Description of the sub-Markov kernel associated to generalized ultrametric matrices. An algorithmic approach

AbstractWe supply a simple algorithm which describes the sub-Markov kernel P associated to a nonsingular generalized ultrametric matrix U. This algorithm is based on the dyadic tree structure of U, it identifies the exiting roots of P and Pt, and the couples i≠j for which Pij>0 (equivalently (U−1)ij<0)

An intracranial EEG study of the neural dynamics of musical valence processing

The processing of valence is known to recruit the amygdala, orbitofrontal cortex and relevant sensory areas. However, how these regions interact remains unclear. We recorded cortical electrical activity from 7 epileptic patients implanted with depth electrodes for presurgical evaluation while they listened to positively and negatively valenced musical chords. Time frequency analysis suggested a specific role of the orbitofrontal cortex in the processing of positively valenced stimuli while, most importantly, Granger causality analysis revealed that the amygdala tends to drive both the orbitofrontal cortex and the auditory cortex in theta and alpha frequency bands, during the processing of valenced stimuli. Results from the current study show the amygdala to be a critical hub in the emotion processing network: specifically one that influences not only the higher order areas involved in the evaluation of the stimulus’s emotional value but also the sensory cortical areas involved in the processing of its low level acoustic features