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1
Zhang, Gui Cai, Jin Chen, Fu Cai Li, and Wei Hua Li. "Extracting Gear Fault Features Using Maximal Bispectrum." Key Engineering Materials 293-294 (September 2005): 167–74. http://dx.doi.org/10.4028/www.scientific.net/kem.293-294.167.
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Bispectrum is a powerful tool for non-Gaussian signal processing and nonlinearity detection. However, it is difficult to use in practical applications due to that it is a 2-dimensional function. Bispectral slices are widely used reduction methods, and they can only represent a small part of the whole bispectral information. Integrated bispectrum contains more signal features than that of the bispectral slices, whereas the integration will lose the focus of some signal features. To overcome these problems, a new approach called maximal bispectrum is proposed to extract signal features. Maximal bispectrum is obtained by selecting the maximal values of every row of the magnitude bispectrum in the whole bispectral plane and it is a 1-dimensional function. Feature extraction based on maximal bispectrum is investigated and the maximal bispectrum is used to extract features of gear fault. Experimental results indicate that the maximal bispectrum is effective for diagnosing gear crack fault.
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Schmittfull, Marcel. "Large-scale structure non-Gaussianities with modal methods." Proceedings of the International Astronomical Union 11, S308 (2014): 67–68. http://dx.doi.org/10.1017/s1743921316009649.
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AbstractRelying on a separable modal expansion of the bispectrum, the implementation of a fast estimator for the full bispectrum of a 3d particle distribution is presented. The computational cost of accurate bispectrum estimation is negligible relative to simulation evolution, so the bispectrum can be used as a standard diagnostic whenever the power spectrum is evaluated. As an application, the time evolution of gravitational and primordial dark matter bispectra was measured in a large suite of N-body simulations. The bispectrum shape changes characteristically when the cosmic web becomes dominated by filaments and halos, therefore providing a quantitative probe of 3d structure formation. Our measured bispectra are determined by ∼ 50 coefficients, which can be used as fitting formulae in the nonlinear regime and for non-Gaussian initial conditions. We also compare the measured bispectra with predictions from the Effective Field Theory of Large Scale Structures (EFTofLSS).
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Wang, Haibin, Junbo Long, Zeliang Liu, and Fang You. "Fault Characteristic Extraction by Fractional Lower-Order Bispectrum Methods." Mathematical Problems in Engineering 2020 (December 31, 2020): 1–24. http://dx.doi.org/10.1155/2020/8823389.
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The generated signals generally contain a large amount of background noise when the mechanical bearing fails, and the fault signals present nonlinear and non-Gaussian feature, which have heavy tail and belong to α -stable distribution ( 1 < α < 2 ); even the background noises are also α -stable distribution process. Then it is difficult to obtain reliable conclusion by using the traditional bispectral analysis method under α -stable distribution environment. Two improved bispectrum methods are proposed based on fractional lower-order covariation in this paper, including fractional low-order direct bispectrum (FLODB) method, fractional low-order indirect bispectrum (FLOIDB) method. In order to decrease the estimate variance and increase the bispectral flatness, the fractional lower-order autoregression (FLOAR) model bispectrum and fractional lower-order autoregressive moving average (FLOARMA) model bispectrum methods are presented, and their calculation steps are summarized. We compare the improved bispectrum methods with the conventional methods employing second-order statistics in Gaussian and S α S distribution environments; the simulation results show that the improved bispectrum methods have performance advantages compared to the traditional methods. Finally, we use the improved methods to estimate the bispectrum of the normal and outer race fault signal; the result indicates that they are feasible and effective for fault diagnosis.
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Nikias, C. L., and M. R. Raghuveer. "On: “Higher order autospectra by maximum entropy method” by R. O. Plaisted and H. G. Peña (GEOPHYSICS, 48, 1409–1410, October, 1983)." GEOPHYSICS 50, no. 1 (1985): 165–66. http://dx.doi.org/10.1190/1.1441827.
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As stated in the short note by R. O. Plaisted and H. G. Peña, they derived what they believed to be “a maximum entropy (MEM) representation for bispectra” and they claimed that their result “can be generalized to an Nth‐order MEM auto‐spectrum.” The purpose of this discussion is to point out the faults in the derivation and show that the claim of MEM is not correct. Furthermore, the parametric representation of the bispectrum that the authors actually attempted to derive is not new but can be found elsewhere (Huber et al., 1971). Plaisted and Peña stated that the random variables [Formula: see text] in their equation (1) can be assumed generally to be normally distributed with zero mean and variance [Formula: see text]. This is a serious mistake. With this assumption the third‐order moment sequence of the [Formula: see text] process given by their equation (3) vanishes, i.e., [Formula: see text] for all (k, l) and therefore the bispectrum of [Formula: see text] is identical to zero. The random variables [Formula: see text] in their equation (1) and hence [Formula: see text] have to be non‐Gaussian for the bispectrum of [Formula: see text] to exist. As a matter of fact, bispectral analysis has been used to obtain information regarding deviations of a process from Gaussianity (Godfrey, 1965).
