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Empirical likelihood confidence regions of the parameters in a partially linear single-index model

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Science china Mathematics 2005年第10期48卷 1333-1348页

作者： XUE Liugen~1 & ZHU Lixing~2.1. college of applied {2.,beijing university of technology,beijing 10002.,china 2. Department of Mathematics,Hong Kong Baptist university,Hong Kong,china 1. college of applied {2. Beijing University of Technology 100022 Beijing China 2. Department of Mathematics Hong Kong Baptist University Hong Kong China

In this paper, a partially linear single-index model is investigated, and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions, and hence can be used to construct the confidence regions of the parameters. Our methods can also deal with the confidence region construction for the index in the pure single-index model. A simulation study indicates that, in terms of coverage probabilities and average areas of the confidence regions, the proposed methods perform better than the least-squares method.

关键词： partially linear single-index model, empirical likelihood, confidence region, chi-square distribution, coverage probability.

Simultaneous variable selection for heteroscedastic regression models

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Science china Mathematics 2011年第3期54卷 515-530页

作者： ZHANG ZhongZhan1 & WANG DaRong2.1college of applied {2., beijing university of technology, beijing 10012., china 2.he Pilot college, beijing university of technology, beijing 101101, china 1. college of applied {2. Beijing University of Technology Beijing 100124 China2. The Pilot College Beijing University of Technology Beijing 101101 China

In this paper, we propose a new criterion, named PICa, to simultaneously select explanatory variables in the mean model and variance model in heteroscedastic linear models based on the model structure. We show that the new criterion can select the true mean model and a correct variance model with probability tending to 1 under mild conditions. Simulation studies and a real example are presented to evaluate the new criterion, and it turns out that the proposed approach performs well.

关键词： variable selection heteroscedastic regression models adjusted profile log-likelihood AIC BIC

Cu(Ⅱ) Potentiation of Alzheimer Aβ1-40 Cytotoxicity and Transition on its Secondary Structure

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Acta Biochimica et Biophysica Sinica 2006年第11期38卷 765-772页

作者： Xue-Ling DAI~1 Ya-Xuan SUN~2.Zhao-Feng JIANG~2. 1 college of Life Science,Capital Normal university,{2. 100037,china 2.college of applied sciences and Humanities,{2. Union university,{2. 100083,china college of Life Science Capital Normal UniversityBeijing 100037 China college of applied {2. and Humanities Beijing Union UniversityBeijing 100083 China

Mounting evidence has shown that dyshomeostasis of the redox-active biometals such as Cuand Fe can lead to oxidative stress,which plays a key role in the neuropathology of Alzheimer's disease（AD）.Here we demonstrate that with the formation of Cu（Ⅱ）·Aβ1-40 complexes,copper markedly potentiatesthe neurotoxicity exhibited by β-amyloid peptide （Aβ）.A greater amount of hydrogen peroxide was releasedwhen Cu（Ⅱ）·Aβ1-40 complexes was added to the xanthine oxidase/xanthine system detected by potassiumiodide *** bound to Aβ1-40 was observed by electron paramagnetic resonance（EPR） *** dichroism （CD） studies indicated that copper chelation could cause a structuraltransition of Aβ.The addition of copper to Aβ introduced an increase on β-sheet as well as α-helix,whichmay be responsible for the aggregation of Aβ.We hypothesized that Aβ aggregation induced by copper maybe responsible for local injury in *** interaction between Cu2.and Aβ also provides a possible mechanismfor the enrichment of metal ions in amyloid plaques in the AD brain.

关键词： Alzheimer’s disease Cu(Ⅱ)·Aβ1-40 complex neuron injury Aβ secondary structure

A new DNA algorithm to solve graph coloring problem

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Progress in Natural Science:Materials International 2007年第6期17卷 733-738页

作者： Jiang Xingpeng1, Li Yin2. Meng Ya3 and Meng Dazhi2.1. National Laboratory of Pattern Recognition,Institute of Automation, Chinese Academy of sciences, beijing 100080,{2. 2. college of applied sciences, beijing university of technology, beijing 10002.,{2. 3. School of Science, beijing Institute of technology, beijing 100081,{2.) National Laboratory of Pattern Recognition Institute of Automation Chinese Academy of Sciences Beijing 100080 China college of applied {2. Beijing University of Technology Beijing 100022 China School of Science Beijing Institute of Technology Beijing 100081 China

Using a small quantity of DNA molecules and little experimental time to solve complex problems successfully is a goal of DNA computing. Some NP-hard problems have been solved by DNA computing with lower time complexity than conventional computing. However, this advantage often brings higher space complexity and needs a large number of DNA encoding molecules. One example is graph coloring problem. Current DNA algorithms need exponentially increasing DNA encoding strands with the growing of problem size. Here we propose a new DNA algorithm of graph coloring problem based on the proof of four-color theorem. This algorithm has good properties of needing a relatively small number of operations in polynomial time and needing a small number of DNA encoding molecules (we need only 6R DNA encoding molecules if the number of regions in a graph is R).

