
20080321Statistical MethodologyPseudoPartial Likelihood for Proportional Hazards Models with BiasedSampling Data
Prof. WeiYann Tsai ( Department of Biostatistics, Columbia University, USA )2008  03  21 (Fri.)
14:30  17:00
502, Freshman Classroom BuildingWe obtain a "pseudopartial likelihood" for proportional hazards models with biasedsampling data by viewing biasedsampling data as lefttruncated data. The log pseudopartial likelihood of the biasedsampling data is the expectation of the log partial likelihood of the lefttruncated data conditioned on the observed data. In addition, asymptotic properties of the estimator which maximizes the pseudopartial likelihood are derived. Applications to lengthbiased data, biased samples with right censoring, stratified samples, and proportional hazards models with missing covariates are also discussed. 
20080321Workshop on Statistical Methodology of Microarray DataReconstruction methods for inverse problems
Prof. Gen Nakamura ( Hokkaido University, Japan )2008  03  21 (Fri.)
11:20  12:20
308, Mathematics Research Center Building (ori. New Math. Bldg.)For the recent 10 years the several reconstruction methods have been proposed for inverse scattering problems and inverse boundary value problems. For instance they are the linear sampling method, factorization method, probe method, singular sources method, noresponse test, range test and enclosure method etc. These reconstruction methods are noniterative methods which means that they are not data fitting methods such as the least square methods or the regularized version of those. They provide how to reconstruct the unknowns directly from the given measured data. The lecture will touch the basic ideas of those methods and discuss about their convergence and relations between them. 
20080321Statistical MethodologyPseudoPartial Likelihood Estimators for Cox Regression Model With Missing Covariates
Prof. WeiYann Tsai ( Department of Biostatistics, Columbia University, USA )2008  03  21 (Fri.)
14:30  17:00
502, Freshman Classroom BuildingBy embedding the missing covariate data into a lefttruncated and rightcensored survival model, a new class of weighted estimating functions is proposed for Cox regression model with missing covariates. The resulting estimators, called the pseudo partial likelihood estimators (PPLEs), are shown to be consistent and asymptotically normal. Simulation study demonstrates that PPLEs, compared with the popular inverse probability weighted estimators, have better performance when the observation probability is small, and improve efficiency of estimating the missing covariate effects. A real data example is applied to illustrate the use of PPLEs. 
20080321Dimension theory for nonconformal repellerJungChao Ban 20080321
15:30:00  16:30:00 Dimension theory for nonconformal repeller308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080321Topological Pressure and Variational PrincipleJungChao Ban 20080321
13:30:00  15:00:00 Topological Pressure and Variational Principle308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080321Small volume imagingHyeonbae Kang20080321
10:00:00  11:00:00Small volume imaging308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080321Reconstruction methods for inverse problemsGen Nakamura20080321
11:20:00  12:20:00Reconstruction methods for inverse problems308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080320Workshop on Statistical Methodology of Microarray DataInvisibility
Prof. Gunther Uhlmann ( Department of Atmospheric Sciences, University of Washington, USA )2008  03  20 (Thu.)
10:00  11:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)We describe construction of electromagnetic parameters that make objects invisible to electromagnetic waves. 
20080320Workshop on Statistical Methodology of Microarray DataReconstruction methods for inverse problems
Prof. Gen Nakamura ( Hokkaido University, Japan )2008  03  20 (Thu.)
11:20  12:20
308, Mathematics Research Center Building (ori. New Math. Bldg.)For the recent 10 years the several reconstruction methods have been proposed for inverse scattering problems and inverse boundary value problems. For instance they are the linear sampling method, factorization method, probe method, singular sources method, noresponse test, range test and enclosure method etc. These reconstruction methods are noniterative methods which means that they are not data fitting methods such as the least square methods or the regularized version of those. They provide how to reconstruct the unknowns directly from the given measured data. The lecture will touch the basic ideas of those methods and discuss about their convergence and relations between them. 
