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改进的6轮Square算法中间相遇攻击
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作者 何峰 董晓丽 韦永壮 《计算机技术与发展》 2025年第2期63-69,共7页
Square分组密码算法是由Daemen等人设计,并在1997年快速软件加密(FSE)国际会议上首次公布。该密码算法基于SPN(Substitution-Permutation Network)结构,其分组长度和密钥长度均为128比特;具有设计新颖、实现高效等优点,也是高级加密标准... Square分组密码算法是由Daemen等人设计,并在1997年快速软件加密(FSE)国际会议上首次公布。该密码算法基于SPN(Substitution-Permutation Network)结构,其分组长度和密钥长度均为128比特;具有设计新颖、实现高效等优点,也是高级加密标准(AES)算法的前身,在密码学界备受关注。中间相遇攻击作为分组密码算法的重要分析方法之一,如何研究Square算法抵抗中间相遇攻击一直是业内讨论的热点问题。该文基于Square算法的结构特点和截断差分特征,利用差分枚举技术,构造了一个3.5轮中间相遇区分器。通过密钥桥技术及Square算法的密钥编排特点,推演出了主密钥与子密钥之间的部分线性关系。由此,将3.5轮区分器向前扩展1轮,向后扩展1.5轮,实现了对6轮Square算法的中间相遇攻击。该攻击所需数据复杂度为2105个选择明文,时间复杂度为2105次6轮加密,存储复杂度为285个分组。与已有攻击结果相比,新的攻击有效地降低了所需的数据复杂度、时间复杂度和存储复杂度。 展开更多
关键词 分组密码 square算法 中间相遇攻击 差分枚举技术 密钥桥技术
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Algorithms and statistical analysis for linear structured weighted total least squares problem
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作者 Jian Xie Tianwei Qiu +2 位作者 Cui Zhou Dongfang Lin Sichun Long 《Geodesy and Geodynamics》 EI CSCD 2024年第2期177-188,共12页
Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with rand... Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations. 展开更多
关键词 Linear structured weighted total least squares ERRORS-IN-VARIABLES Errors-in-observations Functional modelmodification Stochastic model modification Accuracyevaluation
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Least Squares One-Class Support Tensor Machine
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作者 Kaiwen Zhao Yali Fan 《Journal of Computer and Communications》 2024年第4期186-200,共15页
One-class classification problem has become a popular problem in many fields, with a wide range of applications in anomaly detection, fault diagnosis, and face recognition. We investigate the one-class classification ... One-class classification problem has become a popular problem in many fields, with a wide range of applications in anomaly detection, fault diagnosis, and face recognition. We investigate the one-class classification problem for second-order tensor data. Traditional vector-based one-class classification methods such as one-class support vector machine (OCSVM) and least squares one-class support vector machine (LSOCSVM) have limitations when tensor is used as input data, so we propose a new tensor one-class classification method, LSOCSTM, which directly uses tensor as input data. On one hand, using tensor as input data not only enables to classify tensor data, but also for vector data, classifying it after high dimensionalizing it into tensor still improves the classification accuracy and overcomes the over-fitting problem. On the other hand, different from one-class support tensor machine (OCSTM), we use squared loss instead of the original loss function so that we solve a series of linear equations instead of quadratic programming problems. Therefore, we use the distance to the hyperplane as a metric for classification, and the proposed method is more accurate and faster compared to existing methods. The experimental results show the high efficiency of the proposed method compared with several state-of-the-art methods. 展开更多
关键词 Least square One-Class Support Tensor Machine One-Class Classification Upscale Least square One-Class Support Vector Machine One-Class Support Tensor Machine
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Numerical Simulation of Oil-Water Two-Phase Flow in Low Permeability Tight Reservoirs Based on Weighted Least Squares Meshless Method
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作者 Xin Liu Kai Yan +3 位作者 Bo Fang Xiaoyu Sun Daqiang Feng Li Yin 《Fluid Dynamics & Materials Processing》 EI 2024年第7期1539-1552,共14页
