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  • Creator(s):
    Jonathan Hauenstein, Margaret Regan
    Description:

    Polynomials which arise via elimination can be difficult to compute explicitly. By using a pseudo-witness set, we develop an algorithm to explicitly compute the restriction of a polynomial to a given line. The resulting polynomial can then be used to evaluate the original polynomial and directional derivatives along the line at any point on the given line. Several examples are used to demonstrate this new algorithm including examples of computing the critical points of the discriminant locu…

    Date Created:
    2020-03-27
    Record Visibility:
    Public
  • Creator(s):
    Jonathan Hauenstein, Martin Helmer
    Description:

    Alt’s problem, formulated in 1923, is to count the number of four-bar linkages whose coupler curve interpolates nine general points in the plane. This problem can be phrased as counting the number of solutions to a system of polynomial equations which was first solved numerically using homotopy continuation by Wampler, Morgan, and Sommese in 1992. Since there is still not a proof that all solutions were obtained, we consider upper bounds for Alt’s problem by counting the number of sol…

    Date Created:
    2020-03-03
    Record Visibility:
    Public
  • Creator(s):
    Jonathan Hauenstein
    Description:

    Many algorithms for determining properties of real algebraic or semi-algebraic sets rely upon the ability to compute smooth points. Existing methods to compute smooth points on semi-algebraic sets use symbolic quantifier elimination tools. In this paper, we present a simple algorithm based on computing the critical points of some well-chosen function that guarantees the computation of smooth points in each connected compact component of a real (semi)-algebraic set. Our technique is intuitive …

    Date Created:
    2020-01-18
    Record Visibility:
    Public
  • Author:
    Weiping Gan
    Advisory Committee:
    Haifeng Gao, Bradley D. Smith, Olaf Wiest
    Degree Area:
    Chemistry and Biochemistry
    Degree:
    Doctor of Philosophy
    Record Visibility:
    Public
  • Author(s):
    Michael Hildreth, Natalie Meyers
    Abstract:

    The FAIR Hackathon Workshop for Mathematics and the Physical Sciences (MPS) February 27-28, 2019 in Alexandria, Virginia brought together forty-four stakeholders in the physical sciences community to share skills, tools and techniques to FAIRify research data. As one of the first efforts of its kind in the US, the workshop offered participants a way to engage with FAIR principles (Findable, Accessible, Interoperable and Reusable) Data and metrics in the context of a hackathon. The workshop wa…

    Date Created:
    2020-01-05
    Record Visibility:
    Public
    Resource Type
    Report
  • Author:
    Meredith M. Doellman
    Advisory Committee:
    Michael Pfrender, Stewart Berlocher, Jeffrey L. Feder, Michael Ferdig
    Degree Area:
    Biological Sciences
    Degree:
    Doctor of Philosophy
    Defense Date:
    2019-09-13
    Record Visibility:
    Public
  • Author:
    Jeremy Mann
    Advisory Committee:
    Stephan A. Stolz
    Degree Area:
    Mathematics
    Degree:
    Doctor of Philosophy
    Defense Date:
    2019-11-18
    Record Visibility:
    Public
  • Author:
    Cunjia Qiu
    Advisory Committee:
    Paul W. Huber, Holly V. Goodson, Francis J. Castellino, Shaun W. Lee
    Degree Area:
    Chemistry and Biochemistry
    Degree:
    Doctor of Philosophy
    Defense Date:
    2019-11-21
    Record Visibility:
    Public
  • Author:
    Andrew J. Bechter
    Advisory Committee:
    Justin R. Crepp
    Degree Area:
    Physics
    Degree:
    Doctor of Philosophy
    Defense Date:
    2019-10-07
    Record Visibility:
    Public
  • Author:
    Morgan E. Smith
    Advisory Committee:
    Edwin Michael
    Degree Area:
    Biological Sciences
    Degree:
    Doctor of Philosophy
    Record Visibility:
    Public
  • Author:
    Kevin Siegl
    Advisory Committee:
    Ani Aprahamian
    Degree Area:
    Physics
    Degree:
    Doctor of Philosophy
    Defense Date:
    2019-11-15
    Record Visibility:
    Public
  • Author:
    Ricardo Romero-Moreno
    Advisory Committee:
    Sharon Stack, Glen Niebur, Laurie E. Littlepage, Siyuan Zhang
    Degree Area:
    Integrated Biomedical Sciences
    Degree:
    Doctor of Philosophy
    Defense Date:
    2019-06-24
    Record Visibility:
    Public