中国留德学人数学与应用数学学会2012年学术交流年会
(GCMA Jahrestagung 2012 & Workshop)
会议通知
会议地点：德国，卡尔斯鲁厄(Karlsruhe)
会议日期：2012年12月1日，周六
主办：中国留德学人数学与应用数学学会（GCMA，http://www.gcma-ev.de/）
会议通知 （PDF）， 会议日程表 （PDF）
又到岁末，又是一年丰收时。中国留德学人数学与应用数学学会2012年学术交流年会将于12月1日在德国南部城市卡尔斯鲁厄举行。此次学术交流年会的内容包括三部分，即数学学会工作和财务报告，学术报告研讨以及求职和工作介绍。
学术报告研讨的主题为“数学在计算机和经济领域中的应用”，报告者是卡尔斯鲁厄理工学院计算机系和数学系的若干位教授、博士和博士生以及在金融领域工作的一些朋友。报告的内容包括数学在实时系统、算法分析、人脸建模和重构、医学手术领域和燃烧模拟方面的应用，数学在金融市场中最优投资组合模型里的应用，以及数学界中非常有趣的扭结理论和十分著名的朗兰兹纲领的介绍。
在求职和工作介绍模块中，若干位数学系和计算机系毕业的同学将介绍各自的工作经验，同时一位来自国内的访问教授将给大家谈谈中国高校目前引进人才的政策。
此次学术交流会不只针对数学学会的会员，而且面向广大数学爱好者和留学生。在此我们邀请您参加本次学术交流会，也欢迎您向您的朋友们介绍我们的活动。让我们共同期待，在莱茵河畔的卡尔斯鲁厄度过充满数学之美的难忘时光！
会议日程表：
会议报名：
有意参加本次学术交流会的朋友请于11月24日前将姓名、学历、单位和联系方式电邮给李泽旌：zejingli@stoch.uni-karlsruhe.de
会议地点：
卡尔斯鲁厄理工学院（KIT）南校区，Institute for Process Control and Robotics (IPR), Building 40.28, Seminarraum 001.2, Engler-Bunte-Ring 8, 76131 Karlsruhe
会议联系人：
陈琪博士： chenqi@ira.uka.de
李泽旌：zejingli@stoch.uni-karlsruhe.de
中国留德学人数学与应用数学学会理事会
2012年11月17日
学术报告摘要
JProf. Dr. Gabriela Weitze-Schmithüsen (Institute für Algebra und Geometrie, KIT)
Wenige andere mathematische Themen eignen sich so hervorragend um Außenstehende mit Mathematik in Berührung zu bringen und ihnen zu zeigen, wie spannend und voller Spaß dieses Fach sein kann. Gleichzeitig fordert es Mathematiker als eine faszinierende und mit Überraschungen versehene Theorie heraus.
Der besondere Reiz des Themas besteht darin, dass es sich bei der Klassifikation von Knoten um eine mathematische Fragestellung handelt, die auf allgemeinverständlichem Niveau sogar schon für Grundschulkinder zugänglich ist. Trotzdem konnte sie bis heute nicht vollständig gelöst werden und ist ein Beispiel aktueller mathematischen Forschung.
Dr. 陈琪 (Institut für Betriebs- und Dialogsysteme, KIT)
Subdivision curves and surfaces are the limits of sequences of repeatedly refined control polygons. Subdivision surfaces are valued in geometric modeling and in computer graphics for their convenience and flexibility to represent freeform objects of arbitrary topology and for their intimate connection with multiresolution analysis. They can be naturally applied to level-of-detail rendering and adaptive approximation. Nowadays, subdivision is often used in movie production and it is a core technology in game engines.
In this talk we first see some famous stationary subdivision schemes, e.g., the Chaikin scheme, the Doo-Sabin scheme, the Catmull-Clark scheme, the Loop scheme, the Lane-Riesenfeld scheme and the midpoint scheme. We learn some basic properties of stationary subdivision schemes.
The smoothness property of subdivision surfaces is one of the most important properties for subdivision schemes. The analysis of the smoothness property is usually easy at regular points but extremely difficult at extraordinary points. In the second part of this talk, we introduce some methods for analyzing the smoothness property.
In the last part of the talk, a new technique developed by the speaker is introduced, which enables analyzing the smoothness property of infinitely many subdivision schemes at extraordinary points. Some new classes of subdivision schemes are developed and analyzed by this technique.
高华 (Facial Image Processing and Analysis, KIT)
Facial image analysis has found its application in various fields including security, entertainment, multimedia indexing, human-machine interaction, etc. Essentially, as an early step for facial image analysis, face alignment has a large impact on the robustness and quality of the later processes. Face alignment has been studied for several decades, yet it is still an open problem which suffers from the confounding factors of intrinsic and extrinsic imaging conditions. Due to these challenges, it is still an interesting research problem and receives increasing attention. In particular, deformable model based face alignment became very popular since the invention of the Active Shape Model (ASM) and the Active Appearance Model (AAM). Numerous successful application systems have been developed based on the deformable model.
However, the AAM suffers from generalization problem due to generative appearance modeling and least square minimization. In this work, the appearance of a deformable model is modeled in a discriminative manner, which results in a score function of shape parameters for a given image. The score function indicates goodness of an alignment. Aligning a face image is equivalent to optimize the score function subject to shape parameter. The discriminative appearance modeling and the learned cost function for optimization mitigate the generalization problem to some extent.
