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On a Problem of Hornik

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Acta Mathematica Sinica,English Series 2015年第7期31卷 1141-1148页

作者： ting fan XIE Fei Long CAO Department of Mathematics and Information Sciences China Jiliang University

In 1991, Hornik proved that the collection of single hidden layer feedforward neural net- works （SLFNs） with continuous, bounded, and non-constant activation function a is dense in C（K） where K is a compact set in Rs （see Neural Networks, 4（2）, 251-257 （1991））. Meanwhile, he pointed out ＂Whether or not the continuity assumption can entirely be dropped is still an open quite challenging problem＂. This paper replies in the affirmative to the problem and proves that for bounded and continuous almost everywhere （a.e.） activation function σ on R, the collection of SLFNs is dense in C（K） if and only if a is un-constant a.e..

关键词： Neural networks approximation activation function

Improved preparation of(1S,3',4'S,5'S,6'R)-5-chloro-6-[(4-ethylphenyl)methyl]-3',4',5',6'-tetrahydro-6'-(hydroxymethyl)-spiro[isobenzofuran-l(3H),2'-[2H]pyran]-3',4',5'-triol

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Chinese Chemical Letters 2013年第2期24卷 131-133页

作者： Yong-Hai Liu ting-Ming Fu Chun-Yan Ou wen-Ling fan Guo-Ping Peng School of Pharmacy Nanjing University of Chinese Medicine

Received 9 November 2012 Received in revised form 23 November 2012 Accepted 3 December 2012 Available online 29 January 2013

关键词： Type 2 diabetesSodiurn glucose co-transporter 2InhibitorPreparation

The Ridge Function Representation of Polynomials and an Application to Neural Networks

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Acta Mathematica Sinica,English Series 2011年第11期27卷 2169-2176页

作者： ting fan XIE Fei Long CAO Department of Information and Mathematics Sciences China Jiliang University Hangzhou 310018 P. R. China

The first goal of this paper is to establish some properties of the ridge function representation for multivariate polynomials, and the second one is to apply these results to the problem of approximation by neural networks. We find that for continuous functions, the rate of approximation obtained by a neural network with one hidden layer is no slower than that of an algebraic polynomial.

关键词： Ridge function neural network polynomial approximation

The Rate of Approximation of Gaussian Radial Basis Neural Networks in Continuous Function Space

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Acta Mathematica Sinica,English Series 2013年第2期29卷 295-302页

作者： ting fan XIE Fei Long CAO Institute of Metrology and Computational Science China Jiliang University

There have been many studies on the dense theorem of approximation by radial basis feedforword neural networks, and some approximation problems by Gaussian radial basis feedforward neural networks （GRBFNs） in some special function space have also been investigated. This paper considers the approximation by the GRBFNs in continuous function space. It is proved that the rate of approximation by GRNFNs with nd neurons to any continuous function f defined on a compact subset K R^d can be controlled by w（f, n^-1/2）, where w（f, t） is the modulus of continuity of the function f.

关键词： Gaussian radial basis feedforward neural networks approximation rate of convergence modulus of continuity

Encrypting Chemical Reactivity in Protein Sequences toward Information-Coded Reactions

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Chinese Journal of Chemistry 2020年第8期38卷 864-878页

作者： fan Zhang wen-Bin Zhang Beijing National Laboratory for Molecular Sciences Key Laboratory of Polymer Chemistry&Physics of Ministry of EducationCenter for Soft Matter Science and EngineeringCollege of Chemistry and Molecular EngineeringPeking UniversityBeijing 100871China

Contents *** *** Occurring Covalent Crosslinks in Proteins *** Encoded Protein Coupling Reactions *** *** engineering *** bioconjugation ***-based biomaterials *** biology *** from Nature:Information-Coded Chemical Reactions *** and Perspectives *** Controlling chemical reactivity has been a central theme in *** ways to manipulate reactivity include varying concentration and/or temperature,putting the bonds under tension,or changing the electronic states by neighboring substituents,*** the Information Age,one may wonder if information about chemical reactivity could be somehow encrypted in the chemical structure in a simple and straightforward way to allow for facile tailoring of reactivity toward intelligent design ofcompounds and reactions.

