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单双目近景摄影测量联合监测弱胶结覆岩叠合式相似材料模型研究
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作者 张国建 臧耿晨 +4 位作者 郭广礼 李怀展 杨向升 王荟钦 于承新 《中国矿业》 北大核心 2024年第3期113-123,共11页
相似材料模型是研究矿山开采岩层运动的重要手段,随着采深的增大,多采区采动联合影响的区域变形响应问题逐渐成为关注的焦点。为了克服常规相似材料模型研究深部开采问题的结果失真,以及常规监测技术在观测相似材料模型整体动态变形及... 相似材料模型是研究矿山开采岩层运动的重要手段,随着采深的增大,多采区采动联合影响的区域变形响应问题逐渐成为关注的焦点。为了克服常规相似材料模型研究深部开采问题的结果失真,以及常规监测技术在观测相似材料模型整体动态变形及任意点动态变形的不足,本文提出叠合式相似材料模拟的新思路,并采用单双目近景摄影测量联合监测新技术研究弱胶结覆岩运动规律。实验结果表明,叠合式相似材料模拟充分考虑了相似原理及覆岩中的关键层结构,研究结果更加可靠,基于等距虚拟面的数字摄影技术监测精度达到0.12 mm,能够满足大几何相似比物理模型的监测精度。通过研究深部矿区覆岩破坏规律发现,宽深比为0.85是白垩系砂岩的临界破坏点,采空区面长大于临界尺寸时将导致显著的冲击地压甚至矿震。单双目近景摄影测量联合监测新方法为研究深部开采区域性岩层移动响应过程提供了技术支持。 展开更多
关键词 弱胶结覆岩 叠合式相似材料模型 近景摄影测量 岩层移动 动态监测
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基于改进型启发式相似度模型的协同过滤推荐方法 被引量:3
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作者 张南 林晓勇 史晟辉 《计算机应用》 CSCD 北大核心 2016年第8期2246-2251,2281,共7页
为提高协同过滤推荐方法的准确性和有效性,提出一种基于改进型启发式相似度模型的协同过滤推荐方法 PSJ。该方法考虑了用户评分差值、用户全局评分偏好和用户共同评分物品数三个因素。PSJ方法的Proximity因子使用指数函数反映用户评分... 为提高协同过滤推荐方法的准确性和有效性,提出一种基于改进型启发式相似度模型的协同过滤推荐方法 PSJ。该方法考虑了用户评分差值、用户全局评分偏好和用户共同评分物品数三个因素。PSJ方法的Proximity因子使用指数函数反映用户评分差值对用户相似度的影响,这样也可避免零除问题;将NHSM方法中的Significance因子和URP因子合并成PSJ方法的Significance因子,这使得PSJ方法的计算复杂度低于NHSM方法;而且为了提高在数据稀疏情况下的推荐效果,PSJ方法同时考虑了用户间的评分差值和用户全局评分两个因素。实验采用Top-k推荐中的查准率和查全率作为衡量标准。实验结果表明,当推荐物品数大于20时,与NHSM、杰卡尔德算法、自适应余弦相似度(ACOS)算法、杰卡尔德均方差(JMSD)算法和皮尔逊相关系数算法(SPCC)相比,PSJ方法的查准率与查全率均有提升。 展开更多
关键词 协同过滤推荐方法 启发式相似度模型 用户相似 推荐效果 数据稀疏
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二阶常系数齐次线性微分方程边值问题的解的相似结构 被引量:29
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作者 李顺初 《西华大学学报(自然科学版)》 CAS 2007年第1期84-85,共2页
通过对常系数齐次线性微分方程边值问题的解析表达式进行整理和简化,得到了解式的相似结构形式,说明了该类微分方程的解具有类似于实数可表为连分式、图形具有相似性的所谓式相似性质,指出了解式的相似性质的研究有利于进一步分析解的... 通过对常系数齐次线性微分方程边值问题的解析表达式进行整理和简化,得到了解式的相似结构形式,说明了该类微分方程的解具有类似于实数可表为连分式、图形具有相似性的所谓式相似性质,指出了解式的相似性质的研究有利于进一步分析解的内在规律,解决相应的应用问题,方便编制相应的分析软件。它是微分方程理论的新发展。 展开更多
关键词 常微分方程 常系数 二阶齐次线性方程 边值问题 相似结构 式相似
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二阶齐次线性微分方程的边值问题的解的相似结构 被引量:27
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作者 李顺初 《西华大学学报(自然科学版)》 CAS 2009年第5期40-41,90,共3页
通过对二阶齐次线性微分方程边值问题的解析表达式进行整理和简化,得到了解式的相似结构形式;说明了该类微分方程的解,具有类似于实数可表为连分式,图形具有相似性的所谓式相似性质;指出了解式的相似性质的研究,有利于进一步地分析解的... 通过对二阶齐次线性微分方程边值问题的解析表达式进行整理和简化,得到了解式的相似结构形式;说明了该类微分方程的解,具有类似于实数可表为连分式,图形具有相似性的所谓式相似性质;指出了解式的相似性质的研究,有利于进一步地分析解的内在规律,解决相应的应用问题,方便编写相应的分析软件;它是微分方程理论的新发展。 展开更多
关键词 常微分方程 二阶齐次线性方程 边值问题 相似结构 式相似
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基于分流式结构的锂离子动力电池热管理系统研究
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作者 张瀚文 《内燃机与配件》 2022年第9期95-97,共3页
锂离子动力电池作为目前纯电动汽车使用的最主要的动力电池类型,其性能、寿命、成本、安全性对电动汽车的发展具有决定性作用,锂离子动力电池的运行温度对其性能、寿命、安全性等有重要影响,因此,电池的热管理系统便至关重要,本文针对... 锂离子动力电池作为目前纯电动汽车使用的最主要的动力电池类型,其性能、寿命、成本、安全性对电动汽车的发展具有决定性作用,锂离子动力电池的运行温度对其性能、寿命、安全性等有重要影响,因此,电池的热管理系统便至关重要,本文针对方形锂离子动力电池,基于板式和分流式热沉结构,设计了专门的冷却结构,单个冷板采用了自相似热沉结构,由三层结构构成,包含中间的分流通道层和两个对称的溢流通道层。 展开更多
关键词 锂离子动力电池热管理 冷板 分流相似微通道冷板 换热均匀性 数值模拟
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On similarity measures of interval-valued intuitionistic fuzzy sets and their application to pattern recognitions 被引量:29
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作者 徐泽水 《Journal of Southeast University(English Edition)》 EI CAS 2007年第1期139-143,共5页
The concept of the degree of similarity between interval-valued intuitionistic fuzzy sets (IVIFSs) is introduced, and some distance measures between IVIFSs are defined based on the Hamming distance, the normalized H... The concept of the degree of similarity between interval-valued intuitionistic fuzzy sets (IVIFSs) is introduced, and some distance measures between IVIFSs are defined based on the Hamming distance, the normalized Hamming distance, the weighted Hamming distance, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance, etc. Then, by combining the Hausdorff metric with the Hamming distance, the Euclidean distance and their weighted versions, two other similarity measures between IVIFSs, i. e., the weighted Hamming distance based on the Hausdorff metric and the weighted Euclidean distance based on the Hausdorff metric, are defined, and then some of their properties are studied. Finally, based on these distance measures, some similarity measures between IVIFSs are defined, and the similarity measures are applied to pattern recognitions with interval-valued intuitionistic fuzzy information. 展开更多
