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Table of Content

    25 December 2012, Volume 25 Issue 6
    article
    ADAPTIVE TRACKING OF A CLASS OF FIRST-ORDER SYSTEMS WITH BINARY-VALUED OBSERVATIONS AND FIXED THRESHOLDS
    Jin GUO , Ji-Feng ZHANG ,Yanlong ZHAO
    2012, 25(6):  1041-1051.  DOI: 10.1007/s11424-012-1257-0
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    This paper considers the adaptive tracking problem for a class of first-order systems with binary-valued observations generated via fixed thresholds. A  ecursive projection algorithm is proposed for parameter estimation based on the statistical properties of the system noise. Then, an adaptive control law is designed via the certainty equivalence principle. By use of the conditional expectations of the innovation and output prediction with respect to the estimates, the closed-loop system is shown to be stable and asymptotically optimal. Meanwhile, the parameter estimate is proved to be both almost surely and mean square convergent, and the convergence rate of the estimation error is also obtained. A numerical example is given to demonstrate the efficiency of the adaptive control law.
    MODELING GENETIC REGULATORY NETWORKS: A DELAY DISCRETE DYNAMICAL MODEL APPROACH
    Hao JIANG , Wai-Ki CHING , Kiyoko F,AOKI-KINOSHITA , Dianjing GUO
    2012, 25(6):  1052-1067.  DOI: 10.1007/s11424-012-0283-2
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    Modeling genetic regulatory networks is an important research topic in genomic research and computational systems biology. This paper considers the problem of constructing a genetic regulatory network (GRN) using the discrete dynamic system (DDS) model approach. Although considerable research has been devoted to building GRNs, many of the works did not consider the time-delay effect. Here, the authors propose a time-delay DDS model composed of linear difference equations to represent temporal interactions among significantly expressed genes. The authors also introduce interpolation scheme and re-sampling method for equalizing the non-uniformity of sampling time points. Statistical significance plays an active role in obtaining the optimal interaction matrix of GRNs. The constructed genetic network using linear multiple regression matches with the original data very well. Simulation results are given to demonstrate the effectiveness of the proposed method and model.
    GLOBALLY ASYMPTOTICALLY STABLE FORMATION CONTROL OF THREE AGENTS
    Qin WANG ,Yu-Ping TIAN ,Yaojin XU
    2012, 25(6):  1068-1079.  DOI: 10.1007/s11424-012-0332-x
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    This paper considers the formation-shape control of three agents in the plane. By adding an adaptive perturbation to any agent’s movement direction, a novel control strategy is proposed. It is shown that the proposed novel control law can not only guarantee the global asymptotical stability of the desired formation shape, but also ensure the collision avoidance of agents between each other. Simulation results are provided to illustrate the effectiveness of the control algorithm.
    MULTITASK n-VEHICLE EXPLORATION PROBLEM: COMPLEXITY AND ALGORITHM
    Yangyang XU , Jinchuan CUI
    2012, 25(6):  1080-1092.  DOI: 10.1007/s11424-012-9324-0
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    This paper extends the single-task n-Vehicle Exploration Problem to Multitask n-Vehicle Exploration Problem (MTNVEP), by combining n-Vehicle Exploration Problem with Job Scheduling Problem. At first, the authors prove that MTNVEP is NP-hard for fixed number of tasks, and it is strongly NP-hard for general number of tasks. Then they propose an improved accurate algorithm with computing time O(n3n), which is better than O(n!) as n becomes sufficiently large. Moreover, four heuristic algorithms are proposed. Effectiveness of the heuristic algorithms is illustrated by experiments at last.
    A NOVEL METHOD FOR PLANNING A STAGED EVACUATION
    Xiang LI , Bo HUANG , Zhengjun LIU , Xihui ZHANG , Jing SUN
    2012, 25(6):  1093-1107.  DOI: 10.1007/s11424-012-0257-4
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    This paper presents an innovative method to facilitate making such a plan. Using an algorithm to schedule the starting time of each evacuation group, the method guarantees that the time of completing a large-scale evacuation is very close to its theoretically shortest evacuation time. Meanwhile, unlike a simultaneous evacuation, during a staged evacuation planned with the proposed method, all evacuees can take the shortest path to a safe exit. Once evacuees start off, they will not suffer any traffic congestion. The above advantages of this innovative method are achieved by using an algorithm with three nested loops. Experiments have been conducted, and their results have validated the proposed method.
