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Event(s) on February 2017


  • Monday, 6th February, 2017

    Title: Bound-Preserving High Order Schemes for Hyperbolic Equations: Survey and Recent Developments
    Speaker: Prof. Chi-Wang Shu, Brown University, USA
    Time/Place: 17:00  -  18:00 (Preceded by Reception at 4:30pm)
    SCT909, Science Tower, HSH Campus, Hong Kong Baptist University
    Abstract: Solutions to many hyperbolic equations have convex invariant regions, for example solutions to scalar conservation laws satisfy maximum principle, solutions to compressible Euler equations satisfy positivity-preserving property for density and internal energy, etc. It is however a challenge to design schemes whose solutions also honor such invariant regions. This is especially the case for high order accurate schemes. In this talk we will first survey strategies in the literature to design high order bound-preserving schemes, including the general framework in constructing high order bound-preserving finite volume and discontinuous Galerkin schemes for scalar and systems of hyperbolic equations through a simple scaling limiter and a convex combination argument based on first order bound-preserving building blocks, and various flux limiters to design high order bound-preserving finite difference schemes. We will then discuss a few recent developments, including high order bound-preserving schemes for relativistic hydrodynamics, high order discontinuous Galerkin Lagrangian schemes, and high order discontinuous Galerkin methods for radiative transfer equations. Numerical tests demonstrating the good performance of these schemes will be reported.


  • Wednesday, 8th February, 2017

    Title: Steady subsonic Euler flows through a nozzle or past a wall
    Speaker: Prof. Chunjing XIE, Department of Mathematics and Institute of Natural Sciences / Institute of Mathematical Sciences, Shanghai Jiao Tong University / Chinese University of Hong Kong, China
    Time/Place: 15:30  -  16:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: We first discuss the well-posedness theory for subsonic Euler flows in nozzles or past a symmetric body. One of the key observations to achieve these results is that the streamlines in these flows have simple topological structure. This helps us to introduce the stream function formulation so that the compressible Euler system can be reduced into a single second order equation. Finally, the well-posedness theory for subsonic flows through nozzles with multiple ends which share the key features for flows around a non-symmetric body will be addressed. The key ingredients of the analysis are the study for critical points of the solutions of elliptic equations and the regularity of the solutions for elliptic equation around corners with large inner angles.


  • Friday, 10th February, 2017

    Title: Construction of Conjugate Eigenfunctions and Its Application for a Class of Acoustical Waveguides with a PML
    Speaker: Prof. ZHU Jianxin , Department of Mathematics, Zhejiang University, China
    Time/Place: 15:00  -  16:00
    FSC1014, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In the bounded region with a perfectly matched layer (PML), since there is no orthogonal property of the eigenfunctions for the improved and complex Helmholtz equation (ICHE), it is difficult to compute the coordinates under the local bases when the equation is solved by some numerical marching methods. The equation of the conjugate eigenfunctions for ICHE is deduced, and it is proven that there is the cross orthogonal property between the eigenfunctions and their conjugate eigenfunctions. This may ensure the higher efficiency by using the marching methods. Numerical simulation results show that the treatment is more feasible and efficient.


  • Friday, 10th February, 2017

    Title: CMIV Distinguished Lecture: Mathematics in Hyperspectral Image Processing
    Speaker: Prof. Robert J. Plemmons, Wake Forest University, USA
    Time/Place: 16:30  -  17:30 (Preceded by Reception at 4:00pm)
    SCT909, Science Tower, HSH Campus, Hong Kong Baptist University
    Abstract:

    Hyperspectral, Light Detection and Ranging (LiDAR), and Polarimetric imaging are the pervasive optical imaging modalities in remote sensing. Here, we primarily consider hyperspectral imaging (HSI) which also has extensive applications in the life sciences and medicine. A hyperspectral image provides the fraction of light from pixels at many different wavelengths across the electromagnetic, usually between 100 and 1200, leading to 3D dataset carrying significantly more information than a color (RGB) image. A HSI data cube provides a unique spectral signature for each pixel, information that can be used to identify and discriminate materials, and thus analyze scenes and objects.

