of the fluctuations of each cycle about an average waveform. A stability analysis is used to make qualitative inferences concerning the network properties of the ictal generators. Finally, the NLAR fingerprint is analyzed in the context of Volterra-Weiner theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00199895
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  • 6
    Electronic Resource
    Electronic Resource
    Local structure theory: Calculation on hexagonal arrays, and interaction of rule and lattice (1989)
    Springer
    Journal of statistical physics 54 (1989), S. 495-514 
    Details
    ISSN: 1572-9613
    Keywords: Cellular automata ; mean-field theory ; statistical mechanics ; chaos ; dynamical systems ; lattice gas
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Local structure theory calculations7 are applied to the study of cellular automata on the two-dimensional hexagonal lattice. A particular hexagonal lattice rule denoted (3422) is considered in detail. This rule has many features in common with Conway'sLife. The local structure theory captures many of the statistical properties of this rule; this supports hypotheses raised by a study ofLife itself(6). As inLife, the state of a cell under (3422) depends only on the state of the cell itself and the sum of states in its neighborhood at the previous time step. This property implies that evolution rules which operate in the same way can be studied on different lattices. The differences between the behavior of these rules on different lattices are dramatic. The mean field theory cannot reflect these differences. However, a generalization of the mean field theory, the local structure theory, does account for the rule-lattice interaction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01023491
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  • 7
    Electronic Resource
    Electronic Resource
    Asymptotic approach of generalized orthogonal functional expansions to Wiener kernels (1991)
    Springer
    Annals of biomedical engineering 19 (1991), S. 383-399 
    Details
    ISSN: 1573-9686
    Keywords: Central limit theorem ; M-sequence ; Nonlinear systems analysis ; Orthogonal functional ; Sum of sinusoids ; Wiener kernel
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract Wiener-like orthogonal functional expansions may be constructed with respect to test ensembles that are non-Gaussian, nonwhite, or both. Although the original Wiener expansion has particularly advantageous analytical properties, orthogonal expansions constructed with respect to other ensembles have practical advantages for laboratory implementation. We show how functional expansions based on two classes of input ensembles — white but non-Gaussian discrete noises and the sum of sinusoids-converge to the standard Wiener kernels. For discrete noises, the disparity between the standard and nonstandard kernels of a linear-static nonlinear transducer is proportional to the kurtosis of the input signal and inversely proportional to the ratio of the integration time of the linear filter to the time discretization. For the sum of sinusoids, the disparity is inversely proportional to the effective number of sinusoids passed by the initial linear stage.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00000003
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  • 8
    Electronic Resource
    Electronic Resource
    A relation between the Akaike criterion and reliability of parameter estimates, with application to nonlinear autoregressive modelling of ictal EEG (1992)
    Springer
    Annals of biomedical engineering 20 (1992), S. 167-180 
    Details
    ISSN: 1573-9686
    Keywords: Autoregressive models ; EEG ; Information theory ; Nonlinear analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract The Akaike minimum information criterion provides a means to determine the appropriate number of lags in a linear autoregressive model of a time series. We show that the Akaike criterion is closely related to the reliability estimates of successively determined parameters of a linear autoregressive (LAR) model. A similar criterion may be applied to determine whether the addition of a nonlinear term to an LAR model provides a statistically significant improvement in the description of the time series. As an example, we use this method to identify quadratic contributions to a nonlinear autoregressive characterization of a typical 3/s spike and wave seizure discharge.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02368518
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  • 9
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    Analyzing receptive fields, classification images and functional images: challenges with opportunities for synergy (2005)
    Springer Nature
    Details
    Publication Date: 2005-12-01
    Print ISSN: 1097-6256
    Electronic ISSN: 1546-1726
    Topics: Biology , Medicine
    Published by Springer Nature
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  • 10
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    Discriminable textures with identical buffon needle statistics (1978)
    Springer
    Details
    Publication Date: 1978-01-01
    Print ISSN: 0340-1200
    Electronic ISSN: 1432-0770
    Topics: Biology , Computer Science , Physics
    Published by Springer
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