IEEE Transactions on Network Science and Engineering最新文献

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Defense for Displacement Attacks on Distributed Formation Control Systems 防御对分布式编队控制系统的位移攻击
IF 6.7 2区 计算机科学
IEEE Transactions on Network Science and Engineering Pub Date : 2024-09-10 DOI: 10.1109/TNSE.2024.3457382
Yue Yang;Yang Xiao;Tieshan Li;Kezhong Liu
{"title":"Defense for Displacement Attacks on Distributed Formation Control Systems","authors":"Yue Yang;Yang Xiao;Tieshan Li;Kezhong Liu","doi":"10.1109/TNSE.2024.3457382","DOIUrl":"10.1109/TNSE.2024.3457382","url":null,"abstract":"As an effective multi-agent system (MAS) control method, formation control is widely used in uncrewed systems, such as uncrewed surface/underwater/aerial vehicles and spacecrafts. However, the security issues of formation control have received little attention. Compared with traditional industry systems (such as smart grids or intelligence appliances), designing countermeasure approaches for distributed formation systems under attacks has several challenges, such as limited local information, robot mobility, and a chain reaction of attacks. In this paper, based on a classical formation control law on a group of robots, we concentrate on maintaining an acceptable formation performance under Man-in-the-Middle-based (MITM-based) displacement attacks. The MITM-based displacement attacks can utilize the property of formation maintenance and hijack the whole robot group. We propose two kinds of novel countermeasure approaches. An active approach, which is named the comparison-based identification and elimination (CIE) algorithm, can identify attack messages and calculate estimate values to replace attack messages based on local information. A passive approach can tolerate attack effects by designing a task priority adjustment (TPA) controller. The TPA controller can gradually adjust the formation maintenance priority to degrade attack effects. Simulation with several nonholonomic differentially driven mobile robots is conducted, and results show that our schemes can significantly decrease the impact of constant and time-varying attacks.","PeriodicalId":54229,"journal":{"name":"IEEE Transactions on Network Science and Engineering","volume":"11 6","pages":"6560-6573"},"PeriodicalIF":6.7,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142191983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Game-Theoretic Incentive Mechanism for Collaborative Quality Control in Blockchain-Enhanced Carbon Emissions Verification 区块链强化碳排放核查中协作质量控制的博弈论激励机制
IF 6.7 2区 计算机科学
IEEE Transactions on Network Science and Engineering Pub Date : 2024-09-09 DOI: 10.1109/TNSE.2024.3456116
Yunhua He;Zhihao Zhou;Bin Wu;Ke Xiao;Chao Wang;Xiuzhen Cheng
{"title":"Game-Theoretic Incentive Mechanism for Collaborative Quality Control in Blockchain-Enhanced Carbon Emissions Verification","authors":"Yunhua He;Zhihao Zhou;Bin Wu;Ke Xiao;Chao Wang;Xiuzhen Cheng","doi":"10.1109/TNSE.2024.3456116","DOIUrl":"10.1109/TNSE.2024.3456116","url":null,"abstract":"Given the urgency of climate change, many countries have set carbon neutrality targets and adopted cap-and-trade (C&T) systems to regulate carbon emissions. Accurate carbon emission data is crucial for the effective operation of carbon pricing and management systems. Monitoring, Reporting, and Verification (MRV) system is at the core of these systems, facing challenges such as, inefficient verification process, and low-quality carbon emissions verification. Blockchain and smart contracts offer promising solutions to some difficulties, while the quality of carbon emissions verification still needs improvement. Therefore, we propose a blockchain-enhanced carbon emissions verification model to optimize system efficiency and support compliance verification. We employ reputation as the admission criterion, screening reliable and trustworthy verification candidates. We design a game-theoretic incentive mechanism implemented through smart contracts to promote compliance and collaborative quality control among participants. Analysis shows that our scheme drives the game model towards the Nash equilibrium that achieves collaborative quality control. Through security analysis and simulation experiments, we verify the efficacy of our mechanism concerning verification quality and procedural automation, confirming its potential to mitigate malpractices and enhance consistent compliance.","PeriodicalId":54229,"journal":{"name":"IEEE Transactions on Network Science and Engineering","volume":"11 6","pages":"6535-6549"},"PeriodicalIF":6.7,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142191986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamics and Regulatory Mechanisms of Innate Immunity and CD8 T Cells Synergy in Response to Viral Infections 先天免疫与 CD8 T 细胞协同应对病毒感染的动力与调控机制
