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Electroencephalogram (EEG) signals are widely used to study the activity of the brain, such as to determine sleep stages. These EEG signals are nonlinear and non-stationary in nature. It is difficult to perform sleep staging by visual interpretation and linear techniques. Thus, we use a nonlinear technique, higher order spectra (HOS), to extract hidden information in the sleep EEG signal. In this study, unique bispectrum and bicoherence plots for various sleep stages were proposed. These can be used as visual aid for various diagnostics application. A number of HOS based features were extracted from these plots during the various sleep stages (Wakefulness, Rapid Eye Movement (REM), Stage 1-4 Non-REM) and they were found to be statistically significant with p-value lower than 0.001 using ANOVA test. These features were fed to a Gaussian mixture model (GMM) classifier for automatic identification. Our results indicate that the proposed system is able to identify sleep stages with an accuracy of 88.7%.

Consistency relations involving the soft limit of the (n + 1)-correlator functions of dark matter and galaxy overdensities have been recently obtained, thanks to the symmetries enjoyed by the Newtonian equations of motion describing the dark matter and galaxy fluids coupled through gravity. Via an appropriate change of coordinates, the symmetries allow to go to a frame where the zero mode and the first spatial gradient of the long and linear wavelength mode of the gravitational potential have been removed. In such a case, the response of the system on short scales is a uniform displacement leading to the vanishing of the correlators in the soft limit at the equal-time. In this paper, we show that equal-time consistency relations involving the soft limit of the (n + 1)-correlator functions of dark matter can be obtained if there is a well-defined relation between the linear growth factor D(a) and the abundance of dark matter Ω, . We also discuss the consequences of the consistency relations for the halo model.

The problem regarding shapes of bispectral peak of the triplet representing the triharmonic signal is discussed. This triplet can be used as both standard diagnostic signal for a bispectral analyzers and a simplest element of complex informational patterns of bispectrally organized signals. The problem of analyzing and measuring the parameters of bispectral peak is equally fundamental as the well-known problem concerning the shape and width of spectral line of quasi-monochromatic oscillations. The sectional area of bispectral peak restricts the limiting informational volume of complex bispectral patterns. Two models of an actual triplet with frequency fluctuations are analyzed. Universal bispectral-peak shapes are found for a triplet with proportional frequencies for the limiting cases of extremely slow and extremely fast frequency fluctuations. The phenomenon of bispectral-peak superlocalization is discovered for quasi-static fluctuations and analyzed for the most realistic model of 1/f frequency fluctuations. The experiment investigating the bispectral peak of the real high-frequency synthesizer is presented.

I compute the bispectrum of maps of cosmic microwave background (CMB) fluctuations seeded by cosmic strings from large to 30 arcminute scales. Examining the distribution of triangle configurations and comparing with Gaussian realizations with the same power spectrum, I conclude that the CMB bispectrum cannot pick up the mild non-Gaussianity present in the maps and thus that it cannot characterize cosmic string induced non-Gaussianity produced in the regimes probed by these maps.

Electrochemical corrosion processes can be investigated by observation of charge flows between the electrolyte and the corroding metal. Usually, the charge flows are observed as spontaneous current and voltage fluctuations (electrochemical noise) in a three-electrode setup. Different types of corrosion processes can be recognized by electrochemical noise analysis. Uniform corrosion rate can be evaluated by estimation of polarization resistance between the metal and electrolyte. Local corrosion events (breakdowns of the passive layer) that produce characteristic transients observed in noise can be detected as well. Different methods of electrochemical noise analysis are presented in a brief review. The limitations and advantages of the proposed methods for corrosion monitoring and research are underlined. The experimental results are also discussed.

In this study, we analyze nonlinear feature extraction methods in terms of their ability to support the diagnosis of coronary artery disease (CAD) and myocardial infarction (MI). The nonlinear features were extracted from electrocardiogram (ECG) signals that were measured from CAD patients, MI patients as well as normal controls.

We tested 34 recurrence quantification analysis (RQA) features, 14 bispectrum, and 136 cumulant features. The features were extracted from 10,546 normal, 41,545 CAD, and 40,182 MI heart beats. The feature quality was assessed with Student’s $t$-test and the $t$-value was used for feature ranking.

