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    20 September 2021
    Volume 56 Issue 9
    Community discovery algorithm based on attention network feature
    Jing-hong WANG,Li-na LIANG,Hao-kang LI,Yi ZHOU
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(9):  1-12,20.  doi:10.6040/j.issn.1671-9352.4.2021.174
    Abstract ( 1085 )   HTML ( 127 )   PDF (10148KB) ( 465 )   Save
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    In the real world, many networks are closely organized according to the community structure. It has been found that the community is of great help in understanding the structure and relationship of complex networks. This paper proposes a community discovery algorithm based on attention network features (CANF algorithm). It uses the label node frequency and the inverse example node frequency to measure the initial network label characteristics, and introduces the attention mechanism, and updates each neighbor node of the example node. Combined the initial weight with the assigned weight, the network features of the initial measure can obtain more detailed information related to the target. In this paper, complex network preprocessing and community game merge are carried out through distributed attention network features. The experimental results show that the accuracy, modularity and running time of the community discovery algorithm based on attention network features are better than other community discovery algorithms.

    ASR-UNet: an improved retinal vessels segmentation algorithm based on attention mechanism
    San-li YI,Jian-ting CHEN,Jian-feng HE
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(9):  13-20.  doi:10.6040/j.issn.1671-9352.0.2020.655
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    Factors such as tiny blood vessels in the retina and light will cause the problem of low segmentation accuracy of existing algorithms. This paper proposes a new retinal vessel segmentation algorithm model based on U-Net segmentation model combined with attention mechanism. The improved measures of this paper are as follows: first, we use SE-Resnet to replace the common convolution used in U-Net, thereby introducing a channel attention mechanism to enhance the original features. After that, AG are added to the jump connection part to enhance the spatial characteristics, thereby improving the models ability to segment the microstructure of blood vessels. The algorithm of this paper is verified on the public datasets DRIVE and CHASE_DB1, and the results are 0.9697 and 0.9657 on Acc, 0.8044 and 0.7673 on sensitivity, and 0.9859 and 0.9866 on specificity. Experimental results show that the proposed algorithm has better performance than recent retinal blood vessel segmentation algorithms.

    Comparison analysis of microbial community structure in different functional areas of recirculating aquaculture system
    Zhan-sheng GUO,Yi DING,Hai-tao ZHANG,Xu-guang HOU
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(9):  21-27,49.  doi:10.6040/j.issn.1671-9352.0.2020.621
    Abstract ( 1197 )   HTML ( 106 )   PDF (2361KB) ( 439 )   Save
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    In order to explore the microbial community structure in different functional areas of recirculating aquaculture system, as well as to understand the relationship between environmental factors and the microbial community, microbial community structure in recirculating aquaculture system was analyzed by using high-throughput sequencing with 16S rRNA in this study. The results showed that Proteobacteria and Bacteroidetes were the most dominant phyla in overall system, the compositions of dominant genera were quite different in different areas of system, while the relative abundances of Vibrio in whole system were both exceeding 1%. α-diversity (Shannon, ACE and chao1) of samples collected from biofilter and Rapana venosa pond were highest, and that in abalone pond and natural seawater were lowest. Non-metric multi-dimensional scaling (NMDS) analysis showed the system areas possessed distinctive distances of microbial communities except samples between biofilter and culture pond inlet. The removal rates of ammonia nitrogen and nitrite nitrogen from biofilter to the inlet of culture pond were 8.77% and 45.12%, respectively. The concentrations of nitrate nitrogen maintained a high level in the whole system (148.50~200.47 mg/L). There was no significant correlations between environmental factors and microbial community structure, temperature and nitrite nitrogen had relatively stronger effects on microbial community structure. This study provides a reference for the design improvement and daily management of recirculating aquaculture system in the next step.

