Spectral Domain Methods Research Articles

Diagnostic Evaluation of Visual Snow.

Introduction: To determine which patients with visual snow (VS) and VS syndrome (VSS) require standard ophthalmologic testing including automated visual field and which patients require further testing such as macular spectral domain optical coherence tomography (SD-OCT), electrophysiology, and neuroimaging.Materials and Methods: We retrospectively reviewed 52 consecutive patients at three institutions with VS and VSS including the University of Alabama, Callahan Eye Hospital, the University of Missouri-Kansas City School of Medicine, and the Little Rock Eye Clinic from the years 2015 to 2021. We collected historical information, examination findings, ophthalmic testing, electrophysiology, and neuroimaging.Results: Of the 52 patients with VS and VSS, eight of the 52 cases met the clinical criteria for VSS. The ages ranged from 7 to 79 years, with a mean age of 25 years (SD = 14.0). There were 22 males and 30 females. Color vision was tested in 51 cases and was normal in 47 cases (92%). A funduscopic exam was performed in all 52 cases and was normal in 46 cases (88%). The macular SD-OCT was normal in all of the 19 cases that it was performed (100%). A Humphrey visual field was performed in 50 cases and was normal in 43 (86%). A visually evoked potential (VEP) was normal in 18 of the 19 cases where it was obtained (95%). The full-field electroretinography (ffERG) was obtained in 28 cases and was normal in 25 (89%). The multifocal electroretinography (mfERG) was normal in 11 of 12 cases (92%). Only four patients accounted for all of the abnormal electrophysiological tests. In the 37 cases that had an MRI, 29 were normal (78%). Only one patient revealed a lesion in the visual pathway (right optic nerve enhancement in an optic neuritis patient).Conclusions: Patients with VS and VSS, if typical in presentation and with normal testing, do not require a workup beyond a thorough history, neuro-ophthalmologic examination, and automated perimetry. If this testing is abnormal, then ancillary testing is required.

Quasi-periodic Oscillation of Blazar PKS 1424–418 in γ-Ray Band

We perform the quasi-periodic oscillation (QPO) analysis of blazar PKS 1424−418 in the γ-ray (0.1–300 GeV) band from 2009 May 12 to 2019 September 17 (MJD 54963−58743). Using the spectral domain methods, Bhatta & Dhital reported that this source has 353 days periodic flux oscillations in the γ-ray flux. Adopting time domain methods, we confirm the previous detection that a possible γ-ray QPO of ∼355 days with the high significance level. Combining two methods of time domain and spectral domain provides stronger evidence for the existence of the QPO. Especially, after the strongest flare, γ-ray light-curve exhibits stronger periodic significance compared with the whole observation period. Assuming that the QPO is come from the orbital motion in a supermassive binary black hole system, the mass of primary black hole for this source is estimate as M ∼ 3.5 × 108–5.5 × 109 M ⊙.

Fast computation approach for parameterized design and simulation of vertical ground heat exchangers and GCHP systems

Vertical ground heat exchanger (GHE) is an expensive part of vertical GCHP systems. Fast and accurate computation of fluid and ground temperatures is desired for the long-term energy performance prediction of GCHP and optimal sizing of bore field. Hourly simulations and iteration of parameterized design in time domain with thermal response factors is quite time-consuming. In this paper, a new thermal response factors, δ-function is proposed for computing fluid and ground temperatures of bore field. δ-function is a non-dimensional ground temperature response and an accurate analytical solution of finite line source model to a unit rectangular heat pulse. Computation of δ-function is quite fast due to its quite small integral range. The validity and accuracy of δ-function are examined by the simulation results of g-function. Through comparing hourly simulation of various periods between g- and δ-functions in both time and spectral domain methods, the combination of δ-function with Fast Fourier Transform spends the least computing time and is suitable to quickly and accurately compute fluid and ground temperatures in parameterized design and long-period hourly simulation of vertical heat exchanger and GCHP systems.