20080320Seminar on Graph ColoringCircular consecutive choosability of graphs (IV) Total distancetwo labelings of graphs
Prof. Daphne DerFen Liu ( California State University, Los Angeles, USA )2008  03  20 (Thu.)
13:30  15:30
405, Mathematics Research Center Building (ori. New Math. Bldg.) 
20080320Workshop on Statistical Methodology of Microarray DataInvisibility
Prof. Gunther Uhlmann ( Department of Atmospheric Sciences, University of Washington, USA )2008  03  20 (Thu.)
15:20  16:20
308, Mathematics Research Center Building (ori. New Math. Bldg.)We describe construction of electromagnetic parameters that make objects invisible to electromagnetic waves. 
20080320Seminar on Graph ColoringCircular consecutive choosability of graphs (III) Circular consecutive choosibility for odd cycles
Prof. Xuding Zhu ( Zhejiang Normal University, China )2008  03  20 (Thu.)
10:00  12:00
405, Mathematics Research Center Building (ori. New Math. Bldg.) 
20080320Student seminar on differential geometryComparison theorems in Riemann Geometry, ch1.2～1.3
Dr. Ryosuke Takahashi ( The Chinese University of Hong Kong )2008  03  20 (Thu.)
19:00  20:30
405, Mathematics Research Center Building (ori. New Math. Bldg.) 
20080320Workshop on Statistical Methodology of Microarray DataSmall volume imaging
Prof. Hyeonbae Kang ( Inha University, South Korea )2008  03  20 (Thu.)
14:00  15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)Lecture 1. Method of Small Volume Expansions and its Applications to Medical Imaging I will explain the mathematical theory of the small volume expansions in the context of the conductivity equation, which is the simplest possible model. I then discuss how this mathematical theory can be applied to an electrical impedance tomography problem to detect small inclusions buried inside a body. Lecture 2. Mathematical Analysis for MRElastography and Applications MRElastography is a recent modality to image the internal part of body using the internal measurements of the displacement vectors. One of the advantages of the imaging method using MRE over other methods is that it can detect the stiffness parameter of the tissue, by which we can distinguish malign cancer from benign cancer. In this lecture I will explain a new method of reconstruction using MRE data. Lecture 3. New reconstruction methods for Magnetoacoustic Imaging. A new and promising technique in the medical imaging is to excite a local part of body using acoustic or ultrasonic focusing and to measure changes due to the excitation. I will explain new reconstruction methods for the Magnetoacoustic imaging and the vibration potential tomography. 
20080320InvisibilityGunther Uhlmann20080320
10:00:00  11:00:00Invisibility308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080320Reconstruction methods for inverse problemsGen Nakamura20080320
11:20:00  12:20:00Reconstruction methods for inverse problems308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080320Small volume imagingHyeonbae Kang20080320
14:00:00  15:00:00Small volume imaging308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080320InvisibilityGunther Uhlmann20080320
15:20:00  16:20:00Invisibility308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080319Workshop on Statistical Methodology of Microarray DataReconstruction methods for inverse problems
Prof. Gen Nakamura ( Hokkaido University, Japan )2008  03  19 (Wed.)
11:20  12:20
308, Mathematics Research Center Building (ori. New Math. Bldg.)For the recent 10 years the several reconstruction methods have been proposed for inverse scattering problems and inverse boundary value problems. For instance they are the linear sampling method, factorization method, probe method, singular sources method, noresponse test, range test and enclosure method etc. These reconstruction methods are noniterative methods which means that they are not data fitting methods such as the least square methods or the regularized version of those. They provide how to reconstruct the unknowns directly from the given measured data. The lecture will touch the basic ideas of those methods and discuss about their convergence and relations between them. 
20080319Workshop on Statistical Methodology of Microarray DataInvisibility
Prof. Gunther Uhlmann ( Department of Atmospheric Sciences, University of Washington, USA )2008  03  19 (Wed.)
10:00  11:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)We describe construction of electromagnetic parameters that make objects invisible to electromagnetic waves. 
