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Research on self-supervised pre-training for recommender systems Jiyuan YANG,Muyang MA,Pengjie REN,Zhumin CHEN,Zhaochun REN,Xin XIN,Fei CAI,Jun MA JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (7): 1-26.   DOI: 10.6040/j.issn.1671-9352.1.2023.043 Abstract （1255）   HTML （7）    PDF（pc） （7266KB）（4898）       Save Plenty of recent studies explores the application of pre-training techniques within the context of recommendation scenarios and the design of pre-training tasks in order to enhance the overall performance of recommendation. This paper extensively reviews the progress in research of recommendation models based on pre-training, classifies and compares different pre-training methods, and conducts extensive experiments and analyses on some representative models using three benchmark datasets for recommendation systems. The datasets and codes have been made open source. Finally, we summarize and prospect the future development trend of recommendation models based on pre-training. Table and Figures | Reference | Related Articles | Metrics

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Dimensionality reduction and retrieval algorithms for high dimensional data Wei SHAO,Gaoyu ZHU,Lei YU,Jiafeng GUO JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (7): 27-43.   DOI: 10.6040/j.issn.1671-9352.1.2023.062 Abstract （1318）   HTML （21）    PDF（pc） （1007KB）（3922）       Save At present, most studies use some dimensionality reduction methods to convert high-dimensional vectors into low-dimensional vector representations, and then apply related vector retrieval optimization technology to achieve fast similarity retrieval, thereby improving the application performance of large models. Currently, there are many and scattered dimensionality reduction methods for high-dimensional data, and the dimensionality reduction methods used in different research backgrounds are different. Similarly, there are also many different retrieval ideas and optimization methods in vector retrieval technology. By reviewing the main ideas and optimization methods of recent dimensionality reduction and retrieval algorithms, this paper helps to generate inspiring connections between the two and support the development and in-depth research of subsequent high-dimensional vector retrieval optimization algorithms. Table and Figures | Reference | Related Articles | Metrics

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Emoji embedded representation based on emotion distribution Xueqiang ZENG,Yu SUN,Ye LIU,Zhongying WAN,Jiali ZUO,Mingwen WANG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (3): 81-94.   DOI: 10.6040/j.issn.1671-9352.1.2022.3548 Abstract （1215）   HTML （8）    PDF（pc） （6555KB）（2888）       Save This paper proposes an emoji embedded representation based on emotion distribution (EDEER) method. The EDEER method adopts the soft label of BERT-based emotion prediction model to learn emoji embedded representation from real data, and directly models the expression degree of emoji on various sentiments through emotion distribution, so that the embedded representation contains various emotional information of emoji. Multiple sets of comparative experiments on the Chinese Weibo dataset containing emoji shows that the method proposed in this paper can effectively learn emoji embedded representations that are directly related to fine-grained sentiments, and build an emoji representation space with high emotional expression quality. Table and Figures | Reference | Related Articles | Metrics

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Research progress on fabrication and application of self-healing superhydrophobic materials WANG Yutao, LIAN Yuechang, ZHAO Shengyuan, LIU Wendong JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2025, 60 (10): 59-78.   DOI: 10.6040/j.issn.1671-9352.0.2025.155 Abstract （480）      PDF（pc） （20350KB）（2032）       Save Superhydrophobic materials have been widely applied in anti-fouling, oil-water separation, and fluid manipulation due to their excellent liquid repellency. As a result of the synergistic effect between surface micro/nano structures and low surface energy substances, the surface wettability of superhydrophobic materials is highly susceptible to physical damage, UV irradiation, chemical corrosion, etc., which significantly limits their practical applications. Therefore, developing durable superhydrophobic materials is desirable. In the past decade, researchers have extended the service life of superhydrophobic materials by endowing them with self-healing properties, which not only enhances their practical performance but also broadens the application fields. In this review, an overview of the recent development of self-healing superhydrophobic materials focusing on fabrication strategies and possible applications is provided. Finally, an outlook on the future fabrication direction and application of self-healing superhydrophobic materials is presented. Reference | Related Articles | Metrics

