Empirical Spectral Density Research Articles

GARTFIMA process and its empirical spectral density based estimation

ABSTRACT In this article, we introduce a Gegenbauer autoregressive tempered fractionally integrated moving average process. We work on the spectral density and autocovariance function for the introduced process. The parameter estimation is done using the empirical spectral density with the help of the nonlinear least square technique and the Whittle likelihood estimation technique. The performance of the proposed estimation techniques is assessed on simulated data. Further, the introduced process is shown to better model the real-world data in comparison to other time series models.

Limiting spectral distribution of stochastic block model

The stochastic block model (SBM) is an extension of the Erdős–Rényi graph and has applications in numerous fields, such as data analysis, recovering community structure in graph data and social networks. In this paper, we consider the normal central SBM adjacency matrix with [Formula: see text] communities of arbitrary sizes. We derive an explicit formula for the limiting empirical spectral density function when the size of the matrix tends to infinity. We also obtain an upper bound for the operator norm of such random matrices by means of the Stieltjes transform and random matrix theory.

A Measurement System for the Environmental Load Assessment of a Scale Ship Model-Part II.

In the process of ship motion control system design, it is necessary to take into account the impact of environmental disturbances such as winds, waves and sea currents. The commonly used representatives of wave influences in this area are the unidirectional wave power spectral density functions describing sea waves of different form: long-crested, fully developed waves, developing wind waves or multi-modal waves (e.g., with swell). The existing standard PSD models describe the surge of open sea or ocean. However, they are inadequate in the case of control system testing of scale ship models for sailing in open water areas such as lakes or test pools. This paper presents a study of wind-generated wave PSD estimations for a small lake used as a test area for free-running scale ships. The publication provides a brief overview of the wave spectral density functions commonly used for control system design. A measurement instrument using the idea of a water-induced variable capacitance that works synchronously with the wind sensors is also described. The process of collected data analysis is presented. As a result of the study, a series of empirical spectral density functions of lake waves for different wind speeds are obtained. They correspond to the rescaled, two-parametric ITTC model.

Path Large Deviations for the Kinetic Theory of Weak Turbulence

We consider a generic Hamiltonian system of nonlinear interacting waves with 3-wave interactions. In the kinetic regime of wave turbulence, which assumes weak nonlinearity and large system size, the relevant observable associated with the wave amplitude is the empirical spectral density that appears as the natural precursor of the spectral density, or spectrum, for finite system size. Following classical derivations of the Peierls equation for the moment generating function of the wave amplitudes in the kinetic regime, we propose a large deviation estimate for the dynamics of the empirical spectral density, where the number of admissible wavenumbers, which is proportional to the volume of the system, appears as the natural large deviation parameter. The large deviation stochastic Hamiltonian that quantifies the minus of the log probability of a trajectory is computed within the kinetic regime which assumes the Random Phase approximation for weak nonlinearity. We compare this Hamiltonian with the one for a system of modes interacting in a mean-field way with the empirical spectrum. Its relationship with the Random Phase and Amplitude approximation is discussed. Moreover, for the specific case when no forces and dissipation are present, a few fundamental properties of the large deviation dynamics are investigated. We show that the latter conserves total energy and momentum, as expected for a 3-wave interacting systems. In addition, we compute the equilibrium quasipotential and check that global detailed balance is satisfied at the large deviation level. Finally, we discuss briefly some physical applications of the theory.

Facial erythema detects diabetic neuropathy using the fusion of machine learning, random matrix theory and self organized criticality

Rubeosis faciei diabeticorum, caused by microangiopathy and characterized by a chronic facial erythema, is associated with diabetic neuropathy. In clinical practice, facial erythema of patients with diabetes is evaluated based on subjective observations of visible redness, which often goes unnoticed leading to microangiopathic complications. To address this major shortcoming, we designed a contactless, non-invasive diagnostic point-of-care-device (POCD) consisting of a digital camera and a screen. Our solution relies on (1) recording videos of subject’s face (2) applying Eulerian video magnification to videos to reveal important subtle color changes in subject’s skin that fall outside human visual limits (3) obtaining spatio-temporal tensor expression profile of these variations (4) studying empirical spectral density (ESD) function of the largest eigenvalues of the tensors using random matrix theory (5) quantifying ESD functions by modeling the tails and decay rates using power law in systems exhibiting self-organized-criticality and (6) designing an optimal ensemble of learners to classify subjects into those with diabetic neuropathy and those of a control group. By analyzing a short video, we obtained a sensitivity of 100% in detecting subjects diagnosed with diabetic neuropathy. Our POCD paves the way towards the development of an inexpensive home-based solution for early detection of diabetic neuropathy and its associated complications.

Spatio-Temporal Correlation Analysis of Online Monitoring Data for Anomaly Detection and Location in Distribution Networks

The online monitoring data in distribution networks contain rich information on the running states of the networks. By leveraging the data, this paper proposes a spatio-temporal correlation analysis approach for anomaly detection and location in distribution networks. First, spatio-temporal matrix for each feeder line in a distribution network is formulated and the spectrum of its covariance matrix is analyzed. The spectrum is complex and exhibits two aspects: 1) bulk, which arises from random noise or fluctuations and 2) spikes, which represents factors caused by anomaly signals or fault disturbances. Then, by connecting the estimation of the number of factors to the limiting empirical spectral density of covariance matrices of residuals, the spatio-temporal parameters are accurately estimated, during which free random variable techniques are used. Based on the estimators, anomaly indicators are designed to detect and locate the anomalies by exploring the variations of spatio-temporal correlations in the data. The proposed approach is sensitive to the anomalies and robust to random fluctuations, which makes it possible for detecting early anomalies and reducing false alarming rate. Case studies on both synthetic data and real-world online monitoring data verify the effectiveness and advantages of the proposed approach.

