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.
Highlights
In the interest of controlling their functions, neural networks have been treated by means of dynamic linear control systems
Controllability is one of the most important properties of dynamical systems, and that is why a great portion of the literature refers to this concept ([6,8,9], among others)
Liu et al [10], have developed the tools to undertake the study of controllability for arbitrary network sizes and topologies using the controllability matrix considering a few driver nodes on the network
Summary
The brain structure is a complex recurrent neuronal network that can be described by a graph The locution neuronal network makes reference to a particular model for comprehending brain function, in which neurons are the basic computational units and computation is interpreted in terms of network interactions. It has been shown [1] that cognitive control and the ability to control brain dynamics holds great suggestive of improvement of cognitive functions and reversing the possible disorder in learning processes. In the interest of controlling their functions, neural networks have been treated by means of dynamic linear control systems. Neural networks are treated as multi-agent systems, that is, systems of linear dynamic systems related to each other through a previously established topology. Structural controllability theory could be a good tool to control structured linear systems, in this way Garcia-Planas in
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