2009年, 第22卷, 第3期　刊出日期：2009-09-25

  

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  ENERGY FLOWS IN COMPLEX ECOLOGICAL SYSTEMS: A REVIEW

  Jiang ZHANG

  Journal of Systems Science and Complexity. 2009, 22(3): 345-359.

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  Energy flow drives the complex systems to evolve. The allometric scaling as the universal energy flow pattern has been found in different scales of ecological systems. It reflects the general power law relationship between flow and store. The underlying mechanisms of energy flow patterns are explained as the branching transportation networks which can be regarded as the result of systematic optimization of a biological target under constraints. Energy flows in the ecological system may be modelled
  by the food web model and population dynamics on the network. This paper reviews the latest progress on the energy flow patterns, explanatory models for the allometric scaling and modelling approach of flow and network evolution dynamics in ecology.
  Furthermore, the possibility of generalizing these flow patterns, modelling approaches to other complex systems is discussed.
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  SKEWNESS OF RETURN DISTRIBUTION AND COEFFICIENT OF RISK PREMIUM

  Fenghua WEN;Xiaoguang YANG

  Journal of Systems Science and Complexity. 2009, 22(3): 360-371.

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  The skewness of the return distribution is one of the important features of the security price. In this paper, the authors try to explore the relationship between the skewness and the coefficient of risk premium. The coefficient of the risk premium is estimated by a GARCH-$M$ model, and the robust measurement of skewness is calculated by Groeneveld-Meeden method. The empirical evidences for the composite indexes from 33 securities markets in the world indicate that the risk compensation requirement in the market where the return distribution is positively skewed is virtually zero, and the risk compensation requirement is positive in a significant level in the market where the return distribution is negative skewed. Moreover, the skewness is negatively correlated with the coefficient of the risk premium.
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  SINGULAR SPECTRUM ANALYSIS: METHODOLOGY AND APPLICATION TO ECONOMICS DATA

  Hossein HASSANI;Anatoly ZHIGLJAVSKY

  Journal of Systems Science and Complexity. 2009, 22(3): 372-394.

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  This paper describes the methodology of singular spectrum analysis (SSA) and demonstrate that it is a powerful method of time series analysis and forecasting, particulary for economic time series. The authors consider the application of SSA to the
  analysis and forecasting of the Iranian national accounts data as provided by the Central Bank of the Islamic Republic of Iran.
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  ON THE COMPLEXITY OF THE NORMAL BASES VIA PRIME GAUSS PERIOD OVER FINITE FIELDS

  Qunying LIAO;Keqin FENG

  Journal of Systems Science and Complexity. 2009, 22(3): 395-406.

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  A formula on the complexity of the normal bases generated by prime Gauss period over finite fields is presented in terms of cyclotomic numbers. Then, the authors determine explicitly the complexity of such normal bases and their dual bases in several cases where the related cyclotomic numbers have been calculated. Particularly, the authors find several series of such normal bases with low complexity.
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  FINITE-TIME RUIN PROBABILITY WITH NQD DOMINATED VARYING-TAILED CLAIMS AND NLOD INTER-ARRIVAL TIMES

  Jingzhi LI;Kaiyong WANG;Yuebao WANG

  Journal of Systems Science and Complexity. 2009, 22(3): 407-414.

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  In 2007, Chen and Ng investigated infinite-time ruin probability with constant interest force and negatively quadrant dependent and extended regularly varying-tailed claims. Following this work, the authors obtain a weakly asymptotic equivalent
  formula for the finite-time and infinite-time ruin probability with constant interest force, negatively quadrant dependent, and dominated varying-tailed claims and negatively lower orthant dependent inter-arrival times. In particular, when the claims are
  consistently varying-tailed, an asymptotic equivalent formula is presented.
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  A 3-DIMENSIONAL DISCRETE MODEL OF HOUSING PRICE AND ITS INHERENT COMPLEXITY ANALYSIS

  Lingling MU;Junhai MA;Liwen CHEN

  Journal of Systems Science and Complexity. 2009, 22(3): 415-421.

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  A discrete nonlinear model of real estate is derived, with which the evolutionary trend among government, consumers and real estate developers is described. The stability, bifurcation, and chaotic behavior of the system are also analyzed by using nonlinear dynamic method. Results show that chaos can be obtained via quasi-periodic transition and double-periodic bifurcation. The influence of dynamic evolutionary trend among stakeholder on system stability is also studied and some interesting conclusions are derived. This research can effectively explain the complex behavior of housing prices.
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  CONVERGENCE ANALYSIS IN SENSE OF LEBESGUE-P NORM OF DECENTRALIZED NON-REPETITIVE ITERATIVE LEARNING CONTROL FOR LINEAR LARGE-SCALE SYSTEMS

  Xiaoe RUAN;Huizhuo WU;Na LI;Baiwu WAN

  Journal of Systems Science and Complexity. 2009, 22(3): 422-434.

