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15 October 2015, Volume 32 Issue 5 Previous Issue    Next Issue

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An Improved C-V Image Segmentation Model LI Wu-qiang, YANG Qiao, HAN Guo-dong 2015, 32 (5):  633-642.  doi: 10.3969/j.issn.1005-3085.2015.05.001 Abstract ( 16 )   PDF (291KB) ( 4 )   Save Aiming at the deficiency of the traditional C-V model for image segmentation in terms of efficiency and accuracy of segmentation, this paper presents an improved C-V image segmentation model. Firstly, the level set function is restricted as a signed distance function by adding the internal energy term in the model, which could avoid the re-initialization and improve the efficiency of image segmentation. Secondly, the new regularization function of Heaviside function is chosen to improve the approximation effect and the accuracy of image segmentation. Finally, the regularization function is applied to replace the traditional Dirac function in C-V model with positive real functions. On the one hand, it's able to eliminate the latter inhibition of homogeneous areas near the border to detect non-initial active contour lines, and then makes the better global optimization features to improve the accuracy of image segmentation; on the other hand, it gives more simple model and improves the efficiency of image segmentation. Compared with the original C-V model, the numerical experiments show that the improved model has better efficiency and higher accuracy. Related Articles | Metrics

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Number of Solution for the Sparse Signal Recovery Problem LIAO An-ping, YANG Miao, XIE Jia-xin, SHEN Kun 2015, 32 (5):  643-649.  doi: 10.3969/j.issn.1005-3085.2015.05.002 Abstract ( 18 )   PDF (156KB) ( 6 )   Save This paper is concerned with the number of solution to sparse signal recovery problem based on linear measurements, which is an important problem in signal processing. In the noiseless measurement case, by taking advantage of the combinatorial analysis method, an upper bound is established for the number of solution to the sparse signal recovery problem, and by constructing a special linear measuring matrix, the best of the upper bound is proved as well. Moreover, if the measuring matrix satisfies some conditions, the upper bound could be improved. Based on these results, some new ideas of a finite search can be employed to solve the sparse signal recovery problem in some special cases. Related Articles | Metrics

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Method for Risk Ranking Based on Intuitionistic Fuzzy Multi-attribute Group Decision-making CAI Jiu-shun, ZHANG Zhi-guo, SHI Peng, HE Quan 2015, 32 (5):  650-658.  doi: 10.3969/j.issn.1005-3085.2015.05.003 Abstract ( 25 )   PDF (231KB) ( 8 )   Save In order to solve the fuzzy and uncertainty problem of information collection, avoid the mistakes of single-person decision, and describe different characteristics of risk, we combine the intuitionistic triangular fuzzy number and the theory of multi-attribute group decision-making, and propose a new ranking method based on intuitionistic fuzzy multi-attribute group decision-making and improve the accuracy of risk ranking. Firstly, we apply the intuitionistic triangular fuzzy number to collect expert judgment information. Secondly, we calculate the entropy weights of triangular fuzzy number and intuitionistic fuzzy number to get the combined weights, and obtain the comprehensive value of different risk schemes. Then, we rank comprehensive value of different risk schemes by TOPSIS method. Finally, the numerical example is given to verify the feasibility and effectiveness of the method. Related Articles | Metrics

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Blind Deblurring Based on an $L_{1/2}/L_2$ Regularization JING Wen-feng, ZHAO Ren-xing, LI Zhi-min, SONG Wei, ZHENG Yan 2015, 32 (5):  659-666.  doi: 10.3969/j.issn.1005-3085.2015.05.004 Abstract ( 16 )   PDF (1342KB) ( 5 )   Save Image deblurring is the basic work for image recognition and video analysis. In real-world applications, most image deblurring problems are ones of blind image deblurring. The problems are ill-posed and need to be solved by regularization methods. Since the existing regularization models for image deblurring are difficult to restore image details, we propose a novel blind deblurring model based on $L_{1/2}/L_2$ regularization and an alternating projection iteration algorithm to solve it. Experimental results demonstrate that the proposed model and algorithm have very good restoration on the detailed structure of original deblurred images, and have high computational efficiency and fine robustness to parameters as well. Related Articles | Metrics

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Bayesian Estimation of TVaR Measure under Pareto-Gamma Models ZHANG Yi, ZHOU Dong-qiong, WEN Li-min 2015, 32 (5):  667-676.  doi: 10.3969/j.issn.1005-3085.2015.05.005 Abstract ( 19 )   PDF (192KB) ( 6 )   Save In financial risk management, the measurement and assessment of risk are most concerned problems for decision makers. Since TVaR measure is not only an improved VaR measure, but also  meets the consistency axiom of risk measurement, TVaR has been widely used in risk management. In this paper, Bayesian statistical models are given by applying both the sample information and the prior information of risks. The Bayesian estimation is employed in this model, and the strong consistency of Bayesian estimation of TVaR is proved. Finally, the simulation methods are given to investigate the estimation efficiency for different sample sizes. The results indicate that the estimator is still able to meet the needs of actual applications even in the small sizes. Related Articles | Metrics

