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systems science and Mathematical sciences 1998年第3期11卷 272-279页

作者： DONG Jianping(department of Mathematical sciences, Michigan Technological university,Houghton, MI 49931, u.s.a.) Michigan Technological university 美国

This article is concerned with paradoxes in 2×2×n contingency tables, suchas simpson’s paradox, in which the association in the 2 × 2 marginal table is quite different from the associations in the 2 × 2 partial tables. We prove that if the relative number of observations in each row of each partial table or in each column of each partial table is constant, then simpson’s paradox cannot occur. We also prove that under a certain condition, the paradox cannot occur if the odds ratios in the partial tables are uniformly greater than a lower bound (e.g. ＞ 1.125) or uniformly less than some upper ***, we show that simpson’s paradox and an amalgamation paradox cannot occur if certain ratios of cell counts are constant in the partial tables.

关键词： Categorical data simpson’s paradox odds ratio relative risk collapsibility

The spectrum for large sets of pure directed triple systems

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science China mathematics 2006年第8期49卷 1103-1127页

作者： ZHOu Junling, CHANG Yanxun & Jl Lijun Institute of mathematics, Beijing Jiaotong university, Beijing 100044, China department of mathematics, suzhou university, suzhou 215006, China 1. Institute of mathematics Beijing Jiaotong University Beijing 100044 China 2. department of mathematics Suzhou University Suzhou 215006 China

An LPDTs(υ) is a collection of 3(υ - 2) disjoint pure directed triple systems on the same set of υ elements. It is showed in Tian's doctoral thesis that there exists an LPDTs(υ) for υ≡ 0,4 (mod 6), υ≥ 4. In this paper, we establish the existence of an LPDTs(υ) for υ≡ 1, 3 (mod 6), υ＞ 3. Thus the spectrum for LPDTs(υ) is completely determined to be the set {υ:υ≡0, 1 (mod 3),υ≥4}.

关键词： large set, oriented triple system, pure, directed candelabra system.

A global rigidity theorem for weakly Landsberg manifolds

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science China mathematics 2007年第5期50卷 609-614页

作者： Bing-ye Wu department of mathematics, Minjiang university, Fuzhou 350108, China 1. department of mathematics Minjiang University Fuzhou 350108 China

In this paper we study a global rigidity property for weakly Landsberg manifolds and prove that a closed weakly Landsberg manifold with the negative flag curvature must be Riemannian.

关键词： geodesic differentiation flag curvature mean Cartan torsion weakly Landsberg manifold 53C60 53B40

Birkhoff's theorem and viscosity solutions of Hamilton-Jacobi equations

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science China mathematics 2009年第8期52卷 1796-1800页

作者： CHENG Wei department of mathematics, Nanjing university, Nanjing 210093, China department of mathematics Nanjing University Nanjing 210093 China

We obtain a partial generalization of Birkhoff's theorem of invariant curve to higher dimesional case in the context of viscosity solutions of Hamilton-Jacobi equations, or weak KAM theory. This is a new approach afte... 详细信息

关键词： Hamilton-Jacobi equation viscosity solution semiconcave function

synchronization of Chaotic systems by Linear Feedback Controller

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Communications in Nonlinear science and Numerical simulation 1998年第1期3卷 27-30页

作者： Zhenxun HuANG and Jiong RuAN (department of mathematics, Fudan university, shanghai 200433, China) department of mathematics Fudan University Shanghai 200433 China

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｙｎｃｈｒｏｎｉｚａｔｉｏｎａｎｄｃｏｎｔｒｏｌｏｆｃｈａｏｔｉｃｓｙｓｔｅｍｓｈａｖｅｒｅｃｅｎｔｌｙａｒｏｕｓｅｄａｇｒｅａｔｄｅａｌｏｆｉｎｔｅｒｅｓｔ［１－５］．Ｍａｎｙｄｉ... 详细信息

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｙｎｃｈｒｏｎｉｚａｔｉｏｎａｎｄｃｏｎｔｒｏｌｏｆｃｈａｏｔｉｃｓｙｓｔｅｍｓｈａｖｅｒｅｃｅｎｔｌｙａｒｏｕｓｅｄａｇｒｅａｔｄｅａｌｏｆｉｎｔｅｒｅｓｔ［１－５］．Ｍａｎｙｄｉｆｅｒｅｎｔｍｅｔｈｏｄｓｈａｖｅ...

