Abstract

Recent research has revealed the presence of turbulence in brain dynamics and identified turbulent flows as critical supports for large-scale network communication. Traditionally, quantitative descriptors of brain turbulence have been derived primarily from dynamical systems modeling. In this study, we explore a dimensionality reduction approach based on multivariate functional data—data represented as continuous vector functions over a given interval—which are realizations of a spatially indexed random functional variable. These data are modeled in two levels of hierarchy: the first corresponds to independent and identically distributed realizations of the functional variable at each spatial location, and the second encompasses the spatial locations that constitute the main dependent structure generating the multivariate functional data. Within this setting, a functional independent component analysis approach is proposed to model turbulent flows of brain activity observed in electroencephalographic recordings. Through an experimental study of motor-related emotional arousal, we demonstrate that these brain dynamics operate in a turbulent and near-critical regime.