Extension of the cumulant definition for low particle number systems

Cumulants are usually interpreted as the connected components of density matrices, but this interpretation fails and practical problems arise when the rank n of cumulants is larger than the number of particles (N) in the system. In that case, cumulants defined in the traditional way become disconnected. To solve this problem, the definition of cumulants is extended by introducing a simple modulation factor. The modified cumulants reduce to the conventional definition, but they vanish when N < n. Using the modified definition also eliminates the error in the approximation of density matrices by low‐rank cumulants, when N < n. The problem assumes a slightly different form when we work with active space–based theories, and it can be solved by a similar approach. Another problem with cumulants, due to spin coupling [Herbert, Int J Quantum Chem 2007, 107, 703], can be solved via the introduction of a similar modulation factor. A related yet more serious issue, termed as the local particle number constraint problem, is also discussed. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

实值化的4阶累积量切片测向算法

4阶累积量切片测向算法由于具有盲高斯特性,提高了算法的测向性能,其4阶累积量的引入增大了算法的运算量.针对算法运算量大的问题,阐述了4阶累积量切片应用酉变换实值化方法简化运算的原理.提出利用实值化方法对4阶累积量切片进行数据重组,利用实数运算来降低算法的运算量,仿真实验验证了算法在保证测向性能的同时降低运算量.     

Behavior and finite-size effects of the sixth order cumulant in the three-dimensional Ising universality class

The high-order cumulants of conserved charges are suggested to be sensitive observables to search for the critical point of Quantum Chromodynamics(QCD). This has been calculated to the sixth order in experiments.Corresponding theoretical studies on the sixth order cumulant are necessary. Based on the universality of the critical behavior, we study the temperature dependence of the sixth order cumulant of the order parameter using the parametric representation of the three-dimensional Ising model, which is expected to be in the same universality class as QCD. The density plot of the sign of the sixth order cumulant is shown on the temperature and external magnetic field plane. We found that at non-zero external magnetic field, when the critical point is approached from the crossover side, the sixth order cumulant has a negative valley. The width of the negative valley narrows with decreasing external field. Qualitatively, the trend is similar to the result of Monte Carlo simulation on a finite-size system. Quantitatively, the temperature of the sign change is different. Through Monte Carlo simulation of the Ising model, we calculated the sixth order cumulant of different sizes of systems. We discuss the finite-size effects on the temperature at which the cumulant changes sign.     

一种新的虚拟均匀线阵的构造方法

基于四阶累积量的DOA估计具有阵列孔径扩展的功能,在基于四阶累积量的均匀线阵基础上,提出一种新的虚拟均匀线阵的构造方法,真实阵元上形成特定的非均匀线阵的排布,使阵列扩展后的四阶累积量矩阵冗余项转化为有用项.仿真结果表明,新算法不但降低了基于四阶累积量的均匀线阵算法的运算量,而且增加了虚拟阵元个数,也带来了阵列孔径扩展的好处.     

基于规范高阶累积量的盲分离算法

本文给出信号的r阶规范累积量定义,证明了在信号瞬时线性混叠情况下r阶规范累积量绝对值不超过最大源信号的r阶规范累积量,因此可以通过最大化r阶规范累积量的绝对值实现盲分离.最大化r阶规范累积量的绝对值可以得到两种盲分离算法,一种高效快速算法———特征值分解盲分离算法,另外一种盲提取算法.本文为高阶累积量盲分离奠定了严格的理论基础.仿真结果验证了理论的正确性和算法的有效性.     

磁性薄膜热动力学性质的变分累积展开研究

采用变分累积展开方法，研究了立方格点上磁性薄膜的热动力学性质.计算自发磁化强度、 内能和热容到了三级累积展开，并对每一级给出了这些物理量对薄膜原子层数的依赖关系. 虽然变分累积展开的收敛性还没有严格证明，但计算结果显示这些物理量的变分累积展开收 敛很快.三级计算结果足已表明：对低于某一临界厚度的薄膜，自发磁化强度随原子层数的 减少而减小；不论在临界温度以下，还是在临界温度以上，每单位格点的内能都随原子层数 的减少而增大；每单位格点的热容在临界温度以下随原子层数的减少而增大，但在临界温度 以上随原子层数的减 关键词： 磁性薄膜 热动力学性质 变分累积展开     

Parametric estimation for simple branching diffusion processes, II

Consider a simple branching diffusion process, which is a branching process in which the individuals move and live and die in space. The offspring distribution has finite moments of all orders. A parametric estimation theory is presented, using time slice data. This involves the use of third order cumulant spectra to identify and estimate the parameters.     

有限温度阿贝尔格点规范理论相变的解析研究

应用交分累积展开方法系统地研究了（２＋１）维和（３＋１）维的Ｚ（２）、Ｚ（３）、Ｕ（１）阿贝尔格点规范理论在有限温度下的相交．所得结果同已有的严格结果及Ｓｖｅｔｉｔｓｋｙ和Ｙａｆｆ的理论预言相符合．     

Nonparametric Approach for Non-Gaussian Vector Stationary Processes

Suppose that {z(t)} is a non-Gaussian vector stationary process with spectral density matrixf(λ). In this paper we consider the testing problemH: ∫^π_−π K{f(λ)} dλ=cagainstA: ∫^π_−π K{f(λ)} dλ≠c, whereK{·} is an appropriate function andcis a given constant. For this problem we propose a testT_nbased on ∫^π_−π K{f(λ)} dλ=c, wheref(λ) is a nonparametric spectral estimator off(λ), and we define an efficacy ofT_nunder a sequence of nonparametric contiguous alternatives. The efficacy usually depnds on the fourth-order cumulant spectraf₄^Zofz(t). If it does not depend onf₄^Z, we say thatT_nis non-Gaussian robust. We will give sufficient conditions forT_nto be non-Gaussian robust. Since our test setting is very wide we can apply the result to many problems in time series. We discuss interrelation analysis of the components of {z(t)} and eigenvalue analysis off(λ). The essential point of our approach is that we do not assume the parametric form off(λ). Also some numerical studies are given and they confirm the theoretical results.     

Asymptotic normality of cumulant spectral estimates

The paper considers higher-order cumulant spectral estimates obtained by directly Fourier transforming weighted cumulant estimates. Such estimates computationally are different from those based on the finite Fourier transform. These estimates can be looked at continuously as well as directly on submanifolds. The estimates of cumulants are based on unbiased moment estimates. Asymptotic normality is obtained for these estimates and is based on a strong mixing condition and only a finite number of cumulant summability conditions.