In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering comp... In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering complex boundary shapes.Utilizing radial basis function point interpolation,the method approximates shape functions for unknown functions within the nodal influence domain.The shape functions constructed by the aforementioned meshless interpolation method haveδ-function properties,which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells.Moreover,the meshless method offers greater flexibility and freedom compared to grid cell discretization,making it simpler to discretize complex geometries.A variational principle for the flow control equation group is introduced using a weighted least squares meshless method,and the pressure distribution is solved implicitly.Example results demonstrate that the computational outcomes of the meshless point cloud model,which has a relatively small degree of freedom,are in close agreement with those of the Discrete Fracture Model(DFM)employing refined grid partitioning,with pressure calculation accuracy exceeding 98.2%.Compared to high-resolution grid-based computational methods,the meshless method can achieve a better balance between computational efficiency and accuracy.Additionally,the impact of fracture half-length on the productivity of horizontal wells is discussed.The results indicate that increasing the fracture half-length is an effective strategy for enhancing production from the perspective of cumulative oil production. 展开更多
关键词 Weighted least squares method meshless method numerical simulation of low permeability tight reservoirs oil-water two-phase flow fracture half-length
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Comparative Study of Probabilistic and Least-Squares Methods for Developing Predictive Models
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作者 Boribo Kikunda Philippe Thierry Nsabimana +2 位作者 Jules Raymond Kala Jeremie Ndikumagenge Longin Ndayisaba 《Open Journal of Applied Sciences》 2024年第7期1775-1787,共13页
This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations... This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations and can lead to varied or similar results in terms of precision and performance under certain assumptions. The article underlines the importance of comparing these two approaches to choose the one best suited to the context, available data and modeling objectives. 展开更多
关键词 Predictive Models Least squares Bayesian Estimation Methods
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一种基于Least Square Method算法的城轨车辆车门动作时间精准判断的研究
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作者 李宏菱 宋华杰 +3 位作者 马仲智 周辉 李晴 陈龙 《时代汽车》 2025年第3期190-192,共3页
为研究城市轨道交通车辆客室车门动作时间精准性,门的动作主要依靠直流无刷电机的驱动,所以门动作判断的根本,是对电机运动状态的判读,门运动过程中由于电机码盘线受杂波干扰,系统无法准确寻找计时点从而影响系统判断门运动时间;建立波... 为研究城市轨道交通车辆客室车门动作时间精准性,门的动作主要依靠直流无刷电机的驱动,所以门动作判断的根本,是对电机运动状态的判读,门运动过程中由于电机码盘线受杂波干扰,系统无法准确寻找计时点从而影响系统判断门运动时间;建立波形矫正模型,利用数学方法校准波形,让MCU找出最佳计时点并处理(误差不超过10ms),采用最小二乘法模型,通过最小化误差的平方和找到一组数据的最佳函数匹配,求得未知的数据,并使得这些求得的数据与实际数据之间误差的平方和为最小,可精准地得到门动作时间。模拟测试结果表明,门动作时间测算误差所示其误差为7.42ms,小于10ms。 展开更多
关键词 城轨车辆 客室车门 电机码盘 Least square Method算法 门动作时间精准
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Quantity of plant leaf area on three major public squares in Kunming City, China 被引量:8
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作者 董燕 赵林森 赵宇翔 《Journal of Forestry Research》 SCIE CAS CSCD 2004年第4期291-294,共4页
Regressive formulae to calculate the quantity of plant leaf area for 13 species of ornamental plants were set up based on investigation data of 30 species on 3 major public squares (Dongfeng square, Shengli square and... Regressive formulae to calculate the quantity of plant leaf area for 13 species of ornamental plants were set up based on investigation data of 30 species on 3 major public squares (Dongfeng square, Shengli square and Guandu square) in Kun-ming City, China, which were applied to calculate quantities of plant leaf area of these 13 species. The quantities of plant leaf area for the other 17 ornamental plant species on these squares were directly measured, and the total quantity of plant leaf area of each studied square was obtained individually. The results showed that the quantity of plant leaf area on Shengli square with ornamental plants structure composed of arbor tree species, shrub tree species and turf grass was highest among the three squares. It is believed that the design model of multi-storied vertical structure and proper tending of plant community could not only increase the quantity of plant leaf area, but also play an important role in generating ecological and landscaping benefits. Some corresponding suggestions were put forward on the basis of comprehensive analyses on the plant leaf area quantity of the three representative squares in Kunming urban area. 展开更多
关键词 squarE Ornamental plants Quantity of plant leaf area Kunming