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Meta computing: a new computing paradigm under zero trust Xiuzhen CHENG,Weifeng LYU,Minghui XU,Runyu PAN,Dongxiao YU,Chenxu WANG,Yong YU,Xue XIAO JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (9): 1-15.   DOI: 10.6040/j.issn.1671-9352.0.2023.168 Abstract （1556）   HTML （36）    PDF（pc） （7010KB）（1770）       Save The popularity of the Internet has had a significant impact on the development of computing paradigms. With the continuous improvement of the new generation of information technology infrastructures, academia and industry have been constantly exploring new computing paradigms to fully exploit computing powers. The huge data generated by massive IoT devices gradually exceeds the processing capability of the high-performance back-end represented by cloud servers. Edge computing alleviates this problem through cloud-edge-end coordination, but there still exist difficulties and challenges such as low computing power utilization, low computing and storage fault tolerance capability, and low integration of computing resorces. "Meta Computing" is a new computing paradigm that aims to break down the barriers of computing powers in a zero-trust environment. It can integrate all available connected computing and storage resources, provide efficient, byzantine fault-tolerant, and personalized services, while protecting the data and user privacy. Furthermere, meta computing can ensure the correctness of results, and realize "the entire network can be regarded as a giant computer for a user", that is, "Network-as-a-Computer, NaaC", which is also called "Meta Computer". The meta computer architecture includes a number of function modules including a device management module and a zero-trust computing management module, as well as the cloud-edge-end device resources. The device management module abstracts massive heterogeneous device resources into objects that can be freely manipulated, while the zero-trust computing management module can transparently allocate computing resources to user tasks according to service requirements, complete the tasks with strong fault tolerance and verifiable outputs, and finally settle accounts. Based on the analysis of the architecture and the functional characteristics of meta computing, we put forward suggestions and advice on the development path of meta computing, that is, transitioning from local to global, and analyze the most-influential future application scenarios of meta computing and provide a reasonable plan for the implementation and development of meta computing in future. Table and Figures | Reference | Related Articles | Metrics

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Category-wise knowledge probers for representation learning of graph neural networks Xingyu HUANG,Mingyu ZHAO,Ziyu LYU JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (7): 85-94.   DOI: 10.6040/j.issn.1671-9352.1.2023.064 Abstract （600）   HTML （2）    PDF（pc） （3615KB）（1696）       Save In order to solve the problem that the graph neural network model lacks corresponding probes, a knowledge detection framework for graph neural network representation learning is proposed, and two kinds of class-aware knowledge probes are designed based on the category attributes of data in different domains, namely clustering probes and contrastive clustering probes. The two probe the characterization effect of different models and give corresponding scores. On 8 datasets in 3 neighborhoods, including reference networks, social networks and biological networks, the representation learning of 7 classical graph neural network models realizes systematic knowledge detection and evaluation experiments, and summarizes the detection and evaluation conclusions. Table and Figures | Reference | Related Articles | Metrics

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Fuzzy border-peeling clustering Jiarui SUN,Mingjing DU JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (3): 27-36, 50.   DOI: 10.6040/j.issn.1671-9352.4.2023.040 Abstract （797）   HTML （4）    PDF（pc） （4543KB）（1581）       Save A fuzzy border-peeling clustering (FBP) algorithm is proposed. First, a density estimation method based on Cauchy kernel is used to calculate the densities of data points. Secondly, the boundary data are separated from the core data using the layer-by-layer peeling strategy. Thirdly, the reachability between the core data is used to achieve the core region clustering. Finally, a fuzzy assignment strategy is used to achieve the soft partitioning of the boundary data. A comparison is made between the fuzzy border-peeling clustering and 10 benchmark algorithms, including 6 density-based clustering algorithms and 4 fuzzy clustering algorithms, on artificial and real-world datasets. The experimental results show that on all datasets, FBP has the ARI (adjusted rand index) increased by 21% to 60% on average, and FBP has the NMI (normalized mutual information) increased by 12% to 47% on average. The border-peeling clustering algorithm optimized based on Cauchy kernel and fuzzy assignment strategy significantly improves the accuracy of clustering. Table and Figures | Reference | Related Articles | Metrics

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Creditrisk assessment based on Logistic regression and credit strategy optimization modeling of small and medium-sized enterprises Zhongfeng QU,Honghua WU,Fanjun LI JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (8): 94-102.   DOI: 10.6040/j.issn.1671-9352.0.2023.206 Abstract （1409）   HTML （11）    PDF（pc） （1260KB）（1546）       Save In order to facilitate banks to assess the credit risk of small and medium-sized enterprises, and formulate the optimal credit strategy, an indicator system composed of four primary risk assessment indicators, namely, business income ability, profitability, customer stability, and transaction vitality, is constructed by using the bank flow information of enterprises with upstream and downstream partners. The enterprise credit risk is predicted based on Logistic regression, and compares it with error back-propagation neural network. Combining the probability of default and the retention rate under different interest rates, taking the maximum expected return of banks on small and medium-sized enterprises as the objective function, the credit strategy optimization model is established. In order to verify the effectiveness of the model, the credit risk assessment and credit strategy optimization models are empirically analyzed. The results indicate that Logistic regression has high accuracy and recall, and the area under the curve of receiver operating characteristic reaches 0.964, which is suitable for credit risk prediction and assessment of small and medium-sized enterprises. The credit strategy optimization model can determine the loan amount and loan interest rate of each lending enterprise, and maximize the expected return of the bank. Table and Figures | Reference | Related Articles | Metrics

