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
  • 3

    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
  • 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
  • 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
  • 6

    Article

    Author(s):
    Daniel Bates, Andrew Sommese, Jonathan Hauenstein
    Abstract:

    Numerical algebraic geometry is the area devoted to the solution and manipulation of polynomial systems by numerical methods, which are mainly based on continuation. Due to the extreme intrinsic parallelism of continuation, polynomial systems may be successfully dealt with that are much larger than is possible with other methods. Singular solutions require special numerical methods called endgames, and the endgames currently used do not take advantage of parallelism. This article gives an ove…

  • Author(s):
    Charles Wampler II, Daniel Bates, Andrew Sommese, Jonathan Hauenstein
    Abstract:

    Dedicated to our collaborator, mentor, and friend, Andrew Sommese, by Bates, Hauenstein, and Wampler on the occasion of his sixtieth birthday.

    When numerically tracking implicitly-defined paths, such as is required for homotopy continuation methods, efficiency and reliability are enhanced by using adaptive stepsize and adaptive multiprecision methods. Both efficiency and reliability can be further improved by adapting precision and stepsize simultaneously. This paper presents a strategy fo…

  • Author(s):
    Charles Wampler, Andrew Sommese, Jonathan Hauenstein
    Abstract:

    Though numerical methods to find all the isolated solutions of nonlinear systems of multivariate polynomials go back 30 years, it is only over the last decade that numerical methods have been devised for the computation and manipulation of algebraic sets coming from polynomial systems over the complex numbers. Collectively, these algorithms and the underlying theory have come to be known as numerical algebraic geometry. Several software packages are capable of carrying out some of the operati…

  • Author(s):
    Daniel Bates, Andrew Sommese, Jonathan Hauenstein
    Abstract:

    Path tracking is the fundamental computational tool in homotopy continuation and is therefore key in most algorithms in the emerging field of numerical algebraic geometry. Though the basic notions of predictor-corrector methods have been known for years, there is still much to be considered, particularly in the specialized algebraic setting of solving polynomial systems. In this article, the effects of the choice of predictor method on the performance of a tracker is analyzed, and details for…

  • Author(s):
    Daniel Bates, Charles Wampler, Andrew Sommese, Jonathan Hauenstein
    Abstract:

    This book is a guide to concepts and practice in numerical algebraic geometry—the solution of systems of polynomial equations by numerical methods. Through numerous examples, the authors show how to apply the well-received and widely used open-source Bertini software package to compute solutions, including a detailed manual on syntax and usage options. The authors also maintain a complementary web page where readers can find supplementary materials and Bertini input files.

    Date Created:
    2016-02-23
    Resource Type
    Book
  • Author(s):
    Andrew Sommese, Azat M. Gainutdinov, Wenrui Hao, Rafael I. Nepomechie
    Abstract:

    We consider the sl(2)q-invariant open spin-½ XXZ quantum spin chain of finite length N. For the case that q is a root of unity, we propose a formula for the number of admissible solutions of the Bethe ansatz equations in terms of dimensions of irreducible representations of the Temperley-Lieb algebra; and a formula for the degeneracies of the transfer matrix eigenvalues in terms of dimensions of tilting sl(2)q-modules. These formulas include corrections that appear if two or more tilting …

  • Author:
    Amy Lyn Buchmann
    Advisory Committee:
    Zhiliang Xu, Alexandra Jilkine, Martina Bukač, Mark Alber
    Degree Area:
    Applied and Computational Mathematics and Statistics
    Degree:
    PhD
    Defense Date:
    2015-03-26