Third-order Cumulants Research Articles

A theoretical view of the T-web statistical description of the cosmic web

Context. The objective classification of the cosmic web into different environments is an important aspect of large-scale structure studies, as it can be used as a tool to study the formation of structures (halos and galaxies) in mode detail, and it forms a link between their properties and the large-scale environment; these different environments also offer another class of objects whose statistics contain cosmological information. Aims. In this paper, we present an analytical framework to compute the probability of the different environments in the cosmic web based on the so-called T-web formalism, which classifies structures into four different classes (voids, walls, filaments, and knots) based on the eigenvalues of the Hessian of the gravitational potential, often called the tidal tensor. Methods. Our classification method relies on studying whether the eigenvalues of this Hessian matrix are above or below a given threshold and thus requires knowledge of the joint probability distribution of those eigenvalues. We performed a change of variables in terms of rotational invariants, which are polynomials of the field variables and minimally correlated. We studied the distribution of those variables in the linear and quasi-linear regimes with the help of a so-called Gram-Charlier expansion, using tree-order Eulerian perturbation theory to compute the Gram-Charlier coefficients. This expansion then allowed us to predict the probability of the four different environments as a function of the chosen threshold and at a given smoothing scale and redshift for the density field. We checked the validity regime of our predictions by comparing those predictions to measurements made in the N-body Quijote simulations. Results. Working with fields normalised by their linear variance, we find that scaling the threshold value with the non-linear amplitude of fluctuations allows us to capture almost the entire redshift evolution of the probabilities of the four environments, even if we assume that the density field is Gaussian (corresponding to the linear regime of structure formation). We also show that adding mild non-Gaussian corrections with the help of a Gram-Charlier expansion – hence introducing corrections that depend on third-order cumulants of the field – provides even greater accuracy, allowing us to obtain very precise predictions for cosmic web abundances up to scales of as small as ∼5 Mpc h−1 and redshifts down to z ∼ 0.

In situ XAFS-XRD study of the Zr-Y2O3 interaction at extra-high temperatures.

The in situ measurement technique for a metal/metal-oxide mixture at extra-high temperature above 2000 K has been desired in the field of nuclear safety engineering. In the present study, we succeeded in simultaneous XAFS-XRD measurements of the Zr oxidation [Zr + O → Zr(O) + ZrO2] up to 1952 K and ZrO2-Y2O3 reaction from 1952 to 2519 K. The chemical shift during Zr oxidation was observed in the absorption spectra around the Zr K-edge, and the interatomic cation-cation and cation-oxygen distances obtained by the fitting analysis of EXAFS during the Y2O3-ZrO2 reaction are explained. Also, the temperature dependency of the anharmonic effect was investigated by comparing the fitted second- and third-order cumulants with the theoretical ones in which the Morse potential was applied as an interatomic potential, giving a good explanation about the local structure dynamics. Finally, the applicability of the developed system to investigation of nuclear fuel materials, such as UO2-Zr, is discussed.

Experimental and Theoretical Analysis of Bispectrum Characteristics of Phase Coupled Signals

Fourier transform points out that a certain function that meets certain conditions can be decomposed into a linear combination of trigonometric functions (sine or cosine functions). The functions of high-order cumulant include suppressing the Gaussian noise, eliminating independent signal components, and identifying the phase coupling phenomenon of the signal. To prove this hypothesis, this study constructs a cosine signal with the phase coupling phenomenon based on Fourier transform theory which substitutes it into the third-order cumulant expression and performs detailed reasoning. The constructed signal is extended to the complex signal domain and the same conclusion is obtained. The number of coupled signals is expanded from three to a higher value. The results of the study give definite mathematical and physical meaning to the bispectral peaks. The collected mechanical vibration signals are given to demonstrate this conclusion. The demonstrated characteristics of high-order cumulants have made them widely used in many fields.

Stress and anxiety detection: deep learning and higher order statistic approach

<p>Today's teenagers are dealing with anxiety and stress. Anxiety, depression, and suicide rates have increased in recent years because of increased social rivalry. The research is focused on detecting anxiety in students due to exam pressure to reduce the potential harm to a person's wellness. Research is performed on databases for anxious states based on psychological stimulation (DASPS) and our own database. The measured signal is divided into sub bands that correspond to the electroencephalogram (EEG) rhythms using the Butterworth sixth-order order filter. In higher dimensional space, the nonlinearities of each sub-band signal are analyzed using higher order statistics third-order cumulants (TOC). We have classified stress and anxiety using the support vector machine (SVM), K-nearest neighbor (K-NN), and deep learning bidirectional long short-term memory (BiLSTM) network. In comparison to previous techniques, the proposed system's performance using BiLSTM is quite good. The best accuracy in this analysis was 87% on the DASPS database and 98% on the own database. Finally, subjects with high stress levels had more gamma activity than subjects with little stress. This could be an important attribute in the classification of stress.</p>