关键词： reactivity straight bonds

Asymptotic Property for Some Series of Probability

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Acta Mathematicae Applicatae Sinica 2013年第1期29卷 179-186页

作者： Jian-jun HE ting-fan XIE Department of Mathematics China Jiliang University

Abstract Let {X, Xn, n ≥ 1} be a sequence of *** variables with zero mean, and set Sn = n∑k=1Xk, EX2 = σ2 〉 0, λ（ε） = ∞∑n=1P（1Sn1 ≥ ns）. In this paper, we discuss the rate of the approximation of σ2 by ... 详细信息

关键词： asymptotic property the rate of approximation complete convergence

Energy Efficient Social Routing Framework for Mobile Social Sensing Networks

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Tsinghua Science and Technology 2016年第4期21卷 363-373页

作者： fan Li Chenfei Tian ting Li Yu Wang School of Computer Science Beijing Institute of TechnologyBeijing 100081China Department of Computer Science the University of North Carolina at Charlotte9201 University City Blvd.CharlotteNC 28223USA

Mobile social sensing network is one kind of emerging networks in which sensing tasks are performed by mobile users and sensing data are shared and collected by leveraging the intermittent inter-contacts among mobile users. Traditional ad hoc routing protocols are inapplicable or perform poorly for data collection or data sharing in such mobile social networks because nodes are seldom fully connected. In recent years, many routing protocols （especially social-based routing） are proposed to improve the delivery ratio in mobile social networks, but most of them do not consider the load of nodes thus may lead to unbalanced energy consumption among nodes. In this paper, we propose a simple Energy Efficient framework for Social-based Routing （EE-SR） in mobile social sensing networks to balance the load of nodes while maintaining the delivery ratio within an acceptable range by limiting the chances of forwarding in traditional social-based routing. Furthermore, we also propose an improved version of EE-SR to dynamically adjust the controlling parameter. Simulation results on real-life mobile traces demonstrate the efficiency of our proposed framework.

关键词： energy efficient social-based routing delay tolerant networks mobile social sensing networks

New progress in theoretical studies on palladium-catalyzed C-C bond-forming reaction mechanisms

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Science China Chemistry 2016年第11期59卷 1432-1447页

作者： Hujun Xie ting fan Qunfang Lei wenjun fang Department of Applied Chemistry Zhejiang Gongshang University Hangzhou 310018 China Division of Theoretical Chemistry and Biology School of Biotechnology KTH Royal Institute of Technology SE-10044 Stockholm Sweden Department of Chemistry Zhejiang University Hangzhou 310028 China

This review reports a series of mechanistic studies on Pd-catalyzed C-C cross-coupling reactions via density functional theory(DFT) calculations.A brief introduction of fundamental steps involved in these reactions is given,including oxidative addition,transmetallation and reductive *** aim to provide an important review of recent progress on theoretical studies of palladium-catalyzed carbon-carbon cross-coupling reactions,including the C-C bond formation via C-H bond activation,decarboxylation,Pd(Ⅱ)/Pd(Ⅳ) catalytic cycle and double palladiums catalysis.

关键词： density functional theory palladium catalysis C-H bond activation reaction mechanism decarboxylation

EXPONENTIAL CONVERGENCE OF SAMPLE AVERAGE APPROXIMATION METHODS FOR A CLASS OF STOCHASTIC MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

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Journal of Computational Mathematics 2006年第6期24卷 733-748页

作者： fan-wen Meng Hui-fu Xu The Logistics Institute - Asia Pacific National University of Singapore 1 Law Link Singapore School of Mathematics University of Southampton Highfield Southampton S017 1B J UK School of Mathematics University of Southampton Highfield Southampton S017 1B J UK

In this paper, we propose a Sample Average Approximation （SAA） method for a class of Stochastic Mathematical Programs with Complementarity Constraints （SMPCC） recently considered by Birbil, G/irkan and Listes [3]. We study the statistical properties of obtained SAA estimators. In particular we show that under moderate conditions a sequence of weak stationary points of SAA programs converge to a weak stationary point of the true problem with probability approaching one at exponential rate as the sample size tends to infinity. To implement the SAA method more efficiently, we incorporate the method with some techniques such as Scholtes＇ regularization method and the well known smoothing NCP method. Some preliminary numerical results are reported.

关键词： Stochastic mathematical programs with complementarity constraints Sampleaverage approximation Weak stationary points Exponential convergence.