﻿ Department of Mathematics, Hong Kong Baptist University

Colloquium/Seminar

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Event(s) on November 2008

• Tuesday, 4th November, 2008

 Title: A Tailored finite point method for a singular perturbation problem on an unbounded domain Speaker: Prof. HAN Houde, Department of Mathematics, Tsinghua University, China Time/Place: 11:30  -  12:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University Abstract: In this talk, we propose a tailored-finite-point method for a kind of singular perturbation problems in unbounded domains. First, we use the artificial boundary method to reduce the original problem to a problem on bounded computational domain. Then we propose a new approach to construct a discrete scheme for the reduced problem, where our finite point method has been tailored to some particular properties of solutions of the original problem. From the numerical results, we find that our new methods can achieve very high accuracy with very coarse mesh even for very small parameter \$e\$. In the contrast, the traditional finite element method does not get satisfactory numerical results with the same mesh.

• Wednesday, 5th November, 2008

 Title: Laplacian eigenvalues of graphs Speaker: Mr. Li Jianxi, Department of Mathematics, Hong Kong Baptist University, HKSAR, China Time/Place: 10:30  -  11:30 FSC1217 Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University Abstract: Let G = (V; E) be a simple connected graph. The matrix L(G) = D(G) - A(G) is called the Laplacian matrix of G, where D(G) is the diagonal matrix of vertex degrees and A(G) is the adjacency matrix of G, respectively. The eigenvalues of L(G) are called the Laplacian eigenvalues of G, which have numerous applications in various fields. In this talk, we will describe the background and state some problems as well as previous results on the Laplacian spectral radius of graphs. Among these problems, we firstly improve Shi's upper bounds for the Laplacian spectral radius of irregular graphs, and obtain some new upper bounds for the Laplacian spectral radius of graphs (in particular, for bipartite graphs, to some extent, we have obtained better upper bounds). Secondly, we determine graphs with maximum Laplacian spectral radius in some classes of graphs. Lastly, we order some trees according to their Lapla-cian spectral radii. Finally, we provide some directions in further investigations of Laplacian eigenvalues of graphs.

• Friday, 7th November, 2008

 Title: Planning for Disaster - Designing Robust Coverage Networks to Hedge against Worst-Case Facility Losses Speaker: Dr. Jesse Rush O`Hanley, Kent Business School, University of Kent, UK Time/Place: 10:45  -  11:45 FSC1111, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University Abstract: The potential for long-term facility loss has important implications for the reliability of service/supply networks. In order to design a coverage-type service network that is robust to the worst instances of facility loss, we develop a location-interdiction covering model that maximizes a combination of 1) initial coverage given p facilities and 2) the minimum coverage level following the loss of any subset of facilities r < p. The problem is formulated both as a mixed integer program and as a bilevel mixed integer program. To solve the bilevel program optimally, a decomposition algorithm is presented, whereby the original bilevel program is decoupled into an upper level master problem and a lower level subproblem. After sequentially solving these problems, information is fed back to the upper level master by appending supervalid inequalities, which attempt to force the upper level master away from clearly dominated solutions. Supervalid inequalities, unlike standard valid inequalities used in cutting plane algorithms, cut away parts of the feasible region but are guaranteed not to remove all optimal solutions unless an optimal solution has already been found. Computational results show that when solved to optimality, bilevel decomposition is up to several orders of magnitude faster than performing branch and bound on the mixed integer program.

• Monday, 10th November, 2008

 Title: A Hybrid Approach For Solving Sparse Linear Least Squares Problems Speaker: Dr. Esmond G. Ng , Lawrence Berkeley National Laboratory, USA Time/Place: 11:30  -  12:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University Abstract: We propose a hybrid method for solving large sparse linear least squares problems. The method is iterative in nature, as it is based on preconditioned LSQR. However, the preconditioner comes from an orthogonal factorization of a submatrix of the original matrix associated with the least squares problem; the construction of the preconditioner is based on well-known techniques in sparse direct methods. In this talk, we will discuss the quality of the preconditioner and the choices of the submatrix.

• Tuesday, 11th November, 2008

 Title: Quantum Transition State Theory Speaker: Dr. Shi Jing, Assistant Professor of Mathematics, Wayne State University, USA Time/Place: 11:30  -  12:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University Abstract: Quantum tunneling plays crucial roles in some physical and chemical processes, ranging from quantum cosmology to enzymatic reactions. The quantum nature of the motion often comes along with multidimensionality, namely the coupled motion of many degrees of freedom. The high dimensionality of the potential energy surface poses a great challenge in both theoretical and numerical descriptions of tunneling. Numerical simulation based on the Schrodinger equation is often prohibitively expensive. In this talk we discuss an efficient and accurate numerical method to calculate the tunneling transition, based on the quantum t ransition state theory in Feynman path space. It is free from any further ad hoc assumptions ('adiabatic' or 'sudden') and does not require pre-defined reaction coordinates. The application to hydrogen tunneling transfer in polyatomic molecules will also be demonstrated.

