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Neural networks for optimal approximation of continuous functions in R^d

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Applied Mathematics(A Journal of Chinese Universities) 2012年第3期27卷 335-344页

作者： XIE ting-fan ZHOU Xin-long Department of Mathematics China Jiliang University310018 HangzhouChina Department of Mathematics University of Duisburg-Essen47048 DuisburgGermany

Using some regular matrices we present a method to express any multivariate algebraic polynomial of total order n in a normal form. Consequently, we prove constructively that, to approximate continuous target function... 详细信息

关键词： approximation rate neural network ridge function sigmoidal function.

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

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

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

Cytotoxic effect and possible mechanisms of Tetracaine on human corneal epithelial cells in vitro

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International Journal of Ophthalmology(English edition) 2016年第4期9卷 497-504页

作者： Xin Pang ting-Jun fan Key Laboratory for Corneal Tissue Engineering College of Marine Life Sciences Ocean University of China

AIM： To demonstrate the cytotoxic effect and possible mechanisms of Tetracaine on human corneal epithelial（HCEP） cells in vitro.·METHODS： In vitro cultured HCEP cell were treated with Tetracaine hydrochloride at different doses for different times, and their morphology, viability, and plasma membrane permeability were detected by light microscopy, methyl thiazolyl tetrazolium（MTT） assay,and acridine orange（AO）/ethidium bromide（EB） staining,respectively. Their cell cycle progression, phosphati-dylserine orientation in plasma membrane, and mitochondrial membrane potential（MTP） were assessed by flow cytometry. DNA fragmentation, ultrastructure,caspase activation, and the cytoplasmic apoptosis inducing factor（AIF） and cytochrome c（Cyt. c） along with the expression of B-cell lymphoma-2（Bcl-2） family proteins were examined by gel electrophoresis,transmission electron microscope, enzyme linked immunosorbent assay（ELISA）, and Western blot,respectively.·RESULTS： After exposed to Tetracaine at doses from10.0 to 0.3125 g/L, the HCEP cells showed dose- and time-dependent morphological abnormality and typical cytopathic effect, viability decline, and plasma membrane permeability elevation. Tetracaine induced phosphati-dylserine externalization, DNA fragmentation, G1 phase arrest, and ultrastructural abnormality and apoptotic body formation. Furthermore, Tetracaine at a dose of0.3125 g/L also induced caspase-3,-9 and-8 activation,MTP disruption, up-regulation of the cytoplasmic amount of Cyt. c and AIF, the expressions of Bax and Bad, and down-regulation of the expressions of Bcl-2 and Bcl-x L.·CONCLUSION： Tetracaine above 0.3125 g/L（1/32 of its clinical applied dosage） has a dose- and time-dependent cytotoxicity to HCEP cells in vitro, with inducing cellapoptosis via a death receptor-mediated mitochondriondependent pathway.

关键词： Tetracaine cytotoxicity human cornel epithelial cells apoptosis mitochondrion

Systematic Synthesis of Compressive VDTA-Based T-T Filter with Orthogonal Control of f_o and Q

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Journal of Electronic Science and Technology 2020年第3期18卷 276-286页

作者： Yong-An Li Yan-Hua Xi Zhan-ting fan School of Physics and Electronic Engineering Xianyang Normal UniversityXianyang 712000 School of Information Engineering Shaanxi Institute of International Trade&CommerceXi’an 712046

Based on sixteen nullor-mirror models of the voltage differencing transconductance amplifier (VDTA) and port admittance matrices of the tow-Thomas (T-T) filter with orthogonal control between the characteristic frequency(f_0) and figure of merit (Q),two different categories of the voltage-mode and transconductance-mode T-T filters are synthesized by the means of the nodal admittance matrix (NAM) expansion *** category A filter that employs two compressive VDTAs and two grounded capacitors includes four structures,and the category B filter that uses two compressive VDTAs,two grounded capacitors,and one grounded resistor,also includes four *** circuits are suitable for integrated circuit manufacture,and their parameters f_0 and Q can be orthogonally adjusted with varying the bias currents of *** the paper and pencil test is completed,the computer analyses,including alternating current (AC),parameter sweep,Monte Carlo (MC),and noise analyses,are performed to support the synthesis approach.

关键词： Compressive voltage differencing transconductance amplifier(compressive VDTA) nodal admittance matrix(NAM)expansion method systematic synthesis tow-Thomas(T-T)filter

Stretchable Electrochemical Sensors: From Electrode Fabrication to Cell Mechanotransduction Monitoring

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Chinese Journal of Chemistry 2023年第4期41卷 443-457页

作者： Wen-ting fan Wei-Hua Huang Yan-Ling Liu College of Chemistry and Molecular Sciences Wuhan UniversityWuhanHubei430072 China

Electrochemical sensing faces huge challenges in characterizing the transient release of biochemical molecules from deformed cells,due to the severely mechanical mismatch between rigid electrodes and soft *** recent years,the emergence of stretchable electrochemical sensors has made a breakthrough by complying with the deformation of living cells and simultaneous monitoring of mechanically evoked biochemical *** review first summarizes two fundamental strategies for the fabrication of stretchable electrodes from the points of structure and ***,recent progresses in construction of functionalized interface to improve the performance of stretchable electrochemical sensors are ***,the application of stretchable electrochemical sensors in real-time monitoring of biomolecules released by mechanically sensitive cells is ***,some perspectives and challenges of stretchable electrochemical sensors regarding cell detection are discussed.

关键词： Stretchable electrode Electrochemical sensing Fabrication Functionalization Cell mechanotransduction

Molecular insight into the GaP(110)-water interface using machine learning accelerated molecular dynamics

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Journal of Energy Chemistry 2023年第7期82卷 239-247,I0006页

作者： Xue-ting fan Xiao-Jian Wen Yong-Bin Zhuang Jun Cheng State Key Laboratory of Physical Chemistry of Solid Surfaces iChEMCollege of Chemistry and Chemical EngineeringXiamen UniversityXiamen 361005FujianChina Shenzhen Research Institute of Xiamen University Shenzhen 518057GuangdongChina Innovation Laboratory for Sciences and Technologies of Energy Materials of Fujian Province(IKKEM) Xiamen 361005FujianChina

GaP has been shown to be a promising photoelectrocatalyst for selective CO_(2)reduction to *** to the relevance of the interface structure to important processes such as electron/proton transfer,a detailed understanding of the GaP(110)-water interfacial structure is of great *** initio molecular dynamics(AIMD)can be used for obtaining the microscopic information of the interfacial ***,the GaP(110)-water interface cannot converge to an equilibrated structure at the time scale of the AIMD *** this work,we perform the machine learning accelerated molecular dynamics(MLMD)to overcome the difficulty of insufficient sampling by *** the help of MLMD,we unravel the microscopic information of the structure of the GaP(110)-water interface,and obtain a deeper understanding of the mechanisms of proton transfer at the GaP(110)-water interface,which will pave the way for gaining valuable insights into photoelectrocatalytic mechanisms and improving the performance of photoelectrochemical cells.

关键词： Photoelectrocatalysis GaP(110)-water interface Machine learning accelerated molecular dynamics