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Event(s) on November 2014


  • Wednesday, 12th November, 2014

    Title: Efficient penalized likelihood estimation for semiparametric proportional hazard models
    Speaker: Dr. Jun Ma, Department of Statistics, Macquarie University, Australia
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: This talk considers estimation of the regression coefficients and baseline hazard in proportional hazard models using the maximum penalized likelihood (MPL) method where a penalty function is used to smooth the baseline hazard estimate. We first model baseline hazard using basis functions, then estimate this approximate baseline hazard and the regression coefficients simultaneously. The penalty function included in the likelihood is quite general but typically assumes prior knowledge about the smoothness of the baseline hazard. A new iterative optimization algorithm, which combines Newton's method and a multiplicative iterative algorithm, is developed and its convergence properties studied. We show that if the smoothing parameter tends to zero sufficiently fast, the new estimator is consistent, asymptotically normal and retains full efficiency under independent censoring. A simulation study reveals that this method can be more efficient than the partial likelihood method, particularly for small to moderate samples. In addition, our simulation shows that the new estimator is substantially less biased under informative censoring.


  • Wednesday, 12th November, 2014

    Title: Spatially partitioned embedded Runge-Kutta methods
    Speaker: Prof. Steve Ruuth, Department of Mathematics, Simon Fraser University, Canada
    Time/Place: 14:30  -  15:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: This talk considers spatially partitioned embedded Runge-Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different part of the spatial domain. Such methods may be convenient for problems in which the smoothness of the solution or the magnitudes of the PDE coefficients vary strongly in space. We focus on embedded partitioned methods as they offer greater efficiency and avoid the order reduction that may occur in non-embedded schemes. We demonstrate that the lack of conservation in partitioned schemes can lead to non-physical effects and propose conservative additive schemes based on partitioning the fluxes rather than the ordinary differential equations. A variety of SPERK schemes are presented, including an embedded pair suitable for the time evolution of fifth-order weighted non-oscillatory (WENO) spatial discretizations. Numerical experiments are provided to support the theory.


  • Thursday, 13th November, 2014

    Title: CMIV Colloquium: Fast Numerical Methods for Space-fractional Diffusion Equations (Lecture 1)
    Speaker: Prof. Hong Wang, Department of Mathematics, University of South Carolina, United States
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Fractional diffusion equations provide an adequate and accurate description of transport processes that exhibit anomalous diffusion, which can not be modeled properly by second-order diffusion equations. However, fractional diffusion equations raise computational and numerical difficulties that have not been encountered in the context of second-order diffusion equations. Computationally, because of the nonlocal property of fractional differential operators, the numerical methods for fractional diffusion equations often generate dense coefficient matrices, which were traditionally solved by Gaussian type direct solvers that require O(N3) of computational work per time step and O(N2) of storage where N is the number of unknowns. In this talk we go over the development of faithful and efficient numerical methods for space-fractional diffusion equations, without resorting to any lossy compression, but rather by exploring the structure of the stiffness matrices. These methods have computational cost of O(N log2 N) per time step and memory of O(N), while retaining the same accuracy and conservation property of the underlying discretization. We will in particular discuss the structure of these schemes on more general meshes, which call for the development of fast and faithful solvers.


  • Thursday, 13th November, 2014

    Title: CMIV Colloquium: Mathematical Analysis for Fractional Differential Equations (Lecture 2)
    Speaker: Prof. Hong Wang, Department of Mathematics, University of South Carolina, United States
    Time/Place: 14:30  -  15:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Fractional differential equations exhibit mathematical properties, which are significantly different from those of integer-order differential equations and have not been encountered in the context of integer-order differential equations. These properties will have important impact on the performance, analysis, and design of numerical methods for fractional differential equations. In this talk we will go over some of these mathematical issues and report our recent progress in this direction.


  • Wednesday, 19th November, 2014

    Title: Exact Equations of Eigenmodes for Nonhomogeneous Waveguides Terminated by PMLs
    Speaker: Prof. ZHU Jianxin, Department of Mathematics, Zhejiang University, China
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this talk, the exact dispersion equations for both the TM and TE cases are derived by use of the differential transfer matrix method and the matrix similarity transformation when a nonhomogeneous waveguide is terminated by the perfectly matched layers(PMLs). Meanwhile, the asymptotic solutions of Berenger modes for the TM case are deduced, which can be well acted as the initial values of the Newton's iteration. Numerical examples illustrate that both leaky and Berenger modes with higher precision can be obtained by the exact dispersion equations.


  • Wednesday, 19th November, 2014

    Title: Joint Colloquium - GPS-Aided Tsunami Early Detection System
    Speaker: Dr. Y. Tony Song , NASA Jet Propulsion Laboratory, California Institute of Technology, USA
    Time/Place: 16:30  -  17:30
    1/F SPH, Shiu Pong Hall Function Room
    Abstract: This talk reviews how tsunamis form from earthquakes and how GPS technologies can be used to detect tsunami energy scales in real time. Most tsunami fatalities occur in near-field communities of earthquakes at offshore faults. Tsunami early warning is key for reducing the number of fatalities. Unfortunately, an earthquake's magnitude often does not gauge the resulting tsunami power. Here we show that real-time GPS stations along coastlines are able to detect seafloor motions due to big earthquakes, and that the detected seafloor displacements are able to determine tsunami energy and scales instantaneously for early warnings. Our method focuses on estimating tsunami energy directly from seafloor motions because a tsunami's potential or scale, no matter how it is defined, has to be proportional to the tsunami energy.


  • Thursday, 20th November, 2014

    Title: Harry Potter's Cloak
    Speaker: Prof. Gunther Uhlmann, University of Washington, USA
    Time/Place: 17:00  -  18:00 (Preceded by Reception at 4:30pm)
    WLB104, The Wing Lung Bank Building for Business Studies, Shaw Campus, HKBU
    Abstract: Invisibility has been a subject of human fascination for millenia, from the Greek legend of Perseus versus Medusa to the more recent The Invisible Man, The Invisible Woman, Star Trek and Harry Potter, among many others. Over the years, there have been occasional scientific prescriptions for invisibility in various settings but the route to cloaking that has received the most attention has been transformation optics. To achieve invisibility one can design materials that would steer light around a hidden region, returning it to its original path on the far side. Not only would observers be unaware of the contents of the hidden region, they would not even be aware that something was being hidden. As Science Magazine stated in 2006 in naming cloaking one of the 10 breakthroughs of the year: "...no matter how you look at it the ideas behind invisibility are likely to cast a long shadow". I will discuss the Mathematics behind these ideas.