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05 October 2016, Volume 33 Issue 5    Next Issue

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A Graph Partitioning Algorithm Based on SLIC Superpixels ZHAO Yuan, PENG Ji-gen, GAO Yi 2016, 33 (5):  441-449.  doi: 10.3969/j.issn.1005-3085.2016.05.001 Abstract ( 25 )   PDF (3412KB) ( 15 )   Save Image segmentation is a key step in the analysis and understanding of the image, and it is also one of the basic techniques in computer vision field. Computational complexity is an important criterion to judge the quality of an image segmentation algorithm, therefore, it is one of the main tasks to reduce the computational complexity of algorithm in the field of image segmentation. An image segmentation method based on SLIC superpixels is proposed in this paper. This new algorithm generates the super-pixels using SLIC algorithm, and reduces effectively the computational complexity of Ncut algorithm via constructing a corresponding similarity matrix. Furthermore, the new algorithm can reduce greatly the running time of Ncut algorithm. Because of the accuracy of SLIC algorithm, the experiments of three natural images demonstrate that our algorithm is better than Ncut algorithm and its improved algorithm no matter on segmentation results or running time. Related Articles | Metrics

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Global Exponential Stability of a Class of Recurrent Neural Networks with Multi-proportional Delays ZHAO Ning, ZHOU Li-qun 2016, 33 (5):  450-462.  doi: 10.3969/j.issn.1005-3085.2016.05.002 Abstract ( 25 )   PDF (186KB) ( 23 )   Save Proportional delay is an unbounded time-varying delay, which is different from constant delay, bounded time-varying delay and distributed delay. The proportional delay systems often play important roles in some fields such as physics, biology systems and control theory, but at present there are not much dynamics behavior research of neural networks with proportional delays. In this paper, the global exponential stability of a class of recurrent neural networks with multi-proportional delays is studied. Firstly, a class of recurrent neural networks with multi-proportional delays is transformed into the recurrent neural networks with constant delays and variable coefficients by the nonlinear transformation. Secondly, based on the properties of $M$-matrix, the homeomorphism mapping theorem, and the delay differential inequality technique, a delay-independent sufficient condition which ensures the existence, uniqueness and global exponential stability of the equilibrium point of such neural networks is confirmed. This condition depends on the connection weight matrix of neural networks and the activation function of neurons. Finally, the numerical examples verify that the theoretical results are effective and less conservative than previously existing results. Related Articles | Metrics

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Optimal Investment-reinsurance-hybrid Dividend Strategies for Insurance Company under Compound Poisson-Geometric Risk Process SUN Zong-qi, CHEN Zhi-ping 2016, 33 (5):  463-479.  doi: 10.3969/j.issn.1005-3085.2016.05.003 Abstract ( 21 )   PDF (360KB) ( 14 )   Save To better reflect the insurance prectice and help insurance company making more robust strategy, we assume that the number of claims follows the compound Poisson-Geometric process, and investigate the optimal investment-reinsurance-hybrid dividend problem under the assumption that the insurance's reserve price follows a diffusion process. Based on the criterion of maximizing the expected total present value of dividends, the optimal desicion model is utiliting dynamic programming priciple, and the optimal policy is obtained through solving the HJB equation. The closed-form optimal investment-reinsurance-hybrid dividend strategies have been derived under the special case: the loss rate of reinsurance premiums is equal to the dividend discount rate. Finally, some numerical examples and their economic analyses are provided to illustrate the reasonability of the obtained theoretical results. Related Articles | Metrics

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The Spline Curve Approximation for Non-smooth Curve\\ with the Fixed Length HE Guo-liang, ZHANG Yong 2016, 33 (5):  480-494.  doi: 10.3969/j.issn.1005-3085.2016.05.004 Abstract ( 29 )   PDF (1377KB) ( 7 )   Save It is a necessary condition that the curve is continuous and sufficient smooth when we solve the differential equation defined on the curve in engineering calculation. This paper discusses the smooth curve approximation for non-smooth curves with the same length on local interval. We prove that the following theoretical results based on the intermediate value theorem: if the measurable length of non-smooth points in a continuous curve has limit length, on any local sub-intervals, there always existences at least one smooth spline curve can be used to approximate the curve with same length as long as the length can be measured on this fixed sub-intervals. Furthermore, if a reference point is given, the unique smooth spline curve can be derived easily. Based on these theoretic results, we also propose the algorithm and present some numerical results to show the simplicity and efficiency of this method, which leads to the optimal solution for the non-smooth curve approximation. Related Articles | Metrics

