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Layered Coded Cache Placement and Cooperative Delivery with Sharing Links in Satellite-Terrestrial Integrated Networks
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作者 Gu Shushi Chen Zihan +2 位作者 Wu Yaonan Zhang Qinyu Wang Ye 《China Communications》 SCIE CSCD 2024年第3期217-229,共13页
Cooperative utilization of multidimensional resources including cache, power and spectrum in satellite-terrestrial integrated networks(STINs) can provide a feasible approach for massive streaming media content deliver... Cooperative utilization of multidimensional resources including cache, power and spectrum in satellite-terrestrial integrated networks(STINs) can provide a feasible approach for massive streaming media content delivery over the seamless global coverage area. However, the on-board supportable resources of a single satellite are extremely limited and lack of interaction with others. In this paper, we design a network model with two-layered cache deployment, i.e., satellite layer and ground base station layer, and two types of sharing links, i.e., terrestrial-satellite sharing(TSS) links and inter-satellite sharing(ISS) links, to enhance the capability of cooperative delivery over STINs. Thus, we use rateless codes for the content divided-packet transmission, and derive the total energy efficiency(EE) in the whole transmission procedure, which is defined as the ratio of traffic offloading and energy consumption. We formulate two optimization problems about maximizing EE in different sharing scenarios(only TSS and TSS-ISS),and propose two optimized algorithms to obtain the optimal content placement matrixes, respectively.Simulation results demonstrate that, enabling sharing links with optimized cache placement have more than 2 times improvement of EE performance than other traditional placement schemes. Particularly, TSS-ISS schemes have the higher EE performance than only TSS schemes under the conditions of enough number of satellites and smaller inter-satellite distances. 展开更多
关键词 coded content placement cooperative delivery energy efficiency sharing links STINs
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Zhongshan:Embracing New Links
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作者 Liu Xueyun 《China Report ASEAN》 2024年第11期52-53,共2页
On June 30,2024,the much-anticipated Shenzhen-Zhongshan Link officially began trial operation.The world-class cross-sea cluster project integrating two bridges,two islands,and an underwater tunnel is expected to short... On June 30,2024,the much-anticipated Shenzhen-Zhongshan Link officially began trial operation.The world-class cross-sea cluster project integrating two bridges,two islands,and an underwater tunnel is expected to shorten the driving time from Shenzhen to Zhongshan from two hours to 30 minutes,helping create a 30-minute commute circle across the area.As the flow of innovation factors accelerates through the Shenzhen Zhongshan Link,Zhongshan City has been proactively exploring cooperation models such as“Shenzhen headquarters plus Zhongshan manufacturing,”“Shenzhen leading businesses plus Zhongshan support,”and“Shenzhen R&D plus Zhongshan commercialization”to form a one-hour science and technology industrial cooperation circle with Shenzhen and build a more open,coordinated,and efficient regional innovation system. 展开更多
关键词 circle link integrating
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Vibration Reduction of Open-chain Flexible Manipulators by Optimizing Independent Motions of Branch Links 被引量:4
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作者 边宇枢 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2008年第1期79-85,共7页
In order to suppress vibration in flexible manipulators, a new type of manipulator mechanism with controllable local degrees of freedom is proposed. This mechanism consists of a main chain and some branch links. The m... In order to suppress vibration in flexible manipulators, a new type of manipulator mechanism with controllable local degrees of freedom is proposed. This mechanism consists of a main chain and some branch links. The main chain is of a flexible open-chain configuration with an end-effector installed at its tip, and the rigid branch links are able to perform active movements. It is proved by kinematics and dynamic analysis that, the branch links bear no direct kinematic relation to the main chain, but their independent motions can strongly affect the dynamic behavior and performance of the flexible manipulator. Then comes a new idea of suppressing vibration, in which independent motions of the branch links are used to suppress the undesired vibration of the flexible main chain through dynamic coupling. On this basis, an optimal method for reducing vibration of flexible manipulators is proposed. Finally, the effectiveness of this method is verified by numerical simulations. 展开更多
