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Event(s) on April 2016
- Friday, 8th April, 2016
Title: Mathematics of Data Analysis Speaker: Prof. XU Yuesheng, Sun Yat-sen University and Syracuse University, China Time/Place: 14:30 - 15:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: We shall discuss several crucial mathematical issues in data analysis, including representation of data, kernel based sparse learning, learning in Hilbert spaces and in Banach spaces. In particular, we shall discuss native spaces for sparse learning and efficient algorithms for kernel based sparse learning. - Tuesday, 12th April, 2016
Title: Extended ADMM and BCD for Nonseparable Convex Minimization Models with Quadratic Coupling Terms: Convergence Analysis and Insights Speaker: Dr. Caihua Chen, School of Management and Engineering, Nanjing University, China Time/Place: 11:30 - 12:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: In this talk, we consider the large-scale convex non-separable minimization models with quadratic coupling terms. We firstly extend the 2-block ADMM to the linearly constrained convex optimization and prove that the sequence generated by the ADMM converges in point-wise manner to a primal-dual solution pair. Moreover, we apply randomly permuted ADMM (RPADMM) to nonseparable multi-block convex optimization, and prove its expected convergence for a class of nonseparable quadratic programming problems. When the linear constraint vanishes, the 2-block ADMM and RPADMM reduce to the 2-block cyclic BCD method and randomly permuted BCD (RPBCD). Our study provides the first iterate convergence result for 2-block cyclic BCD without assuming the boundedness of the iterates. We also theoretically establish the expected iterate convergence result concerning multi-block RPBCD for convex quadratic optimization. In addition, we demonstrate that RPBCD may have a worse convergence rate than cyclic BCD for 2-block convex quadratic minimization problems. Although the results on RPADMM and RPBCD are restricted to quadratic minimisation models, they provide some interesting insights: 1) random permutation makes ADMM and BCD more robust for multi-block convex minimization problems; 2) cyclic BCD may outperform RPBCD for nice problems, and therefore RPBCD should be applied with caution when solving general convex optimization problems. - Monday, 25th April, 2016
Title: Some reconstruction problems in electrical impedance tomography Speaker: Dr. JIN Bangti, Department of Computer Science, University of College London, UK Time/Place: 14:00 - 15:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Electrical impedance tomography is a noninvasive imaging modality using electrical measurements on the boundary. The related inverse problems are highly ill-posed, and susceptible to modeling errors. In this talk I will discuss some issues in the image reconstruction step at the continuous and discrete level.The talk will be illustrated with numerical results. - Monday, 25th April, 2016
Title: Numerical Reconstruction of a Defect in an Open Waveguide with Multiple Frequency Data Speaker: Prof. ZHU Jianxin, School of Mathematical Sciences, Zhejiang University, China Time/Place: 15:00 - 16:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: The inverse scattering problem arises naturally in diverse applications such as radar, sonar, geophysical exploration, medical imaging and nondestructive testing. In this talk, we consider the scattering problem for the two-dimensional Helmholtz equation in a slab with a defect in the core. To determine the defect, a new numerical method for the inverse medium scattering problem, is developed. At every fixed frequency, by using numerical searching and Newton's iteration, a series of high precision eigenvalues are got. For the large linear system resulting from multiple frequencies, we deal with the equipment of it appropriately, decreasing its size. Finally, we solve the inverse medium problem by singular value decomposition and the regularization iteration method. Numerical simulations show that the proposed method is effective. - Tuesday, 26th April, 2016
Title: Quantitative estimates for the second order elliptic Speaker: Prof. WANG Jenn-Nan, Institute of Applied Mathematical Sciences, National Taiwan University, Taiwan Time/Place: 16:00 - 17:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: In the late 60's, E.M. Landis conjectured that if $Delta u+Vu=0$ in $R^n$ with $|V|_{L^{infty}(R^n)}le 1$ and $|u|_{L^{infty}(R^n)}le C_0$ satisfying $|u(x)|le Cexp(- C|x|^{1+})$, then $uequiv 0$. Landis' conjecture was disproved by Meshkov who constructed such $V$ and nontrivial $u$ satisfying $|u(x)|le Cexp(-C|x|^{frac 43})$. He also showed that if $|u(x)|le Cexp(-C|x|^{frac 43+})$, then $uequiv 0$. A quantitative form of Meshkov's result was derived by Bourgain and Kenig in their resolution of Anderson localization for the Bernoulli model in higher dimensions. It should be noted that both $V$ and $u$ constructed by Meshkov are emph{complexvalued} functions. It remains an open question whether Landis' conjecture is true for real-valued $V$ and $u$. In this talk I would like to discuss recent joint works with C. Kenig, L. Silvestre, B. Davey on Landis' conjecture and related problems in two dimensions. - Thursday, 28th April, 2016
Title: A New Test for Functional One-Way ANOVA with Application to Ischemic Heart Screening 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: Motivated by an ischemic heart screening problem, we study a new global test for one-way ANOVA in functional data analysis, an increasingly important area in the new era of big data. The test statistic is taken as the maximum of the pointwise F-test statistic over the interval the functional responses are observed. Nonparametric bootstrap, which is applicable in more general situations and easier to implement than parametric bootstrap, is employed to approximate the null distribution and to obtain an approximate critical value. The asymptotic distribution of the test statistic is derived, and the asymptotic power of the proposed test is studied. In particular, under mild conditions, asymptotically our test has the correct level and is root-n consistent in detecting local alternatives. Simulation studies show that, in terms of both level accuracy and power, the proposed test outperforms several existing competitors when the within-subject correlation is high or moderate, and it is comparable with the competitors otherwise. Application to an ischemic heart dataset suggests that resting electrocardiogram signals could be used as an effective tool in clinical ischemic heart screening, without the need of further stress tests as required in the current standard procedure.