Table of Content

15 April 2017, Volume 34 Issue 2    Next Issue

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Stochastic Modelling and Analysis of Recombinant Cell Chemostat Based on Markov Chains LI Xiao-yue, JI Xue-hui, YUAN San-ling 2017, 34 (2):  111-123.  doi: 10.3969/j.issn.1005-3085.2017.02.001 Abstract ( 116 )   PDF (966KB) ( 453 )   Save In this paper, a class of continuous time Markov chain model for recombinant cell chemostat culture is investigated. Firstly, applying the cumulant generating function, the moment equations which the digital features satisfy are obtained. Then the moment closure equations are derived by the moment closure techniques based on the lognormal approximation, and the corresponding It$\hat{\rm o}$ stochastic differential equations are given according to the Euler-Maruyama method. To illustrate the rationality of the moment closure, the numerical simulation is given to compare the deterministic model with the stochastic model and moment closure equations，and to analyze trends of the recombinant cell. The result shows that the behaviour of random work is consistent with the corresponding deterministic model. Related Articles | Metrics

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An Improved Non-equidistant Grey Model and Its Application ZHANG Kai, WANG Cheng-yong, HE Li-juan 2017, 34 (2):  124-134.  doi: 10.3969/j.issn.1005-3085.2017.02.002 Abstract ( 448 )   PDF (197KB) ( 260 )   Save There exists a lot of non-homogenous exponential incremental sequence in real life. According to the non-equidistant GM(1,1) modeling mechanism, an improved grey model which uses non-homogenous exponential sequence to fit the original data sequence is proposed. In order to minimize the square sum of relative error between observed values and simulated values, the model's parameters are deduced by means of the least square method as well as the time response function. Finally, the improved model is compared with the classical model by two examples, and the results show that the effectiveness and practicality of the new proposed model. Related Articles | Metrics

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The Method for the Generation of Signature in Multi Attack Network Based on Semantic Perception WANG Qing 2017, 34 (2):  135-142.  doi: 10.3969/j.issn.1005-3085.2017.02.003 Abstract ( 112 )   PDF (215KB) ( 218 )   Save It is difficult to generate the valid signature data for the polymorphic attack signature used in traditional string pattern mining and matching technology. In this paper, the method based on semantic awareness is proposed and tested. Firstly, the condition characteristic of polymorphic attacks data is analyzed in detail. Secondly, the original code of static semantics is extracted by applying static data flow forming process analysis. Finally, the multiple polymorphic signature data are generated in accordance with the classification standards based on SigFree method. Furthermore, the polymorphism of semantic and information related to string pattern of the code is also contained inside the data. By comparing with the experimental data of Hamsa scheme, this method is able to effectively reduce the error distortion rate of digital signature. Related Articles | Metrics

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Exponential Stability of Anti-periodic for a Class of Cellular Neural Networks with Proportional Delays SU Li-juan, ZHOU Li-qun 2017, 34 (2):  143-154.  doi: 10.3969/j.issn.1005-3085.2017.02.004 Abstract ( 200 )   PDF (553KB) ( 340 )   Save In this paper, the global exponential stability of anti-periodic solutions of a class of cellular neural networks with proportional delays is discussed. Firstly, a class of cellular neural networks with proportional delays is transformed equivalently into a class of cellular neural networks with constant delays and variable coefficients by a nonlinear transformation. Then, by establishing appropriate delay differential inequalities and applying inequality technique, a delay-dependent sufficient condition is obtained to ensure the existence and global exponential stability of anti-periodic solutions of the system. Finally, the numerical results indicate the proposed method is correct and less conservative than the existing results. Related Articles | Metrics

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The Exploration of the Stabilized Projection Method for the Time-dependent Navier-Stokes Equations LI Qian, JIA Hui-yong, JIA Hong-en 2017, 34 (2):  155-170.  doi: 10.3969/j.issn.1005-3085.2017.02.005 Abstract ( 207 )   PDF (199KB) ( 185 )   Save In this paper, we discuss a stabilized fractional-step method for numerical solutions of the time-dependent Navier-Stokes equations. The nonlinear term and incompressible condition are separated into two different sub-problems by virtue of the operator splitting method, where the nonlinear term is treated by Oseen iteration. The linear elliptic problem is solved at the first step, and the second step is to solve the generalized Stokes problem. The two problems both satisfy the homogeneous Dirichlet boundary conditions for the velocity. Furthermore, a locally stability term is added in the second step of the scheme, which enhances the numerical stability and efficiency for the equal-order pairs. The convergence analysis and error estimates for the velocity and pressure of the schemes are established via the energy method. Some num-erical results demonstrate the efficiency of the proposed method. Related Articles | Metrics

