Colloquium/Seminar

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Event(s) on December 2012


  • Friday, 7th December, 2012

    Title: On the Euler-Poisson problem in plasma physics
    Speaker: Dr. Li Dong, Mathematics Department, The University of British Columbia, Canada
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The Euler-Poisson system is a fundamental two-fluid model to describe the dynamics of the plasma consisting of compressible electrons and a uniform ion background. In '98 Yan Guo first constructed a 3D global smooth irrotational solution by using dispersive Klein-Gordon effect. It has been conjectured that same results should hold in the two-dimensional case. In this talk I will describe a recent series of works which settles this conjecture in the affirmative.


  • Friday, 7th December, 2012

    Title: DLS: Structural Stability and Genericity in Dynamical Systems
    Speaker: Prof. Lan Wen, Peking University, China
    Time/Place: 16:30  -  17:30 (Preceded by Reception at 4:15pm)
    RRS905, Sir Run Run Shaw Building, HSH Campus, Hong Kong Baptist University
    Abstract: We review some basic ideas and results about structural stability and genericity in differentiable dynamical systems. We wish to share some basic ideas from dynamical systems with colleagues that are interested in but not really working in this field.


  • Tuesday, 11th December, 2012

    Title: DLS: Image Restoration: Wavelet Frame Approach, Total Variation and Beyond
    Speaker: Prof. Zuowei Shen, National University of Singapore, Singapore
    Time/Place: 11:30  -  12:30 (Preceded by Reception at 11:00am)
    RRS905, Sir Run Run Shaw Building, HSH Campus, Hong Kong Baptist University
    Abstract: This talk is about the wavelet frame-based image and video restorations. Main ideas of wavelet frame based models and corresponding algorithms for image restorations will be reviewed. Some of applications of wavelet frame based models image analysis and restorations will be shown. Examples of such applications include image and video inpainting, denoising, decomposition, image deblurring and blind deblurring, segmentation, CT image reconstruction and etc. In all of these applications, spline wavelet frames derived from the unitary extension principle are used. This allows us to establish a connection between wavelet frame base method and the total variation based method. In fact, we will show that when spline wavelet frames are used, a special model of a wavelet frame method can be viewed as a discrete approximation at a given resolution to the total variation based method. A convergence analysis in terms of objective functionals and their approximate minimizers as image resolution increases will be discussed.


  • Monday, 17th December, 2012

    Title: Independent test based on the regularized CCA
    Speaker: Dr. PAN Guangming, Division of Mathematical Sciences, Nanyang Technological University, Singapore
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: We proposes a statistic to test independence between two high dimensional random vectors x and y. The proposed statistic is based on the sum of regularized sample canonical correlation coefficients of x and y. The asymptotic distribution of the statistic under the null hypothesis is established as a corollary of general central limit theorems (CLT) for the linear statistics of classical and regularized sample canonical correlation coefficients when the dimension p_1 and p_2 are both comparable to the sample size n.


  • Tuesday, 18th December, 2012

    Title: DLS: Story of a Theorem in Euclidean Geometry
    Speaker: Prof. Gang Tian, Princeton University, USA
    Time/Place: 16:30  -  17:30 (Preceded by Reception at 4:00pm)
    RRS905, Sir Run Run Shaw Building, HSH Campus, Hong Kong Baptist University
    Abstract: Mathematics is full of mystery and beauty. In this talk, I will illustrate it through a very old theorem in Euclidean geometry. This theorem can be proved in a simple way by using facts in Euclid's "Element". I will show you how it is related to modern geometry and algebra, particularly, the group theory. I will also show our recent researches which have common features based on the same principle and how they interact with the string theory.


  • Wednesday, 19th December, 2012

    Title: Periodic + Smooth Image decomposition
    Speaker: Prof. Lionel Moisan, Laboratoire de Mathématiques Appliquées, Université Paris Descartes, France
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: A well-known issue of the Discrete Fourier Transform is that it implicitely assumes that the processed datum is periodic, in the sense that it can be tiled without creating strong discontinuities between adjacent tiles. When this hypothesis is not satisfied, strong artifacts appear in the Fourier Transform, which may be very limiting for some applications. In this talk, we describe a way to avoid these artifacts by means of a notion of periodic component extracted from the initial datum, and we discuss the advantages of such a decomposition over classical approaches like symmetrization or windowing. We then show several applications to image processing.


  • Thursday, 20th December, 2012

    Title: Statistical Estimation for Informatively Censored Survival Data
    Speaker: Prof. ZHANG Wenyang, Department of Mathematics, The University of York, United Kingdom
    Time/Place: 09:30  -  10:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Semiparametric proportional hazard regression models are the cornerstone in modern survival analysis. Most estimation methodologies developed in the literature, such as the famous partial likelihood based estimation, are built on the ground that the censoring is noninformative. However, in many applications, the censoring is indeed informative. In this talk, we study the survival regression models with an informative censoring that is easy to detect and apply. A very important problem in practice is how to estimate the survival models more efficiently with the information from the informative censoring. We propose a semiparametric maximum likelihood approach that is easilyimplementable to estimate both the nonparametric baseline hazard and the parametric coefficients in the survival models with informative censoring. Differently from the methods in the literature, we do not apply least informative approach to baseline, which does not work well in our simulation. We solve the difficulty in semiparametric estimation by suggesting an indirect application of local kernel smoothing to the baseline. Asymptotic theory of the proposed estimators is established under informative and noninformative likelihoods, respectively. We suggest a cross-validation method to detect the informative censoring in application. The performances of the estimators in finite samples are investigated by Monte Carlo simulation. Both asymptotic theory and simulation show that the suggested semiparametric approach provides more efficient estimators of the parameters for informative censoring, and estimates the baseline function accurately. The proposed method is applied to analyze the data about the infants hospitalized for pneumonia, which leads to interesting findings.


