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Feng Luo

  1. Solving Thurston Equation in a Commutative Ring.

    Thu, 01/12/2012 - 15:01 — SomNambul
    Authors: Feng Luo
    Subjects: Geometric Topology
    Abstract

    We show that solutions of Thurston equation on triangulated 3-manifolds in a
    commutative ring carry topological information. We also introduce a homogeneous
    Thurston equation and a commutative ring associated to triangulated
    3-manifolds.

  2. Cell decompositions of Teichm\"uller spaces of surfaces with boundary.

    Thu, 06/17/2010 - 15:01 — SomNambul
    Authors: Feng Luo, Ren Guo
    Subjects: Geometric Topology
    Abstract

    A family of coordinates $\psi_h$ for the Teichm\"uller space of a compact
    surface with boundary was introduced in \cite{l2}. In the work \cite{m1},
    Mondello showed that the coordinate $\psi_0$ can be used to produce a natural
    cell decomposition of the Teichm\"uller space invariant under the action of the
    mapping class group. In this paper, we show that the similar result also works
    for all other coordinate $\psi_h$ for any $h \geq 0$.

  3. Effectively integrating information content and structural relationship to improve the GO-based similarity measure between proteins.

    Thu, 01/07/2010 - 16:01 — SomNambul
    Authors: Feng Luo, Bo Li, James Z. Wang, F. Alex Feltus, Jizhong Zhou
    Subjects: and Science, Computational Engineering, Finance
    Abstract

    The Gene Ontology (GO) provides a knowledge base to effectively describe
    proteins. However, measuring similarity between proteins based on GO remains a
    challenge. In this paper, we propose a new similarity measure, information
    coefficient similarity measure (SimIC), to effectively integrate both the
    information content (IC) of GO terms and the structural information of GO
    hierarchy to determine the similarity between proteins.

  4. A Note on Gradually Varied Functions and Harmonic Functions.

    Wed, 10/28/2009 - 16:01 — SomNambul
    Authors: Feng Luo, Li Chen, Yong Liu
    Subjects: Discrete Mathematics
    Abstract

    Any constructive continuous function must have a gradually varied
    approximation in compact space. However, the refinement of domain for
    $\sigma-$-net might be very small. Keeping the original discretization (square
    or triangulation), can we get some interesting properties related to gradual
    variation? In this note, we try to prove that many harmonic functions are
    gradually varied or near gradually varied; this means that the value of the
    center point differs from that of its neighbor at most by 2.

  5. Volume maximization and the extended hyperbolic space.

    Mon, 08/17/2009 - 18:30 — SomNambul
    Authors: Feng Luo, Jean-Marc Schlenker
    Subjects: Geometric Topology
    Abstract

    We consider a volume maximization program to construct hyperbolic structures
    on triangulated 3-manifolds, for which previous progress has lead to consider
    angle assignments which do not correspond to a hyperbolic metric on each
    simplex. We show that critical points of the generalized volume are associated
    to geometric structures modeled on the extended hyperbolic space -- the natural
    extension of hyperbolic space by the de Sitter space -- except for the
    degenerate case where all simplices are Euclidean in a generalized sense.

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