Angiotensin‐(1‐7) Attenuates Blood Pressure and Cardiac Hypertrophy in Aged Mice

BackgroundAging is associated with an increase in blood pressure, which is attributed to multiple factors including endothelial dysfunction, cardiac hypertrophy, and changes in cardiovascular autonomic regulation including increased sympathetic tone and reduced measures of parasympathetic tone. In addition, altered responsiveness of the renin‐angiotensin hormone angiotensin (Ang) II has been implicated in age‐related cardiovascular risk. The deleterious actions of Ang II are generally opposed by the vasodilatory and cardioprotective hormone Ang‐(1‐7); however, to our knowledge no studies have evaluated the importance of Ang‐(1‐7) to blood pressure regulation during aging. In this study, we hypothesized that Ang‐(1‐7) would improve blood pressure and cardiac autonomic control in healthy aged mice.MethodsSixteen month‐old male C57BL/6J mice received 6‐week Ang‐(1‐7) [400 ng/kg/min, n=5] or saline infusion (n=3) via subcutaneous osmotic mini‐pumps. All mice were fed standard chow diet (18% kcal from fat). Blood pressure was measured during the last week of treatment via a carotid artery catheter connected to a strain‐gauge transducer and blood pressure analyzer. Cardiac sympathetic and parasympathetic tone and sympathovagal balance were calculated from the blood pressure signal using spectral analysis frequency domain methods. Heart weight and the heart: body weight ratio was determined at end of experiments.ResultsAng‐(1‐7) significantly decreased systolic [Ang‐(1‐7): 102±1 mmHg, saline: 112±6 mmHg, P=0.050] diastolic [Ang‐(1‐7): 78±2 mmHg, saline: 85±2 mmHg, P=0.033], and mean [Ang‐(1‐7): 86±2 mmHg, 94±3 mmHg, P=0.029] blood pressure in aged mice. The blood pressure‐lowering effect of Ang‐(1‐7) was associated with a trend towards reduced sympathetic tone [Ang‐(1‐7): 0.17±0.06, saline: 0.29±0.03, P=0.081], with no effect on vagal tone [Ang‐(1‐7): 0.25±0.11, saline: 0.17±0.06, P=0.625]. Furthermore, Ang‐(1‐7) reduced heart weight [Ang‐(1‐7): 0.19±0.01 g; saline: 0.23±0.02 g, P=0.044] and the heart to body weight ratio [Ang‐(1‐7): 0.004±0.001; saline: 0.006±0.001, P=0.022]. There was no effect of Ang‐(1‐7) on body weight or composition (P > 0.2).ConclusionsChronic Ang‐(1‐7) treatment lowers blood pressure and attenuates cardiac hypertrophy in aged mice, even in the absence of effects on body composition. The blood pressure‐lowering effects of Ang‐(1‐7) appear to involve a decrease in cardiac sympathetic tone; although further studies are needed to confirm these findings. These overall data suggest Ang‐(1‐7) may provide a novel pharmacological target to improve age‐related cardiovascular risk.Support or Funding InformationNIH 5 R00 HL122507‐04, American Heart Association Postdoctoral Fellowship 18POST33960087This abstract is from the Experimental Biology 2019 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

Thermal response factors for fast parameterized design and long-term performance simulation of vertical GCHP systems

Ground-coupled heat pump (GCHP) system is one of the important renewable energy systems. Vertical ground heat exchanger (GHE) is the most expensive part of GCHP systems. Fast and accurate computation of fluid and ground temperatures is desired for the long-term prediction of GCHP performance and the optimal sizing of borehole fields. In this paper, a thermal response factors, δ-function is proposed for computing fluid and ground temperatures of borehole fields. δ-function is a non-dimensional ground temperature response and an accurate analytical solution of finite line source model to a unit rectangular heat pulse. Numerical computation of δ-function is quite fast for its small integral range. The accuracy of δ-function is validated by the simulation results of g-function. The comparative computations are conducted for the hourly simulation of various long periods by combining the g- and δ-functions with both time and spectral domain methods. It is found that the combination of δ-function with fast Fourier transform (FFT) provides dramatically fast computing speed. Therefore, the computation approach of δ-function combined with FFT is the most suitable to quickly and accurately compute the fluid and ground temperatures in parameterized design and long-term simulation of vertical GHE and GCHP systems.