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  In this paper, a decentralized iterative learning control strategy is embedded into the procedure of hierarchical steady-state optimization for a class of linear large-scale
  industrial processes which consists of a number of subsystems. The task of the learning controller for each subsystem is to iteratively generate a sequence of upgraded control inputs to take responsibilities of a sequential step functional control signals with distinct scales which are determined by the local decision-making units in the two-layer hierarchical steady-state optimization processing. The objective of the designated strategy is to consecutively improve the transient performance of the
  system. By means of the generalized Young inequality of convolution integral, the convergence of the learning algorithm is analyzed in the sense of Lebesgue-p norm. It is shown that the inherent feature of system such as the multi-dimensionality and
  the interaction may influence the convergence of the non-repetitive learning rule. Numerical simulations illustrate the effectiveness of the proposed control scheme and the validity of the conclusion.
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  A NEW NEURAL NETWORK-BASED ADAPTIVE ILC FOR NONLINEAR DISCRETE-TIME SYSTEMS WITH DEAD ZONE SCHEME

  Ronghu CHI;Zhongsheng HOU

  Journal of Systems Science and Complexity. 2009, 22(3): 435-445.

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  By introducing a dead-zone scheme, a new neural network based adaptive iterative learning control (ILC) (NN-AILC) scheme is presented for nonlinear discrete-time systems, where the NN weights are time-varying. The most distinct contribution of the
  proposed NN-AILC is the relaxation of the identical conditions of initial state and reference trajectory, which are common requirements in traditional ILC problems. Convergence analysis indicates that the tracking error converges to a bounded ball,
  whose size is determined by the dead-zone nonlinearity. Computer simulations verify the theoretical results.
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  BILEVEL PROGRAMMING MODEL AND SOLUTION METHOD FOR MIXED TRANSPORTATION NETWORK DESIGN PROBLEM

  Haozhi ZHANG;Ziyou GAO

  Journal of Systems Science and Complexity. 2009, 22(3): 446-459.

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  By handling the travel cost function artfully, the authors formulate the transportation mixed network design problem (MNDP) as a mixed-integer, nonlinear bilevel programming problem, in which the lower-level problem, comparing with that of conventional bilevel DNDP models, is not a side constrained user equilibrium
  assignment problem, but a standard user equilibrium assignment problem. Then, the bilevel programming model for MNDP is reformulated as a continuous version of bilevel programming problem by the continuation method. By virtue of the optimal-value
  function, the lower-level assignment problem can be expressed as a nonlinear equality constraint. Therefore, the bilevel programming model for MNDP can be transformed into an equivalent single-level optimization problem. By exploring the inherent nature of the MNDP, the optimal-value function for the lower-level equilibrium assignment problem is proved to be continuously differentiable and its functional value and gradient can be obtained efficiently. Thus, a continuously differentiable but still nonconvex optimization formulation of the MNDP is created, and then a locally convergent algorithm is proposed by applying penalty function method. The inner loop of solving the subproblem is mainly to implement an all-or-nothing assignment. Finally, a small-scale transportation network and a large-scale network are presented to verify the proposed model and algorithm.
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  A MODIFIED LIKELIHOOD RATIO TEST FOR HOMOGENEITY IN BIVARIATE NORMAL MIXTURES OF TWO SAMPLES

  Qingzhu LEI;Yongsong QIN

  Journal of Systems Science and Complexity. 2009, 22(3): 460-468.

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  This paper investigates the asymptotic properties of a modified likelihood ratio statistic for testing homogeneity in bivariate normal mixture models of two samples. The asymptotic null distribution of the modified likelihood ratio statistic is found to be $\chi^2_2$, where $\chi^2_2$ is a chi-squared distribution with $2$ degrees of freedom.
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  ESTIMATION ON SEMIVARYING COEFFICIENT MODELS WITH DIFFERENT DEGREES OF SMOOTHNESS

  Riquan ZHANG;Jingyan FENG;Kaichun WEN;Jianhua DING

  Journal of Systems Science and Complexity. 2009, 22(3): 469-482.

