Aiming at the problems of the traditional method of assessing distribution of particle size in bench blasting, a support vector machines （SVMs） regression methodology was used to predict the mean particle size （X50...Aiming at the problems of the traditional method of assessing distribution of particle size in bench blasting, a support vector machines （SVMs） regression methodology was used to predict the mean particle size （X50） resulting from rock blast fragmentation in various mines based on the statistical learning theory. The data base consisted of blast design parameters, explosive parameters, modulus of elasticity and in-situ block size. The seven input independent variables used for the SVMs model for the prediction of X50 of rock blast fragmentation were the ratio of bench height to drilled burden （H/B）, ratio of spacing to burden （S/B）, ratio of burden to hole diameter （B/D）, ratio of stemming to burden （T/B）, powder factor （Pf）, modulus of elasticity （E） and in-situ block size （XB）. After using the 90 sets of the measured data in various mines and rock formations in the world for training and testing, the model was applied to 12 another blast data for validation of the trained support vector regression （SVR） model. The prediction results of SVR were compared with those of artificial neural network （ANN）, multivariate regression analysis （MVRA） models, conventional Kuznetsov method and the measured X50 values. The proposed method shows promising results and the prediction accuracy of SVMs model is acceptable.展开更多
In the present paper we obtain the following result: Theorem Let M^R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold N^(n+p)(p>1). If the...In the present paper we obtain the following result: Theorem Let M^R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold N^(n+p)(p>1). If then M^n lies in a totally geodesic submanifold N^(n+1).展开更多
标记分布学习是近年来提出的一种新的机器学习范式,它能很好地解决某些标记多义性的问题。现有的标记分布学习算法均利用条件概率建立参数模型,但未能充分利用特征和标记间的联系。本文考虑到特征相似的样本所对应的标记分布也应当相似...标记分布学习是近年来提出的一种新的机器学习范式,它能很好地解决某些标记多义性的问题。现有的标记分布学习算法均利用条件概率建立参数模型,但未能充分利用特征和标记间的联系。本文考虑到特征相似的样本所对应的标记分布也应当相似,利用原型聚类的k均值算法(k-means),将训练集的样本进行聚类,提出基于kmeans算法的标记分布学习(label distribution learning based on k-means algorithm,LDLKM)。首先通过聚类算法kmeans求得每一个簇的均值向量,然后分别求得对应标记分布的均值向量。最后将测试集和训练集的均值向量间的距离作为权重,应用到对测试集标记分布的预测上。在6个公开的数据集上进行实验,并与3种已有的标记分布学习算法在5种评价指标上进行比较,实验结果表明提出的LDLKM算法是有效的。展开更多
Let Mn be a closed submanifold isometrically immersed in a unit sphere Sn . Denote by R, H and S, the normalized +p scalar curvature, the mean curvature, and the square of the length of the second fundamental form of ...Let Mn be a closed submanifold isometrically immersed in a unit sphere Sn . Denote by R, H and S, the normalized +p scalar curvature, the mean curvature, and the square of the length of the second fundamental form of Mn, respectively. Suppose R is constant and ≥1. We study the pinching problem on S and prove a rigidity theorem for Mn immersed in Sn +pwith parallel nor- malized mean curvature vector field. When n≥8 or, n=7 and p≤2, the pinching constant is best.展开更多
Let M^n be a totally real submanifold in a complex projective space CP^(n+p).In this paper,we study the position of the parallel umbilical normal vector field of M^n in the normal bundle.By choosing a suitable frame f...Let M^n be a totally real submanifold in a complex projective space CP^(n+p).In this paper,we study the position of the parallel umbilical normal vector field of M^n in the normal bundle.By choosing a suitable frame field,we obtain a pinching theorem,in the case p>0, for the square of the length of the second fundamental form of a totally real pseudo-umbilical submanifold with parallel mean curvature vector.展开更多