关键词 flexible manipulator vibration local degree of freedom branch link
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Percolation on networks with dependence links 被引量:3
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作者 李明 汪秉宏 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第7期79-87,共9页
As a classical model of statistical physics, the percolation theory provides a powerful approach to analyze the network structure and dynamics. Recently, to model the relations among interacting agents beyond the conn... As a classical model of statistical physics, the percolation theory provides a powerful approach to analyze the network structure and dynamics. Recently, to model the relations among interacting agents beyond the connection of the networked system, the concept of dependence link is proposed to represent the dependence relationship of agents. These studies suggest that the percolation properties of these networks differ greatly from those of the ordinary networks. In particular, unlike the well known continuous transition on the ordinary networks, the percolation transitions on these networks are discontinuous. Moreover, these networks are more fragile for a broader degree distribution, which is opposite to the famous results for the ordinary networks. In this article, we give a summary of the theoretical approaches to study the percolation process on networks with inter- and inner-dependence links, and review the recent advances in this field, focusing on the topology and robustness of such networks. 展开更多
关键词 PERCOLATION network dependence link phase transition
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ON THE DYNAMIC MODELING AND CONTROL OF 2-DOF PLANAR PARALLEL MECHANISM WITH FLEXIBLE LINKS 被引量:2
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作者 LuoLei WangShigang MoJinqiu CaiJianguo 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2005年第1期112-117,共6页
The object of study is about dynamic modeling and control for a 2degree-of-freedom (DOF) planar parallel mechanism (PM) with flexible links. The kinematic anddynamic equations are established according to the characte... The object of study is about dynamic modeling and control for a 2degree-of-freedom (DOF) planar parallel mechanism (PM) with flexible links. The kinematic anddynamic equations are established according to the characteristics of mixed rigid and flexiblestructure. By using the singular perturbation approach (SPA), the model of the mechanism can beseparated into slow and fast subsystems. Based on the feedback linearization theory and inputshaping technique, the large scale rigid motion controller and the flexible link vibrationcontroller can be designed separately to achieve fast and accurate positioning of the PM. 展开更多
关键词 Parallel mechanism Flexible link Dynamic modeling Singular perturbation Input shaping
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电动汽车电控液压制动系统CarSim/Simulink联合仿真研究 被引量:2
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作者 洪诚 李琤 《汽车实用技术》 2024年第5期52-58,共7页
针对某款国产电动汽车的电控液压制动系统,文章基于滑移率的比例-积分-微分(PID)控制提出了防抱死制动系统(ABS)模型,以改善车辆制动性能,提高在对开路面上的制动有效性和安全性。首先,使用Simulink软件建立液压电控制动系统的动力学模... 针对某款国产电动汽车的电控液压制动系统,文章基于滑移率的比例-积分-微分(PID)控制提出了防抱死制动系统(ABS)模型,以改善车辆制动性能,提高在对开路面上的制动有效性和安全性。首先,使用Simulink软件建立液压电控制动系统的动力学模型;然后,基于滑移率设计PID控制器,并通过1/4车辆模型验证其有效性;最后,利用S函数将ABS控制器的Simulink模型输入CarSim平台中,开展CarSim/Simulink双平台联合控制仿真。结果表明,基于滑移率的PID控制的ABS对比无ABS的车辆,制动性能更加优越,在对开路面上制动稳定性更加明显。 展开更多
关键词 ABS 电动汽车 电控液压 汽车动力学 CarSim/Simulink联合仿真 制动性能
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一种MAKLINK图多节点链路建模的路径规划研究
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作者 孙培刚 张全禹 许春和 《电子设计工程》 2024年第4期140-143,148,共5页
针对传统MAKLINK图规划路径线路改变时,其最优化路径易与环境约束条件冲突的问题,提出了在MAKLINK图中各链路上增加节点数目的方法,以提高系统建模的适应性和鲁棒性。设计的多节点链路通过dijkstra算法得到更为理想的次优化路径,由蚁群... 针对传统MAKLINK图规划路径线路改变时,其最优化路径易与环境约束条件冲突的问题,提出了在MAKLINK图中各链路上增加节点数目的方法,以提高系统建模的适应性和鲁棒性。设计的多节点链路通过dijkstra算法得到更为理想的次优化路径,由蚁群算法进行迭代计算获得最优化路径,实现了在保证路径适应度的前提下,提高优化路径对环境约束条件的适应性。实验结果表明,与基本MAKLINK图路径规划算法相比,多节点链路的建模路径规划算法可有效提高次优路径的建模精度,最优路径的适应度值较单节点链路减小了1.43%,具有一定的建模优势。 展开更多
关键词 MAKlink 多节点链路 DIJKSTRA算法 蚁群算法
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Dynamic Characteristics of Inter-Satellite Links in LEO Networks 被引量:1
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作者 王亮 张乃通 温萍萍 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2003年第4期25-29,48,共6页
