Table of Content

15 June 2021, Volume 38 Issue 3 Previous Issue   

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Distributed Variable Selection---MCP Regularization WANG Ge-hua, WANG Pu-yu, ZHANG Hai 2021, 38 (3):  301-314.  doi: 10.3969/j.issn.1005-3085.2021.03.001 Abstract ( 98 )   PDF (314KB) ( 234 )   Save With the development of the digital age, a large number of high-dimensional data has been collected in various disciplines and fields. Faced with the huge amount of collected data, it becomes a great challenge for us to transform it into a form that can not only be stored and analyzed, but also can provide a reference for solving practical problems. In view of the current state of data storage, the distributed storage has emerged properly, in which data are stored in different machines in a certain way without any repetition, so as to solve the problem of data storage. Then, how to design a machine learning algorithm which is suitable for distributed data storage becomes another problem to be solved. As the theory of information technology has developed rapidly, the formulation and development of regularization methods provide us with an effective tool for processing and analyzing massive high-dimensional data, but they are only suitable for single-machine data processing. Concerning the superiority of non-convex regularization for variable selection and feature extraction, we combine distributed storage with non-convex regularization methods. We focus on non-convex regularization methods based on distributed computing to solve the storage and analysis of massive high-dimensional data. This paper studies the variable selection problem in the form of distributed data storage. We store the data separately in multiple computers that can communicate with each other, and propose a distributed MCP method. The distributed MCP algorithm implements interactive information between adjacent computers based on the ADMM algorithm, completes variable selection of full data, and ensures the convergence. The variable selection result of the distributed method is the same as that of the non-distributed method. Finally, the experimental results show that the proposed method is suitable for processing distributed storage data. Related Articles | Metrics

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Dissolved Oxygen Prediction of Xijiang River with the LSTM Deep Network by Artificial Bee Colony Algorithm Based on CEEMDAN JI Guang-yue 2021, 38 (3):  315-329.  doi: 10.3969/j.issn.1005-3085.2021.03.002 Abstract ( 111 )   PDF (11227KB) ( 143 )   Save In order to improve the prediction accuracy of dissolved oxygen content, a complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is proposed and the artificial bee colony (ABC) is used to improve the long and short time memory network (LSTM) model for combined prediction of dissolved oxygen in water quality. First, CEEMDAN is used to calculate the dissolved oxygen content sequence, which is divided into several different natural mode components and trend components. After that, we apply the R/S class to compute the Hurst exponent H of different natural mode components and trend components, and according to the value of H, natural mode components and trend components are re-constructed into microscale, mesoscale and macroscale components, respectively. Finally, for three kinds of components, the ABC-LSTM model is used to predict three species scale components, and the linear weighted reconstruction method is used to obtain the final estimates of dissolved oxygen measured values. The proposed model is applied to the data acquisition system of Henglan water quality monitoring station in Xijiang River. The results show that the model can effectively improve the prediction accuracy of dissolved oxygen in Xijiang River, and the prediction accuracy is as high as 1.6978%. Compared with LSTM, support vector machine (SVM), the ABC-SVM and the artificial bee colony algorithm optimized back propagation neutral network (ABC-BPNN), the prediction accuracy is improved by respectively 2.2867%, 2.7544%, 2.3756% and 2.4448%, indicating that the model in this paper has higher accuracy than the traditional models, with better prediction performance and generalization ability, as well as lower error. This provides the basis for scientific decision-making for the Xijiang water quality monitoring management and maintenance. Related Articles | Metrics

