Generalized dimension of the intersection between EEGs

The generalized dimension defined by [Mandelbrot (1995) J Fourier Anal Appl special J.P. Kahane issue: 409-432] was applied to studying the interrelationship between various parts of human cerebral cortex in different functional conditions. Taking EEG signals from different brain areas as different sets, the generalized dimensions of their intersections were calculated to describe the interrelationship between them. The results showed that the generalized dimensions of intersections in different brain states decreased according to the following order: rest with eyes open, closed, light sleep, and deep sleep. The generalized dimensions of intersections related to the left or right temporal lobe were higher than the others when the subjects was doing mental arithmetic, and there was a decrease when the subjects listened to soft classical music. In addition, it was found that there was a noticeable difference in singular spectra between epileptic patients and normal subjects, irrespective of whether the epileptic patient was experiencing a seizure or not.