IF 6.7 2区 计算机科学
IEEE Transactions on Network Science and Engineering Pub Date : 2024-09-09 DOI: 10.1109/TNSE.2024.3456231
Conghua Wang;Yuan Zhang;Tingwen Huang;Zhichun Yang
{"title":"Dynamics and Regulatory Mechanisms of Innate Immunity and CD8 T Cells Synergy in Response to Viral Infections","authors":"Conghua Wang;Yuan Zhang;Tingwen Huang;Zhichun Yang","doi":"10.1109/TNSE.2024.3456231","DOIUrl":"10.1109/TNSE.2024.3456231","url":null,"abstract":"In immune systems, the innate immune response and CD8 T cells play a crucial synergistic role in combating viral pathogens. In this paper, we develop a delayed viral infection model to investigate the dynamic mechanisms governing infection outcomes. The model categorizes viral infections into five states: clearance, mild, moderate, heavy, and recurrent. A key finding is that diminished innate immune responses create a bistable condition, enabling the initial antigen load and the length of the viral incubation period to act as toggle switches that determine whether infections will be mild or heavy. Furthermore, the viral incubation period induces a Hopf bifurcation, changing mild infections from a stable state to periodic oscillations, potentially leading to recurrent infections. Interestingly, enhancing the innate immune response not only bolsters the CD8 T cell-mediated destruction of infected cells but also delays the onset of the Hopf bifurcation and reduces the adverse effects of incubation periods. These insights suggest that strengthening the innate immune response and developing drugs to shorten the incubation period are viable strategies to combat viral infections.","PeriodicalId":54229,"journal":{"name":"IEEE Transactions on Network Science and Engineering","volume":"11 6","pages":"6550-6559"},"PeriodicalIF":6.7,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142191985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Unique Framework of Heterogeneous Augmentation Graph Contrastive Learning for Both Node and Graph Classification 用于节点和图分类的独特异构增强图对比学习框架
IF 6.7 2区 计算机科学
IEEE Transactions on Network Science and Engineering Pub Date : 2024-09-09 DOI: 10.1109/TNSE.2024.3454993
Qi Shao;Duxin Chen;Wenwu Yu
{"title":"A Unique Framework of Heterogeneous Augmentation Graph Contrastive Learning for Both Node and Graph Classification","authors":"Qi Shao;Duxin Chen;Wenwu Yu","doi":"10.1109/TNSE.2024.3454993","DOIUrl":"10.1109/TNSE.2024.3454993","url":null,"abstract":"Graph contrastive learning has gained significant attention for its effectiveness in leveraging unlabeled data and achieving superior performance. However, prevalent graph contrastive learning methods often resort to graph augmentation, typically involving the removal of anchor graph structures. This strategy may compromise the essential graph information, constraining the adaptability of contrastive learning approaches across diverse tasks. To overcome this limitation, we introduce a novel augmentation technique for graph contrastive learning: \u0000<italic>heterogeneous augmentation</i>\u0000. Through the application of heterogeneous augmentation to homogeneous anchor graphs, our method obviates the need for modifying edges and nodes, preserving the structural integrity of the anchor graph to the fullest extent. The proposed method could become a significant technique in graph augmentation, potentially influencing further research and development in this area. Our work provides a valuable contribution to the advancement of graph contrastive learning methodologies.","PeriodicalId":54229,"journal":{"name":"IEEE Transactions on Network Science and Engineering","volume":"11 6","pages":"5818-5828"},"PeriodicalIF":6.7,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142191988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Edge-Side Cellular Network Traffic Prediction Based on Trend Graph Characterization Network 基于趋势图特征网络的边缘蜂窝网络流量预测
