Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing.By generalizing the resource theory of coherence from von Neumann measurements to positive o...Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing.By generalizing the resource theory of coherence from von Neumann measurements to positive operatorvalued measures(POVMs),POVM-based coherence measures have been proposed with respect to the relative entropy of coherence,the l_(1) norm of coherence,the robustness of coherence and the Tsallis relative entropy of coherence.We derive analytically the lower and upper bounds on these POVM-based coherence of an arbitrary given superposed pure state in terms of the POVM-based coherence of the states in superposition.Our results can be used to estimate range of quantum coherence of superposed states.Detailed examples are presented to verify our analytical bounds.展开更多
针对稀疏MIMO信道系统模型线性均衡过程中输入信号,输出信号都含有噪声的情况提出了一种变遗忘因子的稀疏正则化总体最小二乘算法(VFF-SRTLS)。本算法中采用总体最小二乘(TLS)的代价函数即瑞利商加入正则化的l_1范数和l_0范数作为其代...针对稀疏MIMO信道系统模型线性均衡过程中输入信号,输出信号都含有噪声的情况提出了一种变遗忘因子的稀疏正则化总体最小二乘算法(VFF-SRTLS)。本算法中采用总体最小二乘(TLS)的代价函数即瑞利商加入正则化的l_1范数和l_0范数作为其代价函数,并利用次梯度下降法产生的迭代式用以更新均衡滤波器系数,使均衡过程中代价函数最小;同时为了使算法能够适应信道快变环境而采用变遗忘因子(VFF),并且根据最速下降法得到遗忘因子的迭代式。仿真结果表明,在信噪比为10 d B的2×2 MIMO线性均衡过程中VFF--RTLS算法的收敛MSE值比RLS算法低约2 d B,VFF-l_0-RTLS算法的收敛MSE值比RLS算法低约1.5 d B。展开更多
Consider the standard linear model where x<sub>x</sub>,x<sub>2</sub>… are assumed to be the known p-vectors, β the unknown p-vector of regression coefficients, and e<sub>1</sub>, ...Consider the standard linear model where x<sub>x</sub>,x<sub>2</sub>… are assumed to be the known p-vectors, β the unknown p-vector of regression coefficients, and e<sub>1</sub>, e<sub>2</sub>, …the independent random error sequence, each having a median zero. Define the minimum L<sub>1</sub>norm estimator as,the solution of the minimization problem inf It is proved in this paper that is asymptotically normal under very weak conditions. In particular, the condition imposed on {xi} is exactly the same which ensures the asymptotic normality of least-squares estimate:展开更多
In this paper, the L_1-norm estimators and the random weighted statistic fora semiparametric regression model are constructed, the strong convergence rates of estimators areobtain under certain conditions, the strong ...In this paper, the L_1-norm estimators and the random weighted statistic fora semiparametric regression model are constructed, the strong convergence rates of estimators areobtain under certain conditions, the strong efficiency of the random weighting method is shown. Asimulation study is conducted to compare the L_1-norm estimator with the least square estimator interm of approximate accuracy, and simulation results are given for comparison between the randomweighting method and normal approximation method.展开更多
Let（X,Y） be a pair of R<sup>d</sup>×R<sup>1</sup>-valued random variables.In thispaper we investigate the asymptotic properties of the L<sub>1</sub>-norm kernel estimator oft...Let（X,Y） be a pair of R<sup>d</sup>×R<sup>1</sup>-valued random variables.In thispaper we investigate the asymptotic properties of the L<sub>1</sub>-norm kernel estimator ofthe conditional median function of Y on X.Under appropriate regularity condi-tions,asymptotic normality and the optimal rates of convergence n<sup>（-1）/（2+d）</sup>and(n<sup>-1</sup>log n)<sup>1/（2+d）</sup> in the L<sup>q</sup>（1（?）q【∞）-and L<sup>∞</sup>-norms restricted to a compactset,respectively,are obtained.Our study shows that this estimator and the well-known Nadaraya-Watson’s kernel estimator of the conditional mean function of Yon X have the same asymptotic properties.展开更多
In this paper, we study some packings in a cube, namely, how to pack n points in a cube so as to maximize the minimal distance. The distance is induced by the L1-norm which is analogous to the Hamming distance in codi...In this paper, we study some packings in a cube, namely, how to pack n points in a cube so as to maximize the minimal distance. The distance is induced by the L1-norm which is analogous to the Hamming distance in coding theory. Two constructions with reasonable parameters are obtained, by using some results from a function field including divisor class group, narrow ray class group, and so on. We also present some asymptotic results of the two packings.展开更多
基金the National Natural Science Foundation of China(Grant Nos.12075159,12171044,and 12175147)the Natural Science Foundation of Beijing(Grant No.Z190005)+2 种基金the Academician Innovation Platform of Hainan ProvinceShenzhen Institute for Quantum Science and EngineeringSouthern University of Science and Technology(Grant No.SIQSE202001)。
文摘Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing.By generalizing the resource theory of coherence from von Neumann measurements to positive operatorvalued measures(POVMs),POVM-based coherence measures have been proposed with respect to the relative entropy of coherence,the l_(1) norm of coherence,the robustness of coherence and the Tsallis relative entropy of coherence.We derive analytically the lower and upper bounds on these POVM-based coherence of an arbitrary given superposed pure state in terms of the POVM-based coherence of the states in superposition.Our results can be used to estimate range of quantum coherence of superposed states.Detailed examples are presented to verify our analytical bounds.
