Spectral analysis of seabed elevation from the Danish Wadden Sea

Bedforms both reflect and influence shallow water hydrodynamics and sediment dynamics. A correct characterization of their spatial distribution and dimensions is required for the understanding, assessment and prediction of numerous coastal processes. A method to parameterize geometrical characteristics using two-dimensional (2D) spectral analysis is presented and tested on seabed elevation data from the Knudedyb tidal inlet in the Danish Wadden Sea, where large compound bedforms are found. The bathymetric data were divided into 20x20 m areas on which a 2D spectral analysis was applied. The most energetic peak of the 2D spectrum was found and its energy, frequency and direction were calculated. A power-law was fitted to the average of slices taken through the 2D spectrum; its slope and y-intercept were calculated. Using these results the test area was morphologically classified into 4 distinct morphological regions. The most energetic peak and the slope and intercept of the power-law showed high values above the crest of the primary bedforms and scour holes, low values in areas without bedforms, and intermediate values in areas with secondary bedforms. The secondary bedform dimensions and orientations were calculated. An area of 700x700 m was used to determine the characteristics of the primary bedforms. However, they were less distinctively characterized compared to the secondary bedforms due to relatively large variations in their orientations and wavelengths. The method is thus appropriate for morphological classification of the seabed and for bedform characterization, being most efficient in areas characterized by bedforms with regular dimensions and directions.

Spectral analysis of the effects of daylight saving time on motor vehicle fatal traffic accidents. Final report.

National Highway Traffic Safety Administration, Mathematical Analysis Division, Washington, D.C.

Analysis of β-amyloid (Aβ) deposition in the temporal lobe in Alzheimer's disease using Fourier (spectral) analysis

To determine the spatial pattern of ß-amyloid (Aß) deposition throughout the temporal lobe in Alzheimer's disease (AD). Methods: Sections of the complete temporal lobe from six cases of sporadic AD were immunolabelled with antibody against Aß. Fourier (spectral) analysis was used to identify sinusoidal patterns in the fluctuation of Aß deposition in a direction parallel to the pia mater or alveus. Results: Significant sinusoidal fluctuations in density were evident in 81/99 (82%) analyses. In 64% of analyses, two frequency components were present with density peaks of Aß deposits repeating every 500–1000 µm and at distances greater than 1000 µm. In 25% of analyses, three or more frequency components were present. The estimated period or wavelength (number of sample units to complete one full cycle) of the first and second frequency components did not vary significantly between gyri of the temporal lobe, but there was evidence that the fluctuations of the classic deposits had longer periods than the diffuse and primitive deposits. Conclusions: (i) Aß deposits exhibit complex sinusoidal fluctuations in density in the temporal lobe in AD; (ii) fluctuations in Aß deposition may reflect the formation of Aß deposits in relation to the modular and vascular structure of the cortex; and (iii) Fourier analysis may be a useful statistical method for studying the patterns of Aß deposition both in AD and in transgenic models of disease.

Spectral analysis of four 'hypervariable' AGN: a micro-needle in the haystack?

We analyze four extreme AGN transients to explore the possibility that they are caused by rare, high-amplitude microlensing events. These previously unknown type-I AGN are located in the redshift range 0.6-1.1 and show changes of > 1.5 magnitudes in the g-band on a timescale of ~years. Multi-epoch optical spectroscopy, from the William Herschel Telescope, shows clear differential variability in the broad line fluxes with respect to the continuum changes and also evolution in the line profiles. In two cases a simple point-source, point-lens microlensing model provides an excellent match to the long-term variability seen in these objects. For both models the parameter constraints are consistent with the microlensing being due to an intervening stellar mass object but as yet there is no confirmation of the presence of an intervening galaxy. The models predict a peak amplification of 10.3/13.5 and an Einstein timescale of 7.5/10.8 years respectively. In one case the data also allow constraints on the size of the CIII] emitting region, with some simplifying assumptions, to to be ~1.0-6.5 light-days and a lower limit on the size of the MgII emitting region to be > 9 light-days (half-light radii). This CIII] radius is perhaps surprisingly small. In the remaining two objects there is spectroscopic evidence for an intervening absorber but the extra structure seen in the lightcurves requires a more complex lensing scenario to adequately explain.