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Grey wolf optimization algorithm based on multi-strategy combination and its application Hongwu QIN,Lizheng WANG,Yu FU,Muxuan SUI,Binggao HE JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (3): 51-60.   DOI: 10.6040/j.issn.1671-9352.7.2023.4633 Abstract （1170）   HTML （8）    PDF（pc） （5268KB）（1544）       Save The standard grey wolf optimizer (GWO) algorithm has issues such as difficulty balancing local exploration and global development. A multi-strategy grey wolf optimization algorithm (MSGWO), based on the fusion of various strategies, is presented to address such problems. First, the grey wolf algorithm introduces the Tent map and a nonlinear convergence factor. Then, to coordinate attempts in the GWO optimization process, the paper applies three learning strategies: extensive learning, elite learning, and coordinated learning. Finally, the paper uses roulette wheel for strategy selection to obtain more diverse wolf positions and globally representative individuals and utilizes benchmark function testing to compare algorithm variations. The outcomes demonstrate that the MSGWO algorithm has a faster convergence speed and a good balance between local development and global search. Based on this, the echo state networks (ESN) hyperparameter for regression prediction is optimized using the MSGWO method. The experiment demonstrates that the MSGWO algorithm performs optimally with an average absolute percentage error of 0.38 percent and a fitting degree of 0.98. Table and Figures | Reference | Related Articles | Metrics

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Extension sequential three-way decision model and its application Junyu WANG,Yafeng YANG,Jingxuan XUE,Lihong LI JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (7): 67-79.   DOI: 10.6040/j.issn.1671-9352.4.2022.9768 Abstract （920）   HTML （2）    PDF（pc） （6139KB）（1503）       Save The basic method of extension evaluation and the "rule by three divisions" decision-making idea are integrated, and the sequential idea is introduced to construct an extension sequential three-way decision model and realize the purpose of dynamic decision-making and mining optimization indicators. Firstly, the data is standardized and the weight of attributes is calculated. The extension evaluation method is used as the evaluation criterion of the three-way decisions, new decision rules are defined, and the rationality of dividing the three domains is explained. Then, according to the attribute weight, the sequential evaluation attributes of multiple granularity are obtained, the multi-stage three-way decision is made, and the decision results are given. Finally, according to the decision-making results, the indicators that cause changes in sample division are analyzed, and optimization suggestions are put forward. The model was applied to the analysis of water resources carrying capacity, and compared with the entropy weight matter-element extension decision-making model. The results show that the evaluation results obtained by using the extension sequential three-way decision model and the entropy weight matter-element extension decision-making model are basically consistent, the accuracy rate reaches 84.55%, which verifies the validity and practicability of the model. Table and Figures | Reference | Related Articles | Metrics

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Staining methods on arbuscular mycorrhizal fungi in Lycium barbarum roots and the relationship between colonization rate and soil factors Mu YANG,Shenglian JI,Huan GUO,Guozhen DUAN,Guanghui FAN,Jianling LI,Zhanlin WANG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (11): 40-50.   DOI: 10.6040/j.issn.1671-9352.0.2023.488 Abstract （872）   HTML （41）    PDF（pc） （7023KB）（1485）       Save Understanding the infection and colonization of arbuscular mycorrhizal fungi (AMF) is the basis for mobilizing indigenous AMF to improve plant resistance. Lycium barbarum in nine fields of the Qaidam Basin were the subject. Based on the basic staining method of AMF, previous studies were optimised to investigate the main factors influencing the observation of AMF on the roots of perennial field-grown L.barbarum. The influence of different regions, soil pH, soil physicochemical properties and the colonization rate of AMF on L.barbarum were also compared. The results showed that the optimal observation effect of AMF colonization rate on the roots of Perennial field-grown L.barbarum in the Qaidam Basin was achieved by the following steps. First, the fixed root segments were placed in a 10% KOH 90 ℃ for 90 min, then in the boiling alkaline peroxide (3 mL NaOH+30 mL 10% H2O2+H2O to 600 mL) for 15-20 min, followed by 5 min of H2O2 bleaching, 5 min of lactic acidification, 5 min of acetone ink staining and 30 min of lactic acid glycerol 90 ℃ decolourisation. This method can clearly observe the structures of vesicles and hyphae in the roots of perennial field-grown L.barbarum. The average AMF colonization rate of perennial field-grown L.barbarum in the Qaidam Basin was about 41.32%. RDA analysis showed that the AMF colonization rate in L.barbarum roots was mainly affected by factors such as soil pH, available phosphorous content(xAP), and available potassium content(xAK), among which the soil pH showed a significant positive correlation with the AMF colonization rate, while xAP and xAK showed a significant negative correlation with the colonization rate. Table and Figures | Reference | Related Articles | Metrics

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Probabilistic q-rung hesitant fuzzy TODIM method and its application Yu ZHOU,Ligang ZHOU,Zhichao LIN,Xin XU JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 9-17.   DOI: 10.6040/j.issn.1671-9352.0.2022.260 Abstract （1044）   HTML （12）    PDF（pc） （931KB）（1463）       Save To measure differences in probabilistic q-rung hesitant fuzzy information, a novel measure of the probabilistic q-rung hesitant fuzzy distance is proposed based on the score function and overall hesitancy. The properties of this measure are discussed. A probabilistic q-rung hesitant fuzzy TODIM method is proposed based on the new distance measure. Finally, a practical example is presented to illustrate the reasonableness and effectiveness of the proposed method, and a sensitivity analysis is performed. Table and Figures | Reference | Related Articles | Metrics

