Event(s) on May 2023

• Wednesday, 10th May, 2023

  Title:	Analysis of multigrid methods for multilevel block Toeplitz matrices
  Speaker:	Prof. Dr. Matthias Bolten, School of Mathematics and Natural Sciences, University of Wuppertal, Germany
  Time/Place:	11:00  -  12:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	Multilevel block Toeplitz matrices arise in many applications, for instance when higher-order discretizations are used for scalar PDEs or systems of PDEs are to be solved. For large-scale problems multigrid methods are often the method of choice, as they provide an efficient way of solving the associated linear systems. The analysis of multigrid methods for structured matrices, i.e., Toeplitz matrices or circulant matrices, and traditional multilevel theory is an established technqiue. For scalar problems, including those arising from the discretization of PDEs, it has been studied intensively. Recently, we started transfering these results to the systems case that results in block-Toeplitz matrices or block-circulant matrices [1]. Besides studying higher-order discretizations of scalar PDEs, certain systems of PDEs also fit in this framework. Systems of PDEs that lead to saddle point structure, like the Stokes equations, need another approach. Based on a result by Notay [3] we were able to establish convergence for these matrices, as well [2]. In the talk the analysis technique, the derived sufficient conditions for optimal convergence and numerical results will be presented. [1] M. Bolten, M. Donatelli, P. Ferrari, and I. Furci. A symbol based analysis for multigrid methods for block-circulant and block-Toeplitz systems. SIAM J. Matrix Anal. Appl., 43(1):405–438, 2022. [2] M. Bolten, M. Donatelli, I. Ferrari, and I. Furci. Symbol based convergence analysis in multigrid methods for saddle point problems. Linear Algebra Appl., 671:67–108, 2023. [3] Y. Notay. A new algebraic multigrid approach for Stokes problems. Numer. Math., 132(1):51–84, 2016.

  
  

• Monday, 15th May, 2023

  Title:	Experimental study of cooperative behavior based on evolutionary game and related issues
  Speaker:	Professor Lei Shi, School of Statistics and Mathematics, Yunnan University of Finance and Economics, China
  Time/Place:	15:00  -  16:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	The emergence, maintenance, and evolution of cooperative behavior in selfish groups has long been an important research question in the fields of natural and social sciences. In 2005, Science magazine listed 125 important unsolved scientific questions, with the 16th being "How does human cooperative behavior develop?". This report presents a series of research findings based on social dilemma experiments (using Chinese university students as subjects) carried out through statistical modeling and data analysis, inspiring statisticians to conduct interdisciplinary research with other fields. The topic include: 1. In public goods game experiments under heterogeneous network structures, it was found that autonomous strategy selection contributes to the formation of cooperation. 2. A series of repeated public goods games (PGG) experiments with and without exit options were designed and conducted using experimental economics methods, revealing that free exit can improve cooperation rates and investment environments in a moderate or competitive equal opportunity environment (EOE), thereby alleviating social dilemmas. 3. Cooperation behavior research based on meta-models. This series of studies represents an interdisciplinary research effort combining statistics, evolutionary biology, evolutionary game theory, experimental economics, sociology, behavioral science, and statistical physics.

  
  

• Monday, 15th May, 2023

  Title:	A penalized likelihood estimation for switching regressions with skew-normal errors
  Speaker:	Dr. Libin Jin, School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, China
  Time/Place:	16:00  -  17:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	This paper establishes identifiability results for the switching regression models with skew normal errors under fixed and random designs. In addition, we propose a novel penalized maximum likelihood estimation method in the model and show the strong consistency of the proposed estimator. An EM-type algorithm for deriving the penalized estimator is presented. The finite sample properties of the proposed methodology are studied through simulations and a real data example is used for illustration.

  
  

• Tuesday, 23rd May, 2023

  Title:	Causal Analysis of Multiple Time Series ---- Theory and Application
  Speaker:	Dr. Feng Yao, Faculty of Economics, Kagawa University, Japan
  Time/Place:	16:00  -  17:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	Abstract: We show an approach to investigating a variety of causal relationships between nonstationary multiple time series in terms of the causal measure of one-way effect. The proposed causal measure is discussed in time domain and frequency domain. Based on the error correction model for cointegrated multiple time series, the proposed Wald test of one-way effect causal measure includes testing Granger's non-causality as a special case of its applications. The Wald test of one-way effect causal measure is successfully applied to the analysis of macroeconomics and reality, international trade, global spotlighted stock market composite indices, and also crude oil futures market.

  
  

• Tuesday, 30th May, 2023

  Title:	Kernel-based meshless conservative methods
  Speaker:	Dr. Zhengjie Sun, School of Mathematics and Statistics, Nanjing University of Science and Technology, China
  Time/Place:	15:00  -  16:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	In this talk, I will introduce several meshless conservative methods for solving Hamiltonian partial differential equations. We discretize the equation in space using kernel-based radial basis functions approximation method including interpolation, quasi-interpolation and meshless Galerkin method. The semi-discrete system is then discretized with an appropriate time integrator. We prove that the fully-discrete solution preserves the discretized energy exactly. Finally, some numerical examples are presented to demonstrate the accuracy and the energy conservation.

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