Modeling complex nuclear spectra: Regularity versus chaos

Temporal correlations versus noise in the correlation matrix formalism: an example of the brain auditory response

We adopt the concept of the correlation matrix to study correlations among sequences of time-extended events occurring repeatedly at consecutive time intervals. As an application we analyze the magnetoencephalography recordings obtained from the human auditory cortex in the epoch mode during the delivery of sound stimuli to the left or right ear. We look into statistical properties and the eigenvalue spectrum of the correlation matrix C calculated for signals corresponding to different trials and originating from the same or opposite hemispheres. The spectrum of C largely agrees with the universal properties of the Gaussian orthogonal ensemble of random matrices, with deviations characterized by eigenvectors with high eigenvalues. The properties of these eigenvectors and eigenvalues provide an elegant and powerful way of quantifying the degree of the underlying collectivity during well-defined latency intervals with respect to stimulus onset. We also extend this analysis to study the time-lagged interhemispheric correlations, as a computationally less demanding alternative to other methods such as mutual information.