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  • Author(s):
    Yide Zhang
    Abstract:

    In cancer and all biomedical researches, we always need a microscope with better imaging precision, speed, functionality, and depth, so that the diagnostics and treatments of cancer and other diseases can be accurate, fast, and noninvasive. However, conventional fluorescence microscopes cannot satisfy these needs due to physical limits on resolution, speed, information, and depth. In this work, we aim to overcome these limits using novel super-resolution microscopy and high-speed quantitative…

    Date Created:
    2018-04-09
    Resource Type
    Presentation
  • 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
  • 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
  • 4

    Dataset

    Creator(s):
    Haiyan Meng
    Description:

    The document includes all the necessary artifacts to reproduce a CMS application.

    Date Created:
    2016-03-01