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Convergence analysis of the adaptive finite element method with the red-green refinement

Science China Mathematics 2010年第2期53卷 499-512页

作者： ZHAO XuYing 1, 3 , HU Jun 2,? & SHI ZhongCi 1 1 State key laboratory of scientific and engineering computing, Institute of Computational Mathematics and scientific/engineering computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 2 key laboratory of Mathematics and Applied Mathematics (Peking University), Ministry of Education and School of Mathematical Sciences, Peking University, Beijing 100871, China 3 Graduate University of Chinese Academy of Sciences, Beijing 100190, China 1. State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China3. Graduate University of Chinese Academy of Sciences Beijing 100190 China2. Key Laboratory of Mathematics and Applied Mathematics (Peking University) Ministry of Education and School of Mathematical Sciences Peking University Beijing 100871 China

In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Galerkin-orthogonality does not hold for this case. To overcome such a difficulty, we prove some quasi-orthogonality instead under some mild condition on the initial mesh (Condition A). Consequently, we show convergence of the adaptive method by establishing the reduction of some total error. To weaken the condition on the initial mesh, we propose a modified red-green refinement and prove the convergence of the associated adaptive method under a much weaker condition on the initial mesh (Condition B).

关键词： red-green refinement adaptive finite element method convergence non-nested local refinement

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Vigilance analysis based on continuous wavelet transform of EEG signals

Vigilance analysis based on continuous wavelet transform of ...

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2010 International Conference on Biomedical engineering and Computer Science, ICBECS 2010

作者： Ouyang, Tian Lu, Hong-Tao MOE-MS Key Laboratory for Intelligent Computing and Intelligent Systems Department of Computer Science and Engineering Shanghai Jiao Tong University Shanghai China

ISBN: (纸本)9781424453153

Electroencephalography (EEG) is considered a reliable indicator of a person's vigilance level. In this paper, we use EEG recordings to discriminate three vigilance states of a person, namely alert, drowsy, and sleep, while driving a car in a simulation environment. The proposed framework explores the use of continuous wavelet transform in EEG signal processing. A large set of features is extracted from the wavelet coefficients, which are computed from EEG signals with multiple wavelet functions. We use random forest to rank the plenty of features and select the most important ones for later classification. Samples of EEG data are then trained and classified by SVM (Support Vector Machine). On datasets acquired from 5 subjects, our method reveals high classification accuracy (over 96%). ©2010 IEEE.

关键词： Electroencephalography

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Finite element method for a nonsmooth elliptic equation

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中国高等学校学术文摘·数学 2010年第2期5卷 191-209页

作者： Lili CHANG Wei GONG Ningning YAN State Key Laboratory of Scientific and Engineering Computing Institute of Systems Science Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100190 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100190 China

In this paper, we study the finite element method for a nonsmooth elliptic equation. Error analysis is presented, including a priori and a posteriori error estimates as well as superconvergence analysis. We also propose two algorithms for solving the underlying equation. Numerical experiments are employed to confirm our error estimations and the efficiency of our algorithms.

关键词： Finite element method nonsmooth elliptic equation a priori error estimate a posteriori error estimate superconvergence analysis active set method

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Flatten hierarchies for large-scale hierarchical text categorization

Flatten hierarchies for large-scale hierarchical text catego...

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International Conference on Digital Information Management

作者： Wang, Xiao-Lin Lu, Bao-Liang Center for Brain-Like Computing and Machine Intelligence Department of Computer Science and Engineering China MOE-Microsoft Key Laboratory for Intelligent Computing and Intelligent Systems Shanghai Jiao Tong University China

ISBN: (纸本)9781424475728

Hierarchies are very popular in organizing documents and web pages, hence automated hierarchical classification techniques are desired. However, the current dominant hierarchical approach of top-down method suffers accuracy decrease compared with flat classification approaches, because of error propagation and bottom nodes' data sparsity. In this paper we flatten hierarchies to relieve such accuracy decrease in top-down method, which aims to make hierarchies both effective enough to make large-scale classification tasks feasible, and simple enough to ensure high classification accuracy. We propose two flattening strategies based on these two causes of the accuracy decrease, and experimental results show that the flattening strategy designed for error propagation is more effective, which suggests that hierarchies with lots of branches at top layers can provide high classification accuracy. Besides, we analyze the computational complexity before and after flattening, which approximately agree with the experimental results. ©2010 IEEE.

