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21 April 2008, Volume 19 Issue 2
General and efficient parallel approach of finite elementboundary integral-multilevel fast multipole algorithm
Pan Xiaomin & Sheng Xinqing
2008, 19(2):  207-212. 
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A general and efficient parallel approach is proposed for the first time to parallelize the hybrid finiteelement-boundary-integral-multi-level fast multipole algorithm (FE-BI-MLFMA). Among many algorithms of FEBI-MLFMA, the decomposition algorithm (DA) is chosen as a basis for the parallelization of FE-BI-MLFMA because of its distinct numerical characteristics suitable for parallelization. On the basis of the DA, the parallelization of FE-BI-MLFMA is carried out by employing the parallelized multi-frontal method for the matrix from the finiteelement method and the parallelized MLFMA for the matrix from the boundary integral method respectively. The programming and numerical experiments of the proposed parallel approach are carried out in the high performance computing platform CEMS-Liuhui. Numerical experiments demonstrate that FE-BI-MLFMA is efficiently parallelized and its computational capacity is greatly improved without losing accuracy, efficiency, and generality.

Resource allocation with CCI suppression for multiuser MIMO-OFDM downlink in correlated channels
Zhang Chengwen, Zhang Zhongzhao & Ma Yongkui
2008, 19(2):  213-219. 
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To minimize the overall transmit power while maintaining a constant data rate and target BER, a downlink adaptive resource allocation algorithm with jointing the exclusive manner and the shared manner is proposed for multiuser MIMO-OFDM system in correlated channels. The algorithm allocates all the subcarriers to different users according to their spatial correlations. The users with high spatial correlation are allocated in the same group and the exclusive manner is applied. The shared manner with an improved null broadening method, which improves the performance of co-channel interference (CCI) suppression and decreases the number of transmit antennas required, is applied between the different group users. As the user’s direction of departure (DOD) changes very slowly, a looking up table method is used to reduce the computational complexity. The simulation results show that despite the angle spread of DOD, when compared with the exclusive manner, the proposed algorithm improves the spectral efficiency, and when compared with the TDMA-ZF (zero forcing) shared manner, the proposed algorithm decreases the total transmit power by at least 1 dB.

Design and application of single-antenna GPS/accelerometers attitude determination system
He Jie, Huang Xianlin & Wang Guofeng
2008, 19(2):  220-227. 
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In view of the problem that the current single-antenna GPS attitude determination system can only determine the body attitude when the sideslip angle is zero and the multiantenna GPS/SINS integrated navigation system is of large volume, high cost, and complex structure, this approach is presented to determine the attitude based on vector space with single-antenna GPS and accelerometers in the micro inertial measurement unit (MIMU). It can provide real-time and accurate attitude information. Subsequently, the single-antenna GPS/SINS integrated navigation system is designed based on the combination of position, velocity, and attitude. Finally the semiphysical simulations of single-antenna GPS attitude determination system and single-antenna GPS/SINS integrated navigation system are carried out. The simulation results, based on measured data, show that the single-antenna GPS/SINS system can provide more accurate navigation information compared to the GPS/SINS system, based on the combination of position and velocity. Furthermore, the single-antenna GPS/SINS system is characteristic of lower cost and simpler structure. It provides the basis for the application of a single-antenna GPS/SINS integrated navigation system in a micro aerial vehicle (MAV).

Electronic image stabilization system based on global feature tracking
Zhu Juanjuan & Guo Baolong
2008, 19(2):  228-233. 
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A new robust electronic image stabilization system is presented, which involves feature-point, tracking based global motion estimation and Kalman filtering based motion compensation. First, global motion is estimated from the local motions of selected feature points. Considering the local moving objects or the inevitable mismatch, the matching validation, based on the stable relative distance between the points set is proposed, thus maintaining high accuracy and robustness. Next, the global motion parameters are accumulated for correction by Kalman filteration. The experimental result illustrates that the proposed system is effective to stabilize translational, rotational, and zooming jitter and robust to local motions.

