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Event(s) on August 2012
- Tuesday, 7th August, 2012
Title: Determining Critical Parameters of Sine-Gordon and Nonlinear Schrödinger Equations with a Point-Like Potential Using Generalized Polynomial Chaos Methods Speaker: Prof. JUNG Jae-Hun, Department of Mathematics, University at Buffalo (SUNY Buffalo), USA Time/Place: 11:00 - 12:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: We consider the sine-Gordon and nonlinear Schrödinger equations with a point-like singular source term. The soliton interaction with such a singular potential yields a critical solution behavior. That is, for the given value of the potential strength or the soliton amplitude, there exists a critical velocity of the initial soliton solution, around which the solution is either trapped by or transmitted through the potential. In this talk, we propose an efficient method for finding the critical velocity by using the generalized polynomial chaos (gPC) method. For the proposed method, we assume that the soliton velocity is a random variable and expand the solution in the random space using the orthogonal polynomials. We consider the Legendre and Hermite chaos with both the Galerkin and collocation formulations. The proposed method finds the critical velocity accurately with spectral convergence. Thus the computational complexity is much reduced. The very core of the proposed method lies in using the mean solution instead of reconstructing the solution. The mean solution converges exponentially while the gPC reconstruction may fail to converge to the right solution due to the Gibbs phenomenon in the random space. Numerical results confirm the accuracy and spectral convergence of the method. This is a joint work with Debananda Chakraborty (SUNY Buffalo) and Emmanuel Lorin (Carleton university). - Thursday, 9th August, 2012
Title: CMIV Lecture 1: Computer Algebra and Its Applications to Circuits, Signals, and Systems Speaker: Prof. Zhiping Lin, Nanyang Technological University, Singapore Time/Place: 10:00 - 11:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Computer algebra is playing an increasingly important role in many engineering problems. In particular, Grobner bases, as one of the important tools in computer algebra, have found wide applications in almost every area in circuits, signals and systems. The main reason for the success of Grobner bases is that many problems in mathematics, science and engineering can be represented by multivariate polynomials (ideals, modules, matrices etc.), and Grobner bases are well known to play a similar role in multivariate polynomials as Euclidean Division Algorithm in univariate polynomials. One of the major advantages of Grobner bases, or more general, computer algebra, is that both numerical and symbolic solutions are provided when exist. The objectives of this tutorial are threefold. Firstly, we give an elementary lecture on Grobner bases to further bring awareness of and stimulate interest in Grobner bases among researchers and engineers in circuits, signals and systems. This part includes the basic concepts, unique properties and algorithms for Grobner bases of nD polynomial ideals, such as term ordering, the division for nD polynomials, normal forms and cofactors, (reduced) Grobner basis, S-polynomials, the elimination property etc. Information about several popular software packages for Grobner bases is also provided. Secondly, we present two practical applications of Grobner bases to the testability evaluation for analog linear circuits and to signal reconstruction from multiple unregistered sets of samples. Thirdly, we give a brief survey of applications of Grobner bases to circuits, signals and systems, ranging from the analysis and design of multidimensional control systems, wavelets and filter banks to translinear network synthesis, and biological applications. Many simple examples are illustrated throughout to help participants to understand Grobner bases easily and their applications. - Thursday, 9th August, 2012
Title: CMIV Lecture 2: Computer Algebra and Its Applications to Circuits, Signals, and Systems Speaker: Prof. Zhiping Lin, Nanyang Technological University, Singapore Time/Place: 14:00 - 15:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Computer algebra is playing an increasingly important role in many engineering problems. In particular, Grobner bases, as one of the important tools in computer algebra, have found wide applications in almost every area in circuits, signals and systems. The main reason for the success of Grobner bases is that many problems in mathematics, science and engineering can be represented by multivariate polynomials (ideals, modules, matrices etc.), and Grobner bases are well known to play a similar role in multivariate polynomials as Euclidean Division Algorithm in univariate polynomials. One of the major advantages of Grobner bases, or more general, computer algebra, is that both numerical and symbolic solutions are provided when exist. The objectives of this tutorial are threefold. Firstly, we give an elementary lecture on Grobner bases to further bring awareness of and stimulate interest in Grobner bases among researchers and engineers in circuits, signals and systems. This part includes the basic concepts, unique properties and algorithms for Grobner bases of nD polynomial ideals, such as term ordering, the