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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. {1. of Applied sciences,{2. university of technology,{2. 1.002.,china 2. Department of Mathematics,Hong Kong Baptist university,Hong Kong,china 1. college of Applied {1. 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.

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 1.002.,{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 {1. 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.

Explanation of the mechanism of carcinogenesis and syntheses of anticancer agents with high selectivity

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Science china Chemistry 2006年第1期49卷 44-62页

作者： DAI Qianhuan1.2.1. Center of Chemistry and Bioengineering of Cancer Research, {1. Polytechnic university (Now known as {1. Univer-sity of technology), beijing 1.002., china 2. Center of Environmental sciences, Peking university, {1. 1.0871. china 1. Center of Chemistry and Bioengineering of Cancer Research Beijing Polytechnic University Beijing 100022 China 2. Center of Environmental {1. Peking University Beijing 100871 China

In 1.79, the mechanism of chemical carcinogenesis, a challenging anddifficult scientific problem pending for a number of years, was explained by Dai Qianhuan. Themechanism named di-region theory predicted that a carcinogen always metabolizes to form a specialbi-functional alky-lating agent. This agent induces cross-linkages between the complementary basepairs in DMA and switches on initial mutageneses in genomes including point and frameshiftmutations. This, in turn, induces further deep mutageneses including the production of variouschimeric chromosomes, deletions and other aberrations found in genomes. In the end this initiatescarcinogenesis of the whole cell through the reverse transcription mechanism after a lengthyincubation period. Recently, this laboratory has verified that physical carcinogenesis, includingthe oncogenesis induced by radiation and asbestos as well as the carcinogenesis induced byendogenous factors such as estrogen or diethyl-stilbestrol switch on carcinogenesis by inducing theformation of cross-linkages between the complementary base pairs in DNA. Di-region theory has nowbeen supported by many experimental observations such as mutational spectra of various *** potential for carcinogenesis, teratogenesis, sterility and mutagenesis lumped together asgenetic toxicity appears to originate almost uniformly from the cross-linking between complementarybases, i.e. malignant cross-linking, which is in accordance with di-region theory. Other forms ofcross-linking between non-complementary bases, benign cross-linkings, show bi-functional alkylationanticancer activity but lack genetic toxicity. The predictable design and synthesis of a highselectivity anticancer agent with high efficacy and low genetic toxicity, a goal long pursued incancer chemotherapy, have been realized for the first time in this laboratory by inhibitingmalignant and heightening benign cross-linking using the principles of di-region theory. A series ofpatented new anticanc

关键词： mechanism of carcinogenesis, di-region theory, minoplatin, selectivity of anticancer agent, cross-linking between DNA bases, anticancer platinum complexes, predictive design of anticancer agent, second generation anticancer agent.

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 DaRong2.1.1. of Applied sciences,{2., beijing 1.01.0}, china 2.he Pilot {1.,{2., beijing 1.1.01. china 1. college of Applied {1. 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

On three-dimensional geological modeling and visualization

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Science china Earth {1. 2004年第8期47卷 739-748页

作者： WU Qiang1.& XU Hua2.1. Department of Resource Exploitation Engineering,{1. university of Mining and {2., beijing 1.0083,{1. 2. beijing Institute of Petrochemical {2., beijing 1.2.1.,{1. 1. Department of Resource Exploitation Engineering China University of Mining and Technology 100083 Beijing China 2. {1. Institute of Petrochemical technology 102617 Beijing China

The technology of 3D geological modeling will bring about great changes in the methods of geological data acquiring, storing, processing and displaying. However, no perfect or convenient software systems have been developed up to now since the geologic data which re-flect geological entities bear the feature of diversity, uncertainty and complexity. Some supervoxel models, mathematical models of fault and geometrical models of fold have been contrived so as to show the space geometric configuration of the complicated geologic structures. The application-oriented system architecture for 3D geological modeling is established; and a novel design concept based on spatial data processing is also proposed with the technology of solid modeling as its core and the application of models as its objective. Theories and methods for 3D geological modeling will hopefully be enriched and developed. In the light of these theories and methods, a feature-based navigation visualization technique is also put forward in the paper. By integrating geo-database, graphics libraries and KBS with 3D dynamic simulation systems, geologists will be able to capture the partial characteristics and whole structure embodied in the geological data in a direct-viewing, figurative and accurate manner.

