Colloquium/Seminar

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Event(s) on January 2011


  • Tuesday, 4th January, 2011

    Title: Explicit Estimating Equations for Semiparametric Generalized Linear Latent Variable Models
    Speaker: Dr. MA Yanyuan, Department of Statistics, Texas A&M University, USA
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: We study the generalized linear latent variable models without requiring a distributional assumption of the latent variables. Using a geometric approach, we derive consistent semiparametric estimators. We demonstrate that these models possess a property similar to that of a sufficient complete statistic, which enables us to simplify the estimating procedure and explicitly formulate the semiparametric estimating equations. We further show that the explicit estimators have the usual root-$n$ consistency and asymptotic normality. We explain the computational implementation of our method and illustrate the numerical performance of the estimators in finite sample situations via extensive simulation studies. The advantage of our estimators over the existing likelihood approach is also shown via numerical comparison. We employ the method to analyze a real data example from economics. This is joint work with Marc Genton.


  • Tuesday, 4th January, 2011

    Title: Functional Boxplots for Complex Data Visualization
    Speaker: Prof. Marc GENTON, Department of Statistics, Texas A&M University, USA
    Time/Place: 15:00  -  16:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: This paper proposes an informative exploratory tool, the functional boxplot, for visualizing functional data, as well as its generalization, the enhanced functional boxplot. Based on the center outwards ordering induced by band depth for functional data, the descriptive statistics of a functional boxplot are: the envelope of the 50% central region, the median curve and the maximum non-outlying envelope. In addition, outliers can be detected in a functional boxplot by the 1.5 times the 50% central region empirical rule, analogous to the rule for classical boxplots. The construction of a functional boxplot is illustrated on a series of sea surface temperatures related to the El Nino phenomenon and its outlier detection performance is explored by simulations. As applications, the functional boxplot and enhanced functional boxplot are demonstrated on children growth data and spatio-temporal U.S. precipitation data for nine climatic regions, respectively. Further adjustments of the functional boxplot for outlier detection in spatio-temporal data are discussed as well. The talk is based on joint work with Ying Sun.


  • Friday, 7th January, 2011

    Title: ICM Distinguished Computational Mathematics Lecture: Studies on Wilson Nonconforming Finite Element
    Speaker: Prof. Zhong-Ci Shi, Institute of Computational Mathematics, Chinese Academy of Sciences, China
    Time/Place: 11:00  -  12:00 (Preceded by Reception at 10:30am)
    LT1, Cha Chi-Ming Science Tower, HSH Campus, Hong Kong Baptist University
    Abstract: Wilson nonconforming finite element (1973) is a very useful rectangular element In practice. it has been shown in many engineering applications that the convergence behavior of this element is better than that of the commonly used bilinear element. However, mathematical studies carried out so far cannot justify it. The results obtained by use of standard finite element analysis technique are not satisfied. Recently (2007-) we tackle this problem from a different view point, i.e. from Mechanics, where the Wilson element was originated. We have succeeded in proving both mathematically and numerically that the Wilson element is free of shear locking for a wide class of bending dominated plane elasticity problems, while the bilinear element suffers from the shear locking. Therefore, we elucidate a long-standing folklore: why Wilson element does a better job in many practical applications than the bilinear element.


  • Tuesday, 11th January, 2011

    Title: Dimension Reduction in Regression
    Speaker: Ms. FENG Zhenghui, Department of Mathematics, Hong Kong Baptist University, Hong Kong
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The appearance of massive data lead statistics to a new time. Using traditional statistical method could seldom satisfy the new case. We study some dimension reduction methods in regression. In the first part, we investigate how to select a parsimonious dimension reduction semiparametric model (DRSM) that is of the additive structure with orthogonal projection directions. Different from the classical sufficient dimension reduction, the problem for DRSM involves both selecting nonparametric component functions and estimating projection directions. To implement component function selection and projection direction estimation simultaneously, we propose an alternating selection-optimization algorithm to alternatively search best model fitting and direction estimation. In the second part, for generalized linear model, when dimension of predictor is large, or error has heavy tail, classical estimation method will be unstable. Our two staged method could overcome this in the meaning of dimension reduction. Simulation studies are carried out to examine the performance of the new methods and real data example is also analysed for illustration.


