In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to...In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.展开更多
In this paper, we study on the application of radical B-spline wavelet scaling function in fractal function approximation system. The paper proposes a wavelet-based fractal function approximation algorithm in which th...In this paper, we study on the application of radical B-spline wavelet scaling function in fractal function approximation system. The paper proposes a wavelet-based fractal function approximation algorithm in which the coefficients can be determined by solving a convex quadraticprogramming problem. And the experiment result shows that the approximation error of this algorithm is smaller than that of the polynomial-based fractal function approximation. This newalgorithm exploits the consistency between fractal and scaling function in multi-scale and multiresolution, has a better approximation effect and high potential in data compression, especially inimage compression.展开更多
In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potentia...In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potential depends on the density only,the individual parts,the Pauli kinetic energy and the exchange-correlation energy,however,are orbital dependent and as such mutually influence each other.The numerical investigation is performed for the orbital-based non-interacting Kohn-Sham system in order to avoid additional effects due to further approximations of the kinetic energy.The numerical influence of the exchange-correlation functional on the non-interacting kinetic energy is shown to be of the orderof a few Hartrees.For chemical purposes,however,the energetic performance as a function of the nuclear coordinates is much more important than total energies.Therefore,the effect on the bond dissociation curve was studied exemplarily for the carbon monoxide.The data reveals that,the mutual influence between the exchange-correlation functional and the kinetic energy has a significant influence on bond dissociation energies and bond distances.Therefore,the effect of the exchange-correlation treatment must be considered in the design of orbital-free density functional approximations for the kinetic energy.展开更多
This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ab...This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ability, and adaptability greatly in learning processes of networks. The simulation results have been shown that the method can be applied to the modeling and identification of complex dynamic control systems.展开更多
The electrode regulator system is a complex system with many variables, strong coupling and strong nonlinearity, while conventional control methods such as proportional integral derivative （PID） can not meet the req...The electrode regulator system is a complex system with many variables, strong coupling and strong nonlinearity, while conventional control methods such as proportional integral derivative （PID） can not meet the requirements. A robust adaptive neural network controller （RANNC） for electrode regulator system was proposed. Artificial neural networks were established to learn the system dynamics. The nonlinear control law was derived directly based on an input-output approximating method via the Taylor expansion, which avoids complex control development and intensive computation. The stability of the closed-loop system was established by the Lyapunov method. The current fluctuation relative percentage is less than ±8% and heating rate is up to 6.32 ℃/min when the proposed controller is used. The experiment results show that the proposed control scheme is better than inverse neural network controller （INNC） and PID controller （PIDC）.展开更多
高斯过程通过概率建模能够有效地捕捉数据中的复杂关系,并提供关于预测结果的不确定性评估,是一个强大而灵活的工具.但由于矩阵求逆的较高计算复杂度,限制了模型在其他领域内的应用.本文针对高斯过程模型的矩阵求逆问题,提出了一种基于...高斯过程通过概率建模能够有效地捕捉数据中的复杂关系,并提供关于预测结果的不确定性评估,是一个强大而灵活的工具.但由于矩阵求逆的较高计算复杂度,限制了模型在其他领域内的应用.本文针对高斯过程模型的矩阵求逆问题,提出了一种基于球谐函数的高斯过程近似模型(Variational Sparse Gaussian Processes based on Spherical Harmonic,SHVSGP),通过球谐函数将数据映射到超球面上,在一个不同于数据原始输入域的空间中寻找一个更紧凑的输入特征代表集,使得产生的稀疏高斯过程模型能够包含有更丰富的信息特征,同时获得诱导变量相关的对角协方差矩阵,这极大简化了矩阵运算的复杂度,节省了计算成本.本文将SHVSGP模型与当下流行的其他近似方法在大规模数据集上进行比较,结果表明SHVSGP模型可以获得高效且精确的预测.展开更多
提出一种光强-波长模型和径向基函数网络(radial basis function network,RBFN)相融合的光谱共焦信号峰值提取算法,简称RBFN-I-λ。首先通过高斯拟合法拟合离散光谱响应信号的差分信号粗略得到初始峰值波长,然后基于泰勒近似法得到理想...提出一种光强-波长模型和径向基函数网络(radial basis function network,RBFN)相融合的光谱共焦信号峰值提取算法,简称RBFN-I-λ。首先通过高斯拟合法拟合离散光谱响应信号的差分信号粗略得到初始峰值波长,然后基于泰勒近似法得到理想峰值波长并计算初始峰值波长和理想峰值波长之间的波长差,最后利用RBFN-I-λ建立光谱共焦响应信号与波长描述误差之间的映射关系。实验结果表明,RBFN-I-λ算法的精度与传统抛物线法、质心法和高斯拟合法等方法相比,至少提升30%。展开更多
多粒度模糊粗糙集(multi-granulation fuzzy rough set,MGFRS)是一种重要的粗糙集模型。乐观多粒度模糊粗糙集和悲观多粒度模糊粗糙集分别给出了被描述对象的两种极端描述。从数据聚合角度看,将不同粒度值合并为单一粒度值时,乐观MGFRS...多粒度模糊粗糙集(multi-granulation fuzzy rough set,MGFRS)是一种重要的粗糙集模型。乐观多粒度模糊粗糙集和悲观多粒度模糊粗糙集分别给出了被描述对象的两种极端描述。从数据聚合角度看,将不同粒度值合并为单一粒度值时,乐观MGFRS采用的是取小算子,悲观MGFRS采用的是取大算子。将取小与取大算子拓展为一般的平均型聚合算子,提出了一种新的多粒度模糊粗糙集模型:基于平均型聚合函数的多粒度模糊粗糙集(multi-granulation fuzzy rough set model on the base of average aggregate function,MFA)模型。研究了MFA模型的基本性质,给出了MFA模型与乐观和悲观多粒度模糊粗糙集的关系。同时,基于MFA模型,提出了基于平均型聚合算子的粗糙近似集模型。展开更多
文摘In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.