    A SECOND ORDER MEHROTRA-TYPE PREDICTOR-CORRECTOR ALGORITHM FOR SEMIDEFINITE OPTIMIZATION
    Mingwang ZHANG
    2012, 25(6):  1108-1121.  DOI: 10.1007/s11424-012-0317-9
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    Mehrotra-type predictor-corrector algorithm is one of the most effective primal-dual interiorpoint methods. This paper presents an extension of the recent variant of second order Mehrotra-type predictor-corrector algorithm that was proposed by Salahi, et al.(2006) for linear optimization. Based on the NT direction as Newton search direction, it is shown that the iteration-complexity bound of the algorithm for semidefinite optimization is O(n 3 2 log X0·S0 ε ), which is similar to that of the corresponding algorithm for linear optimization.
    RELIABILITY INDICES OF DISCRETE-TIME GeoX/G/1 QUEUEING SYSTEM WITH UNRELIABLE SERVICE STATION AND MULTIPLE ADAPTIVE DELAYED VACATIONS
    Yinghui TANG, Miaomiao YU, Xi YUN ,Shujuan HUANG
    2012, 25(6):  1122-1135.  DOI: 10.1007/s11424-012-1062-9
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    This paper considers the discrete-time GeoX/G/1 queueing model with unreliable service station and multiple adaptive delayed vacations from the  erspective of reliability research. Following problems will be discussed: 1) The probability that the server is in a “generalized busy period” at time
    n; 2) The probability that the service station is in failure at time n, i.e., the transient unavailability of the service station, and the steady state unavailability of the service station; 3) The expected number of service station failures during the time interval (0, n], and the steady state failure frequency of the service station; 4) The expected number of service station breakdowns in a server’s “generalized busy period”. Finally, the authors demonstrate that some common discrete-time queueing models with unreliable service station are special cases of the model discussed in this paper.
    DEPENDENCE ANALYSIS OF REGRESSION MODELS IN TIME SERIES
    Xuanhe WANG , Maochao XU ,Shengwang MENG
    2012, 25(6):  1136-1142.  DOI: 10.1007/s11424-012-1091-4
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    In this paper, the relative dependence of a linear regression model is studied. In particular,the dependence of autoregressive models in time series are investigated. It is shown that for the first-order non-stationary autoregressive model and the random walk with trend and drift model, the dependence between two states decreases with lag. Some numerical examples are presented as well.
    INFERENCE ON COEFFICIENT FUNCTION FOR VARYING-COEFFICIENT PARTIALLY LINEAR MODEL
    Jingyan FENG , Riquan ZHANG
    2012, 25(6):  1143-1157.  DOI: 10.1007/s11424-012-0324-x
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    One important model in handling the multivariate data is the varying-coefficient partially linear regression model. In this paper, the generalized likelihood ratio test is developed to test whether its coefficient functions are varying or not. It is showed that the normalized proposed test follows asymptotically χ2-distribution and theWilks phenomenon under the null hypothesis, and its asymptotic power achieves the optimal rate of the convergence for the  onparametric hypotheses testing. Some simulation studies illustrate that the test works well.
    INFERENCE FOR REPEATED MEASURES MODELS UNDER HETEROSCEDASTICITY
    Weiyan MU , Xingzhong XU
    2012, 25(6):  1158-1170.  DOI: 10.1007/s11424-012-0170-x
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    This paper considers a widely used mixed effects model in repeated measures under heteroscedasticity. Hypotheses of the equality of the fixed effects and the simultaneous confidence intervals for all pair-wise differences are discussed. A generalized F-test has been proposed to test the equality of the fixed effects in the model, but simulation results for evaluating its performance have not been shown in the literature. Moreover, the generalized F-test cannot be used to deduce the simultaneous confidence intervals for all pair-wise differences of the fixed effects. The authors propose two new p-values to test the hypotheses of equality of the fixed effects and simultaneous confidence intervals of the differences of the effects based on the generalized pivotal quantities derived in this paper. The authors also compare the empirical performances of the proposed tests and the generalized F-test. The type I error rates and powers of these tests are evaluated using the Monte Carlo simulation. The simulation studies show that the generalized F-test does not perform well in terms of type I error rate under various sample size and parameter combinations. However, the type I error probabilities of the proposed tests are always close to the nominal value. It can also be seen that the simultaneous confidence intervals perform well.