Algorithm of sky-ground-wave signal separation in CDMA system
Zhang Jingjuan & Chen Shiru
2008, 19(2):  234-240. 
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To solve the problem of the sky-wave interference in radio positioning system operating in CDMA mode, an algorithm of sky-ground-wave separation is provided. Based on the MLE (maximum likelihood estimate), and by estimating the amplitude and the phase of the sky-wave signal, the provided algorithm for separating skyground-wave is implemented. The mathematics model used for signal processing is established, and the possible solutions are provided. The structure and signal processing flow implementing the presented algorithm in the receiver are presented. A multi-channels signal searching idea is adopted, some of which process the sky-wave signal, and some of which process the ground-wave signal. Numerical analysis and simulation show that the proposed algorithm has higher accuracy, more rapid processing speed, and simpler implementation for the estimation of the sky-wave signal parameter, and can separate the sky-wave signal and ground-wave signal from the arrival combination signal effectively.

Subspace decomposition-based correlation matrix multiplic
Cheng Hao, Guo Wei & Yu Jingdong
2008, 19(2):  241-245. 
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The correlation matrix, which is widely used in eigenvalue decomposition (EVD) or singular value decomposition (SVD), usually can be denoted by R = E[yiy'i]. A novel method for constructing the correlation matrix R is proposed. The proposed algorithm can improve the resolving power of the signal eigenvalues and overcomes the shortcomings of the traditional subspace methods, which cannot be applied to low SNR. Then the proposed method is applied to the direct sequence spread spectrum (DSSS) signal’s signature sequence estimation. The performance of the proposed algorithm is analyzed, and some illustrative simulation results are presented.

Data association based on target signal classification information
Guo Lei, Tang Bin & Liu Gang
2008, 19(2):  246-251. 
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In most of the passive tracking systems, only the target kinematical information is used in the measurement-to-track association, which results in error tracking in a multitarget environment, where the targets are too close to each other. To enhance the tracking accuracy, the target signal classification information (TSCI) should be used to improve the data association. The TSCI is integrated in the data association process using the JPDA (joint probabilistic data association). The use of the TSCI in the data association can improve discrimination by yielding a purer track and preserving continuity. To verify the validity of the application of TSCI, two simulation experiments are done on an air target-tracing problem, that is, one using the TSCI and the other not using the TSCI. The final comparison shows that the use of the TSCI can effectively improve tracking accuracy.

Fast 3D EM scattering and radiation solvers based on MLFMA
Hu Jun, Nie Zaiping, Lei Lin, Hu Jie, Gong Xiaodong & Zhao Huapeng
2008, 19(2):  252-258. 
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As the fastest integral equation solver to date, the multilevel fast multipole algorithm (MLFMA) has been applied successfully to solve electromagnetic scattering and radiation from 3D electrically large objects. But for very large-scale problems, the storage and CPU time required in MLFMA are still expensive. Fast 3D electromagnetic scattering and radiation solvers are introduced based on MLFMA. A brief review of MLFMA is first given. Then, four fast methods including higher-order MLFMA (HO-MLFMA), fast far field approximation combined with adaptive ray propagation MLFMA (FAFFA-ARP-MLFMA), local MLFMA and parallel MLFMA are introduced. Some typical numerical results demonstrate the efficiency of these fast methods.

Link reliability based hybrid routing for tactical mobile ad hoc network
Xie Xiaochuan, Wei Gang, Wu Keping, Wang Gang & Jia Shilou
2008, 19(2):  259-267. 
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Tactical mobile ad hoc network (MANET) is a collection of mobile nodes forming a temporary network, without the aid of pre-established network infrastructure. The routing protocol has a crucial impact on the network performance in battlefields. Link reliability based hybrid routing (LRHR) is proposed, which is a novel hybrid routing protocol, for tactical MANET. Contrary to the traditional single path routing strategy, multiple paths are established between a pair of source-destination nodes. In the hybrid routing strategy, the rate of topological change provides a natural mechanism for switching dynamically between table-driven and on-demand routing. The simulation results indicate that the performances of the protocol in packet delivery ratio, routing overhead, and average end-to-end delay are better than the conventional routing protocol.

Research on the frequency domain ΣΔ–DPCA
Shen Mingwei, Zhu Daiyin & Zhu Zhaoda
2008, 19(2):  268-272. 
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The frequency domain ΣΔ–DPCA processing (F–ΣΔ–DPCA) is investigated in detail, and an improved scheme for the F–ΣΔ–DPCA is proposed, which can significantly reduce the computational burden. In practice, because of the sum and difference beam pattern designed independently and other system errors, the clutter suppression of the time domain ΣΔ–DPCA processing (T–ΣΔ–DPCA) is significantly degraded. However, the F–ΣΔ–DPCA adaptively calculates the optimum gain ratio for motion compensation within each Doppler cell, which is robust to system errors. Theoretical analysis and simulation results are presented to validate that the F–ΣΔ–DPCA can achieve superior performance of clutter cancellation than the time domain processing, and its performance can be significantly increased if more pulses are used for the Doppler filtering. The improved approach is efficient, and feasible for real-time application.