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Expression of Indigenous Landscapes in the Design of Modern Urban Squares 被引量:1
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作者 吴国荣 郭青媛 王长富 《Journal of Landscape Research》 2010年第4期24-26,30,共4页
Modern urban square landscapes have been evolved to be with more regional and cultural features, yet the phenomenon of duplication is serious in urban square landscapes in China. In this study, the connotation of indi... Modern urban square landscapes have been evolved to be with more regional and cultural features, yet the phenomenon of duplication is serious in urban square landscapes in China. In this study, the connotation of indigenous landscape is analyzed from the perspectives of local culture, integration of Chinese and western cultures, folk cultures and modern marketing, the causes of duplicated urban square landscapes are thoroughly elaborated. In view of the deficiencies of modern urban square landscapes, it is proposed that local plants, local ornamental materials and patterns should be fully applied in square designs, and the expression of detail landscapes should be attached sufficient importance, to completely demonstrate regional features of landscapes and better apply indigenous landscapes into the design of modern urban squares. 展开更多
关键词 URBAN square MODERN landscapes INDIGENIZATION CULTURAL COGNITION Landscape planning
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ONLINE PARSIMONIOUS LEAST SQUARES SUPPORT VECTOR REGRESSION AND ITS APPLICATION 被引量:2
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作者 赵永平 孙健国 王健康 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2009年第4期280-287,共8页
A simple and effective mechanism is proposed to realize the parsimoniousness of the online least squares support vector regression (LS-SVR), and the approach is called the OPLS-SVR for short. Hence, the response tim... A simple and effective mechanism is proposed to realize the parsimoniousness of the online least squares support vector regression (LS-SVR), and the approach is called the OPLS-SVR for short. Hence, the response time is curtailed. Besides, an OPLS-SVR based analytical redundancy technique is presented to cope with the sensor failure and drift problems to guarantee that the provided signals for the aeroengine controller are correct and acceptable. Experiments on the sensor failure and drift show the effectiveness and the validity of the proposed analytical redundancy. 展开更多
关键词 support vector machines SENSORS least squares analytical redundancy aeroengines
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Landscape Design Practices for Urban Squares 被引量:1
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作者 孟瑾 陈良 《Journal of Landscape Research》 2010年第4期38-41,共4页
Urban squares are significant nodes of urban spaces, which should be able to improve urban ecological environment and provide residents with outdoor activity spaces. The authors studied some excellent square designs i... Urban squares are significant nodes of urban spaces, which should be able to improve urban ecological environment and provide residents with outdoor activity spaces. The authors studied some excellent square designs in Inner Mongolia, China and even overseas countries, summarized the standards of "best urban squares" in vision, culture, craft, human-concerned design, science and technology, and then applied such standards in the landscape design of Central Plaza in Zhungeer Banner. Through analyzing surrounding environment and constructions, design schemes with regional and cultural features were created to provide references for designing better green square landscapes which can demonstrate local cultural context and regional cultures, are moderate in size, diversified in spatial form and closely integrated with the social life of citizens. 展开更多
关键词 URBAN square LANDSCAPE design INNER Mongolia Zhungeer BANNER
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NOVEL WEIGHTED LEAST SQUARES SUPPORT VECTOR REGRESSION FOR THRUST ESTIMATION ON PERFORMANCE DETERIORATION OF AERO-ENGINE 被引量:2
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作者 苏伟生 赵永平 孙健国 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2012年第1期25-32,共8页
