Open Access. Powered by Scholars. Published by Universities.®
- Institution
- Publication
Articles 1 - 2 of 2
Full-Text Articles in Mathematics
A Contraction Based Approach To Tensor Isomorphism, Anh Kieu
A Contraction Based Approach To Tensor Isomorphism, Anh Kieu
Honors Theses
Tensor isomorphism is a hard problem in computational complexity theory. Tensor isomorphism arises not just in mathematics, but also in other applied fields like Machine Learning, Cryptography, and Quantum Information Theory (QIT). In this thesis, we develop a new approach to testing (non)-isomorphism of tensors that uses local information from "contractions" of a tensor to detect differences in global structures. Specifically, we use projective geometry and tensor contractions to create a labelling data structure for a given tensor, which can be used to compare and distinguish tensors. This contraction labelling isomorphism test is quite general, and its practical potential remains …
Counting The Moduli Space Of Pentagons On Finite Projective Planes, Maxwell Hosler
Counting The Moduli Space Of Pentagons On Finite Projective Planes, Maxwell Hosler
Senior Independent Study Theses
Finite projective planes are finite incidence structures which generalize the concept of the real projective plane. In this paper, we consider structures of points embedded in these planes. In particular, we investigate pentagons in general position, meaning no three vertices are colinear. We are interested in properties of these pentagons that are preserved by collineation of the plane, and so can be conceived as properties of the equivalence class of polygons up to collineation as a whole. Amongst these are the symmetries of a pentagon and the periodicity of the pentagon under the pentagram map, and a generalization of …