Chronic Angiotensin‐(1‐7) Treatment Prevents Obesity Hypertension in Mice

Obesity is associated with overactivation of the renin‐angiotensin system hormone angiotensin (Ang) II, which increases blood pressure via multiple mechanisms. Conversely, Ang‐(1‐7), a vasodilatory hormone that opposes the actions of Ang II, is deficient in animal models of obesity. Our previous data show that in obese mice chronic systemic Ang‐(1‐7) administration can attenuate weight gain by increasing energy expenditure as well as improve insulin sensitivity. In this study, we hypothesized that Ang‐(1‐7) would prevent the hypertension and increased sympathetic tone also associated with this mouse model of obesity. To test this, adult male C57BL/6J mice received 12‐week Ang‐(1‐7) (400 ng/kg/min) or saline infusion via subcutaneous osmotic mini‐pumps. Immediately following mini‐pump implantation, mice were placed on a 60% high fat diet (HFD) or a standard chow diet. The three groups of mice in this study were chow diet saline (chow; n=6), HFD saline (HFD; n=3) and HFD Ang‐(1‐7) [n=8]. Blood pressure was measured during the last week of treatment via a carotid artery catheter connected to a strain‐gauge transducer and blood pressure analyzer. Cardiac sympathetic and parasympathetic tone and sympathovagal balance were calculated from the blood pressure signal using spectral analysis frequency domain methods. Consistent with our previous studies, Ang‐(1‐7) attenuated weight gain in HFD mice (36±2 chow vs. 44±2, HFD vs. 38±1 grams HFD Ang‐(1‐7); P=0.013). Ang‐(1‐7) also prevented the rise in systolic blood pressure with HFD (105±6 chow vs. 134±9 HFD vs. 111±5 mm Hg HFD Ang‐(1‐7); P=0.031), with a similar trend for diastolic blood pressure (P=0.084). There was no significant effect of Ang‐(1‐7) on heart rate (P=0.973). The Ang‐(1‐7)‐mediated blood pressure lowering in HFD mice was not associated with significant changes in cardiac sympathetic tone (P=0.303), parasympathetic tone (P=0.115), or sympathovagal balance (P=0.521). These data suggest that Ang‐(1‐7) prevents obesity hypertension in mice perhaps through autonomic‐independent mechanisms. Overall, these findings provide rationale for targeting Ang‐(1‐7) for treatment of obesity‐related hypertension.Support or Funding InformationHL122507This abstract is from the Experimental Biology 2018 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

A Nonlinear Frequency-Domain Approach for Numerical Simulation of Wave Energy Converters

Nonlinear, analytical wave-energy converter (WEC) models are generally simulated through time-domain (TD) numerical integration. However, the relatively high computational requirements of TD integration are not compatible with applications where a large number of simulations are needed. Spectral domain (SD) linearization has also been proposed to take into account some nonlinear effects, while being much faster than TD integration. However, as explained in this paper, such SD models have limited accuracy, and cannot extend to the static nonlinear forces. In this paper, a nonlinear frequency-domain (NLFD) method is investigated for WEC simulation, using a projection of the dynamical equations onto a basis of trigonometric functions. A comparison with TD integration (second-order Runge$-$Kutta-RK2) and SD methods is provided, through theoretical considerations, and by means of numerical simulations based on two case studies. In the cases considered, the proposed NLFD method allows for significant computational savings compared to RK2 integration, without requiring any approximation for the radiation forces. NLFD thus shows promising potential for applications involving extensive WEC simulation, such as power production assessment, while preserving the WEC model accuracy. Although slower than SD, NLFD has significant benefits in terms of accuracy and range of applicability.