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  Semivarying coefficient models are frequently used in statistical models. In this paper, under the condition that the coefficient functions possess different degrees of smoothness, a two-step method is proposed. In the case, one-step method for the
  smoother coefficient functions cannot be optimal. This drawback can be repaired by using the two-step estimation procedure. The asymptotic mean-squared error for the two-step procedure is obtained and is shown to achieve the optimal rate of convergence. A few simulation studies are conducted to evaluate the proposed
  estimation methods.
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  TESTING SERIAL CORRELATION IN SEMIPARAMETRIC VARYING COEFFICIENT PARTIALLY LINEAR ERRORS-IN-VARIABLES MODEL

  Xuemei HU;Feng LIU;Zhizhong WANG

  Journal of Systems Science and Complexity. 2009, 22(3): 483-494.

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  The authors propose a $V_{N,p}$ test statistic for testing finite-order serial correlation in a semiparametric varying coefficient partially linear errors-in-variables model. The test statistic is shown to have asymptotic normal distribution under the null hypothesis of no serial correlation. Some Monte Carlo experiments are conducted to examine the finite sample performance of the proposed $V_{N,p}$ test statistic.
  Simulation results confirm that the proposed test performs satisfactorily in estimated size and power.
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  A POSTERIORI ERROR ANALYSIS OF NONCONFORMING METHODS FOR THE EIGENVALUE PROBLEM

  Youai LI

  Journal of Systems Science and Complexity. 2009, 22(3): 495-502.

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  This paper extends the unifying theory for a posteriori error analysis of the nonconforming finite element methods to the second order elliptic eigenvalue problem. In particular, the author proposes the a posteriori error estimator for nonconforming
  methods of the eigenvalue problems and prove its reliability and efficiency based on two assumptions concerning both the weak continuity and the weak orthogonality of the nonconforming finite element spaces, respectively. In addition, the author
  examines these two assumptions for those nonconforming methods checked in literature for the Laplace, Stokes, and the linear elasticity problems.
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  A GENERAL ITERATIVE METHOD OF FIXED POINTS FOR EQUILIBRIUM PROBLEMS AND OPTIMIZATION PROBLEMS

  Fang ZHANG;Yongfu SU

  Journal of Systems Science and Complexity. 2009, 22(3): 503-517.

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  The purpose of this paper is to present a general iterative scheme as below: $$\begin{cases} F(u_n,y)+\frac{1}{r_n}\langle y-u_n,u_n-x_n\rangle \geq 0,\quad \forall y\in C ,\\ x_{n+1}=(I-\alpha_nA)Su_n+\alpha_n\gamma f(x_n),\end{cases}$$ and to prove that, if $\{\alpha_n\}$ and $\{r_n\}$ satisfy appropriate conditions, then iteration sequences $\{x_n\}$ and $\{u_n\}$ converge strongly to a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping and the set of solution of a variational inequality, too. Furthermore, by using the above result, we can also obtain an iterative algorithm for solution of an optimization problem $\min\limits_{x\in C}h(x)$, where $h(x)$ is a convex and lower semicontinuous functional defined on a closed convex subset $C$ of
  a Hilbert space $H$. The results presented in this paper extend, generalize and improve the results of Combettes and Hirstoaga, Wittmann, S.Takahashi, Giuseppe Marino, Hong-Kun Xu, and some others.
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  A LOW ORDER NONCONFORMING ANISOTROPIC FINITE ELEMENT APPROXIMATION TO PARABOLIC PROBLEM

  Dongyang SHI;Wei GONG

  Journal of Systems Science and Complexity. 2009, 22(3): 518-532.

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  A low order nonconforming finite element is applied to the parabolic problem with anisotropic meshes. Both the semidiscrete and fully discrete forms are studied. Some superclose properties and superconvergence are obtained through some novel approaches and techniques.
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  ON THE LAPLACIAN SPECTRAL RADII OF TREES WITH NEARLY PERFECT MATCHINGS

  Li ZHANG;Jiayu SHAO

  Journal of Systems Science and Complexity. 2009, 22(3): 533-540.

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  Let ${\cal T}_{2k+1}$ be the set of trees on $2k+1$ vertices with nearly perfect matchings, and let ${\cal S}_{2k+2}$ be the set of trees on $2k+2$ vertices with perfect matchings. The largest Laplacian spectral radii of trees in ${\cal T}_{2k+1}$ and ${\cal S}_{2k+2}$ and the corresponding trees were given by Guo (2003).
  In this paper, the authors determine the second to the sixth largest Laplacian spectral radii among all trees in ${\cal T}_{2k+1}$ and give the corresponding trees.