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Online Learning Approaches in Maximizing Weighted Throughput in an Unreliable Channel

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Tsinghua Science and Technology 2012年第5期17卷 567-574页

作者： zhi Zhang fei Li Department of Computer Science George Mason University Fairfax VA 22030 USA

We design online algorithms to schedule unit-length packets with values and deadlines through an unreliable communication channel. In this model, time is discrete. Packets arrive over time; each packet has a non-negative value and an integer deadline. In each time step, at most one packet can be sent. The ratio of successfully delivering a packet depends on the channel＇s quality of reliability. The objective is to maximize the total value gained by delivering packets no later than their respective deadlines. In this paper, we conduct theoretical and empirical studies of online learning approaches for this model and a few of its variants. These online learning algorithms are analyzed in terms of external regret. We conclude that no online learning algorithms have constant regrets. Our online learning algorithms outperform online competitive algorithms in terms of algorithmic simplicity and running complexity. In general, these online learning algorithms work no worse than the best known competitive online algorithm for maximizing weighted throughput in practice.

关键词： online learning algorithm unreliable communication channel competitive online algorithm

Approach for analyzing the ultimate strength of concrete filled steel tubular arch bridges with stiffening girder

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第5期8卷 682-692页

作者： ZHANG zhi-cheng xie Xu ZHANG He CHEN Heng-zhi Department of Civil Engineering Zhejiang University Hangzhou 310027 China

A convenient approach is proposed for analyzing the ultimate load carrying capacity of concrete filled steel tubular (CFST) arch bridge with stiffening girders. A fiber model beam element is specially used to simulate the stiffening girder and CFST arch rib. The geometric nonlinearity, material nonlinearity, influence of the construction process and the contribution of prestressing reinforcement are all taken into consideration. The accuracy of this method is validated by comparing its results with experimental results. Finally, the ultimate strength of an abnormal CFST arch bridge with stiffening girders is investigated and the effect of construction method is discussed. It is concluded that the construction process has little effect on the ultimate strength of the bridge.

关键词： Ultimate strength Concrete filled steel tubular (CFST) arch bridge Stiffening girder Fiber model beam element Construction process

Predictability of Chinese Summer Extreme Rainfall Based on Arctic Sea Ice and Tropical Sea Surface Temperature

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Journal of Ocean University of China 2019年第3期18卷 626-632页

作者： ZHU zhihui HUANG fei xie Xiao Shanghai Marine Meteorological Center Shanghai 201306 China Key Laboratory of Physical Oceanography Ocean University of China Qingdao 266100 China Ningbo Collaborative Innovation Center of Nonlinear Harzard System of Ocean and Atmosphere Ningbo University Ningbo 315211 China

Chinese summer extreme rainfall often brings huge economic losses, so the prediction of summer extreme rainfall is necessary. This study focuses on the predictability of the leading mode of Chinese summer extreme rainfall from empirical orthogonal function(EOF) analysis. The predictors used in this study are Arctic sea ice concentration(ASIC) and regional sea surface temperature(SST) in selected optimal time periods. The most important role that Arctic sea ice(ASI) plays in the appearance of EOF1 may be strengthening the high pressure over North China, thereby preventing water vapor from going north. The contribution of SST is mainly at low latitudes and characterized by a significant cyclone anomaly over South China. The forecast models using predictor ASIC(PA), SST(PS), and the two together(PAS) are established by using data from 1980 to 2004. An independent forecast is made for the last 11 years(2005-2015). The correlation coefficient(COR) skills between the observed and cross-validation reforecast principal components(PC) of the PA, PS, and PAS models are 0.47, 0.66, and 0.76, respectively. These values indicate that SST is a major cause of Chinese summer extreme rainfall during 1980-2004. The COR skill of the PA model during the independent forecast period of 2004-2015 is 0.7, which is significantly higher than those of the PS and PAS models. Thus, the main factor influencing Chinese summer extreme rainfall in recent years has changed from low latitudes to high latitudes. The impact of ASI on Chinese summer extreme rainfall is becoming increasingly significant.

关键词： ASI summer extreme rainfall prediction

Sign-changing Solutions to Nonlinear Elliptic Equations with Hardy Potential and Critical Parameter in R^2

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Acta Mathematicae Applicatae Sinica 2019年第3期35卷 689-694页

作者： Chao-dong xie zhi-hui CHEN School of Economics&Management Guizhou University for Ethinic MinoritiesGuizhou 550025China chool of Mathematics South China University of TechnologyGuangzhou 510640China

In this paper,a new Hilbert space is defined which is embedded into W01,q(Ω)for 1≤q<*** using sign-changing critical point theory,we prove the existence of infinitely many sign-changing solutions in this new space f... 详细信息

关键词： elliptic PDE sign-changing solution critical point

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

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

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

A CASCADIC MULTIGRID METHOD FOR EIGENVALUE PROBLEM

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Journal of Computational Mathematics 2017年第1期35卷 74-90页

作者： Xiaole Han Hehu xie fei Xu IAPCM Institute of Applied Physics and Computational Mathematics Beijing 100093 China LSEC NCMIS Institute of Computational Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China Beijing Institute for Scientific and Engineering Computing Beijing University of Technology Beijing 100124 China

A cascadic multigrid method is proposed for eigenvalue problems based on the multilevel correction scheme. With this new scheme, an eigenvalue problem on the finest space can be solved by linear smoothing steps on a series of multilevel finite element spaces and nonlinear correcting steps on special coarsest spaces. Once the sequence of finite element spaces and the number of smoothing steps are appropriately chosen, the optimal convergence rate with the optimal computational work can be obtained. Some numerical experiments are presented to validate our theoretical analysis.

关键词： Eigenvalue problem Cascadic multigrid Multilevel correction scheme Finiteelement method.

The construction and approximation of feedforward neural network with hyperbolic tangent function

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Applied Mathematics(A Journal of Chinese Universities) 2015年第2期30卷 151-162页

作者： CHEN zhi-xiang CAO fei-long Department of Mathematics Shaoxing University Department of Mathematics China Jiliang University

In this paper, we discuss some analytic properties of hyperbolic tangent function and estimate some approximation errors of neural network operators with the hyperbolic tan- gent activation function. Firstly, an equation of partitions of unity for the hyperbolic tangent function is given. Then, two kinds of quasi-interpolation type neural network operators are con- structed to approximate univariate and bivariate functions, respectively. Also, the errors of the approximation are estimated by means of the modulus of continuity of function. Moreover, for approximated functions with high order derivatives, the approximation errors of the constructed operators are estimated.

关键词： Hyperbolic tangent function neural networks approximation modulus of continuity