We found that nonlinear features can effectively represent the physiological realities of the human heart.

The enhanced tear film evaporation and diminished tear production causes a dry eye (DE) condition. A non-invasive infrared (IR) thermography is most commonly used as a diagnostic tool for diagnosis of DE. However, the availability of high-quality IR thermal camera at low cost is difficult. Hence, an efficient DE detection system which can perform efficiently by using low-cost and low-quality images instead of conventional IR images would be a significant contribution. Therefore, in this work, we have evaluated the performance of automated non-invasive DE detection system using low-quality images obtained by adding different levels of noise to high-quality IR images. In this work, the performances of two non-linear higher-order spectra (HOS) cumulants and bispectrum features are compared. These features are extracted from the IR images with different levels of Gaussian noise. Principal component analysis (PCA) is performed on these extracted features and they are ranked using $t$-value and later fed to different classifiers. We have achieved the accuracies, sensitivities and specificities of: (i) 86.90%, 85.71% and 88.10%, with noise level 0 using 24 bispectrum features, and (ii) 80.95%, 85.71% and 76.19%, with noise level 10 using 15 bispectrum features for right eye IR images. This study exhibits that even in the presence of high levels of noise, the detection of DE is possible and our proposed method performs efficiently using HOS bispectrum features. Thus, our proposed method can be used to detect DE using low-quality and inexpensive cameras instead of high-cost IR camera.

Epilepsy is a neurological disorder characterized by epileptic seizures inside the human brain. An authentic localization of epileptogenic area will help the clinicians for a successful epilepsy surgery. The epileptogenic area can be characterized by the focal electroencephalogram (EEG) signals. Hence, in this article, a bispectrum-based approach is implemented to characterize the focal EEG signals. The highest twenty-five magnitudes of bispectrum from the principal domain are used as features. The locality sensitive discriminant analysis (LSDA), data reduction technique, is implemented to reduce the number of attributes. The ranked LSDA attributes are input to the support vector machine (SVM) classifier yielding 96.2% classification accuracy using the entire Bern Barcelona EEG database. Hence, the proposed technique can be employed to confirm the epileptogenic area for successful epilepsy surgery and can be employed in the community health care centers and hospitals.

Glaucoma is one of the leading causes of blindness. The raised intraocular pressure is one of the important modifiable risk factor causing glaucomatous optic nerve damage. Glaucomatous optic nerve damage is seen as increase in the cupping of the optic disc and loss of neuroretinal rim. An automated detection system using nonlinear higher order statistics (HOS) based method is used to capture the detailed information present in the fundus image efficiently. The center slice of bispectrum and bicepstrum are applied on fundus images. Various features are extracted from the diagonal of these central slices. In order to reduce the number of features the locality sensitive discriminant analysis (LSDA) data reduction technique method is implemented. The ranked LSDA features are fed to support vector machine (SVM) classifier with various kernels for automated glaucoma detection. The simulation is performed on two databases. The proposed algorithm has yielded classification accuracy of 98.8% and 95% using entire private and public databases, respectively. The proposed technique achieved the highest classification accuracy, hence, confirm the diagnosis of ophthalmologists and can be employed in the community health care centers and hospitals.