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Kamran, Mohd, Raghunath Ghara, Suman Majumdar, et al. "Redshifted 21-cm bispectrum – II. Impact of the spin temperature fluctuations and redshift space distortions on the signal from the Cosmic Dawn." Monthly Notices of the Royal Astronomical Society 502, no. 3 (2021): 3800–3813. http://dx.doi.org/10.1093/mnras/stab216.
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ABSTRACT We present a study of the 21-cm signal bispectrum (which quantifies the non-Gaussianity in the signal) from the Cosmic Dawn (CD). For our analysis, we have simulated the 21-cm signal using radiative transfer code grizzly, while considering two types of sources (mini-QSOs and HMXBs) for Ly α coupling and the X-ray heating of the IGM. Using this simulated signal, we have, for the first time, estimated the CD 21-cm bispectra for all unique k-triangles and for a range of k modes. We observe that the redshift evolution of the bispectrum magnitude and sign follow a generic trend for both source models. However, the redshifts at which the bispectrum magnitude reaches their maximum and minimum values and show their sign reversal depends on the source model. When the Ly α coupling and the X-ray heating of the IGM occur simultaneously, we observe two consecutive sign reversals in the bispectra for small k-triangles (irrespective of the source models). One arising at the beginning of the IGM heating and the other at the end of Ly α-coupling saturation. This feature can be used in principle to constrain the CD history and/or to identify the specific CD scenarios. We also quantify the impact of the spin temperature (TS) fluctuations on the bispectra. We find that TS fluctuations have maximum impact on the bispectrum magnitude for small k-triangles and at the stage when Ly α coupling reaches saturation. Furthermore, we are also the first to quantify the impact of redshift space distortions (RSD), on the CD bispectra. We find that the impact of RSD on the CD 21-cm bispectra is significant ($\gt 20{{\ \rm per\ cent}}$) and the level depends on the stages of the CD and the k-triangles for which the bispectra are being estimated.
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Matsumoto, Y., K. Toriumi, I. Tsuchiya, and K. Harakawa. "Bispectrum Evaluation of Combination and Blend Yarns." Textile Research Journal 62, no. 7 (1992): 414–22. http://dx.doi.org/10.1177/004051759206200709.
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The bispectra of combination and blend yarns made on a spun silk spinning system are discussed, along with bispectra of mathematically idealized combination yarns. For comparison, the bispectra of a random combination yarn and two types of pseudorandom combination yarns generated by a computer simulation are calculated. Furthermore, the effect of periodic yarn irregularity on the bispectrum is estimated.
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Majumdar, Suman, Mohd Kamran, Jonathan R. Pritchard, et al. "Redshifted 21-cm bispectrum – I. Impact of the redshift space distortions on the signal from the Epoch of Reionization." Monthly Notices of the Royal Astronomical Society 499, no. 4 (2020): 5090–106. http://dx.doi.org/10.1093/mnras/staa3168.
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ABSTRACT The bispectrum can quantify the non-Gussianity present in the redshifted 21-cm signal produced by the neutral hydrogen ($\rm {H \small {I}}$) during the Epoch of Reionization (EoR). Motivated by this, we perform a comprehensive study of the EoR 21-cm bispectrum using simulated signals. Given a model of reionization, we demonstrate the behaviour of the bispectrum for all unique triangles in k space. For ease of identification of the unique triangles we parametrize the k-triangle space with two parameters, namely the ratio of the two arms of the triangle (n = k2/k1) and the cosine of the angle between them (cos θ). Furthermore, for the first time we quantify the impact of the redshift space distortions (RSD) on the spherically averaged EoR 21-cm bispectrum in the entire unique triangle space. We find that the real space signal bispectra for small and intermediate k1-triangles ($k_1 \le 0.6 \, \, {\rm Mpc}^{-1}$) is negative in most of the unique triangle space. It takes a positive sign for squeezed, stretched, and linear k1-triangles, specifically for large k1 values ($k_1 \ge 0.6 \, \, {\rm Mpc}^{-1}$). The RSD affects both the sign and magnitude of the bispectra significantly. It changes (increases/decreases) the magnitude of the bispectra by $50\!-\!100{{\ \rm per\ cent}}$ without changing its sign (mostly) during the entire period of the EoR for small and intermediate k1-triangles. For larger k1-triangles, RSD affects the magnitude by $100\!-\!200{{\ \rm per\ cent}}$ and also flips the sign from negative to positive. We conclude that it is important to take into account the impact of RSD for a correct interpretation of the EoR 21-cm bispectra.