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Identification and statistical analysis methods of personal information disclosure in open government data Haisu CHEN,Jiachun LIAO,Sicheng YAO JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (3): 95-106.   DOI: 10.6040/j.issn.1671-9352.7.2023.2681 Abstract （1101）   HTML （6）    PDF（pc） （1846KB）（1387）       Save To promote the protection of personal information during data opening, an in-depth analysis of the current status of disclosure of personal information in the open government data is conducted. Firstly, the paper obtains the datasets from relevant platforms and pre-process to classify the datasets that containing personal information based on features such as field and table names, etc. Then, methods of sensitive information identification are applied to identify and extract various types of personal information in the data, and map the information back to individuals to summarise the total number of individuals and detect their associated data. Through data visualizations, the current status of personal information disclosure could be examined. Although some open government data platforms may have implemented certain measures such as data categorization and de-identification, the published open datasets still contain a large amount of personal information, which is required to be improved in terms of data categorization and classification, sensitive information identification and data desensitization in a normative and accurate manner. Table and Figures | Reference | Related Articles | Metrics

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A prompt learning approach for telecom network fraud case classification Jie JI,Chengjie SUN,Lili SHAN,Boyue SHANG,Lei LIN JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (7): 113-121.   DOI: 10.6040/j.issn.1671-9352.1.2023.040 Abstract （1432）   HTML （17）    PDF（pc） （3845KB）（1286）       Save For the automatic classification technology of telecom fraud cases, a classification system of telecom network fraud based on situational analysis is formulated, the privacy protection method of case text de-identification is realized, and accuracy and F1-score of a classification method of telecom network fraud cases based on prompt learning is proposed. The experimental results show that the method is on average 1 to 2 percentage points higher than the BERT-based classification method on the data set constructed in the paper. Table and Figures | Reference | Related Articles | Metrics

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Bilinear θ-type Calderón-Zygmund operators on generalized weighted variable exponent Morrey spaces Li RUI,Guanghui LU,Xuemei LI JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (4): 62-72.   DOI: 10.6040/j.issn.1671-9352.0.2022.624 Abstract （609）   HTML （3）    PDF（pc） （830KB）（1220）       Save Via the boundedness of the bilinear θ-type Calderón-Zygmund operators in the variable index Lebesgue space and the control relations in the function spaces, and assuming that the functions u meet certain conditions, the authors prove that the bilinear θ-type Calderón-Zygmund operators are bounded from product generalized weighted variable exponent Morrey spaces to generalized weighted variable exponent Morrey spaces. Furthermore, the authors also prove that the commutators generated by the bilinear θ-type Calderón-Zygmund operators and b1, b2 ∈ BMO(Rn) are bounded on generalized weighted variable exponent Morrey spaces. Reference | Related Articles | Metrics

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Perpetual American lookback option pricing under mixed bi-fractional Brownian motion Yaru ZHANG,Li XIA,Dianqiu ZHANG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (4): 98-107.   DOI: 10.6040/j.issn.1671-9352.0.2022.629 Abstract （909）   HTML （6）    PDF（pc） （4114KB）（1208）       Save A pricing model for a perpetual American lookback option with dividends driven by mixed bi-fractional Brownian motion is constructed in this paper. First, the partial differential equations of mixed bi-fractional Brownian motion for perpetual American lookback call and put options are given by the Δ-hedging principle. Then, the established partial differential equations are solved by variable substitution method and characteristic equation method. Finally, numerical experiments are adopted to verify the linear proportional scaling properties of the solution, and the effects of mixed bi-fractional Brownian motion parameters H, K and volatility on the option prices are further discussed. Table and Figures | Reference | Related Articles | Metrics

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Comprehensive credit evaluation of transportation enterprises based on game theory combinatorial weighting-TOPSIS method Antao LYU,Yongbin GAO,Wen HAN,Ying DONG,Zhenfang ZHONG,Qingchun MENG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (9): 88-97.   DOI: 10.6040/j.issn.1671-9352.0.2023.153 Abstract （665）   HTML （13）    PDF（pc） （1970KB）（1040）       Save Firstly, the index system of comprehensive credit evaluation of transportation enterprises is constructed from four aspects: basic information, reward recognition, reputation assessment and administrative penalty. Secondly, the weights of each index are obtained by using game theory combination assignment method, and the comprehensive credit evaluation model of enterprises by game theory combination assignment-TOPSIS method is constructed. Finally, the data of transportation enterprises in Shandong Province are used for experimental analysis to obtain the credit evaluation results. The study shows that: the weighting of each first-level index is ranked as administrative penalty, award recognition, reputation assessment, basic information, indicating that the relevant departments should focus on assessing the administrative punishment index of enterprises; the credit evaluation results are consistent with the actual, which verifies the rationality of the evaluation model. Table and Figures | Reference | Related Articles | Metrics

