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Correlation of zeros of automorphic L-functions

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Science China Mathematics 2008年第7期51卷 1147-1166页

作者： LIU JianYa1 & YE YangBo1,2.1 School of Mathematics,Shandong university,Jinan 2.0100, China 2.1} of Mathematics,The university of iowa,iowa city,ia 52.42.1419,USA 1. School of Mathematics Shandong University Jinan 250100 China 2. department of Mathematics The University of Iowa Iowa City IA 52242-1419 USA

We compute the n-level correlation of normalized nontrivial zeros of a product of Lfunctions: L(s, π1) … L(s, π k ), where πj, j = 1, …, k, are automorphic cuspidal representations of GL mj (?A). Here the sizes of the groups GL mj (?A) are not necessarily the same. When these L(s, π j ) are distinct, we prove that their nontrivial zeros are uncorrelated, as predicted by random matrix theory and verified numerically. When L(s, π j ) are not necessarily distinct, our results will lead to a proof that the n-level correlation of normalized nontrivial zeros of the product L-function follows the superposition of Gaussian Unitary Ensemble (GUE) models of individual L-functions and products of lower rank GUEs. The results are unconditional when m 1, …, m k ? 4, but are under Hypothesis H in other cases.

关键词： automorphic L-function zero correlation Selberg’s orthogonality conjecture 11F70 11M2. 11M41

Mining and Integrating Reliable Decision Rules for Imbalanced Cancer Gene Expression Data Sets

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Tsinghua Science and Technology 2012年第6期17卷 666-673页

作者： Hualong Yu 1 , Jun Ni 2., Yuanyuan Dan 3 , Sen Xu 4 1. School of Computer Science and Engineering, Jiangsu university of Science and Technology, Zhenjiang 2.2.03, China 2. department of radiology,{2., the university of iowa, iowa city, ia 52.42. USA 3. School of Biology and Chemical Engineering, Jiangsu university of Science and Technology, Zhenjiang 2.2.03, China 4. School of Information Engineering, Yancheng Institute of Technology, Yancheng 2.4051, China School of Computer Science and Engineering Jiangsu University of Science and Technology Zhenjiang 212003 China|c|

There have been many skewed cancer gene expression datasets in the post-genomic era. Extraction of differential expression genes or construction of decision rules using these skewed datasets by traditional algorithms will seriously underestimate the performance of the minority class, leading to inaccurate diagnosis in clinical trails. This paper presents a skewed gene selection algorithm that introduces a weighted metric into the gene selection procedure. The extracted genes are paired as decision rules to distinguish both classes, with these decision rules then integrated into an ensemble learning framework by majority voting to recognize test examples; thus avoiding tedious data normalization and classifier construction. The mining and integrating of a few reliable decision rules gave higher or at least comparable classification performance than many traditional class imbalance learning algorithms on four benchmark imbalanced cancer gene expression datasets.

关键词： cancer gene expression data class imbalance paired differential expression genes decision ruleensemble learning majority voting

Resonance between automorphic forms and exponential functions

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Science China Mathematics 2010年第9期53卷 2463-2472页

作者： REN XiuMin1,& YE YangBo1,2.1School of Mathematics,Shandong university,Jinan 2.0100,China 2.1} of Mathematics,The university of iowa,iowa city,iowa 52.42.1419,USA 1. School of Mathematics Shandong University Jinan 250100 China2. Department of Mathematics The University of Iowa Iowa City Iowa 52242-1419 USA

Let f be a holomorphic cusp form of weight k for SL2.Z) and λf(n) its n-th Fourier *** this paper,the exponential sum X2. λf(n)e(αnβ) twisted by Fourier coefficients λf(n) is proved toh ave a main term of siz... 详细信息

关键词： automorphic form exponential sum resonance

Design and implementation of an optical simulation environment for bioluminescent tomography studies

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Progress in Natural Science:Materials International 2007年第1期17卷 87-94页

