The goal of this study was to investigate the potential of breathing sounds recorded during wakefulness for Obstructive Sleep Apnea (OSA) screening and severity estimation. Breathing sounds were recorded from 189 subjects in supine and sitting postures during nose and mouth breathing. Features were extracted from power spectrum and bispectrum of the signals. Data from 70 subjects were used for training. Validation accuracy, specificity, and sensitivity for non-OSA and OSA groups were 78%, 77%, and 82%, respectively. Screening based on six OSA risk factors was less accurate. Parallel classification by both breathing sound features and risk factors had high sensitivity (94%). OSA severity estimation, by classifying subjects into three classes of OSA severity, achieved a maximum validation accuracy of 71%. The results demonstrate the potential of breathing sounds for OSA screening. The proposed method can lead to significant improvements in efficient use of resources such as sleep laboratories.

The goal of this study was to investigate the potential of breathing sounds recorded during wakefulness for Obstructive Sleep Apnea (OSA) screening and severity estimation. Breathing sounds were recorded from 189 subjects in supine and sitting postures during nose and mouth breathing. Features were extracted from power spectrum and bispectrum of the signals. Data from 70 subjects were used for training. Validation accuracy, specificity, and sensitivity for non-OSA and OSA groups were 78%, 77%, and 82%, respectively. Screening based on six OSA risk factors was less accurate. Parallel classification by both breathing sound features and risk factors had high sensitivity (94%). OSA severity estimation, by classifying subjects into three classes of OSA severity, achieved a maximum validation accuracy of 71%. The results demonstrate the potential of breathing sounds for OSA screening. The proposed method can lead to significant improvements in efficient use of resources such as sleep laboratories.

Informally a discrete time series is a set of repeated and, normally, equally spaced observations from the same process over time. The statistical analysis of time series has two functions: to understand better the generating process underlying the time series, and to forecast future values. The first analytical methods developed were based upon linear series. A linear series can be represented as a linear function of its own past and current values and the past and current values of some noise process, which can be interpreted as the innovations to the system. A non-linear series has a generally more complex structure that depends upon non-linear interactions between its past and current values and the sequence of innovations. Existing linear statistical methods can only approximate non-linear series. As there is evidence to show that non-linear series are common in real life, two important problems are to detect and then to classify non-linearity. In moving from a linear to a non-linear structure the choice of possible models has moved from a countably infinite to an uncountably infinite set. Hence the need for methods that not only detect non-linearity, but classify the non-linear relationship between the past and current values and innovations. The third order moment is the expectation of the product of three series values lagged in time. The bispectrum is the double Fourier transform of the third order moment. Both statistics are useful tools for eliciting information on non-linear time series. There are concerns with the assumption of asymptotic independence between the values of the bispectrum estimate used by an existing test of non-linearity. We develop a method with a greater power than this existing method to detect non-linear series by using a model-based bootstrap. Further we show how patterns in the bispectrum are useful for classifying the locations of the non-linear interactions. To understand better tests of non-linearity and related inference, we investigate the variance of two estimates of the bispectrum. The two estimates are shown to have different inferential properties. One estimate is generally better able than the other to detect non-linearity and give information on the location of the non-linear interactions. The third order moment is statistically equivalent to the bispectrum. A particular estimate of the bispectrum is the double Fourier transform of all the estimated third order moment values in a specified region. When using the third order moment to test for non-linearity we can examine any subset of these values in the specified region. Hence an advantage to using the third order moment, instead of the bispectrum, when testing for non-linearity is a greater flexibility in the range of values selected. We show an improved test for non-linearity over the bispectrum-based test, using a reduced set of the third order moment and a phase scrambling-based bootstrap. Time series can often be observed in a multiple or repeated form, such as the exchange rate between a set of currencies. There is then interest in summarising the common features of the grouped series. An existing linear method based on the spectrum assumes that an observed series (within a population) can be described as a common population spectrum perturbed by an individual effect. The observational noise in the spectrum is modelled using the known asymptotic properties of the spectral estimate. By modelling (and then removing) the individual effects and noise, the method summarises the population linear characteristics through the spectrum. We modify and then extend this method to summarise the common features of the underlying non-linear generating process of a set of repeated time series using the bispectrum normalised by the spectrum.