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The Latent Variable Metropolis-Hastings Algorithm for Exchange Rate Series in Case of Missing Data and Pricing the Triggered Financial Products DONG Yan 2021, 38 (3):  330-342.  doi: 10.3969/j.issn.1005-3085.2021.03.003 Abstract ( 90 )   PDF (440KB) ( 148 )   Save Parametric estimation of financial assets is one of the hot topics in modern finance, and also one of the important research fields in mathematical finance. In this paper, the MCMC method is used to study the parameter estimation problem of ARMA exchange rate series in case of missing data. Firstly, the latent variable interpolation method is integrated into the MCMC sampling process. The new MCMC parameter estimation method allows the missing data in the sequence. Secondly, combined with the latent variable, the conjugate posterior distributions of autoregressive coefficients and the white noise variance are obtained. Thirdly, a parameter estimation method based on multiple regression is constructed, due to the difficulty in obtaining the conjugate posterior distributions of moving average coefficients. Finally, using the Metropolis-Hastings sampling instead of Gibbs sampling and incorporating the above results, a new MCMC parameter estimation method is developed. This method effectively overcomes the shortcomings of the volatility aggregation phenomenon of the pure Gibbs sampling sequence. In addition, the euro-dollar exchange rate from September 20 to September 27, 2018 is used as the simulation object, and the empirical analysis of triggered wealth management products is carried out. Related Articles | Metrics

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The Augmented Lagrange Multiplier Algorithm for Sign Matrix Completion WANG Jun-xia, SHEN Qian-ying, WANG Chuan-long 2021, 38 (3):  343-352.  doi: 10.3969/j.issn.1005-3085.2021.03.004 Abstract ( 75 )   PDF (197KB) ( 184 )   Save Matrix completion is one of research hotspots in recent years. Especially, the problem of sign matrix completion has wide applications in fields such as biomedical. In this paper, based on the singular value threshold algorithm, we propose a modified augmented Lagrange multiplier algorithm for sign matrix completion. The threshold matrix generated at each step of the modified algorithm is projected to form a new sign matrix, which forms an iteration on the discrete set of sign matrices. Meanwhile, we prove that under the reasonable conditions, the modified algorithm converges when the penalty factor is large enough. Finally, the numerical examples show that compared with the augmented Lagrange multiplier algorithm and the genetic algorithm, the modified algorithm has obvious advantages in terms of time and error. Related Articles | Metrics

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An Analysis for Geo/Geo/1 Queue with Multiple Working Vacations Based on GI/M/1 Type Markov Process ZHANG Hong-bo, PENG Pei-rang 2021, 38 (3):  353-361.  doi: 10.3969/j.issn.1005-3085.2021.03.005 Abstract ( 88 )   PDF (273KB) ( 164 )   Save In this paper, the classical Geo/Geo/1 queueing system is investigated. First of all, a new GI/M/1 type Markov Chain model for the queue is proposed. Moreover, by using the matrix analytic method, the joint stationary distribution for the Markov chain is given, the results enable us not only obtain an explicit expression for the stationary queue length distribution of the queueing system, but also give the probability of the exact number of vacations that the sever has taken. Such accurate descriptions for the status of the server are new results for the queueing model. Finally, numerical examples are demonstrated to illustrate the effectiveness of the results. Related Articles | Metrics

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The Weak Rupture Degree of Graphs and the Network Invulnerability LIU Yong, YANG Shu-shu, WEI Zong-tian, YUE Chao 2021, 38 (3):  362-368.  doi: 10.3969/j.issn.1005-3085.2021.03.006 Abstract ( 66 )   PDF (156KB) ( 188 )   Save Weak rupture degree is an important parameter for measuring the invulnerability of networks. It combines the difficulty of destroying a network and the severity of the network being destroyed, and considers the number of edges in the remaining subgraph. In order to reveal the internal relationship between the weak rupture degree and the network structure, so as to accurately quantify networks' invulnerability, we initially give some basic properties of the weak rupture degree. Based on this, the relationship between this parameter and several important graphic parameters is studied by combinatorial optimization and analogy methods. These relationships are given in the form of the upper and lower bounds of weak rupture degree, which essentially reflect the characteristics of the network structure in the sense of the weak rupture degree, or invulnerability. These results show that weak rupture degree has obvious advantages in measuring the invulnerability of certain networks. The methods used in this paper have important guidence for network invulnerability analysis, and the obtained results have certain promotion and application value for network invulnerability design. Related Articles | Metrics

