2010年, 第23卷, 第2期　刊出日期：2010-04-25

  

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  DISTRIBUTED FINITE-TIME $\chi$-CONSENSUS ALGORITHMS FORMULTI-AGENT SYSTEMS WITH VARIABLE COUPLING TOPOLOGY

  Xiaoli WANG;Yiguang HONG

  Journal of Systems Science and Complexity. 2010, 23(2): 209-218. https://doi.org/10.1007/s11424-010-7254-2

  摘要 ( ) PDF全文 ( )   可视化   收藏

  This paper considers finite-time $\chi$-consensus problem for a multi-agent system with first-order individual dynamics and switching interaction topologies. Several distributed finite-time consensus rules are constructed for multi-agent dynamics in a
  unified way with the help of Lyapunov function and graph theory as well as homogeneity. Time-invariant non-smooth forms of finite-time neighbor-based controllers are proposed and a numerical example is shown for illustration.
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  MAXIMUM PRINCIPLE FOR FORWARD-BACKWARD STOCHASTIC CONTROLSYSTEM WITH RANDOM JUMPS AND APPLICATIONS TO FINANCE

  Jingtao SHI;Zhen WU

  Journal of Systems Science and Complexity. 2010, 23(2): 219-231. https://doi.org/10.1007/s11424-010-7224-8

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  Both necessary and sufficient maximum principles for optimal control of stochastic system with random jumps consisting of forward and backward state variables are proved. The control variable is allowed to enter both diffusion and jump coefficients. The result is applied to a mean-variance portfolio selection mixed with a
  recursive utility functional optimization problem. Explicit expression of the optimal portfolio selection strategy is obtained in the state feedback form.
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  A VIRTUAL FIELD-BASED CONCEPTUAL FRAMEWORK FOR THESIMULATION OF COMPLEX SOCIAL SYSTEMS

  Darius PLIKYNAS

  Journal of Systems Science and Complexity. 2010, 23(2): 232-248. https://doi.org/10.1007/s11424-010-7239-1

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  This highly interdisciplinary research paper discusses some new insights into the fundamental properties of information-rich social networks. It mainly focuses on: i) Postulating the general properties of an information-based networking economy; ii) Modeling emergent and self-organizing features of social networks; iii) Discussing how to simulate complex social systems using a field-based approach and multi-agent platforms. Additionally, this paper gives some ideas of how to construct a virtual field-based communications network of intelligent agents using currently
  available computational intelligence methods. A new simulation paradigm offers some useful concepts to transform multidimensional factor space (representing a multiplicity of phenomenal forms and interactions) into the most universal spectral coding system. This paper gives some ideas of how not only the communication mechanism but also the social agents can be simulated as oscillating processes.
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  A MULTI-PERIOD PRICING AND INVENTORY CONTROL MODEL

  Juliang ZHANG;Jian CHEN

  Journal of Systems Science and Complexity. 2010, 23(2): 249-260. https://doi.org/10.1007/s11424-010-7066-4

  摘要 ( ) PDF全文 ( )   可视化   收藏

  The authors analyze a finite horizon, single product, period review model in which pricing and inventory decisions are made simultaneously. Demands in different periods are random variables that are independent of each other and their distributions depend on the product price. Pricing and ordering decisions are made at the beginning of each period and all shortage are backlogged. Ordering cost is a convex function of the amount ordered. The objective is to find an inventory and pricing policy maximizing expected discounted profit over the finite horizon. The authors characterize the structure of the optimal combined pricing and
  inventory strategy for this model. Moreover, the authors demonstrate how the profit-to-go function, order up to level, reorder point and optimal price change with respect to state and time.
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  PRICING OF LIBOR FUTURES BY MARTINGALE METHOD IN COX-INGERSOLL-ROSS MODEL

  Ping LI;Peng SHI;Guangdong HUANG;Xiaojun SHI

  Journal of Systems Science and Complexity. 2010, 23(2): 261-269. https://doi.org/10.1007/s11424-010-6042-3