IF 6.7 2区 计算机科学
IEEE Transactions on Network Science and Engineering Pub Date : 2024-09-09 DOI: 10.1109/TNSE.2024.3455784
Mingxiang Hao;Xiaochuan Sun;Yingqi Li;Haijun Zhang
{"title":"Edge-Side Cellular Network Traffic Prediction Based on Trend Graph Characterization Network","authors":"Mingxiang Hao;Xiaochuan Sun;Yingqi Li;Haijun Zhang","doi":"10.1109/TNSE.2024.3455784","DOIUrl":"10.1109/TNSE.2024.3455784","url":null,"abstract":"Predicting edge-side cellular network traffic stands as a pivotal facilitator for network automation in next-generation communication systems. However, the traffic data at the edge exhibits significant heterogeneity, inhomogeneity, and volatility due to geographic location, human activities, and demand diversification, thus making accurate network traffic prediction a rigorous challenge. To solve this problem, this paper proposes a novel cellular network traffic prediction model in the edge-managed multi-base station (BS) scenarios, named trend graph characterization network (TGCN). Structurally, TGCN has three key components of trend feature extractor, temporal feature extractor and predictor. Firstly, the high-dimensional trend feature of traffic can be captured by the combination of ordinal pattern transition network (OPTN) and graph attention network (GAT). Furthermore, in the temporal feature extractor neural circuit policy (NCP) is introduced for multi-scale time-varying dependent features. Finally, a fully-connected layer serves as the approximator of BS traffic. On real-world datasets, we verify the superiority of our proposal via statistical analysis, prediction accuracy and ablation experiments.","PeriodicalId":54229,"journal":{"name":"IEEE Transactions on Network Science and Engineering","volume":"11 6","pages":"6118-6129"},"PeriodicalIF":6.7,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142191984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Pattern-Based Attention Recurrent Autoencoder for Anomaly Detection in Air Quality Sensor Networks 基于模式的注意力递归自动编码器用于空气质量传感器网络中的异常检测
IF 6.7 2区 计算机科学
IEEE Transactions on Network Science and Engineering Pub Date : 2024-09-06 DOI: 10.1109/TNSE.2024.3454459
Xhensilda Allka;Pau Ferrer-Cid;Jose M. Barcelo-Ordinas;Jorge Garcia-Vidal
{"title":"Pattern-Based Attention Recurrent Autoencoder for Anomaly Detection in Air Quality Sensor Networks","authors":"Xhensilda Allka;Pau Ferrer-Cid;Jose M. Barcelo-Ordinas;Jorge Garcia-Vidal","doi":"10.1109/TNSE.2024.3454459","DOIUrl":"10.1109/TNSE.2024.3454459","url":null,"abstract":"Sensor networks play an essential role in today's air quality monitoring platforms. Nevertheless, sensors often malfunction, leading to data anomalies. In this paper, an unsupervised pattern-based attention recurrent autoencoder for anomaly detection (PARAAD) is proposed to detect and locate anomalies in a network of air quality sensors. The novelty of the proposal lies in the use of temporal patterns, i.e., blocks of data, instead of point values. By looking at temporal patterns and through an attention mechanism, the architecture captures data dependencies in the feature space and latent space, enhancing the model's ability to focus on the most relevant parts. Its performance is evaluated with two categories of anomalies, bias fault and drift anomalies, and compared with baseline models such as a feed-forward autoencoder and a transformer architecture, as well as with models not based on temporal patterns. The results show that PARAAD achieves anomalous sensor detection and localization rates higher than 80%, outperforming existing baseline models in air quality sensor networks for both bias and drift faults.","PeriodicalId":54229,"journal":{"name":"IEEE Transactions on Network Science and Engineering","volume":"11 6","pages":"6372-6381"},"PeriodicalIF":6.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142191987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Estimating Age of Information in Wireless Systems With Unknown Distributions of Inter-Arrival/Service Time 在到达/服务时间分布未知的情况下估算无线系统中的信息年龄
