Colloquium/Seminar
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Event(s) on October 2015
- Saturday, 3rd October, 2015
Title: 香港浸會大學數學系四十五週年校友講座 - 數學畢業生在金融市場的就業機會 Speaker: 朱志釗校友 蔡子弘先生 嚴維樂先生, Hong Kong Time/Place: 14:30 - 16:30
RRS905, Sir Run Run Shaw Building, HSH Campus, Hong Kong Baptist UniversityAbstract: 本講座的目的是讓數學系同學了解金融市場的工作機會和前景,及讓有關的金融專業人士分享他們的工作經驗。 - Wednesday, 7th October, 2015
Title: The CMIV Short Course on Proximal Optimization Speaker: Prof. Patrick Louis COMBETTES, Pierre and Marie Curie University, France Time/Place: 16:00 - 18:00
SCT909, Science Tower, HSH Campus, Hong Kong Baptist University - Tuesday, 13th October, 2015
Title: The Neuman-Poincare operator and cloaking by anomalous localized resonance for linear elasticity Speaker: Prof. KANG Hyeonbae, Department of Mathematics, Inha University , Korea Time/Place: 16:30 - 17:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Recently the spectral theory of the Neuman-Poincare operator has been extended to the Lame system of linear elasticity, and applied to cloaking by anomalous localized resonance. I will talk about recent results in this direction of research. - Friday, 16th October, 2015
Title: CMIV Colloquium: Data-driven Atomic Decomposition of Real-world Signals (Lecture 1) Speaker: Prof. Charles K. Chui, Stanford University, USA Time/Place: 11:00 - 12:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: The strategy of divide-and-conquer applies to just about all scientific and engineering disciplines for theoretical and algorithmic development as well as experimental implementations for various applications. In mathematics, a periodic function can be decomposed as its Fourier series, with building blocks of sinusoids. For data analysis and visualization, when the given data are represented by spline curves or spline surfaces, the spline functions can be written, respectively, as linear combinations of Bsplines or box splines, which may be considered as building blocks of the corresponding spline spaces. Hence, sinusoids, B-splines, and certain box splines, could be viewed as “atoms” of their corresponding function spaces. Perhaps the most exciting theoretical development in this direction is the notion of “atomic decomposition” of functions for the Hardy spaces $H^p(\R), 0<p\le1$, introduced by Raphy Coifman in his 1974 article, which contributed to motivate his joint work with Yves Meyer and Elias Stein, published some 10 years later, on the introduction and characterization of the so-called Tent spaces. This significant piece of work has important applications to the unification and simplification of the basic techniques in harmonic analysis. Furthermore, the atomic decomposition of these and other function spaces, contributed by others, has profound impact to the advancement of both harmonic and functional analyses over the decades of the 80’s and 90’s. An important property of the atoms for $H^p(\R)$, with $0<p\le1$, is their vanishing moments of order up to $1/p$, leading to the introduction of wavelets and the rapid advances of wavelet analysis and algorithmic development, with applications to most engineering and physical science disciplines for a duration of over two decades. With the popularity of wavelets, several other families of wavelet-like basis functions were introduced, including: wavelet packets, localized cosines, chirplets, warplets, and mulit-scale Gabor dictionaries. Using this large collection of basis functions as “atoms” to compile desirable dictionaries, the powerful mathematical tool of “basis pursuit”, introduced and studied in some depth by Scott Chen, David Donoho, and Michael Saunders in their popular 1999 SIAM J. Scientific Computing paper, provides a more attractive alternative of the standard iterative computational schemes based on “matching pursuit”. On the other hand, it is very difficult, even if feasible at all, to compile an effective dictionary for sufficiently accurate decomposition of real-world signals in general. In this regard, the basis pursuit approach was recently modified by Thomas Hou and Zuoqiang Shi to “nonlinear basis pursuit”, using a nonlinear optimization scheme. Unfortunately, this approach requires appropriate guesses of initial phase functions, and perhaps the effectiveness of the guess might also depend on the (unknown) number of atoms. The goal of this seminar is to initiate a study of the construction of atoms for signal decomposition directly from the input signal itself. In other words, we are interested in the problem of “data-driven” atomic decomposition, with atoms constructed from the real-world signal data. The highlights of our discussion include derivation of a natural formulation of the data-driven atoms, a modified sifting process for real-time implementation, further decomposition of the intrinsic mode functions, motivation of the signal separation operator, and the problem of super-resolution, leading to superEMD. - Monday, 19th October, 2015
Title: CMIV Colloquium: Data-driven Atomic Decomposition of Real-world Signals (Lecture 2) Speaker: Prof. Charles K. Chui, Stanford University, USA Time/Place: 14:00 - 15:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: The strategy of divide-and-conquer applies to just about all scientific and engineering disciplines for theoretical and algorithmic development as well as experimental implementations for various applications. In mathematics, a periodic function can be decomposed as its Fourier series, with building blocks of sinusoids. For data analysis and visualization, when the given data are represented by spline curves or spline surfaces, the spline functions can be written, respectively, as linear combinations of Bsplines or box splines, which may be considered as building blocks of the corresponding spline spaces. Hence, sinusoids, B-splines, and certain box splines, could be viewed as “atoms” of their corresponding function spaces. Perhaps the most exciting theoretical development in this direction is the notion of “atomic decomposition” of functions for the Hardy spaces $H^p(\R), 0<p\le1$, introduced by Raphy Coifman in his 1974 