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Modifying ShortLoop Software to run in Higher Dimensions

Neidecker, Peter Johannes

Abstract Details

2017, Master of Mathematical Sciences, Ohio State University, Mathematical Sciences.
Many problems in science and engineering involve determining geometrical and topological information about a structure based on a point cloud derived from the structure. One such problem involves computing a shortest basis for the first homology group H1(M) where M is a smooth manifold. Dey, Sun, and Wang have already come up with an algorithm to approximate H1(M) from a point cloud P derived from M. This algorithm was implemented in C++ by the Jyamiti research group at The Ohio State University; however, it was only implemented to run on three dimensional surfaces or point clouds. Although many problems in science and engineering involve three dimensional complexes, there are certainly problems where finding a shortest basis for the first homology group of a higher dimensional complex may be useful or necessary. In this thesis, we will describe the method of updating the code to run on higher dimensional complexes. Additionally, we aim to provide some flexibility to how a potential user might use the code by updating the code to work for different types of input files.
Tamal Dey (Advisor)
Anastasios Sidiropoulos (Committee Member)
38 p.

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Citations

  • Neidecker, P. J. (2017). Modifying ShortLoop Software to run in Higher Dimensions [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1492707443943863

    APA Style (7th edition)

  • Neidecker, Peter. Modifying ShortLoop Software to run in Higher Dimensions. 2017. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1492707443943863.

    MLA Style (8th edition)

  • Neidecker, Peter. "Modifying ShortLoop Software to run in Higher Dimensions." Master's thesis, Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1492707443943863

    Chicago Manual of Style (17th edition)