New algorithm of target classification in polarimetric SAR
Wang Yang, Lu Jiaguo & Wu Xianliang
2008, 19(2):  273-279. 
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The different approaches used for target decomposition (TD) theory in radar polarimetry are reviewed and three main types of theorems are introduced: those based on Mueller matrix, those using an eigenvector analysis of the coherency matrix, and those employing coherent decomposition of the scattering matrix. Support vector machine (SVM), as a novel approach in pattern recognition, has demonstrated success in many fields. A new algorithm of target classification, by combining target decomposition and the support vector machine, is proposed. To conduct the experiment, the polarimetric synthetic aperture radar (SAR) data are used. Experimental results show that it is feasible and efficient to target classification by applying target decomposition to extract scattering mechanisms, and the effects of kernel function and its parameters on the classification efficiency are significant.

Improved method for the feature extraction of laser scanner using genetic clustering
Yu Jinxia, Cai Zixing & Duan Zhuohua
2008, 19(2):  280-285. 
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Feature extraction of range images provided by ranging sensor is a key issue of pattern recognition. To automatically extract the environmental feature sensed by a 2D ranging sensor laser scanner, an improved method based on genetic clustering VGA-clustering is presented. By integrating the spatial neighbouring information of range data into fuzzy clustering algorithm, a weighted fuzzy clustering algorithm (WFCA) instead of standard clustering algorithm is introduced to realize feature extraction of laser scanner. Aimed at the unknown clustering number in advance, several validation index functions are used to estimate the validity of different clustering algorithms and one validation index is selected as the fitness function of genetic algorithm so as to determine the accurate clustering number automatically. At the same time, an improved genetic algorithm IVGA on the basis of VGA is proposed to solve the local optimum of clustering algorithm, which is implemented by increasing the population diversity and improving the genetic operators of elitist rule to enhance the local search capacity and to quicken the convergence speed. By the comparison with other algorithms, the effectiveness of the algorithm introduced is demonstrated.

SVD-TLS extending Prony algorithm for extracting UWB radar target feature
Liu Donghong, Hu Wenlong & Chen Zhijie
2008, 19(2):  286-291. 
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A new method, SVD-TLS extending Prony algorithm, is introduced for extracting UWB radar target features. The method is a modified classical Prony method based on singular value decomposition and total least squares that can improve robust for spectrum estimation. Simulation results show that poles and residuum of target echo can be extracted effectively using this method, and at the same time, random noises can be restrained to some degree. It is applicable for target feature extraction such as UWB radar or other high resolution range radars.

Novel cued search strategy based on information gain for phased array radar
Lu Jianbin, Hu Weidong, Xiao Hui & Yu Wenxian
2008, 19(2):  292-297. 
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A search strategy based on the maximal information gain principle is presented for the cued search of phased array radars. First, the method for the determination of the cued search region, arrangement of beam positions, and the calculation of the prior probability distribution of each beam position is discussed. And then, two search algorithms based on information gain are proposed using Shannon entropy and Kullback-Leibler entropy, respectively. With the proposed strategy, the information gain of each beam position is predicted before the radar detection, and the observation is made in the beam position with the maximal information gain. Compared with the conventional method of sequential search and confirm search, simulation results show that the proposed search strategy can distinctly improve the search performance and save radar time resources with the same given detection probability.

Method for multiple attribute decision making based on incomplete linguistic judgment matrix
Zhang Yao & Fan Zhiping
2008, 19(2):  298-303. 
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With respect to the multiple attribute decision making problems with linguistic preference relations on alternatives in the form of incomplete linguistic judgment matrix, a method is proposed to analyze the decision problem. The incomplete linguistic judgment matrix is transformed into incomplete fuzzy judgment matrix and an optimization model is developed on the basis of incomplete fuzzy judgment matrix provided by the decision maker and the decision matrix to determine attribute weights by Lagrange multiplier method. Then the overall values of all alternatives are calculated to rank them. A numerical example is given to illustrate the feasibility and practicality of the proposed method.