关键词 interval-valued intuitionistic fuzzy set SIMILARITY pattern recognition
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Mining maximal pattern-based subspace clusters in high dimensional space
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作者 卢炎生 胡蓉 +1 位作者 邹磊 周翀 《Journal of Southeast University(English Edition)》 EI CAS 2006年第4期490-495,共6页
The problem of pattern-based subspace clustering, a special type of subspace clustering that uses pattern similarity as a measure of similarity, is studied. Unlike most traditional clustering algorithms that group the... The problem of pattern-based subspace clustering, a special type of subspace clustering that uses pattern similarity as a measure of similarity, is studied. Unlike most traditional clustering algorithms that group the close values of objects in all the dimensions or a set of dimensions, clustering by pattern similarity shows an interesting pattern, where objects exhibit a coherent pattern of rise and fall in subspaces. A novel approach, named EMaPle to mine the maximal pattern-based subspace clusters, is designed. The EMaPle searches clusters only in the attribute enumeration spaces which are relatively few compared to the large number of row combinations in the typical datasets, and it exploits novel pruning techniques. EMaPle can find the clusters satisfying coherent constraints, size constraints and sign constraints neglected in MaPle. Both synthetic data sets and real data sets are used to evaluate EMaPle and demonstrate that it is more effective and scalable than MaPle. 展开更多
关键词 subspace clustering pattern similarity maximal pattern-based subspace clusters
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一种基于哈夫曼判定的蛋白质分类方法
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作者 何红洲 周明天 《计算机工程》 CAS CSCD 2013年第12期181-185,190,共6页
已有的仿射传播聚类算法不能很好地反映复杂蛋白质序列本身的聚类结构。为此,提出一种基于哈夫曼判定的蛋白质分类方法。在计算广义置换式匹配相似度的基础上,使用已有的自适应仿射传播算法聚类蛋白质序列。采用哈夫曼编码方法,通过限... 已有的仿射传播聚类算法不能很好地反映复杂蛋白质序列本身的聚类结构。为此,提出一种基于哈夫曼判定的蛋白质分类方法。在计算广义置换式匹配相似度的基础上,使用已有的自适应仿射传播算法聚类蛋白质序列。采用哈夫曼编码方法,通过限制平均码长使聚类结果能反映蛋白质序列家族的聚类结构。在蛋白质同源聚类数据库和蛋白质结构分类数据库的6个数据集上进行实验,结果表明,该方法与adAP、谱聚类、SMS和TribeMCL方法相比,不仅能获得更接近于数据集家族的聚类数目及更紧凑的聚类结构,而且F-measure指标平均估值分别高出19.67%、8.7%、9.5%和43.51%。 展开更多
关键词 聚类分析 蛋白质序列 广义置换匹配相似 仿射传播聚类 哈夫曼判定 F-measure指标
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Modeling and monitoring of nonlinear multi-mode processes based on similarity measure-KPCA 被引量:9
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作者 WANG Xiao-gang HUANG Li-wei ZHANG Ying-wei 《Journal of Central South University》 SCIE EI CAS CSCD 2017年第3期665-674,共10页
A new modeling and monitoring approach for multi-mode processes is proposed.The method of similarity measure(SM) and kernel principal component analysis(KPCA) are integrated to construct SM-KPCA monitoring scheme,wher... A new modeling and monitoring approach for multi-mode processes is proposed.The method of similarity measure(SM) and kernel principal component analysis(KPCA) are integrated to construct SM-KPCA monitoring scheme,where SM method serves as the separation of common subspace and specific subspace.Compared with the traditional methods,the main contributions of this work are:1) SM consisted of two measures of distance and angle to accommodate process characters.The different monitoring effect involves putting on the different weight,which would simplify the monitoring model structure and enhance its reliability and robustness.2) The proposed method can be used to find faults by the common space and judge which mode the fault belongs to by the specific subspace.Results of algorithm analysis and fault detection experiments indicate the validity and practicability of the presented method. 展开更多
关键词 process monitoring kernel principal component analysis (KPCA) similarity measure subspace separation
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Incremental semi-supervised learning for intelligent seismic facies identification 被引量:1
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作者 He Su-Mei Song Zhao-Hui +2 位作者 Zhang Meng-Ke Yuan San-Yi Wang Shang-Xu 《Applied Geophysics》 SCIE CSCD 2022年第1期41-52,144,共13页