    OPTIMAL PROPORTIONAL REINSURANCE UNDER DEPENDENT RISKS
    Fengqing HU , Kam C YUEN
    2012, 25(6):  1171-1184.  DOI: 10.1007/s11424-012-1045-x
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    This paper considers a correlated risk model with thinning-dependence structure. The authors investigate the optimal proportional reinsurance that maximizes the adjustment coefficient and  he optimal proportional reinsurance under mean variance principle for the proposed model. The authors derive the optimal solutions and the numerical illustrations to show the impact of the dependence among the classes of business on the optimal reinsurance arrangements.
    ZERO FINITE-ORDER SERIAL CORRELATION TEST IN A PARTIALLY LINEAR SINGLE-INDEX MODEL
    Xiaohui LIU, Guofu WANG, Xuemei HU ,Bo LI
    2012, 25(6):  1185-1201.  DOI: 10.1007/s11424-012-0033-5
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    The purpose of this paper is to test the underlying serial correlation in a partially linear single-index model. Under mild conditions, the proposed test  tatistics are shown to have standard chisquared distribution asymptotically when there is no serial correlation in the error terms. To illustrate their finite sample properties, simulation experiments, as well as a real data example, are also provided. It is revealed that the finite sample performances of the proposed test statistics are satisfactory in terms of both estimated sizes and powers.
    LACK-OF-FIT TESTS BASED ON WEIGHTED RATIO OF RESIDUALS AND VARIANCES
    Maozai TIAN , Youxi LUO , Yunan SU , Yan FAN , Junlin HAN
    2012, 25(6):  1202-1214.  DOI: 10.1007/s11424-012-0193-3
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    This article proposes a new lack-of-test based on the weighted ratio of residuals and variances for partially linear regression models. The large and small sampling properties of the proposed test are established. The testing procedure is illustrated via several examples. Simulation studies show that
    the testing procedures are powerful even in small samples. An application of the test to a real data set is presented.
    ON THE NONEXISTENCE OF NONTRIVIAL SMALL CYCLES OF THE μ FUNCTION IN 3x+1 CONJECTURE
    Dengguo FENG, Xiubin FAN , Liping DING ,Zhangyi WANG
    2012, 25(6):  1215-1222.  DOI: 10.1007/s11424-012-0280-5
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    This paper studies the property of the recursive sequences in the 3x + 1 conjecture. The authors introduce the concept of μ function, with which the 3x+1 conjecture can be transformed into two other conjectures: one is eventually periodic conjecture of the μ function and the other is periodic point conjecture. The authors prove that the 3x + 1 conjecture is equivalent to the two conjectures above. In 2007, J. L. Simons proved the non-existence of nontrivial 2-cycle for the T function. In this paper, the authors prove that the μ function has no l-periodic points for 2 ≤ l ≤ 12. In 2005, J. L. Simons and B. M. M de Weger proved that there is no nontrivial l-cycle for the T function for  l ≤ 68, and in this paper, the authors prove that there is no nontrivial l-cycle for the μ function for 2 ≤ l ≤ 102.
    DISTRIBUTION OF ONE-ERROR LINEAR COMPLEXITY OF BINARY SEQUENCES FOR ARBITRARY PRIME PERIOD
    Lin TAN , Wenfeng QI , Hong XU
    2012, 25(6):  1223-1233.  DOI: 10.1007/s11424-012-1101-6
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    Complexity measures for sequences, such as the linear complexity and the k-error linear complexity, play an important role in stream ciphers. This  ontribution studies the distribution of 1-error linear complexity of binary sequences with arbitrary prime period. For any odd prime N, the authors present all possible values of 1-error linear complexity of N-periodic binary sequences, and derive the exact formulas to count the number of N-periodic binary  equences with any given 1-error linear complexity.
    AUTOMATED DERIVATION OF THE CONSERVATION LAWS FOR NONLINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS
    Jiaofeng ZHU,Yinping LIU
    2012, 25(6):  1234-1248.  DOI: 10.1007/s11424-012-9297-z
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    Based on Wu’s elimination method and “divide-and-conquer” strategy, the undetermined coefficient algorithm to construct polynomial form conservation laws for nonlinear differential-difference equations (DDEs) is improved. Furthermore, a Maple package named CLawDDEs, which can entirely automatically derive polynomial form conservation laws of nonlinear DDEs is presented. The effectiveness of CLawDDEs is demonstrated by application to different kinds of examples.