Colloquium/Seminar

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Event(s) on April 2017


  • Wednesday, 5th April, 2017

    Title: Stability estimates for some inverse boundary value problems
    Speaker: Prof. Jenn-Nan Wang, Institute of Applied Mathematical Sciences, National Taiwan University, Taiwan
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this talk I would like to discuss stability estimates for some identification problems using boundary measurements. The main point is to see how stability estimates depend on parameters in the equations.  For the problem of determining an embedded inclusion, it is expected that the reconstruction is more stable when the inclusion is close to the boundary than when it is hidden away from the boundary. I will discuss a case in which we can rigorously justify this property. Increasing stability phenomena for inverse boundary value problems with large energy/frequency have attract a lot of attention recently.  I plan to talk about recent results on this subject for the Schr"odinger and Maxwell equations.


  • Tuesday, 25th April, 2017

    Title: Interpolation with Radial Basis Functions with Parameters
    Speaker: Prof. Martin D. Buhmann, Mathematics Science Centre, University of Giessen, Germany
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this talk we will present the background and new results about interpolation with radial basis functions. That is, we use interpolants from spaces spanned by arbitrary shifts of radially symmetric functions φ(1 · 12) : Rn → R,φ(r)being a univariate function that depends on parameters, such as the multiquadrics φ(r) = √r2 + c2 and its generalisation that φ(r) = (r2 + c2)γ . The interpolants match given functions at given scattered points in Rn. The attractive facts about these interpolants are that they are not only well-defined and exist uniquely in any space dimension n with very moderate conditions on the men- tioned scattered data points (such as that they be distinct) but also they converge quickly to sufficiently smooth functions that are to be approximated. These characteristics are true especially for the generalised multiquadrics, and we will study in detail (and give new results about) their convergence behaviour. This applies both to the situation when the scattered points become dense and when the parameter c in the multiquadrics is adjusted. We study applications to solving partial differential equations too.


  • Thursday, 27th April, 2017

    Title: SVD Approximations for Large Scale Imaging Problems
    Speaker: Prof. James Nagy, Department of Mathematics and Computer Science, Emory University, USA
    Time/Place: 17:00  -  18:00 (Preceded by Reception at 4:30pm)
    WLB104, Lam Woo International Conference Centre, Shaw Campus, Hong Kong Baptist University
    Abstract: A fundamental tool for analyzing and solving ill-posed inverse problems is the singular value decomposition (SVD). However, in imaging applications the matrices are often too large to be able to efficiently compute the SVD. In this talk we present a general approach to describe how an approximate SVD can be used to efficiently compute approximate solutions for large-scale ill-posed problems, which can then be used either as an initial guess in a nonlinear iterative scheme, or as a preconditioner for linear iterative methods. We show more specifically how to efficiently compute the an SVD approximation for certain applications in image processing.


  • Friday, 28th April, 2017

    Title: A Computational Method for Optimal Control Problems Governed by Nonlinear Switched Systems
    Speaker: Prof. Kok Lay Teo, Department of Mathematics and Statistics, Curtin University of Technology, Australia
    Time/Place: 11:00  -  12:00 (Preceded by Reception at 10:30am)
    WLB104, Lam Woo International Conference Centre, Shaw Campus, Hong Kong Baptist University
    Abstract: Switched systems operate by switching among various modes or subsystems. This talk considers optimal control problems governed by nonlinear switched systems in which the mode dynamics are described by nonlinear differential equations. A computational method for computing the optimal control for this optimal control problem is to be presented. This computational method is based on some key ideas in optimal control computation, which include control parameterization, time-scaling transformation, and the constraint transcription method. Several examples are discussed.


  • Friday, 28th April, 2017

    Title: Kernel machine association testing for longitudinal phenotypes
    Speaker: Dr. WANG Zuoheng, Department of Biostatistics, Yale School of Public Health, U.S.A.
    Time/Place: 15:00  -  16:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Recent developments in high-throughput sequencing technologies have made it possible to search for both rare and common genetic variants associated with complex diseases.  Many phenotypes in health studies are measured at multiple time points.  The rich information on repeated measurements on each subject not only provides a more accurate assessment of disease condition, but also allows us to explore the genetic influence on disease onset and progression.  However, many association tests available are designed for a single measurement.  To address this limitation, we propose two kernel machine association tests.  The first test is based on linear mixed model/generalized linear mixed model that use several variance components to account for the within-subject correlation of the longitudinal data.  The second test is a generalized estimating equations (GEE)-based kernel association test to assess association between a set of genetic variants and longitudinal data, which extends the GEE method for a single SNP to a set of SNPs.  The proposed methods allow for both longitudinally-measured continuous and discrete traits, where within-subject correlation is account for.  In simulation studies, we evaluate the performance of the new methods, and demonstrate their improved power, by making full use of multiple measurements, as comparing to previously proposed tests on a single measurement or average measurements for each subject.  We illustrate the new methods in the Framingham Heart Study.


  • Friday, 28th April, 2017

    Title: Dimensionality Reduction and Variable Selection in Multivariate Varying-Coefficient Models
    Speaker: Dr. LIAN, Heng , Department of Mathematics, City University of Hong Kong, HKSAR
    Time/Place: 16:00  -  17:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Motivated by the study of gene and environment interactions, we consider a multivariate response varying-coefficient model with a large number of covariates. The need of nonparametrically estimating a large number of coefficient functions given relatively limited data poses a big challenge for fitting such a model. To overcome the challenge, we develop a method that reduce the number of unknown functions to be estimated by using principal components and apply sparsity-inducing penalization to select relevant covariates. Our asymptotic theory shows that the proposed method can consistently identify relevant covariates and can estimate the corresponding coefficient functions with the same convergence rate as when only the relevant variables are included in the model. Our method is illustrated using data from Framingham Heart Study.