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  This paper considers the pricing of LIBOR futures in the Cox-Ingersoll-Ross
  (CIR) model under Pozdnyakov and Steele (2004)'s martingale framework for futures prices. Under the CIR model for short term interest rate, we prove that there exists a unique futures price process associated with the terminal value and the standard financial market, and that this unique futures price process has a martingale representation. Moreover, a general closed-form pricing formula for
  LIBOR futures contracts is obtained in the CIR model.
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  ON CONTROLLABILITY FOR STOCHASTIC CONTROL SYSTEMS WHEN THECOEFFICIENT IS TIME-VARIANT

  Feng LIU;Shige PENG

  Journal of Systems Science and Complexity. 2010, 23(2): 270-278. https://doi.org/10.1007/s11424-010-8158-x

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  This paper investigates the controllability problem of time-variant linear stochastic control systems. A sufficient and necessary condition is established for stochastic exact controllability, which provides a useful algebraic criterion for stochastic control systems. Furthermore, when the stochastic systems degenerate to deterministic systems, the algebraic criterion becomes the counterpart for the complete controllability of deterministic control systems.
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  GLOBAL STABILITY OF AN EPIDEMIC MODEL FOR VECTOR-BORNEDISEASE

  Hongzhi YANG;Huiming WEI;Xuezhi LI

  Journal of Systems Science and Complexity. 2010, 23(2): 279-292. https://doi.org/10.1007/s11424-010-8436-7

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  This paper considers an epidemic model of a vector-borne disease which has the vector-mediated transmission only. The incidence term is of the bilinear mass-action form. It is shown that the global dynamics is completely determined by the basic
  reproduction number $ R_0 $. If $ R_0\leq 1 $, the disease-free equilibrium is globally stable and the disease dies out. If $ R_0>1 $, a unique endemic equilibrium is globally stable in the interior of the feasible region and the disease persists at the endemic equilibrium. Numerical simulations are presented to illustrate the
  results.
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  CHOVER'S LAW OF THE ITERATED LOGARITHM FOR NEGATIVELYASSOCIATED SEQUENCES

  Qunying WU;Yuanying JIANG

  Journal of Systems Science and Complexity. 2010, 23(2): 293-302. https://doi.org/10.1007/s11424-010-7258-y

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  Consider a sequence of negatively associated and identically
  distributed random variables with the underlying distribution in the
  domain of attraction of a stable distribution with an exponent in
  $(0,2)$. A Chover's law of the iterated logarithm is established for
  negatively associated random variables. Our results generalize and
  improve those on Chover's law of the iterated logarithm (LIL) type
  behavior previously obtained by Mikosch (1984), Vasudeva (1984), and
  Qi and Cheng (1996) from the i.i.d. case to NA sequences.
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  CONSTRUCTION AND COMPARISONS OF SIMULTANEOUS CONFIDENCEINTERVALS FOR THE MEAN DIFFERENCE OF MULTIVARIATE NORMALDISTRIBUTIONS

  Xianhua MENG;Jinglong WANG;Xianyi WU

  Journal of Systems Science and Complexity. 2010, 23(2): 303-314. https://doi.org/10.1007/s11424-010-7058-4

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  In this paper, Scheff\'{e} and Simplified Scheff\'{e}
  simultaneous confidence intervals are first constructed for mean
  difference of several multivariate normal distributions. Then the
  authors theoretically prove that when there are only two
  populations, Bonferroni bounds and Simplified Scheff\'{e} bounds are
  the same and they are shorter than Scheff\'{e} bounds for $p\leq10$.
  In the case for $3\leq k\leq10$ and $2\leq p\leq10$, there exists
  $n(p,k)$ such that Bonferroni method is better than Simplified
  Scheff\'{e} procedure for $n\geq n(p,k)$, otherwise Simplified
  Scheff\'{e} procedure is better. Finally, the authors find out that
  neither of Scheff\'{e} critical values nor Simplified Scheff\'{e}\
  critical values\ are always larger than another through numerical
  calculation.
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  A NOTE ON THE PROPERTIES OF STEIN-RULE AND INEQUALITY RESTRICTED ESTIMATORS WHEN THE REGRESSION MODEL IS OVER-FITTED

  Sherry Zhefang ZHOU

  Journal of Systems Science and Complexity. 2010, 23(2): 315-320. https://doi.org/10.1007/s11424-010-9087-4