Ultrasonic Spectral Analysis for Nuclear Fuel Characterization

Ceramic materials have been widely used for various purposes in many different industries due to certain characteristics, such as high melting point and high resistance to corrosion. Concerning the areas of applications, automobile, aeronautics, naval and even nuclear, the characteristics of these materials should be strictly controlled. In the nuclear area, ceramics are of great importance once they are the nuclear fuel pellets and must have, among other features, a well controlled porosity due to mechanical strength and thermal conductivity required by the application. Generally, the techniques used to characterize nuclear fuel are destructive and require costly equipment and facilities. This paper aims to present a nondestructive technique for ceramic characterization using ultrasound. This technique differs from other ultrasonic techniques because it uses ultrasonic pulse in frequency domain instead of time domain, associating the characteristics of the analyzed material with its frequency spectrum. In the present work, 40 Alumina (Al2O3) ceramic pellets with porosities ranging from 5% to 37%, in absolute terms measured by Archimedes technique, were tested. It can be observed that the frequency spectrum of each pellet varies according to its respective porosity and microstructure, allowing a fast and non-destructive association of the same characteristics with the same spectra pellets.

Spectral waveform analysis of intranodal arterial blood flow in abnormally large superficial lymph nodes in dogs

Objective-To evaluate pulsed-wave Doppler spectral parameters as a method for distinguishing between neoplastic and inflammatory peripheral lymphadenopathy in dogs. Sample Population-40 superficial lymph nodes from 33 dogs with peripheral lymphadenopathy. Procedures-3 Doppler spectral tracings were recorded from each node. Spectral Doppler analysis including assessment of the resistive index, peak systolic velocity-to-end diastolic velocity (S:D) ratio, diastolic notch velocity-to-peak systolic velocity (N:S) ratio, and end diastolic velocity-to-diastolic notch velocity ratio was performed for each tracing. Several calculation methods were used to determine the Doppler indices for each lymph node. After the ultrasonographic examination, fine needle aspirates or excisional biopsy specimens of the examined lymph nodes were obtained, and lymphadenopathy was classified as either inflammatory or neoplastic (lymphomatous or metastatic) via cytologic or histologic examination. Results of Doppler analysis were compared with cytologic or histopathologic findings. Results-The Doppler index with the highest diagnostic accuracy was the S:D ratio calculated from the first recorded tracing; a cutoff value of 3.22 yielded sensitivity of 91%, specificity of 100%, and negative predictive value of 89% for detection of neoplasia. Overall diagnostic accuracy was 95%. At a sensitivity of 100%, the most accurate index was the N:S ratio calculated from the first recorded tracing; a cutoff value of 0.45 yielded specificity of 67%, positive predictive value of 81%, and overall diagnostic accuracy of 86.5%. Conclusions and Clinical Relevance-Results suggested that noninvasive Doppler spectral analysis may be useful in the diagnosis of neoplastic versus inflammatory peripheral lymphadenopathy in dogs.

Spectral Frame Analysis and Learning through Graph Structure

This dissertation investigates the connection between spectral analysis and frame theory. When considering the spectral properties of a frame, we present a few novel results relating to the spectral decomposition. We first show that scalable frames have the property that the inner product of the scaling coefficients and the eigenvectors must equal the inverse eigenvalues. From this, we prove a similar result when an approximate scaling is obtained. We then focus on the optimization problems inherent to the scalable frames by first showing that there is an equivalence between scaling a frame and optimization problems with a non-restrictive objective function. Various objective functions are considered, and an analysis of the solution type is presented. For linear objectives, we can encourage sparse scalings, and with barrier objective functions, we force dense solutions. We further consider frames in high dimensions, and derive various solution techniques. From here, we restrict ourselves to various frame classes, to add more specificity to the results. Using frames generated from distributions allows for the placement of probabilistic bounds on scalability. For discrete distributions (Bernoulli and Rademacher), we bound the probability of encountering an ONB, and for continuous symmetric distributions (Uniform and Gaussian), we show that symmetry is retained in the transformed domain. We also prove several hyperplane-separation results. With the theory developed, we discuss graph applications of the scalability framework. We make a connection with graph conditioning, and show the in-feasibility of the problem in the general case. After a modification, we show that any complete graph can be conditioned. We then present a modification of standard PCA (robust PCA) developed by Cand\`es, and give some background into Electron Energy-Loss Spectroscopy (EELS). We design a novel scheme for the processing of EELS through robust PCA and least-squares regression, and test this scheme on biological samples. Finally, we take the idea of robust PCA and apply the technique of kernel PCA to perform robust manifold learning. We derive the problem and present an algorithm for its solution. There is also discussion of the differences with RPCA that make theoretical guarantees difficult.

