Colloquium/Seminar

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Event(s) on May 2010


  • Tuesday, 4th May, 2010

    Title: A Hybrid Approach for Solving Immersed Interface Problems
    Speaker: Dr. Anita Layton, Department of Mathematics, Duke University, USA
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: We consider immersed interface problems in which the fluid flow is described by the Stokes equations. A singular force is exerted along the immersed interface, thereby introducing discontinuities into the fluid solutions and their derivatives. Because the solutions are not sufficiently smooth, approximations computed by means of a standard finite difference method lacks accuracy. We present a hybrid approach that combines boundary integrals with a standard finite difference method. The Stokes solutions are computed by solving three Poisson equations in sequence, for the pressure and fluid velocities. To solve each Poisson equation, we approximate the Laplacian, using boundary integrals and a standard centered differencing scheme, at grid-points at which the finite difference stencil crosses the immersed interface. Those approximate Laplacian values are incorporated into the Poisson equation, which is then solved, to second-order accuracy, using the standard centered difference approximation. The hybrid approach can be used to resolve boundary layers, the presence of which reduces the accuracy of standard finite difference methods, unless the spatial discretization is sufficiently refined.


  • Thursday, 6th May, 2010

    Title: Spreading Speeds and Traveling Waves for Monostable Evolution Systems
    Speaker: Prof. Zhao Xiaoqiang, Department of Mathematics and Statistics, Memorial University of Newfoundland, Canada
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this talk, I will first give a brief review on asymptotic speeds of spread (in short, spreading speeds) and traveling waves for evolution systems with monostable nonlinearities. Then I will present the mathematical theory of spreading speeds and traveling waves for monotone semiflows. Finally I will discuss its applications to some deterministic models on biological invasions and disease spread.


  • Tuesday, 11th May, 2010

    Title: Lattice Basis Reduction
    Speaker: Prof. Qiao Sanzheng, Department of Computing and Software, McMaster University, Canada
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: This talk has two parts. In the first part, after introducing the concept of a reduced basis for a lattice, we compare several definitions of a reduced lattice basis and propose a new definition of optimally reduced basis. In the second part, we discuss some existing lattice basis reduction algorithms and present a new algorithm for computing an approximation of an optimally reduced basis.


  • Monday, 17th May, 2010

    Title: Variable Selection For Linear Mixed Effect Models
    Speaker: Dr. Lu Ying, Department of Humanity and Social Sciences in the Professions, New York University, USA
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Mixed effect models are fundamental tools for the analysis of longitudinal data, panel data and cross-sectional data. They are widely used by various fields of social sciences, medical and biological sciences. However, the complex nature of these models has made variable selection and parameter estimation a challenging problem. In this paper, we propose a simple iterative procedure that estimates and selects fixed and random effects for linear mixed models. In particular, we propose to utilize the partial consistency property of the random effect coefficients and select groups of random effects simultaneously via a data-oriented penalty function (the smoothly clipped absolute deviation penalty function). We show that the proposed method is a consistent variable selection procedure and possesses the Oracle properties. Simulation studies and a real data analysis are also conducted to empirically examine the performance of this procedure.

 

 


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