A thrust estimator with high precision and excellent real-time performance is needed to mitigate perfor- mance deterioration for future aero-engines. A weight least squares support vector regression is proposed using ... A thrust estimator with high precision and excellent real-time performance is needed to mitigate perfor- mance deterioration for future aero-engines. A weight least squares support vector regression is proposed using a novel weighting strategy. Then a thrust estimator based on the proposed regression is designed for the perfor- mance deterioration. Compared with the existing weighting strategy, the novel one not only satisfies the require- ment of precision but also enhances the real-time performance. Finally, numerical experiments demonstrate the effectiveness and feasibility of the proposed weighted least squares support vector regression for thrust estimator. Key words : intelligent engine control; least squares ; support vector machine ; performance deterioration 展开更多
关键词 intelligent engine control least squares support vector machine performance deterioration
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BOOSTING SPARSE LEAST SQUARES SUPPORT VECTOR REGRESSION (BSLSSVR) AND ITS APPLICATION TO THRUST ESTIMATION 被引量:2
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作者 赵永平 孙健国 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2008年第4期254-261,共8页
In order to realize direct thrust control instead of conventional sensors-based control for aero-engine, a thrust estimator with high accuracy is designed by using the boosting technique to improve the performance of ... In order to realize direct thrust control instead of conventional sensors-based control for aero-engine, a thrust estimator with high accuracy is designed by using the boosting technique to improve the performance of least squares support vector regression (LSSVR). There exist two distinct features compared with the conven- tional boosting technique: (1) Sampling without replacement is used to avoid numerical instability for modeling LSSVR. (2) To realize the sparseness of LSSVR and reduce the computational complexity, only a subset of the training samples is used to construct LSSVR. Thus, this boosting method for LSSVR is called the boosting sparse LSSVR (BSLSSVR). Finally, simulation results show that BSLSSVR-based thrust estimator can satisfy the requirement of direct thrust control, i.e. , maximum absolute value of relative error of thrust estimation is not more than 5‰. 展开更多
关键词 least squares support vector machines direct thrust control boosting technique
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An Effective Multiple Model Least Squares Method in Tracking of a Maneuvering Target 被引量:3
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作者 杨位钦 贾朝晖 《Journal of Beijing Institute of Technology》 EI CAS 1995年第1期35+29-34,共7页
A polynomial model, time origin shifting model(TOSM, is used to describe the trajectory of a moving target .Based on TOSM, a recursive laeast squares(RLS) algorithm with varied forgetting factor is derived for tracki... A polynomial model, time origin shifting model(TOSM, is used to describe the trajectory of a moving target .Based on TOSM, a recursive laeast squares(RLS) algorithm with varied forgetting factor is derived for tracking of a non-maneuvering target. In order to apply this algorithm to maneuvering targets tracking ,a tracking signal is performed on-line to determine what kind of TOSm will be in effect to track a target with different dynamics. An effective multiple model least squares filtering and forecasting method dadpted to real tracking of a maneuvering target is formulated. The algorithm is computationally more effcient than Kalman filter and the percentage improvement from simulations show both of them are considerably alike to some extent. 展开更多
关键词 Kalman filters tracking/recursive least squares maneuvering target polynomial model forgetting factor
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Semi-supervised least squares support vector machine algorithm:application to offshore oil reservoir 被引量:1
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作者 罗伟平 李洪奇 石宁 《Applied Geophysics》 SCIE CSCD 2016年第2期406-415,421,共11页