Analysis of cardiac and epileptic signals using higher order spectra

The theory of nonlinear dyamic systems provides some new methods to handle complex systems. Chaos theory offers new concepts, algorithms and methods for processing, enhancing and analyzing the measured signals. In recent years, researchers are applying the concepts from this theory to bio-signal analysis. In this work, the complex dynamics of the bio-signals such as electrocardiogram (ECG) and electroencephalogram (EEG) are analyzed using the tools of nonlinear systems theory. In the modern industrialized countries every year several hundred thousands of people die due to sudden cardiac death. The Electrocardiogram (ECG) is an important biosignal representing the sum total of millions of cardiac cell depolarization potentials. It contains important insight into the state of health and nature of the disease afflicting the heart. Heart rate variability (HRV) refers to the regulation of the sinoatrial node, the natural pacemaker of the heart by the sympathetic and parasympathetic branches of the autonomic nervous system. Heart rate variability analysis is an important tool to observe the heart's ability to respond to normal regulatory impulses that affect its rhythm. A computerbased intelligent system for analysis of cardiac states is very useful in diagnostics and disease management. Like many bio-signals, HRV signals are non-linear in nature. Higher order spectral analysis (HOS) is known to be a good tool for the analysis of non-linear systems and provides good noise immunity. In this work, we studied the HOS of the HRV signals of normal heartbeat and four classes of arrhythmia. This thesis presents some general characteristics for each of these classes of HRV signals in the bispectrum and bicoherence plots. Several features were extracted from the HOS and subjected an Analysis of Variance (ANOVA) test. The results are very promising for cardiac arrhythmia classification with a number of features yielding a p-value < 0.02 in the ANOVA test. An automated intelligent system for the identification of cardiac health is very useful in healthcare technology. In this work, seven features were extracted from the heart rate signals using HOS and fed to a support vector machine (SVM) for classification. The performance evaluation protocol in this thesis uses 330 subjects consisting of five different kinds of cardiac disease conditions. The classifier achieved a sensitivity of 90% and a specificity of 89%. This system is ready to run on larger data sets. In EEG analysis, the search for hidden information for identification of seizures has a long history. Epilepsy is a pathological condition characterized by spontaneous and unforeseeable occurrence of seizures, during which the perception or behavior of patients is disturbed. An automatic early detection of the seizure onsets would help the patients and observers to take appropriate precautions. Various methods have been proposed to predict the onset of seizures based on EEG recordings. The use of nonlinear features motivated by the higher order spectra (HOS) has been reported to be a promising approach to differentiate between normal, background (pre-ictal) and epileptic EEG signals. In this work, these features are used to train both a Gaussian mixture model (GMM) classifier and a Support Vector Machine (SVM) classifier. Results show that the classifiers were able to achieve 93.11% and 92.67% classification accuracy, respectively, with selected HOS based features. About 2 hours of EEG recordings from 10 patients were used in this study. This thesis introduces unique bispectrum and bicoherence plots for various cardiac conditions and for normal, background and epileptic EEG signals. These plots reveal distinct patterns. The patterns are useful for visual interpretation by those without a deep understanding of spectral analysis such as medical practitioners. It includes original contributions in extracting features from HRV and EEG signals using HOS and entropy, in analyzing the statistical properties of such features on real data and in automated classification using these features with GMM and SVM classifiers.

