Event(s) on January 2019

• Tuesday, 8th January, 2019

  Title:	Exploiting Multiprecision Arithmetic
  Speaker:	Prof. Nicholas J. Higham, Department of Mathematics, The University of Manchester, United Kingdom
  Time/Place:	10:30  -  11:30 (Preceded by Reception at 10:00am) LT1, Cha Chi-ming Science Tower, HSH Campus, Hong Kong Baptist University
  Abstract:	There is a growing availability of multiprecision arithmetic: floating point arithmetic in multiple, possibly arbitrary, precisions. Demand in applications includes for both low precision (deep learning and climate modelling) and high precision (long-term simulations and solving very ill conditioned problems). We discuss - Half-precision arithmetic (fp16 and bfloat16): its characteristics, availability, attractions, pitfalls, and rounding error analysis implications. - Quadruple precision arithmetic (fp128): the need for it in applications, its cost, and how to exploit it. As an example of the use of multiple precisions we discuss iterative refinement for solving linear systems. We explain the benefits of combining three different precisions of arithmetic (say, half, single, and double) and show how a new form of preconditioned iterative refinement can be used to solve very ill conditioned sparse linear systems to high accuracy.

  
  

• Monday, 21st January, 2019

  Title:	Quantitative unique continuation for the fractional Schrodinger operator
  Speaker:	Prof Jenn-Nan WANG, Institute of Applied Mathematical Sciences, National Taiwan University, Taiwan
  Time/Place:	11:00  -  12:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	"In this talk, I would like to discuss some quantitative uniqueness estimates related to the strong unique continuation property and the unique continuation at in nity for the fractional Schrodinger operator. These kinds of estimates are useful in understanding the local properties of the solution. For the classical Schrodinger operator, these estimates have been extensively studied and successfully applied to other problems. Recently, the study of the local properties of solutions to the fractional equation became possible thanks to the Ca arelli-Silvestre extension theorem. For the fractional Schrodinger operator, we are especially interested in the dependence of the estimates on the size of the potential."

  
  

• Tuesday, 22nd January, 2019

  Title:	Mathematical analysis of bubbly metamaterials
  Speaker:	Prof. Hyundae LEE, Department of Mathematics, Inha University, Korea
  Time/Place:	10:00  -  11:00 FSC703, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	The study of metamaterials has drawn increasing interest nowadays because of their many important applications in fields such as super-resolution, cloaking, and novel optic and phononic devices. The bubbly media, because of the simplicity of the acoustic properties of the air bubbles, becomes a natural model for such study. It is known that a single bubble in the water possesses a quasi-static resonance which is called the Minneart resonance. Our analysis shows that near and below the Minneart resonant frequency, the effective media has high refractive index, which explains the super-focusing phenomenon observed in the experiment while near and above the Minneart resonant frequency, the effective media is dissipative. We also present some works on bubbly meta-surface which is a homogenization theory for a thin layer of periodically arranged bubbles mounted on a perfect reflection surface.

  
  

• Tuesday, 22nd January, 2019

  Title:	Time-domain metamaterial models and finite element simulations
  Speaker:	Prof Wei YANG, School of Mathematics and Computational Science, Xiangtan University, China
  Time/Place:	11:00  -  12:00 FSC703, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	In this talk, we first introduce the development history of mematerials and present some time-domain metamaterial models to simulate negative refraction phenomenon, zeros index metamaterials and optical black holes. Then, we focus on the time-domain cloak models. The explicit expressions of the cloak parameters without the contour curve expressions of the objects and 2d arbitrary shape cloak model are established. A new time-domain finite element scheme is developed to solve the governing equations, and it's stability is also provided. Numerical results are presented to confirm the theoretical analysis and the effectiveness of our cloak model and FETD method.

  
  

• Tuesday, 22nd January, 2019

  Title:	An interior point path following algorithm of a parameterized central path for linearly constrained convex programming
  Speaker:	Mr Liangshao HOU, MATH, HKBU, HKSAR
  Time/Place:	15:00  -  16:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	An interior point path-following algorithm for linearly constrained convex programming is proposed. The algorithm applies continuation method to follow a parameterized central path. The convergence and polynomial complexity are proved under the assumption that Hessian matrix of objective function is locally Lipschitz continuous. In addition, the initialization of the algorithm is discussed.