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Multimodal sentiment analysis based on text-guided hierarchical adaptive fusion Chan LU,Junjun GUO,Kaiwen TAN,Yan XIANG,Zhengtao YU JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (12): 31-40, 51.   DOI: 10.6040/j.issn.1671-9352.1.2022.421 Abstract （1134）   HTML （26）    PDF（pc） （1947KB）（1036）       Save The paper proposes a multi-modal hierarchical fusion method based on text modal guidance, which uses text modal information as the guidance to achieve hierarchical adaptive screening and fusion of multi-modal information. Firstly, the importance information representation between two modalities is realized based on the cross-modal attention mechanism, then the hierarchical adaptive fusion based on the multimodal important information is realized through the multimodal adaptive gating mechanism, and finally the multimodal features are synthesized. and modal importance information to implement multimodal sentiment analysis. The experimental results on the public datasets MOSI and MOSEI show that the accuracy and F1 value of the baseline model have increased by 0.76% and 0.7%, respectively. Table and Figures | Reference | Related Articles | Metrics

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2-distance sum distinguishing coloring of trees Huan LIU,Huiying QIANG,Hongshen WANG,Yu BAI JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (2): 47-52, 58.   DOI: 10.6040/j.issn.1671-9352.0.2022.347 Abstract （611）   HTML （3）    PDF（pc） （764KB）（1033）       Save Based on the structural characteristics of the trees, the 2-distance sum distinguishing edge(total) coloring of trees are studied by using the mathematical induction, combination analytic method and Combinatorial Nullstellensatz, and the 2-distance sum distinguishing edge(total) chromatic numbers are obtained. Table and Figures | Reference | Related Articles | Metrics

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Global existence of large solutions for a class of chemotaxis-fluid model Zhongbo CAI,Jihong ZHAO JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 84-91.   DOI: 10.6040/j.issn.1671-9352.0.2022.414 Abstract （975）   HTML （9）    PDF（pc） （697KB）（1018）       Save In this paper, we are concerned with a class of chemotaxis-fluid models, which is a coupled system by parabolic-parabolic Keller-Segel equations and incompressible Navier-Stokes equations. Making full use of the weighted Chemin-Lerner type norm, the interpolation theory in Besov spaces and Fourier localization technique, the global existence of large solutions is obtained in critical Besov spaces. Reference | Related Articles | Metrics

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An automatic protocol vulnerability detection framework for resource-constrained devices of LPWAN Feixu LI,Fei YAN,Binlin CHENG,Liqiang ZHANG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (9): 39-50.   DOI: 10.6040/j.issn.1671-9352.0.2022.660 Abstract （807）   HTML （18）    PDF（pc） （1396KB）（980）       Save LPWAN(low power wide area network)as a protocol that emphasizes low power consumption usually runs on resource-constrained devices. On the one hand, limited resources bring serious challenges to the security of protocol implementation. Manufacturers may have trouble balancing security demands and resource consumption. On the other hand, protocol stacks are deployed on constrained devices as bare-metal firmware. The varying hardware characteristics make automatic analysis difficult. Therefore, a protocol stack analysis framework called ProSE is proposed. Based on symbolic execution and taint analysis, ProSE is specifically designed for protocol vulnerability detection on the firmware of constrained devices. LoRaWAN is chosen for analysis due to its popularity. The framework is capable of detecting various types of vulnerability. ProSE successfully detected 20 potential security vulnerabilities in the implementation of LoRaWAN of 6 manufacturers. Table and Figures | Reference | Related Articles | Metrics

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Entire solutions of differential-difference equation of Fermat type Mingxin ZHAO,Guirong SUN,Zhigang HUANG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 107-112.   DOI: 10.6040/j.issn.1671-9352.0.2022.540 Abstract （859）   HTML （7）    PDF（pc） （625KB）（909）       Save By using Nevanlinna value distribution theory, this paper investigates the existence of transcendental entire solution with finite order of Fermat type differential-difference equation, and obtains one result. Reference | Related Articles | Metrics

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Quasi-J-clean rings Yao WANG,Jianghuan CHEN,Yanli REN JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 1-8.   DOI: 10.6040/j.issn.1671-9352.0.2022.507 Abstract （955）   HTML （5）    PDF（pc） （692KB）（888）       Save The concept of quasi-J-clean rings is introduced using quasi-idempotent elements. Some examples of quasi-J-clean rings are given and their basic properties are discussed. The following results are proved. (1) If R is a quasi-J-clean ring, then the full matrix ring Mn(R) is a quasi-J-clean ring; (2) A ring R is a UJ-ring if and only if all quasi-clean elements in R are quasi-J-clean elements; (3) If R is a commutative ring, then the necessary and sufficient condition for R to be a quasi-J-clean ring is that R/I=J(R/I)∪U(R/I) if I is an ideal of R contained in J(R) and such that R/I is an indecomposable ring. Reference | Related Articles | Metrics

