Foundations of human problem solving
Despite great strides in both machine learning and neuroscience, we do not know how the human brain solves problems in the general sense. We approach this question by drawing on the framework of engineering control theory. We demonstrate a computational neural model with only localist learning laws that is able to find solutions to arbitrary problems. Using a combination of computational neural modeling, human fMRI, and representational similarity analysis, we show here that the roles of a number of brain regions can be reinterpreted as interacting mechanisms of a control theoretic system. The results suggest a new set of functional perspectives on the orbitofrontal cortex, hippocampus, basal ganglia, anterior temporal lobe, lateral prefrontal cortex, and visual cortex, as well as a new path toward artificial general intelligence.
We study advancing front methods for surface reconstruction. We propose a topological framework based on handlebody theory to implement such methods in a simple and robust way. As an example of the application of this framework we show an implementation of the Ball-Pivoting algorithm.