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Akrami, Y., F. Arroja, M. Ashdown, et al. "Planck 2018 results." Astronomy & Astrophysics 641 (September 2020): A9. http://dx.doi.org/10.1051/0004-6361/201935891.
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We analyse the Planck full-mission cosmic microwave background (CMB) temperature and E-mode polarization maps to obtain constraints on primordial non-Gaussianity (NG). We compare estimates obtained from separable template-fitting, binned, and optimal modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following final results: fNLlocal = −0.9 ± 5.1; fNLequil = −26 ± 47; and fNLortho = −38 ± 24 (68% CL, statistical). These results include low-multipole (4 ≤ ℓ < 40) polarization data that are not included in our previous analysis. The results also pass an extensive battery of tests (with additional tests regarding foreground residuals compared to 2015), and they are stable with respect to our 2015 measurements (with small fluctuations, at the level of a fraction of a standard deviation, which is consistent with changes in data processing). Polarization-only bispectra display a significant improvement in robustness; they can now be used independently to set primordial NG constraints with a sensitivity comparable to WMAP temperature-based results and they give excellent agreement. In addition to the analysis of the standard local, equilateral, and orthogonal bispectrum shapes, we consider a large number of additional cases, such as scale-dependent feature and resonance bispectra, isocurvature primordial NG, and parity-breaking models, where we also place tight constraints but do not detect any signal. The non-primordial lensing bispectrum is, however, detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5σ. Beyond estimates of individual shape amplitudes, we also present model-independent reconstructions and analyses of the Planck CMB bispectrum. Our final constraint on the local primordial trispectrum shape is gNLlocal = (−5.8 ± 6.5) × 104 (68% CL, statistical), while constraints for other trispectrum shapes are also determined. Exploiting the tight limits on various bispectrum and trispectrum shapes, we constrain the parameter space of different early-Universe scenarios that generate primordial NG, including general single-field models of inflation, multi-field models (e.g. curvaton models), models of inflation with axion fields producing parity-violation bispectra in the tensor sector, and inflationary models involving vector-like fields with directionally-dependent bispectra. Our results provide a high-precision test for structure-formation scenarios, showing complete agreement with the basic picture of the ΛCDM cosmology regarding the statistics of the initial conditions, with cosmic structures arising from adiabatic, passive, Gaussian, and primordial seed perturbations.
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Sezgin, Necmettin. "Nonlinear Analysis of Electrocardiography Signals for Atrial Fibrillation." Scientific World Journal 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/509784.
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This paper aims to analyze the electrocardiography (ECG) signals for patient with atrial fibrillation (AF) by using bispectrum and extreme learning machine (ELM). AF is the most common irregular heart beat disease which may cause many cardiac diseases as well. Bispectral analysis was used to extract the nonlinear information in the ECG signals. The bispectral features of each ECG episode were determined and fed to the ELM classifier. The classification accuracy of ELM to distinguish nonterminating, terminating AF, and terminating immediately AF was 96.25%. In this study, the normal ECG signal was also compared with AF ECG signal due to the nonlinearity which was determined by bispectrum. The classification result of ELM was 99.15% to distinguish AF ECGs from normal ECGs.
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Zhang, Mingming, Jiangtian Yang, and Zhang Zhang. "Locomotive Gear Fault Diagnosis Based on Wavelet Bispectrum of Motor Current." Shock and Vibration 2021 (July 12, 2021): 1–12. http://dx.doi.org/10.1155/2021/5554777.
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The motor current signature analysis (MCSA) provides a nondestructive method for gear fault detection. The motor current in the faulty gear system not only involves the frequency information related to the fault but also the electric supply frequency and gear meshing-related frequency, which not only contaminates the fault characteristics but also increases the difficulty of fault extraction. To extract the fault characteristic frequency effectively, an innovative method based on the wavelet bispectrum (WB) is proposed. Bispectrum is an effective tool for identifying the fault-related quadratic phase coupling (QPC). However, it requires a large amount of data averaging, which is not suitable for short data analysis. In this paper, the wavelet bispectrum is introduced to motor current analysis and the problem of QPC extraction under variable speed conditions is preliminarily solved. Furthermore, a fault diagnostic approach for locomotive gears using the wavelet bispectrum and wavelet bispectral entropy is suggested. The presented method was effectively applied to the locomotive online running operations, and faults of the drive gear were successfully diagnosed.