IF 6.7 2区 计算机科学
IEEE Transactions on Network Science and Engineering Pub Date : 2024-09-03 DOI: 10.1109/TNSE.2024.3453959
Licheng Chen;Yunquan Dong
{"title":"Estimating Age of Information in Wireless Systems With Unknown Distributions of Inter-Arrival/Service Time","authors":"Licheng Chen;Yunquan Dong","doi":"10.1109/TNSE.2024.3453959","DOIUrl":"10.1109/TNSE.2024.3453959","url":null,"abstract":"In this paper, we estimate the average age of information (AoI) of the status updating over a wireless channel with an unknown fading model. Different from most related works which take the distributions of the inter-arrival time and transmission time of updates as known information, we approximate the average AoI of the system by using their first and second-order moments. Note that these distributions are often not accessible or known with inevitable errors while their moments are much easier to obtain, e.g., by using counting and statistics. We model the communications over the fading channel with a continuous transmission model and a discrete transmission model, which use the variable-rate scheme and the fixed-rate scheme, respectively. We assume that the arrival of the continuous transmission model is a Bernoulli process and make no assumptions about the arrival process of the discrete transmission model. Based on these information, we present two pairs of tight lower and upper bounds for the AoI of the two models. We show that obtained bounds are the tightest when the inter-arrival time (or transmission time) follows the degenerate distribution and are the loosest when it follows the two-point distribution, which randomly takes value from two possible outcomes. We also show that tighter bounds can be obtained by using higher order moments.","PeriodicalId":54229,"journal":{"name":"IEEE Transactions on Network Science and Engineering","volume":"11 6","pages":"6090-6104"},"PeriodicalIF":6.7,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142191989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Subnetwork Enumeration Algorithms for Multilayer Networks 多层网络的子网络枚举算法
IF 6.7 2区 计算机科学
IEEE Transactions on Network Science and Engineering Pub Date : 2024-09-02 DOI: 10.1109/TNSE.2024.3447893
Tarmo Nurmi;Mikko Kivelä
{"title":"Subnetwork Enumeration Algorithms for Multilayer Networks","authors":"Tarmo Nurmi;Mikko Kivelä","doi":"10.1109/TNSE.2024.3447893","DOIUrl":"10.1109/TNSE.2024.3447893","url":null,"abstract":"To understand the structure of a network, it can be useful to break it down into its constituent pieces. This is the approach taken in a multitude of successful network analysis methods, such as motif analysis. These methods require one to enumerate or sample small connected subgraphs of a network. Efficient algorithms exists for both enumeration and uniform sampling of subgraphs, and here we generalize the \u0000<sc>esu</small>\u0000 algorithm for a very general notion of multilayer networks. We show that multilayer network subnetwork enumeration introduces nontrivial complications to the existing algorithm, and present two different generalized algorithms that preserve the desired features of unbiased sampling and scalable, communication-free parallelization. In addition, we introduce a straightforward aggregation-disaggregation-based enumeration algorithm that leverages existing subgraph enumeration algorithms. We evaluate these algorithms in synthetic networks and with real-world data, and show that none of the algorithms is strictly more efficient but rather the choice depends on the features of the data. Having a general algorithm for finding subnetworks makes advanced multilayer network analysis possible, and enables researchers to apply a variety of methods to previously difficult-to-handle multilayer networks in a variety of domains and across many different types of multilayer networks.","PeriodicalId":54229,"journal":{"name":"IEEE Transactions on Network Science and Engineering","volume":"11 6","pages":"5803-5817"},"PeriodicalIF":6.7,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10663535","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142191991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Robustness Analysis of High-Speed Railway Networks Against Cascading Failures: From a Multi-Layer Network Perspective 高速铁路网对级联故障的鲁棒性分析:从多层网络的角度
