HighDimensional Brain in a HighDimensional World: Blessing of Dimensionality Highdimensional data and highdimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The wellknown phenomenon of the xe2x80x9ccurse of dimensionalityxe2x80x9d states: many problems become exponentially difficult in high dimensions. Recently, the other side of the coin, the xe2x80x9cblessing of dimensionalityxe2x80x9d, has attracted much attention. It turns out that generic highdimensional datasets exhibit fairly simple geometric properties. Thus, there is a fundamental tradeoff between complexity and simplicity in high dimensional spaces. Here we present a brief explanatory review of recent ideas, results and hypotheses about the blessing of dimensionality and related simplifying effects relevant to machine learning and neuroscience.

Permutation Entropy and Statistical Complexity in Mild Cognitive Impairment and Alzheimerxe2x80x99s Disease: An Analysis Based on Frequency Bands We present one of the first applications of Permutation Entropy (PE) and Statistical Complexity (SC) (measured as the product of PE and JensenShanon Divergence) on Magnetoencephalography (MEG) recordings of 46 subjects suffering from Mild Cognitive Impairment (MCI), 17 individuals diagnosed with Alzheimerxe2x80x99s Disease (AD) and 48 healthy controls. We studied the differences in PE and SC in broadband signals and their decomposition into frequency bands (   xcexb4   ,    xcexb8   ,    xcexb1    and    xcexb2   ), considering two modalities: (i) raw time series obtained from the magnetometers and (ii) a reconstruction into cortical sources or regions of interest (ROIs). We conducted our analyses at three levels: (i) at the group level we compared SC in each frequency band and modality between groups; (ii) at the individual level we compared how the PE, SC plane differs in each modality; and (iii) at the local level we explored differences in scalp and cortical space. We recovered classical results that considered only broadband signals and found a nontrivial pattern of alterations in each frequency band, showing that SC does not necessarily decrease in AD or MCI.