Information-theoretic basis of spectral estimates of entropy minimax

The relationship between the entropy-minimax method and other methods of spectral analysis, such as the maximum-entropy, eigenvector, and maximum-likelihood methods, is discussed. The method is shown to be optimal in the Kullback-Leibler information metric for a wide class of problems.Nizhny Novgorod State Technical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 11, pp. 1002–1010, November, 1993.     

Minimum entropy density method for the time series analysis

The entropy density is an intuitive and powerful concept to study the complicated nonlinear processes derived from physical systems. We develop the minimum entropy density method (MEDM) to detect the structure scale of a given time series, which is defined as the scale in which the uncertainty is minimized, hence the pattern is revealed most. The MEDM is applied to the financial time series of Standard and Poor’s 500 index from February 1983 to April 2006. Then the temporal behavior of structure scale is obtained and analyzed in relation to the information delivery time and efficient market hypothesis.     

Approach to an irregular time series on the basis of the fractal theory

We present a technique to measure the fractal dimension of the set of points (t, f(t)) forming the graph of a function f defined on the unit interval. First we apply it to a fractional Brownian function [1] which has a property of self-similarity for all scales, and we can get the stable and precise fractal dimension. This technique is also applied to the observational data of natural phenomena. It does not show self-similarity all over the scale but has a different self-similarity across the characteristic time scale. The present method gives us a stable characteristic time scale as well as the fractal dimension.     

Quasi-energy spectral series for a nonlocal Gross-Pitaevskii equation

For a nonlocal Gross-Pitaevskii operator, quasi-energy spectral series have been constructed accurate to O(?^3/2). These series correspond to the closed phase trajectories of the Hamilton-Ehrenfest system, which are stable in a linear approximation. The corresponding monodromy operator has been constructed accurate to Õ(?^3/2) in the class of trajectory-coherent functions.     

Some effects of signal bandwidth and spectral density on the acoustic-reflex threshold in the elderly

The acoustic-reflex thresholds (ART) for multicomponent tonal complexes of varying bandwidth and spectral density were obtained from 20 normal-hearing (air-conduction thresholds less than or equal to 20 dB HL at 250-8000 Hz) young adults ranging in age from 20-30 years and 20 normal-hearing, old subjects ranging in age from 60-71 years. The results revealed that the ART decreased with spectral density, plateauing after seven components in the young group and after five components in the old group; the decrease in the acoustic-reflex threshold as a result of the increase in spectral density was less in the old than in the young group. The bandwidth effect (when bandwidth was plotted in hertz or octaves) on the acoustic-reflex threshold was present in the young adults, but substantially reduced in the elderly, as evidenced by the statistically significant interaction between subject group and signal bandwidth. The spectral density results are discussed in terms of their theoretic implications for the energy summation capacity and frequency resolution of the auditory system. The bandwidth results are discussed in terms of their theoretic implications for the frequency-resolving power of the auditory system.     

一种新型广义RBF神经网络在混沌时间序列预测中的研究

提出了一种新颖的广义径向基函数神经网络模型,其径向基函数(RBF)的形式由生成函数确定.然后,给出了易实现的梯度学习算法,同时为了进一步提高网络的收敛速度和网络性能,又给出了基于卡尔曼滤波的动态学习算法.为了验证网络的学习性能，采用基于卡尔曼滤波算法的新型广义RBF网络预测模型对Mackey-Glass混沌时间序列和Henon映射进行了仿真.结果表明,所提出的新型广义RBF神经网络模型能快速、精确地预测混沌时间序列,是研究复杂非线性动力系统辨识和控制的一种有效方法. 关键词： 广义径向基函数神经网络 卡尔曼滤波 梯度下降学习算法 混沌时间序列 预测     

Analysis of indolylfulgide spectral properties using time dependent density functional theory

An analysis of absorbance maxima of 10 indolylfulgides (open and closed isomeric forms) by time-dependent density functional theory (TD-DFT) is presented. Ground state structures were examined using density functional theory (DFT), using five different functionals. TD-DFT was applied to each structure using four different functionals and the theoretical calculations were compared to experimental data. Comparison of these data was used to determine which functional best describes the ground and excitation energies of the investigated indolylfulgides. Overall we found that by using TD-M06//M06, the vertical excitation energy could be determined within ±0.058 eV (±11 nm).     

基于改进教学优化算法的Hermite正交基神经网络混沌时间序列预测

针对传统预测模型对混沌时间序列预测精度低、收敛速度慢及模型结构复杂的问题, 提出了基于改进教学优化算法的Hermite正交基神经网络预测模型. 首先, 将自相关法和Cao方法相结合对混沌时间序列进行相空间重构, 以获得重构延迟时间向量; 其次, 以Hermite正交基函数为激励函数构成Hermite正交基神经网络, 作为预测模型; 最后, 将模型参数优化问题转化为多维空间上的函数优化问题, 利用改进教学优化算法对预测模型进行参数优化, 以建立预测模型并进行预测分析. 分别以Lorenz 系统和Liu系统为模型, 通过四阶Runge-Kutta法产生混沌时间序列作为仿真对象, 并进行单步及多步预测对比实验. 仿真结果表明, 与径向基函数神经网络、回声状态网络、最小二乘支持向量机及基于教学优化算法的Hermite正交基神经网络预测模型相比, 所提预测模型具有更高的预测精度、更快的收敛速度和更简单的模型结构, 验证了该模型的高效性, 便于推广和应用.     

