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Rehearsal:learning from prediction to decision

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Frontiers of Computer Science 2022年第4期16卷 1-3页

作者： zhi-hua Zhou National Key Laboratory for Novel Software Technology Nanjing UniversityNanjing210023China

Machine learning[1]studies focus mostly on prediction,where a model is built from a set of observational data formaking correct predictions on unseen *** has beenaddressed very well by modem techniques such as deeplea... 详细信息

关键词： such has see

A Characterization of Generalized Frame MRAs Deriving Orthonormal Wavelets

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Acta Mathematica Sinica,English Series 2006年第4期22卷 1251-1260页

作者： zhi hua ZHANG Department of Mathematics University of California Davis California 95616 USA

In 2000, Papadakis announced that any orthonormal wavelet must be derived by a generalized frame MRA （GFMRA）. In this paper, we give a characterization of GFMRAs which can derive orthonormal wavelets, and show a gen... 详细信息

关键词： orthonormal wavelets generalized frame MRA non-MRA wavelets

Local Analysis, Cardinality, and Split Trick of Quasi-biorthogonal Frame Wavelets

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Acta Mathematica Sinica,English Series 2011年第1期27卷 203-218页

作者： zhi hua ZHANG College of Global Change and Earth System Science Beijing Normal University Beijing 100875 P. R. China

The notion of quasi-biorthogonal frame wavelets is a generalization of the notion of orthog- onal wavelets. A quasi-biorthogonal frame wavelet with the cardinality r consists of r pairs of functions. In this paper we first analyze the local property of the quasi-biorthogonal frame wavelet and show that its each pair of functions generates reconstruction formulas of the corresponding subspaces. Next we show that the lower bound of its cardinalities depends on a pair of dual frame multiresolution analyses deriving it. Finally, we present a split trick and show that any quasi-biorthogonal frame wavelet can be split into a new quasi-biorthogonal frame wavelet with an arbitrarily large cardinality. For generality, we work in the setting of matrix dilations.

关键词： Local analysis cardinality split trick quasi-biorthogonal frame wavelets

Pointwise Convergence and Uniform Convergence of Wavelet Frame Series

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Acta Mathematica Sinica,English Series 2006年第3期22卷 653-658页

作者： zhi hua ZHANG Department of Mathematics University of California

Pointwise convergence and uniform convergence for wavelet frame series is a new topic. With the help of band-limited dual wavelet frames, this topic is first researched.

关键词： Wavelet frame series Wavelet orthonormal basis Uniform convergence Pointwise convergence

A brief introduction to weakly supervised learning

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National Science Review 2018年第1期5卷 44-53页

作者： zhi-hua Zhou National Key Laboratory for Novel Software Technology Nanjing University

Supervised learning techniques construct predictive models by learning from a large number of training examples, where each training example has a label indicating its ground-truth output. Though current techniques have achieved great success; it is noteworthy that in many tasks it is difficult to get strong supervision information like fully ground-truth labels due to the high cost of the data-labeling process. Thus,it is desirable for machine-learning techniques to work with weak supervision. This article reviews some research progress of weakly supervised learning, focusing on three typical types of weak supervision:incomplete supervision, where only a subset of training data is given with labels; inexact supervision, where the training data are given with only coarse-grained labels; and inaccurate supervision, where the given labels are not always ground-truth.

关键词： machine learning weakly supervised learning supervised learning

Decomposition and Approximation of Multivariate Functions on the Cube

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Acta Mathematica Sinica,English Series 2013年第1期29卷 119-136页

作者： zhi hua ZHANG College of Global Change and Earth System Science Beijing Normal University

In this paper, we present a decomposition method of multivariate functions. This method shows that any multivariate function f on [0, 1]d is a finite sum of the form ∑jФjψj, where each Фj can be extended to a smooth periodic function, each ψj is an algebraic polynomial, and each Фjψj is a product of separated variable type and its smoothness is same as f. Since any smooth periodic function can be approximated well by trigonometric polynomials, using our decomposition method, we find that any smooth multivariate function on [0, 1]d can be approximated well by a combination of algebraic polynomials and trigonometric polynomials. Meanwhile, we give a precise estimate of the approximation error.