Topographic gravitational potential up to second-order derivatives: an examination of approximation errors caused by rock-equivalent topography (RET)

In gravity forward modelling, the concept of Rock-Equivalent Topography (RET) is often used to simplify the computation of gravity implied by rock, water, ice and other topographic masses. In the RET concept, topographic masses are compressed (approximated) into equivalent rock, allowing the use of a single constant mass–density value. Many studies acknowledge the approximate character of the RET, but few have attempted yet to quantify and analyse the approximation errors in detail for various gravity field functionals and heights of computation points. Here, we provide an in-depth examination of approximation errors associated with the RET compression for the topographic gravitational potential and its first- and second-order derivatives. Using the Earth2014 layered topography suite we apply Newtonian integration in the spatial domain in the variants (a) rigorous forward modelling of all mass bodies, (b) approximative modelling using RET. The differences among both variants, which reflect the RET approximation error, are formed and studied for an ensemble of 10 different gravity field functionals at three levels of altitude (on and 3 km above the Earth’s surface and at 250 km satellite height). The approximation errors are found to be largest at the Earth’s surface over RET compression areas (oceans, ice shields) and to increase for the first- and second-order derivatives. Relative errors, computed here as ratio between the range of differences between both variants relative to the range in signal, are at the level of 0.06–0.08 % for the potential, \(\sim \)3–7 % for the first-order derivatives at the Earth’s surface (\(\sim \)0.1 % at satellite altitude). For the second-order derivatives, relative errors are below 1 % at satellite altitude, at the 10–20 % level at 3 km and reach maximum values as large as \(\sim \)20 to 110 % near the surface. As such, the RET approximation errors may be acceptable for functionals computed far away from the Earth’s surface or studies focussing on the topographic potential only. However, for derivatives of the functionals computed near the Earth’s surface, the use of RET introduces very spurious errors, in some cases as large as the signal, rendering it useless for smoothing or reducing of field observation, thus rigorous mass modelling should be used for both spatial and spectral domain methods.

Detection of Early Rottenness on Apples by Using Hyperspectral Imaging Combined with Spectral Analysis and Image Processing

Detection of early rottenness on apples is still a challenging task for the automatic grading system due to the highly similarity between the rotten and sound tissues both in spectral and spatial domains. This research was conducted to develop an algorithm for detecting the early rottenness on apples by using hyperspectral reflectance imaging system combined with spectral analysis and image processing. In spectral domain, chemometric and pattern recognition methods were conducted for spectral analysis. In order to select the candidate optimal wavelengths that carry the most important information for distinguishing the rottenness from the sound tissues, successive projections algorithm (SPA) was conducted on the full range of average spectra extracted from the (regions of interest (ROIs) of sound and rotten tissues. The efficiency of the selected candidate optimal wavelengths for rottenness detection was also testified by using a binary particle least square discriminant analysis (PLS-DA) classifier in the spectral domain. In spatial domain, combined image processing methods were conducted for spatial analysis. In order to verify that the images at the optimal wavelengths were efficient and develop a robust detection algorithm, both principal component analysis (PCA) and minimum noise fraction (MNF) combined with conventional image processing methods were conducted on the images at the optimal wavelengths for image processing. Finally, the whole detection algorithm based on SPA-PLS-DA-MNF by using hyperspectral imaging combined with spectral analysis and image processing was designed and testified by the 120 testing apples. The results with 98 % overall detection accuracy indicated that the proposed algorithm was efficient and suitable for the rottenness apple detection. This research provides a foundational basis to develop the fast online inspection or real-time monitoring system for rottenness detection on apples both in the postharvest processing line or storage shelf.

A cohesive analysis of DNA/RNA sequences via entropy, energetics and spectral-domain methods to assess genomic features across single viral diversity.

In virology context, a particular virus may prevail in different forms of serotypes (as in the case of dengue 1-4 viral strains) with common and distinct genomic features. Finding such genomic details of a serogroup is useful in knowing related information for unique vaccine designs compatible for immunity across the viral diversity. For robust comparison of genomes of serovars of a virus in order to decide on their common and differential genomic details, proposed here is a set of sequence analyses exercised side-by-side via entropy, energetic and spectral-domain methods. Results obtained thereof with dengue viral serotypes, namely DEN1, DEN2, DEN3 and DEN4, are presented. Hence, inferences on distinct as well as common features extracted are annotated and indicated for possible vaccine design applications.