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Boosting Variable Selection Algorithm for Linear Regression Models LI Yu, ZHANG Chun-xia, WANG Guan-wei 2015, 32 (5):  677-689.  doi: 10.3969/j.issn.1005-3085.2015.05.006 Abstract ( 19 )   PDF (351KB) ( 11 )   Save With respect to variable selection for linear regression models, this paper proposes a novel Boosting learning method based on genetic algorithm. In the novel algorithm, all training examples are firstly assigned equal weights and a traditional genetic algorithm is adopted as the base learning algorithm of Boosting. Then, the training set associated with a weight distribution is taken as the input of genetic algorithm to do variable selection. Subsequently, the weight distribution is updated according to the quality of the previous variable selection results. Through repeating the above steps for multiple times, the results are then fused via a weighted combination rule. The performance of the proposed Boosting method is investigated on some simulated and real-world data. The experimental results show that our method can significantly improve the variable selection performance of traditional genetic algorithm and accurately identify the relevant variables. Thus, the novel Boosting method can be deemed as an effective technique for handling variable selection problems in linear regression models. Related Articles | Metrics

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Existence of Periodic Solution for Semi-linear Second-order Differential Equations ZHOU Tong-fan 2015, 32 (5):  690-696.  doi: 10.3969/j.issn.1005-3085.2015.05.007 Abstract ( 20 )   PDF (140KB) ( 6 )   Save In this paper, we consider the existence of periodic solutions for a class of semi-linear second-order differential equations. The difficulty of traditional methods lies in a mass of detailed estimates. By applying the viscosity solutions method and the classical upper-lower solutions method, as well as the Leray-Schauder fixed point principle, we establish the existence of periodic solutions to the equation under some weaker conditions. Our result improves and generalizes many results on the ropes mechanics equations in the previous literature. Related Articles | Metrics

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A Coupled Volume of Fluid and Level Set (CVOFLS) Method for Tracking Moving Interfaces ZHOU Wen, OUYANG Jie, CUI Li-ying 2015, 32 (5):  697-708.  doi: 10.3969/j.issn.1005-3085.2015.05.008 Abstract ( 17 )   PDF (2443KB) ( 2 )   Save A new coupled volume of fluid and level set (CVOFLS) method is proposed to capture the moving interface, in order to improve both the inaccurate evaluation of the interface normal vector in volume of fluid (VOF) method and the poor mass conservation ability in level set (LS) method. The method takes the advantages of the VOF method and the LS method. At each time step, the LS equation is solved at first, and the interface normal vector is evaluated via the LS signed distance function. Then the VOF equation is evaluated, and the interface reconstruction and the mass correction are performed by the volume fraction. The method is applied in some benchmark cases, such as rotation of the Zalesak's disk, and stretching and shrinking of a circular fluid element. The numerical results indicate that the proposed CVOFLS method not only accurately captures the complex interface evolution and preserves the mass conservation, but also greatly improves the computational efficiency. Related Articles | Metrics

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A Set of New Criterion for Judging Nonsingular $H$-matrices XUE Yuan, LIU Jian-zhou 2015, 32 (5):  709-718.  doi: 10.3969/j.issn.1005-3085.2015.05.009 Abstract ( 16 )   PDF (140KB) ( 4 )   Save Nonsingular $H$-matrix is a special class of matrices which has wide applications in computational mathematics, matrix theory, economic mathematics and control theory. In this paper, according to the special properties of $M$-matrices and $\gamma$-chain diagonally dominant matrices, and constructing positive diagonal matrices and subdividing the index set of matrices, we obtain several new conditions for judging $H$-matrices by applying some special inequalities and inequality techniques. The criteria extend some of the recent results, and the numerical examples illustrate the effectiveness of the theoretical results. Related Articles | Metrics

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Estimation on Upper Bounds for the Infinity Norm of Inverse Matrix of Strictly Diagonally Dominant $M$-matrix WANG Yong 2015, 32 (5):  719-725.  doi: 10.3969/j.issn.1005-3085.2015.05.010 Abstract ( 15 )   PDF (124KB) ( 5 )   Save $M$-matrix is applied widely in mathematical physics, cybernetics, electric system and so on. In recent years, the upper bound estimate on the infinity norm of inverse matrix of a strictly diagonally dominant $M$-matrix has become an important problem. Firstly, some new notations are introduced in this paper. Then, applying the range for the elements of inverse matrix and algebra methods, some new upper bounds for the infinity norm of inverse matrix of a strictly diagonally dominant $M$-matrix are obtained. Finally, the theory analysis and numerical results show that the new upper bound estimates improve some of the related results. Related Articles | Metrics