20080319Workshop on Statistical Methodology of Microarray DataSmall volume imaging
Prof. Hyeonbae Kang ( Inha University, South Korea )2008  03  19 (Wed.)
14:00  15:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)Lecture 1. Method of Small Volume Expansions and its Applications to Medical Imaging I will explain the mathematical theory of the small volume expansions in the context of the conductivity equation, which is the simplest possible model. I then discuss how this mathematical theory can be applied to an electrical impedance tomography problem to detect small inclusions buried inside a body. Lecture 2. Mathematical Analysis for MRElastography and Applications MRElastography is a recent modality to image the internal part of body using the internal measurements of the displacement vectors. One of the advantages of the imaging method using MRE over other methods is that it can detect the stiffness parameter of the tissue, by which we can distinguish malign cancer from benign cancer. In this lecture I will explain a new method of reconstruction using MRE data. Lecture 3. New reconstruction methods for Magnetoacoustic Imaging. A new and promising technique in the medical imaging is to excite a local part of body using acoustic or ultrasonic focusing and to measure changes due to the excitation. I will explain new reconstruction methods for the Magnetoacoustic imaging and the vibration potential tomography. 
20080319InvisibilityGunther Uhlmann20080319
10:00:00  11:00:00Invisibility308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080319Reconstruction methods for inverse problemsGen Nakamura20080319
11:20:00  12:20:00Reconstruction methods for inverse problems308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080319Small volume imagingHyeonbae Kang20080319
14:00:00  15:00:00Small volume imaging308 , Mathematics Research Center Building (ori. New Math. Bldg.) 
20080318Geometric AnalysisRicci flow
Prof. ChangShou Lin ( Department of Mathematics, National Taiwan University )2008  03  18 (Tue.)
09:10  12:00
405, Mathematics Research Center Building (ori. New Math. Bldg.) 
20080318Statistical MethodologyModel Checking for ROC Regression Analysis2008  03  18 (Tue.)
13:30  15:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)An overview of the paper “Model Checking for ROC Regression Analysis” by Cai and Zheng (2007) is given. A possible research topic and extension is also explored in this talk. 
20080314An Brief Introduction to Inverse Problems and InvisibilityProf. JennNan Wang ( Department of Mathematics, National Taiwan University )

20080314New Euler sums with two branchesProf. Minking Eie ( National Chung Cheng University )

20080314Computational Science on MedicineModelling, Simulation and ApplicationScientific Computing on HemodynamicsComputational Challenges and its Application to Surgical Planning for Cardiovascular Diseases
Prof. Tony WenHann Sheu ( Department of Engineering Science and Ocean Engineering, National Taiwan University )2008  03  14 (Fri.)
15:00  16:00
405, Mathematics Research Center Building (ori. New Math. Bldg.) 
20080314Seminar on multiscale Analysis and ComputationMultiscale modeling, asymptotic analysis, and their applications in finance (I,II)
Prof. ChuanHsiang Han ( Department of Quantitative Finance, National Tsing Hua University )2008  03  14 (Fri.)
10:20  12:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)During the last two decades, financial mathematics has emerging as an active branch in applied mathematics. Problems arising from modern finance are often resolved from applications of various techniques including probability and statistics, differential equations, optimization and control theory, scientific computations, etc. In this talk, the evaluation of financial derivatives under an incomplete market is treated by two approaches. First, multiscale modeling in volatility processes is shown to be powerful for calibration to the term structure of implied volatility surface. In mathematical terms, an inverse problem is solved from asymptotics of a PDE by means of singular and regular perturbations. Second, we consider the usage of Monte Carlo and Quasi Monte Carlo simulations to solve high dimensional PDEs. A variance reduction method, namely the martingale control variate method is proposed to improve the convergent speed. The martingale control comprises of a low dimensional PDE obtained from the homogenization of multiple time scales. This method turns out to be general enough to solve for variational inequalities. In financial terms, a delta hedging portfolio is effective to reduce the risk of a financial derivative. In the end, some challenging problems are discussed.