One considers a group S of subjects and one uses the measured values of EEG waves and the levels of anxiety given by the psychologists for the members of S in order to construct a monotone measure µ . This measure µ is such that the levels of anxiety of the members of S are Choquet integrals with respect to µ . One infers that this is true for any other subject. This inference is validated by comparing the values obtained via the above mentioned method with the results given by the psychologists for another group of subjects S’. We think that this procedure is completely new for the computation of the anxiety degree.

This paper investigates how neuronal networks modify their functional organization according to cognitive demands, using the percolation threshold as an indicator of the distance from the critical state. Based on EEG recordings collected during rest and two cognitive tasks (working memory and inhibitory control), functional networks were constructed, and variations in the giant cluster were analyzed in relation to the connectivity threshold. Results show that under high cognitive load, the neuronal network approaches a near-critical zone, characterized by efficient integration and functional dynamism. Moreover, lower percolation threshold values correlate with better cognitive performance, suggesting that optimal information processing occurs near criticality. The study confirms the relevance of the critical brain theory and highlights the potential of pc as a functional biomarker for assessing cognitive flexibility. Keywords: percolation, EEG, neuronal networks, criticality, giant cluster, connectivity, working memory, synchronization, cognitive performance