关键词： Decomposition of multivariate functions approximation of multivariate functions fundamental polynomial projection operator classification of boundary points

Synthesis of N-Aryl-2-(1′,6′-dihydro-6′-pyridazinone-3′-carbonyl) Thiosemicarbazides and Their Related heterocyclic Compounds

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Chemical Research in Chinese Universities 2005年第2期21卷 172-176页

作者： WANGDuo-zhi CAOLing-hua DepartmentofChemistry XinjiangUniversityUrumqi830046P.R.China DepartmentofChemistry XinjiangUniversityUrumqi830046P.R.China／／StateKeyLaboratoryofElemento-organicChemistryNankaiUniversityTianjin300071P.R.China

Dihydro-3-hydrozinocarbonyl-6-pyridazinone(compound 2) were prepared from α-ketoglutaric acid and hydrazine hydrate. A series of N-aryl-2-(1′,6′-dihydro-6′-pyridazinone-3′-carbonyl) thiosemicarbazides 3a_3f were synthesized from the reaction of aryl isothiocyanates with compound 2. The terminal compounds 1,3,4-thiadiazole, 1,3,4-oxadiazole and 1,2,4-triazol-5-thione derivatives were cyclized from compounds 3a_3f. Their structures were confirmed by IR, 1H NMR, MS and elemental analyses.

关键词： Pyridazinone 1,3,4-Thiadiazole 1,3,4-Oxadiazole 1,2,4-Triazol-5-thione Synthesis.

Application of dynamic vibration absorber for vertical vibration control of corrugated rolling mill

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Journal of Iron and Steel Research International 2023年第4期30卷 736-748页

作者： Dong-ping he Hui-dong Xu Ming Wang Tao Wang Chao-ran Ren zhi-hua Wang College of Mechanical and Vehicle Engineering Taiyuan University of TechnologyTaiyuan 030024ShanxiChina Engineering Research Center of Advanced Metal Composites Forming Technology and Equipment Ministry of EducationTaiyuan 030024ShanxiChina

A variable mass tuned particle absorber is designed for the nonlinear vertical vibration control of the corrugated rolling mill in the composite plate rolling *** the nonlinear damping and nonlinear stiffness between the corrugated interface,a three-degree-of-freedom nonlinear vertical vibration mathematical model of corrugated rolling mill based on dynamic vibration absorber control is *** multi-scale method is used to solve the amplitude–frequency characteristic curve equation of the installed dynamic vibration absorber(DVA)*** effects of stiffness coefficient and damping coefficient on the amplitude–frequency characteristic curve are *** expressions of the dynamic developed factor of the corrugated roll are derived,and the influence laws of mass ratio,frequency ratio and damping ratio on the dynamic amplification factor are *** optimal parameters of the DVA are obtained by adaptive genetic *** control effect of the DVA on the nonlinear vertical vibration is studied by numerical *** feasibility of the designed dynamic absorber is verified through *** results show that the designed dynamic absorber can effectively suppress the vertical vibration of the corrugated roller.

关键词： Corrugated rolling mill Nonlinear vertical vibration Adaptive genetic algorithm Multiscale method Dynamic vibration absorber

Dropout Rademacher complexity of deep neural networks

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Science China(Information Sciences) 2016年第7期59卷 173-184页

作者： Wei GAO zhi-hua ZHOU National Key Laboratory for Novel Software Technology Nanjing University Collaborative Innovation Center of Novel Software Technology and Industrialization Nanjing University

Great successes of deep neural networks have been witnessed in various real applications. Many algorithmic and implementation techniques have been developed; however, theoretical understanding of many aspects of deep neural networks is far from clear. A particular interesting issue is the usefulness of dropout,which was motivated from the intuition of preventing complex co-adaptation of feature detectors. In this paper,we study the Rademacher complexity of different types of dropouts, and our theoretical results disclose that for shallow neural networks(with one or none hidden layer) dropout is able to reduce the Rademacher complexity in polynomial, whereas for deep neural networks it can amazingly lead to an exponential reduction.

关键词： artificial intelligence machine learning deep learning dropout Rademacher complexity