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A Fast Propagation Method for the Helmholtz Equation LENG Wei 2015, 32 (5):  726-742.  doi: 10.3969/j.issn.1005-3085.2015.05.011 Abstract ( 15 )   PDF (1736KB) ( 4 )   Save A fast method is proposed for solving the high frequency Helmholtz equation. The building block of the new fast method is an overlapping domain decomposition method for layered medium. In the new fast method, the computation domain is firstly decomposed hierarchically into many subdomains on different levels. Then the mapping from incident waves to out-going waves on all the subdomains are set up. Finally, the wave propagates on the subdomain boundaries on different levels to reach the solution to the Helmholtz equation. The new fast method is of low complexity, and suitable for parallel computing. Numerical experiments show that with the new fast method, 2D Helmholtz equations with half billion unknowns could be solved efficiently on massively parallel machines. Related Articles | Metrics

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Fixed Cost Allocation Based on Efficiency Maximization and Min-max Relative Difference LIN Rui-yue 2015, 32 (5):  743-758.  doi: 10.3969/j.issn.1005-3085.2015.05.012 Abstract ( 13 )   PDF (147KB) ( 4 )   Save In this paper, we apply the data envelopment analysis technique to propose a minimax model for the fixed cost allocation problem under two assumptions: all decision making units (DMUs) become strong CCR-efficient under common weights after the fixed cost allocation; the maximum relative difference between allocated costs and the corresponding scale sharing costs is minimized. In the pure input case and the pure output case, we deduce the analytical solution of the minimax model; in the general case, we propose an algorithm for the minimax model, which always produces a unique fixed cost allocation solution with good computational efficiency. Compared with other allocation methods based on the similar assumption, the new approach can avoid inappropriate gaps among costs with the help of appropriately allocating costs among DMUs according to their individual inputs and outputs. Numerical analysis shows the validity and superiorities of the new approach. Related Articles | Metrics

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Applications of Adaptive Elastic Net Procedure for Logistic Regression Model LI Chun-hong, HUANG Deng-xiang, DAI Hong-shuai 2015, 32 (5):  759-771.  doi: 10.3969/j.issn.1005-3085.2015.05.013 Abstract ( 19 )   PDF (137KB) ( 3 )   Save In this paper, we consider the adaptive Elastic Net procedure for the Logistic reg-ression model and prove the Oracle property of its estimates. Compared with the Lasso, the adaptive Lasso and the Elastic Net procedure, we obtain that the proposed procedure has good performance, owing to the Oracle property. Related Articles | Metrics

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The Maximal SNS-pattern Matrix for a Signed Digraph MOU Gu-fang, HUANG Ting-zhu 2015, 32 (5):  772-782.  doi: 10.3969/j.issn.1005-3085.2015.05.014 Abstract ( 13 )   PDF (142KB) ( 3 )   Save For an asymmetric sign pattern matrix $P$, we analyze the sign characteristic of $P$ with the help of a signed digraph in this paper. The maximal SNS-pattern matrix for a signed digraph is the maximal sign-nonsingular sub-pattern among all real matrices having the given sign pattern $P$. In this paper, SNS problems for signed digraphs are studied by converting a signed digraph $\Gamma$ into a signed bipartite graph $G(U,V)$. We propose the algorithms for searching for a sub-signed bipartite graph $G(U',V')$ with the maximum perfect matching $M'$ corresponding to every set of disjoint $M'$-interlacing cycles, which contain an even number of $M'$-interlacing $e$-cycles. The maximal SNS-pattern for a signed digraph is obtained according to algorithms. Related Articles | Metrics

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Analyticity and Persistence Properties of Solutions to the Fornberg-Whitham Equation ZHAO Cai-xia, FU Ying 2015, 32 (5):  783-790.  doi: 10.3969/j.issn.1005-3085.2015.05.015 Abstract ( 15 )   PDF (109KB) ( 4 )   Save The long time behavior of solutions is one of important problems in the study of partial differential equations. To a great degree, the properties of solutions will depend on those of initial values. In this paper, the analyticity and persistence properties of solutions to the Cauchy problem of the Fornberg-Whitham equation are considered respectively when the initial values are analytic or decaying. It is shown that the solutions of this equation are analytic in both variables, globally in space and locally in time. The solutions uniformly have the same decay property at any later time when the initial datum decays at infinity. Related Articles | Metrics