文摘针对稀疏MIMO信道系统模型线性均衡过程中输入信号,输出信号都含有噪声的情况提出了一种变遗忘因子的稀疏正则化总体最小二乘算法(VFF-SRTLS)。本算法中采用总体最小二乘(TLS)的代价函数即瑞利商加入正则化的l_1范数和l_0范数作为其代价函数,并利用次梯度下降法产生的迭代式用以更新均衡滤波器系数,使均衡过程中代价函数最小;同时为了使算法能够适应信道快变环境而采用变遗忘因子(VFF),并且根据最速下降法得到遗忘因子的迭代式。仿真结果表明,在信噪比为10 d B的2×2 MIMO线性均衡过程中VFF--RTLS算法的收敛MSE值比RLS算法低约2 d B,VFF-l_0-RTLS算法的收敛MSE值比RLS算法低约1.5 d B。
基金Project supported by the National Natural Science Foundation of China and also supported by the U. S. Office of Naval Research and Air Force Office of Scientific Research.
文摘Consider the standard linear model where x<sub>x</sub>,x<sub>2</sub>… are assumed to be the known p-vectors, β the unknown p-vector of regression coefficients, and e<sub>1</sub>, e<sub>2</sub>, …the independent random error sequence, each having a median zero. Define the minimum L<sub>1</sub>norm estimator as,the solution of the minimization problem inf It is proved in this paper that is asymptotically normal under very weak conditions. In particular, the condition imposed on {xi} is exactly the same which ensures the asymptotic normality of least-squares estimate:
基金Supported by the Natural Science Foundation of Beijing City of China (1042002)the Science and Technology Development Foundation of Education Committee of Beijing Citythe Special Expenditure of Excellent Person Education of Beijing(20041D0501515)
文摘In this paper, the L_1-norm estimators and the random weighted statistic fora semiparametric regression model are constructed, the strong convergence rates of estimators areobtain under certain conditions, the strong efficiency of the random weighting method is shown. Asimulation study is conducted to compare the L_1-norm estimator with the least square estimator interm of approximate accuracy, and simulation results are given for comparison between the randomweighting method and normal approximation method.
基金Research supported by National Natural Science Foundation of China
文摘Let（X,Y） be a pair of R<sup>d</sup>×R<sup>1</sup>-valued random variables.In thispaper we investigate the asymptotic properties of the L<sub>1</sub>-norm kernel estimator ofthe conditional median function of Y on X.Under appropriate regularity condi-tions,asymptotic normality and the optimal rates of convergence n<sup>（-1）/（2+d）</sup>and(n<sup>-1</sup>log n)<sup>1/（2+d）</sup> in the L<sup>q</sup>（1（?）q【∞）-and L<sup>∞</sup>-norms restricted to a compactset,respectively,are obtained.Our study shows that this estimator and the well-known Nadaraya-Watson’s kernel estimator of the conditional mean function of Yon X have the same asymptotic properties.
文摘In this paper, we study some packings in a cube, namely, how to pack n points in a cube so as to maximize the minimal distance. The distance is induced by the L1-norm which is analogous to the Hamming distance in coding theory. Two constructions with reasonable parameters are obtained, by using some results from a function field including divisor class group, narrow ray class group, and so on. We also present some asymptotic results of the two packings.