To establish an efficient inter-satellite link (ISL) in an LEO network, the effect of geometric characteristics of ISL on the ISLs and the devices on the LEO satellite should be examined. Because of the continuous mov... To establish an efficient inter-satellite link (ISL) in an LEO network, the effect of geometric characteristics of ISL on the ISLs and the devices on the LEO satellite should be examined. Because of the continuous movement of the LEO satellite, the time-varying behaviours of the ISL's geometric charactersistics continuously change with the changes of the satellite's position on the orbit. These dynamic geometric characteristics of the ISLs are important for ISL's performance analyzing and the design of the devices on the LEO satellite. This paper describes dynamic geometric characteristics of ISL, analyzes the impact of these regulations on the tracking system of the satellite's antenna and the power adjusting system of the satellite's transmitter, with the Iridium system as an example. 展开更多
关键词 inter-satellite link LEO constellation dynamic characteristics.
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Finite element investigation of steel built-up shear links subjected to inelastic deformations 被引量:1
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作者 Peter Dusicka Ahmad M.Itani Ian G.Buckle 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2004年第2期195-203,共9页
Non-linear finite element models accounting for large displacements have been used to investigate the behavior of steel built-up shear links that had previously been tested using large-scale experiments. The links wer... Non-linear finite element models accounting for large displacements have been used to investigate the behavior of steel built-up shear links that had previously been tested using large-scale experiments. The links were designed using steel grades with yield points ranging from high to low strengths. The objectives of the numerical analyses were to further investigate the non-linear behavior and to correlate the numerical results with experimental observations. Elasto-plastic as well as cyclic stress-strain material properties were incorporated to study the influence of material behavior on the overall shear link response. Non-linear monotonie analyses of the shear links incorporating the cyclic stress-strain steel properties resulted in similar trends in the response as the backbone curves recorded from the physical experiments. The numerical models of built-up shear links utilizing structural grade steels closely correlated to the experimentally recorded shear strength. Models utilizing low yield point steels overestimated the shear strength, which was caused by the characteristics of cyclic behavior of those steels. The detailed numerical models also allowed for investigation of the plastic strain demands on the different components of the link. It was shown that finite element models combined with appropriate stress-strain relationship may be used with confidence to check the design of shear links of different steel grades and sectional geometries. 展开更多
关键词 finite element investigation steel built-up shear link inelastic deformation
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Numerical Investigation of Mooring Line Damping and the Drag Coefficients of Studless Chain Links 被引量:1
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作者 Zhengqiang Xu Shan Huang 《Journal of Marine Science and Application》 2014年第1期76-84,共9页
The chain/wire rope/chain combination is a common choice for mooring offshore floating platforms. However, data of the drag coefficients of chain links are rather limited, resulting in uncertainties with the calculati... The chain/wire rope/chain combination is a common choice for mooring offshore floating platforms. However, data of the drag coefficients of chain links are rather limited, resulting in uncertainties with the calculations of the drag force, and hence the damping of the mooring system. In this paper, the importance of the selection of the drag coefficient is first investigated. The computational fluid dynamics(CFD) method is then used to determine the drag coefficients of a studless chain under steady flows. Numerical model validation is first completed by simulating a smooth circular cylinder under steady flows. In particular, the performance of different turbulence models is assessed through the comparisons between the calculations and the experimental results. The large eddy simulation(LES) model is finally selected for the simulation of steady flows past a chain. The effects of the Reynolds number on the drag coefficient of a stud-less chain is also studied. The results show that the calculated drag coefficients of a stud-less chain are fairly consistent with the available experimental data. 展开更多
