应用数学研讨班每周举办一次，旨在促进应用数学与其它学科的交叉合作与交流。目前涵盖了计算科学、信息科学、生物信息和数理金融等研究方向。研讨班邀请国内外应用数学及相关领域中的专家学者报告他们的最新研究成果和学科发展动态。


联系人：袁燕 yyan AT math.pku.edu.cn Tel: 010-62751802 Fax: 010-62751801

2006年05月11日 星期四 下午（14:00-16:00, 1560）

Xiaoou Tang   MSRA Manager

题目：Subspace Face Recognition

摘要：Automatic face recognition has great potential in a large array of application areas, including security system access control, video surveillance, mug-shot matching for law enforcement, duplicate ID card detection, and multimedia information retrieval. In this talk, we focus on several recently developed algorithms in face recognition research. We first describe a framework that unifies current subspace face recognition algorithms. Under this framework, we can clearly see the advantage and disadvantage of each individual algorithm and discover the inherent relationship among different subspaces as well as their unique contributions to the extraction of discriminating information from the face images. We will also briefly discuss extension of the work based on random sampling and mixture models. At the end of the talk, we will show a few demos of other computer vision research topics from the visual computing group of MSRA.

2006年04月21日 星期五 上午（9:30-11:00, 1490）

Wei-Ying Ma 　MSRA Senior Researcher

题目：Object-level Vertical Search

摘要：Current Web search engines can be considered page-level general search engines with the main function of ranking web pages according to the relevance of given queries. However, we see an opportunity of further improving search technologies by developing specialty search engines that go deeper into vertical domains to provide more precise answers in search results. Vertical search will also be able to provide more relevant and intelligent search results since the method can data-mine associations and relations within data. In this talk, I will introduce the current status of web search and discuss this new trend toward building what I call “object-level vertical search engines.” The research problems we need to address include large-scale web classification, structured data extraction, and information aggregation and integration from a variety of sources, including data feeds and crawl. I will introduce recent research progress at MSR Asia and show how we are applying our developed technologies to build more advanced vertical search engines for such areas as shopping, academic search, and multimedia.

2006年04月04日 星期二 下午（14:00-15:30, 1303）

李航 微软亚洲研究院研究员

题目：Machine Learning Approaches to Information Retrieval.

摘要：In this talk, I will introduce the fundamental problem of 'search' from the viewpoint of machine learning. I will explain problem settings, existing methodologies, and challenges for the application task. I will also list up open problems for future research.

2005年12月28日星期三上午（10:10-11:30, 1560）

孙剑 微软亚洲研究院研究员

题目：Belief Propagation and its Applications on Stereo Matching and Image Completion.

摘要：Belief propagation is a generally applicable algorithm for statistics inference. In the first part of the talk, I will give the background and the basic idea of belief propagation algorithm. In the second part, I will introduce how to apply this algorithm to solve a computer vision problem - stereo matching, and a computer graphics problem – image completion.

2005年11月30日星期三上午（9:30-10:30, 1560）

Prof. Arie E. Kaufman
Distinguished Professor & Chair, Computer Science Department
Director, Center for Visual Computing，Stony Brook University (SUNY)

讲座题目： Virtual Colonoscopy

摘要：A combination of computed tomography (CT) scanning and volume visualization technology, called virtual colonoscopy (VC) is poised to become the procedure of choice in lieu of the conventional optical colonoscopy for mass screening for colon polyps – the precursor of colorectal cancer. The patient abdomen is imaged by a helical CT scanner during a 40-second single-breath-hold.? A 3D model of the colon is then reconstructed from the CT scan by automatically segmenting the colon out of the rest of the abdomen and employing an "electronic cleansing" algorithm for computer-based removal of the residual material. The visualization software, running on a PC, allows the physician to interactively navigate through the colon using volume rendering. An intuitive user interface with customized tools supports 3D measurements, "virtual biopsy" to inspect suspicious regions and "painting" to help in visualizing 100% of the colon surface. Unlike conventional optical colonoscopy, VC is patient friendly, fast, non-invasive, more accurate, cost-effective procedure for mass screening of colon polyps. Our university research of VC led to a license to a Stony Brook, NY company that has installed the technology in numerous sites, thousands of patients have been screened, and the lives of hundreds of patients have been saved. VC has been extended to 3D virtual endoscopy of other organs, such as the heart, arteries, lungs, stomach and bladder. The primary future challenge in VC is in the development of computer-aided detection (CAD) of colonic polyps.

