Data processing system utilizing topological methods to manipulate and categorize n-dimensional datasets

摘要

Methods are constructed for defining equivalence relations on embedded manifolds. A continuous path in the space of equivalence relations that spans from “homologous” to “diffeomorphic” and another similar path with endpoints “homologous” and “isometric” are given. Underlying the methodology is a convolution algebra of homology sampling functions. The methodology has applications for describing geometrical arrangements in material science, molecular biology, data science and physics. The methods are implemented in program code stored in a computer readable media and executable on a computer system to provide data analysis functions for a user.