New approach to multiple attribute decision making with interval numbers
Zhang Quan, Gao Qisheng & Geng Jinhua
2008, 19(2):  304-310. 
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In an ambiguous decision domain, the evaluation values of alternatives against attributes would be interval numbers because of the inherent, uncertain property of the problems. By using a number of linear programming models, Bryson and Mobolurin propose an approach to compute attribute weights and overall values of the alternatives in the form of interval numbers. The intervals of the overall values of alternatives are then transformed into points or crisp values for comparisons among the alternatives. However, the attribute weights are different because of the use of linear programming models in Bryson and Mobolurin’s approach. Thus, the alternatives are not comparable because different attribute weights are employed to calculate the overall values of the alternatives. A new approach is proposed to overcome the drawbacks of Bryson and Mobolurin’s approach. By transforming the decision matrix with intervals into the one with crisp values, a new linear programming model is proposed, to calculate the attribute weights for conducting alternative ranking.

Static rough similarity degree and its applications
Xu Xiaojing, Li Jian & Shi Kaiquan
2008, 19(2):  311-315. 
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The definition of rough similarity degree is given based on the axiomatic similarity degree, and the properties of rough similarity degree are listed. Using the properties of rough similarity degree, the method of clustering in rough systems can be obtained. After clustering, a new sample can be recognized by the principle of maximal rough similarity degree.

Comparison on neural networks and support vector machines in suppliers’ selection
Hu Guosheng & Zhang Guohong
2008, 19(2):  316-320. 
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Suppliers’ selection in supply chain management (SCM) has attracted considerable research interests in recent years. Recent literatures show that neural networks achieve better performance than traditional statistical methods. However, neural networks have inherent drawbacks, such as local optimization solution, lack generalization, and uncontrolled convergence. A relatively new machine learning technique, support vector machine (SVM), which overcomes the drawbacks of neural networks, is introduced to provide a model with better explanatory power to select ideal supplier partners. Meanwhile, in practice, the suppliers’ samples are very insufficient. SVMs are adaptive to deal with small samples’ training and testing. The prediction accuracies for BPNN and SVM methods are compared to choose the appreciating suppliers. The actual examples illustrate that SVM methods are superior to BPNN.

Non-fragile decentralized H∞ controller design for uncertain linear systems
Zhao Zhihua, Chen Yuepeng & Zhang Qingling
2008, 19(2):  321-328. 
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Considering the design problem of non-fragile decentralized H∞ controller with gain variations, the dynamic feedback controller by measurement feedback for uncertain linear systems is constructed and studied. The parameter uncertainties are considered to be unknown but norm bounded. The design procedures are investigated in terms of positive definite solutions to modify algebraic Riccati inequalities. Using information exchange among local controllers, the designed non-fragile decentralized H∞ controllers guarantee that the uncertain closed-loop linear systems are stable and with H∞ -norm bound on disturbance attenuation. A sufficient condition that there are such non-fragile H∞ controllers is obtained by algebraic Riccati inequalities. The approaches to solve modified algebraic Riccati inequalities are carried out preliminarily. Finally, a numerical example to show the validity of the proposed approach is given.

Adaptive SPC monitoring scheme for DOE-based APC
Ye Liang, Pan Ershun & Xi Lifeng
2008, 19(2):  329-336. 
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Automatic process control (APC) based on design of experiment (DOE) is a cost-efficient approach for variation reduction. The process changes both in mean and variance owing to online parameter adjustment make it hard to apply traditional SPC charts in such DOE-based APC applied process. An adaptive SPC scheme is developed, which can better track the process transitions and achieve the possible SPC run cost reduction when the process is stable. The control law of SPC parameters is designed by fully utilizing the estimation properties of the process model instead of traditionally using the data collected from the production line. An example is provided to illustrate the proposed adaptive SPC design approach.

Variable structure guidance law for attacking surface maneuver targets
Han Yanhua & Xu Bo
2008, 19(2):  337-341. 
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The characteristics of surface maneuver targets are analyzed and a 3-D relative motion model for missiles and targets is established. A variable structure guidance law is designed considering the characteristics of targets. In the guidance law, the distance between missiles and targets as well as the missile-target relative velocity are all substituted by estimation values. The estimation errors, the target’s velocity, and the maneuver acceleration are all treated as bounded disturbance. The guidance law proposed can be implemented conveniently in engineering with little target information. The performance of the guidance system is analyzed theoretically and the numerical simulation result shows the effectiveness of the guidance law.