2005年11月23日星期三上午（10:00-11:30, 1560）

沈向洋博士 微软亚洲研究院院长兼首席科学家

题目： Prior, Context and Interactive Computer Vision

2004年12月13日(4:30-5:30,1560S) 陈艳萍 教授，湘潭大学数学与计算科学学院

题目：Mixed Finite Element Methods for Optimal Control Problems

摘要:We consider the mixed finite element method for optimal control problems governed by elliptic equation. A priori and posteriori error estimator are developed at first. Furthurmore, certain super-convergence can be obtained for the problem under consideration.At last, we consider the problem with oscillatory quadratic coefficients and give the priori error estimator.

2004年10月26日(4:30-5:30,1560S) 丘枫 教授，复旦大学 高分子科学系

题目：Simulations of Structure and Dynamics of Complex Fluids

2004年10月12日(4:30-5:30,1303M)严大东 研究员，中国科学院化学所

题目:On the ordering of polymer melts

2004年 8月4日(4:00-5:00,1114M)徐鉴君 教授,McGill University, Canada

题目:Interfacial Wave Theory of Pattern Formation:Selection of dendritic growth and Viscous Fingering in Hele-Shaw Flow

2004年7月30日(4:00-5:00,1418M)An-Chang Shi,Department of Physics and Astronomy，McMaster University

题目:Self-Assembly of Block Copolymers

摘要:Due to their amphiphilic nature, block copolymers form a variety of ordered microphases. The phase behavior of diblock copolymer melts has attracted considerable experimental and theoretical attention. Theoretical studies of block copolymer phase behavior have been mostly within mean-field
approximation. A theoretical framework beyond the mean-field approximation
has been developed to study the stability of, and the kinetic pathways between, the ordered phases. After a brief survey of the block copolymer phase behavior, I will use two examples to illustrate the application of the theory to block copolymer systems. (1) The Gaussian fluctuation theory allows the study of spinodal lines, fluctuation modes, and scattering functions of the ordered phases. (2) The mean field theory allows the study of nucleation in order-order phase transitions.

2004年7月26日(4:30-5:30,1114M)Prof. Wolfgang Hackbusch,Max-Planck-Institut Mathematik in den Naturwissenschaften

题目:Hierarchical matrices

2004年7月5日(10:30-11:30,1560S)林治武 教授,Courant Institute, New York University

题目:Nonlinear instability of ideal plane flows

2004年7月5日(8:30-9:30,1560S)罗智全 教授,University of Minnesota

题目:Extensions of S-procedure and Their Applications

摘要:Nonlinear instability of ideal plane flowsIn this talk, we discuss issues related to the characterization of specific convex cones of multivariate and nonlinear mappings that are nonnegative over a given domain. The nonnegativity is defined by a pre-described conic order. In particular, we give linear matrix inequality description for the cone of affine linear/quadratic mappings in the order defined by a positive semidefinite matrix cone. We will also describe some applications of our results in robust optimization and digital beamforming.

2004年7月1日(16:30-17:30,1560S)李彤 教授,University of Iowa, US

题目:On the dynamics of traffic jams

2004年6月25日(16:00-17:00,1560S)Prof.Xue-Cheng Tai, Department of Mathematics University of Bergen, Norway.