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  This paper considers the effect of an erroneous inclusion of
  regressors on the risk properties of the Stein-rule, positive-part
  Stein-rule and inequality restricted and pre-test estimators in a
  linear regression model. The two Stein-rule estimators are
  considered when extraneous information is available in the form of a
  set of multiple equality constraints on the coefficients, while the
  inequality estimators are considered under the case of a single
  inequality constraint. It is shown that the inclusion of wrong
  regressors has only minimal effect on the properties of the
  Stein-rule and positive-part Stein-rule estimators, and no effect at
  all on the inequality restricted and pre-test estimators when there
  is a single inequality constraint.
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  OPTIMAL CONTROL OF MULTISOLUTION ORDINARY DIFFERENTIALEQUATIONS IN THE ABSENCE OF CONVEXITY

  Shu LUAN;Hang GAO

  Journal of Systems Science and Complexity. 2010, 23(2): 321-333. https://doi.org/10.1007/s11424-010-8237-z

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  In this paper, the authors study an optimal control problem governed by a class of multistate ordinary differential equations in the absence of convexity. To overcome the difficulty that the corresponding approximate optimal control problem may have no solution, relaxed controls are introduced. With the help of relaxation theory, Pontryagin's maximum principle for the optimal pairs of the original control problem is obtained. In the end of this paper, the authors discuss the application of the maximum principle by an example.
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  INFER OBJECTIVE FUNCTION OF GLYCEROL METABOLISM INKLEBSIELLA PNEUMONIAE BASING ON BILEVEL PROGRAMMING

  Zhaohua GONG;Yongsheng YU;Enmin FENG

  Journal of Systems Science and Complexity. 2010, 23(2): 334-342. https://doi.org/10.1007/s11424-010-8235-1

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  Mathematical modelling of cellular metabolism plays an important role in understanding biological functions and providing identification of targets for biotechnological modification. This paper proposes a nonlinear bilevel programming (NBP) model to infer the objective function of anaerobic glycerol metabolism in {Klebsiella Pneumoniae (K. Pneumoniae)} for 1, 3-propanediol (1, 3-PD) production.
  Based on the Kuhn-Tucker optimality condition of the lower level problem, NBP is transformed into a nonlinear programming with complementary and slackness conditions. The authors give the existence theorem of solutions to NBP. An efficient algorithm is proposed to solve NBP and its convergence is also simply analyzed.
  Numerical results reveal some interesting conclusions, e.g., biomass production is the main force to drive glycerol metabolism, and the objective functions, which are obtained in term of several different groups of flux distributions, are similar.
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  A LINE SEARCH FILTER SECANT METHOD FOR NONLINEAR EQUALITYCONSTRAINED OPTIMIZATION

  Zhujun WANG;Detong ZHU

  Journal of Systems Science and Complexity. 2010, 23(2): 343-361. https://doi.org/10.1007/s11424-010-8012-1

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  This paper formulates and analyzes a line search method for general nonlinear equality constrained optimization based on filter methods for step acceptance and secant methods for search direction. The feature of the new algorithm is that the secant algorithm is used to produce a search direction, a backtracking line search
  procedure is used to generate step size, some filtered rules are used to determine step acceptance, second order correction technique is used to reduce infeasibility and overcome the Maratos effect. Global convergence properties of this method are analyzed: under mild assumptions it is showed that every limit point of the sequence of iterates generated by the algorithm is feasible, and that there exists at least one limit point that is a stationary point for the problem. Moreover, it is also established that the Maratos effect can be overcome in our new approach by adding second order correction steps so that fast local superlinear convergence to a second order sufficient local solution is achieved. Finally, the results of numerical experiments are reported to show the effectiveness of the line search filter secant method.
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  DISCRIMINANT ANALYSIS BASED ON STATISTICAL DEPTH

  Jiao JIN;Hengjian CUI

  Journal of Systems Science and Complexity. 2010, 23(2): 362-371. https://doi.org/10.1007/s11424-010-7214-x