关键词 CFD drag coefficient low frequency motion mooringline DAMPING CHAIN links offshore FLOATING PLATFORMS
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DYNAMIC SUBSTRUCTURING ANALYSISOF COMPOSITE STRUCTURES WITHNONLINEAR LINKS 被引量:1
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作者 Hu Haiyan, Li Yuefeng and Zhang AzhouNanjing Aeronautical Institute 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 1990年第3期168-177,共10页
The paper deals with the dynamic response prediction of the composite structure,which consists of two linear components coupled by some nonlinear vibration isolators. Based on the measured impulse response functions o... The paper deals with the dynamic response prediction of the composite structure,which consists of two linear components coupled by some nonlinear vibration isolators. Based on the measured impulse response functions of the linear components, three kinds of dynamic equations of interfacial integration are proposed and a procedure to transform the dynamic equations of integral type into a set of ordinary differential equations is suggested. Computer simulations and a real test are given to verify the effectiveness of the theoretical results. 展开更多
关键词 DYNAMIC SUBSTRUCTURING ANALYSISOF COMPOSITE STRUCTURES WITHNONLINEAR links MODE link
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《关注石油》教学设计及实施——World Links远程合作学习实践 被引量:1
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作者 郭小渠 《中国电化教育》 CSSCI 北大核心 2006年第4期75-77,共3页
笔者运用"做中学"的方式,以美国WorldLinks组织的"远程合作学习项目"为理论指导,设计制作了专题网站《关注石油》,并在Internet上开展了这一项目的实践活动。本文介绍了从项目的创建、设计、促进,直到最终成功的完... 笔者运用"做中学"的方式,以美国WorldLinks组织的"远程合作学习项目"为理论指导,设计制作了专题网站《关注石油》,并在Internet上开展了这一项目的实践活动。本文介绍了从项目的创建、设计、促进,直到最终成功的完整过程,并对项目学习的案例和成果等内容进行了总结。 展开更多
关键词 World links 程合作 实践
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Anti-Dead-Zone Integral Sliding Control and Active Vibration Suppression of a Free-floating Space Robot with Elastic Base and Flexible Links 被引量:2
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作者 Xiaoqin Huang Li Chen 《Journal of Beijing Institute of Technology》 EI CAS 2020年第1期120-128,共9页
Under the conditions of joint torque output dead-zone and external disturbance,the trajectory tracking and vibration suppression for a free-floating space robot(FFSR)system with elastic base and flexible links were di... Under the conditions of joint torque output dead-zone and external disturbance,the trajectory tracking and vibration suppression for a free-floating space robot(FFSR)system with elastic base and flexible links were discussed.First,using the Lagrange equation of the second kind,the dynamic model of the system was derived.Second,utilizing singular perturbation theory,a slow subsystem describing the rigid motion and a fast subsystem corresponding to flexible vibration were obtained.For the slow subsystem,when the width of deadzone is uncertain,a dead-zone pre-compensator was designed to eliminate the impact of joint torque output dead-zone,and an integral sliding mode neural network control was proposed.The integral sliding mode term can reduce the steady state error.For the fast subsystem,an optimal linear quadratic regulator(LQR)controller was adopted to damp out the vibration of the flexible links and elastic base simultaneously.Finally,computer simulations show the effectiveness of the compound control method. 展开更多
关键词 space robot with flexible links ELASTIC BASE DEAD-ZONE proportional-integral SLIDING mode control active vibration suppression
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A novel similarity measure for mining missing links in long-path networks 被引量:1
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作者 Yijun Ran Tianyu Liu +1 位作者 Tao Jia Xiao-Ke Xu 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第6期56-64,共9页