关键词： DNA computing NP-hard problem graph coloring problem.

Existence of solutions for the dynamic equation of ferrimagnets

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Progress in Natural Science:Materials International 2007年第11期17卷 1279-1283页

作者： Zeng Ming1, Guo Boling2.and Cheng Caozong1(1. college of applied {2., beijing university of technology, beijing 10002., china 2. Center for Nonlinear Studies, Institute of applied Physics and Computational Mathematics, beijing 100088, china) college of applied {2. Beijing University of Technology Beijing 100022 China Center for Nonlinear Studies Institute of Applied Physics and Computational Mathematics Beijing 100088 China

Ferrimagnet is a kind of basic and important multi-sublattice magnet material. It has attracted more and more attention of physicists and mathematicians. Many results of solitons and numerical computations on this topic have appeared. In this article, the dynamic equation for an isotropic ferrimagnet with two non-equivalent sublattices is studied, existence of weak solutions in multi dimension case is proved through the penalized method, the uniqueness and smoothness of the solution in one dimension case are also obtained by the relation between this equation and hyperbolic equation.

关键词： ferrimagnet weak solutions penalized method finite difference method

On some tests-based projection pursuit for elliptical symmetry of a high-dimensional distribution

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Chinese Science Bulletin 1998年第6期43卷 450-458页

作者： JING Ping 1 and ZHU Lixing 2.1. Mathematics Lab, china university of Mining & {2., beijing 100083, china 2. Probability Lab, Institute of applied Mathematics, Chinese Academy of sciences, beijing 100080, china Mathematics Lab China University of Mining & Technology Beijing China Probability Lab Institute of Applied Mathematics Chinese Academy of Sciences Beijing China

Some test statistics of Kolmogorov type and Cramér-von Mises type based on projection pursuit technique are proposed for the testing problem of sphericity of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and under any fixed alternative. The asymptotic properties of bootstrap approximation are investigated. Furthermore, for computational reasons, an approximation for the statistics, based on the number theoretic method, is suggested.

关键词： bootstrap approximation projection pursuit type statistic elliptical symmetry.

Theorems for Testing Local Activity of CNN and Application to Cardiac Purkinje Equations

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International Journal of Minerals,Metallurgy and Materials 2000年第2期14卷 139-146页

作者： Lequan Min(applied Science School, university of Science and {2. beijing, beijing 100083, china) applied Science School University of Science and Technology Beijing Beijing 100083 China

The theorems for testing the local in one-port cellular neural/inear network (CNN) cells with four local state variables are presented. Using the theorems computes the bifurcation diagrams of the cardiac Purkinje fiber (CPE) equations Which describethe long-lasting action and pace-maker potentials of the Purkinje fiber of the heart. The computer simulation shows that periodic trajectories or convergent trajectories of the CPF Equations can be foun if the cormsponing cell Parameters are located in a positive domainbut nearby edge of chaos. In particular a heart with approximate normal frequency of heartbeat but non-normal electrocardiogram maysuddenly stop by slightly perturbing the parameters of the corresponding CPF Equations when the Paramders are located nearby the edge of chaos in the bifurcation diagrams. This research seems to interpret reasonbly the phenomena that patients with cardiac diseases might suddenly die without warning.

关键词： cellular neural network local activity cardiac Purkinje fiber heartbeat

Empirical likelihood-based inference in a partially linear model for longitudinal data

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Science china Mathematics 2008年第1期51卷 115-130页

作者： XUE LiuGen~(1+) & ZHU LiXing~2.1 college of applied {2., beijing university of technology, beijing 10002., china 2.Department of Mathematics, Hong Kong Baptist university, Hong Kong, china college of applied {2. Beijing University of Technology Beijing 100022 China Department of Mathematics Hong Kong Baptist University Hong Kong China

A partially linear model with longitudinal data is considered, empirical likelihood to infer- ence for the regression coefficients and the baseline function is investigated, the empirical log-likelihood ratios is proven to be asymptotically chi-squared, and the corresponding confidence regions for the pa- rameters of interest are then constructed. Also by the empirical likelihood ratio functions, we can obtain the maximum empirical likelihood estimates of the regression coefficients and the baseline function, and prove the asymptotic normality. The numerical results are conducted to compare the performance of the empirical likelihood and the normal approximation-based method, and a real example is analysed.

关键词： partially linear model empirical likelihood confidence region longitudinal data 62.05 62.15 62.2.

Finite-dimensional (*)-serial algebras

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Science china Mathematics 2010年第12期53卷 3049-3056页

作者： YAO HaiLou & FAN WeiLi college of applied Science,{2., beijing 10012., china 1. college of applied Science Beijing University of Technology Beijing 100124 China

Let A be a finite-dimensional associative algebra with identity over a field k. In this paper we introduce the concept of (*)-serial algebras which is a generalization of serial algebras. We investigate the properties of (*)-serial algebras, and we obtain suficient and necessary conditions for an associative algebra to be (*)-serial.

关键词： (*)-serial algebras biserial modules uniserial modules