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  In the past two decades, many statistical depth functions seemed as powerful exploratory and inferential tools for multivariate data analysis have been presented. In this paper, a new depth function family that meets four properties mentioned in Zuo and Serfling (2000) is proposed. Then a classification rule based on the depth function family is proposed. The classification parameter $b$ could be modified according to the type-I error $\alpha$, and the estimator of $b$ has the consistency and achieves the convergence rate $n^{-1/2}$. With the help of the proper selection for depth family parameter $c$, the approach for discriminant
  analysis could minimize the type-II error $\beta$. A simulation study and a real data example compare the performance of the different discriminant methods.
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  REMOVABLE EARS OF 1-EXTENDABLE GRAPHS

  Shaohui ZHAI;Xiaofeng GUO

  Journal of Systems Science and Complexity. 2010, 23(2): 372-378. https://doi.org/10.1007/s11424-010-7122-0

  摘要 ( ) PDF全文 ( )   可视化   收藏

  Carvalho, Lucchesi and Murty proved that any 1-extendable graph
  $G$ different from $K_2$ and $C_{2n}$ has at least $\Delta(G)$
  edge-disjoint removable ears, and any brick $G$ distinct from $K_4$
  and $\overline{C_6}$ has at least $\Delta(G)-2$ removable edges,
  where $\Delta(G)$ denotes the maximum degree of $G$. In this paper,
  we improve the lower bounds for numbers of removable ears and
  removable edges of 1-extendable graphs. It is proved that any
  1-extendable graph $G$ different from $K_2$ and $C_{2n}$ has at
  least $\chi'(G)$ edge-disjoint removable ears, and any brick $G$
  distinct from $K_4$ and $\overline{C_6}$ has at least $\chi'(G)-2$
  removable edges, where $\chi'(G)$ denotes the edge-chromatic number
  of $G$.
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  A NEW SIMPLE 2-D PIECEWISE LINEAR MAP

  Zeraoulia ELHADJ;Julien Clinton SPROTT

  Journal of Systems Science and Complexity. 2010, 23(2): 379-389. https://doi.org/10.1007/s11424-010-7184-z

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  A new simple piecewise linear map of the plane is presented and analyzed, then a detailed study of its dynamical behaviour is described, along with some other dynamical phenomena, especially fixed points and their stability, observation of a new chaotic attractors obtained via border collision bifurcation. An important
  result about coexisting chaotic attractors is also numerically studied and discussed.
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  ON A BOUNDARY VALUE PROBLEM FOR A STURM-LIOUVILLE TYPEDIFFERENTIAL INCLUSION

  Aurelian CERNEA

  Journal of Systems Science and Complexity. 2010, 23(2): 390-394. https://doi.org/10.1007/s11424-010-8017-9

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  This paper proves a Filippov type existence theorem for solutions of a boundary value problem for a Sturm-Liouville type differential inclusion defined by a nonconvex set-valued map. The method consists in application of the contraction principle in the space of selections of the set-valued map instead of the space of
  solutions.
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  NONCONFORMING FINITE ELEMENT METHOD FOR NONLINEARPARABOLIC EQUATIONS

  Dongyang SHI;Buying ZHANG

  Journal of Systems Science and Complexity. 2010, 23(2): 395-402. https://doi.org/10.1007/s11424-010-7120-2

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  A nonconforming finite element method for the nonlinear parabolic equations is studied in this paper. The convergence analysis is presented and the optimal error estimate in $L^{2}(\|\cdot\|_{h})$ norm is obtained through Ritz projection
  technique, where $\|\cdot\|_{h}$ is a norm over the finite element space.
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  NEW DESIGN AND ANALYSIS OF FINITE DIFFERENCE DOMAIN DECOMPOSITION ALGORITHM FOR THE TWO-DIMENSIONAL HEAT EQUATION

  Zhengsu WAN;Baolin ZHANG;Guangnan CHENG

  Journal of Systems Science and Complexity. 2010, 23(2): 403-412. https://doi.org/10.1007/s11424-010-7054-8

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  It is presented in this paper that the new design and its analysis of finite difference domain decomposition algorithms for the two-dimensional heat equation, and the numerical results have shown the stability and accuracy of the algorithms, where Saul'yev asymmetric schemes have been used at the interface points. The
  Algorithm {II} in this paper has further extended those developed by Dawson and the others, Zhang and Shen.