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Numerous studies have documented the existence of nonlinearity within various financial time series. But how important of a finding is this? This dissertation examines this issue from a number of perspectives. First, is the nonlinearity that has been found a statistical anomaly that is isolated to a few of the more widely known financial time series or is nonlinearity a statistical regularity inherent in such series? Second, even if nonlinearity is pervasive, does this finding have any practical relevance for finance practitioners or academics? Using the relatively financially isolated but nonetheless well-traded Taiwan Stock Exchange as a case study, it is found that virtually all of the stocks trading on this exchange exhibit nonlinearity. The pervasiveness of nonlinearity within this market, combined with earlier results from other markets, suggests that nonlinearity is an inherent aspect of financial time series. Furthermore, closer examination of the time-paths of various measures of this nonlinearity via both windowed testing and recursive testing and parameter estimation reveals an additional complication, the possibility of nonstationarity. The serial dependency structures, especially for the nonlinear dependencies, do not appear to be constant, but instead appear to exhibit a number of brief episodes of extremely strong dependencies, followed by longer stretches of relatively quiet behavior. On average, though, these nonlinearities appear with sufficient strength to be significant for the full sample. Continuing on to examine the relevance of such nonlinearities for empirical work in finance, a variety of conditionally heteroskedastic models were fit to the returns for a subsample Taiwanese stocks, the Taiwanese stock index, and stock indices for other stock markets, including New York, London, Tokyo, Hong Kong, and Singapore. In a majority of cases, such models appear to be successful at filtering out the extant nonlinearity from these series of returns; however, a variety of indicators suggest that these models are not statistically well-specified for these returns, calling into question the inferences obtained from these models. Furthermore, a comparison of the various conditionally heteroskedastic models with each other and with a dynamic linear regression model reveals that, for many of the data series, the inferences obtained from these models regarding the day-of-the-week effect and the extant autocorrelation within the data varied from model to model. This finding suggests the importance of adequately accounting for nonlinear serial dependencies (and of ensuring data stationarity) when studying financial time series, even when other empirical aspects of the data are the focus of attention. / Ph. D.

A hypothetical causal link between ventilatory regulation of carbon dioxide anddevelopment of syncope during orthostatic challenges is reduction in arterial partialpressure of carbon dioxide and resultant reduction in cerebral blood flow. We performedtwo experiments to investigate the ventilatory sensitivity to carbon dioxide and factorsaffecting cerebral autoregulation (CA). We also studied the nonlinear phase couplingbetween cardio-respiratory parameters before syncope.For experiment one, in 30 healthy adults, we stimulated chemo and baro reflexesby breathing either room-air or room-air with 5 percent carbon dioxide in a pseudorandom binary sequence during supine and 70 degree head up tilt (HUT). Six subjectsdeveloped presyncope during tilt.To determine whether changes in ventilatory control contribute to the observeddecrease in PaCO2 during HUT, we assessed ventilatory dynamic sensitivity to changesin PaCO2 during supine and 70 degrees HUT. The sensitivity of the ventilatory controlsystem to perturbations in end tidal carbon dioxide increased during tilt.To investigate nonlinear phase coupling between cardio-respiratory parametersbefore syncope, bispectra were estimated and compared between presyncopal andnon-presyncopal subjects. Our results indicate that preceding presyncope, nonlinearphase coupling is altered by perturbations to baro and chemo reflexes.To investigate the effects of gender in CA, we selected 10 men and 10age-matched women and used spectral analysis to compare differences in CA betweenmen and women. Our results showed that gender-related differences in CA did exist andgender may need to be considered as a factor in investigating CA.To investigate the influence of induced hypocapnia on CA in absence ofventilatory variability, we performed experiment two in which subjects were randomlyassigned to a Control (under normocapnia) or Treatment (under hypocapnia) group. Bothgroups voluntarily controlled their breathing pattern yet two groups breathed in air withdifferent levels of carbon dioxide. Our results show that changes in mean blood pressureat middle cerebral artery level were less transferred into mean cerebral blood flow in theTreatment group than in the Control group, suggesting better CA under hypocapniarelative to under normocapnia.

The ultrasonic NDE technique to characterize the ultrasonic nonlinear response of the cyclically load 7075-T6 aluminum is described in this thesis. In order to estimate the nonlinear relation of the ultrasonic waves due to material fatigue damage or degradation, the spectral analysis techniques such as the power spectrum, bispectrum, and bicoherence spectrum are applied. The ultrasonic nonlinearity parameters by Cantrell and Jhang are introduced and presented as a function of the material fatigue growth, the number of fatigue cycles. This thesis presents the effectiveness of the bispectral analysis for evaluating the nonlinear aspects of the ultrasonic wave propagation. The results show that the nonlinearity parameters by Cantrell and Jhang are responsive to the output amplitude of the received signal and vary for the various materials, and independent of the input frequency and the ultrasonic wave propagation distance. By using the bispectral analysis tools, particularly the bicoherence spectrum, the increase of the coupling levels between the fundamental, its harmonic, and subharmonic frequency components is presented as the number of fatigue cycles is increased. This thesis suggests that the application of the bicoherence spectrum based on the nonlinear wave coupling relations be more effective for estimating the level of the material fatigue life. / Master of Science

