Eigenvector method for texture recognition

We investigate the electron-boson spectral density function, $I^2\chi(\omega,T)$, of CuO$_2$ plane in underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212) and underdoped YBa$_2$Cu$_3$O$_{6.50}$ (Y-123) using the Eliashberg formalism. We apply a new (in-plane) pseudogap model to extract the electron-boson spectral function. For extracting the spectral function we assume that the spectral density function consists of two components: a sharp mode and the broad Millis-Monien-Pines (MMP) mode. We observe that both the resulting spectral density function and the intensity of the pseudogap show strong temperature dependences: the sharp mode takes most spectral weight of the function and the peak position of the sharp mode shifts to lower frequency and the depth of pseudogap, $1-\tilde{N}(0,T)$, is getting deeper as temperature decreases. We observe also that the total spectral weight of the electron-boson density and the mass enhancement coefficient increase as temperature decreases. We estimate fictitious (maximum) superconducting transition temperatures, $T_c(T)$, from the extracted spectral functions at various temperatures using a generalized McMillan formula. The estimated (maximum) $T_c$ also shows a strong temperature dependence; it is higher than the actual $T_c$ at all measured temperatures and decreases with temperature lowering. Since as lowering temperature the pseudogap is getting stronger and the maximum $T_c$ is getting lower we propose that the pseudogap may suppress the superconductivity in cuprates.

Analysis of NMR Spin-Relaxation Data Using an Inverse Gaussian Distribution Function

This paper presents a new method of texture characterization, recognition and defect detection in textures, based on mathematical morphology transformations: structural opening and top-hat. The structural opening and its properties of invariance allow the extraction of primitive patterns from a texture, some kind of textons which entirely characterize it. As a result, defect detection can be performed by a top-hat transformation for a similar textural set with defects, and texture recognition can be led by a reference set.

We introduce a differential-geometric structure for spectral density functions of discrete-time random processes. This is quite analogous to the Riemannian structure of information geometry, which is used to study perturbations of probability density functions, and which is based on the Fisher information metric. Herein, we introduce an analogous Riemannian metric, which we motivate with a problem in prediction theory. It turns out that this problem also provides a prediction theoretic interpretation to the Itakura distortion measure, which relates to our metric. Geodesies and geodesic distances are characterized in closed form and, hence, the geodesic distance between two spectral density functions provides an explicit, intrinsic (pseudo)metric on the cone of density functions. Certain other distortion measures that involve generalized means of spectral density functions are shown to lead to the same Riemannian metric. Finally, an alternative Riemannian metric is introduced, which is motivated by an analogous problem involving smoothing instead of prediction.

The author focuses on the frequency domain approach, which provides a complete characterization of frequency. The standard characterization of frequency stability in the frequency domain is the spectral density function (SDF). The author describes SDFs that model sampled frequency stability data and that are related to the SDFs of the standard characterization. On the basis of standard techniques in spectral analysis, he outlines a systematic way of estimating SDFs typical of frequency stability data. The recommended procedure is to check for broadband bias in the periodogram using a sequence of data tapers and, if bias is in evidence, to design an autoregressive prewhitening filter to prewhiten the data. The author considers the relationship between the Allan variance and the SDF and outlines two nonparametric ways of translating stability measures between the two domains-one based upon pilot analysis and the other upon J. Rutman's bandpass variance (1978).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The acoustic peak in the CMB power spectrum is sensitive to causal processes and cosmological parameters in the early universe up to the time of last scattering. We provide limits on correlated spatial variations of the peak height and peak position and interpret these as constraints on the spatial variation of the cosmological parameters (baryon density, cold dark matter density and cosmological constant as well as the amplitude and tilt of the original fluctuations). We utilize recent work of Hansen, Banday and Gorski (HBG) who have studied the spatial isotropy of the power spectrum as measured by WMAP by performing the power spectrum analysis on smaller patches of the sky. We find that there is no statistically significant correlated asymmetry of the peak. HBG have also provided preliminary indications of a preferred direction in the lower angular momentum range(~ 2-40) and we show how possible explanations of this asymmetry are severely constrained by the data on the acoustic peak. Finally we show a possible non-gaussian feature in the data, associated with a difference in the northern and southern galactic hemispheres.

We describe a project (HETDEX) to measure the evolution of dark energy out to z∼4 with high precision. The galaxy power spectrum contains the baryonic oscillations seen in the CMB, and these features remain in the linear regime at high redshift. The separation of these peaks in the power spectrum is a standard ruler imprinted on both the angular and redshift space distribution of galaxies, providing direct constraints on the local Hubble constant H(z) and the angular diameter distance DA(z), both of which are related to the dark energy equation of state parameter w(z).We propose the use of Ly‐α emitting galaxies as the tracer of the power spectrum, and describe the Visible IFU Replicable Ultra‐cheap Spectrograph (VIRUS), capable of undertaking such a survey. VIRUS will be a very wide field integral field spectrograph of a new replicated design, consisting of more than a hundred individual spectrograph units. The VIRUS instrument mounted on a new wide field corrector on the Hobby‐Eberly Telescope (HET) will allow 1 million Ly‐α emitting galaxies to be mapped over 1.8 < z < 3.8 in 200 square degrees of sky, a volume 10 times that of the Sloan Digital Sky Survey (SDSS) in 100 nights of operation. This survey of large scale structure is sufficient to measure the power spectrum to 2–3% accuracy and constrain the positions of the baryonic acoustical peaks on the matter spectrum to ⩽ 1%. This in turn provides sufficient accuracy on H(z) and DA(z) to challenge the level of dark energy constraint expected from the SNAP satellite at a fraction of the cost, while providing unique constraints at z>2. The baryonic acoustical peaks method is largely free of systematic biases and provides an independent test of results found by other methods.