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A Full Polynomial-time Approximation Scheme of Two-agent Scheduling with Job Rejection FENG Qi, YANG Li-hua, DI Shuai 2021, 38 (3):  369-376.  doi: 10.3969/j.issn.1005-3085.2021.03.007 Abstract ( 85 )   PDF (201KB) ( 146 )   Save We consider a two-agent scheduling problem with rejection on a single machine. For the problem, we have two agents A and B and each agent has its own job set and cost function. A job of agent A is either accepted or rejected with a certain rejection penalty having to be paid. The jobs of agent B must be accepted. The cost function of agent A is the sum of the makespan of the accepted jobs and the total rejection penalty of the rejected jobs. The cost function of agent B is the maximum lateness. The objective of the scheduling problem is to minimize the cost function of agent A, given that the cost function of agent B does not exceed a fixed value. For this problem, we give a full polynomial-time approximation scheme. Related Articles | Metrics

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Bifurcation Solution of a Diffusive Predator-prey Model with Allee Effect in Prey CAO Qian, LI Yan-ling 2021, 38 (3):  377-388.  doi: 10.3969/j.issn.1005-3085.2021.03.008 Abstract ( 118 )   PDF (455KB) ( 427 )   Save Allee effect is very common in population ecology. It is very important to study Allee effect for the survival and development of population. Therefore, we consider the bifurcation solutions of a diffusive predator-prey model with double Allee effect in prey. Firstly, we analyze the stability of constant solutions by stability theory. Secondly, by taking the diffusion coefficient of prey as the bifurcation parameter, we investigate that the local bifurcation solutions evolve from a positive constant solution under strong Allee effect and weak Allee effect, respectively, by local bifurcation theory, which gives a sufficient condition for the existence of coexistence solutions. Finally, we visually present theoretical results by numerical simulation. The results show that the predator and prey can coexist under strong Allee effect or weak Allee effect when the death rate, diffusion rate and predation rate of the predator satisfy certain conditions. Related Articles | Metrics

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Propagation Problem about a Three-dimensional Wave with Fractional Damping GE Zhi-xin, LI Chun-yuan, CHEN Xian-jiang 2021, 38 (3):  389-398.  doi: 10.3969/j.issn.1005-3085.2021.03.009 Abstract ( 69 )   PDF (345KB) ( 159 )   Save In this paper, a class of three-dimensional wave equations with small fractional damping and sine-waving on the boundary is investigated. The boundary of the problem contains small parameters. Using the multi-scale method and the definition and properties of the Riemann-Liouville fractional derivative, the Taylor formula is applied to the original boundary value problem. The zero-order and first-order boundary value problems with respect to small parameters are obtained. Using the method of separating variables, introducing the detuning parameters, and analyzing the solvability conditions of the boundary value problem, the amplitude and phase of the zero-order approximate solution are obtained. Then, the uniformly valid behavior of the solution is illustrated by the theory of differential inequalities. Finally, the difference between the two-dimensional wave solution and the three-dimensional wave solution is analyzed. The changes in the amplitude of the three-dimensional wave with respect to relevant parameters are shown. The three-dimensional fluctuation boundary value problem shows that, when the boundary has small sinusoidal fluctuations and the external force perpendicular to the boundary changes regularly, the wave has an approximate solution. The instantaneous rate of change of the amplitude mode and phase of the solution is determined by the boundary value, the initially mode value and the value of the fractional derivative. It can be found that the amplitudes of the solutions of undamped two-dimensional waves and those of three-dimensional waves are obviously different. The two-dimensional wave only changes the amplitude and phase periodically, but the amplitude mode is constant, and the approximate solution is periodic. The three-dimensional wave changes in both amplitude mode and phase, but small parameters have little effect on its fluctuation. Related Articles | Metrics