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Practical application of property-oriented concepts in adaptive assessment of skills Qiuhong HE,Jinjin LI,Yinfeng ZHOU,Jing WU JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (12): 63-76.   DOI: 10.6040/j.issn.1671-9352.4.2022.5723 Abstract （712）   HTML （3）    PDF（pc） （1331KB）（884）       Save Certain concepts (X, B) can be obtained via the combination of skill multimaps with property-oriented concepts, which leads to a method for constructing knowledge and skill structures that can be applied to the adaptive assessment of skills. The processis as follows. First, expert teachers provide the question set Q, skill set S, and their corresponding skill multimaps (Q, S; μ). Next, the knowledge and skill structures are obtained from the extension and the intention of (X, B). Thereafter the knowledge structure is used to conduct the adaptive assessment of the sample, and the proportion of their knowledge states is calculated. Subsequently, the equal proportion selection rule of knowledge space theory "binary responses" is optimized to the sample proportion selection rule, facilitate faster assessment effects for examinees in different regions and age groups. Finally, the figure of learning paths for skill sets is drawn. Table and Figures | Reference | Related Articles | Metrics

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The k-path vertex cover in some products graphs of star graph and bipartite graph Huiling YIN,Jingrong CHEN,Xiaoyan SU JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 18-24, 39.   DOI: 10.6040/j.issn.1671-9352.0.2021.420 Abstract （920）   HTML （7）    PDF（pc） （671KB）（879）       Save For a subset $S \subset V(G)$, if any k-path contains at least one vertex from S, then it is called a k-path vertex cover set of the graph G. The minimum cardinality of k-path vertex cover set is called the k-path vertex cover number, which is denoted by ψk(G). The k-path vertex cover problem is studied for Cartesian product graphs, lexicographic product graphs, directed product graphs of star graph and bipartite graph, and obtain an upper and a lower bound by enumeration and related concepts of subgraphs. Reference | Related Articles | Metrics

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Restricted burning connectivity of graphs Ruiying XUE,Zongtian WEI,Meijuan ZHAI JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (2): 91-99, 109.   DOI: 10.6040/j.issn.1671-9352.0.2022.326 Abstract （764）   HTML （4）    PDF（pc） （784KB）（876）       Save Connectivity is an important indicator to measure the invulnerability of a network. This parameter is generalized from the perspective of graph burning, and the concept of restricted burning connectivity of graphs is proposed. On the basis of giving some basic graphs' restricted burning connectivity, the restricted burning connectivity calculation problems of the Cartesian product graph of paths and the spider graphs are studied by the mathematical programming method. By analyzing the relationship between restricted burning connectivity and graph structures, the advantages of this parameter in characterizing the invulnerability of networks are clarified. Table and Figures | Reference | Related Articles | Metrics

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Strategic limit theory and strategic statistical learning Xiaodong YAN JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (1): 1-10, 45.   DOI: 10.6040/j.issn.1671-9352.0.2023.512 Abstract （1030）   HTML （21）    PDF（pc） （2306KB）（868）       Save The nonlinear expectation is an original research direction pioneered by Academician Peng Shige of Shandong University, which is becoming increasingly important in various fields of scientific research. The rise of big data and artificial intelligence has provided stronger impetus for innovative theoretical and applied research in nonlinear expectation. Recently, Shandong University's Nonlinear Probability Team has developed the "Strategy Limit Theory" based on the strategic game process of multi-armed bandits, representing a significant breakthrough in the intersection of nonlinear probability theory and reinforcement learning. This has tran-sformed the research paradigm of traditional statistical methods. Based on the proposed 10 basic mathematical problems of artificial intelligence by Academician Xu Zongben, the declaration guide of 2022 major research plan projects issued by the National Natural Science Foundation of China for the research about universal and interpretable artificial intelligence technologies, and the application guide for basic mathematical theory research of artificial intelligence in 2021 and 2022 the key projects of "Mathematics and Applied Research" issued by the Ministry of Science and Technology, this article adopts the concept of "strategy" to reveal the nature of artificial intelligence and explore and the motivation source and theoretical basis for initiating and promoting the innovation of artificial intelligence technology. Different from the applications of the traditional law of large numbers and the central limit theorem in the field of artificial intelligence, we propose novel theory about the strategic law of large numbers and the central limit theorem in the new generation of artificial intelligence. The discussed topics in this work include but not limited to: (1) strategic sampling of massive data; (2) online learning of streaming data; (3) the central limit theorem of reinforcement learning; (4) differential privacy protection of data; (5) strategic integration of federal learning; (6) information reconstruction of transfer learning and meta learning; (7) the fusion of knowledge reasoning and data driving. Table and Figures | Reference | Related Articles | Metrics

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Analysis for the M/M/c+m queueing model with non-preemptive priority and contact matching Yuting TAN,Xiuli XU,Rui ZHENG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (11): 45-52.   DOI: 10.6040/j.issn.1671-9352.0.2022.212 Abstract （987）   HTML （9）    PDF（pc） （874KB）（861）       Save The M/M/c+m queueing model with non-preemptive priority contact matching is established, and the state transition rule and infinitesimal generator matrix of the quasi-birth-and-death process are obtained. Then, the steady-state equilibrium condition, steady-state probability distribution, and main performance indices of the system are given by using the matrix geometric solution method. Finally, numerical examples are presented to discuss the influence of system parameters on the performance indices. Table and Figures | Reference | Related Articles | Metrics