Modal Participation Estimated from the Response Correlation Matrix

In this paper, we are considering the case of estimating the modal participation vectors from the operating response of a structure. Normally, this is done using a fitting technique either in the time domain using the correlation function matrix or in the frequency domain using the spectral density matrix. In this paper, a more simple approach is proposed based on estimating the modal participation from the correlation matrix of the operating responses. For the case of general damping, it is shown how the response correlation matrix is formed by the mode shape matrix and two transformation matrices T1 and T1 that contain information about the modal parameters, the generalized modal masses, and the input load spectral density matrix Gx. For the case of real mode shapes, it is shown how the response correlation matrix can be given a simple analytical form where the corresponding real modal participation vectors can be obtained in a simple way. Finally, it is shown how the real version of the modal participation vectors can be used to synthesize empirical spectral density functions.

Circulant matrices and time-series analysis

This paper sets forth some salient results in the algebra of circulant matrices which can be used in time-series analysis. It provides easy derivations of some results that are central to the analysis of statistical periodograms and empirical spectral density functions. A statistical test for the stationarity or homogeneity of empirical processes is also presented.

Circulant Matrices And Time-Series Analysis

This paper sets forth some of the salient results in the algebra of circulant matrices which can be used in time-series analysis. It provides easy derivations of some results that are central to the analysis of statistical periodograms and empirical spectral density functions. A statistical test for the stationarity or homogeneity of empirical processes is also presented.

Mapping of the spectral density function of a C alpha-H alpha bond vector from NMR relaxation rates of a 13C-labelled alpha-carbon in motilin.

The peptide hormone motilin was synthesised with a 13C-enriched alpha-carbon in the leucine at position 10. In aqueous solution, six different relaxation rates were measured for the 13C alpha-H alpha fragment as a function of temperature and with and without the addition of 30% (v/v) of the cosolvent d2-1,1,1,3,3,3-hexafluoro-2-propanol (HFP). The relaxation rates were analysed employing the spectral density mapping technique introduced by Peng and Wagner [(1992) J. Magn. Reson., 98, 308-332] and using the model-free approach by Lipari and Szabo [(1982) J. Am. Chem. Soc., 104, 4546-4570]. The fit to various models of dynamics was also considered. Different procedures to evaluate the overall rotational correlation time were compared. A single exponential time correlation function was found to give a good fit to the measured spectral densities only for motilin in 30% (v/v) HFP at low temperatures, whereas at high temperatures in this solvent, and in D2O at all temperatures, none of the considered models gave an acceptable fit. A new empirical spectral density function was tested and found to accurately fit the experimental spectral density mapping points. The application of spectral density mapping based on NMR relaxation data for a specific 13C-1H vector is shown to be a highly useful method to study biomolecular dynamics. Advantages are high sensitivity, high precision and uniform sampling of the spectral density function over the frequency range.

Anisotropic optical properties of YBa2Cu3O7

Based upon the published results of YBa2Cu3O7 single-crystal reflectance spectra measured at room temperature, the empirical anisotropic spectral density functions and quasidielectric functions ε1j+iε2j [j=a,b,c] are determined in the 0.05 to 6 eV spectral range. These functions are an excellent fit to the reflectance spectra of samples in single-crystal, twin-crystal, and polycrystalline forms; they agree well with the published anisotropic transport and ellipsometry data. For polarizations along the a and b axes, the numerically determined empirical spectral density functions have shown two interband absorption peaks at 2.5 and 5 eV. For energy above 3 eV, the spectral density functions do not agree with the published theoretical interband conductivities that are derived from the band structure calculations.

1H nuclear magnetic resonance studies of Hf 2RhH 2.2 and Hf 2CoH 3.8: Structure and diffusion

Proton nuclear magnetic resonance relaxation times T 1 T 1 ρ , T 2 and T 1 D are reported for the intermetallic hydrides Hf 2RhH 2.2 and Hf 2CoH 3.8 in the temperature range 77–450 K at 16 and 60 MHz. X-ray diffraction studies showed that the hydrides are cubic ( Fd3m) with lattice parameters a of 12.76 Å and 12.74 Å respectively. A model for the location of the hydrogen atoms is described which is consistent with the observed second moments (16 G 2 and 31 G 2 respectively). Above about 200 K, relaxation is determined by translational diffusion of the hydrogen atoms. The frequency dependence of an empirical spectral density function for hydrogen diffusion was determined from the temperature dependence of T 1, T 1 ρ and T 2 by temperature-frequency superposition. The form of the empirical function and the possible involvement of an IR divergence phenomenon are discussed. Below about 200 K T 1, T 1 ρ and T 1 D become dominated by paramagnetic effects.

Zeeman exchange cross relaxation time TZX1 in BCC3 He

Abstract Measurements are reported of T ZX 1 in BCC 3 He whose molar volume dependence is obtained in high accuracy. This dependence is described with an empirical spectral density function different from the often used theoretical one consistently with the thermostatic results.