Exponential Moments of Solutions for Nonlinear Equations with Catalytic Noise and Large Deviation

Nonlinear equation with catalytic noise is considered. We discuss the existence of catalytic superprocess associated with the equation and derive the exponential moment formula. Moreover, we prove the large deviation principle for catalytic superprocesses.     

引入高阶累积量的数据库访问特征选择算法

在进行数据库访问的过程中,由于受到很多不确定性因素的干扰,使数据库中存在大量噪声,影响了数据库访问的效率。提出一种引入高阶累积量的数据库访问特征选择算法,依据高阶累积量两个统计独立随机过程之和的累积量等于各个随机过程累积量之和的性质,对数据库进行去噪处理。在此基础上,采用SVM无监督算法实现数据库访问特征选择。仿真实验结果表明,采用所提算法进行数据库访问特征选择,不仅具有较高的特征选择精度,而且特征选择效率也明显高于传统算法,同时特征选择结果所含冗余特征低于传统算法,验证了所提算法在数据库访问特征选择方面的性能。     

The Invariant Measures of Markov Chains on Product Spaces and a Measurement of Dependence

For probability measures on product spaces, we define a notion of dependence among each coordinate. We study Markov chains on product spaces in which the time developement of each coordinate corresponds to the movement of a particle in an interacting particle system described by the Markov chain. If there is no interaction among these particles, the dependence of them decreases monotonically. We establish an inequality which states that if the interaction among each particle is small, then, in stationarity, the dependence among each particle is small.     

色噪声背景下的正弦信号相位估计方法

噪声背景下的正弦信号相位估计在雷达、导航、波达方向估计等领域有着广泛的应用。提出了一种基于互高阶累计量的正弦信号相位估计方法——奇异值分解法。这种方法通过对互高阶累积量矩阵进行奇异值分解,得到信号子空间和噪声子空间。由于信号子空间不包含噪声信息,因此是提取信号成分与抑制噪声意义下的最优解。信号的自高阶累积量矩阵是共轭对称矩阵,它的左、右奇异矢量是相同的,而两个幅值和频率都相同、只有相位不同的正弦信号的互高阶累积量矩阵却是非共轭对称矩阵,左右奇异矢量也不相同,这说明是谐波信号之间存在相位差导致了这一结果。因此,从这一点出发,证明了谐波信号的互高阶累积量矩阵左、右奇异矢量内积的相角等于正弦信号相位差这一重要定理。并根据这一定理推导出估计正弦信号相位差的奇异值分解法。仿真结果验证了这种方法的有效性。     

Spin-One Ferromagnetic Model with Anisotropic Exchange Interaction and Dsz2 Single-Ion Anisotropy

A quantum spin Heisenberg model with exchange and single-ion anisotropy is investigated by variational cumulant expansion method. Easy-axis and easy-plane cases are considered separately. Dependence of critical temperature and type of ordered phase on anisotropy parameters are examined in full detail. Thermodynamic functions are calculated for some instances.     

Algebraic connectivity analysis in molecular electronic structure theory II: total exponential formulation of second-quantised correlated methods

The fundamentality of the exponential representation of a second-quantised correlated wave function is emphasised with an accent on the physical sense of cluster amplitudes as cumulants of the correlated ansatz. Three main wave function formalisms, namely, the configuration-interaction theory, the coupled-cluster approach, and the many-body perturbation theory (as well as their extensions, e.g. the equation-of-motion coupled-cluster method, multireference schemes, etc.), are represented in an exponential form, leading to a formulation of the working equations in terms of cluster amplitudes. By expressing the corresponding many-body tensor equations in terms of cluster amplitudes, we could unambiguously check connectivity types and the asymptotic behaviour of all tensors/scalars involved (in the formal limit of an infinite number of correlated particles). In particular, the appearance of disconnected cluster amplitudes corresponds to unphysical correlations. Besides, we demonstrate that the equation-of-motion coupled-cluster approach, as well as certain excited-state configuration-interaction methods, can be recast in a fully connected (exponential) form, thus breaking the common belief that all truncated configuration-interaction methods violate connectivity. Our work is based on the recently developed algebraic framework which can be viewed as a complement to the classical diagrammatic analysis.     

Cumulants in perturbation expansions for non-equilibrium field theory

The formulation of perturbation expansions for a quantum field theory of strongly interacting systems in a general non-equilibrium state is discussed. Non-vanishing initial correlations are included in the formulation of the perturbation expansion in terms of cumulants. The cumulants are shown to be the suitable candidate for summing up the perturbation expansion. Also a linked-cluster theorem for the perturbation series with cumulants is presented. Finally, a generating functional of the perturbation series with initial correlations is studied. We apply the methods to a simple model of a fermion-boson system.     

On the Domain of Hyperbolicity of the Cumulant Equations

In this article we consider the influence of non-equilibirum values of classical variables on the eigenvalues of the advection part of the cumulant equations. Real and finite eigenvalues are a neccessary condition for the cumulant equations to be hyperbolic which can be used to obtain estimates on admissible deviations from equilibrium for a model of particular order still to be valid. We find that this condition puts no constraints on velocity and shear stress values, but specific energy must be positive, normal stress must be bounded by specific energy and heat flux not be too large.     

高分辨率谐波恢复的互四阶累积量ESPRIT-SVD方法1

在互功率谱和高阶统计量理论基础上，提出了基于互四阶累积量的ESPRIT(estimation of signal parameters via rotational invariance techneques)SVD(singular value discompose)方法。仿真结果表明，在混合色噪声背景下，该方法能够有效地抑制噪声，且具有良好的频率估计性能。     

Initial transient detection in simulations using the second-order cumulant spectrum

Procedures for detecting an initial transient in simulation output data are developed. The tests use the second-order cumulant spectrum which differs from the power spectrum in that the stationarity constraint is not required for the former. The second-order cumulant spectrum can be interpreted as the nonstationary power spectrum and is an orthogonal decomposition of the variance of a nonstationary process. The null hypothesis is that the simulation output data series is a covariance stationary process. Equivalently, all estimates of the second-order cumulant spectrum in the region which excludes the estimates of the power spectrum will have an expected value of zero. The test procedures are designed to detect initialization bias in the estimation of the mean and the variance. These procedures can be extended to detect bias in the moments of cumulants of ordern, wheren>2. Results are presented from the application of the test to simulated processes with superimposed mean and variance transients and anM/M/1 queue example.