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Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Table of Content

    15 April 2015, Volume 32 Issue 2 Previous Issue    Next Issue
    Restricted Boltzmann Machines
    ZHANG Chun-xia, JI Nan-nan, WANG Guan-wei
    2015, 32 (2):  159-173.  doi: 10.3969/j.issn.1005-3085.2015.02.001
    Abstract ( 18 )   PDF (928KB) ( 1 )   Save
    A restricted Boltzmann machine (RBM) is a particular type of random neural network model which has two-layer architecture, symmetric connections and no self-feedback. The two layers in an RBM are fully connected but there are no connections within the same layer. Recently, with the advent of a fast learning algorithm for RBMs (i.e., contrastive divergence), the machine learning community set off a surge to study the theory and applications of RBMs since it has many advantages. For example, a RBM provides us an effective tool to detect features. When a feed-forward neural network is initialized with an RBM, its generalization capability can be significantly improved. A deep belief network composed of several RBMs can detect more abstract features. Due to the advantages and wide applications of RBMs in deep learning, this paper attempts to provide a introductory guide for novice. It presents a detailed introduction of basic RBM model, its representative learning algorithm, parametric settings, evaluation methods, its variants and etc. Finally, some research directions of RBMs that are deserved to be further studied are discussed.
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    Fault-tolerant Output Feedback Control for a Class of Multiple Input Fuzzy Bilinear Systems
    YU Yang, WANG Wei
    2015, 32 (2):  174-184.  doi: 10.3969/j.issn.1005-3085.2015.02.002
    Abstract ( 19 )   PDF (256KB) ( 1 )   Save
    In this paper, a fuzzy fault-tolerant control approach is proposed for a class of multiple input fuzzy bilinear systems with unmeasurable states. First of all, a fuzzy detective observer is designed to detect the fault. Based on the developed detective observer, a fuzzy controller is proposed to guarantee the closed-loop system without faults is asymptotically stable. Then, a fuzzy adaptive diagnostic observer is developed to estimate the fault. Finally, the fault estimation is applied to fault accommodation and a fault-tolerant controller is designed. Based on Lyapunov stability, it is proved that the fault-tolerant controller ensures the closed-loop system with faults is asymptotically stable. An example is presented to show the effectiveness of the proposed control method.
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    Accuracy Analysis of Monte Carlo Method and its Application in the Arithmetic Average Asian Option Pricing
    ZHANG Ying-ying, DAI Chun-lan
    2015, 32 (2):  185-196.  doi: 10.3969/j.issn.1005-3085.2015.02.003
    Abstract ( 19 )   PDF (249KB) ( 2 )   Save
    This paper discusses the accuracy analysis of the Monte Carlo (MC) method and its application in the arithmetic average Asian option pricing. First of all, we analyze the accuracy of the MC method and discuss two kinds of convergence in distribution to the standard normal distribution (namely standardizing the sample mean with the standard deviation and the standard error). Furthermore, we discuss the accuracy and the standard deviation (error) of the three kinds of MC methods (namely Crude MC, Antithetic MC, and Control MC). Then, we introduce the application of the MC method in the calculation of Asian option price. Finally, the numerical simulations of the arithmetic average Asian call option price show the following results: the two simulated success frequencies are both close to the theoretical probabilities; when the sample mean is standardized to be the standard normal distribution, the standard deviation is better than the standard error.
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    Analysis on the Electric Power Cable Fault Location
    LI Min
    2015, 32 (2):  197-204.  doi: 10.3969/j.issn.1005-3085.2015.02.004
    Abstract ( 16 )   PDF (1864KB) ( 2 )   Save
    Pulse current method is applied to locate the fault of sub-way cables in practice, due to the complexity of the sub-way failures and the attenuation of transmit waves, a certain error exists. This paper introduces a method that combines the measurement with pulse current method and multiple-layer wavelet analysis, and the measurement accuracy is then approved. Daubechies (db2) wavelet analysis method is implemented with five-layer decomposition of raw waveforms, which could well eliminate the cable clutters, improve the signal recognition rate, reduce the measuring errors, and finally effectively improve the accuracy of online fault distance measurement.