division for nD polynomials, normal forms and cofactors, (reduced) Grobner basis, S-polynomials, the elimination property etc. Information about several popular software packages for Grobner bases is also provided. Secondly, we present two practical applications of Grobner bases to the testability evaluation for analog linear circuits and to signal reconstruction from multiple unregistered sets of samples. Thirdly, we give a brief survey of applications of Grobner bases to circuits, signals and systems, ranging from the analysis and design of multidimensional control systems, wavelets and filter banks to translinear network synthesis, and biological applications. Many simple examples are illustrated throughout to help participants to understand Grobner bases easily and their applications. - Tuesday, 14th August, 2012
Title: What is Math Education? --Its past, present and possible future trends Speaker: Prof. WU Zhijian, Department of Mathematics, The University of Alabama, USA Time/Place: 11:30 - 12:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: For many educators in higher education, especially in the areas of science, technology, engineering and mathematics (STEM), math education reform has been and will continue to be a hot topic. In this talk, we revisit the path of math education, its objectives, methods, and outcomes. We discuss possible future trends of mathematics in higher education and lifetime learning. - Tuesday, 14th August, 2012
Title: CMIV Lecture: 2D and 3D Multiscale Geometric Transforms Speaker: Prof. Jean-Luc STARCK, CosmoStat lab, UMR AIM, Service dAstrophysique, CEA/Saclay, France Time/Place: 14:00 - 15:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: We present several 2D multiscale geometric transforms such as ridgelet and curvelet. We show how they can be extended to the third dimension and how these new decompositions can be used for applications such as denoising or inpainting. - Tuesday, 14th August, 2012
Title: Online education and its current practices Speaker: Prof. WU Zhijian, Department of Mathematics, The University of Alabama, USA Time/Place: 15:30 - 16:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Based on more than a decade math online teaching and learning practices at the University of Alabama, we demonstrate the significance of using online technology and discuss its great potential and further improvements. - Monday, 20th August, 2012
Title: A Semiparametric Threshold Model for Censored Longitudinal Data Analysis Speaker: Prof. Zhang Wenyang, Department of Mathematics, The University of York, UK Time/Place: 10:00 - 11:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Motivated by an investigation of the relationship between blood pressure change and progression of microalbuminuria (MA) among individuals with Type I diabetes, we propose a new semiparametric threshold model for censored longitudinal data analysis. We also study a new semiparametric BIC-type criterion for identifying the parametric component of the proposed model. Cluster effects in the model are implemented as unknown fixed effects. Asymptotic properties are established for the proposed estimators. A quadratic approximation used to implement the estimation procedure renders the method very easy to implement by avoiding the computation of multiple integrals and the need for iterative algorithms. Simulation studies show that the proposed methods work well in practice. An illustration using the Wisconsin Diabetes data suggests some interesting findings. - Monday, 20th August, 2012
Title: Local Linear Regression on Manifolds and its Geometric Interpretation Speaker: Prof. Cheng Ming-Yen, Department of Mathematics, National Taiwan University, Taiwan Time/Place: 11:00 - 12:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: High-dimensional data analysis has been an active research area, and the main focuses have been variable selection and dimension reduction. In practice, it occurs often that the variables are located on an unknown, lower-dimensional nonlinear manifold. Under this manifold assumption, one purpose of this paper is nonparametric regression on the manifold, and another goal is developing a new tool for manifold learning. To the first aim, we suggest directly reducing the dimensionality to the intrinsic dimension of the manifold, and performing the popular local linear regression (LLR) on a tangent plane estimate. An immediate consequence is a substantial gain in the computational speed when the ambient space dimension is much larger than the intrinsic dimension. We provide detailed theoretical justification of the convergence of the proposed regression and gradient estimators by carefully analyzing the curvature, boundary, and non-uniform sampling effects. A bandwidth selector that can handle heteroscedastic errors is proposed. To the second aim, we analyze carefully the behavior of our regression estimator both in the interior and near the boundary of the manifold, and make explicit its relationship with manifold learning, in particular estimating the Laplace operator of the manifold. The subtle relationship between the bandwidth used in the tangent plane estimation and the one used in the LLR is also made explicit. Numerical results show our regression estimator outperform existing methods in terms of both computational speed and estimation accuracy. This is joint work with Hau-Tieng Wu.