  • Friday, 21st December, 2012

    Title: Pathway analysis & improved discriminant analysis of microarray data
    Speaker: Dr. PANG Herbert, Department of Biostatistics & Bioinformatics, Duke University, USA
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The availability of high-dimensional genomic data from public domains has provided us with opportunities to develop data analytical methods, statistical modeling strategies, and computational algorithms. These data vary in dimensions and properties. The high-dimensional nature and relatively small sample size present statistical challenges. These challenges in translational genomics have encouraged a boom in methodological investigations. In this talk, I will present examples of statistical methodologies developed as a result of secondary analysis of public genomic data. Several real datasets from genomic expression omnibus will be used as illustrations.


  • Monday, 24th December, 2012

    Title: Low-Rank Optimization Problems with Hard Constraints: An Adaptive Semi-Nuclear Norm Regularization Approach
    Speaker: Prof. Defeng Sun, Department of Mathematics, National University of Singapore , Singapore
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Rank regularized problems and rank constrained problems arise in diverse areas such as engineering, statistics, quantum information, finance and graph theory. The nuclear norm technique has been widely-used but its efficiency is not universal. Several iterative algorithms have been proposed in the literature to go beyond the nuclear norm regularization. However, when hard constraints are involved, how to efficiently address such low-rank optimization problems remains much unexplored. In this talk, we propose an adaptive semi-nuclear norm regularization approach to address this issue. This approach iteratively solves a sequence of convex optimization problems, in which the objective functions are regularized by a semi-nuclear norm. Each subproblem can be solved by recently developed methodologies. Numerical experiments show that the iterative scheme of our proposed approach has the advantage of achieving both high computational efficiency and the low-rank structure-preserving ability. We will also talk about some challenges that need to be dealt with.


  • Thursday, 27th December, 2012

    Title: A parameterless trajectory detection algorithm
    Speaker: Prof. Lionel Moisan, Laboratoire de Mathématiques Appliquées, Université Paris Descartes , France
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this talk, we present a new generic point tracking algorithm that relies on an a-contrario formulation of the trajectory detection problem.We obtain a criterion for trajectory selection, that naturally includes data characteristics (number of frames, number of points) and trajectory parameters (smoothness, length). It can then be used either as a detection method (when associated to a dynamic programming algorithm) or as a post-processing device that can filter out spurious trajectories from the result provided by another algorithm. Contrary to standard methods, that generally require a crucial parameter tuning stage to process a particular kind of data, this algorithm can be directly used on various data and can handle sequences with a high variability of trajectory speeds.


  • Thursday, 27th December, 2012

    Title: Numerical methods for the optimal design of optical coatings
    Speaker: Mr. Wang Yuliang, Department of Mathematics, Michigan State University, USA
    Time/Place: 14:30  -  15:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: Abstract: Optical coatings are technologically very important. They have been undergoing active study for more than half a century and various design methods have been invented. New methods are still desirable since different methods can provide different designs, and one design may be superior than another in practice. In this talk we present a few new design methods based on numerical optimization, which can produce similar or different solutions compared with existing ones. A brief review of this field and a discussion of our future work will also be given.


  • Monday, 31st December, 2012

    Title: A Fast Global Optimization-Based Approach to Evolving Contours with Generic Shape Prior
    Speaker: Prof. Tai Xue-Cheng, Department of Mathematics, University of Bergen , Norway
    Time/Place: 11:00  -  12:00
    Abstract: In this talk, we present a new global optimization based approach to contour evolution, with or without the novel variational shape constraint that imposes a generic star shape using a continuous max-flow framework. In theory, the proposed continuous max-flow model provides a dual perspective to the reduced continuous min-cut formulation of the contour evolution at each discrete time frame, which proves the global optimality of the discrete time contour propagation. The variational analysis of the flow conservation condition of the continuous max-flow model shows that the proposed approach does provide a fully time implicit solver to the contour convection PDE, which allows a large time-step size to significantly speed up the contour evolution. For the contour evolution with a star shape prior, a novel variational representation of the star shape is integrated to the continuous max-flow-based scheme by introducing an additional spatial flow. In numerics, the proposed continuous max-flow formulations lead to efficient duality-based algorithms using modern convex optimization theories. Our approach is implemented in a GPU, which significantly improves computing efficiency. We show the high performance of our approach in terms of speed and reliability to both poor initialization and large evolution step-size, using numerous experiments on synthetic, real-world and 2D/3D medical images. This talk is based in a joint work by J. Yuan, E. Ukwatta1, X.C. Tai, A. Fenster1, C. Schnorr.