The main purpose of blasting operation is to produce desired and optimum mean size rock fragments.Smaller or fine fragments cause the loss of ore during loading and transportation,whereas large or coarser fragments ne...The main purpose of blasting operation is to produce desired and optimum mean size rock fragments.Smaller or fine fragments cause the loss of ore during loading and transportation,whereas large or coarser fragments need to be further processed,which enhances production cost.Therefore,accurate prediction of rock fragmentation is crucial in blasting operations.Mean fragment size(MFS) is a crucial index that measures the goodness of blasting designs.Over the past decades,various models have been proposed to evaluate and predict blasting fragmentation.Among these models,artificial intelligence(AI)-based models are becoming more popular due to their outstanding prediction results for multiinfluential factors.In this study,support vector regression(SVR) techniques are adopted as the basic prediction tools,and five types of optimization algorithms,i.e.grid search(GS),grey wolf optimization(GWO),particle swarm optimization(PSO),genetic algorithm(GA) and salp swarm algorithm(SSA),are implemented to improve the prediction performance and optimize the hyper-parameters.The prediction model involves 19 influential factors that constitute a comprehensive blasting MFS evaluation system based on AI techniques.Among all the models,the GWO-v-SVR-based model shows the best comprehensive performance in predicting MFS in blasting operation.Three types of mathematical indices,i.e.mean square error(MSE),coefficient of determination(R^(2)) and variance accounted for(VAF),are utilized for evaluating the performance of different prediction models.The R^(2),MSE and VAF values for the training set are 0.8355,0.00138 and 80.98,respectively,whereas 0.8353,0.00348 and 82.41,respectively for the testing set.Finally,sensitivity analysis is performed to understand the influence of input parameters on MFS.It shows that the most sensitive factor in blasting MFS is the uniaxial compressive strength.展开更多
BackgroundTo compare the arithmetic mean (M-SIA) and the summated vector mean of surgically induced astigmatism (SVM-SIA) according to the incision site after phakic intraocular lens (Visian implantable collamer lens ...BackgroundTo compare the arithmetic mean (M-SIA) and the summated vector mean of surgically induced astigmatism (SVM-SIA) according to the incision site after phakic intraocular lens (Visian implantable collamer lens (ICL), STAAR Surgical) implantation.MethodsThis study comprised 121 eyes of 121 consecutive patients undergoing ICL surgery through a 3.0-mm temporal or superior clear corneal incision. The magnitude and the axis of corneal astigmatism preoperatively and 3 months postoperatively were measured using an automated keratometer. The M-SIA and the SVM-SIA were determined according to the incision site.ResultsThe magnitude of corneal astigmatism significantly increased from 1.23 ± 0.59 D preoperatively to 1.46 ± 0.72 D postoperatively in the temporal incision group (Wilcoxon signed-rank test, P < 0.001), but it significantly decreased from 1.09 ± 0.36 D preoperatively to 0.86 ± 0.41 D postoperatively in the superior incision group (P < 0.001). The M-SIA was 0.48 ± 0.30 D, and the SVM-SIA was 0.23 ± 0.52 D at a meridian of 82° in the temporal incision group. The M-SIA was 0.57 ± 0.30 D, and the SVM-SIA was 0.47 ± 0.45 D at a meridian of 1° in the superior incision group.ConclusionsICL implantation induces the M-SIA by approximately 0.5 D, but the SVM-SIA decreased to 50% and 80% of the M-SIA in magnitude through temporal and superior incisions, respectively. The direction of the SVM-SIA showed a tendency toward corneal flattening to the incisional site. It should be noted that the M-SIA is somewhat different from the SVM-SIA according to the incision site.展开更多
提出了一种基于二元过程质量特性标准样本方差(Standardized sample variance,VMAX)和Hotelling统计量的联合控制图,这一控制图用于同时监控二元过程均值向量和协方差的变异。通过平均运行链长(Average Run Length,ARL)的方法对比研究表...提出了一种基于二元过程质量特性标准样本方差(Standardized sample variance,VMAX)和Hotelling统计量的联合控制图,这一控制图用于同时监控二元过程均值向量和协方差的变异。通过平均运行链长(Average Run Length,ARL)的方法对比研究表明,该控制图在过程参数发生小变异的情况下比联合T2与S控制图具有更优的性能。展开更多
