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Event(s) on November 2006
- Tuesday, 14th November, 2006
Title: Optimisation-based Multilevel Methods for Image Restoration Speaker: Prof. Ke Chen, Department of Mathematical Sciences, University of Liverpool, UK Time/Place: 11:30 - 12:30
Abstract: Development of fast multilevel methods is of fundamental importance in variational image processing and Computer vision. Digital images are often of extremely large scale and the usual solution methods (e.g. the gradient descent approach) can be very slow to converge. Standard multilevel methods (either the algorithms or convergence theories) are not immediately applicable to many variational models that are either associated with either non-smooth and non-differentiable Functionals or partial differential equations with discontinuous and highly non-smooth coefficients. In this talk, we consider the basic ROF(Rudin_Osher_Fatemi 1992) denoising model in both the primal variable and its dual variable. Firstly for the primal formulation, previous multilevel work involved regularizing the non-smooth terms in the models in order to apply the standard nonlinear algorithms. Our work aims to solve the minimisation problem without regularizing the non-smooth term. Using piecewise constant corrections from local coordinate descent optimisation in A multilevel setting, we can ensure the locally stuck solutions to converge to the global minimizer. The convergence proof involves a detailed study of the otal variation norm and its hemivariateness. Finally we shall give a brief introduction to recent work on solving the dual formulation by Chambolle (2004) and on restoration models for salt-and-pepper type images. This talk summarises various joint works with T F Chan (UCLA), J L Carter (UCB), J Savage (Liverpool), R Chan (CUHK) and X C Tai (Bergen).
- Tuesday, 14th November, 2006
Title: On Preconditioned Iterative Methods for Burgers Equations Speaker: Ms. Yumei Huang, Department of Mathematics, Hong Kong Baptist University, HKSAR, China Time/Place: 14:00 - 15:00
Abstract: We study the Newton method and a fixed-point method for solving the system of nonlinear equations arising from the Sinc-Galerkin discretization of the Burgers equations are studied. In each step of the Newton method or the fixed-point method, a structured sub-system of linear equations is obtained and needs to be solved numerically. In this paper, preconditioning techniques are applied to solve such linear sub-systems. The bounds for eigenvalues of the preconditioned matrices are derived and numerical examples are given to illustrate the effectiveness of the proposed methods. We also find that a combination of the Newton/fixed-point iteration with the preconditioned GMRES method is quite efficient for the Sinc-Galerkin discretization of the Burgers equations. Future work is also proposed in this report.
- Tuesday, 21st November, 2006
Title: Dimension Reduction Method for Multivariate Response Data Speaker: Mr. Songqiao Wen, Department of Mathematics, Hong Kong Baptist University, HKSAR, China Time/Place: 14:00 - 15:00
Abstract: As the focus of dimension reduction is on reducing the dimensionality of predictors, most of the existing work assume that the response variable is univariate. In this paper, we propose a general principle that can convert any existing dimension reduction method for univariate response into an estimator that can be applied to dimension reduction problems with multivariate response data. We also discuss the root n consistency and the asymptotic distribution of our new estimator. The simulation studies show that our method perform well.
- Tuesday, 28th November, 2006
Title: Detection of Spaced Motifs Speaker: Dr. Siu-Ming Yiu, Department of Computer Science, The University of Hong Kong, HKSAR, China Time/Place: 11:00 - 12:00
Abstract: In this talk, we will start with some background information about motifs, binding sites, and transcription factors. Then, we will introduce the motif finding problem and discuss briefly why this problem is difficult. In particular, we will talk about spaced motifs and why existing approaches may not be appropriate for locating this type of motifs. Finally, we will present an approach we proposed for identifying spaced motifs, followed by some experimental results. This solution is a joint work with Dr Ken Sung and Dr Rajaraman Kanagasabai of the National University of Singapore.
- Wednesday, 29th November, 2006
Title: A Truck Driver's Question, Sharing a Glass of Water, Cantor sets, and an Interesting Probability Distribution Speaker: Prof. Kevin Iga, Department of Mathematics, Pepperdine University, USA Time/Place: 11:30 - 12:30
Abstract: A professional mover asked my colleague a math question. The initial math question is a problem relating to moving water between two glasses with a straw, which can be solved using fairly simple techniques. But variations on this question lead to some surprising connections with some beautiful mathematics, including Cantor sets, doing infinite series backwards, and a very mysterious probability distribution that seems to have stumped Erdös.