关键词： 3D geological modeling,geometrical model,system architecture,visualization

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,{1. university of Mining & {2., beijing 1.0083,{1. 2. Probability Lab, Institute of Applied Mathematics, Chinese Academy of sciences, beijing 1.0080,{1. 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.

Mineralogy and crystal structure determination of Mg-fillowite

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Science china Earth {1. 2005年第5期48卷 635-646页

作者： MA Zhesheng 1., SHI Nicheng 1.& YE Danian 2.1.{1. university of Geo{2., beijing 1.0083,{1. 2. Institute of Geology, Chinese Academy of {2., beijing 1.002.,{1. 1. china {1. of Geo{2. 100083 Beijing China 2. Institute of Geology Chinese Academy of Sciences 100029 Beijing China

Accurate crystal structure determination of complex phosphate Mg-fillowite ? Na2.a(Mn4Mg2.e)7[PO4]6 has been finished. Mg-fillowite occurs in muscovite-pegmatite in the Altay area, Xinjiang, china. It is of the trigonal lattice, with space group R-3, unit cell a=1.51.3(3) nm, c=4.31.1.2. nm, V=8.5736 nm3, Z = 1.. The R-factor of the determination accuracy is R (I > 2. ( I )) = 0.0776. The cationic polyhedra consist of two kinds of structural units: compound col- umn and screw column. In three-dimensional space, they are linked with each other through corner sharing or edge sharing to build the entire structure. There are 45 atoms in an asymmetric unit and 72. atoms in a unit cell. In terms of types and connection manners of the coordination polyhedra, the degree of complicity is rarely seen in all mineral crystal structures. Study of such a structure is significant for the classification of phosphate and the building rule of coordination polyhedra in a complex crystal structure.

关键词： Mg-fillowite, complex phosphate, crystal structure, coordination polyhedron.

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. {1. of Applied sciences,{2., beijing 1.002., china 2. Center for Nonlinear Studies, Institute of Applied Physics and Computational Mathematics, beijing 1.0088, china) college of Applied {1. 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

Research on the method for retrieving soil moisture using thermal inertia model

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Science china Earth {1. 2006年第5期49卷 539-545页

作者： LIU Zhenhua1.& ZHAO Yingshi2.1. Information {1., South china Agricultural {2., Guangzhou 51.642. china 2. Graduate {2. of Chinese Academy of sciences, beijing 1.0049, china 1. Information college South China Agricultural University Guangzhou 510642 China 2. Graduate {1. of Chinese Academy of sciences Beijing 100049 China

In order to improve accuracy of soil moisture inversion using remote sensing, a new thermal inertia model is proposed in this paper. The improved model needs only surface maximum temperature as the temperature parameter input instead of input of the surface temperature difference, as well as the surface sensible and latent fluxes are introduced into boundary conditions of thermal conductivity equation. Furthermore, surface soil conductive heat transfer equation of two-layer model is used to solve the soil thermal inertia so that the remote sensing thermal inertia method can be ap- plied to regions with better-covered vegetation, but usually only for the bare areas or worse vegetation covered areas. The model has been tested at several locations in the area of west Inner Mongolia. Comparing the simulation of the new model with the measurements obtained by apparent thermal inertia and by field test, the result shows that the inertia thermal model can be used to estimate soil moisture in more reasonable accuracy.

关键词： thermal model, thermal conductivity equation, soil initial, sensible flux, latent flux, two-layer model.