Intelligent seismic facies identification based on deep learning can alleviate the time-consuming and labor-intensive problem of manual interpretation,which has been widely applied.Supervised learning can realize faci... Intelligent seismic facies identification based on deep learning can alleviate the time-consuming and labor-intensive problem of manual interpretation,which has been widely applied.Supervised learning can realize facies identification with high efficiency and accuracy;however,it depends on the usage of a large amount of well-labeled data.To solve this issue,we propose herein an incremental semi-supervised method for intelligent facies identification.Our method considers the continuity of the lateral variation of strata and uses cosine similarity to quantify the similarity of the seismic data feature domain.The maximum-diff erence sample in the neighborhood of the currently used training data is then found to reasonably expand the training sets.This process continuously increases the amount of training data and learns its distribution.We integrate old knowledge while absorbing new ones to realize incremental semi-supervised learning and achieve the purpose of evolving the network models.In this work,accuracy and confusion matrix are employed to jointly control the predicted results of the model from both overall and partial aspects.The obtained values are then applied to a three-dimensional(3D)real dataset and used to quantitatively evaluate the results.Using unlabeled data,our proposed method acquires more accurate and stable testing results compared to conventional supervised learning algorithms that only use well-labeled data.A considerable improvement for small-sample categories is also observed.Using less than 1%of the training data,the proposed method can achieve an average accuracy of over 95%on the 3D dataset.In contrast,the conventional supervised learning algorithm achieved only approximately 85%. 展开更多
关键词 seismic facies identification semi-supervised learning incremental learning cosine similarity
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SERVICE COMMUNITY CONSTRUCTION METHOD OF INTERNET OF THINGS BASED ON SEMANTIC SIMILARITY 被引量:1
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作者 Wang Yang Zhang Linjing +2 位作者 Huang Yakun Zhao Baohua Zhao Chuanxin 《Journal of Electronics(China)》 2013年第1期49-56,共8页
Internet of Things (IoT) as an important and ubiquitous service paradigm is one of the most important issues in IoT applications to provide terminal users with effective and efficient services based on service communi... Internet of Things (IoT) as an important and ubiquitous service paradigm is one of the most important issues in IoT applications to provide terminal users with effective and efficient services based on service community. This paper presents a semantic-based similarity algorithm to build the IoT service community. Firstly, the algorithm reflects that the nodes of IoT contain a wealth of semantic information and makes them to build into the concept tree. Then tap the similarity of the semantic information based on the concept tree. Finally, we achieve the optimization of the service community through greedy algorithm and control the size of the service community by adjusting the threshold. Simulation results show the effectiveness and feasibility of this algorithm. 展开更多
关键词 Internet of Things (IoT) Service community Semantic similarity Concept tree
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A New Procedure to Solve the Non-Linear Reaction-Diffusion Equation
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作者 吴燕翔 王良恩 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2000年第1期92-94,共3页
1 INTRODUCTIONThe concentration distribution of reactant in porouscatalyst pellet not only is the basis of calculating theeffectiveness factor,but also has a great significancein investigating the reaction and mass tr... 1 INTRODUCTIONThe concentration distribution of reactant in porouscatalyst pellet not only is the basis of calculating theeffectiveness factor,but also has a great significancein investigating the reaction and mass transfer in thecatalyst pellet.In principle,the concentration distri-bution and the effectiveness factor of a catalyst pelletcan be obtained by solving the reaction-diffusion equation.However,most of the differential equations haveno analytical solution except for some simple cases.The previous investigators have made great efforts to calculate the effectiveness factors of catalysts.They first obtained asymptotic solutions of effective-ness factor in the cases of the Thiele modulus φ→Oand φ→oo by means of perturbation method,thensynthesized the information of the asymptotic solu- 展开更多
