Prof. Chang-Shou Lin  ( Department of Mathematics, National Taiwan University )

Mr. Chenyi Hu  ( University of Central Arkansas, USA )

Nonparametric Estimation For Time-Dependent AUC
Prof. Chin-Tsang Chiang ( Department of Mathematics, National Taiwan University )2008 - 01 - 08 (Tue.)
13:30 - 15:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)The area under the receiver operating characteristic curve (AUC) is the commonly used measure to evaluate or compare the predictive ability of markers to the disease status . Motivated by an angiographic coronary artery disease (CAD) study, our objective is mainly to compare the performance of different plasma markers in the prediction of CAD-related vital status at different time points within the study period. Instead of integrating the area under the estimated receiver operating characteristic curve (ROC) at a specified time point, a class of nonparametric estimators is proposed for the time-dependent AUC under the different censoring mechanisms. Moreover, the asymptotic properties of the estimators are developed and used to construct the approximated confidence regions of the AUCs and test for the performance of different markers. The finite sample properties and the usefulness of the estimators and procedures are investigated through extensive simulations. Finally, our proposed methods are applied to the illustrated empirical example.

Tautness and Algebraicity
Prof. Quo-Shin Chi ( Washington University in St. Louis, USA )2008 - 01 - 08 (Tue.)
14:00 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)A compact submanifold in a sphere (or in an Euclidean space) is taut if all the spherical (Euclidean) distance functions are perfect Morse-Bott functions with respect to Z 2 coefficients. Tautness is preserved by stereographic projection, and so the theories in the two ambient spaces are essentially the same. Two important classes of taut submanifolds are isoparametric submanifolds and compact proper Dupin hypersurfaces in spheres, among many others. In a paper published in 1984, Kuiper raised the question as to whether a taut submanifold is real algebraic, i.e., whether a taut submanifold is an irreducible component of a real algebraic subvariety of the ambient space. In the 1980's the answer to this question was widely thought to be true, for a good reason, because intuitively a perfect Morse-Bott function should not be flabby anywhere. In this talk, I shall indicate a proof that the answer to this question of Kuiper's is affirmative if the dimension of the taut submanifold is less than or equal to four.

Prof. Shu-Cheng Chang ( Department of Mathematics, National Taiwan University )2008 - 01 - 08 (Tue.)
11:00 - 12:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Chenyi Hu 2008-01-08
16:30:00 - 17:20:00 308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Chang-Shou Lin 2008-01-08
09:10:00 - 10:50:00 405 , Mathematics Research Center Building (ori. New Math. Bldg.)

Shu-Cheng Chang 2008-01-08
11:00:00 - 12:00:00 405 , Mathematics Research Center Building (ori. New Math. Bldg.)

Chin-Tsang Chiang 2008-01-08
13:30:00 - 15:00:00 Nonparametric Estimation For Time-Dependent AUC405 , Mathematics Research Center Building (ori. New Math. Bldg.)

Quo-Shin Chi 2008-01-08
14:00:00 - 15:00:00 Tautness and Algebraicity308 , Mathematics Research Center Building (ori. New Math. Bldg.)

2008 - 01 - 03 (Thu.)
14:00 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

2008-01-03
14:00:00 - 15:00:00 308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Prof. Hung-Chi Kuo  ( Department of Atmospheric Sciences, National Taiwan University )

Hung-Chi Kuo 2007-12-27
10:00:00 - 13:00:00 308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Multiscale Computations and Engineering Applications
Prof. Yizhao Thomas Hou ( California Institute of Technology, USA )2007 - 12 - 21 (Fri.)
10:00 - 11:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)Many problems of fundamental and practical importance contain multiple scale solutions. Composite materials, flow and transport in heterogeneous porous media, and turbulent flow are examples of this type. Direct numerical simulations of these multiscale problems are extremely difficult due to the wide range of length scales in the underlying physical problems. In this talk, I describe some of our recent efforts in developing multiscale computational methods to upscale two-phase flows in strongly heterogeneous porous media. For some challenging problems with long range scale interaction arising from engineering applications, we show how to use limited global information to improve the accuracy of the multiscale method. Another important application is how to quantify uncertainty in modeling the heterogeneous random media. We show that by using a coarse multiscale model to precondition the Markov Chain Monte Carlo method, we can significantly improve the efficiency of the MCMC method in generating the probability distribution of the random media subject to some production data. Finally, we will discuss some recent progress in developing multiscale methods for incompressible Navier-Stokes equations with high Reynolds number.

Yizhao Hou 2007-12-21
10:00:00 - 11:00:00 Multiscale Computations and Engineering Applications308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Prof. Hung-Chi Kuo  ( Department of Atmospheric ScienProf. Jun Zou   ( The Chinese University of Hong Kong )

Prof. Jun Zou   ( The Chinese University of Hong Kong )

Jun Zou 2007-12-20
14:10:00 - 15:00:00 Some efficient numerical methods for inverse problems308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Prof. Hung-Chi Kuo  ( Department of Atmospheric Sciences, National Taiwan University )

Hung-Chi Kuo 2007-12-14
11:20:00 - 12:30:00 308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Prof. Hung-Chi Kuo  ( Department of Atmospheric Sciences, National Taiwan University )

Hung-Chi Kuo 2007-12-07
11:20:00 - 12:30:00 Typhoon and Vortex Dynamics 308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Solutions of elliptic PDE concerned with Toda system
Dr. Yuko Nagase ( Taida Institute for Mathematical Sciences )2007 - 12 - 06 (Thu.)
14:00 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Yuko Nagase 2007-12-06
14:00:00 - 15:00:00 Solutions of elliptic PDE concerned with Toda system308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Ricci flow and Poincaré Conjecture
Prof. Chang-Shou Lin ( Department of Mathematics, National Taiwan University )2007 - 12 - 04 (Tue.)
09:10 - 12:10
405, Mathematics Research Center Building (ori. New Math. Bldg.)

The balance between existence and nonexistence theorems via an index theory
Prof. Shihshu Walter Wei ( University of Oklahoma, USA )2007 - 12 - 04 (Tue.)
13:30 - 14:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Model Selection via the Group Lasso
Ms. Yen-Shiu Chin ( Department of Mathematics, National Taiwan University )2007 - 12 - 04 (Tue.)
13:30 - 15:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Concentration phenomena for some singularly perturbed elliptic PDEs
Prof. Andrea Malchiodi ( SISSA, Italy )2007 - 12 - 04 (Tue.)
15:00 - 16:00We study singularly perturbed elliptic equations arising from models in physics or biology, and investigate the asymptotic behavior of some special solutions as some parameter tends to zero. We also discuss some connections with related problems arising in differential geometry.

Yen-Shiu Chin 2007-12-04
13:30:00 - 15:00:00 Model Selection via the Group Lasso405 , Mathematics Research Center Building (ori. New Math. Bldg.)