Applied and Computational Mathematics and Statistics

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  • Author:
    Christopher L. Ebsch
    Advisory Committee:
    Robert Rosenbaum
    Degree Area:
    Applied and Computational Mathematics and Statistics
    Degree:
    Doctor of Philosophy
    Defense Date:
    2019-03-29
    Record Visibility:
    Public
  • Author:
    Martin P. Barron
    Advisory Committee:
    Fang Liu, Steven Buechler, Jun Li
    Degree Area:
    Applied and Computational Mathematics and Statistics
    Degree:
    PhD
    Defense Date:
    2018-06-14
    Record Visibility:
    Public
  • Creator(s):
    Jonathan Hauenstein, Alan Liddell, Sanesha McPherson, Yi Zhang
    Description:

    Standard interior point methods in semidefinite programming can be viewed as tracking a solution path for a homotopy defined by a system of bilinear equations. By considering this in the context of numerical algebraic geometry, we employ numerical algebraic geometric techniques such as adaptive precision path tracking, endgames, and projective space to accurately solve semidefinite programs. We develop feasibility tests for both primal and dual problems which can distinguish between the fou…

    Date Created:
    2018-04-10
    Record Visibility:
    Public
  • Author:
    Claire McKay Bowen
    Advisory Committee:
    Fang Liu
    Degree Area:
    Applied and Computational Mathematics and Statistics
    Degree:
    PhD
    Defense Date:
    2018-03-27
    Record Visibility:
    Public
  • Creator(s):
    Jonathan Hauenstein
    Description:

    A common problem when analyzing models, such as a mathematical modeling of a biological process, is to determine if the unknown parameters of the model can be determined from given input-output data. Identifiable models are models such that the unknown parameters can be determined to have a finite number of values given input-output data. The total number of such values over the complex numbers is called the identifiability degree of the model. Unidentifiable models are models such that th…

    Date Created:
    2018-03-09
    Record Visibility:
    Public
  • Creator(s):
    Samantha Sherman, Jonathan Hauenstein
    Description:

    Computational tools in numerical algebraic geometry can be used to numerically approximate solutions to a system of polynomial equations. If the system is well-constrained (i.e., square), Newton’s method is locally quadratically convergent near each nonsingular solution. In such cases, Smale’s alpha theory can be used to certify that a given point is in the quadratic convergence basin of some solution. This was extended to certifiably determine the reality of the corresponding sol…

    Date Created:
    2018-03-08
    Record Visibility:
    Public
  • Creator(s):
    Margaret Regan, Jonathan Hauenstein
    Description:

    A common computational problem is to compute topological information about a real surface defined by a system of polynomial equations. Our software, called polyTop, leverages numerical algebraic geometry computations from Bertini and Bertini_real with topological computations in javaPlex to compute the Euler characteristic, genus, Betti numbers, and generators of the fundamental group of a real surface. Several examples are used to demonstrate this new software.

    Date Created:
    2018-03-02
    Record Visibility:
    Public
  • 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
    Record Visibility:
    Public
    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
    Record Visibility:
    Public
  • 22

    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
    Record Visibility:
    Public
  • 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
    Record Visibility:
    Public
  • Author:
    Dong Lu
    Advisory Committee:
    Yongtao Zhang
    Degree Area:
    Applied and Computational Mathematics and Statistics
    Degree:
    PhD
    Defense Date:
    2017-04-27
    Record Visibility:
    Public