作者： LI Hui, TiaN Jie, LUO Jie, LU Yujie, CONG Wenxiang and WANG Ge ( department of Education Technology, Capital Normal university, Beijing 100037, China Key Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, Beijing 100080, China Bioluminescent Tomography Laboratory, department of radiology & department of Biomedical Engineering, university of iowa, iowa city, iowa 52.42. USA) [a]Departhent of Education Technology Capital Normal University Beijing China [b]Key Laboratoiy of Omplex Systems and Intelligence Science Institute of Automation Chinese Academy of Sciences Beijing China [c]Bioluminescent Tomography Laboratoiy Department of Radiology & Department of Biomedical Engineering University of Iowa Iowa City tIowa USA

As a challenging task for bioluminescent tomography simulation, a virtual optical environment is needed to solve the forward problem accurately, that is, to achieve a high precision for bioluminescent signal synthesis on the external body surface of a small animal. The molecular optical simulation environment named MOSE is implemented using the C++ programming language and the OpenGL techniques, including a user-friendly interface with interactive tools facilitating users' operations. The accuracy of the virtual optical environment is verified by error analysis of mesh simplification and comparison between MOSE results and experimental data. This virtual optical environment is accurate, flexible and efficient to simulate the photon propagation in complicated tissues, which has a great potential to become a software platform for bioluminescent tomography studies and other molecular imaging applications.

关键词： molecular imaging biolumlnescent tomography photon propagation Monte Carlo method.

THE KACANOV METHOD FOR A NONLINEAR VARiaTIONAL INEQUALITY OF THE SECOND KIND ARISING IN ELASTOPLASTIcity

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Chinese Annals of Mathematics,Series B 1996年第2期17卷 129-138页

作者： HAN WEIMIN S. JENSEN department of Mathematics University of Iowa Iowa City IA 52242 U.S.A.Department of Mathematics University of Maryland Baltimore County Baltimore MD 21228 U.S.A.

The authors first prove a convergence result on the Ka(?)anov method for solving generalnonlinear variational inequalities of the second kind and then apply the Kacanov method tosolve a nonlinear variational inequality of the second kind arising in elastoplasticity. In additionto the convergence result, an a posteriori error estimate is shown for the Kacanov iterates. Ineach step of the Ka(?)anov iteration, one has a (linear) variational inequality of the secondkind, which can be solved by using a regularization technique. The Ka(?)anov iteration andthe regularization technique together provide approximations which can be readily computednumerically. An a posteriori error estimate is derived for the combined effect of the Ka(?)anoviteration and the regularization.

关键词： Kacanov method Nonlinear variational inequality of the second kind Convergence Regularization A posteriori error estimate

ON DISTRIBUTIVE MODULES AND LOCALLY DISTRIBUTIVE RINGS

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Chinese Annals of Mathematics,Series B 1991年第1期12卷 26-32页

作者： K.R.Fuller 薛卫民 department of Mathematics University of Iowalowa CityIowaU.S.A. department of Mathematics Fujian Normal UniversityFuzhouFujianChina.

Distributive modules over artinian rings are characterized via module diagrams,andit is shown that a left artinian ring is(two-sided)locally distributive in case its leftindecomposable injective modules and projective modules are *** latter resultis used to show that a locally distributive artinian ring and the endomorphism ring of itsminimal cogenerator have identical diagrams.