Ageing effects on HRV dynamics: a comparative study with FFT and AR models

The present study aims to establish normal limits of short–term Heart Rate Variability (HRV) indices with the two popular spectral domain methods of Fast Fourier Transform (FFT) and Autoregressive (AR) model in three psychosomatically important age groups of healthy male subjects. The three considered age groups are 18–30 years, 30–45 years and 45–60 years and HRV decreases in the higher age groups when evaluated with both the FFT and AR models. Vagal control becomes weak with the ageing process. However, the corresponding HRV indices computed with both the FFT and AR models differ quantitatively, which may be due to methodological differences. The FFT–based technique evaluates HRV indices on the actual RR interval series length and hence, the HRV indices using this technique are considered to be highly accurate, where as the AR model works on the basis of linear prediction. This study may help towards optimisation of AR models such that the HRV indices calculated with both FFT and AR models are nearly the same.

A Conversation with Murray Rosenblatt

On an exquisite March day in 2006, David Brillinger and Richard Davis sat down with Murray and Ady Rosenblatt at their home in La Jolla, California for an enjoyable day of reminiscences and conversation. Our mentor, Murray Rosenblatt, was born on September 7, 1926 in New York City and attended City College of New York before entering graduate school at Cornell University in 1946. After completing his Ph.D. in 1949 under the direction of the renowned probabilist Mark Kac, the Rosenblatts’ moved to Chicago where Murray became an instructor/assistant professor in the Committee of Statistics at the University of Chicago. Murray’s academic career then took him to the University of Indiana and Brown University before his joining the University of California at San Diego in 1964. Along the way, Murray established himself as one of the most celebrated and leading figures in probability and statistics with particular emphasis on time series and Markov processes. In addition to being a fellow of the Institute of Mathematical Statistics and American Association for the Advancement of Science, he was a Guggenheim fellow (1965–1966, 1971–1972) and was elected to the National Academy of Sciences in 1984. Among his many contributions, Murray conducted seminal work on density estimation, central limit theorems under strong mixing, spectral domain methods and long memory processes. Murray and Ady Rosenblatt were married in 1949 and have two children, Karin and Daniel.

Clustering of biological time series by cepstral coefficients based distances

Clustering of stationary time series has become an important tool in many scientific applications, like medicine, finance, etc. Time series clustering methods are based on the calculation of suitable similarity measures which identify the distance between two or more time series. These measures are either computed in the time domain or in the spectral domain. Since the computation of time domain measures is rather cumbersome we resort to spectral domain methods. A new measure of distance is proposed and it is based on the so-called cepstral coefficients which carry information about the log spectrum of a stationary time series. These coefficients are estimated by means of a semiparametric model which assumes that the log-likelihood ratio of two or more unknown spectral densities has a linear parametric form. After estimation, the estimated cepstral distance measure is given as an input to a clustering method to produce the disjoint groups of data. Simulated examples show that the method yields good results, even when the processes are not necessarily linear. These cepstral-based clustering algorithms are applied to biological time series. In particular, the proposed methodology effectively identifies distinct and biologically relevant classes of amino acid sequences with the same physicochemical properties, such as hydrophobicity.

Improved finite-element method for the analysis of multilayer coupled cylindrical striplines and microstrip lines

A novel method, the finite-element method (FEM) using Fourier series as the interpolating function, is presented in this paper for calculating the quasi-static characteristics of coupled cylindrical striplines and microstrip lines filled with multilayered dielectrics. This method is very similar to the normal FEM, but has a much lower-order matrix equation, smaller computational contents, and higher accuracy. It is simpler and more flexible for application than the conformal transformation method. Compared with the integral-equation and spectral-domain methods, this new method is more obvious with regard to its physics and, also, it is not involved in the difficult task of selecting the base functions and relative convergence. The numerical results shown here for several examples are in good agreement with those in the references. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 47: 265–270, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21143

Time-Frequency Analysis for Music Signals: A Mathematical Approach

This paper establishes a link between certain problems that arise when digital audio signals are processed, and a branch of mathematical theory, called Gabor analysis. Going back to the work of D. Gabor in 1946, Gabor analysis is based on the idea of representing arbitrary signals of finite energy in terms of building blocks which have a well-defined “center of gravity” in a time-frequency sense. Indeed, various widely used spectral domain methods correspond to the use of particular Gabor frames. The interpretation of this situation from the point of view of Gabor analysis makes the calculation of the so called dual window computationally efficient and postprocessing by a weighting function unnecessary. Furthermore the idea of locally adaptive sets of building blocks will yield a generalisation of spectral domain methods especially helpful in the investigation of music signals.