Network information mining is the study of the network topology,which may answer a large number of applicationbased questions towards the structural evolution and the function of a real system.The question can be rela... Network information mining is the study of the network topology,which may answer a large number of applicationbased questions towards the structural evolution and the function of a real system.The question can be related to how the real system evolves or how individuals interact with each other in social networks.Although the evolution of the real system may seem to be found regularly,capturing patterns on the whole process of evolution is not trivial.Link prediction is one of the most important technologies in network information mining,which can help us understand the evolution mechanism of real-life network.Link prediction aims to uncover missing links or quantify the likelihood of the emergence of nonexistent links from known network structures.Currently,widely existing methods of link prediction almost focus on short-path networks that usually have a myriad of close triangular structures.However,these algorithms on highly sparse or longpath networks have poor performance.Here,we propose a new index that is associated with the principles of structural equivalence and shortest path length(SESPL)to estimate the likelihood of link existence in long-path networks.Through a test of 548 real networks,we find that SESPL is more effective and efficient than other similarity-based predictors in long-path networks.Meanwhile,we also exploit the performance of SESPL predictor and of embedding-based approaches via machine learning techniques.The results show that the performance of SESPL can achieve a gain of 44.09%over GraphWave and 7.93%over Node2vec.Finally,according to the matrix of maximal information coefficient(MIC)between all the similarity-based predictors,SESPL is a new independent feature in the space of traditional similarity features. 展开更多
关键词 structural equivalence shortest path length long-path networks missing links
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Deciding whether manufacturing firms share product links on owned social media considering fan effects 被引量:1
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作者 Li Peipei Mei Shu’e Zhong Weijun 《Journal of Southeast University(English Edition)》 EI CAS 2022年第4期425-432,共8页
An optimization model is proposed to examine the choice of sharing or not sharing the product link for manufacturing firms with owned social media by considering the role of fan effects.The equilibrium marketing effor... An optimization model is proposed to examine the choice of sharing or not sharing the product link for manufacturing firms with owned social media by considering the role of fan effects.The equilibrium marketing effort level and firm profit in both cases are compared.The results show that the firm chooses to share(not share)the product link when the social platform commission rate is low(high).Moreover,the likelihood of sharing the product link increases as the fan effect weakens and the perceived conversion cost strengthens.Interestingly,the marketing effort level increases with the product price,but firm profit does not always follow.Additionally,as the fan effect and fan count grow,so does the firm s profit.Furthermore,when the firm shares the product link,the level of marketing effort and firm profit decrease with the commission rate.Conversely,when the firm does not share the product link,those aforementioned factors increase as the perceived conversion cost declines.These results thus suggest that firms should enhance the influence of owned social media to attract more high-quality fans,and social platforms should optimize the product link functionality. 展开更多
关键词 fan effect self-media marketing product link marketing effort
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面向Link16的QualNet与虚拟机信息交互接口设计与实现
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作者 杨昊伟 龚鹏 +4 位作者 张继豪 王卫东 唐飞喜 周子骄 张广为 《兵工学报》 EI CAS CSCD 北大核心 2024年第4期1186-1195,共10页
Link16是美国国防部采用的高速视距战术数据链,广泛应用于美国海军、联合部队和北约部队,针对其开展测试评估具有重要军事意义。通过硬件在环技术将Link16实物设备接入到仿真测试中,可有效提高测试结果的真实性和准确性。然而当测试场... Link16是美国国防部采用的高速视距战术数据链,广泛应用于美国海军、联合部队和北约部队,针对其开展测试评估具有重要军事意义。通过硬件在环技术将Link16实物设备接入到仿真测试中,可有效提高测试结果的真实性和准确性。然而当测试场景需要进行实物设备组网测试时,仍会带来成本问题。为此,提出一种面向QualNet MAC层的Link16专属模型以及与之匹配的虚拟机信息交互接口。该模型可高逼真模拟Link16通信行为,实现Link16节点竞争接入、时隙划分、NPG分组等功能。并基于数据分布式服务实现了虚拟机交互接口,将运行在虚拟机的Link16设备模型接入QualNet测试场景。实验测试结果表明,所设计模型具有较高真实性和准确性且接口引入延时不超过1 ms,为大规模数据链网络测试提供一种新方法。 展开更多
关键词 交互接口 link16数据链 虚拟机 QualNet MAC层 网络仿真
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AN APPROACH TO QUANTITATIVE ANALYSIS OF REGIONAL ECONOMIC LINKS──A Case Study on Economic Links Between Su-Xi-Chang Region and Shanghai
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作者 王德忠 庄仁兴 《Chinese Geographical Science》 SCIE CSCD 1997年第2期149-156,共8页