关键词： Websites

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Flexible alignment of images using B-spline reparameterization and L 2-gradient flows

Flexible alignment of images using B-spline reparameterizati...

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International Congress on Image and Signal Processing

作者： Xu, Guoliang Zheng, Yanmei State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100190 China

ISBN: (纸本)9781424465149

In this paper, we present a new flexible alignment method to align two or more similar images. By minimizing an energy functional measuring the difference of the initial image and target image, a L2-gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and a semi-implicit Euler scheme in the temporal direction. The experimental results show that the proposed method is efficient, effective and capable of capturing large variation of the initial and the target images. ©2010 IEEE.

关键词： Finite element method

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A unified character-based tagging framework for chinese word segmentation

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ACM Transactions on Asian Language Information Processing 2010年第2期9卷 1–32页

作者： Zhao, Hai Huang, Chang-Ning Li, Mu. Lu, Bao-Liang Department of Computer Science and Engineering MOE-Microsoft Key Laboratory for Intelligent Computing and Intelligent Systems Shanghai Jiao Tong University 800 Dongchuan Road Minhang District Shanghai 200240 China Language Computing Group Microsoft Research Asia 49 Zhichun Road Haidian District Beijing 100080 China

Chinese word segmentation is an active area in Chinese language processing though it is suffering from the argument about what precisely is a word in Chinese. Based on corpus-based segmentation standard, we launched this study. In detail, we regard Chinese word segmentation as a character-based tagging problem. We show that there has been a potent trend of using a character-based tagging approach in this field. In particular, learning from segmented corpus with or without additional linguistic resources is treated in a unified way in which the only difference depends on how the feature template set is selected. It differs from existing work in that both feature template selection and tag set selection are considered in our approach, instead of the previous feature template focus only technique. We show that there is a significant performance difference as different tag sets are selected. This is especially applied to a six-tag set, which is good enough for most current segmented corpora. The linguistic meaning of a tag set is also discussed. Our results show that a simple learning system with six n-gram feature templates and a six-tag set can obtain competitive performance in the cases of learning only from a training corpus. In cases when additional linguistic resources are available, an ensemble learning technique, assistant segmenter, is proposed and its effectiveness is verified. Assistant segmenter is also proven to be an effective method as segmentation standard adaptation that outperforms existing ones. Based on the proposed approach, our system provides state-of-the-art performance in all 12 corpora of three international Chinese word segmentation bakeoffs. © 2010 ACM 1530-0226/2010/06-ART5 $10.00.

关键词： Learning systems

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Fast facial fitting based on mixture appearance model with 3D constraint

Fast facial fitting based on mixture appearance model with 3...

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Chinese Conference on Pattern Recognition

作者： Huang, Xiangsheng Gong, Lujin Wang, Xiaoyan Institute of Automation Chinese Academy of Sciences Beijing 100190 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Beijing 100190 China College of Computer Science and Technology Zhejiang University of Technology Hangzhou 310023 China

ISBN: (纸本)9781424472109

Fast facial points fitting plays an important role in applications such as Human-Computer Interaction, entertainment, surveillance, and is highly relevant to the techniques of facial expression analysis, face recognition, 3D face model generation, etc. Active Appearance Models (AAMs) are generative models commonly used to fit face. They are sensitive to illumination and expression changes because they use only raw intensity to build observation models. In this paper, a real time facial points fitting approach using mixture observation models is presented. Furthermore, the 3D modes are used to constrain the AAM so that it can only generate model instances that can also be generated with the 3D modes. Finally, we give a derivative process for fast energy minimization using the inverse compositional algorithm. A coarse-to-fine fitting strategy is used for realtime and robust facial points fitting. We apply this algorithm to facial expression cloning of 3D Avatar system. Experimental results demonstrate that fitting the AAM with mixture observation models and 3D constraint outperforms other classical algorithms. ©2010 IEEE.