文摘In this paper, we study on the application of radical B-spline wavelet scaling function in fractal function approximation system. The paper proposes a wavelet-based fractal function approximation algorithm in which the coefficients can be determined by solving a convex quadraticprogramming problem. And the experiment result shows that the approximation error of this algorithm is smaller than that of the polynomial-based fractal function approximation. This newalgorithm exploits the consistency between fractal and scaling function in multi-scale and multiresolution, has a better approximation effect and high potential in data compression, especially inimage compression.
基金The project was supported by the Fund for Scientific Research in Flanders (FWO-Vlaanderen) for Research Grant G021115N.
文摘In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potential depends on the density only,the individual parts,the Pauli kinetic energy and the exchange-correlation energy,however,are orbital dependent and as such mutually influence each other.The numerical investigation is performed for the orbital-based non-interacting Kohn-Sham system in order to avoid additional effects due to further approximations of the kinetic energy.The numerical influence of the exchange-correlation functional on the non-interacting kinetic energy is shown to be of the orderof a few Hartrees.For chemical purposes,however,the energetic performance as a function of the nuclear coordinates is much more important than total energies.Therefore,the effect on the bond dissociation curve was studied exemplarily for the carbon monoxide.The data reveals that,the mutual influence between the exchange-correlation functional and the kinetic energy has a significant influence on bond dissociation energies and bond distances.Therefore,the effect of the exchange-correlation treatment must be considered in the design of orbital-free density functional approximations for the kinetic energy.
文摘This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ability, and adaptability greatly in learning processes of networks. The simulation results have been shown that the method can be applied to the modeling and identification of complex dynamic control systems.
基金Project(N100604002) supported by the Fundamental Research Funds for Central Universities of ChinaProject(61074074) supported by the National Natural Science Foundation of China
文摘The electrode regulator system is a complex system with many variables, strong coupling and strong nonlinearity, while conventional control methods such as proportional integral derivative （PID） can not meet the requirements. A robust adaptive neural network controller （RANNC） for electrode regulator system was proposed. Artificial neural networks were established to learn the system dynamics. The nonlinear control law was derived directly based on an input-output approximating method via the Taylor expansion, which avoids complex control development and intensive computation. The stability of the closed-loop system was established by the Lyapunov method. The current fluctuation relative percentage is less than ±8% and heating rate is up to 6.32 ℃/min when the proposed controller is used. The experiment results show that the proposed control scheme is better than inverse neural network controller （INNC） and PID controller （PIDC）.
文摘高斯过程通过概率建模能够有效地捕捉数据中的复杂关系,并提供关于预测结果的不确定性评估,是一个强大而灵活的工具.但由于矩阵求逆的较高计算复杂度,限制了模型在其他领域内的应用.本文针对高斯过程模型的矩阵求逆问题,提出了一种基于球谐函数的高斯过程近似模型(Variational Sparse Gaussian Processes based on Spherical Harmonic,SHVSGP),通过球谐函数将数据映射到超球面上,在一个不同于数据原始输入域的空间中寻找一个更紧凑的输入特征代表集,使得产生的稀疏高斯过程模型能够包含有更丰富的信息特征,同时获得诱导变量相关的对角协方差矩阵,这极大简化了矩阵运算的复杂度,节省了计算成本.本文将SHVSGP模型与当下流行的其他近似方法在大规模数据集上进行比较,结果表明SHVSGP模型可以获得高效且精确的预测.
文摘提出一种光强-波长模型和径向基函数网络(radial basis function network,RBFN)相融合的光谱共焦信号峰值提取算法,简称RBFN-I-λ。首先通过高斯拟合法拟合离散光谱响应信号的差分信号粗略得到初始峰值波长,然后基于泰勒近似法得到理想峰值波长并计算初始峰值波长和理想峰值波长之间的波长差,最后利用RBFN-I-λ建立光谱共焦响应信号与波长描述误差之间的映射关系。实验结果表明,RBFN-I-λ算法的精度与传统抛物线法、质心法和高斯拟合法等方法相比,至少提升30%。
文摘多粒度模糊粗糙集(multi-granulation fuzzy rough set,MGFRS)是一种重要的粗糙集模型。乐观多粒度模糊粗糙集和悲观多粒度模糊粗糙集分别给出了被描述对象的两种极端描述。从数据聚合角度看,将不同粒度值合并为单一粒度值时,乐观MGFRS采用的是取小算子,悲观MGFRS采用的是取大算子。将取小与取大算子拓展为一般的平均型聚合算子,提出了一种新的多粒度模糊粗糙集模型:基于平均型聚合函数的多粒度模糊粗糙集(multi-granulation fuzzy rough set model on the base of average aggregate function,MFA)模型。研究了MFA模型的基本性质,给出了MFA模型与乐观和悲观多粒度模糊粗糙集的关系。同时,基于MFA模型,提出了基于平均型聚合算子的粗糙近似集模型。
