We introduce a framework for generating, organizing, and reasoning with computational knowledge. It is motivated by the observation that most problems in Computational Sciences Engineering (CSE) can be described as of completing (from data) graph (or hypergraph) representing dependencies between functions variables. In setting nodes represent variables edges hyperedges) functionals). Functions ...

Nonlinear dimensionality reduction is an active area of research. In this paper, we present a thematically different approach to detect low-dimensional manifold that lies within set bounds derived from given point cloud. A matrix representing distances on low-rank, and our method based current low-rank Matrix Completion (MC) techniques for recovering partially observed fully entries. MC methods...

Any non-complete orthonormal system in a Hilbert space can be transformed into basis by small perturbations.