关键词： Mixtures

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Comparative analysis of motor imagery on different scales based on brain computer interface

Comparative analysis of motor imagery on different scales ba...

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作者： Li, Junhua Zhang, Liqing Department of Computer Science and Engineering MOE-Microsoft Key Laboratory for Intelligent Computing and Intelligent Systems Shanghai Jiao Tong University Shanghai 200240 China

The event-related brain oscillatory responses have a substantial role in motor imagery experiments. There are two patterns, i.e. event-related desynchronization (ERD) and eventrelated synchronization (ERS). In clinical applications and scientific experiments, an obvious event-related potential (ERP) is pivotal to achieve required tasks. Therefore, we explore how subjects generate the obvious ERP more easily. Eight healthy subjects participated in the experiments and completed motor imagery on two different scales (index finger versus arm). The results indicate that the motor imagery of arm reaches the better performance compared with the motor imagery of index finger. Furthermore, we make a comparative analysis in averaged power spectrum in order to reveal inherent phenomenon. The analysis of power spectrum further confirms that arm motor imagery has an advantage over index finger motor imagery.

关键词： Brain computer interface

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A new reconstruction algorithm in tomography with geometric feature-preserving regularization

A new reconstruction algorithm in tomography with geometric ...

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International Conference on BioMedical engineering and Informatics (BMEI)

作者： Chong Chen Guoliang Xu Institute of Computational Mathematics and Scientific Engineering Computing State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences Beijing China Institute of Computational Mathematics and Scientific Engineering Computing State Key Laboratory of Scientific and Engineering Computing Chinese Academy and Sciences Beijing China

We present a new optimization-based reconstruction model with geometric feature-preserving regularization. The previous construction approach of optimization-based requires generally solving a tremendously large discrete linear system. In addition, the analytic algorithms, such as, back-projection related methods, Fourier transform based reconstruction algorithms, are sensitive to noise. These disadvantages motivate us naturally to present a new optimization-based regularization algorithm, as distinct from traditionally constructing a discrete linear system, that is based upon a continuous energy functional model like analytic one. Some theoretical derivations and numerical computing of our model are discussed. Experimental results illustrate the desirable performance of the algorithm under various noiseless data situations. And the geometric feature-preserving regularizer is used in numerical simulations to demonstrate the robustness and effectiveness of the algorithm under various contaminated data scenarios.

关键词： Image reconstruction Noise Distributed databases Mathematical model Computational modeling Numerical models Computed tomography

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Kinetics of diffusion-controlled enzymatic reactions with charged substrates

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PMC Biophysics 2010年第1期3卷 1-5页

作者： Lu, Benzhuo McCammon, J Andrew State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China Department of Chemistry and Biochemistry Center for Theoretical Biological Physics Department of Pharmacology Howard Hughes Medical Institute La Jolla CA 92093-0365 United States

The Debye-Hückel limiting law (DHL) has often been used to estimate rate constants of diffusion-controlled reactions under different ionic strengths. Two main approximations are adopted in DHL: one is that the solution of the linearized Poisson-Boltzmann equation for a spherical cavity is used to estimate the excess electrostatic free energy of a solution;the other is that details of electrostatic interactions of the solutes are neglected. This makes DHL applicable only at low ionic strengths and dilute solutions (very low substrate/solute concentrations). We show in this work that through numerical solution of the Poisson-Nernst-Planck equations, diffusion-reaction processes can be studied at a variety of conditions including realistically concentrated solutions, high ionic strength, and certainly with non-equilibrium charge distributions. Reaction rate coefficients for the acetylcholine-acetylcholinesterase system are predicted to strongly depend on both ionic strength and substrate concentration. In particular, they increase considerably with increase of substrate concentrations at a fixed ionic strength, which is open to experimental testing. This phenomenon is also verified on a simple model, and is expected to be general for electrostatically attracting enzyme-substrate systems. © 2010 Lu and McCammon.

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