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Lattice Boltzmann Model for the Generalized Ginzburg-Landau Equation LI Jing-wei, LIU De-min, ZHANG Guo-liang, LIN Yu-ting 2016, 33 (5):  495-505.  doi: 10.3969/j.issn.1005-3085.2016.05.005 Abstract ( 24 )   PDF (642KB) ( 12 )   Save In this paper, a 5-bit single relaxation lattice Boltzmann model with additional terms is proposed for solving the generalized Ginzburg-Landau equation. Firstly, by using Chapman-Enskog expansion and Taylor expansion, we obtain a series of partial differential equations in different time scales and several high-order moments of equilibrium distribution functions. Then we establish a lattice Boltzmann model with truncation error by applying a series of moments of equilibrium distribution functions and derive the numerical dissipation term. Moreover, we obtain the stability condition of the model by ultilizing the Hirt heuristic method. Finally, we provide some numerical examples of the generalized Ginzburg-Landau equation. Numerical results indicate that the method can be used to simulate the generalized Ginzburg-Landau equation. Related Articles | Metrics

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A Modified Block-by-block Numerical Scheme for Impulsive Differential Equations CAO Jun-ying, MA Qun-zhang, WANG Zi-qiang 2016, 33 (5):  506-516.  doi: 10.3969/j.issn.1005-3085.2016.05.006 Abstract ( 28 )   PDF (182KB) ( 9 )   Save In the paper, we use a modified block-by-block method to establish a high order numerical scheme for the impulsive differential equation. The modified block-by-block method is an improvement of classical block-by-block method. It is the high order numerical method for solving integral equation, and it has the advantages of the decoupled solution form at every block except the first block. Firstly, we transform the impulsive differential equation into the impulsive integral equation. Based on the impulsive integral equation form of impulsive differential equation, we establish its high order numerical scheme via modified block-by-block method. The high order numerical scheme is a decoupled solution form at each block in two adjacent impulsive points except the first block. Secondly, using the discrete Grownwall inequality, we prove that the convergence order of the numerical solution is 4. Finally, we present a series of numerical examples to support the theoretical results. Related Articles | Metrics

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A Modified Slanting Filter Method for Nonlinear Programming LIU Mei-ling, LI Xue-qian 2016, 33 (5):  517-533.  doi: 10.3969/j.issn.1005-3085.2016.05.007 Abstract ( 25 )   PDF (170KB) ( 12 )   Save In this paper, we propose a modified slanting filter technique combined with sequ-ential quadratic programming (SQP) method to solve nonlinear programming problems. In order to produce the sufficient reduction conditions, the slanting envelopes are set in the objective function direction and the constraint violation direction. Comparing with the classic filter, the new filter accepts reasonable steps flexibly. It provides a mechanism whereby the acceptance chance of the iterates is improved and shares the feature with the classic filter approach, called the inclusion property. The new filter criterion is also used for a restoration filter in feasibility restoration phase. Under some mild conditions, the global convergence properties are obtained. The preliminary numerical results are presented. Related Articles | Metrics

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General Coulson-type Integral Formula for the Energy of Digraphs GAO Nan, LV Wei 2016, 33 (5):  534-540.  doi: 10.3969/j.issn.1005-3085.2016.05.008 Abstract ( 22 )   PDF (108KB) ( 12 )   Save For a simple digraph $D$, the energy $E(D)$ is defined to be the sum of the absolute values of the real part of all eigenvalues of its adjacent matrix. In this paper, we give a general Coulson-type integral formula for the energy of digraphs by using the method of complex analysis. This integral formula establishes the relationship between the energy and the characteristic polynomial of the digraphs. Related Articles | Metrics

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Unique Continuation Property for a Class of Fifth-order Korteweg-de-Vries Equations GAO Xiao-hong, ZHENG Xiao-cui 2016, 33 (5):  541-550.  doi: 10.3969/j.issn.1005-3085.2016.05.009 Abstract ( 29 )   PDF (121KB) ( 13 )   Save The unique continuation property is one of the important properties of the solutions to the integrable systems. The properties of the solutions of the initial value problems are bound up with the smoothness of the initial values. In this paper, we mainly discuss the unique continuation property of the solutions to the initial value problem associated with a class of fifth-order KdV equations. We prove that, if a sufficiently smooth solution to the initial value problem associated with the fifth-order Korteweg-de-Vries equations is supported compactly in a nontrivial time interval, then it vanishes identically. Related Articles | Metrics