Bifurcation theory and its applications on the convection problems
Prof. Chun-Hsiung Hsia ( Department of Mathematics, National Taiwan University )2008 - 10 - 02 (Thu.)
15:30 - 16:30
308, Mathematics Research Center Building (ori. New Math. Bldg.)In the talk, we introduce the concepts and the machinery of bifurcation theory. Bifurcation theory studies the qualitative changes of the solutions for a system of equations while the control parameters of the equations vary. We will start with algebraic equations and ordinary differential equations to demonstrate basic ideas of bifurcation theory. We present different types of bifurcations including steady-state bifurcation, Hopf bifurcation and attractor bifurcation. We will conclude this talk by showing applications on the convection problems.

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.)

Introducing a complexity to spatial graphs
Prof. Akio Kawauchi ( Osaka City University, Japan )2008 - 10 - 01 (Wed.)
14:00 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)We introduce a notion which we call the warping degree for every connected spatial graph (possibly, with vertices of degree one) by defining admissible regular diagrams of the spatial graph. By definition the warping degree takes a value in non-negative integers, by which we can define a notion of a complexity among all the spatial graphs of any given connected graph.
For every connected spatial graph without vertices of degree one, this notion is used to define two kinds of notions of topological invariants. We observe that one of the notions coincides with the unknotting number for a spatial connected plane graph, in particular for a knot.

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.)

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.)

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.

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.

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.)

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.

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.)

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.)

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.

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.)

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.)

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.

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.

Golbarg-Trudinger, second order, Elliptic PDE
Dr. Hidemitsu Wadade ( Math. Division, NCTS/Taipei & Taida Institute for Mathematical Sciences )2008 - 08 - 19 (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. Takeshi Miki ( Institute of Oceanography, National Taiwan University )

Review of the paper “Analysis of interval-censored longitudinal data with application to onco-haematology”2008 - 08 - 12 (Tue.)
13:30 - 15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)An overview of the paper “Analysis of interval-censored longitudinal data with application to onco-haematology” by Paola De Lorenzo , Robin Henderson and Maria Grazia Valsecchi(2005) is given. The presence of minimal residual disease (MRD) following therapy for acute lymphoblastic leukemia (ALL) has been shown to be an important prognostic marker in many studies. However, it is not yet clear how information on MRD can be applied to treatment more. The aim of this paper is to investigate the relationship between MRD and the disease process. They propose a linear mixed model with a Gaussian process that allows for interval-censored data and can be used both to track the biomarker trajectory and to estimate the probability of relapse occurrence.

Golbarg-Trudinger, second order, Elliptic PDE
Dr. Hidemitsu Wadade ( Math. Division, NCTS/Taipei & Taida Institute for Mathematical Sciences )2008 - 08 - 12 (Tue.)
18:30 - 20:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

2008 - 08 - 07 (Thu.)
10:00 - 11:30
405, Mathematics Research Center Building (ori. New Math. Bldg.)

2008 - 08 - 07 (Thu.)
10:00 - 11:30
405, 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 - 08 - 05 (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. Haizhong Li ( Tsinghua University, China )

Haizhong Li 2008-08-05
14:00:00 - 15:00:00 Willmore submanifolds in a Riemannian manifold405 , Mathematics Research Center Building (ori. New Math. Bldg.)

The Bernstein problem on the Heisenbeg Groups
Prof. Duy-Minh Nhieu ( Department of Mathematics, National Central University )2008 - 07 - 31 (Thu.)
11:00 - 12:00
405, 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 - 29 (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。

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 )