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Xin Li

  1. Nuclearity of semigroup C*-algebras and the connection to amenability.

    Fri, 03/02/2012 - 15:01 — SomNambul
    Authors: Xin Li
    Subjects: Operator Algebras
    Abstract

    We study C*-algebras associated with subsemigroups of groups. For a large
    class of such semigroups including positive cones in quasi-lattice ordered
    groups and left Ore semigroups, we describe the corresponding semigroup
    C*-algebras as C*-algebras of inverse semigroups, groupoid C*-algebras and full
    corners in associated group crossed products. These descriptions allow us to
    characterize nuclearity of semigroup C*-algebras in terms of faithfulness of
    left regular representations and amenability of group actions.

  2. All Roads Lead To Rome.

    Fri, 03/11/2011 - 16:01 — SomNambul
    Authors: Xin Li
    Subjects: Computer Vision and Pattern Recognition
    Abstract

    This short article presents a class of projection-based solution algorithms
    to the problem considered in the pioneering work on compressed sensing -
    perfect reconstruction of a phantom image from 22 radial lines in the frequency
    domain. Under the framework of projection-based image reconstruction, we will
    show experimentally that several old and new tools of nonlinear filtering
    (including Perona-Malik diffusion, nonlinear diffusion, Translation-Invariant
    thresholding and SA-DCT thresholding) all lead to perfect reconstruction of the
    phantom image.

  3. On the Problem of Local Randomness in Privacy Amplification with an Active Adversary.

    Fri, 11/12/2010 - 16:01 — SomNambul
    Authors: Xin Li
    Subjects: Computational Complexity
    Abstract

    We study the problem of privacy amplification with an active adversary in the
    information theoretic setting. In this setting, two parties Alice and Bob start
    out with a shared $n$-bit weak random string $W$, and try to agree on a secret
    random key $R$ over a public channel fully controlled by an active and
    unbounded adversary. Typical assumptions are that these two parties have access
    to local private uniform random bits. In this paper we seek to minimize the
    requirements on the local randomness used by the two parties.

  4. Apologizing Comment on `Quantum Quasi-Cyclic Low-Density Parity-Check codes$\,$".

    Tue, 04/27/2010 - 15:02 — SomNambul
    Authors: Xin Li, Dazu Huang, Zhigang Chen, Ying Guo
    Subjects: Information Theory
    Abstract

    In our recent paper entitled "Quantum Quasi-Cyclic Low-Density Parity-Check
    codes" [ICIC 2009. LNCS 5754], it was claimed that some new quantum codes can
    be constructed via the CSS encoding/decoding approach with various lengths and
    rates. However, the further investigation shows that the proposed construction
    may steal some ideas from the paper entitled "Quantum Quasi-Cyclic LDPC codes"
    [quant-ph/0701020v2].

  5. K-theory for ring C*-algebras attached to function fields.

    Mon, 11/30/2009 - 16:01 — SomNambul
    Authors: Joachim Cuntz, Xin Li
    Subjects: Operator Algebras
    Abstract

    We compute the K-theory of ring C*-algebras for polynomial rings over finite
    fields. The key ingredient is a duality theorem which we had obtained in a
    previous paper. It allows us to show that the K-theory of these algebras has a
    ring structure and to determine explicit generators. Our main result also
    reveals striking similarities between the number field case and the function
    field case.

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