Prof. Norden E. Huang ( Research Center for Adaptive Data Analysis, National Central University )2008 - 10 - 01 (Wed.)
09:00 - 11:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Akio Kawauchi 2008-10-01
14:00:00 - 15:00:00 Introducing a complexity to spatial graphs308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Norden Huang 2008-10-01
09:00:00 - 11:00:00 Introduction to HHT308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Prof. Norden E. Huang ( Research Center for Adaptive Data Analysis, National Central University )2008 - 09 - 26 (Fri.)
09:00 - 11:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Data-driven Selection of Penalty in Lasso
Prof. Hung Chen ( Department of Mathematics, National Taiwan University )2008 - 09 - 26 (Fri.)
15:30 - 17:00
301, Freshman Classroom BuildingDue to rapid development in large dimensional data acquisitions such as microarray, scientists look for useful methods on predicting a quantitative measurement when number of predictors p is much greater than n, the sample size. In this talk, we will address issues arose from the data-driven selection of penalty in Lasso when n is of the same order p. In particular, we discuss orthogonal predictors and Mallows’ Cp. BIC will also be addressed.

Mathematical Modeling
Prof. Hung-Chi Kuo ( Department of Atmospheric Sciences, National Taiwan University )2008 - 09 - 26 (Fri.)
15:30 - 17:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Introduction to Homogenization Theory I, II
Prof. Ying-Hong Liu ( Research Center for Applied Sciences, Academia Sinica )2008 - 09 - 26 (Fri.)
12:30 - 14:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)With the development of the modern technique, we have ability to construct the composite material needed in the environment. Usually, these devices are weaved in the micro- or nano-scales and they satisfy the inhomogeneous electromagnetic or elastic wave equations. However, for our human sensors, we always investigate them in the long wavelength or in the low frequency limit, mathematically, that means averaged governing equations describe the bulk behaviors of the composite system in the macro-scale. Therefore, how to carry out the transformation from the inhomogeneous to homogeneous governing equations is the main issue we want to address. In this talk, we start with one-dimensional elastodynamics and then introduce the typical procedure of homogenization analysis. In addition, several examples would be addressed: Darcy’s law, heat conduction in a composite and other applications.

Ying-Hong Liu 2008-09-26
12:30:00 - 14:30:00 Introduction to Homogenization Theory I, II308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Hung-Chi Kuo 2008-09-26
15:30:00 - 17:30:00 Mathematical Modeling308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Hung Chen 2008-09-26
15:30:00 - 17:00:00 Data-driven Selection of Penalty in Lasso301 , Freshman Classroom Building

Norden Huang 2008-09-26
09:00:00 - 11:00:00 Introduction to HHT308 , Mathematics Research Center Building (ori. New Math. Bldg.)

PARTIAL DIFFERENTIAL EQUATIONS-I
Prof. Chang-Shou Lin ( Department of Mathematics, National Taiwan University )2008 - 09 - 25 (Thu.)
09:00 - 12:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Chang-Shou Lin 2008-09-25
09:00:00 - 12:00:00 PARTIAL DIFFERENTIAL EQUATIONS-I308 , Mathematics Research Center Building (ori. New Math. Bldg.)

The Tian-Yau-Zelditch asymptotic expansion
Prof. Chiung-Ju Liu ( Department of Mathematics, National Taiwan University )2008 - 09 - 23 (Tue.)
14:00 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)The asymptotic expansion of the projection of the Szego kernel has been approached in different methods. In this talk, we will study the Tian-Yau-Zeldtich expansion based on Lu?s set-up. I will also talk about the result of my reason work on Riemann surfaces with constant curvature.