At the early stages of deep-water oil exploration and development, fewer and further apart wells are drilled than in onshore oilfields. Supervised least squares support vector machine algorithms are used to predict th... At the early stages of deep-water oil exploration and development, fewer and further apart wells are drilled than in onshore oilfields. Supervised least squares support vector machine algorithms are used to predict the reservoir parameters but the prediction accuracy is low. We combined the least squares support vector machine (LSSVM) algorithm with semi-supervised learning and established a semi-supervised regression model, which we call the semi-supervised least squares support vector machine (SLSSVM) model. The iterative matrix inversion is also introduced to improve the training ability and training time of the model. We use the UCI data to test the generalization of a semi-supervised and a supervised LSSVM models. The test results suggest that the generalization performance of the LSSVM model greatly improves and with decreasing training samples the generalization performance is better. Moreover, for small-sample models, the SLSSVM method has higher precision than the semi-supervised K-nearest neighbor (SKNN) method. The new semi- supervised LSSVM algorithm was used to predict the distribution of porosity and sandstone in the Jingzhou study area. 展开更多
关键词 Semi-supervised learning least squares support vector machine seismic attributes reservoir prediction
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Analysis of Current Situation and Countermeasures of Plant Landscapes on Tianjin Urban Squares of China
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作者 孟瑾 陈良 +1 位作者 王月 刘志波 《Journal of Landscape Research》 2011年第11期29-31,35,共4页
Through the survey of plant landscapes on eight representative squares in Tianjin City,the paper had pointed out that plant landscapes on Tianjin squares were improper in terms of plants richness,cultivation layer and... Through the survey of plant landscapes on eight representative squares in Tianjin City,the paper had pointed out that plant landscapes on Tianjin squares were improper in terms of plants richness,cultivation layer and color change.It had suggested selecting regional characteristic tree species,applying salt-tolerant plants,emphasizing the diversity of plants species,highlighting the application of towering arbors,stressing the use of color-leaved plants,and creating abundant plant communities,so as to provide citizens with a more practical and ornamental square landscape environment through improving plant landscapes on squares in Tianjin City. 展开更多
关键词 TIANJIN City squarE Plant LANDSCAPE Current SITUATION COUNTERMEASURES
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A stabilized least-squares imaging condition with structure constraints
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作者 刘国昌 陈小宏 +1 位作者 宋建勇 芮振华 《Applied Geophysics》 SCIE CSCD 2012年第4期459-467,496,共10页
Conventional shot-gather migration uses a cross-correlation imaging condition proposed by Clarebout (1971), which cannot preserve imaging amplitudes. The deconvolution imaging condition can improve the imaging ampli... Conventional shot-gather migration uses a cross-correlation imaging condition proposed by Clarebout (1971), which cannot preserve imaging amplitudes. The deconvolution imaging condition can improve the imaging amplitude and compensate for illumination. However, the deconvolution imaging condition introduces instability issues. The least-squares imaging condition first computes the sum of the cross-correlation of the forward and backward wavefields over all frequencies and sources, and then divides the result by the total energy of the forward wavefield. Therefore, the least-squares imaging condition is more stable than the classic imaging condition. However, the least-squares imaging condition cannot provide accurate results in areas where the illumination is very poor and unbalanced. To stabilize the least-squares imaging condition and balance the imaging amplitude, we propose a novel imaging condition with structure constraints that is based on the least-squares imaging condition. Our novel imaging condition uses a plane wave construction that constrains the imaging result to be smooth along geological structure boundaries in the inversion frame. The proposed imaging condition improves the stability of the imaging condition and balances the imaging amplitude. The proposed condition is applied to two examples, the horizontal layered model and the Sigsbee 2A model. These tests show that, in comparison to the damped least-squares imaging condition, the stabilized least-squares imaging condition with structure constraints improves illumination stability and balance, makes events more consecutive, adjusts the amplitude of the depth layers where the illumination is poor and unbalanced, suppresses imaging artifacts, and is conducive to amplitude preserving imaging of deep layers. 展开更多
