Abstract neural automata on compact Riemannian manifold

By means of topological conjugate transformation, the previous theory of abstract neural automata (ANA) on d-dimensional (d greater than or equal to 1) integer lattice is extended to compact Riemannian manifold This paper points out emphatically that intelligence ofANA is related to the geometrical features. The greater the volume of relative plane, the stronger the intelligence; curved Riemannian manifold (X) over tilde configuration space of ANA are locally flat such that the cognitive process of NAN Emits the Gibbs' probability measure for a sufficiently small time i. e. the cognitive process of ANA can determine the solution in a sufficiently small time the problem. This hypothesis was supported by studying the human brain, in particular by studying Einstein's brain.