Event(s) on April 2005

• Wednesday, 6th April, 2005

  Title:	Different Approach for VaR Evaluation
  Speaker:	Ms Zhenghong Wei, Department of Mathematics, Hong Kong Baptist University, Hong Kong
  Time/Place:	14:30  -  15:30 FSC1217
  Abstract:	Value at Risk (VaR) is one of the most popular tools used to estimate exposure to market risks, and it measures the worst expected loss at a given confidence level. In this report, we explain the concept of VaR, and then describe in detail some methods of the computation of VaR. including (a)GARCH model, (b)historical simulation and(c) extreme value theory, etc. particularly for (a) we studied the GARCH effect presented in IBM stock data and Chinese stock market. As for (b) and (c) we studied IBM stock data in detailed comparison. More over the theoretical and Monte Carlo of the most popular EVT approach with Generalized Pareto Distribution scheme is also performed.

  
  

• Tuesday, 12th April, 2005

  Title:	Adaptive Moving Meshes for Scale Invariant Partial Differential Equations
  Speaker:	Prof. Mike Baines, Department of Mathematics, University of Reading, England
  Time/Place:	11:30  -  12:30 FSC1217
  Abstract:	Two key features of numerical methods for partial differential equations are their capability of reproducing the properties of the equations and their ability to resolve distinctive features of the solution. The GCL method of Cao, Huang and Russell is a velocity-based moving mesh method which uses a monitor function to determine the movement. For the simplest monitor it generates a semi-discrete finite element scheme which is locally conservative and preserves scale invariance of the underlying PDE. For more general monitors, however, conservation is only approximate and the scale invariance property does not hold. We show how scale invariance can be restored while still following distinctive features by using a scaled monitor function, and also propose a time-stepping scheme with a truncation error which is scale-invariant. Two dimensional results are shown for second and fourth order nonlinear moving boundary problems and for a hyperbolic system.

  
  

• Tuesday, 19th April, 2005

  Title:	The Artificial Boundary Method - Numerical Solutions of Partial Differential Equations on Unbounded Domains
  Speaker:	Prof. Houde Han, Department of Mathematics Sciences, Tsinghua University, China
  Time/Place:	11:30  -  14:30 FSC1217
  Abstract:	The aim of this talk is to introduce the artificial boundary method. Many problems arising in science and engineering lead to solving the boundary value problem of partial differential equations on unbounded domains, such as the stress analysis of a dam with infinite foundation, fluid flow around the obstacle and fluid flow in an infinite channel. The great new difficulty in finding the numerical solution of these problems is the unboundedness of the physical domain. The finite element method and finite difference method can not be used for these problems in a straight forward manner. Therefore how to solve partial differential equations on unbounded domain numerically has attracted the attention of many engineers and mathematicians. The artificial boundary method is established as a powerful and effective technique to obtain the numerical solutions of partial differential equations on unbounded domains. In the recent years, more and more mathematicians and engineers have attended this subject and the artificial boundary method have attained successful applications in the many fields in science and engineering.

  
  

• Tuesday, 19th April, 2005

  Title:	Non-negative Matrix Factorization for Face Recognition
  Speaker:	Mr Yun Xue, Department of Mathematics, Hong Kong Baptist University, Hong Kong
  Time/Place:	14:30  -  15:30 FSC1217
  Abstract:	In this paper we demonstrate an algorithm called non-negative matrix factorization that is able to learn parts of faces. This is in contrast to other methods, such as principal components analysis, that learn holistic, not parts-based, representations. Non-negative matrix factorization is distinguished from the other methods by its use of non-negativity constraints. These constraints lead to a parts-based representation because they allow only additive, not subtractive, combinations. Using a well-known face database, the Yale Face Database, the nonnegative matrix factorization (NMF) technique is applied in the context of face classification and a direct comparison with Principal Component Analysis (PCA) is also analyzed. Two leading techniques in face recognition are also considered in this study noticing that NMF is able to improve the result. In the experiment, different distance metrics are evaluated in the feature space defined by NMF in order to determine the best one for this specific problem. Experiments demonstrate that the Chi square distance is the most suitable metric for this problem. And we also consider the problem of feature selection for the NMF algorithm and build a criterion to find the most significant component in feature vector. Some relevant techniques which maybe can improve result when integrated with NMF are also introduced.

  
  

• Tuesday, 26th April, 2005

  Title:	Multilevel Methods Based on Subspace Corrections
  Speaker:	Prof. Xu Jinchao, Department of Mathematics, Penn State University and HKUST, USA
  Time/Place:	11:30  -  12:30 FSC1217
  Abstract:	This talk is to give an introduction to multilevel iterative methods through a general framework of space decomposition and subspace corrections. The relationship between the method of alternating projections and the method of subspace corrections will be discussed. A sharp convergence rate identity will be presented for these methods. Some very recent results for singular and nearly singular systems will also be given.