Applied and Computational Mathematics and Statistics

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  • 1

    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(s):
    Parker Ladwig, Andrew Sommese
    Abstract:

    “Supplying accurate CPU [cost-per-serial use] information to faculty and appropriate marketing of the alternate modes of delivery … become the key to achieving an optimal cost-efficient serials collection in an academic library.” (Marisa Scigliano, “Serial Use in a Small Academic Library: Determining Cost-effectiveness,” Serials Review 26 (2000): 43–52.)

    A model is presented for adjusting use statistics using a journal’s ISI Journal Citation Reports cited half-life.The goal is to improve t…

  • Inventor(s):
    Steven Buechler, Amanda B. Hummon
    Patent Number:
    US 9580756 B2
    Description:

    Compositions/methods for employing fresh-frozen or FFPE colon cancer tissue in left side colon cancer (LCC) and right-side colon cancer (RCC) disease patients for risk of relapse assessment/stratification is provided (3 strata and a 4 strata methodology). An RCC gene panel of 4 genes (FAM69A, CDX2, FAM84A, ITGA3), and 9 genes (FAM69A, CDX2, ITGA3, FAM84A, ITPRIP, RAB3B, SMAD3, PCSK5, MMP28), is provided. An LCC gene panel of 4 genes (NOX4, WNT5A, MMP3, IBSP), and a 9 genes (MMP3, WINT5A, NOX4…

    Date Issued:
    2017-02-28
    Resource Type
    Patent
  • Inventor(s):
    Steven Buechler, Amanda B. Hummon
    Patent Number:
    US 9464328 B2
    Description:

    Genetic biomarkers for left side colon cancer (LCC) (such as expression levels of an RNA transcript or expression product of NOX4, MMP3, or a combination) and right side colon cancer (RCC) (such as expression levels of an RNA transcript or expression product of CDCX2, FAM69A, or a combination), are disclosed. Methods for using the biomarkers in providing a prognosis of relapse-free survival probability in patients having LCC or RCC are also presented. Prognostic panels using gene expression v…

    Date Issued:
    2016-10-11
    Resource Type
    Patent
  • Inventor(s):
    Steven Buechler
    Patent Number:
    US 9721067 B2
    Description:

    An Accelerated Progression Relapse Test (APRT) and method is provided for use in the prognosis of a patient having an ER+ breast cancer. The APRT provides a determination of when a patient in a particular diseased state is likely to benefit from further disease treatment, or does not have a high probability of benefit with additional treatment. Four genetic probes are disclosed that target the MKI67, CDC6 and SPAG5 gene and gene products. The ER+ breast cancer patient population is stratified…

    Date Issued:
    2017-08-01
    Resource Type
    Patent
  • Inventor(s):
    Steven Buechler, Amanda B. Hummon
    Patent Number:
    US 10,087,489 B2
    Description:

    Genetic biomarkers for left side colon cancer (LCC) (such as expression levels of an RNA transcript or expression product of NOX4, MMP3, or a combination) and right side colon cancer (RCC) (such as expression levels of an RNA transcript or expression product of CDCX2, FAM69A, or a combination), are disclosed. Methods for using the biomarkers in providing a prognosis of relapse-free survival probability in patients having LCC or RCC are also presented. Prognostic panels using gene expression v…

    Date Issued:
    2018-10-02
    Resource Type
    Patent
  • Inventor(s):
    Sunil Badve, Steven Buechler, Yesim Gokmen-Polar
    Patent Number:
    US 10174382 B2
    Description:

    A genetic biomarker panel is provided for prognosing late onset ER+ breast cancer relapse, in a breast cancer survivor patient. Kits are also provided for measuring levels or the presence of an identified panel of genetic biomarkers. Methods are also provided for identifying a breast cancer survivor patient at a relatively high risk of suffering a breast cancer relapse within 8 years of diagnosis, and therefore suitable for treatment with an aggressive chemotherapeutic regimen. The method may…

    Date Issued:
    2019-01-08
    Resource Type
    Patent