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Maria Angelica Cueto

  1. Implicitization of surfaces via geometric tropicalization.

    Wed, 05/04/2011 - 15:01 — SomNambul
    Authors: Maria Angelica Cueto
    Subjects: Algebraic Geometry
    Abstract

    In this paper we describe tropical methods for implicitization of surfaces.
    We construct the corresponding tropical surfaces via the theory of geometric
    tropicalization due to Hacking, Keel and Tevelev, which we enrich with a
    formula for computing tropical multiplicities of regular points in any
    dimension. We extend previous results for tropical implicitization of generic
    surfaces due to Sturmfels, Tevelev and Yu and provide methods for the
    non-generic case.

  2. Geometry of the restricted Boltzmann machine.

    Tue, 09/01/2009 - 12:47 — SomNambul
    Authors: Bernd Sturmfels, Maria Angelica Cueto, Jason Morton
    Subjects: Machine Learning
    Abstract

    The restricted Boltzmann machine is a graphical model for binary random
    variables. Based on a complete bipartite graph separating hidden and observed
    variables, it is the binary analog to the factor analysis model. We study this
    graphical model from the perspectives of algebraic statistics and tropical
    geometry, starting with the observation that its Zariski closure is a Hadamard
    power of the first secant variety of the Segre variety of projective lines.

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