Colloquium/Seminar

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Event(s) on March 2008


  • Tuesday, 4th March, 2008

    Title: New Theories on Stochastic Dominance and Mean-Variance criteria with Applications in Economics and Finance
    Speaker: Prof. Alan Wing Keung Wong, Department of Economics, Hong Kong Baptist University, Hong Kong
    Time/Place: 11:30  -  12:30
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    Abstract: We first summarize our contributions in stochastic dominance (SD) theories including SD for risk averters and risk seekers, SD for investors with S-shaped and reverse S-shaped utility functions, convex SD, SD for profit and risk, SD for location-scale family, new SD statistics, the relationships between SD and Value at Risk, and a study of relationships between SD and majorization theory. We then summarize our contributions in mean-variance analysis including making Markowitz's portfolio principle become practically useful, applying Markowitz's portfolio principle to self-financing portfolios, developing the multiple Sharpe Ratios and the mean-variance test, and study the relationships between MV and SD. Subsequently, we will discuss some applications of our SD and MV theories in the areas of Economics and Finance, including international trade, risk analysis, fund and portfolio management, momentum strategies, calendar anomalies, and internet bubbles.


  • Tuesday, 11th March, 2008

    Title: Efficient Parallel Spectral-Element Methods and Applications
    Speaker: Dr. Yuen Yick Kwan, Department of Mathematics, Purdue University, USA
    Time/Place: 11:30  -  12:30
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    Abstract: We will describe an efficient elliptic solver based on the spectral element discretization. The direct solver is based on a matrix decomposition approach which reduces multi-dimensional separable problems to a sequence of one-dimensional problems that can be efficiently handled by a static condensation process. The solver is spectrally accurate and can be efficiently parallelized, and it can serve as an essential building block for large scale high-performance solvers in computational fluid dynamics. Applications of the solver to physical problems will also be discussed.


  • Thursday, 13th March, 2008

    Title: Kernel-Based Meshless Methods for Solving PDEs
    Speaker: Prof. Robert Schaback, Georg-August-Universität Göttingen, Germany
    Time/Place: 14:30  -  15:30
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    Abstract: Kernels arise in many areas of Mathematics, and they turned out to be practically useful for a large number of applications ranging from Machine Learning to PDE solving. The talk will provide the mathematical background of kernel applications, i.e.: the Approximation Theory of spaces spanned by ``translates'' of kernels. After presentation of the basic facts concerning positive definite kernels and their use for handling multivariate functions, the talk will focus on translates of kernels as trial or test functions for solving Partial Differential Equations. A mathematical framework is provided that allows convergence proofs of methods like Kansa's unsymmetric collocation or Atluri's Meshless Petrov--Galerkin (MLPG) technique. The framework is based on certain a-priori "sampling" and "stability" inequalities which are of general interest outside of kernel techniques. Additional examples will show how specially designed new kernels lead to new numerical methods.


  • Tuesday, 18th March, 2008

    Title: Some Recent Developments on the Extragradient Method for Variational Inequalities
    Speaker: Dr. Xiaoming Yuan, Pacific Institute for the Mathematical Sciences, Canada
    Time/Place: 11:30  -  12:30
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    Abstract: This talk presents some recent developments on the classical extragradient method for solving variational inequalities (VI). Theoretically, we will discuss the possibility to replace the Lipschitz continuity of the underlying mapping that is required by all extragradient type methods with the regular continuity. Algorithmically, we will present an efficient strategy to identify the optimal step sizes along the extragradient directions. Thus, the efficiency of extragradient type methods is improved. For applications, we will reformulate the well-known problem of minimizing the sum of p-norm into a VI, and then an extragradient method integrating with the Gauss-Seidel characteristics will be introduced. Finally, we will extend the extragradient methods to solving general VIs.


  • Thursday, 20th March, 2008

    Title: Challenges and Opportunities in Acute Ischemic Stroke Management
    Speaker: Dr. Kelvin Wong, Translational Multimodality Optical Imaging Laboratory, The Methodist Hospital Research Institute, USA
    Time/Place: 11:30  -  12:30
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    Abstract: In acute ischemic management, the standard of care protocol requires the patient to receive tissue plasminogen activator (tPA) within the 3-hour window after the onset of stroke. Radiological imaging such as MRI and CT play a crucial role in acute diagnostic settings to evaluate the potential benefit of reducing infarction volume and improving neurological function of patients. In this talk, we will introduce a new concept in the treatment paradigm by combining the benefit of imaging and proteomic to evaluate the risk and benefit in tPA therapy. We will highlight some of the technical advancements in stroke diagnosis in CT and MRI which may hold promise in acute and sub-acute settings.