Chiung-Ju Liu 2008-09-23
14:00:00 - 15:00:00 The Tian-Yau-Zelditch asymptotic expansion308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Comparison theorems in Riemannian geometry
Mr. Jui-En Chang ( Department of Mathematics, National Taiwan University )2008 - 09 - 22 (Mon.)
10:00 - 12:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Jui-En Chang 2008-09-22
10:00:00 - 12:00:00 Comparison theorems in Riemannian geometry308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Model Selection in Regression Analysis: Classical Development
Prof. Hung Chen ( Department of Mathematics, National Taiwan University )2008 - 09 - 19 (Fri.)
15:30 - 17:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)Due to rapid development in large dimensional data acquisitions such as microarray, scientists look for useful methods on predicting a quantitative measurement when number of predictors p is much greater than n, the sample size. In this talk, we will present classical approaches in model selection through estimated prediction error for linear regression analysis when n is much larger than p. In particular, we discuss Mallows’ Cp (AIC), BIC, and cross-validation.In addition, we address the selection of penalty for ridge regression which no longer gives unbiased estimators of regression coefficients. This leads us to next week’s discussion on model selection with p is greater than n.

Prof. Norden E. Huang ( Research Center for Adaptive Data Analysis, National Central University )2008 - 09 - 19 (Fri.)
09:00 - 10:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Hung Chen 2008-09-19
15:30:00 - 17:00:00 Model Selection in Regression Analysis: Classical Development405 , Mathematics Research Center Building (ori. New Math. Bldg.)

Norden Huang 2008-09-19
09:00:00 - 10:00:00 Introduction to HHT308 , Mathematics Research Center Building (ori. New Math. Bldg.)

PARTIAL DIFFERENTIAL EQUATIONS-I
Prof. Chang-Shou Lin ( Department of Mathematics, National Taiwan University )2008 - 09 - 18 (Thu.)
11:00 - 12:10
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Chang-Shou Lin 2008-09-18
11:00:00 - 12:10:00 PARTIAL DIFFERENTIAL EQUATIONS-I405 , Mathematics Research Center Building (ori. New Math. Bldg.)

Prof. Norden E. Huang ( Research Center for Adaptive Data Analysis, National Central University )2008 - 09 - 17 (Wed.)
09:00 - 10:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Norden Huang 2008-09-17
09:00:00 - 10:30:00 Introduction to HHT308 , Mathematics Research Center Building (ori. New Math. Bldg.)

An overview of "Functional Convex Averaging and Synchronization for Time-Warped Random Curve" by Liu and Muller (2004)2008 - 09 - 09 (Tue.)
13:30 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)When the dynamics of regulatory processes over time are at issue, data can be described as a sample of curve in science and engineering. For functional data where trajectories may be individually time-transformed, it is usually inadequate to use commonly used sample statistics, such as the cross-sectional mean or cross-sectional sample variance, and the usual L2 metric. Curve registration is a statistical method to find a suitable overall structural representation. Liu and Muller (2004) proposed a time warping model including random time-synchronizing maps and concepts of functional calculus. The observed curves are assumed to be generated by a latent bivariate stochastic process, where one component corresponds to the random time warping function and the other component corresponds to a random amplitude function. An overview of the paper “Functional Convex Averaging and Synchronization for Time-Warped Random Curve” by Liu and Muller (2004) is given in this talk.

2008-09-09
13:30:00 - 15:00:00 An overview of "Functional Convex Averaging and Synchronization for Time-Warped Random Curve" by Liu and Muller (2004)308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Potential sampling bias of regression models and evolving population models
Ms. Yibi Huang ( Department of Statistics, University of Chicago, USA )2008 - 08 - 26 (Tue.)
13:30 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)In a regression model, the joint distributionfor each finite sample of units is determined by a function f x(y) depending only on the list of covariate values x = (x(u 1), x(u 2),...,x(u n)) on the sampled units (u 1,u 2,...,u n). Often it is implicitly assumed that the population is fixed. However, in biological work, random population is usually unavoidable, in which case the joint distribution p(y,x) depends on the sampling scheme. The conditional distribution p(y|x) might not agree with p x(y), the distribution of y in a fixed sample with a non-random configuration x. A model that avoids the concept of a fixed populaon of units is proposed. In this model, the sampling distribution of (x, y)will very with the sampling plan. For some specific sampling scheme, the sampling distribution agrees with the standard logistic model with correlated components. For others the conditional distribution p(y|x) is not the sample as the regression distribution unless p x(y) has independent components.

Yibi Huang 2008-08-26
13:30:00 - 15:00:00 Potential sampling bias of regression models and evolving population models308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Prof. Takeshi Miki ( Institute of Oceanography, National Taiwan University )