    Here, we provide an overview of our recent work on mathematical algorithms for HSI processing, including: deblurring images taken through atmospheric turbulence, the use of nonnegative matrix factorization and convolutional neural networks for material unmixing and feature classification, and random projections for HSI compression and data transmission. The work is funded by the Air Force and the National Geospatial Agency. Several U.S. co-authors who are involved with this research will be referenced. We also point out joint work with Raymond Chan at CUHK, Michael Ng at HKBU, and their students.


  • Tuesday, 14th February, 2017

    Title: Regularized t distribution and its applications
    Speaker: Mr Hu Zongliang, Department of Mathematics, Hong Kong Baptist University, Hong Kong
    Time/Place: 15:00  -  16:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Microarrays can simultaneously measure the expression level of thousands of genes. One major goal in microarray studies is to identify genes that are differentially expressed between two or more groups. Statistical significance of differential expression can be tested by performing a test for each gene. It is noted, however, that microarray experiments are often performed with a small number of replicates, and consequently, the Student’s t tests using the sample means and standard deviations may suffer a low power for detecting differentially expressed genes. To overcome this problem, we first propose a regularized t distribution and derive its properties including the probability density function and the moments. The non-central regularized t distribution is also introduced and investigated for the power analysis. We then apply the regularized t distribution to the gene expression detection problem. Simulation studies show that the regularized t test outperforms some existing test methods including the Student’s t test and the Bayesian t test when the sample size is small to moderate.


  • Wednesday, 15th February, 2017

    Title: Optimal Dividend Strategies of Two Collaborating Businesses in the Diffusion Approximation Model
    Speaker: Dr. Jiawen Gu, Department of Mathematics, University of Hong Kong, Hong Kong
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this talk, we discuss the optimal dividend payment strategy for an insurance company, having two collaborating business lines. The surpluses of the business lines are modeled by diffusion processes. The collaboration between the two business lines permits that money can be transferred from one line to another with or without proportional transaction costs while money must be transferred from one line to another to help both business lines keep running before simultaneous ruin of the two lines eventually occur.


  • Wednesday, 15th February, 2017

    Title: CMIV Distinguished Lecture: Security Printing Fundamentals
    Speaker: Prof. Steven J. Simske, Printing and Life Sciences Portfolios, HP Labs, USA
    Time/Place: 16:30  -  17:30 (Preceded by Reception at 4:00pm)
    SCT909, Science Tower, HSH Campus, Hong Kong Baptist University
    Abstract: In this lecture, I give an overview of security printing, including a 15-year historical perspective focused on variable data printing (VDP), the core engine to effective countermeasures to counterfeiting of branded/labeled goods. Among the security printing approaches, I will cover color & progressive barcodes, the image based forensic service, the global product authentication service, other product recall and authentication services, and VDP security features such as microtext, guilloches and other graphical alphanumerics, and void pantographs. I close with the future of illicit economy prevention by describing multi-VDP workflows, illuminating the relationship between tracking, authentication, forensics and inspection.


  • Thursday, 16th February, 2017

    Title: Meta-algorithmics for intelligent systems
    Speaker: Prof. Steven J. Simske, Printing and Life Sciences Portfolios, HP Labs, USA
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Meta-Algorithmics are a set of design patterns for building intelligent systems. They comprise a plurality of systems, which are used in combination to improve the overall system in measurable ways: (1) Accuracy; (2) Robustness; (3) Adaptability; and (4) Cost. Meta-algorithmics are a “third form” of parallelism (complementing parallelism by task and by component), and as such allow different intelligent algorithms and systems to be used modularly as design atomics. Designing systems to support meta-algorithmics from incipience therefore provides two distinct advantages for information reuse: (1) innate scalability and (2) re-purposability through re-introduction of training content. Flexibility comes from the ability to set the extent of re-use of components. In this talk, the design advantages of meta-algorithmics to software reuse for building intelligent systems in a wide variety of application areas will be shown.


