Die präiktale Phase von epileptischen Anfällen - Untersuchung mit neuen Ansätzen der multivariaten Zeitreihenanalyse

本文件的目的有两个：首先，提供了一份关于在Cuernavaca（墨西哥）与DFG研究资助“Die präiktale Phase von epileptischen Anfällen - Untersuchung mit neuen Ansätzen der multivariaten zeitreihenanalyze”（RU 1401/1-1）有关的工作的临时报告。采用随机矩阵理论（RMT）中的方法，将其应用于脑电图（EEG）的多变量时间序列分析。这些新工具在分离随机与非随机相关性方面被证明是强大而有价值的。即使是EEG中微弱的真实相关性也能被可靠地检测出来。由于在调查期间出现了许多新的和紧急的问题，建议将补助金再延长3个月，以便能够完成调查。完成聚类参与向量（CPV）概念的发展，该概念可用于EEG通道之间的聚类检测。此外，还计划详细研究在脑电图非平稳性存在下等时相关矩阵特征值的单独展开的最近邻间距分布的度量行为。

The purpose of the present document is twofold: First, an interim report is given about the work done in Cuernavaca (Mexico) in connection with the DFG research grant “Die präiktale Phase von epileptischen Anfällen - Untersuchung mit neuen Ansätzen der multivariaten Zeitreihenanalyse” (RU 1401/1-1). Measures taken from Random Matrix Theory (RMT) were adapted in order to be applied to multivariate time series analysis of the electroencephalogram (EEG). The novel tools turned out powerful and valuable for separation of random from non-random correlations. Even weak genuine correlations in the EEG can be detected reliably.As during the investigation many new and urgent questions came up it is suggested to extend the grant for another 3 months in order to be able to complete the investigation. The development of the concept of the Cluster Participation Vectors (CPV), which can be used for detection of clusters among the EEG channels, shall be finished. Furthermore it is planned to study in detail the behavior of the measure of the individually unfolded nearest neighbor spacing distribution of the eigenvalues of the equal-time correlation matrix in the presence of EEG non-stationarity.