In this paper we present several results for three different canonical forms of linear prediction on a plane. These filters have causal, semicausal, and noncausal prediction geometries. Starting from their properties we consider the problem of realization of these filters from a given power spectral density function (SDF). Since it is not possible in general to obtain rational spectral factors of a two-dimensional SDF, we propose algorithms for obtaining rational approximations which are stable and converge to their limit (irrational) factors as the order of approximation is increased. It is also shown that the normal equations associated with the minimum variance two-dimensional prediction filters give a useful algorithm for obtaining rational approximations which are stable and converge to their unique limit filters. This result allows design of finite-order stable filters by solving a finite number of equations while realizing the given SDF arbitrarily closely.

Variability response functions for beams with nonlinear constitutive laws

Reduction of leakage and increase of resolution in power spectral density and coherence functions

Homogenization of spectral problem for locally periodic elliptic operators with sign-changing density function

This paper deals with a large class of nonstationary stochastic processes generated by passing white noise through a general linear time-varying filter. It is shown that such processes can be characterized in terms of a family of jointly wide-sense stationary processes. This formulation is used to define the spectral density function for the nonstationary processes considered in the paper. Then the spectral density function is used to give a suboptimal solution to the nonstationary Wiener filtering problem. This suboptimal solution is shown to be nearly optimal under conditions corresponding to a sufficiently small rate of variation. A numerical example compares this suboptimal Wiener filter solution to an optimal solution.

Signal processing of flutter flight test data enables verification of aircraft flutter design, and the signal from a flutter flight test excited by atmospheric turbulence is a particularly important form of the flutter test. Owing to the randomness of atmospheric turbulence excitation, multi-channel analysis of turbulence responses at various positions in the same component can improve the analytical accuracy of flutter signal processing. The relationship between the maximum singular value of the multi-channel turbulence response power spectral density matrix and the system self-power spectral density function is elucidated herein using a frequency domain decomposition method. However, there is a contradiction in the power spectral density function between the spectral line density and the spectral line smoothing calculated based on the periodogram of the frequency domain decomposition. By applying an autoregressive spectral model, the power spectral density function of the turbulence response is calculated to achieve spectral line smoothing and sufficient spectral line density. Additionally, the power spectral density function is then used to construct the power spectral density function matrix of the multi-channel turbulence response, and the maximum singular value curve is calculated based on the singular value decomposition of each spectral pin. Finally, the modal parameters of the turbulence response signal are estimated via multi-modal frequency domain fitting. The developed approach is validated based on simulations and flutter flight test turbulence response signals.

谱峰的检测分析在色谱技术研究中具有十分重要的作用,但在色谱数据采集、传输的过程中,不同程度的噪声干扰给谱峰检测带来了极大的困难。目前传统的谱峰检测算法普遍通过基底扣除的方式对谱峰的形态进行预定义,将谱峰分为单峰、重叠峰等多个种类。针对不同种类的谱峰采用不同的检测方法,这就导致了传统的谱峰检测算法具有高复杂度、低自动化程度以及容易失真等缺点。因此,该文从另一个角度出发提出了一种新型的谱峰检测算法。该算法取消基底扣除以及谱峰分类这一步骤,直接在源数据曲线的基础上进行谱峰检测,主要分为离散差分、趋势累积以及遍历寻峰3个步骤。首先通过信号量表征数据升降趋势;然后进行数据趋势累积,根据累积总和定位谱峰,采用三点定位的方式,即峰起点、极值点和峰终点描述一个谱峰的位置;最后根据遍历排序的方式进行谱峰的筛选。此外,通过谱峰扣除的方式得到曲线基底部分。采用C语言设计编写了算法程序,并对多个动态比表面积分析仪测定的色谱图进行了检测分析,结果显示使用该算法可以精准区分谱峰部分与基底部分,受数据曲线毛刺、震荡等噪声干扰很小,谱峰的三点定位十分准确,且不受其复杂形态的影响,具有很强的普适性。与其他算法相比,该算法定位准确,结构清晰,具有较好的稳定性以及可靠性。该文报道了无基底扣除以及趋势累积等新型谱峰检测思想在吸脱附色谱曲线中的应用,证明了其在吸脱附色谱峰检测中的有效性和良好的应用前景。

In many engineering problems, the power spectra of random signals have to be measured. In this paper, a method for estimating the unknown parameters in the power spectral density functions of discrete random processes is presented. The spectral density functions are represented by a ratio of two real polynomials in z. It is assumed that only a finite record of the random process is observed and no knowledge about its probability distribution is required. An estimation procedure is developed. It is shown that the denominator parameter estimates can be first obtained. Then the numerator parameters are estimated by filtering the poles from the spectrum. A four parameter example is given to demonstrate the method.