Prof. Shouhong Wang ( Indiana University, USA )

An explanation of "Kernel trick" and the construction of kernels for discrete structures
Mr. Kuang-Yao Lee ( Department of Statistics, Pennsylvania State University, USA )2008 - 07 - 29 (Tue.)
13:30 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)In statistical learning community, kernel-based methods are becom­ing widely used, such as Support vector machines (SVMs) and Kernel Principle Component Analysis (KPCA). The central idea behind them is the so called “kernel trick”. Via Mercer’s theorem, for an appro­priate kernel function defined on input space, K :Ω × Ω → R, there exists a mapping, φK :Ω → ΦK , which maps the original data space into a higher (generally infinite) dimension space ΦK. ΦK is a repro­ducing kernel Hilbert space so that non-linear extension for common statistical problem can be reasonably constructed. An interpretation by Minh et al. (2006) will be introduced here. Then, I will focus on kernels for discrete structures. Categorical data and more general, graph-like data, are often seen in real world; for example, the hyper-link in WWW and citations in scientific articles. Therefore, how to use kernels to capture the relationship between graph points might be interesting. Two possible methods, R-convolution (Haussler 1999) and diffusion kernels (Kondor & Lafferty 2002) will also be discussed.

Prof. Jian-Guo Liu ( University of Maryland, USA )

Prof. Shouhong Wang ( Indiana University, USA )

Prof. Shouhong Wang ( Indiana University, USA )

Prof. Shouhong Wang  ( Indiana University, USA )

Golbarg-Trudinger, second order, Elliptic PDE
Dr. Hidemitsu Wadade ( Math. Division, NCTS/Taipei & Taida Institute for Mathematical Sciences )2008 - 07 - 22 (Tue.)
18:30 - 20:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)這個seminar的目的是由一群學幾何幾析及偏 微分方程的學生組成，主要要學習elliptic PDE 的基本理論，歡迎有興趣的同學來參加。

Classification of gradient shrinking solitons
Prof. Lei Ni ( University of California, San Diego, USA )2008 - 07 - 18 (Fri.)
14:00 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Prof. Shouhong Wang  ( Indiana University, USA )

2008 - 07 - 16 (Wed.)
14:00 - 15:10
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Golbarg-Trudinger, second order, Elliptic PDE
Dr. Hidemitsu Wadade ( Math. Division, NCTS/Taipei & Taida Institute for Mathematical Sciences )2008 - 07 - 15 (Tue.)
18:30 - 20:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)這個seminar的目的是由一群學幾何幾析及偏 微分方程的學生組成，主要要學習elliptic PDE 的基本理論，歡迎有興趣的同學來參加。

Nonparametric Estimation Methods for the Optimal Composite Markers with Censored Survival Data
Prof. Hung Hung ( Graduate Institute of Epidemiology and Preventive Medicine, National Taiwan University )2008 - 07 - 15 (Tue.)
13:30 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)To increase the predictive abilities of several markers on the vital statuses over time, our research interest mainly focuses on seeking appropriate composite markers with the highest time-dependent receiver operating characteristic (ROC) curves. An extended generalized linear model (EGLM) with time-varying coefficients and an unknown bivariate link function is used to characterize the conditional distribution of the time to CAD-related death. Two nonparametric procedures are proposed to estimate the optimal composite markers, linear predictors in the EGLM model. The estimation methods for the accuracy measurements of the optimal composite markers are also proposed. In this study, we establish the theoretical results of the estimators and examine the corresponding finite sample properties through a series of simulations with different sample sizes, censoring rates, and censoring mechanisms. Our optimization procedures and estimators are further shown to be useful through an application to a prospective cohort study of patients undergoing angiography.