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Prediction of average queue time in multi-server tandem queueing systems Yiran LI,Ning ZHAO,Zhijian ZHANG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (1): 17-26.   DOI: 10.6040/j.issn.1671-9352.4.2022.8254 Abstract （936）   HTML （8）    PDF（pc） （1206KB）（846）       Save This paper studies a multi-server tandem queueing system with two stations and infinite buffers before each station. The average queueing time of the two stations is predicted by linear regression models and nonlinear methods of machine learning, and the error in the prediction results of various machine learning methods is analyzed. Numerical experiments show that the nonlinear method exhibits better performance than the linear regression model. Moreover, the RF, XGBoost and GBDT methods are effective to predict the average waiting time of multi-server tandem queueing networks. Table and Figures | Reference | Related Articles | Metrics

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A new filled function method for global optimization Haiyan LIU,Shouheng TUO JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (7): 80-87.   DOI: 10.6040/j.issn.1671-9352.0.2022.344 Abstract （840）   HTML （5）    PDF（pc） （1357KB）（843）       Save A new hybrid single-parameter filled function is proposed which is also continuous and differentiable. Combined with an evolutionary algorithm, a new filled function algorithm is proposed. The new filled function algorithm can improve the efficiency of the optimization by repeatedly escaping from current local optimum to better areas with better solutions. To enhance the explore ability of the proposed algorithm, we use uniform distribution to make better population diversity. Numerical experiments show the simplicity and efficiency of the proposed algorithm. Table and Figures | Reference | Related Articles | Metrics

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Existence of mild solutions for the nonlocal problem of second-order impulsive evolution equations Li LI,He YANG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 57-67.   DOI: 10.6040/j.issn.1671-9352.0.2022.595 Abstract （889）   HTML （6）    PDF（pc） （685KB）（831）       Save A new definition of mild solutions of the second-order impulsive evolution equations involving nonlocal condition $ u(0)=\sum\limits_{k=1}^n C_k u\left(\tau_k\right)$ is given by introducing a Green function. Then, the existence of mild solutions of the concerned problem is proved by applying the Sadovskii fixed point theorem. At last, an example is provided as an application of the obtained abstract result. Reference | Related Articles | Metrics

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The number of homomorphisms from dihedral groups to any finite groups Jie TAN,Liang ZHANG,Jidong GUO JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 31-34.   DOI: 10.6040/j.issn.1671-9352.0.2022.305 Abstract （991）   HTML （8）    PDF（pc） （613KB）（819）       Save Automorphism groups and normal subgroups of dihedral groups are studied, and the number of homomorphisms from dihedral groups to any finite group is obtained. As an application of this result, the conjecture of Asai and Yoshida is verified for dihedral groups. Reference | Related Articles | Metrics

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Noise network alignment method integrating multiple features Ning XIAN,Yixing FAN,Tao LIAN,Jiafeng GUO JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (7): 64-75.   DOI: 10.6040/j.issn.1671-9352.1.2023.102 Abstract （563）   HTML （4）    PDF（pc） （1975KB）（797）       Save A multi-round iterative network alignment method is proposed to address the challenges of large structural differences and high noise sensitivity in anchor nodes in network alignment tasks. The method calculates node features of different dimensions using various heuristic approaches at each iteration, utilizing the combination of multiple features to assess the reliability of anchor nodes, filter potential noise, and enhance the confidence of each alignment round. Additionally, a graph neural network is employed to improve the consistency between nodes without attributes, mitigating the impact of structural differences in networks. Experimental results demonstrate that this method achieves high accuracy under high noise conditions, verifying its effectiveness. Table and Figures | Reference | Related Articles | Metrics

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Characterizing properties of (signless) Laplacian permanental polynomials of bicyclic graphs Tingzeng WU,Tian ZHOU JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (12): 151-160.   DOI: 10.6040/j.issn.1671-9352.0.2022.316 Abstract （692）   HTML （2）    PDF（pc） （904KB）（790）       Save Let G be a graph with n vertices, and let L(G) and Q(G) be the Laplacian matrix and signless Laplacian matrix of G, respectively. The polynomial π(L(G); x)=per(xI-L(G)) (resp. π(Q(G); x)=per(xI-Q(G))) is called Laplacian permanental polynomial (resp. signless Laplacian permanental polynomial) of G. In this paper, we show that two classes of bicyclic graphs are determined by their (signless) Laplacian permanental polynomials. Table and Figures | Reference | Related Articles | Metrics

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Heuristic construction method of fuzzy concept set and its recommended application Zhonghui LIU,Shuai JIANG,Fan MIN JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (3): 14-26.   DOI: 10.6040/j.issn.1671-9352.7.2023.9950 Abstract （757）   HTML （4）    PDF（pc） （1376KB）（789）       Save Aiming at the problem that fuzzy formal concept analysis is difficult to apply to large-scale datasets in recommendation applications, a recommendation method based on a heuristic construction of fuzzy concept set is proposed. Sub-contexts are constructed for each user based on the similarity between users. Then, new heuristic information is used on the sub-contexts to generate fuzzy concepts with users and items as clues, respectively. Finally, using the internal information of fuzzy concepts, a recommendation confidence integrated with user weights is designed to achieve personalized recommendations for users. The experimental results on six real datasets show that the proposed method has higher recommendation efficiency, and can achieve better recommendation results on sparse data sets compared with classical collaborative filtering algorithms. Table and Figures | Reference | Related Articles | Metrics

