Colloquium/Seminar

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Event(s) on April 2007


  • Tuesday, 3rd April, 2007

    Title: CMIV Lecture Series: Optimization for Image Processing (Lecture 7)
    Speaker: Prof. Mila Nikolova, CMLA ENS de Cachan, France
    Time/Place: 14:30  -  16:30
    FSC 1217


  • Tuesday, 24th April, 2007

    Title: A Moving Mesh Method Based on Harmonic Mapping and Its Application
    Speaker: Dr. Ruo Li, School of Mathematical Sciences, Peking University, China
    Time/Place: 11:30  -  12:30
    FSC 1111
    Abstract: In this talk, I will introduce briefly a moving mesh method based on harmonic mapping. As a rare character, the unique existence of the harmonic mapping is the basic motivation for us to develop this method. The method is implemented in finite element and an iterative procedure is adopted to avoid mesh tangling caused by numerical factors. Our method can move the mesh interior the domain and mesh on the boundary in coupling for both 2D and 3D problems. The moving mesh module can be a black box added on the whole solver to the PDE under consideration that it is very convenient for coding - no modifications to the solver of the PDE are required. The inter-mesh mesh updation is implemented by a linear convection equation instead of generally adopted interpolation methods, thus the method can be easily to applied to problem as incompressible Navier-Stokes equation where the divergence free interpolation can be a big problem, and problem as conservation laws where the conservative interpolation is not trival to be implemented. Numerical results including viscos Burgers equation, reaction-diffusion equation, incompressible Navier-Stokes equation and its coupling with level set method will be shown.


  • Thursday, 26th April, 2007

    Title: Polynomial Numerical Hulls of Matrices
    Speaker: Prof. Chi-Kwong Li, Department of Mathematics, College of William & Mary, USA
    Time/Place: 11:30  -  12:30
    FSC 1217
    Abstract: Let A be an n-by-n complex matrix, and k be a positive integer. Motivated by the study of GMRES method, researchers introduced and studied the polynomial hull of A of order k defined as the collection of complex number μ such that |p(μ)|≦|| p(A)|| for all complex polynomials p(z) with degree at most k. We use the joint numerical range W(A,A^2,,A^k) to study the polynomial numerical hull of order k of A, denoted by V^k(A). We give an analytic description of V^2(A) when A is normal. The result is then used to characterize those normal matrices A satisfying V^2(A) = σ(A), and to show that a unitary matrix A satisfies V^2(A) = σ(A) if and only if its eigenvalues lie in a semicircle, where σ(A) denotes the spectrum of A. When A= diag(1, w,, w^{n-1}) with w = e^{i2π/n}, we determine V^k(A) for k є {2}∪{j є N : j ≧ n/2}. We also consider matrices A є M_n such that A^2 is Hermitian. For such matrices we show that V^4(A) is the spectrum of A, and give a description of the set V^2(A).


  • Friday, 27th April, 2007

    Title: Transmission Disequilibrium Tests and Imprinting Effects Tests Based on Case-parents Trios and Case-parent Pairs
    Speaker: Prof. Wing Kam Fung, Department of Statistics and Actuarial Science, The University of Hong Kong, HKSAR, China
    Time/Place: 11:30  -  12:30
    FSC 1217
    Abstract: Based on case-parents trios, two statistics POET and TDTI are developed to test for imprinting and linkage/association, respectively. When only one parent is available, the 1-TDTI and 1-POET are proposed accordingly. The asymptotic results of the tests are derived. Simulations are conducted to investigate the validity and other properties of these proposed statistics. The way to combine case-parents trios and case-parent pairs information in testing for imprinting and linkage/association is addressed.