Suppose Y - N（β, σ^2 In）, where β ∈ R^n and σ^2 〉 0 are unknown. We study the admissibility of linear estimators of mean vector under a quadratic loss function. A necessary and sufficient condition of the admi...Suppose Y - N（β, σ^2 In）, where β ∈ R^n and σ^2 〉 0 are unknown. We study the admissibility of linear estimators of mean vector under a quadratic loss function. A necessary and sufficient condition of the admissible linear estimator is given.展开更多
基金Foundation item:Project (2006BAB02A02) supported by the National Key Technology R&D Program during the 11th Five-year Plan Period of ChinaProject (CX2011B119) supported by the Graduated Students' Research and Innovation Fund of Hunan Province, ChinaProject (2009ssxt230) supported by the Central South University Innovation Fund,China
文摘Aiming at the problems of the traditional method of assessing distribution of particle size in bench blasting, a support vector machines （SVMs） regression methodology was used to predict the mean particle size （X50） resulting from rock blast fragmentation in various mines based on the statistical learning theory. The data base consisted of blast design parameters, explosive parameters, modulus of elasticity and in-situ block size. The seven input independent variables used for the SVMs model for the prediction of X50 of rock blast fragmentation were the ratio of bench height to drilled burden （H/B）, ratio of spacing to burden （S/B）, ratio of burden to hole diameter （B/D）, ratio of stemming to burden （T/B）, powder factor （Pf）, modulus of elasticity （E） and in-situ block size （XB）. After using the 90 sets of the measured data in various mines and rock formations in the world for training and testing, the model was applied to 12 another blast data for validation of the trained support vector regression （SVR） model. The prediction results of SVR were compared with those of artificial neural network （ANN）, multivariate regression analysis （MVRA） models, conventional Kuznetsov method and the measured X50 values. The proposed method shows promising results and the prediction accuracy of SVMs model is acceptable.
文摘In the present paper we obtain the following result: Theorem Let M^R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold N^(n+p)(p>1). If then M^n lies in a totally geodesic submanifold N^(n+1).
文摘标记分布学习是近年来提出的一种新的机器学习范式,它能很好地解决某些标记多义性的问题。现有的标记分布学习算法均利用条件概率建立参数模型,但未能充分利用特征和标记间的联系。本文考虑到特征相似的样本所对应的标记分布也应当相似,利用原型聚类的k均值算法(k-means),将训练集的样本进行聚类,提出基于kmeans算法的标记分布学习(label distribution learning based on k-means algorithm,LDLKM)。首先通过聚类算法kmeans求得每一个簇的均值向量,然后分别求得对应标记分布的均值向量。最后将测试集和训练集的均值向量间的距离作为权重,应用到对测试集标记分布的预测上。在6个公开的数据集上进行实验,并与3种已有的标记分布学习算法在5种评价指标上进行比较,实验结果表明提出的LDLKM算法是有效的。
基金Project supported by the Stress Supporting Subject Foundation of Zhejiang Province, China
文摘Let Mn be a closed submanifold isometrically immersed in a unit sphere Sn . Denote by R, H and S, the normalized +p scalar curvature, the mean curvature, and the square of the length of the second fundamental form of Mn, respectively. Suppose R is constant and ≥1. We study the pinching problem on S and prove a rigidity theorem for Mn immersed in Sn +pwith parallel nor- malized mean curvature vector field. When n≥8 or, n=7 and p≤2, the pinching constant is best.
基金Foundation item： the Natural Science Foundation of Anhui Educational Committee （No. KJ2008A05ZC） the Younger Teachers of Anhui Normal University （No. 2005xqn01）.
文摘Let M^n be a totally real submanifold in a complex projective space CP^(n+p).In this paper,we study the position of the parallel umbilical normal vector field of M^n in the normal bundle.By choosing a suitable frame field,we obtain a pinching theorem,in the case p>0, for the square of the length of the second fundamental form of a totally real pseudo-umbilical submanifold with parallel mean curvature vector.
