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Event(s) on December 2011
- Tuesday, 13th December, 2011
Title: Expectation-Maximization algorithm for accelerated life tests on one-shot devices Speaker: Dr. Man Ho Ling, Department of Mathematics and Statistics, McMaster University, Canada Time/Place: 11:00 - 12:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: In reliability analysis, real lifetime of devices is critical information collected from experiments for analysis. Due to destructive tests in which devices are destroyed and cannot be used any further after testing, only the condition of the devices at a specified time can be observed and thus the real lifetimes are all censored, no matter whether the test is a success or a failure. Such kind of data is collected often and natural of interest. Nowadays, products have become highly reliable with long lifetime, there is few or even no failures in normal operating condition within a limited time, accelerated life tests wherein devices are subject to higher-than-usual stress are, therefore, often used for inducting earlier failures in testing. Through log-linear functions relating stress levels and parameters in model, the data collected in the elevated stress levels can be transformed and then used to describe the lifetime of devices in normal operating condition. In presence of censored data, Expectation-Maximization algorithm is a powerful technique and is proposed for finding the maximum likelihood estimates of the parameter of interest. Furthermore, a data collected from a tumorgencity experiment in mice is analyzed to illustrate the proposed method and the results are also presented. - Wednesday, 14th December, 2011
Title: A Proximal Point Algorithm for Nuclear Norm Regularized Matrix Least Squares Problems Speaker: Prof. Kim Chuan TOH, Department of Mathematics, National University of Singapore Time/Place: 11:00 - 12:00
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: We consider a proximal point method for solving the nuclear norm regularized matrix least squares problem with equality and inequality constraints. We show that the soft thresholding operator is strongly semismooth everywhere. For the inner subproblems, due to the presence of inequality constraints, we reformulate the problem as a system of semismooth equations. Then an inexact smoothing Newton method is proposed to solve this reformulated semismooth system. At each iteration, we apply the BiCGStab iterative solver to obtain an approximate solution to the generated smoothing Newton linear system. Numerical experiments on a variety of large scale matrix least squares problems, where the matrices involved have some special structures, show that the proposed proximal point method is efficient. - Friday, 16th December, 2011
Title: The L(j; k)-labeling number of some product graphs Speaker: Miss WU Qiong, Department of Mathematics, Hong Kong Baptist University, Hong Kong Time/Place: 10:30 - 11:30
FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist UniversityAbstract: Let j, k and m be three positive numbers. An L(j; k)-labeling f of G is an assignment of integers to the vertices of G such that jf(u) ¡ f(v)j ¸ j if uv 2 E(G), and jf(u) ¡ f(v)j ¸ k if u and v are distance two apart. Then the span of f is the di®erence between the maximum and the minimum integers assigned by f. The L(j; k)-labeling number of G, denoted by ¸j;k(G), is the minimum span over all L(j; k)-labelings of G. A circular m-L(j; k)-labeling of a graph G is a function f : V (G) ! [0;m) such that jf(u) ¡ f(v)jm ¸ j if u and v are adjacent, and jf(u) ¡ f(v)jm ¸ k if u and v are at distance two, where ja ¡ bjm = minfja ¡ bj;m ¡ ja ¡ bjg: The minimum m such that there exist a circular m-L(j; k)-labeling of G is called the circular-L(j; k)-labeling number of G and is denoted by ¾j;k(G). In this talk, for any two positive integers j and k with j · k, we give some results about the L(j; k)-labeling numbers of Cartesian product and direct product of path and cycle, and the circular L(j; k)-labeling number of direct product of path and cycle.