Deficits in the ability to process emotions characterize several neuropsychiatric disorders and are traits of Parkinson's disease (PD), and there is need for a method of quantifying emotion, which is currently performed by clinical diagnosis. Electroencephalogram (EEG) signals, being an activity of central nervous system (CNS), can reflect the underlying true emotional state of a person. This study applied machine-learning algorithms to categorize EEG emotional states in PD patients that would classify six basic emotions (happiness and sadness, fear, anger, surprise and disgust) in comparison with healthy controls (HC). Emotional EEG data were recorded from 20 PD patients and 20 healthy age-, education level- and sex-matched controls using multimodal (audio-visual) stimuli. The use of nonlinear features motivated by the higher-order spectra (HOS) has been reported to be a promising approach to classify the emotional states. In this work, we made the comparative study of the performance of k-nearest neighbor (kNN) and support vector machine (SVM) classifiers using the features derived from HOS and from the power spectrum. Analysis of variance (ANOVA) showed that power spectrum and HOS based features were statistically significant among the six emotional states (p < 0.0001). Classification results shows that using the selected HOS based features instead of power spectrum based features provided comparatively better accuracy for all the six classes with an overall accuracy of 70.10% ± 2.83% and 77.29% ± 1.73% for PD patients and HC in beta (13–30 Hz) band using SVM classifier. Besides, PD patients achieved less accuracy in the processing of negative emotions (sadness, fear, anger and disgust) than in processing of positive emotions (happiness, surprise) compared with HC. These results demonstrate the effectiveness of applying machine learning techniques to the classification of emotional states in PD patients in a user independent manner using EEG signals. The accuracy of the system can be improved by investigating the other HOS based features. This study might lead to a practical system for noninvasive assessment of the emotional impairments associated with neurological disorders.

Feature extraction plays an important role in brain-computer interface (BCI) systems. In order to characterize the motor imagery related rhythm and higher-order statistics information contained within the EEG signals, a novel feature extraction method based on harmonic wavelet transform and bispectrum is developed and applied to the recognition of right and left motor imageries for developing EEG-based BCI systems. The experimental results on the Graz BCI data set have shown that the separability of the two classes features extracted by the proposed method is notable. Its performance was evaluated by a linear discriminant analysis (LDA) classifier. The recognition accuracy of 90% was obtained. The recognition results have demonstrated the effectiveness of the proposed method. This method provides an effective way for EEG feature extraction in BCI system.

Electrochemical corrosion processes can be investigated by observation of charge flows between the electrolyte and the corroding metal. Usually, the charge flows are observed as spontaneous current and voltage fluctuations (electrochemical noise) in a three electrode setup. Different types of corrosion processes can be recognized by electrochemical noise analysis. Uniform corrosion rate can be evaluated by estimation of polarization resistance between the metal and electrolyte. Local corrosion events (breakdowns of the passive layer) that produce characteristic transients observed in noise can be detected as well. Different methods of electrochemical noise analysis are presented in a brief review. The limitations and advantages of the proposed methods for corrosion monitoring and research are underlined. The experimental results are also discussed.

We investigate the relativistic corrections to the standard model of formation of large scale structures. In matter domination and in the Poisson gauge, we use the weak- field approximation which allows to keep compact expressions even for the one-loop bispectrum. Whereas in the Newtonian limit, the choice of gauge is marginally important as all gauge coincides, when relativistic corrections are taken into account, it matters as a change of gauge may induce a change of gravitational potential and introduce fictitious modes in the finial result for the power spectrum. It is precisely what happens in the example presented in this talk as the equivalence principle is not fulfilled in the Poisson gauge and the cancellation of the IR divergence at one-loop does not occur. We will discuss how other choices of gauge may solve this issue.

Commom method have low sorting rates and is rensitive to the Signal Noise Radio (SNR), thus, resemblance coefficient of bispectrum two dimensions characteristic is applied to sort unknown complicated radar signal to obtain high sorting rate. The bispectrum of received signal is extracted, and it is predigested to two dimensions characteristic. A rectangle pulse sequence and triangle pulse sequence are constructed. Then, the resemblance coefficient of two dimensions characteristic with rectangle pulse sequence and triangle pulse sequence are gained, and they are used as the sorting parameters. The bispectrum of different signal is distinguishing and it is not sensitive to SNR and the resemblance coefficient is divisible and steady. The advantage of this new method is validated by simulation results and the sorting rate is not less than 86% at SNR of 5 dB.

This contribution provides a brief update on the transport approach to calculating the statistics of perturbations produced during inflation. It is based in particular on work in collaboration with Gemma Anderson and David Seery.

We find constraints on inflationary dynamics that yield a large local bispectrum and/or trispectrum during two-field slow-roll inflation. This leads to simple relations between the non-Gaussianity parameters, simplifying the Suyama–Yamaguchi inequality and also producing a new result between the trispectrum parameters τ_NL and g_NL.