Philosophiae Doctor - PhD / Next-generation galaxy surveys will usher in a new era of high precision cosmology. They will increasingly rely on the galaxy bispectrum to provide improved constraints on the key parameters of a cosmological model to percent level or even beyond. Hereby, it is imperative to understand the theory of the galaxy bispectrum to at least the same level of precision. By this, we mean to include all the general relativistic projection effects arising from observing on the past lightcone, which still remains a theoretical challenge. This is because unlike the galaxy power spectrum, the galaxy bispectrum requires these lightcone corrections at second-order. For the rst time, this PhD project looks at all the local relativistic lightcone e ects in the galaxy bispectrum for a at Friedmann-Lemaitre-Robertson-Walker Universe, giving full details on the second-order scalars, vectors and tensors. These lightcone effects are mostly Doppler and gravitational potential contributions. The vector and tensor modes are induced at second order by scalars. We focus on the squeezed shapes for the monopole of the galaxy bispectrum because non-Gaussianity of the local form shows high signatures for these triangular con gurations. In the exact squeezed limit, the contributions from the vectors and tensors vanish. These relativistic projection effects, if not included in the analysis of observations, can be mistaken for primordial non-Gaussianity. For future surveys which will probe equality scales and beyond, all the relativistic corrections will need to be considered for an accurate measurement of primordial non-Gaussianity.

Atrial fibrillation (AF) is a troublesome disease often overlooked by more serious myocardial infarctions. Up until now, there has been very little or no use of high order spectral techniques in order to evaluate the organization of the atrium during AF. Cross-bicoherence algorithm can be used alongside a surrogate data threshold in order to determine significant phase coupling interactions, giving rise to an organizational metric. This proposed algorithm is used to show rotigaptide, a gap junction coupling drug, significantly increases the organization of the atria during episodes of AF due to improvement of cell-to-cell coupling.

Obstructive Sleep Apnea-Hypopnea Syndrome (OSAHS) is a serious sleep disordered affecting up to 24% of men and 9% of woman in the middle aged population. The current standard for the OSAHS diagnosis is Polysomnography (PSG), which refers to the continuous monitoring of multiple physiological variables over the course of a night. The main outcomes of the PSG test are the OSAHS severity measures, such as the Respiratory Disturbance Index (RDI), Arousal Index, Latencies and other information to determine the macro sleep architecture (MSA), which is defined by Wake, Rapid-eye-movement (REM) and non-REM states of sleep. The MSA results are essential for computing the diagnostic measures reported in a PSG. The existing methods of the MSA analysis require the recording of 5-7 electrophysiological signals, including the Electroencephalogram (EEG), Electroculogram (EOG), and the Electromyogram (EMG). Sleep clinicians have to depend on the manual scoring of the overnight data records using the criteria given by Rechtschaffen and Kales (R&K, 1968). The manual analysis of MSA is tedious, subjective and suffers from inter- and intra-scorer variability. Additionally, the RDI and the Apnea-Hypopnea Index (AHI) parameters although used as the primary measures of the OSAHS severity, suffers from subjectivity, low reproducibility and a poor correlation with the symptoms of OSAHS. Sleep is essentially a neuropsychological phenomenon, and the EEG remains the best technique for the functional imaging of the brain during sleep. The EEG is the direct result of the neuronal activity of the brain. However, despite the potential, the wealth of information available in the EEG signal remains virtually untapped in current OSAHS diagnosis. Although the EEG is extensively used in traditional sleep analysis, its usage is mainly limited to staging sleep, based on the four-decade old R&K criteria. This thesis addresses these issues plaguing the PSG. We develop a novel, fully-automated algorithm (Higher-order Estimated Sleep States, HESS-algorithm) for the MSA analysis, which requires only one channel of the EEG data. We also develop an objective MSA analysis technique that uses a single, one-dimensional slice of the Bispectrum of the EEG, representing a nonlinear transformation of a system function that can be considered as the EEG generator. The agreement between the human and the proposed technology was found to be in the range of 70%-87%, which are similar to those, possible between expert human scorers. The ability of the HESS algorithm to compute the MSA parameters reliably and objectively will make a dramatic impact on the diagnosis and treatment of OSAHS and other sleep diseases, such as insomnia. The proposed technology uses low-computation-load Bispectrum techniques independent of R&K Criteria (1968) making real-time automated analysis a reality. In the thesis we also propose a new index (the IHSI) to characterise the severity of sleep apnea. The new index is based on the hemispherical asymmetry of the brain and is computed from the EEG coherence analysis. We achieved a significant (p=0.0001) accuracy of up to 91% in classifying patients into apneic and non-apneic group. Our statistical analysis results show that the IHSI carries potential for providing us with a reproducible measure to assist in diagnosing of OSAHS. With the proposed methods in this thesis it may be possible to develop the technology that will not only attempt to screen the OSAHS patients but will be able to provide OSAHS diagnosis with detailed sleep architecture via home based test. These technologies will simplify the instrumentation dramatically and will make possible to extend EEG/MSA analysis to portable systems as well.