Neurophysiological correlates to the human brain complexity through $q$-statistical analysis of electroencephalogram

The prospects of assessing neural complexity (NC) by $q$-statistics of the systemic organization of different types and levels of brain activity were studied. In 70 adult subjects, NC was assessed via the parameter $q$ of $q$-statistics, applied to the ongoing and EEG and its spectral power of 20 scalp points (channels). The NC were estimated both globally for all channels (AllCh) and locally (for each single channel) in different Functional States (FSs). The values of $q$ was compared among FSs and single channels, as well they were correlated with the power of $\theta$ (4-8Hz), $\beta_1$ (15-25Hz) and others EEG bands, in each FS. The value of $q$ across all FSs was higher for AllCh than for the single channels FSs. Consistently with previous studies, we found a negative correlation between NC and age. The FSs did not influence the $q$ of the EEG in AllCh, although locally the FS modulated $q$ in a consistent manner (e.g., reducing $q$ in posterior sites with eyes closed). The $q$ was correlated positively with the power of the $\theta$ and negatively with that of the $\beta_1$ band in general. These findings support the idea that, as a first approach, $q$-statistics can describe the human NC. The relationship between $q$ and $\theta$ power aligns with greater NC during FSs such as listening music and resting with eyes open, which is consistent with high-order representations rather than low-informative attentional tasks (OddBall).