关键词 reaction-diffusion equation SOLUTION similarity transformation perturbation analysis effectiveness factor
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SHAPE-BASED TIME SERIES SIMILARITY MEASURE AND PATTERN DISCOVERY ALGORITHM
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作者 ZengFanzi QiuZhengding +1 位作者 LiDongsheng YueJianhai 《Journal of Electronics(China)》 2005年第2期142-148,共7页
Pattern discovery from time series is of fundamental importance. Most of the algorithms of pattern discovery in time series capture the values of time series based on some kinds of similarity measures. Affected by the... Pattern discovery from time series is of fundamental importance. Most of the algorithms of pattern discovery in time series capture the values of time series based on some kinds of similarity measures. Affected by the scale and baseline, value-based methods bring about problem when the objective is to capture the shape. Thus, a similarity measure based on shape, Sh measure, is originally proposed, andthe properties of this similarity and corresponding proofs are given. Then a time series shape pattern discovery algorithm based on Sh measure is put forward. The proposed algorithm is terminated in finite iteration with given computational and storage complexity. Finally the experiments on synthetic datasets and sunspot datasets demonstrate that the time series shape pattern algorithm is valid. 展开更多
关键词 Shape similarity measure Pattern discovery algorithm Time series data mining
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Statistical Superposition of Crosstalk Effects in Cable Bundles
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作者 Diego Bellan Sergio A.Pignari 《China Communications》 SCIE CSCD 2013年第11期119-128,共10页
This paper deals with the analytical derivation of phasor-domain statistical properties of crosstalk in random wire cables due to the superposition of several sources of electromagnetic interference.In this study,stat... This paper deals with the analytical derivation of phasor-domain statistical properties of crosstalk in random wire cables due to the superposition of several sources of electromagnetic interference.In this study,statistical characterization of crosstalk in cable bundles,which is available in literature for the case of one source of interference,is extended to the case of several sources operating simultaneously.The superposition of crosstalk effects is analysed in statistical terms,also taking into account the correlation between crosstalk contributions.A further random contribution,which is included in the proposed statistical model,is given by the phase relationship between the sources of interference.Analytical approximate expressions for the crosstalk mean value,variance,and probability density function are derived as functions of the cable bundle features and sources. 展开更多
关键词 CROSSTALK multiconductor transmi-ssion lines cable bundles statistical modelling
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Self-Organizing Mechanism for Cloud Services and Performance Analysis 被引量:1
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作者 Zhang Changyou Shao Lixiang +2 位作者 Li Wenqing Li Hangtong Chen Sicong 《China Communications》 SCIE CSCD 2012年第6期135-144,共10页
To improve the performance and robustness in service discovery, a self-organizing mechanism for service alliances of Service Providers (SPs) is proposed in this paper. According to the similarity of service content, a... To improve the performance and robustness in service discovery, a self-organizing mechanism for service alliances of Service Providers (SPs) is proposed in this paper. According to the similarity of service content, an SP publishes its services in a partition of SPs to construct connections between highly similar SPs. These SPs constitute a self-organized distributed environment. A self-organizing protocol is designed to ensure the correctness of the construction of the alliances. The protocol consists of four stages - initiating stage, developing stage, developed stage and degradation stage. The experimental results demonstrate that this protocol ensures the self-property. The visualization of alliance developing stages illustrates that sub-alliances are sp lit in balance and self-connected. Compared with the Random Walker algorithm, the time cost and the number of forwarded messages in alliance-based mechanism is lower in service discovery. On three typical topologies (Grid, Random-Graph, Power-Law), the success rate of service discovery is much higher, which shows that self-organized alliances are helpful to enhance the discovery performance. 展开更多