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Asymptotic Distributions of Empirical Likelihood Ratio Statistics for Regression Coefficients in a Linear Model under $\phi$-mixing Samples with Missing Data ZHENG Li-ling, QIN Yong-song, LI Ying-hua 2017, 34 (2):  171-181.  doi: 10.3969/j.issn.1005-3085.2017.02.006 Abstract ( 125 )   PDF (172KB) ( 507 )   Save The concept of $\phi$-mixing has been used extensively as measures of the weak depen-dence, and the phenomenon of missing data often occurs in various application fields. In existing literatures, the statistical inference under the dependence and missing data, has been deeply studied. However, there are few studies on the case of the dependent and missing data simultaneously. This paper is concerned with the statistical inference simultaneously under the dependence and missing data. In other words, this paper discusses the asymptotic distributions of empirical likelihood ratio statistics for regression coefficients in a linear model under $\phi$-mixing samples with missing data. The regression imputation method is applied to impute the missing data of the response variables, and thus `complete' data for regression coefficients in the linear model are obtained. Furthermore, we employ the score functions to establish the empirical likelihood ratio statistics for the regression vector in the linear model. Under some conditions, it is proved that the empirical likelihood ratio statistics are asymptotically Chi square distributed. This conclusion provides a theoretical basis for the confidence region of the regression coefficients of a linear model under $\phi$-mixing samples with missing data. Related Articles | Metrics

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Stability and Traveling Fronts of a Three-species Diffusive Prey-predator System with Delays LI Cheng-lin 2017, 34 (2):  182-198.  doi: 10.3969/j.issn.1005-3085.2017.02.007 Abstract ( 69 )   PDF (139KB) ( 454 )   Save This paper is concerned with a three-species delayed reaction-diffusion predator-prey system in a bounded domain with Neumann boundary condition. The sufficient conditions of stability are found for equilibria of this system by the method of eigenvalue and Lyapunov function, and these conditions imply that delays often restrain stability. One of the main results about stabilities shows that if the intra-specific competitions of the predator and preys dominate their inter-specific interaction, then the positive equilibria are globally stable. Furthermore, the existence of the traveling wavefront is considered by constructing upper-lower solution and it is derived that this system always has a traveling wave solution connecting the trivial steady state and the positive steady state when the wave speed is relatively big. Related Articles | Metrics

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Duality Theorems for a Nonconvex Set-valued Optimization Problem YU Guo-lin, MA Xiao-jun 2017, 34 (2):  199-208.  doi: 10.3969/j.issn.1005-3085.2017.02.008 Abstract ( 154 )   PDF (112KB) ( 214 )   Save Duality is of great importance in mathematical programming, since it allows to study a minimization problem through a maximization problem and to know what one can expect in the best case and has resulted in many applications. The aim of this paper is to establish the duality theorems for a kind of nonconvex constraint set-valued optimization problems. Based on the notion of invexity in terms of cone-approximating multifunction for a set-valued map, Mond-Weir and Wolfe dual problems are investigated for a primal constraint set-valued optimization. By employing the analytic method, the weak duality theorems, the strong theorems and the converse duality theorems between Mond-Weir and Wolfe dual problems and the primal constraint set-valued optimization problem are established in sense of weak efficiency. These duality theorems disclose that there exist the precise dual relationships between the primal optimization and the involved dual problems. The results obtained in present paper enrich and deepen the theory and applications of set-valued optimization. Related Articles | Metrics

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The Generalization Ability of Online Algorithm for $\alpha$-mixing Sequence HU Xiao-yun, ZOU Bin, GONG Tie-liang, YANG Yan 2017, 34 (2):  209-220.  doi: 10.3969/j.issn.1005-3085.2017.02.009 Abstract ( 147 )   PDF (133KB) ( 234 )   Save Theoretical investigation of the online algorithms has received considerable attention recently. The previous generalization bounds of online learning algorithms are usually established on the base of independent and identically distributed (i.i.d.) samples. In this paper, we go far beyond this classical framework to investigate the generalization ability of online algorithm with $\alpha$-mixing sequence. We define $\alpha$-mixing sequence by using the total variation, and our analysis requires only martingale convergence arguments. At last, ``regret" is utilized to measure the performance of online algorithms. Our main result is a tighter generalization error estimation than that of $\beta$-mixing sequence. Related Articles | Metrics