Realization of nonlinear PID with feed-forward controller for 3-DOF flight simulator and hardware-in-the-loop simulation
Duan Haibin, Wang Daobo & Yu Xiufen
2008, 19(2):  342-345. 
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As friction, intrinsic steady-state nonlinearity poses a challenging dilemma to the control system of 3-DOF (three degree of freedom) flight simulator, a novel hybrid control strategy of nonlinear PID (proportional-integral-derivative) with additional FFC (feed-forward controller) is proposed, and the hardware-in-the-loop simulation results are also given. Based on the description of 3-DOF flight simulator, a novel nonlinear PID theory is well introduced. Then a nonlinear PID controller with additional FFC is designed. Subsequently, the loop structure of 3-DOF flight simulator is also designed. Finally, a series of hardware-in-the-loop simulation experiments are undertaken to verify the feasibility and effectiveness of the proposed nonlinear PID controller with additional FFC for 3-DOF flight simulator.

Delay-dependent passive control of linear systems with nonlinear perturbation
Li Caina & Cui Baotong
2008, 19(2):  346-350. 
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The problem of delay-dependent passive control of a class of linear systems with nonlinear perturbation and time-varying delay in states is studied. The main idea aims at designing a state-feedback controller such that for a time-varying delay in states, the linear system with nonlinear perturbation remains robustly stable and passive. In the system, the delay is time-varying. And the derivation of delay has the maximum and minimum value. The time-varying nonlinear perturbation is allowed to be norm-bounded. Using the effective linear matrix inequality methodology, the sufficient condition is primarily obtained for the system to have robust stability and passivity. Subsequently the existent condition of a state feedback controller is given, and the explicit expression of the controller is obtained by means of the solution of linear matrix inequalities (LMIs). In the end, a numerical example is given to demonstrate the validity and applicability of the proposed approach.

Recurrent neural network for vehicle dead-reckoning
Ma Haibo, Zhang Liguo & Chen Yangzhou
2008, 19(2):  351-355. 
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For vehicle integrated navigation systems, real-time estimating states of the dead reckoning (DR) unit is much more difficult than that of the other measuring sensors under indefinite noises and nonlinear characteristics. Compared with the well known, extended Kalman filter (EKF), a recurrent neural network is proposed for the solution, which not only improves the location precision and the adaptive ability of resisting disturbances, but also avoids calculating the analytic derivation and Jacobian matrices of the nonlinear system model. To test the performances of the recurrent neural network, these two methods are used to estimate the state of the vehicle’s DR navigation system. Simulation results show that the recurrent neural network is superior to the EKF and is a more ideal filtering method for vehicle DR navigation.

Research on ballistic missile laser SIMU error propagation mechanism
Wei Shihui & Xiao Longxu
2008, 19(2):  356-362. 
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It is necessary that the laser inertial system is used to further improve the fire accuracy and quick reaction capability in the ballistic missile strapdown inertial navigation system. According to the guidance controlling method and the output and error model of ballistic missile laser SIMU, the mathematical model of error propagation mechanism is set up and any transfer environmental function of error coefficient that affects the fire accuracy is deduced. Also, the missile longitudinal/lateral impact point is calculated using MATLAB. These establish the technical foundation for further researching the dispersion characteristics of impact point and reducing the laser guidance error.

Grover quantum searching algorithm based on weighted targets
Li Panchi & Li Shiyong
2008, 19(2):  363-369. 
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The current Grover quantum searching algorithm cannot identify the difference in importance of the search targets when it is applied to an unsorted quantum database, and the probability for each search target is equal. To solve this problem, a Grover searching algorithm based on weighted targets is proposed. First, each target is endowed a weight coefficient according to its importance. Applying these different weight coefficients, the targets are represented as quantum superposition states. Second, the novel Grover searching algorithm based on the quantum superposition of the weighted targets is constructed. Using this algorithm, the probability of getting each target can be approximated to the corresponding weight coefficient, which shows the flexibility of this algorithm. Finally, the validity of the algorithm is proved by a simple searching example.

Research on secure buyer-seller watermarking protocol
Liu Quan, Chen Zheng & Zhou Zude
2008, 19(2):  370-376. 
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A new buyer-seller watermarking protocol is proposed by applying a double encryption method and a novel mechanism of embedding a buyer’s watermark. The protocol can effectively prevent against collusion attacks and the man in the middle attack if the third party is not trusted. Also, based on the proposed scheme for the first-hand transaction, a new buyer-reseller watermarking protocol and a formal multi-party watermarking protocol are also proposed. The proposed buyer-resell watermarking protocol only needs the original seller to provide transfer certificate and encryption-decryption service to support the second-hand transaction, and the multi-party watermarking protocol with distributed certificate authorities can overcome the difficulty in the combination of multicast mechanism with multiple unique watermarks and allow a seller to multicast the watermarked digital contents and key transaction information to n buyers. Furthermore, the idea of zero knowledge proof is also applied into the proposed scheme to allow the seller to take an effective control on the task performed by the third party.