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Newton Type Iteration Methods for Solving Nonlinear Equations XU Hao, SI Zhi-yong 2021, 38 (3):  399-415.  doi: 10.3969/j.issn.1005-3085.2021.03.010 Abstract ( 79 )   PDF (207KB) ( 174 )   Save The Newton iteration method is an important method for solving nonlinear equations. Many other types of iterative methods currently used are based on the Newton iteration method after some extension and expansion. But in these methods, only the properties of the current iteration point and the Jacobi matrix are used, the information about other points and corresponding Jacobi matrices are not fully utilized. In this paper, we use the idea of multiple iterations to improve the Newton iteration method for solving nonlinear equations, and combines the modified Newton iteration method and simplified Newton iteration method to improve the algorithm. We obtain four new types of Newton-type iteration methods for solving nonlinear equations. Rigorous theoretical analyses show that these four Newton-type iterative methods are all convergent. In order to show the effectiveness of proposed algorithms, we present some numerical experimental results. The numerical results show that the four methods all have a fast convergence rate, indicating their efficiency. Related Articles | Metrics

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Threshold Dynamics of Discrete Meningococcal Meningitis Model with Vaccination and Therapy MA Xia, CAO Hui, ZHANG Jin-zhu, GUO Zun-guang 2021, 38 (3):  416-430.  doi: 10.3969/j.issn.1005-3085.2021.03.011 Abstract ( 68 )   PDF (2045KB) ( 237 )   Save According to the epidemic characteristics of Meningococcal Meningitis in China and the influence of vaccination factors, we formulate a discrete-time SCIRS model with vaccination and therapy by using the backward Euler method and investigate its dynamic characteristics. We obtain sufficient conditions for the global behavior of the equilibrium points by constructing suitable Lyapunov functions. We further conclude that the disease is permanent by using the theory of persistence in dynamical systems.~Numerical simulations are carried out to illustrate the main theoretical results. Related Articles | Metrics

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The Numerical Solution of 3D Free Surface Wave for Double Hydrofoils ZHAO Le-ping, LUO Zhi-qiang 2021, 38 (3):  431-440.  doi: 10.3969/j.issn.1005-3085.2021.03.012 Abstract ( 60 )   PDF (1953KB) ( 256 )   Save In this paper, a source panel method with dissipative Green function is applied to explore the internal evolution mechanisms under the interaction between the complicated 3D flow field and double hydrofoils. Based on the dissipative source Green function, the different wave profiles of free surface are presented in the double hydrofoils flow. From the benchmark tests, we can draw a conclusion that the accuracy and robustness of the numerical algorithm can be confirmed. Numerical results show that the evolution of wave profile of single hydrofoil and double hydrofoils can be demonstrated clearly. The parallel wave ripple will interact with the other waves and the crest and trough can be overlapped. The double hydrofoils systems can present different wave ripple profiles obviously corresponding with the different staggered position. Related Articles | Metrics

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Relationships between Vector Variational Inequality and Multi-objective Optimization for Strict Minimizer of Higher Order ZHANG Ya-meng, YU Guo-lin 2021, 38 (3):  441-450.  doi: 10.3969/j.issn.1005-3085.2021.03.013 Abstract ( 60 )   PDF (120KB) ( 444 )   Save This paper is devoted to the study of the relations between vector variational inequality and nonsmooth multi-objective optimization in the sense of strict minimizers of higher order. We firstly introduce an extension of higher-order strong pseudoconvexity for Lipschitz functions, termed higher-order strongly pseudoconvex functions of type I, and some examples are presented in the support of this generalization. Then, we identify the strict minimizers of higher order, the vector critical points and the solutions of the weak vector variational inequality problem under the higher-order strong pseudoconvexity of type I hypothesis. It is our understanding that such results have not been established till now. Related Articles | Metrics