关键词 Kecloud service SELF-ORGANIZING alliance-based PERFORMANCE
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How similar are annual and summer temperature variability in central Sweden?
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作者 ZHANG Peng Deliang CHEN +1 位作者 Hans W.LINDERHOLM ZHANG Qiong 《Advances in Climate Change Research》 SCIE CSCD 2015年第3期159-170,共12页
Tree-ring based temperature reconstructions have successfully inferred the past inter-annual to millennium scales summer temperature variability. A clear relationship between annual and summer temperatures can provide... Tree-ring based temperature reconstructions have successfully inferred the past inter-annual to millennium scales summer temperature variability. A clear relationship between annual and summer temperatures can provide insights into tile variability of past annual mean tem- perature from the reconstructed summer temperature. However, how similar are summer and annual temperatures is to a large extent still unknown. This study aims at investigating the relationship between annual and summer temperatures at different timescales in central Sweden during the last millennium. The temperature variability in central Sweden can represent large parts of Scandinavia which has been a key region for dendroclimatological research. The observed annual and summer temperatures during 1901-2005 were firstly decomposed into different frequency bands using ensemble empirical mode decomposition (EEMD) method, and then the scale-dependent relationship was quantified using Pearson correlation coefficients. The relationship between the observed annual and summer temperatures determined by the instrumental data was subsequently used to evaluate 7 climate models. The model with the best performance was used to infer the relationship for the last millennium. The results show that the relationship between the observed annual and summer temperatures becomes stronger as the timescale increases, except for the 4--16 years timescales at which it does not show any relationship. The summer temperature variability at short timescales (2--4 years) shows much higher variance than the annual variability, while the annual temperature variability at long timescales (〉32 years) has a much higher variance than the summer one. During the last millennium, the simulated summer temperature also shows higher variance at the short timescales (2-4 years) and lower variance at the long timescales (〉1024 years) than those of the annual temperature. The relationship between the two temperatures is generally close at the long timescales, and weak at the short timescales. Overall the summer temperature variability cannot well reflect the annual mean temperature variability for the study region during both the 20th century and the last millennium. Furthermore, all the climate models examined overestimate the annual mean temperature variance at the 2--4 years timescales, which indicates that the overestimate could be one of reasons why the volcanic eruption induced cooling is larger in climate models than in proxy data. 展开更多
关键词 Annual temperature Summer temperature Central Sweden Climate model simulation Scale-dependent similarity
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Novel similarity measures for face representation based on local binary pattern
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作者 祝世虎 封举富 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2009年第2期223-226,共4页
The successful face recognition based on local binary pattern(LBP)relies on the effective extraction of LBP features and the inferring of similarity between the extracted features.In this paper,we focus on the latter ... The successful face recognition based on local binary pattern(LBP)relies on the effective extraction of LBP features and the inferring of similarity between the extracted features.In this paper,we focus on the latter and propose two novel similarity measures for the local matching methods and the holistic matching methods respectively.One is Earth Mover's Distance with Hamming and Lp ground distance(EMD-HammingLp),which is a cross-bin dissimilarity measure for LBP histograms.The other is IMage Hamming Distance(IMHD),which is a dissimilarity measure for the whole LBP images.Experiments on FERET database show that the proposed two similarity measures outperform the state-of-the-art Chi-square similarity measure for extraction of LBP features. 展开更多