Third-Order Nested Array: An Optimal Geometry for Third-Order Cumulants Based Array Processing

Third-Order Nested Array: An Optimal Geometry for Third-Order Cumulants Based Array Processing

First Arrival Enhancement and Extrapolation via Third-Order Cumulant Interferometry Method

First Arrival Enhancement and Extrapolation via Third-Order Cumulant Interferometry Method

Closing in on critical net-baryon fluctuations at LHC energies: Cumulants up to third order in Pb–Pb collisions

Fluctuation measurements are important sources of information on the mechanism of particle production at LHC energies. This article reports the first experimental results on third-order cumulants of the net-proton distributions in Pb–Pb collisions at a center-of-mass energy sNN=5.02 TeV recorded by the ALICE detector. The results on the second-order cumulants of net-proton distributions at sNN=2.76 and 5.02 TeV are also discussed in view of effects due to the global and local baryon number conservation. The results demonstrate the presence of long-range rapidity correlations between protons and antiprotons. Such correlations originate from the early phase of the collision. The experimental results are compared with HIJING and EPOS model calculations, and the dependence of the fluctuation measurements on the phase-space coverage is examined in the context of lattice quantum chromodynamics (LQCD) and hadron resonance gas (HRG) model estimations. The measured third-order cumulants are consistent with zero within experimental uncertainties of about 4% and are described well by LQCD and HRG predictions.

Research and Application of Third-Order Cumulants in Delay Estimation of Chaotic Spread Spectrum

Research and Application of Third-Order Cumulants in Delay Estimation of Chaotic Spread Spectrum

A New Technique for ARMA-System Identification Based on QR-Decomposition of Third Order Cumulants Matrix

In this paper a new technique to estimate the coefficients of a general Autoregressive Moving Average (ARMA) (p, q) model is proposed. The ARMA system is excited by an un-observable independently identically distributed (i.i.d) non-Gaussian process. The proposed ARMA coefficients estimation method uses the QR-Decomposition (QRD) of a special matrix built with entries of third order cumulants (TOC) of the available output data only. The observed output may be corrupted with additive colored or white Gaussian noise of unknown power spectral density. The proposed technique was compared with several good methods such as the residual time series (RTS) and the Q-slice algorithm (QSA) methods. Simulations for several examples were tested. The results for these examples confirm the good performance of the proposed technique with respect to existing well-known methods.

Equatorial aberration for powder diffraction data collected by continuous-scan integration of a silicon strip X-ray detector

The application of continuous-scan integration to collect X-ray diffraction data with a Si strip X-ray detector (CSI-SSXD) introduces additional effects on the peak shift and deformation of peak shape caused by the equatorial aberration. A deconvolutional method to correct the effects of equatorial aberration in CSI-SSXD data is proposed in this study. There are four critical angles related to the effects of spillover of the incident X-ray beam from the specimen face in the CSI-SSXD data. Exact values of cumulants of the equatorial aberration function are efficiently evaluated by 4 × 4 point two-dimensional Gauss–Legendre integral. A naïve two-step deconvolutional method has been applied to remove the effects of the first and third-order cumulants of the equatorial aberration function from the observed CSI-SSXD data. The performance of the algorithm has been tested by analyses of CSI-SSXD data of three LaB6 powder specimens with the widths of 20, 10, and 5 mm, collected with a diffractometer with the goniometer radius of 150 mm.

A Fourier-cumulant analysis for multiharmonic flow fluctuation

The Fourier analysis of the final particle distribution followed by cumulant study of the Fourier coefficient event-by-event fluctuation is one of the main approaches for testing the collective evolution in the heavy-ion collision. Using a multidimensional generating function, we propose a method to extract any possible cumulant of multiharmonic flow fluctuations and classify them in terms of the order of cumulants and harmonics involved in them. In particular, we show that there are 33 distinct cumulants with order 2, 3, 4, 5 and harmonics 2, 3, 4, 5. We compute the normalized version of these cumulants from hydrodynamic simulation for Pb–Pb collisions based on T_mathtt{R}ENTo+VISH2+1+UrQMD. We compare the simulation with those normalized cumulants that the LHC has measured and predict the unmeasured ones. Comparing the initial and final state fluctuation normalized cumulants, we compute the linear and nonlinear hydrodynamic response couplings. We finally introduce the genuine three-particle correlation function containing information of all third-order cumulants.