题目:Image processing using PDE tools and Shape identification using level set methods

摘要：In this talk, we will try to explain some of the ideas we have used in image analysis which include noise removal, image segmentation and image registration. We have used both TV-norm (total variation norm) regularization and level-set method for these problems. The talk will be divided into two parts.
In the first part, we try try to explain the essential ideas behind PDE (partial differential equation) methods used for noise removal. We will start with the linear removal methods used earlier and then come to the recent nonlinear filters including the well-known TV-filters. In the end, we will present a new 4th order PDE nonlinear filter. The advantages of the new filter will be explained and some of the other appraoches that are still under testing will also be explained.
In the second part, we will try to present the elementarty idea of the level-set methods. For some applications, we need to find the geometry of curves in 2D and surfaces in 3D to fit some criteria we impose. As a computational tool, level set methods are rather flexible and have proved to be able to capture rather complicated geometries in some design problems. In this part, I will summarize several joint works done with different colloborators recently about using level set methods and total variation regularization for inverse type of problems. The unifying theme is using total variation for regularization and using level sets for representing the geometry of discontinuities. Applications include elliptic inverse problems, positron emission tomography, electrical impedance tomography, digital image segmentation.

2004年6月7日 (16:15-17:00; 1560S) Prof Tao Pang, North Carolina State University

题目：A Stochastic Control Model of Investment, Production and Consumption

摘要：We consider a stochastic control model in which an economic unit has productive capital and also liabilities in the form of debt. The worth of capital changes over time through investment, and also through random Brownian fluctuations in the unit price of capital. Income from production is also subject to random Brownian fluctuations. The goal is to choose investment and consumption controls which maximize total expected discounted HARA utility of consumption. Optimal control policies are found using the method of dynamic programming. In the case of logarithmic utility, these policies have an explicit form. This is a joint work with Wendell Fleming.



2004年6月7日 (17:00-17:45; 1560S) Prof Shi-Jie Deng,  Georgia Institute of Technology

题目：A Semi-Dynamic Approach for Valuing and Hedging a Spread Option with Continuous Payout

摘要： We consider the problem of replicating the payoffs of a spread option with a fixed finite maturity which pays the spread between two underlying assets’ prices for every day that the spread is positive. Following Carr et al. (2001), we present an alternative approach which combines dynamic trading in the underlying assets with static positions in either one spread option or a couple of Call/Put options of one single maturity. In markets where not many options are liquidly traded such as in the electricity markets, this approach provides a practical way for hedging long-term financial/physical assets with underlying commodities and a few options.
　　

2004年5月20日 (4:00pm-5:00pm,1560S)  Prof.Youlan Zhu (美国.北卡罗大学)

题目：Three-Factor Interest Rate Models & Numerical Solution of American Swaptions

摘要：In the talk, the prices of three zero-coupon bonds are chosen as state random variables. These random variables are defined on a finite domain and pricing of interest rate derivatives are reduced to solving a final-value problem of degenerate parabolic equations on a finite domain. All the coefficients in the P.D.E. can be easily obtained by the market data and the model can be really applied to evaluting interest rate derivatives in practice. As an example, numerical solution of American swaptions will be described and numerical results will be given. 

2004年5月20日 (2:30pm-3:30pm,1560S)  Prof. E. Platen (Uinv.of Tech.Sydney,澳大利亚)

题目：Modeling the Volatility and Expected Value of a Diversified World Index

摘要: This paper considers a diversified world stock index in a continuous financial market with the growth optimal portfolio (GOP) as reference unit or benchmark. Diversified broadly based indices and portfolios, which include major world stock market indices, are shown to approximate the GOP. It is demonstrated that a key financial quantity is the trend of a world index. It turns out that it can be directly observed since the expected increments of the index equal four times those of the quadratic variation of its square root. Using a world stock index as approximation of the discounted GOP it is shown that, in reality, the trend of the discounted GOP does not vary greatly in the long term. This leads for a diversified world index to a natural model, where the index is a transformed square root process of dimension four. The squared index volatility appears then as the inverse of the square root process. This feature explains most of the properties of an index and its volatility.

