Title: | Fast algorithms for direct and inverse problems in mathematical geophysics |
Speaker: | Prof. Jianliang Qian, Department of Mathematics, Michigan State University |
Time/Place: | 16:00 - 17:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | I will overview my works on developing fast algorithms for solving direct and inverse problems in mathematical geophysics. In particular, I will emphasize fast Huygens sweeping methods for direct simulation and imaging of seismic waves and fast level-set methods for inversion of gravity gradient and magnetic data. Synthetic and field data sets will be used to illustrate the effectiveness of these methods. |
Title: | Improved Data-dependent Kernel Bases in RBF Interpolation |
Speaker: | Prof. Francesco Marchetti, Department of Mathematics, University of Padua, Italy |
Time/Place: | 11:00 - 12:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | In the field of Radial Basis Function (RBF) interpolation, the choice of the basis function plays a fundamental role in designing accurate interpolants. In particular, RBFs usually depend on the so-called shape parameter, whose value heavily affects the quality and the stability of the reconstruction process. In this talk, we first present a Cross Validation (CV) algorithm for kernel-based schemes that substantially outperforms standard CV implementations in terms of efficiency. Then, the presented algorithm is employed for tuning the shape parameter of the basis function in some numerical tests. In the second part of the talk we provide a different perspective, in which the tuning of the shape parameter is substituted by a scaling function, which can be chosen by exploiting some possible prior information on the underlying function to be recovered. The so-constructed Variably Scaled Kernels (VSKs), which include the case of discontinuous scaling functions, are then effectively applied in medical and solar imaging applications. |
Title: | A Polynomial Lower Approximation Approach for Two-stage Stochastic Optimization |
Speaker: | Dr. Suhan ZHONG, Department of Mathematics, Texas A&M University, USA |
Time/Place: | 15:00 - 16:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | This talk focuses on two-stage stochastic programs (SPs) with polynomial defining functions and continuous random distributions. An efficient polynomial lower approximation approach is introduced to solve such problems. It can be used to find convincing lower bound of the optimal value and candidate global optimizer of the original problem. Our method can also be used to verify the global optimality of solutions computed from other methods. |
Title: | Moment deviation subspaces of dimension reduction for high dimensional data with change structure |
Speaker: | Ms. Huang Jiaqi, Department of Mathematics, Beijing Normal University, China |
Time/Place: | 15:00 - 16:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | This paper introduces the notion of moment deviation subspaces of dimension reduction for high-dimensional data with change structure. We propose a novel estimation method to identify subspaces by combining the Mahalanobis matrix and the pooled covariance matrix. The theoretical properties are investigated to show that the change point detection and clustering can be equivalently implemented in the dimension reduction subspaces, whether the data structure is dense or sparse, whenever the dimension divided by the sample size goes to zero. We propose an iterative algorithm based on dimension reduction subspaces that can be applied for data clustering of high-dimensional data. The numerical studies on synthetic and real data sets suggest that the dimension reduction versions of existing methods of change point detection and clustering methods significantly improve the performances of existing approaches in finite sample scenarios. |
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Learn MoreProf. M. Cheng, Dr. Y. S. Hon, Dr. K. F. Lam, Prof. L. Ling, Dr. T. Tong and Prof. L. Zhu have been awarded research grants by Hong Kong Research Grant Council (RGC) — congratulations!
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