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Yuan Zhou

  1. Constant Factor Lasserre Integrality Gaps for Graph Partitioning Problems.

    Ср, 02/29/2012 - 15:01 — SomNambul
    Authors: Yuan Zhou, Venkatesan Guruswami, Ali Kemal Sinop
    Subjects: Computational Complexity
    Abstract

    Partitioning the vertices of a graph into two roughly equal parts while
    minimizing the number of edges crossing the cut is a fundamental problem
    (called Balanced Separator) that arises in many settings. For this problem, and
    variants such as the Uniform Sparsest Cut problem where the goal is to minimize
    the fraction of pairs on opposite sides of the cut that are connected by an
    edge, there are large gaps between the known approximation algorithms and
    non-approximability results. While no constant factor approximation algorithms
    are known, even APX-hardness is not known either.

  2. Characterizations of Besov and Triebel-Lizorkin Spaces on Metric Measure Spaces.

    Ср, 06/15/2011 - 15:01 — SomNambul
    Authors: Pekka Koskela, Yuan Zhou, Amiran Gogatishvili
    Subjects: Classical Analysis and ODEs
    Abstract

    On a metric measure space satisfying the doubling property, we establish
    several optimal characterizations of Besov and Triebel-Lizorkin spaces,
    including a pointwise characterization. Moreover, we discuss their
    (non)triviality under a Poincar\'e inequality.

  3. Optimal lower bounds for locality sensitive hashing (except when q is tiny).

    Ср, 12/02/2009 - 16:01 — SomNambul
    Authors: Yuan Zhou, Ryan O'Donnell, Yi Wu
    Subjects: Data Structures and Algorithms
    Abstract

    We study lower bounds for Locality Sensitive Hashing (LSH) in the strongest
    setting: point sets in {0,1}^d under the Hamming distance. Recall that here H
    is said to be an (r, cr, p, q)-sensitive hash family if all pairs x, y in
    {0,1}^d with dist(x,y) at most r have probability at least p of collision under
    a randomly chosen h in H, whereas all pairs x, y in {0,1}^d with dist(x,y) at
    least cr have probability at most q of collision. Typically, one considers d
    tending to infinity, with c fixed and q bounded away from 0.

  4. Localized Hardy Spaces $H^1$ Related to Admissible Functions on RD-Spaces and Applications to Schr\"odinger Operators.

    Ср, 09/16/2009 - 13:15 — SomNambul
    Authors: Dachun Yang, Yuan Zhou
    Subjects: Classical Analysis and ODEs
    Abstract

    Let ${\mathcal X}$ be an RD-space, which means that ${\mathcal X}$ is a space
    of homogenous type in the sense of Coifman and Weiss with the additional
    property that a reverse doubling property holds in ${\mathcal X}$.

  5. Localized Hardy Spaces $H^1$ Related to Admissible Functions on RD-Spaces and Applications to Schr\"odinger Operators.

    Ср, 09/16/2009 - 13:15 — SomNambul
    Authors: Dachun Yang, Yuan Zhou
    Subjects: Classical Analysis and ODEs
    Abstract

    Let ${\mathcal X}$ be an RD-space, which means that ${\mathcal X}$ is a space
    of homogenous type in the sense of Coifman and Weiss with the additional
    property that a reverse doubling property holds in ${\mathcal X}$.

  6. A Characterization of Haj{\l}asz-Sobolev and Triebel-Lizorkin Spaces via Grand Littlewood-Paley Functions.

    Пнд, 09/14/2009 - 09:01 — SomNambul
    Authors: Pekka Koskela, Dachun Yang, Yuan Zhou
    Subjects: Classical Analysis and ODEs
    Abstract

    In this paper, we establish the equivalence between the Haj{\l}asz-Sobolev
    spaces or classical Triebel-Lizorkin spaces and a class of grand
    Triebel-Lizorkin spaces on Euclidean spaces and also on metric spaces that are
    both doubling and reverse doubling. In particular, when $p\in(n/(n+1),\fz)$, we
    give a new characterization of the Haj{\l}asz-Sobolev spaces $\dot M^{1,
    p}(\rn)$ via a grand Littlewood-Paley function.

Math-arch

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