Event(s) on April 2009

• Wednesday, 1st April, 2009

  Title:	CMIV Lecture: Qualitaive Features of the Minimizers of Energies and Implications on Modelling
  Speaker:	Prof. Mila Nikolova, Centre de Mathematiques et de Leurs Applications (CMLA), ENS de Cachan, France
  Time/Place:	16:30  -  18:00 DLB614, David C. Lam Building, Shaw Campus, Hong Kong Baptist University
  Abstract:	We address all applications that are solved by minimizing an energy function combining a data-fidelity and a regularization term. Energy functions are classically defined either from a PDE standpoint or in a Bayesian estimation framework. Our approach is to characterize the essential features exhibited by the minimizers of such energies as a function of the shape of the energy. For instance, the recovery of homogeneous regions, textures and edges, the processing of outliers or spikes, the obtaining of sparsity, are shown to be determined by some attributes of the energy relevant to its (non)smoothness or its (non)convexity. Our point of view provides a framework to address rigorously the problem of the choice of energies for image reconstruction and invokes a new understanding of modelling. (The lecture is a plenary talk in SIAM Conference on Imaging Science (2008) given by Prof. Mila Nikolova)

  
  

• Friday, 17th April, 2009

  Title:	CMIV Lecture: On the Geometry of Moment Problems
  Speaker:	Prof. Patrick L. Combettes, Université Pierre et Marie Curie - Paris 6, France
  Time/Place:	16:30  -  17:30 DLB614, David C. Lam Building, Shaw Campus, Hong Kong Baptist University
  Abstract:	An ubiquitous problem in applied mathematics is to find a function in a Hilbert space with prescribed best approximations from a finite number of closed vector subspaces. In this paper we study the question of the existence of solutions to such problems. A finite family of closed vector subspaces of a Hilbert space is said to have the Inverse Best Approximation Property (IBAP) if there exists a point that admits any selection of points from these subspaces as best approximations. We provide various characterizations of IBAP in terms of the geometry of the subspaces. Connections between IBAP and the linear convergence rate of the periodic projection algorithm for solving the underlying affine feasibility problems are also established. The results are applied to problems in signal processing, harmonic analysis, integral equations, and wavelet frames.

  
  

• Wednesday, 22nd April, 2009

  Title:	New Theories on Stochastic Dominance and Mean-Variance criteria with Applications in Economics and Finance
  Speaker:	Prof. Wing-Keung Wong , Hong Kong Baptist University, Hong Kong
  Time/Place:	15:00  -  17:00 DLB614, David C. Lam Building, Shaw Campus, Hong Kong Baptist University
  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, a study of relationships between SD and majorization theory, and a study of the diversification preferences for Markowitz investors and prospect investors. 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, etc.

  
  

• Thursday, 23rd April, 2009

  Title:	ICM Distinguished Computational Mathematics Lecture: The Best of Both Worlds: Hybrid Approximation on the Sphere
  Speaker:	Prof. Ian H. Sloan, School of Mathematics, The University of New South Wales, Australia
  Time/Place:	11:00  -  12:00 (Preceded by Reception at 10:30am) DLB802, David C. Lam Building, Shaw Campus, Hong Kong Baptist University
  Abstract:	Many researchers have discussed approximation by radial basis functions on a sphere, using scattered data. Usually there is no polynomial component in such approximations if, as here, the kernel that generates the radial functions is (strictly) positive definite. On the other hand, the utility of polynomials for approximating slowly varying components is well known - an extreme case is the NASA model of the earth's gravitational potential, which represents the potential by a purely polynomial approximation of high degree. In this joint work with Alvise Sommariva we consider a hybrid approximation, in which there is a radial basis functions component to handle the rapidly varying and localised aspects, but also a polynomial component to handle the more slowly varying and global parts. The convergence theory (including a doubled rate of convergence for sufficiently smooth functions) make use of the "native space" associated with the positive definite kernel (with no polynomial involvement in the definition). A numerical experiment for a simple model with a geophysical flavour establishes the potential value of the hybrid approach.

  
  

• Tuesday, 28th April, 2009

  Title:	Model localization in video search and biometric problems
  Speaker:	Dr. Zhu LI, Department of Computing, Hong Kong Polytechnic University, HKSAR, China
  Time/Place:	10:30  -  11:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	Recent advances in computing and communication technology have unleashed a new wave of innovation and application in multimedia distribution, consumption, and multimedia based interaction. In this talk I will give an overview of my research in multimedia computing and communication at Motorola Labs and then focused on the problem of large subject set visual pattern recognition. Large visual pattern set appearance manifolds have complex non-linear structures under image formation variations, we developed a piece-wise local linear modeling approach to capture this complex non-linear structure and avoid model accuracy and computational complexity problems in existing global linear and non-linear solutions. For the video indexing/search problem, we have a hierarchical tree structured piece-wise linear model while for the pose/face recognition problem, the structure is query-driven and totally adaptive. Simulation results demonstrated the effectiveness of this solution, and outstanding speed/accuracy performance in video search case in particular. The framework also has an intuitive graph embedding interpretation and motivates several interesting new problems.

  
  

• Thursday, 30th April, 2009

  Title:	ROCK and S-ROCK: explicit methods for multiscale ordinary or stochastic differential equations
  Speaker:	Professor Assyr Abdulle, EPFL, Swiss Federal Institute of Technology, Switzerland
  Time/Place:	14:30  -  15:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	The common wisdom is to use implicit solvers for stiff or multiscale time-dependent problems. In this talk I will discuss a class of explicit methods (the ROCK methods) which share the simplicity of implementation of traditional explicit solvers but enjoy much better stability properties. New developments of the ROCK methods for stochastic problems will be discussed. Applications to ODEs, SDEs, time dependent PDEs and SPDE will be presented.