基金funded by the National Natural Science Foundation of China(Grant No.42177164)the Innovation-Driven Project of Central South University(Grant No.2020CX040)supported by China Scholarship Council(Grant No.202006370006)。
文摘The main purpose of blasting operation is to produce desired and optimum mean size rock fragments.Smaller or fine fragments cause the loss of ore during loading and transportation,whereas large or coarser fragments need to be further processed,which enhances production cost.Therefore,accurate prediction of rock fragmentation is crucial in blasting operations.Mean fragment size(MFS) is a crucial index that measures the goodness of blasting designs.Over the past decades,various models have been proposed to evaluate and predict blasting fragmentation.Among these models,artificial intelligence(AI)-based models are becoming more popular due to their outstanding prediction results for multiinfluential factors.In this study,support vector regression(SVR) techniques are adopted as the basic prediction tools,and five types of optimization algorithms,i.e.grid search(GS),grey wolf optimization(GWO),particle swarm optimization(PSO),genetic algorithm(GA) and salp swarm algorithm(SSA),are implemented to improve the prediction performance and optimize the hyper-parameters.The prediction model involves 19 influential factors that constitute a comprehensive blasting MFS evaluation system based on AI techniques.Among all the models,the GWO-v-SVR-based model shows the best comprehensive performance in predicting MFS in blasting operation.Three types of mathematical indices,i.e.mean square error(MSE),coefficient of determination(R^(2)) and variance accounted for(VAF),are utilized for evaluating the performance of different prediction models.The R^(2),MSE and VAF values for the training set are 0.8355,0.00138 and 80.98,respectively,whereas 0.8353,0.00348 and 82.41,respectively for the testing set.Finally,sensitivity analysis is performed to understand the influence of input parameters on MFS.It shows that the most sensitive factor in blasting MFS is the uniaxial compressive strength.
文摘BackgroundTo compare the arithmetic mean (M-SIA) and the summated vector mean of surgically induced astigmatism (SVM-SIA) according to the incision site after phakic intraocular lens (Visian implantable collamer lens (ICL), STAAR Surgical) implantation.MethodsThis study comprised 121 eyes of 121 consecutive patients undergoing ICL surgery through a 3.0-mm temporal or superior clear corneal incision. The magnitude and the axis of corneal astigmatism preoperatively and 3 months postoperatively were measured using an automated keratometer. The M-SIA and the SVM-SIA were determined according to the incision site.ResultsThe magnitude of corneal astigmatism significantly increased from 1.23 ± 0.59 D preoperatively to 1.46 ± 0.72 D postoperatively in the temporal incision group (Wilcoxon signed-rank test, P < 0.001), but it significantly decreased from 1.09 ± 0.36 D preoperatively to 0.86 ± 0.41 D postoperatively in the superior incision group (P < 0.001). The M-SIA was 0.48 ± 0.30 D, and the SVM-SIA was 0.23 ± 0.52 D at a meridian of 82° in the temporal incision group. The M-SIA was 0.57 ± 0.30 D, and the SVM-SIA was 0.47 ± 0.45 D at a meridian of 1° in the superior incision group.ConclusionsICL implantation induces the M-SIA by approximately 0.5 D, but the SVM-SIA decreased to 50% and 80% of the M-SIA in magnitude through temporal and superior incisions, respectively. The direction of the SVM-SIA showed a tendency toward corneal flattening to the incisional site. It should be noted that the M-SIA is somewhat different from the SVM-SIA according to the incision site.
文摘提出了一种基于二元过程质量特性标准样本方差(Standardized sample variance,VMAX)和Hotelling统计量的联合控制图,这一控制图用于同时监控二元过程均值向量和协方差的变异。通过平均运行链长(Average Run Length,ARL)的方法对比研究表明,该控制图在过程参数发生小变异的情况下比联合T2与S控制图具有更优的性能。
基金This work is supported by The NNSF of China with Nos.10071090 and 10271013
文摘Suppose Y - N（β, σ^2 In）, where β ∈ R^n and σ^2 〉 0 are unknown. We study the admissibility of linear estimators of mean vector under a quadratic loss function. A necessary and sufficient condition of the admissible linear estimator is given.