关键词： projective identical sided latter rings locally maximal 任尹 algebra indeed

On Extension of Isometries in (F)-Spaces

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Acta Mathematica Sinica,English Series 1996年第1期12卷 1-9页

作者： Ding Guanggui Huang Senzhong department of Mathematics Nankai university Tianjin, 300071 China department of Mathematics university of iowa iowa city ia 52.42.USA department of Mathematics Nankai university Tianjin, 300071 China Mathematisehes Institut Universitat Tubingen Auf der Morgenstelle 10 72.76 Tubingen Germany 南开大学数学系天津

An(F)-space E is said to be locally midpoint constricted (in short, Imp-constricted) if there exists some δ>0 such that D(A/2.iameter of A. Our m... 详细信息

An(F)-space E is said to be locally midpoint constricted (in short, Imp-constricted) if there exists some δ>0 such that D(A/2.iameter of A. Our main result goes as follow: Let E be an Imp-constricted (F)-space and U an open connected subset of E. Assume that T:U→F is an isometry (i.e., a distance-preserving map) which maps U onto an open subset of the (F)-space F. Then T can be extended to an affine homeomorphism from E to F. Also, some other results about the question whether each isometry between two (F)-spaces is affine are obtained.

关键词： Locally midpoint constricted Isometry Affine homeomorphism

Fuzzy controllers based on some fuzzy implication operators and their response functions

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Progress in Natural Science:Materials International 2004年第1期14卷 16-21页

作者： LI Hongxing 1*, YOU Fei 1 and PENG Jiayin 2.1. department of Mathematics, Beijing Normal university, Beijing 100875, China 2. department of Mathematics, Neijiang Teacher's college, Neijiang 641112. China) Beijing Normal Univ Dept Math Beijing 100875 Peoples R China

The fuzzy controllers constructed by 2. fuzzy implication operators based on CRI algorithm and their response functions are discussed. The conclusions show that the fuzzy controllers constructed by 9 fuzzy implication operators are universal approximators to continuous functions and can be used in practical fuzzy control systems. And these 9 fuzzy implication operators except for Einstein operator intersection are all the adjoint pairs of some fuzzy implication operators. Besides, there are 3 other fuzzy controllers formed by fuzzy implication operators being regarded approximately as fitted functions.

关键词： fuzzy implication operators CRI algorithm fuzzy controllers response functions universal approximators

Taurine Inhibits Myocardial Fibrosis via PKC-ERK1/2.Signaling Pathways

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Chemical Research in Chinese Universities 2012年第1期28卷 84-90页

作者： WANG Li-ying1,2. LI Hong1 and YANG Shi-jie1 1. department of Pharmacology, Norman Bethune college of {2., Jilin university, Changchun 13002., P. R. China 2. department of Physiology, Basic {2. college, Beihua university, Jilin 132.13, P. R. China Jilin Univ Norman Bethune Coll Med Dept Pharmacol Changchun 130021 Peoples R China Beihua Univ Basic Med Coll Dept Physiol Jilin 132013 Jilin Peoples R China

Previous studies have demonstrated the important role of taurine in inhibiting proliferation of myofibrob lasts（myoFb） and myocardial fibrosis. However, the underlying mechanisms are unclear. The present study was de signed to shed light on this issue through exploring the signal pathways via in vitro experiments. Angiotension II （AngII） treatment significantly increased myoFb proliferation and the levels of collagens I and III（P〈0.05）, whereas taurine, PKCα（PKC： protein kinase C） specific inhibitor L-threo-dihydro-sphingosine（D4681）, ERK1/2.inhibitor （PD98095） abrogated myoFb proliferation and collagen levels（P〈0.05, P〈0.01, respectively）, and increased the G0/G1 phase rate and decreased S phase rate. Immunocytochemistry, confocal fluorescence staining and image analy sis showed that taurine could inhibit the translocation and expression of p-PKCαin membrane, and then inhibit nuc lear translocation and expression of p-ERK1/2. These results have statistically significant differences compared with those of AngII group（P〈0.01）. Western blot results also show that taurine could inhibit the protein expression of p-PKCα and p-ERK1/2. We used p-PKCα specific inhibitor D4681 in order to elucidate the relationship between p-PKCα and p-ERK1/2.in signal transduction pathways. Finally, the results show that the protein expression of p-ERK1/2.and nuclear translocation were suppressed in D4681 group.

关键词： Taurine Myocardial fibrosis Proliferation Signal transduction Cardiac remodeling