• Wednesday, 12th November, 2008

 Title: Symbolic Computations in Mathematics by Maple Speaker: Prof. Wen-Xiu Ma, Department of Mathematics and Statistics, University of South Florida, USA Time/Place: 14:00  -  15:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University Abstract: This is an introductory talk about a course on symbolic computations in mathematics by Maple. The course aims to teach students to use symbolic programming systems to solve mathematics problems. Upon completing the course, s tudents will be able to employ computer algebra systems to perform various symbolic computations in mathematics, particularly in linear algebra, number theory and calculus. I will focus on what audience the course is targeted at and what it is about, etc.

• Wednesday, 12th November, 2008

 Title: ICM Distinguished Computational Mathematics Lecture: Sublinear Algebra for Multidimensional Tensor Problems Speaker: Prof. Eugene Tyrtyshnikov , Institute of Numerical Mathematics, Russian Academy of Sciences, Russia Time/Place: 15:30  -  16:30 RRS905, Sir Run Run Shaw Building, Ho Sin Hang Campus, Hong Kong Baptist University Abstract: By a tensor problem in general, we mean one where all data on input and output are given exactly or approximately in tensor formats defined by a small number of parameters compared to the total amount of data. For such problems we propose to seek for algorithms that work with data exclusively in tensor formats, the price we pay is a contamination of data through some approximation (recompression) at each operation. We show that a certain intentional corruption of data, under pretty mild assumptions, still preserves the convergence rate of superlinear iterations. Then, we discuss which tensor formats are best suitable and advocate to deal with the Tucker format for all operands. As an application, we present new approximate matrix inversion algorithms with linear and even sublinear complexity in the matrix size and recent suggestions for construction of eigenvalue solvers. Also, we discuss the gains of combination of tensor and typical Toeplitzlike structures. In particular, doubly Toeplitz (block Toeplitz with Toeplitz blocks) matrices of a wide class can be approximately inverted with the complexity of order of square root of the matrix size.

• Monday, 17th November, 2008

 Title: NAG Seminar: Introduction to the Numerical Algorithms Group (NAG) Speaker: Prof. John Holden and Dr. Yuhe, Vice President Business Develpment, The Numerical Algorithms Group Limited, UK Time/Place: 11:00  -  12:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University Abstract: This seminar will be valuable for anyone wanting to write mathematical and statistical code or applications and individuals wanting to learn more about using NAG's numerical libraries. The NAG Libraries contain more than 1,500 routines making them the largest available collection of mathematical and statistical algorithms. The libraries coverage is extensive including: * Optimization, * Ordinary and Partial Differential Equations * Numerical integration and integral equations * Linear Algebra * Special functions * Curve and surface fitting and interpolation * Statistical functions * And much more... The presenters will also explain how NAG software can be used within other software packages such as Maple, LabView, R, S-Plus and C# / .NET, and demonstrate NAG's new Compiler for Windows, Fortran Builder. In the last part of the seminar we will give a few specific examples for financial mathematics / engineering.

• Monday, 17th November, 2008

 Title: On Neural Network Conditional Autoregressive Value at Risk Speaker: Dr. Eric Fung, Department of Mathematics, Hong Kong Baptist University, Hong Kong Time/Place: 14:30  -  15:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University

• Tuesday, 18th November, 2008

 Title: Gamma Frailty Transformation Models for Multivariate Failure Times Speaker: Prof. Donglin Zeng, Department of Biostatistics School of Public Health, University of North Carolina, Chapel Hill, USA Time/Place: 11:30  -  12:30 FSC1111, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University Abstract: We propose a class of transformation models for multivariate failure times. The class of transformation models generalize the usual gamma-frailty model and yields a marginally linear transformation model for each failure time. Nonparametric maximum likelihood estimation is used for inference. The maximum likelihood estimators for the regression coefficients are shown to be consistent and asymptotically normal, and their asymptotic variances attain the semiparametric efficiency bound. Simulation studies show that the proposed estimation procedure provides asymptotically efficient estimates and yields good inferential properties for small sample sizes. The method is illustrated using real data from a cardiovascular study.

• Tuesday, 25th November, 2008

 Title: DLS: Some Solved and Unsolved Problems in High Accuracy Finite Elements Speaker: Prof. Lin Qun, Chinese Academy of Sciences, China Time/Place: 11:00  -  12:30 ACC109, Jockey Club Academic Community Centre, Baptist University Road Campus, HKBU Abstract: The simplest problem is the so-called “2p-conjecture”: people guess a p-order finite element solution does has a 2p order accuracy at nodes. This is true for ODEs and has been proved in 1970's for Poisson equation for p<=3. There is no essential advance before 2000. Recently, people work for p=4. Problem for p>4 is still unsolved. There are more unsolved problems which will be talked in this lecture.

• Wednesday, 26th November, 2008

 Title: Graph Cut Algorithms Speaker: Dr. Andy C. Yau, Division of Mathematical Science, Nanyang Technological University, Singapore Time/Place: 15:30  -  17:00 FSC 1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University

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