Aimed at promoting regional editions and expanding the approach to economic links,this Paper puts forward some new concepts such as link intensity and receiving coefficinet, exounds expounds the indexes of quantitativ... Aimed at promoting regional editions and expanding the approach to economic links,this Paper puts forward some new concepts such as link intensity and receiving coefficinet, exounds expounds the indexes of quantitative analysis of economic links and establishes the quantitative-analysis model of economic links. With help of the model, this paper calculates the values of the link intensities between Su-Xi-Chang (Suzhou-Wuxi-Changzhou) region and Shanghai, and analyzes the regional difference of the economic links. 展开更多
关键词 link intensity receiving coefficient quantitative-analysis matrix of ECONOMIC link regional difference of ECONOMIC link
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Dancing Links X在智能导检中的应用研究
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作者 付冰 胡云 周作建 《计算机时代》 2022年第3期61-64,69,共5页
为了缩短健康体检排队等待时间、预测待检项目整体顺序,以X算法、精确覆盖、广义覆盖、Dancing Links作为理论基础,提出了应用Dancing Links X解决体检时间广义覆盖问题的方法。通过构建以服务时间成本、排队等待时间成本的总成本最小... 为了缩短健康体检排队等待时间、预测待检项目整体顺序,以X算法、精确覆盖、广义覆盖、Dancing Links作为理论基础,提出了应用Dancing Links X解决体检时间广义覆盖问题的方法。通过构建以服务时间成本、排队等待时间成本的总成本最小化为目标的Dancing Links X三重约束来搜索可行性解,并摘选最小值。以此模型完成的规划体检顺序,实现了对体检路线的预测,表明基于Dancing Links X三重约束的智能导检路径优化模型可以对待检项目顺序及时间节点预测,为导检的智能化研究提供新思路。 展开更多
关键词 智能导检 Dancing links X算法 广义覆盖 精确覆盖
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Benchmarking the Robustness of Cellular Up-Links in Automatic Weather Station Networks
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作者 Emmanuel A. Kondela Amos Nungu +2 位作者 Joseph W. Matiko Julianne S. Otim Bjorn Pehrson 《Communications and Network》 2018年第3期78-92,共15页
We present a problem for benchmarking the robustness of cellular up-links, in an automatic weather station (AWS) testbed. Based on the problem, we conduct a small-scale measurement study of robustness, where the AWS i... We present a problem for benchmarking the robustness of cellular up-links, in an automatic weather station (AWS) testbed. Based on the problem, we conduct a small-scale measurement study of robustness, where the AWS is equipped with four (4) cellular modems for weather data delivery. The effectiveness of up-links is challenging because of overlapping spatial-temporal factors such as the presence of good reflectors that lead to multi-path effects, interference, network load or other reasons. We argue that, there is a strong need for independent assessments of their robustness, to perform end-to-end network measurement. However, it is yet difficult to go from a particular measurement to an assessment of the entire network. We extensively measure the variability of Radio Signal Strength (RSSI) as link metric on the cellular modems. The RSSI is one of the important link metrics that can determine the robustness of received RF signals, and explore how they differed from one another at a particular location and instant time. We also apply the statistical analysis that quantifies the level of stability by considering the robustness, referring short-term variation, and determines good up-link in comparison to weak one. The results show that the robustness of cellular up-links exists for an unpredictable period of time and lower than one could hope. More than 50% of up-links are intermittent. Therefore, we plan to extend our work by exploring RSSI thresholds, to develop a classification scheme supporting a decision whether a link is either intermittent or not. This will help in normalizing the level of stability, to design the RSSI estimation metric for the robust routing protocol in weather data networks. 展开更多
关键词 CELLULAR links ROBUSTNESS Automatic Weather Station TERRESTRIAL Wireless links INTERMITTENT links
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Zeros Distribution of the Jones Polynomial for Pretzel Links
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作者 Han You-fa Huang Dong-yue +2 位作者 Wang Lin-lin Ma Xiao-sha Lei Feng-chun 《Communications in Mathematical Research》 CSCD 2015年第2期141-148,共8页
In this paper, we deal with basic properties of some pretzel links and properties of the Jones polynomials of some pretzel links. By using these properties, the zero distribution of pretzel links is studied. We discus... In this paper, we deal with basic properties of some pretzel links and properties of the Jones polynomials of some pretzel links. By using these properties, the zero distribution of pretzel links is studied. We discuss the properties of the Jones polynomial of non-tame pretzel links and give that zeros of the Jones polynomial of these pretzel links are distributed on the planar curves. 展开更多
关键词 Jones polynomial ZERO pretzel link
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