IF 6.7 2区 计算机科学
IEEE Transactions on Network Science and Engineering Pub Date : 2024-08-28 DOI: 10.1109/TNSE.2024.3451118
Junfeng Ma;Shan Ma;Xiaotian Xie;Weihua Gui
{"title":"Robustness Analysis of High-Speed Railway Networks Against Cascading Failures: From a Multi-Layer Network Perspective","authors":"Junfeng Ma;Shan Ma;Xiaotian Xie;Weihua Gui","doi":"10.1109/TNSE.2024.3451118","DOIUrl":"10.1109/TNSE.2024.3451118","url":null,"abstract":"In this study, we model the high-speed railway (HSR) network as a directed multi-layer network. Specifically, each node is viewed as a tuple of a train with a station it passes through. A directed edge within a layer means that a train passes through two consecutive stations in its scheduled train route, while an edge between different layers means that two trains pass through the same station sequentially. Then we assess the robustness against cascading failures of these multi-layer networks by introducing metrics such as network efficiency and the ratio of failed nodes under disturbances. Furthermore, we propose a cascading failure model based on train delay propagation to investigate the cascading dynamics within the multi-layer HSR network. To better characterize the delay propagation patterns in the network, train delays at each station are treated as the load of the corresponding node, while the time supplements and buffer time are considered as the capacities of the edges. Finally, we propose two strategies to enhance the robustness of HSR networks against cascading failures. Numerical experiments are conducted to demonstrate the effectiveness of these strategies.","PeriodicalId":54229,"journal":{"name":"IEEE Transactions on Network Science and Engineering","volume":"11 6","pages":"6522-6534"},"PeriodicalIF":6.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142191990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Poisson Game-Based Incentive Mechanism for Federated Learning in Web 3.0 基于泊松游戏的 Web 3.0 联合学习激励机制
IF 6.7 2区 计算机科学
IEEE Transactions on Network Science and Engineering Pub Date : 2024-08-28 DOI: 10.1109/TNSE.2024.3450932
Mingshun Luo;Yunhua He;Tingli Yuan;Bin Wu;Yongdong Wu;Ke Xiao
{"title":"A Poisson Game-Based Incentive Mechanism for Federated Learning in Web 3.0","authors":"Mingshun Luo;Yunhua He;Tingli Yuan;Bin Wu;Yongdong Wu;Ke Xiao","doi":"10.1109/TNSE.2024.3450932","DOIUrl":"10.1109/TNSE.2024.3450932","url":null,"abstract":"As the next generation of the internet, Web 3.0 is expected to revolutionize the Internet and enable users to have greater control over their data and privacy. Federated learning (FL) enables data to be usable yet invisible during its use, thereby facilitating the transfer of data ownership and value. However, the issues of data size and blockchain computing power are of paramount importance for FL in Web 3.0. Due to the openness of Web 3.0, individuals can freely join or leave training and adjust data size, creating population uncertainty and making it difficult to design incentive mechanisms. Therefore, we propose a Poisson game-based FL incentive mechanism that motivates participants to contribute more data and computing power, considering the variability of data size and computing power requirements, and provides a feasible solution to the uncertainty of the number of participants using a Poisson game model. Additionally, our proposed FL architecture in Web 3.0 integrates FL with Decentralized Autonomous Organizations (DAO), utilizing smart contracts for contribution calculation and revenue distribution. This enables an open, free, and autonomous federated learning environment. Experimental evaluation shows that our incentive mechanism is feasible in blockchain with efficiency, robustness, and low overhead.","PeriodicalId":54229,"journal":{"name":"IEEE Transactions on Network Science and Engineering","volume":"11 6","pages":"5576-5588"},"PeriodicalIF":6.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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