Applied and Computational Mathematics and Statistics

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  • Author(s):
    Michael Hildreth
    Abstract:

    This report is a direct result of consultation with the research communities funded by the Mathematical and Physical Sciences (MPS) Directorate at the National Science Foundation (NSF). The goal of this effort is to provide feedback to NSF on current best practices with regard to research data curation, discovery, access, preservation, and re-use, and suggestions for areas of improvement and investment that could facilitate broader curation of, access to, and re-use of research data in the fu…

    Date Created:
    2017-08-31
    Resource Type
    Report
  • Author:
    Francesco Pancaldi
    Advisory Committee:
    Andrew Sommese, Mark Alber
    Degree Area:
    Applied and Computational Mathematics and Statistics
    Degree:
    PhD
    Defense Date:
    2017-06-20
  • 15

    Doctoral Dissertation

    Author:
    Alan Claude Liddell, Jr.
    Advisory Committee:
    Jonathan Hauenstein, Alan Lindsay, Andrew Sommese
    Degree Area:
    Applied and Computational Mathematics and Statistics
    Degree:
    PhD
    Defense Date:
    2017-06-22
  • Creator(s):
    Margaret Regan, Jonathan Hauenstein
    Description:

    Three key aspects of applying homotopy continuation to parameterized systems of polynomial equations are investigated. First, for parameterized systems which are homogenized with solutions in projective space, we investigate options for selecting the affine patch where computations are performed. Second, for parameterized systems which are overdetermined, we investigate options for randomizing the system for improving the numerically stability of the computations. Finally, since one is typica…

    Date Created:
    2017-07-06
  • Author:
    Dong Lu
    Advisory Committee:
    Yongtao Zhang
    Degree Area:
    Applied and Computational Mathematics and Statistics
    Degree:
    PhD
    Defense Date:
    2017-04-27
  • Author:
    Michael B Machen
    Advisory Committee:
    Dr. Yong-Tao Zhang
    Degree Area:
    Applied and Computational Mathematics and Statistics
    Degree:
    PhD
    Defense Date:
    2017-04-04
  • Author:
    Alicia T. Specht
    Advisory Committee:
    Jun Li
    Degree Area:
    Applied and Computational Mathematics and Statistics
    Degree:
    PhD
    Defense Date:
    2017-04-06
  • Author:
    Shant M. Mahserejian
    Advisory Committee:
    Dr. Mark Alber, Dr. Jun Li, Dr. Alexandra Jilkine, Dr. Holly Goodson
    Degree Area:
    Applied and Computational Mathematics and Statistics
    Degree:
    PhD
    Defense Date:
    2017-03-30
  • Creator(s):
    Jonathan Hauenstein
    Description:

    The Kuramoto model describes synchronization behavior among coupled oscillators and enjoys successful application in a wide variety of fields. Many of these applications seek phase-coherent solutions, i.e., equilibria of the model. Historically, research has focused on situations where the number of oscillators, n, is extremely large and can be treated as being infinite. More recently, however, applications have arisen in areas such as electrical engineering with more modest values of n. For…

    Date Created:
    2017-04-07
  • Description(s):
    A movie showing the change in the number of stable steady-state solutions as a function of the cell-to-cell communication. Software code using Matlab and Bertini is also provided which was used to generate the frames of this movie.
    Creator(s):
    Jonathan Hauenstein
    Date Published:
    2016
  • Creator(s):
    Jonathan Hauenstein
    Description:

    Stewart-Gough platforms are mechanisms which consist of two rigid objects, a base and a platform, connected by six legs via spherical joints. For fixed leg lengths, a generic Stewart-Gough platform is rigid with 40 assembly configurations (over the complex numbers) while exceptional Stewart-Gough platforms have infinitely many assembly configurations and thus have self-motion. We define a family of exceptional Stewart-Gough platforms called Segre-dependent Stewart-Gough platforms which aris…

    Date Created:
    2017-01-17
  • Creator(s):
    Jonathan Hauenstein
    Description:

    We define tensors, most of which correspond with cubic polynomials, which have the same exponent w as the matrix multiplication tensor. In particular, we study the symmetrized matrix multiplication tensor defined on an nxn matrix A by trace(A^3). The use of polynomials enables the introduction of additional techniques from algebraic geometry in the study of the matrix multiplication exponent w.

    Date Created:
    2017-01-07