article, which contributed to motivate his joint work with Yves Meyer and Elias Stein, published some 10 years later, on the introduction and characterization of the so-called Tent spaces. This significant piece of work has important applications to the unification and simplification of the basic techniques in harmonic analysis. Furthermore, the atomic decomposition of these and other function spaces, contributed by others, has profound impact to the advancement of both harmonic and functional analyses over the decades of the 80’s and 90’s. An important property of the atoms for $H^p(\R)$, with $0<p\le1$, is their vanishing moments of order up to $1/p$, leading to the introduction of wavelets and the rapid advances of wavelet analysis and algorithmic development, with applications to most engineering and physical science disciplines for a duration of over two decades. With the popularity of wavelets, several other families of wavelet-like basis functions were introduced, including: wavelet packets, localized cosines, chirplets, warplets, and mulit-scale Gabor dictionaries. Using this large collection of basis functions as “atoms” to compile desirable dictionaries, the powerful mathematical tool of “basis pursuit”, introduced and studied in some depth by Scott Chen, David Donoho, and Michael Saunders in their popular 1999 SIAM J. Scientific Computing paper, provides a more attractive alternative of the standard iterative computational schemes based on “matching pursuit”. On the other hand, it is very difficult, even if feasible at all, to compile an effective dictionary for sufficiently accurate decomposition of real-world signals in general. In this regard, the basis pursuit approach was recently modified by Thomas Hou and Zuoqiang Shi to “nonlinear basis pursuit”, using a nonlinear optimization scheme. Unfortunately, this approach requires appropriate guesses of initial phase functions, and perhaps the effectiveness of the guess might also depend on the (unknown) number of atoms. The goal of this seminar is to initiate a study of the construction of atoms for signal decomposition directly from the input signal itself. In other words, we are interested in the problem of “data-driven” atomic decomposition, with atoms constructed from the real-world signal data. The highlights of our discussion include derivation of a natural formulation of the data-driven atoms, a modified sifting process for real-time implementation, further decomposition of the intrinsic mode functions, motivation of the signal separation operator, and the problem of super-resolution, leading to superEMD. - Thursday, 22nd October, 2015
Title: Metamaterial Rapid Modeling and Design Speaker: Mr. GUO Xiao, Department of Mathematics, Hong Kong Baptist University, Hong Kong Time/Place: 11:30 - 12:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: This research work addresses the time-consuming problem of design process of metamaterial, caused by extensive full-wave simulation. Previous efforts made to increase the speed of massive metamaterial microstructures design are first reviewed. A faster, non-iterative approach is used to replace the numerical simulation when dealing with dielectric composites. The frequency response of metamaterial is fitted by fraction approximation in order to build equivalent circuits. Regression and inference methods are also used to establish relationship between functions of metamaterial and its physical dimensions. The intended approach is capable to obtain a comprehensive model in terms of electromagnetic incidence condition frequency. With the aids of statistical tools, rapid metamaterial design can be achieved. - Thursday, 22nd October, 2015
Title: HKBU MATH 45th Anniversary Distinguished Lecture - Innovative Spectral and Imaging Methods with applications to Telemedicine, Telehealth and Non-invasive Diagnosis Speaker: Prof. Charles Chui, Stanford 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 UniversityAbstract: This is a lecture for the general audience without advanced mathematics background and only very minimal knowledge of signal and image processing. The topics of discussion include: 1. The state-of-the-art (nonlinear and non-stationary) signal and image decomposition and reconstruction methods that extend to higher dimensional data manifolds. 2. What is telemedicine? Why is it necessary? What are the benefits? 3. Telehealth prolongs healthy lives and is a multi-trillion-$ industry and beyond. 4. Everyone wants non-invasive medical diagnosis, but what are the options? 5. A brief discussion of traditional Chinese medical (TCM) practice. 6. How does the knowledge of TCM benefit the advancement of bio-medical research? 7. Perhaps modern spectral, imaging, and data manifold methods could provide the solutions, at least partially. - Wednesday, 28th October, 2015
Title: Splitting Methods and the Numerical Solution of Kawarada Equations Speaker: Prof. SHENG Qin, Department of Mathematics, Baylor University, USA Time/Place: 11:30 - 12:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: This talk is dedicated to the study of splitting methods and simulations of some thermal combustion equation problems. We will start with a brief look at some simplest, yet extremely powerful, splitting strategies. They serve as a foundation to modern decomposition theory and methods. Then an overview of important issues involving the numerical solution of nonlinear Kawarada problems will be given. The degenerate reaction-diffusion partial differential equations concerned are for modeling quenching-combustion processes, in particular when solid fuels are applied. Adaptive splitting finite difference approximations of the underlying equations will be discussed. Numerical analysis of the monotonicity, convergence and stability of the numerical solution, as well as ideas behind one of the latest exponential evolving grid strategies will be given. The highly efficient computational procedures can further be extended for solving similar singular problems in biophysics, oil pipeline decays and laser-materials interactions. This talk will also be suitable for graduate students.