Pseudo-Partial Likelihood for Proportional Hazards Models with Biased-Sampling Data
Prof. Wei-Yann Tsai ( Department of Biostatistics, Columbia University, USA )2008 - 03 - 21 (Fri.)
14:30 - 17:00
502, Freshman Classroom BuildingWe obtain a "pseudo-partial likelihood" for proportional hazards models with biased-sampling data by viewing biased-sampling data as left-truncated data. The log pseudo-partial likelihood of the biased-sampling data is the expectation of the log partial likelihood of the left-truncated data conditioned on the observed data. In addition, asymptotic properties of the estimator which maximizes the pseudo-partial likelihood are derived. Applications to length-biased data, biased samples with right censoring, stratified samples, and proportional hazards models with missing covariates are also discussed.

Reconstruction 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, no-response test, range test and enclosure method etc. These reconstruction methods are non-iterative 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.

Pseudo-Partial Likelihood Estimators for Cox Regression Model With Missing Covariates
Prof. Wei-Yann 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 left-truncated and right-censored 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.

Jung-Chao Ban 2008-03-21
15:30:00 - 16:30:00 Dimension theory for non-conformal repeller308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Jung-Chao Ban 2008-03-21
13:30:00 - 15:00:00 Topological Pressure and Variational Principle308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Hyeonbae Kang2008-03-21
10:00:00 - 11:00:00Small volume imaging308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Gen Nakamura2008-03-21
11:20:00 - 12:20:00Reconstruction methods for inverse problems308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Invisibility
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.

Reconstruction 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, no-response test, range test and enclosure method etc. These reconstruction methods are non-iterative 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.

Circular consecutive choosability of graphs (IV) Total distance-two labelings of graphs
Prof. Daphne Der-Fen Liu ( California State University, Los Angeles, USA )2008 - 03 - 20 (Thu.)
13:30 - 15:30
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Invisibility
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.

Circular 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.)

Comparison 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.)

Small 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 Magneto-acoustic 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 Magneto-acoustic imaging and the vibration potential tomography.

Gunther Uhlmann2008-03-20
10:00:00 - 11:00:00Invisibility308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Gen Nakamura2008-03-20
11:20:00 - 12:20:00Reconstruction methods for inverse problems308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Hyeonbae Kang2008-03-20
14:00:00 - 15:00:00Small volume imaging308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Gunther Uhlmann2008-03-20
15:20:00 - 16:20:00Invisibility308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Reconstruction 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, no-response test, range test and enclosure method etc. These reconstruction methods are non-iterative 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.

Invisibility
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.

Small 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 Magneto-acoustic 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 Magneto-acoustic imaging and the vibration potential tomography.

Gunther Uhlmann2008-03-19
10:00:00 - 11:00:00Invisibility308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Gen Nakamura2008-03-19
11:20:00 - 12:20:00Reconstruction methods for inverse problems308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Hyeonbae Kang2008-03-19
14:00:00 - 15:00:00Small volume imaging308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Ricci flow
Prof. Chang-Shou Lin ( Department of Mathematics, National Taiwan University )2008 - 03 - 18 (Tue.)
09:10 - 12:00
405, Mathematics Research Center Building (ori. New Math. Bldg.)

Model 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.

Prof. Jenn-Nan Wang  ( Department of Mathematics, National Taiwan University )

Prof. Minking Eie  ( National Chung Cheng University )

Scientific Computing on Hemodynamics-Computational Challenges and its Application to Surgical Planning for Cardiovascular Diseases
Prof. Tony Wen-Hann 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.)

Multiscale modeling, asymptotic analysis, and their applications in finance (I,II)
Prof. Chuan-Hsiang 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.