In order to obtain with simplicity the known and new properties of linear canonical transformations (LCTs), we show that any relation between a couple of operators (A,B) having commutator identical to unity, called du...In order to obtain with simplicity the known and new properties of linear canonical transformations (LCTs), we show that any relation between a couple of operators (A,B) having commutator identical to unity, called dual couple in this work, is valuable for any other dual couple, so that from the known translation operator exp(a∂<sub>x</sub>) one may obtain the explicit form and properties of a category of linear and linear canonical transformations in 2N-phase spaces. Moreover, other forms of LCTs are also obtained in this work as so as the transforms by them of functions by integrations as so as by derivations. In this way, different kinds of LCTs such as Fast Fourier, Fourier, Laplace, Xin Ma and Rhodes, Baker-Campbell-Haussdorf, Bargman transforms are found again.展开更多
In this paper,the improved canonical quantization method of the self dual field is given in order to overcome linear combination problem about the second class constraint and the first class constraint number maximiza...In this paper,the improved canonical quantization method of the self dual field is given in order to overcome linear combination problem about the second class constraint and the first class constraint number maximization problem in the Dirac method.In the improved canonical quantization method,there are no artificial linear combination and the first class constraint number maximization problems,at the same time,the stability of the system is considered.Therefore,the improved canonical quantization method is more natural and easier accepted by people than the usual Dirac method.We use the improved canonical quantization method to realize the canonical quantization of the self dual field,which has relation with string theory successfully and the results are equal to the results by using the Dirac method.展开更多
In this paper, we give an operator parameterization for the set of dilations of a given pair of dual g-frames and the set of dilations of pairs of dual g-frames of a given g-frame. In particular,for the dilations of a...In this paper, we give an operator parameterization for the set of dilations of a given pair of dual g-frames and the set of dilations of pairs of dual g-frames of a given g-frame. In particular,for the dilations of a given pair of dual g-frames, we introduce the concept of joint complementary g-frames and prove that the joint complementary g-frames of a pair of dual g-frames are unique in the sense of joint similarity, which then helps to obtain a sufficient condition such that the complementary g-frames of a g-frame are unique in the sense of similarity and show that the set of dilations of a given dual g-frame pair are parameterized by a set of invertible diagonal operators. For the dilations of pairs of dual g-frames, we prove that the set of dilations of pairs of dual g-frames are parameterized by a set of invertible upper triangular operators.展开更多
针对跨年龄人脸验证任务中面部纹理、形状特征变化的问题,提出一种基于双编码平均局部二值模式(dual-coded average local binary pattern,DCALBP)与深度学习算法相结合的多任务人脸验证算法。首先,使用多任务卷积神经网络(multi-task c...针对跨年龄人脸验证任务中面部纹理、形状特征变化的问题,提出一种基于双编码平均局部二值模式(dual-coded average local binary pattern,DCALBP)与深度学习算法相结合的多任务人脸验证算法。首先,使用多任务卷积神经网络(multi-task convolutional neural network,MTCNN)对人脸检测图片进行预处理,引入双编码平均局部二值模式(DCALBP)和梯度直方图算法(histogram of oriented gradient,HOG)提取人脸的局部纹理特征和形状特征,运用典型相关性分析(canonical correlation analysis,CCA)算法将两种特征融合,得到人脸年龄特征。然后,孪生网络(siamese network)提取人脸面部特征,并将纹理形状特征从中分离,抑制年龄因素对人脸验证的影响,从而得到具有年龄不变性的人脸特征。最后进行人脸特征匹配,实现跨年龄人脸验证。通过在数据集FG-NET、MORPH Album2以及经过处理的综合数据集上进行实验,准确率分别为89.73%、98.32%和98.27%,充分验证了该方法的有效性。展开更多
This paper considers a new canonical duality theory for solving mixed integer quadratic programming problem. It shows that this well-known NP-hard problem can be converted into concave maximization dual problems witho...This paper considers a new canonical duality theory for solving mixed integer quadratic programming problem. It shows that this well-known NP-hard problem can be converted into concave maximization dual problems without duality gap. And the dual problems can be solved, under certain conditions, by polynomial algorithms.展开更多
文摘In order to obtain with simplicity the known and new properties of linear canonical transformations (LCTs), we show that any relation between a couple of operators (A,B) having commutator identical to unity, called dual couple in this work, is valuable for any other dual couple, so that from the known translation operator exp(a∂<sub>x</sub>) one may obtain the explicit form and properties of a category of linear and linear canonical transformations in 2N-phase spaces. Moreover, other forms of LCTs are also obtained in this work as so as the transforms by them of functions by integrations as so as by derivations. In this way, different kinds of LCTs such as Fast Fourier, Fourier, Laplace, Xin Ma and Rhodes, Baker-Campbell-Haussdorf, Bargman transforms are found again.
基金Supported by National Natural Science Foundation of China under Grant Nos. 11275017 and 11173028
文摘In this paper,the improved canonical quantization method of the self dual field is given in order to overcome linear combination problem about the second class constraint and the first class constraint number maximization problem in the Dirac method.In the improved canonical quantization method,there are no artificial linear combination and the first class constraint number maximization problems,at the same time,the stability of the system is considered.Therefore,the improved canonical quantization method is more natural and easier accepted by people than the usual Dirac method.We use the improved canonical quantization method to realize the canonical quantization of the self dual field,which has relation with string theory successfully and the results are equal to the results by using the Dirac method.
文摘In this paper, we give an operator parameterization for the set of dilations of a given pair of dual g-frames and the set of dilations of pairs of dual g-frames of a given g-frame. In particular,for the dilations of a given pair of dual g-frames, we introduce the concept of joint complementary g-frames and prove that the joint complementary g-frames of a pair of dual g-frames are unique in the sense of joint similarity, which then helps to obtain a sufficient condition such that the complementary g-frames of a g-frame are unique in the sense of similarity and show that the set of dilations of a given dual g-frame pair are parameterized by a set of invertible diagonal operators. For the dilations of pairs of dual g-frames, we prove that the set of dilations of pairs of dual g-frames are parameterized by a set of invertible upper triangular operators.
文摘针对跨年龄人脸验证任务中面部纹理、形状特征变化的问题,提出一种基于双编码平均局部二值模式(dual-coded average local binary pattern,DCALBP)与深度学习算法相结合的多任务人脸验证算法。首先,使用多任务卷积神经网络(multi-task convolutional neural network,MTCNN)对人脸检测图片进行预处理,引入双编码平均局部二值模式(DCALBP)和梯度直方图算法(histogram of oriented gradient,HOG)提取人脸的局部纹理特征和形状特征,运用典型相关性分析(canonical correlation analysis,CCA)算法将两种特征融合,得到人脸年龄特征。然后,孪生网络(siamese network)提取人脸面部特征,并将纹理形状特征从中分离,抑制年龄因素对人脸验证的影响,从而得到具有年龄不变性的人脸特征。最后进行人脸特征匹配,实现跨年龄人脸验证。通过在数据集FG-NET、MORPH Album2以及经过处理的综合数据集上进行实验,准确率分别为89.73%、98.32%和98.27%,充分验证了该方法的有效性。
文摘This paper considers a new canonical duality theory for solving mixed integer quadratic programming problem. It shows that this well-known NP-hard problem can be converted into concave maximization dual problems without duality gap. And the dual problems can be solved, under certain conditions, by polynomial algorithms.