Influence of age on the parasympatholytic property of tricyclic antidepressants

Clinical evidence indicates that parasympatholytic effects of tricyclic antidepressants increase with age. The aim of the present study was to determine the possible physiological reason for this phenomenon. Subjects included 23 patients (14 female) with major depression, melancholic type, and 23 age- and sex-matched healthy control subjects. Cardiac vagal tone was measured at rest using both spectral analysis and a time domain beat-to-beat method. Results of the spectral and time domain methods for the estimation of vagal tone used in this study were highly correlated in control subjects as well as in medicated depressed subjects. Both patients and control subjects showed an age-related decline in cardiac vagal tone. Tricyclic antidepressants decreased vagal tone significantly by 25–49% depending on age (20–60 years), although the age difference was not significant. The greater effect of tricyclic antidepressants on parasympathetic activity typically seen in older age groups may reflect the fact that predrug levels of vagal tone are already low in older patients. Measurement of vagal tone prior to drug administration may therefore be of prognostic value for anticholinergic side effects.

A Comparison of Spectral-Domain Methods with Direct Solutions to the One-Dimensional Wave Equation

This paper compares the first- and second-order moments computed by applying two distinctly different methods to the one-dimensional wave equation. The transmission-line form of the one-dimensional wave equation is a special case of a spectral-domain formulation that we developed earlier, but the principal results derived in this paper can be generalized to three dimensions. An essentially complete statistical description of the scattered wave field can be obtained from the method of invariant imbedding, but that method is difficult apply to the three-dimensional problem. The more restrictive Markov approximation, which is used to characterize forward scattering in continuous random media, can be applied in general treatments that accommodate backscatter. We show first that the closure hypothesis obtained by using the Novikov-Furutsu theorem provides a closed system for computing field moments that is correct to terms that are second-order in the perturbation to the constitutive parameter. The Markov approximation is then used to simplify these equations, whereby simple solutions are obtained. We compare these results to the more general results obtained from invariant imbedding. The effective wavenumbers for the coherent wave fields obtained by the two methods differ only by a phase factor that can be neglected under the Markov approximation. For the second-order moments, we develop some general constraints that apply to all solutions, and then show that the Markov approximation leads to the equations of radiative transfer ; however, the radiative transfer equations agree with the more general solution only if an optical-depth parameter is less than unity. The ramifications of these results are discussed.

Application of the FD-TD method to the analysis of H-plane waveguide discontinuities

A direct finite-difference time-domain (FD-TD) method is applied to the analysis of waveguide discontinuities. Both the validity and efficiency of the method ate demonstrated in the case of an H-plane right-angle corner bend with and without dielectric loading. Comparisons of the present results with those obtained using the spectral-domain methods are made and they are shown to be in good agreement.

A Frequency Domain Analysis of Groundwater Quality Fluctuations: Interpretation of Field Data

Environmental tracer or pollution patterns in groundwater have been regarded as a qualitative means of studying complex or large‐scale hydrogeologic systems. However, questions have arisen as to whether the “natural state” analog has quantitative value, such as for the estimation of transport or aquifer parameters. In this paper we demonstrate the application of spectral analysis and frequency domain methods to temporal tracer patterns for the physical interpretation of transient environmental tracers in a variety of hydrologic settings. Three case studies are examined where the source of environmental tracer is represented as a stochastic process. Process and parameter estimation is performed by comparison of the theoretical transfer function and phase spectrum. The most important result of this paper is that different source configurations (nonpoint, point, etc.) and different groundwater flow patterns produce unique frequency response characteristics for solutes within each system. It is this feature which allows us to make inference about the governing physical processes and parameters.

Analysis and applications of modified coupled coplanar lines

Modified coupled coplanar lines, compatible with the classical and conductor-backed coplanar waveguides, are analysed using the quasistatic and full-wave spectral domain methods. Results of the analysis are utilised for designing a 10 dB directional coupler. Measured isolation of the coupler is higher than 33 dB in the bandwidth up to 5 GHz.