Biomedical subjects

Gerold Baier

Publications and source records attributed to Gerold Baier.

7 recordsLinked to original sources

PubMed2006

Localized short-range correlations in the spectrum of the equal-time correlation matrix.

We suggest a procedure to identify those parts of the spectrum of the equal-time correlation matrix C where relevant information about correlations of a multivariate time series is induced. Using an ensemble average over each of the distances between eigenvalues, all nearest-neighbor distributions can be calculated individually. We present numerical examples, where (a) information about cross correlations is found in the so-called "bulk" of eigenvalues (which generally is thought to contain only random correlations) and where (b) the information extracted from the lower edge of the spectrum of C is statistically more significant than that extracted from the upper edge. We apply the analysis to electroencephalographic recordings with epileptic events.

Journal Article↗

PubMed2006

Quantification of cross correlations in complex spatiotemporal systems.

We propose a design of the equal time correlation matrix suitable for the analysis of multivariate time series with ill-defined phases. We present the cross-correlation analysis of model data sets taken from coupled stochastic oscillators and compare the concept with the results obtained from a conventional correlation matrix analysis. We show that the concept provides a higher sensitivity combined with a better statistical significance when quantifying weak cross correlations.

Journal Article↗

PubMed2005

Detection and characterization of changes of the correlation structure in multivariate time series.

We propose a method based on the equal-time correlation matrix as a sensitive detector for phase-shape correlations in multivariate data sets. The key point of the method is that changes of the degree of synchronization between time series provoke level repulsions between eigenstates at both edges of the spectrum of the correlation matrix. Consequently, detailed information about the correlation structure of the multivariate data set is imprinted into the dynamics of the eigenvalues and into the structure of the corresponding eigenvectors. The performance of the technique is demonstrated by application to N(f)-tori, autoregressive models, and coupled chaotic systems. The high sensitivity, the comparatively small computational effort, and the excellent time resolution of the method recommend it for application to the analysis of complex, spatially extended, nonstationary systems.

Journal Article↗

PubMed2005

EEG analysis with nonlinear excitable media.

The detection of patterns embedded within a complex, nonstationary, and noisy background activity is a crucial and important task in EEG analysis. The authors present a biologically inspired, analog approach to EEG analysis that is conceptually different from a variety of statistical approaches currently used. A nonlinear, excitable, spatially extended medium that is composed of diffusively coupled model neurons is considered. When EEG recordings are applied as local perturbations to such an excitable neural tissue, the induced transient changes in the dynamics of the perturbed system can be regarded as an instantaneous characterization of transient processes in the brain reflected by the EEG, e.g., in the form of a sequence of correlated dynamical events (patterns). Nonlinear excitable media can be implemented in form of an array of locally coupled integrated analog nonlinear electrical circuits called cellular neural networks, which represent a next evolutionary step in the parallel analog computer architecture. Using cellular neural networks, the authors show that the concept of signal-induced pattern generation allows an almost instantaneous and unsupervised detection of seizure onsets in EEG recordings. In addition, they show that a cellular neural network can be trained in a supervised way to approximate the degree of synchronization in EEG recordings. The resulting pattern-recognition device may be suitable for the prediction of epileptic seizures.

Animals↗

PubMed2004

Nonlinear dynamic conversion of analog signals into excitation patterns.

Local periodic perturbations induce frequency-dependent propagation waves in an excitable spatiotemporally chaotic system. We show how segments of noise-contaminated and chaotic perturbations induce characteristic sequences of excitations in the model system. Using a set of "tuned" excitable systems, it is possible to characterize signals by their spectral composition of excitation pattern. As an example, we analyze an epileptic "spike-and-wave" time series.

Journal Article↗

PubMed2002

Resonant forcing of a silent Hodgkin-Huxley neuron.

Dynamical behavior of a silent Hodgkin-Huxley neuron subjected to external periodic perturbations is investigated. Induced dynamics for this forced system, exhibit nonlinear resonance with respect to the forcing frequency. Within the U-shaped resonance curve, both regular (phase locked) and irregular spike sequences are invoked. For appropriate tuning frequencies, this simple system generates spike trains recordings similar to ones observed in actual experiments.

Journal Article↗

PubMed2002

Interaction of the IP(3)-Ca(2+) and the FGF-MAPK signaling pathways in the Xenopus laevis embryo: a qualitative approach to the mesodermal induction problem.

In this work we propose that the animal-vegetal gradient spatial distribution of the IP(3) receptors observed in the Xenopus embryo can effect a uniform FGF inducting input signal, allowing for different modes of transcription of the Xbra gene, producing the differentiation of the cells of the marginal zone. We analyze this hypothesis with a model for the interaction of the calcium signaling system with the MAPK cascade during the FGF mesodermal induction process, consisting of five non-linear coupled differential equations. A numerical treatment of a one- and two-cell system shows that the calcium flux between cells enhances the Raf activity levels, leading to oscillatory behavior. This qualitative result may be of consequence for the expression of the ventralizing characteristics of the FGF inducting signal.

Animals↗