  • Friday, 14th January, 2011

    Title: CMIV Colloquium: A Fast Algorithm for Euler’s Elastica Model Using Augmented Lagrangian Method
    Speaker: Prof. Xue-Cheng Tai, Nanyang Technological University, Singapore
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Minimization of functionals related to Euler's elastica energy has a wide range of applications in computer vision and image processing. An issue is that a high order nonlinear partial differential equation (PDE) needs to be solved and the conventional algorithm usually takes high computational cost. In this paper, we propose a fast and efficient numerical algorithm to solve minimization problems related to the Euler's elastica energy and show applications to variational image denoising, image inpainting, and image zooming. We reformulate the minimization problem as a constrained minimization problem, followed by an operator splitting method and relaxation. The proposed constrained minimization problem is solved by using an augmented Lagrangian approach. Numerical tests on real and synthetic cases are supplied to demonstrate the efficiency of our method.


  • Friday, 14th January, 2011

    Title: Variational Surface reconstruction based on Delaunay triangulation and graph cut
    Speaker: Dr. WANG Desheng, Division of Mathematical Sciences, School of Physical & Mathematical Sciences, Nanyang Technological University, Singapore
    Time/Place: 15:00  -  16:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this talk, we shall start with a review on surface reconstruction based on Delaunay triangulation from sectional contours and unoriented points set. Motivated by addressing the difficulties in surface reconstruction from noisy, under-sampling, multiphase data input, we developed a robust and efficient approach which is based on minimizing a geometrical functional defined on the dual-graph to the Delaunay tetrahedral mesh constructed using all or part of the given points set. The application to open surface reconstruction will be discussed. The issue on how to keep the features involving ridges and corners will be addressed as well.


  • Tuesday, 18th January, 2011

    Title: Perfectly matched layers for the fluid equations
    Speaker: Mr. GAO Zhen, Division of Applied Mathematics, Brown University, USA , & School of Mathematical Sciences, Ocean University of China, China
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The perfectly matched layer (PML) is to design an artificial layer surrounding the computational domain so that the outgoing wave are absorbed in the layer and reflections are only exponentially small in terms of the layer width. It works as a relatively simple and efficient tool for truncating a computational domain in an infinity or semi-infinity spatial domain. In this talk, we discuss the development of perfectly matched layers for the fluid equations which are the Boltzmann equation and the Navier-Stokes equation respectively. First of all, the discretization of the Boltzmann equation in velocity space via a Galerkin approach based on Hermite polynomials, is presented. Secondly, The PML formulation for the Boltzmann equation is constructed via a modal analysis, that is, to perform Laplace transformation in time-direction and Fourier transformation in spatial variables. By properly choosing a set of auxiliary parameters, it is a long time stable PML model. Last but not least, the PML model for the Navier-Stokes equation is designed by assigning the Navier-Stokes equation and the Boltzmann equation in the computational domain and the artificial layer separately. The results are compared with reference solutions computed from a larger domain in several standard test examples, confirming the accuracy and efficiency of the proposed approaches. This is a joint work with Prof. Jan S. Hesthaven at Brown University, USA and Prof. Tim Warburton at Rice University, USA.


  • Wednesday, 19th January, 2011

    Title: Parallel Time Integrators
    Speaker: Dr. Benjamin ONG, Department of Mathematics, Michigan State University, USA
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: We discuss a family of parallel time integrators based on defect correction for multi-core, multi-node or multi-gpgpu systems. The key idea is to re-write the defect correction framework so that, after initial startup costs, each correction loop can be lagged behind the previous correction loop in a manner that facilitates running the predictor and correctors in parallel. Time permitting, we will discuss present work in generating a parallel space-time algorithm for solving Poisson's or Helmholtz's equation using boundary integral treecode algorithms.


  • Wednesday, 26th January, 2011

    Title: CMIV Colloquium: Quantum Error Correction and Generalized Numerical Ranges
    Speaker: Professor Chi-Kwong Li, 2011 Fulbright Fellow, Hong Kong University of Science & Technology, Hong Kong
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The numerical range is a useful tool for studying matrices and operators, and there are many generalizations of the concept motivated by theory and applications. In this talk, we will focus on the higher rank numerical range, which arises from the study of quantum error correction. Recent results and open problems on the topic will be described.