ECG heartbeat arrhythmias classification: a comparison study between different types of spectrum representation and convolutional neural networks architectures

This research presents a comparison study between different representations of spectrograms and then feeding them to different convolutional neural network (CNN) architectures. The study uses two short-time Fourier transform (STFT) representations, namely, Log-scale and Mel-Scale in addition to Bi-Spectrum and the third-order cumulant. Meanwhile, four different CNN architectures have been utilized in the present study, namely, AOCT-NET, Mobile-Net, Squeeze-Net, and Shuffle-Net. The study has exploited 10,502 beats extracted from the standard MIT-BIH arrhythmia database and represent six different classes: normal beat (N), left bundle branch block beat (LBBB), right bundle branch block beat (RBBB), premature ventricular contraction (PVC), atrial premature beat (APB), and aberrated atrial premature (aAP). The study compares the accuracy, sensitivity, precision, and specificity rates of the spectrogram-based and CNN architecture models under study. This paper hypothesizes that ECG features can be extracted from different spectral representations and can lead to improving the understanding and detection of the human heart's different arrhythmias by feeding these features to different CNN models. The suggested models’ performance was evaluated by dividing the dataset into three subsets (Training 70%, Validation 15%, and Testing 15%) and the best overall performance among all used CNN architectures was MobileNet with an overall accuracy of 93.8%, while the best spectrum representation among all used was the bispectrum with an overall accuracy of 93.7%. It has been shown that the spectrum representations of ECG beat have provided significant information about heart performance and can be used significantly in arrhythmia classification using deep learning techniques.

Third-Order Statistics Reconstruction From Compressive Measurements

Estimation of third-order statistics relies on the availability of a huge amount of data records, which can pose severe challenges on the data collecting hardware in terms of considerable storage costs, overwhelming energy consumption, and unaffordably high sampling rate especially when dealing with high-dimensional data such as wideband signals. To overcome these challenges, this paper focuses on the reconstruction of the third-order cumulants under the compressive sensing framework. Specifically, this paper derives a transformed linear system that directly connects the cross-cumulants of compressive measurements to the desired third-order statistics. We provide sufficient conditions for lossless third-order statistics reconstruction via solving simple least-squares, along with the strongest achievable compression ratio. To reduce the computational burden, we also propose an approach to recover diagonal cumulant slices directly from compressive measurements, which is useful when the cumulant slices are sufficient for the inference task at hand. All the proposed techniques are tested via extensive simulations. The developed joint sampling and reconstruction approach to third-order statistics estimation is able to reduce the required sampling rates significantly by exploiting the cumulant structure resulting from signal stationarity, even in the absence of any sparsity constraints on the signal or cumulants.

Seizures classification based on higher order statistics and deep neural network

The epileptic seizure is a transient and abnormal discharge of nerve cells in the brain that leads to a chronic disease of brain dysfunction. There are various features-based seizures classification algorithms listed in the literature. But, there is no standardized set of attributes that can perfectly capture the relevant information regarding the signal dynamics. In this paper, a computationally-fast seizure classification algorithm is presented. The obtained results through the proposed algorithm are consistent and repeatable. This paper describes an automated seizures classification technique using the nonlinear higher-order statistics and deep neural network algorithms. The sparse autoencoder based deep neural network is used to extract the essential structural details from the third-order cumulant coefficients matrix. The proposed algorithm achieves a reliable classification accuracy for both categories, i.e., binary classes and three-classes of electroencephalogram (EEG) signals with the softmax classifier. The proposed study is simulated on the publicly-available Bonn university EEG database. The achieved results show the effectiveness of the proposed algorithm for seizures classification.

Automated emotion recognition based on higher order statistics and deep learning algorithm

The objective of this paper is online recognition of human emotions based on electroencephalogram (EEG) signals. The emotions are originated from the central and peripheral nervous systems. Hence, it can be adequately characterized by the EEG signal, as it directly reflects changes in the human emotional states. This paper describes an automated classification of emotions-labeled EEG signals using nonlinear higher order statistics and deep learning algorithm. The discrete wavelet transform is used to decompose the studied signal into sub-bands, known as rhythms of the EEG signal. The third-order cumulants (ToC) are used to explore the nonlinear dynamics of each sub-band signal in higher dimensional space. The data in the higher dimensional space contain repeated and redundant information due to presence of various symmetries in the ToC. Hence, an evolutionary data reduction technique, namely, the particle swarm optimization, is employed to get rid of irrelevant information. The long short-term memory based deep learning technique is used to retrieve the emotion variation from the optimized data corresponding to the labeled EEG signals. This study is carried out with the web-available DEAP dataset that yields 82.01% average classification accuracy with 10-fold cross-validation technique corresponding to four-labeled emotions classes. The achieved results have confirmed that the proposed algorithm has the potential for accurate and rapid recognition of human emotions.

