
20080116PDE WorkShopJanuary 16, 2008
Website http://140.112.50.155/workshop/TIMS/20080116PDEWorkShop.htm 
20080115Statistical MethodologyIdentify Design Conditions to Achieve the Optimal Rate of Convergence in a Bivariate Additive Model2008  01  15 (Tue.)
13:30  15:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)This paper considers the estimation problem in a bivariate additive model, for . Here and is a random error and is assumed to be smooth which is approximated by Bsplines. However, is not necessary to be smooth. This problem is motivated by the normalization needed in correcting intensity effects in microarray study. In this talk, an almost necessary and sufficient condition is given to guarantee that can be estimated with the usual onedimensional optimal rate of convergence. We also present a simulation study to illustrate various convergence rate can be obtained when the proposed design condition is not satisfied. 
20080115Identify Design Conditions to Achieve the Optimal Rate of Convergence in a Bivariate Additive Model20080115
13:30:00  15:00:00 Identify Design Conditions to Achieve the Optimal Rate of Convergence in a Bivariate Additive Model405 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080111Typhoon and Vortex Dynamics2D Turbulence and a Course SummaryProf. HungChi Kuo ( Department of Atmospheric Sciences, National Taiwan University )

20080111Typhoon and Vortex Dynamics2D Turbulence and a Course SummaryHungChi Kuo 20080111
10:30:00  12:30:00 308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080108Ricci flow and Poincaré ConjectureProf. ChangShou Lin ( Department of Mathematics, National Taiwan University )

20080108Interval Methods in Computational FinanceMr. Chenyi Hu ( University of Central Arkansas, USA )

20080108Statistical MethodologyNonparametric Estimation For TimeDependent AUC
Prof. ChinTsang 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 CADrelated 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 timedependent 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. 
20080108NCTS/TPE & TIMS Joint Geometry Seminar (20092010)Tautness and Algebraicity
Prof. QuoShin 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 MorseBott 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 MorseBott 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. 
20080108Subgradient estimates for CR heat equationProf. ShuCheng Chang ( Department of Mathematics, National Taiwan University )2008  01  08 (Tue.)
11:00  12:00
405, Mathematics Research Center Building (ori. New Math. Bldg.) 
20080108Interval Methods in Computational FinanceChenyi Hu 20080108
16:30:00  17:20:00 308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080108Ricci flow and Poincaré ConjectureChangShou Lin 20080108
09:10:00  10:50:00 405 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080108Subgradient estimates for CR heat equationShuCheng Chang 20080108
11:00:00  12:00:00 405 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080108Nonparametric Estimation For TimeDependent AUCChinTsang Chiang 20080108
13:30:00  15:00:00 Nonparametric Estimation For TimeDependent AUC405 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080108Tautness and AlgebraicityQuoShin Chi 20080108
14:00:00  15:00:00 Tautness and Algebraicity308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080103Invariance of plurigenera2008  01  03 (Thu.)
14:00  15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.) 
20080103Invariance of plurigenera20080103
14:00:00  15:00:00 308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20071227Typhoon and Vortex Dynamics ***Rescheduled from Dec. 21(Fri.)Prof. HungChi Kuo ( Department of Atmospheric Sciences, National Taiwan University )

20071227Typhoon and Vortex Dynamics ***Rescheduled from Dec. 21(Fri.)HungChi Kuo 20071227
10:00:00  13:00:00 308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20071221Computational SciencesMultiscale 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 twophase 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 NavierStokes equations with high Reynolds number. 
20071221Multiscale Computations and Engineering ApplicationsYizhao Hou 20071221
10:00:00  11:00:00 Multiscale Computations and Engineering Applications308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20071220Some efficient numerical methods for inverse problemsProf. HungChi Kuo ( Department of Atmospheric ScienProf. Jun Zou ( The Chinese University of Hong Kong )

20071220Inverse obstacle scattering problems: theory and numericsProf. Jun Zou ( The Chinese University of Hong Kong )

20071220Some efficient numerical methods for inverse problemsJun Zou 20071220
14:10:00  15:00:00 Some efficient numerical methods for inverse problems308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20071214Typhoon and Vortex DynamicsProf. HungChi Kuo ( Department of Atmospheric Sciences, National Taiwan University )

20071214Typhoon and Vortex DynamicsHungChi Kuo 20071214
11:20:00  12:30:00 308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20071207Typhoon and Vortex DynamicsProf. HungChi Kuo ( Department of Atmospheric Sciences, National Taiwan University )

20071207Typhoon and Vortex DynamicsHungChi Kuo 20071207
11:20:00  12:30:00 Typhoon and Vortex Dynamics 308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20071206Nonlinear PDESolutions 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.) 
20071206Solutions of elliptic PDE concerned with Toda systemYuko Nagase 20071206
14:00:00  15:00:00 Solutions of elliptic PDE concerned with Toda system308 , Mathematics Research Center Building (ori. New Math. Bldg.)