  
  

• Wednesday, 23rd January, 2019

  Title:	Regularized Softmax for Semantic Image Segmentation
  Speaker:	Mr Fan JIA, MATH, HKBU, HKSAR
  Time/Place:	10:00  -  11:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	Convolutional neural networks (CNNs) have achieved prominent performance in a series of image processing problems. Leading other traditional methods by a large margin, CNNs become the first choice for dense classification problems such as semantic segmentation. Despite higher accuracy and mIoU as CNNs achieved, no one has proposed an effective method to regularize the segmentation result. Thus the edge of segmentation result is often coarse, sometimes even serrated. Isolated and scattered small regions often appear in all kinds of segmentation CNNs. We give the soft-max activation function a new statistical interpretation with linear mixture model. In our method, the spatial regularization such as total variation (TV) can be easily integrated into CNN network and it can make the segmentation results to be robust to noise. We test our proposed method on Unet and Segnet. The results show that the regularized networks could achieve prominent regularization effect and better segmentation result.

  
  

• Wednesday, 23rd January, 2019

  Title:	Meta-analysis methods, publication bias and beyond
  Speaker:	Dr Yong CHEN, Department of Biostatistics and Epidemiology, University of Pennsylvania, United States
  Time/Place:	15:00  -  16:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	In this talk, I will introduce the state-of-art methods for multivariate meta-analysis of continuous and/or binary outcomes in randomized controlled trials, meta-analysis of diagnostic tests with/without gold standard, as well as methods to identify and correct for publication biases or small study effects. I will discuss the current challenges in meta-analysis, and describe some of our efforts in addressing these challenges. Motivating examples will be given during the talk.

  
  

• Friday, 25th January, 2019

  Title:	Semiparametric Efficient Estimation for Semiparametric Exponential Family via Profile Likelihood
  Speaker:	Prof Lu LIN, Zhongtai Securities Institute for Financial Studies, Shandong University, China
  Time/Place:	14:00  -  15:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	Semiparametric exponential family is an extension of the parametric exponential family to the case with a nonparametric base measure function. Such a distribution family has potential application in the cases of incomplete data, selection bias, heterogeneity and so on. However, the methodology for achieving the semiparametric efficiency has not been proposed in the existing literature. In this paper, we propose a profile likelihood to efficiently estimate both parameter and nonparametric function. Due to the use of the least favorable curve in the procedure of profile likelihood, the semiparametric efficiency is achieved successfully and the estimation bias is reduced significantly. Moreover, by making the most of the structure information of the semiparametric exponential family, the estimator of the least favorable curve has an explicit expression. It ensures that the newly proposed profile likelihood can be implemented and is computationally simple. Simulation studies can illustrate that our proposal is much better than the existing methodology for most cases under study, and is robust to the different model conditions.

  
  

• Friday, 25th January, 2019

  Title:	An adaptive estimation for covariate-adjusted nonparametric regression model
  Speaker:	Dr Feng LI, School of Mathematics and Statistics, Zhengzhou University, China
  Time/Place:	15:00  -  16:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	For covariate-adjusted nonparametric regression model, an adaptive estimation method is proposed for estimating the nonparametric regression function. Compared with the procedures introduced in the existing literatures, the new method needs less strict conditions and is adaptive to covariate-adjusted nonparametric regression with asymmetric variables. More specifically, when the distributions of the variables are asymmetric, the new procedures can gain more efficient estimators and recover data more accurately by elaborately choosing proper weights; and for the symmetric case, the new estimators can obtain the same asymptotic properties as those obtained by the existing method via designing equal bandwidths and weights. Simulation studies are carried out to examine the performance of the new method in finite sample situations and the Boston Housing data is analyzed as an illustration.

  
  

• Tuesday, 29th January, 2019

  Title:	Novel Reformulations and Efficient Algorithms for the Generalized Trust Region Subproblem
  Speaker:	Dr. Rujun JIANG, School of Data Science, Fudan University, China
  Time/Place:	10:00  -  11:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	We present a new solution framework to solve the generalized trust region subproblem (GTRS) of minimizing a quadratic objective over a quadratic constraint. More specifically, we derive a convex quadratic reformulation (CQR) via minimizing a linear objective over two convex quadratic constraints for the GTRS. We show that an optimal solution of the GTRS can be recovered from an optimal solution of the CQR. We further prove that this CQR is equivalent to minimizing the maximum of the two convex quadratic functions derived from the CQR for the case under our investigation. Although the latter minimax problem is nonsmooth, it is well-structured and convex. We thus develop two steepest descent algorithms corresponding to two different line search rules. We prove for both algorithms their global sublinear convergence rates. We also obtain a local linear convergence rate of the first algorithm by estimating the Kurdyka-{L}ojasiewicz exponent at any optimal solution under mild conditions. We finally demonstrate the efficiency of our algorithms in our numerical experiments.

All years