Using integral equations to capture spatiotemporal relations in the brain

Project Summary Medical recordings contain dynamical information that can provide quantitative pathological fingerprints that prove crucial to correct diagnostic. Brain recordings are particularly important for cognitive studies, as the state of the brain at a single instant is not sufficient to determine cognition, which is a highly complex dynamical process. Consequently, in order to correctly diagnose the severity of cognitive pathologies, it is important to analyze brain dynamics through their recordings. Machine Learning (ML) algorithms based on static approaches tend to miss the dynamical spatiotemporal relations of the recordings, while ML methods based on local equations do not take into account the long-distance spatiotemporal relations. Here, we propose to use ML methods based on nonlocal equations and operators that allow us to extract a dynamical fingerprint of the brain, and use this to develop diagnostic continuous scores (spectra of severity). The use of nonlocal equations such as integral equations and integro-differential equations to model the brain has been pioneered decades ago. However, these studies have never been extended to ML methods, except in our recent preliminary studies. Our focus, therefore, is to apply such methodologies to model (predict) brain dynamics, and employ the learned models to extract the model states (self-attention) that characterize brain cognition. These states will therefore be used to develop diagnostic scores.