关键词 Imaging condition least squares plane wave construction operator local event slopes
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Application of Eastern River Culture on Squares of Yuncheng City
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作者 程朝霞 《Journal of Landscape Research》 2009年第11期23-26,共4页
Taking South-wind Square in Yuncheng City for an example,the application of Eastern River Culture as a kind of regional culture in the construction of urban squares were analyzed in this study,to provide references fo... Taking South-wind Square in Yuncheng City for an example,the application of Eastern River Culture as a kind of regional culture in the construction of urban squares were analyzed in this study,to provide references for the future construction of squares in this city. 展开更多
关键词 EASTERN RIVER CULTURE Urban squarE Regional CULTURE South-wind squarE
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PSR-SQUARES:基于程序空间约简器的SQL逆向合成系统
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作者 窦全胜 张顺 +2 位作者 潘浩 王荟贤 唐焕玲 《通信学报》 EI CSCD 北大核心 2023年第11期249-259,共11页
针对SQUARES程序空间增长过快,导致程序合成效率偏低的问题,在SQUARES的基础上,增加了以深度神经网络为核心的程序空间约简器,将给定的<被查询表,查询结果>示例表示成二维张量,作为深度神经网络的输入,网络的输出是关于目标SQL语... 针对SQUARES程序空间增长过快,导致程序合成效率偏低的问题,在SQUARES的基础上,增加了以深度神经网络为核心的程序空间约简器,将给定的<被查询表,查询结果>示例表示成二维张量,作为深度神经网络的输入,网络的输出是关于目标SQL语句合成规则的相关性标记向量。约简器根据神经网络的输出结果,采用末N位淘汰策略,删除与目标SQL语句相关性弱的合成规则,以减少候选SQL语句的生成和验证,提升系统合成效率。对约简器中深度神经网络的结构设计、训练样本集的生成方法和网络训练过程进行了详细描述。同时将PSR-SQUARES与当前有代表性SQL逆向合成系统进行实验对比,实验结果表明,PSR-SQUARES的综合性能不同程度地优于其他合成系统,平均合成时间由SQUARES的251 s降低至130 s,目标程序合成成功率由80%提升至89%。 展开更多
关键词 程序合成 SQL逆向合成 squares 程序空间约简器 领域特定语言
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Constrained least squares algorithm for channel vector estimation in 2-D RAKE receiver
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作者 王建明 赵春明 《Journal of Southeast University(English Edition)》 EI CAS 2003年第1期1-4,共4页
Based on the fact that the variation of tile direction of arrival (DOA) isslower than that of the channel fading, the steering vector of the desired signal is estimatedfirstly using a subspace decomposition method and... Based on the fact that the variation of tile direction of arrival (DOA) isslower than that of the channel fading, the steering vector of the desired signal is estimatedfirstly using a subspace decomposition method and then a constrained condition is configured.Traffic signals are further employed to estimate the channel vector based on the constrained leastsquares criterion. We use the iterative least squares with projection (ILSP) algorithm initializedby the pilot to get the estimation. The accuracy of channel estimation and symbol detection can beprogressively increased through the iteration procedure of the ILSP algorithm. Simulation resultsdemonstrate that the proposed algorithm improves the system performance effectively compared withthe conventional 2-D RAKE receiver. 展开更多
关键词 2-D RAKE receiver channel estimation subspace decomposition constrained least squares
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Least-Squares及Galerkin谱元方法求解环形区域内的泊松方程 被引量:1
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作者 王亚洲 秦国良 《西安交通大学学报》 EI CAS CSCD 北大核心 2017年第5期121-127,共7页
为研究基于Least-Squares变分及Galerkin变分两种形式的谱元方法的求解特性,推导了极坐标系中采用两种变分方法求解环形区域内Poisson方程时对应的弱解形式,采用Chebyshev多项式构造插值基函数进行空间离散,得到两种谱元方法对应的代数... 为研究基于Least-Squares变分及Galerkin变分两种形式的谱元方法的求解特性,推导了极坐标系中采用两种变分方法求解环形区域内Poisson方程时对应的弱解形式,采用Chebyshev多项式构造插值基函数进行空间离散,得到两种谱元方法对应的代数方程组,由此分析了系数矩阵结构的特点。数值计算结果显示:Least-Squares谱元方法为实现方程的降阶而引入新的求解变量,使得代数方程组形式更为复杂,但边界条件的处理比Galerkin谱元方法更为简单;两种谱元方法均能求解极坐标系中的Poisson方程且能获得高精度的数值解,二者绝对误差分布基本一致;固定单元内的插值阶数时,增加单元数可减小数值误差,且表现出代数精度的特点,误差降低速度较慢,而固定单元数时,在一定范围内数值误差随插值阶数的增加而减小的速度更快,表现出谱精度的特点;单元内插值阶数较高时,代数方程组系数矩阵的条件数急剧增多,方程组呈现病态,数值误差增大,这一特点限制了单元内插值阶数的取值。研究内容对深入了解两种谱元方法在极坐标系中求解Poisson方程时的特点、进一步采用相关分裂算法求解实际流动问题具有参考价值。 展开更多
关键词 Least-squares变分 Galerkin变分 谱元方法 POISSON方程 极坐标系
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