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Event(s) on February 2014


  • Tuesday, 11th February, 2014

    Title: Strong laws of large numbers for sublinear
    Speaker: Prof. CHEN Zengjing , School of Mathematics, Shandong University, China
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this paper, with the notion of independent identically distributed random variables under sub-linear expectations initiated by Peng, we derive three kinds of strong laws of large numbers for capacities. Moreover, these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. Finally, an important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities. Keywords: capacity, strong law of large number, independently and identically distributed(IID), sub-linear expectation.


  • Wednesday, 12th February, 2014

    Title: Regression Analysis of `Yes' or `No' Recurrent Events with Application to Wenchuan Earthquake Data
    Speaker: Prof. TONG Xingwei , School of Mathematical Sciences, Beijing Normal University, China
    Time/Place: 14:30  -  15:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this article, we introduce a new type of recurrent event data, named ‘Yes’ or ‘No’recurrent event data. In such a setting, the exact onset time and the number of recurrent event of interest cannot be observed. The only available information was whether the recurrent event of interest happened or not during some observe interval. Our interest focuses on the estimation of the effect of risk factors on ‘Yes’ or ‘No’ recurrent event data. B-spline functions are used to estimate the baseline hazard function. The covariate coefficients are estimated by maximizing the observed log pseudo-likelihood function. We show that the proposed estimates are consistent and have asymptotic normal distribution. Simulation studies with moderate samples show that the estimation approach can be done easily and efficiently. The approach is illustrated through application to a data set from an post-traumatic stress disorder study.


  • Thursday, 13th February, 2014

    Title: On Fourth Order PDEs in Affine Differential Geometry and Complex Differential Geometry
    Speaker: Prof. Anmin Li, Sichuan University, China
    Time/Place: 16:00  -  17:00 (Preceded by Reception at 3:30pm)
    SPH, Shiu Pong Hall, Hong Kong Baptist University
    Abstract: Consider the following equation sum_{i,j=1}^n U^{ij} w_{ij} = - L, w =[det((partial^2 u)/(partial xi_i partial xi_j))]^a, where L is some given C^infty function, u(xi) is a smooth and strictly convex function defined in a convex domain in R^n, (U^{ij}) denotes the cofactor matrix of the Hessian matrix (partial^2 u)/(partial xi_i partial xi_j) and a <> 0 is a constant. When a = -(n+1)/(n+2) and L=0, the above equation is the equation for affine maximal hypersurfaces. When a = -1 it is called the Abreu equation, which appears in the study of the differential geometry of toric varieties, where L is the scalar curvature of the Kahler metric. In this talk, we will discuss some recent development on the study of the relevant differential equations in the differential geometry.


  • Friday, 14th February, 2014

    Title: Dispersion Relations of the Modes in Open Nonhomogeneous Waveguide Terminated by PMLs
    Speaker: Prof. Jianxin ZHU, Department of Mathematics, Zhejiang University, China
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The perfectly matched layer (PML) is a widely used tool to truncate the infinite domain in modal analysis for optical waveguides. Since the PML mimics the unbounded domain, propagation modes and leaky modes of the original unbounded waveguide can be derived. However, the presence of PML will introduce a series of new modes, which depend on the parameters of PML, and they are named as Berenger modes. For two-dimensional step-index waveguides, the eigenmode problem is usually transformed into an algebraic equation by the transfer matrix method (TMM). When the waveguide is nonhomogeneous, in which the refractive index in the core is varied, TMM is not available. In this talk, we use the differential TMM to derive the dispersion relation. We also deduced the asymptotic formulas for leaky modes and Berenger modes separately, which are accurate for large modes.


  • Tuesday, 18th February, 2014

    Title: Convex Variational Models for Processing Blurry Images with Rician noise: Denoising, Deblurring and Segmentation
    Speaker: Ms. CHEN Liyuan , Department of Mathematics, Hong Kong Baptist University , Hong Kong
    Time/Place: 10:00  -  11:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In recent years, with the development of Magnetic Resonance Imaging (MRI), Rician noise, as a very important kind of noise, has been taken into account gradually. The main goal of our research is to propose convex models for processing blurry images with Rician noise. In our research, we firstly establish a new convex variational model for restoring images degraded by blur and Rician noise. The new model is inspired by previous works in which a non-convex model was obtained by MAP estimation. Based on the statistical property of Rician noise, we put forward to adding a quadratic penalty term into it, which leads a strictly convex model under mild condition. The new model guarantees the uniqueness of the solution and stabilization of the algorithm. We utilize a primal-dual algorithm to solve it. Based on this model and two-stage segmentation method, a new two-stage method for segmenting blurry images accompanied by Rician noise is also proposed. Numerical results are presented in the end to demonstrate that our method outperforms some of the state-of-the-art methods in very general images.


  • Friday, 21st February, 2014

    Title: Shrinkage-Based Diagonal Hotelling's Tests for High-Dimensional Small Sample Size Data
    Speaker: Mr. DONG Kai, 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: High-throughput sequencing techniques bring novel tools and also statistical challenges to genetic research. In addition to detecting differentially expressed genes, testing the significance of gene sets or pathway analysis has been recognized as an equally important problem. Owing to the “large p small n” paradigm, the traditional Hotelling’s T2 test suffers from the singularity problem and therefore is not valid in this setting. In this paper, we propose a shrinkage-based diagonal Hotelling’s test for both one-sample and two-sample cases. We also suggest several different ways to derive the approximate null distribution under different scenarios of p and n for our proposed shrinkage-based test. Simulation studies show that the proposed method performs comparably to existing competitors when n is moderate or large, but it is better when n is small. In addition, we analyze four gene expression data sets and they demonstrate the advantage of our proposed shrinkage-based diagonal Hotelling’s test.


  • Tuesday, 25th February, 2014

    Title: Finite Element Approximation for Optimal Control Problem Governed by Time Fractional Diffusion Equation
    Speaker: Mr. TIAN Wenyi, 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: We consider the numerical solution to a optimal control problem with control constraints governed by time fractional diffusion equation. The problem is discretized by the standard piecewise linear and continuous finite elements in space and the difference formulae for the time fractional derivative. And then we give the error estimates for the optimal control problem. Finally the projection gradient method is applied to solving the resulted fully discrete optimization problem.


  • Thursday, 27th February, 2014

    Title: Transience of diffusion on Heisenberg ad Grushin distributions
    Speaker: Prof. Ovidiu Calin, Department of Mathematics, Eastern Michigan University, USA
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In the absence of a general theory of diffusion on non-integrable distributions, an important role is played by the investigation on some particular examples. This talk deals with a couple of these examples. The first one is the Heisenberg diffusion, which is a degenerate diffusion with non-holonomic constraints living on the horizontal distribution of the Heisenberg group. The second example is the Grushin diffusion, also a degenerate diffusion, which moves in the plane along the Grushin distribution. A special emphasize will be put on the transience property of the Heisenberg and Grushin diffusion as well as on a stochastic variant of the Chow-Rashewski connectivity theorem.