Automated focal EEG signal detection based on third order cumulant function

Epilepsy is a chronic neurological disorder which occurs due to recurrent seizures. The epilepsy surgery is the only cure of epileptic seizures as it cannot be controlled with medication. Hence, it becomes the primary task to localize the epileptogenic zone for successful epilepsy surgery. The epileptic surgical area can be recognized by the focal intracranial electroencephalogram (EEG) signals. In this paper, a nonlinear third-order cumulant has been proposed for the classification of the non-focal and focal intracranial EEG signals efficiently. The attributes are measured from the logarithm of the diagonal slice of third-order cumulant. It provides relevant subtle information about the nonlinear dynamics of EEG signals. A data reduction technique, locality sensitive discriminant analysis (LSDA), has been introduced to map the measured features at higher dimensional space and ranked them according to the probability of discrimination. The achieved results reveal that the ranked LSDA features with the support vector machine (SVM) classifier have yielded maximum classification accuracy of 99% on the Bern Barcelona EEG database. Thus, the proposed algorithm helps a clinician to localize the epileptogenic zone for successful brain surgery.

A machine learning study to identify spinodal clumping in high energy nuclear collisions

The coordinate and momentum space configurations of the net baryon number in heavy ion collisions that undergo spinodal decomposition, due to a first-order phase transition, are investigated using state-of-the-art machine-learning methods. Coordinate space clumping, which appears in the spinodal decomposition, leaves strong characteristic imprints on the spatial net density distribution in nearly every event which can be detected by modern machine learning techniques. On the other hand, the corresponding features in the momentum distributions cannot clearly be detected, by the same machine learning methods, in individual events. Only a small subset of events can be systematically differ- entiated if only the momentum space information is available. This is due to the strong similarity of the two event classes, with and without spinodal decomposition. In such sce- narios, conventional event-averaged observables like the baryon number cumulants signal a spinodal non-equilibrium phase transition. Indeed the third-order cumulant, the skewness, does exhibit a peak at the beam energy (Elab = 3–4 A GeV), where the transient hot and dense system created in the heavy ion collision reaches the first-order phase transition.

Chaotic Analysis of Hippocampal and Cortical Sleep EEG during Various Vigilance States.

In this paper, we investigate the hippocampal and cortical sleep EEG of adult rats at different sleep stages by employing Lyapunov exponent and third-order cumulant measures to quantify and compare the chaotic and nonlinear behavior of EEG obtained during vigilance states of quiet- waking, slow-wave sleep, and rapid eye movement (REM) sleep. Lyapunov exponent was computed to characterize the EEG for chaos and third-order cumulant was used to measure the deviations from Gaussianity of the signal. Our results show positive Lyapunov exponents for all EEG states indicating a Iow- dimensional chaos for both REM and non-REM system. Furthermore, REM sleep EEG exhibits the largest Lyapunov exponent in both hippocampal and cortical EEG amongst other vigilance states. We also identified non-zero third-order cumulant for all the vigilance states which suggests their non- Gaussian behavior.

The Application of Cumulants Slices in Fault Diagnosis

Complex third-order cumulant has different definition forms. Different forms have different coupling properties, and the generated complex cumulants slices contain different coupling information of signals. In experiments, using the different definitions, the same coupling method is applied to both specific fault signals and normal signals. Furthermore, complex third-order cumulant slices spectrum is defined, and it is used to analyse the coupling features of normal signals and fault signals. Experiments indicate that the detection accuracy rate on the same fault is not the same with the different coupling method, thus, it provides an alternative method to diagnose the specific fault.

Research on Bearing Fault Diagnosis Based on Slice Spectrum and Cepstrum

In this paper, high-order spectral analysis and cepstrum analysis are combined to diagnosis of bearing failure. The high-order spectrum can effectively suppress the Gaussian noise and extract the weak fault signal, but it has the limitation when dealing with the added signal. The cepstrum, which less affected by the transmission path, can distinguish the periodic components in the sideband and simplify the clustered sideband into a single spectral line. In this paper, the two methods are combined to conduct the bispectrum analysis of the vibration signal, and then do the Inverse Fourier transform to the logarithm of the bispectrum model, that is, the cepstrum analysis of the third-order cumulant. The method proposed in this paper is verified by the vibration signal data of a bearing, and the results show that the method proposed in this paper can overcome the shortcomings of the traditional single method and make effective diagnosis of the bearing failure.