Novel ensemble learning based on multiple section distribution in distributed environment
Fang Min
2008, 19(2):  377-380. 
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Because most ensemble learning algorithms use the centralized model, and the training instances must be centralized on a single station, it is difficult to centralize the training data on a station. A distributed ensemble learning algorithm is proposed which has two kinds of weight genes of instances that denote the global distribution and the local distribution. Instead of the repeated sampling method in the standard ensemble learning, non-balance sampling from each station is used to train the base classifier set of each station. The concept of the effective nearby region for local integration classifier is proposed, and is used for the dynamic integration method of multiple classifiers in distributed environment. The experiments show that the ensemble learning algorithm in distributed environment proposed could reduce the time of training the base classifiers effectively, and ensure the classify performance is as same as the centralized learning method.

New recursive algorithm for matrix inversion
Cao Jianshu & Wang Xuegang
2008, 19(2):  381-384. 
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To reduce the computational complexity of matrix inversion, which is the majority of processing in many practical applications, two numerically efficient recursive algorithms (called algorithms I and II, respectively) are presented. Algorithm I is used to calculate the inverse of such a matrix, whose leading principal minors are all nonzero. Algorithm II, whereby, the inverse of an arbitrary nonsingular matrix can be evaluated is derived via improving the algorithm I. The implementation, for algorithm II or I, involves matrix-vector multiplications and vector outer products. These operations are computationally fast and highly parallelizable. MATLAB simulations show that both recursive algorithms are valid.

Uniformed model of networked control systems with long time delay
Zhu Qixin, Liu Hongli & Hu Shousong
2008, 19(2):  385-390. 
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Feedback control systems wherein the control loops are closed through a real-time network are called networked control systems (NCS). The defining feature of an NCS is that information is exchanged using a network among control system components. Two new concepts including long time delay and short time delay are proposed. The sensor is almost always clock driven. The controller or the actuator is either clock driven or event driven. Four possible driving modes of networked control systems are presented. The open loop mathematic models of networked control systems with long time delay are developed when the system is driven by anyone of the four different modes. The uniformed modeling method of networked control systems with long time delay is proposed. The simulation results are given in the end.

Multilevel security model for ad hoc networks
Wang Changda & Ju Shiguang
2008, 19(2):  391-397. 
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Modern battlefield doctrine is based on mobility, flexibility, and rapid response to changing situations. As is well known, mobile ad hoc network systems are among the best utilities for battlefield activity. Although much research has been done on secure routing, security issues have largely been ignored in applying mobile ad hoc network theory to computer technology. An ad hoc network is usually assumed to be homogeneous, which is an irrational assumption for armies. It is clear that soldiers, commanders, and commanders-in-chief should have different security levels and computation powers as they have access to asymmetric resources. Imitating basic military rank levels in battlefield situations, how multilevel security can be introduced into ad hoc networks is indicated, thereby controlling restricted classified information flows among nodes that have different security levels.

Scheduling algorithm based on critical tasks in heterogeneous environments
Lan Zhou & Sun Shixin
2008, 19(2):  398-405. 
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Heterogeneous computing is one effective method of high performance computing with many advantages. Task scheduling is a critical issue in heterogeneous environments as well as in homogeneous environments. A number of task scheduling algorithms for homogeneous environments have been proposed, whereas, a few for heterogeneous environments can be found in the literature. A novel task scheduling algorithm for heterogeneous environments, called the heterogeneous critical task (HCT) scheduling algorithm is presented. By means of the directed acyclic graph and the gantt graph, the HCT algorithm defines the critical task and the idle time slot. After determining the critical tasks of a given task, the HCT algorithm tentatively duplicates the critical tasks onto the processor that has the given task in the idle time slot, to reduce the start time of the given task. To compare the performance of the HCT algorithm with several recently proposed algorithms, a large set of randomly generated applications and the Gaussian elimination application are randomly generated. The experimental result has shown that the HCT algorithm outperforms the other algorithm.