Controllability of Brain Neural Networks in Learning Disorders—A Geometric Approach

Maria Isabel García-Planas and Maria Victoria García-Camba
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Maria Isabel García-Planas: Departament de Matemàtiques, Universitat Politècnica de Catalunya, 08028 Barcelona, Spain
Maria Victoria García-Camba: Neurofisiología Clínica, Clínica Corachan, 08017 Barcelona, Spain

Mathematics, 2022, vol. 10, issue 3, 1-13

Abstract: The human brain can be interpreted mathematically as a linear dynamical system that shifts through various cognitive regions promoting more or less complicated behaviors. The dynamics of brain neural network play a considerable role in cognitive function and therefore of interest in the bid to understand the learning processes and the evolution of possible disorders. The mathematical theory of systems and control makes available procedures, concepts, and criteria that can be applied to ease the perception of the dynamic processes that administer the evolution of the brain with learning and its control with treatment in case of disorder. In this work, a geometric study through the conception of exact controllability is comprehended to detect the minimum set and the location of the driving nodes of learning. We will describe the different roles of the nodes in the control of the paths of brain networks and show the transition of some driving nodes and the preservation of the rest in the course of learning in patients with some learning disability.

Keywords: neural network; controllability; exact controllability; eigenvalues; eigenvectors; linear systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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