2004年4月27日 (16:30-17:30)  侯一钊 教授   加州理工大学

题目：流体的几何性质对奇异解的影响

摘要：Whether the three-dimensional incompressible Euler or Navier-Stokes equation can develop a finite time singualrity from smooth initial data has been an outstanding open problem. It has been believed that a finite singularity of the 3D Euler equation could be the onset of turbulence. Here we will review some existing computational and theoretical work on possible finite blow-up of the 3D Euler equation. Further, we show that there is a sharp relationship between the geometric properties of the vorticity field and the maximum vortex stretching. Such a sharp relationship enables us to obtain a global existence of the 3D Euler equation with a very localized and mild regularity of vorticity field. The local weak geometric regularity of the vorticity field seems to be consistent with the observations from recent numerical computations. Our study offers a possible scenario of a dynamic nonlinearity depletion for the 3D incompressible flow. Implication of this finding on turbulent flow will be discussed.

2004年4月22日 (16:00-17:00, 1560S)  彭实戈  教授 山东大学数学系

题目：关于未定权益定价机制的研究

2004年3月2日 (16:30-17:30)  唐少强  副教授,  北京大学力学与工程科学系

题目：半导体VQHD模型的数值研究

摘要：The viscous quantum hydrodynamic equations for semiconductors with constant temperature are numerically studied. They consist of the one-dimensional Euler equations for the electron density and current density, including a quantum correction and viscous terms, coupled to the Poisson equation for the electrostatic potential. The equations can be derived formally from a Wigner-Fokker-Planck model by a moment method. Two different numerical techniques are used: a hyperbolic relaxation scheme and a central finite-difference method. By simulating a ballistic diode and a resonant tunneling diode, it is shown that numerical or physical viscosity changes significantly the behavior of the solutions. Moreover, the crurent-voltage characteristics show negative differential resistance and hysteresis effects.
　　　　　　　

2004年1月13日 (16:00-17:00)  Prof. Qing Nie,  Department of Mathematics，Department of Biomedical Engineering，Center for Complex Biological Systems, University of California, Irvine）

题目：Numerical Simulations of  Tumor Growth

摘要：In this talk, we study solid tumor growth using numerical simulations.The tumor evolution is described by a classical model of moving boundary with a reduced set of two new dimensionless parameters.One parameter describes the relative rate of mitosis to the relaxation mechanisms (cell-mobility and cell-to-cell adhesion). The other describes the balance between apoptosis (programmed cell-death)and mitosis. Our analysis and simulations reveal that the new dimensionless parameters divide tumor growth into three regimes associated with increasing degrees of vascularization. We demonstrate that critical conditions exist for which the tumor evolves to non-trivial dormant states or grows self-similarly.  Away from these critical conditions, evolution may be unstable leading to invasive fingering and topological transitions such as the capture of healthy tissue by the tumor.

2004年1月6日 (16:00-17:00)  Prof. Chi-Kwong Li Department of Mathematics, College of William And Mary

题目：Eigenvalues, singular values, and Littlewood -Richardson Coefficients

摘要：We characterize the relationship between the singular values of a Hermitian (resp., real symmetric, complex symmetric) matrix and the singular values of its off-diagonal block. We also characterize the eigenvalues of a Hermitian (or real symmetric) matrix C=A+B in terms of the combined list of eigenvalues of A and B. The answers are given by Horn-type linear inequalities The proofs depend on a new inequality among Littlewood-Richardson coefficients.

2003年12月23日  廖琦 教授 中科院化学所

题目：MD simulation of polymer system

2003年12月16日 欧阳钟灿 院士 中科院理论物理所

题目：Mathematical Problems in Elastic Theories of Biomembranes and Single-Molecule DNA/RNA/Protein.

