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2008-10-16PARTIAL DIFFERENTIAL EQUATIONS-IPARTIAL DIFFERENTIAL EQUATIONS-I
Prof. Chang-Shou Lin ( Department of Mathematics, National Taiwan University )2008 - 10 - 16 (Thu.)
09:00 - 12:10
405, Mathematics Research Center Building (ori. New Math. Bldg.) -
2008-10-16TIMS PDE SeminarQuantitative uniqueness for the Stokes Equations
Prof. Ching-Lung Lin ( National Cheng Kung University )2008 - 10 - 16 (Thu.)
15:30 - 16:30
405, Mathematics Research Center Building (ori. New Math. Bldg.)I would like to talk about a recent study on the local behavior of a solution to the Stokes Equations. One of the main results is the bound on the vanishing order of the pair of solution and pressure, which is a quantitative estimate of the strong unique continuation property. Our proofs use Carleman estimates with carefully chosen weights. We will derive optimal three-sphere inequalities and doubling inequalities. -
2008-10-15Introduction Hilbert-Huang TransformIntroduction to HHT
Prof. Norden E. Huang ( Research Center for Adaptive Data Analysis, National Central University )2008 - 10 - 15 (Wed.)
09:00 - 11:00
308, Mathematics Research Center Building (ori. New Math. Bldg.) -
2008-10-14Student seminar on PDEGolbarg-Trudinger, second order, Elliptic PDE
Dr. Hidemitsu Wadade ( Math. Division, NCTS/Taipei & Taida Institute for Mathematical Sciences )2008 - 10 - 14 (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。 -
2008-10-14NCTS/TPE & TIMS Joint Geometry Seminar (2009-2010)A resent result of Phong on Kähler-Ricci flow
Dr. Jun-Nan Tsai ( Department of Mathematics, National Taiwan University )2008 - 10 - 14 (Tue.)
14:00 - 15:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)It has been an important topic to find a Kähler-Einstein metric (Rc=cg) on a given Kähler manifold X. Several researchers have contributed to this problem. For example, Yau used continuity method to study the case when c=-1, 0 and gave a complete proof, and later his student H.D. Cao used Kähler-Ricci flow to reprove this result. In this talk, I will present Phong’s recent work in the case when c=1 and explain how it is related to Perelman’s new estimate. -
2008-10-09PARTIAL DIFFERENTIAL EQUATIONS-IPARTIAL DIFFERENTIAL EQUATIONS-I
Prof. Chang-Shou Lin ( Department of Mathematics, National Taiwan University )2008 - 10 - 09 (Thu.)
09:10 - 12:00
308, Mathematics Research Center Building (ori. New Math. Bldg.) -
2008-10-08Introduction to HHTProf. Norden E. Huang ( Research Center for Adaptive Data Analysis, National Central University )2008 - 10 - 08 (Wed.)
09:00 - 11:00
308, Mathematics Research Center Building (ori. New Math. Bldg.) -
2008-10-07Student seminar on PDEGolbarg-Trudinger, second order, Elliptic PDE
Dr. Hidemitsu Wadade ( Math. Division, NCTS/Taipei & Taida Institute for Mathematical Sciences )2008 - 10 - 07 (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。 -
2008-10-07NCTS/TPE & TIMS Joint Geometry Seminar (2009-2010)On the singularities of the Szego projection for ''0,q'' forms
Dr. Chin-Yu Hsiao ( École Polytechnique, France & Göteborgs universitet, Sweden )2008 - 10 - 07 (Tue.)
14:00 - 15:50
308, Mathematics Research Center Building (ori. New Math. Bldg.)In this work we completely study the heat equation method of Menikoff-Sjostrand and apply it to the Kohn Laplacian defined on a compact orientable connected CR manifold. We then get the full asymptotic expansion of the Szego projection for (0,q) forms. This generalizes a result of Boutet de Monvel and Sjostrand for (0,0) forms. Our mail tool is Fourier integral operators with complex valued phase functions of Melin and Sjostrand. We hope that this talk can serve as an introduction to certain micolocal techniques with applications to CR geometry and complex geometry. -
2008-10-03Introduction to HHTProf. Norden E. Huang ( Research Center for Adaptive Data Analysis, National Central University )008 - 10 - 03 (Fri.)
09:00 - 11:00
308, Mathematics Research Center Building (ori. New Math. Bldg.) -
2008-10-03Statistical MethodologyOnline Learning with Matrix Exponentiated Gradient Updates
Dr. Hsin-Hsiung Huang ( Institute of Statistical Science , Academia Sinica )2008 - 10 - 03 (Fri.)
13:30 - 15:00
404, Freshman Classroom BuildingTsuda, Ratsch and Warmuth (2006) address the problem of learning a symmetric positive definite matrix. They offer kernelized updates which involve a calculation based on matrix logs and matrix exponentials. These updates preserve the symmetry and positive definiteness. On the other hand, Vishwanathan, Schraudolph and Smola (2006) provide an online support vector machine (SVM) that uses the stochastic meta-descent (SMD) algorithm to adapt its step size automatically. Based on their method, we derive updates that allow us to perform the step size adaptation of kernel principal component analysis (PCA). Further, the online kernel PCA is an online SVM framework to loss functions, where its gradient trace parameter is no longer a coefficient vector but an element of the RKHS. -
2008-10-03Seminar on multiscale Analysis and ComputationTwo-Scale Convergence and Homogenization of Periodic Structures
Prof. Jiann-Sheng Jiang ( Tung Fang Institute of Technology )2008 - 10 - 03 (Fri.)
12:30 - 14:30
308, Mathematics Research Center Building (ori. New Math. Bldg.) -
2008-10-03Mathematical modelingMathematical Modeling
Prof. Hung-Chi Kuo ( Department of Atmospheric Sciences, National Taiwan University )2008 - 10 - 03 (Fri.)
15:30 - 17:30
308, Mathematics Research Center Building (ori. New Math. Bldg.) -
2008-10-02PARTIAL DIFFERENTIAL EQUATIONS-IPARTIAL DIFFERENTIAL EQUATIONS-I
Prof. Chang-Shou Lin ( Department of Mathematics, National Taiwan University )2008 - 10 - 02 (Thu.)
09:00 - 12:00
308, Mathematics Research Center Building (ori. New Math. Bldg.) -
2008-10-02TIMS PDE SeminarBifurcation 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. -
2008-10-01Introduction to HHTProf. 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.) -
2008-10-01NCTS/TPE & TIMS Joint Geometry Seminar (2009-2010)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. -
2008-09-26Introduction to HHTProf. 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.) -
2008-09-26Mathematical modelingMathematical 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.) -
2008-09-26Statistical MethodologyData-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. -
2008-09-26Seminar on multiscale Analysis and ComputationIntroduction 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. -
2008-09-25PARTIAL DIFFERENTIAL EQUATIONS-IPARTIAL 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.) -
2008-09-23NCTS/TPE & TIMS Joint Geometry Seminar (2009-2010)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. -
2008-09-22Student seminar on differential geometryComparison 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.) -
2008-09-19Introduction to HHTProf. 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.) -
2008-09-19Statistical MethodologyModel 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. -
2008-09-18PARTIAL DIFFERENTIAL EQUATIONS-IPARTIAL 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.) -
2008-09-17Introduction to HHTProf. 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.) -
2008-09-09Statistical MethodologyAn 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. -
2008-08-26Statistical MethodologyPotential 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.