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A new probabilistic hesitant fuzzy multi-attribute group decision making method based on improved distance measures Mengdi LIU,Xianyong ZHANG,Zhiwen MO JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (3): 118-126.   DOI: 10.6040/j.issn.1671-9352.7.2023.4667 Abstract （1080）   HTML （4）    PDF（pc） （2368KB）（768）       Save Aiming at the multi-attribute group decision making problem with known attribute weights under probabilistic hesitant fuzzy environments, hesitation degrees of probabilistic hesitant fuzzy sets are considered, and thus a new method of probabilistic hesitant fuzzy multi-attribute group decision making is proposed based on improved distance measures. Firstly, combining the traditional probabilistic hesitant fuzzy distance measures, improved probabilistic hesitant fuzzy distance measures with hesitation degrees are defined through information fusion, including the Hamming distance, Euclidean distance, and generalized Euclidean distance. These new measures depend on combination coefficients to achieve the theoretical expansion and fusion optimization, and size relationships and parameter monotonicity of distance measures are studied. Secondly, according to the improved distance measures, a new method of multi-attribute group decision making is constructed by using the technique for order preference by similarity to ideal solution(TOPSIS) method, and an example of company location is used to make decision selection. The effectiveness of the proposed method is revealed by parameter analysis and decision comparison. Related researches systematically deepen probabilistic hesitant fuzzy distance measures, and effectively enrich multi-attribute group decision-making methods. Table and Figures | Reference | Related Articles | Metrics

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Stability of a single population delayed reaction-diffusion model with Dirichlet boundary condition Yonghua LI,Cunhua ZHANG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (10): 122-126.   DOI: 10.6040/j.issn.1671-9352.0.2023.131 Abstract （705）   HTML （6）    PDF（pc） （344KB）（760）       Save This paper studies the dynamics of a single population delayed reaction-diffusion model with Dirichlet boundary condition in a bounded domain. The existence and multiplicity of spatially nonhomogeneous steady-state solution is investigated by employing Lyapunov-Schmidt reduction method. Then, the stability of spatially nonhomogeneous steady-state solution is derived by analyzing the distribution of the eigenvalues. Reference | Related Articles | Metrics

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Time-controlled designated tester proxy re-encryption with keyword search scheme Jiao LYU,Xi ZHANG,Jing QIN JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (9): 16-27.   DOI: 10.6040/j.issn.1671-9352.0.2022.154 Abstract （735）   HTML （8）    PDF（pc） （1881KB）（759）       Save To solve the problem that the proxy re-encryption with keyword search is used to implement ciphertext data exchange and sharing, but it does not support time-controlled access authorization and cannot resist off-line keyword guessing attack, a time-controlled designated tester proxy re-encryption with keyword search scheme is proposed, which supports the data owner to grant dynamically the search and decryption rights of the ciphertext data in the cloud to the data user within a specified time range, and can resist the off-line keyword guessing attack by external adversaries. In addition, the scheme is applied to the scenario of sharing patients electronic medical records between different hospitals, and a specific electronic medical records sharing scheme is designed based on the consortium blockchain. Table and Figures | Reference | Related Articles | Metrics

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A new modified efficient Shamanskii-like Levenberg-Marquardt method for solving systems of nonlinear equations Minglei FANG,Defeng DING,Ming WANG,Yuting SHENG JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (8): 118-126.   DOI: 10.6040/j.issn.1671-9352.0.2022.597 Abstract （758）   HTML （12）    PDF（pc） （721KB）（751）       Save A new Shamanskii-like Levenberg-Marquardt method(SLM) to solve systems of nonlinear equations is presented by introducing parameters in this paper. With m order nonmonotone Armijo line search, the global convergence of the new algorithm is proved and the convergence rate of whom is shown to be m+1. Numerical experiments demonstrate that the new algorithm can solve large scale problems effectively. Table and Figures | Reference | Related Articles | Metrics

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Parameter estimation for the sub-fractional Vasicek model based on discrete observation Cuiyun ZHANG,Jingjun GUO,Aiqin MA JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (11): 15-26.   DOI: 10.6040/j.issn.1671-9352.0.2022.317 Abstract （876）   HTML （7）    PDF（pc） （457KB）（750）       Save The problem of statistical analysis of the Vasicek model driven by sub-fractional Brownian motion is mainly investigated. Firstly, based on discrete observations, the estimation of drift parameters μ and θ in Vasicek model are given by the least square estimation method. Secondly, for the θ≠0 and θ=0 cases, the consistency and the asymptotic distribution of the estimators are obtained, respectively. Finally, simulations are performed with the Monte Carlo method to demonstrate the unbiasedness and validity of the estimates. Table and Figures | Reference | Related Articles | Metrics