Mean and variance of estimates of the bispectrum of a harmonic random process-an analysis including leakage effects

Analytical expressions are derived for the mean and variance, of estimates of the bispectrum of a real-time series assuming a cosinusoidal model. The effects of spectral leakage, inherent in discrete Fourier transform operation when the modes present in the signal have a nonintegral number of wavelengths in the record, are included in the analysis. A single phase-coupled triad of modes can cause the bispectrum to have a nonzero mean value over the entire region of computation owing to leakage. The variance of bispectral estimates in the presence of leakage has contributions from individual modes and from triads of phase-coupled modes. Time-domain windowing reduces the leakage. The theoretical expressions for the mean and variance of bispectral estimates are derived in terms of a function dependent on an arbitrary symmetric time-domain window applied to the record. the number of data, and the statistics of the phase coupling among triads of modes. The theoretical results are verified by numerical simulations for simple test cases and applied to laboratory data to examine phase coupling in a hypothesis testing framework

Time-varying bispectral analysis of visually evoked multi-channel EEG

Theoretical foundations of higher order spectral analysis are revisited to examine the use of time-varying bicoherence on non-stationary signals using a classical short-time Fourier approach. A methodology is developed to apply this to evoked EEG responses where a stimulus-locked time reference is available. Short-time windowed ensembles of the response at the same offset from the reference are considered as ergodic cyclostationary processes within a non-stationary random process. Bicoherence can be estimated reliably with known levels at which it is significantly different from zero and can be tracked as a function of offset from the stimulus. When this methodology is applied to multi-channel EEG, it is possible to obtain information about phase synchronization at different regions of the brain as the neural response develops. The methodology is applied to analyze evoked EEG response to flash visual stimulii to the left and right eye separately. The EEG electrode array is segmented based on bicoherence evolution with time using the mean absolute difference as a measure of dissimilarity. Segment maps confirm the importance of the occipital region in visual processing and demonstrate a link between the frontal and occipital regions during the response. Maps are constructed using bicoherence at bifrequencies that include the alpha band frequency of 8Hz as well as 4 and 20Hz. Differences are observed between responses from the left eye and the right eye, and also between subjects. The methodology shows potential as a neurological functional imaging technique that can be further developed for diagnosis and monitoring using scalp EEG which is less invasive and less expensive than magnetic resonance imaging.

In-cylinder pressure and inter-cycle variability analysis for a compression ignition engine : Bayesian approaches

This thesis introduced Bayesian statistics as an analysis technique to isolate resonant frequency information in in-cylinder pressure signals taken from internal combustion engines. Applications of these techniques are relevant to engine design (performance and noise), energy conservation (fuel consumption) and alternative fuel evaluation. The use of Bayesian statistics, over traditional techniques, allowed for a more in-depth investigation into previously difficult to isolate engine parameters on a cycle-by-cycle basis. Specifically, these techniques facilitated the determination of the start of pre-mixed and diffusion combustion and for the in-cylinder temperature profile to be resolved on individual consecutive engine cycles. Dr Bodisco further showed the utility of the Bayesian analysis techniques by applying them to in-cylinder pressure signals taken from a compression ignition engine run with fumigated ethanol.

Analysis and modelling of the hydraulic conductivity in aquitards : application to the Galilee Basin and the Great Artesian Basin, Australia

In large sedimentary basins with layers of different rocks, the groundwater flow between aquifers depends on the hydraulic conductivity (K) of the separating low-permeable rocks, or aquitards. Three methods were developed to evaluate K in aquitards for areas with limited field data: • Coherence and harmonic analysis: estimates the regional-scale K based on water-level fluctuations in adjacent aquifers. • Cokriging and Bayes' rule: infers K from downhole geophysical logs. • Fluvial process model: reproduces the lithology architecture of sediment formations which can be converted to K. These proposed methods enable good estimates of K and better planning of further drillholes.

Statistical analysis of the position of the monsoon trough

Using surface charts at 0330GMT, the movement df the monsoon trough during the months June to September 1990 al two fixed longitudes, namely 79 degrees E and 85 degrees E, is studied. The probability distribution of trough position shows that the median, mean and mode occur at progressively more northern latitudes, especially at 85 degrees E, with a pronounced mode that is close to the northern-most limit reached by the trough. A spectral analysis of the fluctuating latitudinal position of the trough is carried out using FFT and the Maximum Entropy Method (MEM). Both methods show significant peaks around 7.5 and 2.6 days, and a less significant one around 40-50 days. The two peaks at the shorter period are more prominent at the eastern longitude. MEM shows an additional peak around 15 days. A study of the weather systems that occurred during the season shows them to have a duration around 3 days and an interval between systems of around 9 days, suggesting a possible correlation with the dominant short periods observed in the spectrum of trough position.