Geometry for a brain. Optimal control in a network of adaptive memristors
Germano Resconi, Ignazio Francesco Licata · Advanced Studies in Theoretical Physics · 2013
Copyright © 2013 Germano Resconi and Ignazio Licata. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In the brain the relations between free neurons and the conditioned ones establish the constraints for the informational neural processes. These constraints reflect the systemenvironment state, i.e. the dynamics of homeocognitive activities. The constraints allow us to define the cost function in the phase space of free neurons so as to trace the trajectories of the possible configurations at minimal cost while respecting the constraints imposed. Since the space of the free states is a manifold or a non orthogonal space, the minimum distance is not a straight line but a geodesic. The minimum condition is expressed by a set of ordinary differential equation ( ODE) that in general are not linear. In the brain there is not an algorithm or a physical field that regulates the computation, then we must consider an emergent process coming out of the neural collective behavior triggered by synaptic variability. We define the neural computation as the study of the classes of trajectories on a