2003年12月4日(周四4:30pm-5:30pm,1490) 曹天仁 博士 CmpuSensor Technology Corporation

题目：图像识别与跟踪的泛函分析和李群方法

2003年12月2日  O'Brien 教授 加洲大学伯克利分校金融工程班负责人

题目：Fund Investment Strategy: A New Paradigm

2003年11月18日 Dr. Liu Tiegang, Institute of High Performance Computing (IHPC), Singapore

题目：Ghost Fluid Method in Compressible Gas-Water Flow

2003年11月14日(周五2:30pm-3:30pm,1114M)  周迅宇教授 香港中文大学
 
题目：Continuous-Time Mean--Variance Portfolio Selection with Bankruptcy Prohibition

摘要：A continuous-time mean--variance portfolio selection problem is studied where all the market coefficients are random and the wealth process under any admissible trading strategy is not allowed to be below zero at any time. The problem is completely solved using a decomposition approach. Specifically, a (constrained) variance minimizing problem is formulated and its feasibility is characterized. Then, after having solved a system of equations for two Lagrange multipliers, variance minimizing portfolios are derived as the replicating portfolios of some contingent claims, and the variance minimizing frontier is obtained. Finally, the efficient frontier is identified as an appropriate portion of the variance minimizing frontier after the monotonicity of the minimum variance on the expected terminal wealth over this portion is proved, and all the efficient portfolios are found. In the special case where the market coefficients are deterministic, efficient portfolios are explicitly expressed as feedback of the current wealth, and the efficient frontier is represented by parameterized equations. Our results indicate that the efficient policy for a mean--variance investor is simply to purchase a European put option that is chosen, according to his or her risk preferences, from a particular class of options. This is a joint work with Tomasz R. Bielecki, Hanqing Jin, and Stanley R. Pliska.
　

2003年11月11日  戴民博士 北京大学数学学院金融数学系

题目: 衍生证券定价中的一些数学问题

2003年10月28日(3：30pm－4：30pm,1114M)  王辰树教授 台湾成功大学数学系
 
题目：A structure-preserving doubling algorithm for periodic algebraic Riccati Equations

2003年10月28日(4：30pm－5：30pm,1114M)  林文伟教授 台湾清华大学数学系

题目: Numerical Methods for Positive Bound States of A Multi-Component Bose-Einstein Condensate

2003年10月24日 鄂维南教授 北京大学数学学院、Princeton University

题目: Applied Math and Computational Science: A Personal Perspective


2003年10月21日：Prof Jian-feng Yao IRMAR, University of Rennes 1, France.

题目：A multiple-imputation Metropolis version of the EM algorithm
摘要：In this paper we introduce a new stochastic variant of the EM algorithm. The algorithm combines the principle of multiple imputaion and the theory of simulated annealing to deal with cases where the E-step and the M-step can be intractable or numerically inefficient.

2003年10月14日：郝鹏威博士 北京大学信息科学中心、英国伦敦大学Queen Mary学院计算机系

题目：矩阵的PLUS分解及其应用
摘要：在线性变换的一些应用中，我们希望变换矩阵能分解为若干具有用户要求的某种形式或功能的矩阵，如单位三角、整数可逆。我们把这种可以根据用户要求定制的三角分解称为可定制三角分解（Customizable Triangular Factorizations），在形式上是A=PLUS，P为置换矩阵或伪置换矩阵，L为单位下三角矩阵，U为上三角矩阵且所有对角线元素可以由用户给定，S为一个用户有很大自由度可以选择的特殊矩阵。因此，我们也称之为矩阵的PLUS分解。在PLUS分解的基础上，矩阵就可以很容易进一步分解为一系列的用户可以定制的特殊矩阵。PLUS分解在信号变换中可以实现整数信号的无损可逆变换，这可以用于信号的无损压缩、信息隐藏等。PLUS分解在图形学中，可以实现投影变换的错切分解，而每一个错切变换都可以在存储器一级高速实现，所以PLUS分解还可以用于图象或体数据绘制中的变换加速。类似地，在图象或体数据的配准或拼接中，PLUS分解也可以应用于变换的高速实现。

2003年10月7日：欧阳颀教授 北京大学物理学院

题目：“蛋白质网络动力学研究”
摘要：分子生物学的动力学研究是生物学向定量化迈进的一个较好的突破口。我们研究了酵母菌细胞分裂的网络动力学，发现该网络具有一下特殊性质：（1）生物定态是一个全局稳定态；（2）细胞分裂的生物路径是一个一维稳定流形。这些动力学性质可能是生物系统共有的动力学性质。