  • Thursday, 23rd February, 2017

    Title: Adaptive-to-model Hybrid Test for Model Checking
    Speaker: Ms Li Lingzhu, 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: Although local smoothing methods are popularly used for checking the model adequacy due to their powerfulness of detecting high-frequency regression models, the use of nonparametric estimation in test statistics causes inefficiency with slow rate to their weak limits. In contrast, global smoothing tests can detect local alternatives distinct from the null model at faster rate, but are less sensitive to high-frequency models and the limiting null distributions often requires assistance of Monte Carlo approximation, which is computationally expensive. To benefit from these two types of tests, we propose an adaptive-to-model hybrid test which is a combination of the moment-based and the conditional moment-based tests. Invoking the model adaptation property, the proposed test statistic can have a tractable limiting null distribution for critical value determination and can detect local alternatives converging to the null at the rate existing global smoothing tests can achieve and at the same time, is sensitive to high-frequency models that local smoothing tests can deal with. Numerical studies are conducted to examine the performance of the test in finite sample cases.


  • Thursday, 23rd February, 2017

    Title: A statistical framework for integrating functional annotations with genome-wide association studies
    Speaker: Ms Ming Jingsi, 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: Research on Genome-Wide Association Studies (GWAS) has shown that complex diseases or traits are related to the joint influence of many genetic variants, most of which have only small and moderate effects. As the rising of Big Data in genomics, more and more functional annotation data have become available. Here we propose a statistical framework for integrating functional annotations with GWAS data. Not only it increases statistical power to identify risk variants, but also offers more biological insights by detect relevant functional annotations. We have developed a variational EM algorithm for estimating model parameters, which is scalable to genome-wide analysis. We applied our method to analyze four Schizophrenia GWAS datasets with 130 functional annotations from the Roadmap project, gaining more statistical power over conventional methods and deeper understanding of genetic architecture of Schizophrenia.


  • Monday, 27th February, 2017

    Title: Tensor Research: Theory and Computation
    Speaker: Dr. Weiyang Ding, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: This talk introduces some of our related work on tensor theory and computation, which attempts to expand the numerical linear algebra to the numerical multilinear algebra. The absence of linearity and the complexity of indices make it impossible to generalize the results from matrices to tensors straightforwardly. It needs some additional conditions or special structures of tensors, so that some theories stay true or algorithms still be practical under proper modifications. The first topic is about Hankel tensors. Decompositions of Hankel-type tensors are widely employed in signal processing, and tensor-vector multiplications are the basis operations. We propose a fast algorithm for Hankel tensor-vector multiplications by introducing a special class of Hankel tensors that can be diagonalized by Fourier matrices, called anti-circulant tensors. The computational complexity is reduced from O}(n^m) to O}(m^2 n log mn). The second part is contributed to M-tensors, arising from the hypergraph theory, computation of the spectral radii of nonnegative tensors, and numerical solutions of PDEs. We obtain several equivalent definitions of nonsingular M-tensors. Furthermore, the generalization of the “nonnegative inverse” property inspires the study of multilinear system of equations. We prove the existence and uniqueness of the positive solutions of nonsingular M-equations with positive right-hand sides, and also propose several iterative methods for computing the positive solutions. Then we introduce the generalized tensor eigenvalue problems, which are regarded as a unified framework of different kinds of tensor eigenvalue problems arising from applications. We focus on the perturbation theory and the error analysis of regular tensor pairs. Employing various techniques, we extend several classical results from matrices or matrix pairs to tensor pairs, such as the Gershgorin circle theorem, the Collatz-Wielandt formula, the Bauer-Fike theorem, the Rayleigh-Ritz theorem, backward error analysis, the componentwise distance of a nonsingular tensor to singularity. Finally, tensor logarithmic norms are proposed for locating tensor eigenvalues and studying the stability of a class of ODEs. The explicit forms of several specific tensor logarithmic (semi)norms are proved.