关键词： control and synchronization of chaos heterogeneous synchronization ω limit point global asymptotical stability

AutoML: A systematic review on automated machine learning with neural architecture search

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Journal of Information and Intelligence 2024年第1期2卷 52-81页

作者： Imrus salehin md.shamiul Islam Pritom saha s.M.Noman Azra Tuni md.Mehedi Hasan md.Abu Baten department of Computer Engineering Dongseo University47 Jurye-roSasang-guBusan 47011Republic of Korea department of Computer science and Engineering Daffodil International UniversityDhaka 1216Bangladesh department of Computer science and Engineering Bangladesh University of Business and TechnologyDhaka 1216Bangladesh Faculty of Computer science and Engineering Frankfurt University of Applied SciencesFrankfurt 60318Germany department of Computer science and Engineering University of Asia PacificDhaka 1205Bangladesh department of Computer science and Engineering Ahsanullah University of Science and TechnologyDhaka 1208Bangladesh department of Computer science and Engineering Northern University BangladeshDhaka 1215Bangladesh

AutoML(Automated Machine Learning)is an emerging field that aims to automate the process of building machine learning *** emerged to increase productivity and efficiency by automating as much as possible the inefficient work that occurs while repeating this process whenever machine learning is *** particular,research has been conducted for a long time on technologies that can effectively develop high-quality models by minimizing the intervention of model developers in the process from data preprocessing to algorithm selection and *** this semantic review research,we summarize the data processing requirements for AutoML approaches and provide a detailed *** place greater emphasis on neural architecture search(NAs)as it currently represents a highly popular sub-topic within the field of *** methods use machine learning algorithms to search through a large space of possible architectures and find the one that performs best on a given *** provide a summary of the performance achieved by representative NAs algorithms on the CIFAR-10,CIFAR-100,ImageNet and wellknown benchmark ***,we delve into several noteworthy research directions in NAs methods including one/two-stage NAs,one-shot NAs and joint hyperparameter with architecture *** discussed how the search space size and complexity in NAs can vary depending on the specific problem being *** conclude,we examine several open problems(sOTA problems)within current AutoML methods that assure further investigation in future research.

关键词： AutoML Neural architecture search Advance machine learning search space Hyperparameter optimization

(s,t,d)-bi-Koszul algebras

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science China mathematics 2009年第11期52卷 2419-2431页

作者： sI JunRu department of mathematics,Hangzhou Dianzi university,Hangzhou 310018,China 1. department of mathematics Hangzhou Dianzi University Hangzhou 310018 China

The paper focuses on the 1-generated positively graded algebras with non-pure resolutions and mainly discusses a new kind of algebras called(s,t,d)-bi-Koszul algebras as the generalization of bi-Koszul algebras. An(s,t,d)-bi-Koszul algebra can be obtained from two periodic algebras with pure resolutions. The generation of the Koszul dual of an(s,t,d)-bi-Koszul algebra is discussed. Based on it,the notion of strongly(s,t,d)-bi-Koszul algebras is raised and their homological properties are further discussed.

关键词： bi-Koszul algebra periodic algebra pure resolution 16E05 16E40 16s37 16W50

Recent Development of OCT Technologies

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生物物理学报 2009年第S1期25卷 162-162页

作者： Xingde Li department of Biomedical Engineering, johns hopkins university, baltimore, md 21205

Optical coherence tomography (OCT) was first reported about 18 years ago. OCT was originally developed for imaging the relatively transparent eye tissue, and later applied

关键词： OCT optical biopsy functional imaging

sTABILITIEs OF (A,B,C) AND NPDIRK METHODs FOR sYsTEMs OF NEuTRAL DELAY-DIFFERENTIAL EQuATIONs WITH MuLTIPLE DELAYs

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Journal of Computational mathematics 2003年第3期21卷 375-382页

作者： Guo-feng Zhang (department of mathematics, Lanzhou university, Lanzhou 730000, China) department of mathematics Lanzhou University Lanzhou 730000

Consider the following neutral delay-differential equations with multiple delays (NmdDE)where γ> 0, L, Mj and Nj are constant complex- value d×d matrices. A sufficient condition for the asymptotic stability of NmdDE system (0.1) is given. The stability of Butcher's (A,B,C)-method for systems of NmdDE are studied. In addition, we present a parallel diagonally-implicit iteration RK (PDIRK) methods(NPDIRK) for systems of NmdDE, which is easier to be implemented than fully implicit RK methods. We also investigate the stability of a special class of NPDIRK methods by analyzing their stability behaviors of the solutions of (0.1).

关键词： Neutral delay differential equations (A,B,C)-method RK method Parallel diagonally-implicit iteration RK method.