One-Dimensional Dynamics-V
Prof. Jung-Chao Ban ( National Dong Hwa University (Meilun Campus) )2008 - 07 - 14 (Mon.)
10:00 - 12:10
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Prof. Kuo-Chang Chen  ( National Tsing Hua University ) 

Prof. Tai-Chia Lin  ( Department of Mathematics, National Taiwan University ) 

Prof. Li Chen  ( Tsinghua University, China )

Golbarg-Trudinger, second order, Elliptic PDE.
Dr. Hidemitsu Wadade ( Math. Division, NCTS/Taipei & Taida Institute for Mathematical Sciences )2008 - 07 - 08 (Tue.)
18:30 - 20:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)這個seminar的目的是由一群學幾何幾析及偏 微分方程的學生組成，主要要學習elliptic PDE 的基本理論，歡迎有興趣的同學來參加。

Golbarg-Trudinger, second order, Elliptic PDE.
Dr. Hidemitsu Wadade ( Math. Division, NCTS/Taipei & Taida Institute for Mathematical Sciences )2008 - 07 - 01 (Tue.)
18:30 - 20:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)這個seminar的目的是由一群學幾何幾析及偏 微分方程的學生組成，主要要學習elliptic PDE 的基本理論，歡迎有興趣的同學來參加。

Prof. Wei-Cheng Wang  ( National Tsing Hua University )

Golbarg-Trudinger, second order, Elliptic PDE.
Dr. Hidemitsu Wadade ( Math. Division, NCTS/Taipei & Taida Institute for Mathematical Sciences )2008 - 06 - 24 (Tue.)
18:30 - 20:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)這個seminar的目的是由一群學幾何幾析及偏 微分方程的學生組成，主要要學習elliptic PDE 的基本理論，歡迎有興趣的同學來參加。

A Torelli type theorem of birational equivalence
Prof. Chen-Yu Chi ( Department of Mathematics, National Taiwan University )2008 - 06 - 24 (Tue.)
14:00 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

A tale of rational triangles
Prof. Wen-Ching Winnie Li ( & Pennsylvania State University, USA )2008 - 06 - 23 (Mon.)
11:00 - 12:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Modeling and simulations of physiological flows:-Applications to blood circulation and body respiration-Liver blood flow and mini-invasive cancer therapies
Prof. Marc Thiriet ( Université Pierre et Marie Curie (Paris 6), France )2008 - 06 - 19 (Thu.)
14:10 - 17:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

Comparison theorems in Riemannian geometry2008 - 06 - 19 (Thu.)
19:00 - 20:30
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Modeling and simulations of physiological flows:-Applications to blood circulation and body respiration-Liver blood flow and mini-invasive cancer therapies
Prof. Marc Thiriet ( Université Pierre et Marie Curie (Paris 6), France )2008 - 06 - 18 (Wed.)
09:00 - 12:10
308, Mathematics Research Center Building (ori. New Math. Bldg.)The final week will be devoted to joint work with SCCS team in the framework of the CFT associated team.

Golbarg-Trudinger, second order, Elliptic PDE
Dr. Hidemitsu Wadade ( Math. Division, NCTS/Taipei & Taida Institute for Mathematical Sciences )2008 - 06 - 18 (Wed.)
16:00 - 17:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)這個seminar的目的是由一群學幾何幾析及偏 微分方程的學生組成，主要要學習elliptic PDE 的基本理論，歡迎有興趣的同學來參加。

Constant Mean Curvature Foliation of Isolated Physical Systems
Ms. Lan-Hsuan Huang ( Stanford University, USA )2008 - 06 - 17 (Tue.)
10:30 - 11:30
405, Mathematics Research Center Building (ori. New Math. Bldg.)

The positivity of quasi-local mass
Mr. Bo-Ning Chen ( Harvard University, USA )2008 - 06 - 17 (Tue.)
14:00 - 15:30
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Hawking’s singularity theorem
Dr. Yen-Wen Fan ( Center for Advanced Study in Theoretical Sciences, National Taiwan University )2008 - 06 - 17 (Tue.)
16:10 - 17:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)

The positivity of quasi-local mass
Prof. Bo-Ning Chen ( Columbia University, USA )2008 - 06 - 17 (Tue.)
14:00 - 15:30
405, Mathematics Research Center Building (ori. New Math. Bldg.)