The main contribution of the research in this work is two-fold. First, an efficient feature representation for learning the discriminative appearance models is proposed. The proposed feature representation is robust to illumination variations. Second, we explore discriminative appearance modeling in three difference perspectives of machine learning problems. The first model considers alignment as classification, in which correct alignment is regarded as positive sample and incorrect alignment as negative sample. The second model learns the partial ordering of alignments based on learning to rank problem, while the third model learns total constraint ordering of alignments based on regression.
The optimization of the learned score functions is based on gradient ascent or derivative-free method. We conduct experiments on different data-sets to show different levels of generalizability. Extensive experiments demonstrate that the discriminative appearance models are superior to generative models in terms of generalizability. Models based on ranking and regression are superior to classification based models due to the increased smoothness in the score function. Furthermore, ordinal regression-based on ensemble of regression trees achieves best performance in this study.
张耀坤 (Institut für Prozessrechentechnik, Automation und Robotik, KIT)
Cochleostomy is a vital step of cochlear implantation (CI) to create an insertion channel on the cochlea for the electrode array of the implant. During the process, the lining membrane under the bone tissue of cochlea is not allowed to be injured.
As a contactless tool with high precision, laser is ideal to perform the cochleostomy. With an axial resolution on the micrometer scale and penetration depth up to 1 mm into bone tissue, optical coherence tomography is a promising candidate for monitoring the bottom of the drilled channel and guide the ablation laser to avoid injury to the critical structure. Meanwhile, OCT can be also used as a tracking system with the accuracy of several tens micrometers, which is ten times more accurate compared with conventional marker based tracking system.
JProf. Dr. 陈建佳 (Chair of Micro Hardware Technologies for Automation, KIT)
Real-time systems play a crucial role in many applications, such as avionic control systems, automotive electronics, telecommunications, industrial automation, and robotics. Such safety-critical applications require high reliability in timing assurance to prevent from serious damage to the environment and significant human loss. In this talk, I will give a brief historical overview of the development of real-time systems, and provide the mathematical rationales for the design and analysis of scheduling algorithms for such timing critical systems.
赵经纬 (Institute für Algebra und Geometrie, KIT)
During the last half-century the theory of automorphic forms has become a major focal point of development in number theory and algebraic geometry, with applications in many diverse areas, including combinatorics and mathematical physics.
The Langlands programme gives a very broad picture connection automorphic forms and L-functions. It roughly states that, among other things, any L-function defined number-theoretically is the same as the one which can be defined as the automorphic L-function of some GL(n). In this loose way, every L-function is conjecturally viewed as one and the same object.
This talk will give a brief introduction to the theory of automorphic forms and an overview of the Langlands programme.
李泽旌 (Institut für Stochastik, KIT)
We consider a multi asset financial market with stochastic volatility modeled by a Wishart process. In this framework we study the problem of maximizing the expected utility of terminal wealth. The Wishart model is called correlated, if the stock price process and the Wishart volatility process are correlated. In this talk we take 4 cases into consideration: the logarithmic utility case in the uncorrelated and correlated models; the power utility case in the uncorrelated and correlated models. We obtain the optimal portfolio strategies and study the value functions. In particular for the power utility, the explicit finite value function is derived in the case that the assets drift is a linear function of the volatility matrix and the conditions for its existence are also obtained.
张飞驰 (Engler-Bunte-Institut Bereich Verbrennungstechnik, KIT)
At present, over 80% of our worldwide energy support (e.g., for cars, air planes, electrical power generation, heating) is provided by combustion of fossil fuels. In current technology, it is impossible to replace fossil fuel usage by wind, solar cell power, or any other renewable energy source. However, combustion also produces pollutants such as NOx and soot. Ever more stringent regulations are forcing industries (automobile, power plants etc.) to reduce pollutant emissions, for the sake of our environment. In addition, unavoidable emissions of CO2 are believed to contribute to the greenhouse effect. We are faced with a serious energy problem related with the diminishing reserves of fossil fuels as the population of the planet increases. Therefore, improving the efficiency of the combustion process, thereby increasing fuel economy still remains as key technology today and for the foreseeable future.
Computational fluid dynamics (CFD) is a numerical tool to simulate fluid motions related with different chemico-physical phenomena like turbulent flow and combustion. In general, CFD modeling of turbulent combustion demands the solution of the basic conservation equations for total mass, momentum, species mass and energy. Once a stable and reliable mathematical model is developed for the underlying physics such as combustion or turbulence, the application of the model to new design geometries could be tested much more economically by CFD methods compared to the conventional diagnostic measurement. Popularity of CFD has been drastically increased in the last decade due to the tremendous progress in computational powers.
The current talk gives an introduction about numerical simulation of turbulent combustion, where additionally to the standard complexities of turbulent non-reacting simulation, other difficulties, such as the strong heat release and the complex chemical reaction behind the combustion process, have to be taken into account. During the talk, basic equations governing the fluid motion and combustion reaction will be discussed and the numerical method to solve the coupled, nonlinear partial differential equations will be described briefly. Some application cases from author’s research work will be presented at the end.