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    Equivalent Definitions of T-indexed Hidden Markov Chains
    WANG Bao, YANG Wei-guo
    2015, 32 (2):  205-212.  doi: 10.3969/j.issn.1005-3085.2015.02.005
    Abstract ( 14 )   PDF (147KB) ( 1 )   Save
    In this paper, we give the definition of tree indexed hidden Markov chain with finite state space based on the concept of hidden Markov model. In our definition, tree indexed hidden Markov chain consists of two tree indexed random processes. The underlying process is a tree indexed Markov chain and can not be observed, and the second process is conditional independent of the former. For the arbitrary vertex in tree, the second process only dependents on the underlying process. Finally, we propose three equivalent definitions.
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    A Modified Finite Volume Method for Solving Interface Problem of Elliptic Equation
    XU Xiao-lei, FENG Xiu-fang
    2015, 32 (2):  213-225.  doi: 10.3969/j.issn.1005-3085.2015.02.006
    Abstract ( 21 )   PDF (539KB) ( 1 )   Save
    Based on classical finite volume method for solving two dimensional elliptic equation with discontinuous efficient, a modified finite volume method is presented in this paper. The finite difference method is cooperated with for dealing with some grid point around boundary, and more Taylor expansion items of flux function are intercepted in order to obtain higher numerical accuracy. There is first order accuracy at interface and second order accuracy in the whole domain. Numerical results indicate that the modified finite volume method is effective.
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    Natural BEM with Non-uniform Grids and its Coupling Method for Exterior Anisotropic Problems
    ZHENG Quan, QIN Feng, GAO Yue
    2015, 32 (2):  226-238.  doi: 10.3969/j.issn.1005-3085.2015.02.007
    Abstract ( 18 )   PDF (216KB) ( 1 )   Save
    For the anisotropic problems in 2-D unbounded domains, this paper proposes a natural BEM with non-uniform grids on the elliptic boundary and a coupling of NBEM and FEM with non-uniform grids on the elliptic artificial boundary. Then, the convergence theorems of the NBEM and the coupling method are proved. In addition, the moving mesh method based on equidistribution principle is introduced into the NBEM and the coupling method, respectively. Numerical examples verify the convergence theorems and demonstrate the advantage in accuracy and efficiency of the proposed methods.
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    New Robust Stability Criteria for Neutral Systems with Mixed Time-varying Delays and Nonlinear Perturbation
    WU Yu-bin, ZHANG He-xin, HUI Jun-jun, ZHOU Xin
    2015, 32 (2):  239-250.  doi: 10.3969/j.issn.1005-3085.2015.02.008
    Abstract ( 17 )   PDF (158KB) ( 2 )   Save
    Neutral time delay system is a special system which has wide application in prac-tical systems. In this paper, we consider the delay-dependent robust stability problem for neutral system with mixed time-varying delays and nonlinear perturbation. Based on the direct Lyapunov method, a new Lyapunov-Krasovskii (L-K) functional with triple integral terms involving lower and upper bounds of interval time-varying delays is constructed for the system. Then, combined with the integral inequalities method, the free weighting matrix approach and the convex combination technique, a neutral and discrete delay-dependent stability criteria for the system is formulated in terms of linear matrix inequalities (LMIs). Finally, the numerical examples are presented to illustrate the effectiveness and improvement over some existing results in the literature with the proposed results.
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    A Set of New Criterion for Judging Nonsingular $H$-matrices
    WANG Lei-lei, XUE Yuan, LIU Jian-zhou
    2015, 32 (2):  251-260.  doi: 10.3969/j.issn.1005-3085.2015.02.009
    Abstract ( 16 )   PDF (143KB) ( 1 )   Save
    Nonsingular $H$-matrix plays a significant role in the control theory, the scientific computation and the applications in engineering. However, it is difficult to specify a non-singular $H$-matrix in practice. In this paper, we partition the row index set by studying the elements of a matrix, and construct a positive diagonal matrix. Then, we apply some techniques in inequalities to obtain a new criterion for nonsingular $H$-matrices. We also obtain several similar results in the cases of irreducible matrices and matrices with non-zero elements chains. These consequences improve and generalize the related results, and the advantage of the proposed consequences are illustrated by several numerical examples.
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    Retarded Nonlinear Integral Inequalities with Iterative Integral and Their Applications
    ZHANG Qian, XUE Shu-wen, ZHENG Zhao-wen
    2015, 32 (2):  261-268.  doi: 10.3969/j.issn.1005-3085.2015.02.010
    Abstract ( 19 )   PDF (125KB) ( 1 )   Save
    Growall-Bellman inequality is one of the most important inequalities investigating the qualitative and quantitative properties of solutions for differential equations such as stability, boundedness, asymptotic property. In this paper, some new generalized retarded nonlinear integral inequalities are discussed, and upper bound estimations of unknown functions are given by applying analysis technique and classical inequalities theories. These estimations can be employed ied to the certain nonlinear differential-integral equations. Finally, the upper bound of all solutions is given, which is the theoretic\, basis for the estimation of solutions, dynamical systems and control system.