Robustness of entropy-minimax spectral estimates

The robustness of the entropy-minimax method with respect to perturbations in the sampled data is investigated. The limits and conditions of robustness are determined on the basis of an information-theoretic test of efficiency.Nizhny Novgorod State Technical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 12, pp. 1113–1117, December, 1993.     

Sampling test of spectral estimates

The problem of testing spectral power density by a finite sample of observations is formulated and solved. The efficiency of a synthesized algorithm is studied in the theoretical and information sense. State Technical University, Nizhny Novgorod, Russia Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 4, pp. 530–537, April, 1997.     

Multilayer structures for the water-window spectral range on the basis of scandium

The problems of creating multilayer structures for the soft X-ray range are discussed. The search for an absorbing material for multilayer mirrors and phase shifters based on scandium for the water-window spectral range (wavelength of 2.3?C4 nm) is performed. A comparison of the reflection characteristics of normal-incidence mirrors and the properties of phase shifters during numerical simulation of different pairs of materials shows the possibility of using cobalt as an absorbent in a pair with scandium.     

Some estimates for magnetic fluctuations in a turbulent medium

A new integral relationship between the fluctuations b(r, t) of a magnetic field and its mean B ₀(r, t) is derived for the steady-state magnetic field in a turbulent medium. This formula provides the estimate 〈b?curlb〉=?B ₀?curlB ₀. Simultaneously, the coefficient of amplification of the mean magnetic field α effect) is obtained: α=(η+β)B ₀? curlB ₀/B ₀ ² . The formula for α allows for a decrease in this coefficient owing to the back action of the magnetic field on the turbulent velocity field. It is shown that the Zel’dovich’s estimate 〈 b ²〉?β/η B ₀ ² for two-dimensional turbulence holds for magnetic fields at the instant the fluctuations 〈a ²〉 of the vector potential, rather than 〈b ²〉, reach a maximum. Here, η and β are the ohmic (molecular) and turbulent diffusion coefficients, respectively. This estimate is refined with allowance made for the fact that the condition for diffusion approximation itself relates the β, b, and B ₀ quantities to each other.     

Semiclassical spectral series for the two-component Hartree-type equation

Semiclassical spectral series for the two-component nonlinear Hartree-type operator corresponding to the rest point of the phase curve are constructed on the basis of the Maslov complex germ theory.     

Large-order estimates for ground-state energy perturbation series

A general treatment is given, using path integral methods, of obtaining accurate estimates on the rate of growth at large order of the perturbation coefficients for the lowest eigenvalue (ground-state energy) of a large class of anharmonic oscillators. Simple sufficient conditions are given on the potentialV(x) so that accurate upper and lower bounds on the perturbation coefficients may be derived. Several examples are given which generalize previous results. Examples from Euclidean quantum field theory are also considered.This paper is dedicated to the memory of Mark Kac.     

Some a priori estimates in mechanics

The scope for quantitative a priori estimators is considered and some of the input data are of probabilistic type subject to given constraints. Corresponding estimates are given for the stability of a rod with initial imperfections on pulsed loading, boundary-value problems for a planar potential, and topics in planar elasticity; these relate the constraints imposed on the initial data to certain solution characteristics. Methods are given for determining the coefficients in the corresponding inequalities.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 114–120, August, 1992.     

Transition density estimates for Brownian motion on affine nested fractals

A class of affine nested fractals is introduced which have different scale factors for different similitudes but still have the symmetry assumptions of nested fractals. For these fractals estimates on the transition density for the Brownian motion are obtained using the associated Dirichlet form. An upper bound for the diagonal can be found using a Nash-type inequality, then probabilistic techniques are used to obtain the off-diagonal bound. The approach differs from previous treatments as it uses only the Dirichlet form and no estimates on the resolvent. The bounds obtained are expressed in terms of an intrinsic metric on the fractal.     

Discrimination of spectral density

Experiments were performed to determine the ability of human listeners to discriminate between a sound with a large number of spectral components in a band, of given characteristic frequency and bandwidth, and a sound with a smaller number of components in that band. A pseudorandom placement of the components within the band ensured that no two sounds were identical. The data suggested that discrimination is primarily based upon the perception of temporal fluctuations in the intensity of the sound and secondarily upon resolved structure in the spectrum, perceived as tone color. Experiments using clusters of complex harmonic sounds showed that listeners are able to use the information in upper harmonic bands to discriminate spectral density.