    Nontrivial periodic solution of a stochastic non-autonomous SIS model with public health education
    WANG Qi, JIA Jian-wen
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(9):  28-34.  doi:10.6040/j.issn.1671-9352.0.2020.519
    Abstract ( 809 )   PDF (414KB) ( 406 )   Save
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    A stochastic SIS epidemic model with public health education and periodic parameters is considered. Firstly, the sufficient conditions for persistence and extinction of the disease are obtained. Then by using Hasminskiis theory, the sufficient conditions for existence of nontrivial periodic solutions to stochastic model is given.
    Existence of positive solutions for a class of fourth-order boundary value problems with parameter
    YANG Li-juan
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(9):  35-41.  doi:10.6040/j.issn.1671-9352.0.2020.457
    Abstract ( 835 )   PDF (381KB) ( 319 )   Save
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    This article studies the boundary value problems of fourth-order ordinary differential equations with parameter{u'(t)+au(t)+bu″(t)+cu'(t)+du(t)=rf(t,u(t),u″(t)), 0<t<1,u(0)=u(1)=u″(0)=u″(1)=0,where r is a positive parameter, a,b,c,d are constant coefficients, and the nonlinearity f: [0,1]×[0,∞)×(-∞,0]→[0,∞) is a continuous function. When r is in a cetain range of values, the existence of positive solutions are obtained by using global bifurcation theorem.
    Spectrum of a class of discrete left-definite Sturm-Liouville problems
    CAO Xue-qin, GAO Cheng-hua
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(9):  42-49.  doi:10.6040/j.issn.1671-9352.0.2020.350
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    Considering the spectrum of a class of discrete left-definite Sturm-Liouville problems with eigenparameter dependent boundary conditions, the interlacing properties of the eigenvalues and oscillation properties of the eigenfunctions are obtained.
    Existence and multiplicity of positive periodic solutions for a class of nonlinear third-order difference equations
    ZHAO Jiao
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(9):  50-58.  doi:10.6040/j.issn.1671-9352.0.2020.394
    Abstract ( 678 )   PDF (395KB) ( 468 )   Save
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    This paper considers the existence and multiplicity of positive periodic solutions for a class of nonlinear third-order difference equationΔ3u(t-3)+αΔ2u(t-2)+βΔu(t-1)=f(t,u(t)), t∈[3,T]Z,where T>4, α>0, -1<β<0, f:[3,T]Z×[0,∞)→R is continuous with respect to u∈[0,∞), f(t+ω,u)=f(t,u), ω∈Z+. The proof of the main results is based on Guo-Krasnoselskii fixed point theorem.
    Global nonexistence of solutions to a class of semilinear double-wave equations with space-dependent coefficients on the nonlinearity
    OUYANG Bai-ping, XIAO Sheng-zhong
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(9):  59-65.  doi:10.6040/j.issn.1671-9352.0.2020.675
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    Blow-up of solutions to a class of semilinear double-wave equations with space-dependent coefficients on the nonlinearity is considered. By using the methods of differential inequalities and an iteration argument, the global nonexistence and the upper bound of the lifespan of solutions to the Cauchy problem for semilinear double-wave equations in the subcritical case are obtained, which generalize further the facts on the Cauchy problem for wave equations of high orders.
    Attractors for the non-autonomous nonclassical diffusion equation with fading memory
    LI You-ling, WANG Xuan
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(9):  66-80.  doi:10.6040/j.issn.1671-9352.0.2020.711
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    The long-time dynamical behavior of solutions for the non-autonomous nonclassical diffusion equation with fading memory and subcritical nonlinearity is discussed in the space H10(Ω)×L2μ(R+;H10(Ω)). When the external term g(x,t) is only translation bounded instead of translation compact, by means of the asymptotic regularity estimate technique, the existence and topological structure of a compact uniform attractor is obtained.
    Variable selection based on DP algorithm
    WANG Xiu-li
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(9):  81-86.  doi:10.6040/j.issn.1671-9352.0.2020.673
    Abstract ( 854 )   PDF (396KB) ( 287 )   Save
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    This paper proposes a new algorithm to compute the estimates of parameters in the objective function with the penalty function. This algorithm is given based on the DP algorithm, and provides an alternative approach to work out the minimization of penalized least squares function. Simulation studies are conducted to assess the finite sample performance of the proposed algorithm.
    A class of newly modified WYL conjugate gradient algorithms
    WANG Song-hua, LUO Dan, LI Yong
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(9):  87-95.  doi:10.6040/j.issn.1671-9352.0.2020.257
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    A class of newly WYL conjugate gradient algorithms is proposed for a large scale unconstrained problem. The new algorithms does not depend on any line research and possesses sufficient descent property and trust region trait. The global convergence has proven with weakness Wolfe-Powell line search. Preliminary numerical result has shown that the algorithms are more efficient and more competitive than classical WYL conjugate gradient method.
    Maximum norm error estimate and extrapolation of the ADI-FDTD scheme for plasma model
    LI Wei-zhi, LI Wan-shan, LI Jian-liang
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(9):  96-110.  doi:10.6040/j.issn.1671-9352.0.2020.458
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    The ADI-FDTD scheme for solving the two-dimensional Maxwells equations in plasma media is proposed under periodical boundary conditions. A prior estimate of the proposed scheme is given by using the discrete energy method, and it is proved that the scheme is of second-order accuracy both in time and space in the sense of the maximum norm. In order to improve the accuracy of the numerical results, Richardson extrapolation is applied to the proposed ADI-FDTD scheme by using the asymptotic expansion of the truncation error, and we obtain the algorithm having fourth-order accuracy both in time and space. Finally, the theoretical results are verified by numerical experiments.