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    A New One-parameter Filled Function Algorithm
    LI Bo, LU Dian-jun
    2015, 32 (2):  269-275.  doi: 10.3969/j.issn.1005-3085.2015.02.011
    Abstract ( 18 )   PDF (136KB) ( 1 )   Save
    This paper is concerned a deterministic solution method for global optimization of functions with continuous variables. A filled function with one parameter is presented and the theoretical properties of the filled function are proved. Moreover, a filled function algorithm is proposed for continuous global optimization problem. The filled function algorithm consists of two phases: a local search phase and a function filling phase. In the local search phase, we apply local minimization methods to obtain a local minimizer of the filled function. The unconstrained minimization of the filled function allows to escape from any local minima of the original objective function. In the function filling phase, based on the current local minimizer, we construct a filled function. The two phases repeat alternatively until the termination criterion is met. Finally, the numerical results of the proposed filled function algorithm are presented.
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    Confidence Regions for Regression Coefficients in Linear Models under Associated Errors
    LI Ying-hua, QIN Yong-song, LEI Qing-zhu
    2015, 32 (2):  276-290.  doi: 10.3969/j.issn.1005-3085.2015.02.012
    Abstract ( 21 )   PDF (145KB) ( 1 )   Save
    Association often occurs in certain reliability theory problems, as well as in some important models employed in statistical mechanics. In this paper, we investigate the construction of the confidence regions for the regression vector $\beta$ in a linear model under stationary and associated errors. It is shown that the blockwise empirical likelihood (EL) ratio statistic for $\beta$ asymptotically has $\chi^2$ distribution. The result is applied to obtain an EL-based confidence region for $\beta$.
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    Singular Perturbation Problem for Reaction Diffusion Time Delay Equation with Boundary Perturbation
    WANG Wei-gang, SHI Lan-fang, HAN Xiang-lin, MO Jia-qi
    2015, 32 (2):  291-297.  doi: 10.3969/j.issn.1005-3085.2015.02.013
    Abstract ( 16 )   PDF (106KB) ( 1 )   Save
    The nonlinear singular perturbation problem for the reaction diffusion time delay equation with boundary perturbation is considered in this paper. Firstly, the redu-ced solution is obtained. Secondly, the outer solution of the original problem is constructed. Then, introducing a stretched variable, the initial layer correction of solution is obtained. Finally, under the suitable conditions, applying the theory of differential inequalities the uniformly valid asymptotic expansion of solution for the original initial boundary value problem is proved.
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    Two Strongly Convergent CQ Algorithms for Split Feasibility Problem
    DANG Ya-zheng, XUE Zhong-hui, GAO Yan
    2015, 32 (2):  298-306.  doi: 10.3969/j.issn.1005-3085.2015.02.014
    Abstract ( 17 )   PDF (106KB) ( 2 )   Save
    In thins paper, in order to ensure the strong convergence of the iterative procedure for solving split feasibility problem in a real Hilbert space. We firstly construct a modified CQ algorithm by introducing three parametric sequences and prove its strong convergence under some weak conditions. Furthermore, we put another parametric sequence in one operator in the presented algorithm to get a new algorithm, and also prove its strong convergence under some conditions on the parametric sequence. The results in this paper improve and extend the corresponding results.
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    Global Exponential Stability of the Single Commodity Price Fluctuation Model with Delays and Impulses
    SONG Xue-li, ZHAO Pan, WANG Xiao-wei
    2015, 32 (2):  307-316.  doi: 10.3969/j.issn.1005-3085.2015.02.015
    Abstract ( 16 )   PDF (134KB) ( 1 )   Save
    This paper is devoted to the global exponential stability of the single commodity price fluctuation model with delayed and impulsive factors. Particularly, by means of nonlinear measure method, we provide a sufficient condition for global exponential stability of the price fluctuation model. Compared with some existing results, our method abandons the conventional monotonicity of demand and supply functions and considers the impulsive effect on the price fluctuating process, which means that our model is a generalization of existing ones. Moreover, our result is partial improvement and extension of some existing ones. An illustrative example and its simulation are provided to illustrate validity of our method and result.
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