关键词 similarity measurement local binary pattern Earth Mover's Distance IMage Euclidean Distance
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Quantum entanglement of the binomial field interacting with a cascade three-level atom beyond the rotating wave approximation 被引量:6
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作者 PEN XueZao CONG HongLu +1 位作者 WANG XuWen XIA JianPing 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2011年第9期1625-1630,共6页
In this paper, the quantum entanglement between a single mode binomial field and a cascade three-level atom is calculated mechanically without the rotating wave approximation. The numerical results indicate that the q... In this paper, the quantum entanglement between a single mode binomial field and a cascade three-level atom is calculated mechanically without the rotating wave approximation. The numerical results indicate that the quantum entanglement at the first few periods is reduced notably due to the fact that the atom is initially in the superposition state. With increasing field parameter 17, the period of the entanglement evolution becomes obvious and the quantum decoherence phenomenon emerges in a short time. 展开更多
关键词 binomial state field quantum entanglement field entropy
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Monitoring correlative financial data streams by local pattern similarity
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作者 Tao JIANG Yu-cai FENG +3 位作者 Bin ZHANG Zhong-sheng CAO Ge FU Jie SHI 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2009年第7期937-951,共15页
Developing tools for monitoring the correlations among thousands of financial data streams in an online fashion can be interesting and useful work. We aimed to find highly correlative financial data streams in local p... Developing tools for monitoring the correlations among thousands of financial data streams in an online fashion can be interesting and useful work. We aimed to find highly correlative financial data streams in local patterns. A novel distance metric function slope duration distance (SDD) is proposed, which is compatible with the characteristics of actual financial data streams. Moreover, a model monitoring correlations among local patterns (MCALP) is presented, which dramatically decreases the computational cost using an algorithm quickly online segmenting and pruning (QONSP) with O(1) time cost at each time tick t, and our proposed new grid structure. Experimental results showed that MCALP provides an improvement of several orders of magnitude in performance relative to traditional naive linear scan techniques and maintains high precision. Furthermore, the model is incremental, parallelizable, and has a quick response time. 展开更多
关键词 Data mining Model Data streams Correlation Local pattern Pattern similarity
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New Similarity Reduction Solutions for the(2+1)-Dimensional Nizhnik-Novikov-Veselov Equation 被引量:1
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作者 智红燕 《Communications in Theoretical Physics》 SCIE CAS CSCD 2013年第3期263-267,共5页
In this paper,some new formal similarity reduction solutions for the(2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived.Firstly,we derive the similarity reduction of the NNV equation with the optimal system... In this paper,some new formal similarity reduction solutions for the(2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived.Firstly,we derive the similarity reduction of the NNV equation with the optimal system of the admitted one-dimensional subalgebras.Secondly,by analyzing the reduced equation,three types of similarity solutions are derived,such as multi-soliton like solutions,variable separations solutions,and KdV type solutions. 展开更多
关键词 similarity reduction solution (2+1)-dimensional Nizknik-Novikov-Veselov equation multi-solitonlike solution
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