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LIPTON, J. M., K. P. DABKE, and M. LAKSHMANAN. "BISPECTRAL PROPERTIES OF THE SIMPLEST DISSIPATIVE NONAUTONOMOUS CHAOTIC CIRCUIT." International Journal of Bifurcation and Chaos 06, no. 12a (1996): 2419–25. http://dx.doi.org/10.1142/s0218127496001569.
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The transition from periodicity to chaos for the simplest dissipative nonautonomous circuit is examined in the bispectral domain. The bispectrum and the corresponding bicoherence spectrum demonstrate the complex nonlinear interactions that the circuit exhibits.
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Nakamura, M. "Waveform and Latency Estimation from Neuroelectric Signals Using the Bispectrum." Methods of Information in Medicine 33, no. 01 (1994): 32–34. http://dx.doi.org/10.1055/s-0038-1634992.
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Abstract:A technique based on bispectra and cross-bispectra is described for estimating waveform and latency from a set of noisy signals with variable latency. Waveform estimation is performed by averaging bispectra of observed noisy signals. Latency estimation is performed by using the product function of a function derived from the cross-bispectrum and the cross-correlation. The method is numerically assessed by simulations, using a signal with uniformly distributed latency and computer-generated noise sequences.
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Hutter, Anne, Catherine A. Watkinson, Jacob Seiler, Pratika Dayal, Manodeep Sinha, and Darren J. Croton. "The 21 cm bispectrum during reionization: a tracer of the ionization topology." Monthly Notices of the Royal Astronomical Society 492, no. 1 (2019): 653–67. http://dx.doi.org/10.1093/mnras/stz3139.
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ABSTRACT We compute the bispectra of the 21cm signal during the epoch of reionization for three different reionization scenarios that are based on a dark matter N-body simulation combined with a self-consistent, semi-numerical model of galaxy evolution and reionization. Our reionization scenarios differ in their trends of ionizing escape fractions (fesc) with the underlying galaxy properties and cover the physically plausible range, i.e. fesc effectively decreasing, being constant, or increasing with halo mass. We find the 21 cm bispectrum to be sensitive to the resulting ionization topologies that significantly differ in their size distribution of ionized and neutral regions throughout reionization. From squeezed to stretched triangles, the 21 cm bispectra features a change of sign from negative to positive values, with ionized and neutral regions representing below-average and above-average concentrations contributing negatively and positively, respectively. The position of the change of sign provides a tracer of the size distribution of the ionized and neutral regions, and allows us to identify three major regimes that the 21 cm bispectrum undergoes during reionization. In particular the regime during the early stages of reionization, where the 21 cm bispectrum tracks the peak of the size distribution of the ionized regions, provides exciting prospects for pinning down reionization with the forthcoming Square Kilometre Array.
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Eiselt, M., C. Schelenz, H. Witte, and K. Schwab. "Time-variant Parametric Estimation of Transient Quadratic Phase Couplings during Electroencephalographic Burst Activity." Methods of Information in Medicine 44, no. 03 (2005): 374–83. http://dx.doi.org/10.1055/s-0038-1633980.
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Summary Objectives: Electroencephalographic burst activity characteristic of burst-suppression pattern (BSP) in sedated patients and of burst-interburst pattern (BIP) in the quiet sleep of healthy neonates have similar linear and non-linear signal properties. Strong interrelations between a slow frequency component and rhythmic, spindle-like activities with higher frequencies have been identified in previous studies. Time-varying characteristics of BSP and BIP prevent a definite pattern-related analysis. A continuous estimation of the bispectrum is essential to analyze these patterns. Parametric bispectral approaches provide this opportunity. Methods: The adaptation of an AR model leads to a parametric bispectrum by using the transfer function of the estimated AR filter. Time-variant parametric bispectral approaches require an estimation of AR parameters which consider higher order moments to preserve phase information. Accordingly, a time-variant parametric estimation of the bispectrum was introduced. Data driven simulations were performed to provide optimal parameters. BSP (12 patients) and BIP (6 neonates) were analyzed using this novel approach. Results: Significant differences in the time course of burst pattern during BSP and burst-like pattern before the onset of BSP could be shown. A rhythmic quadratic phase coupling (period 10 sec) was identified during BIP in all neonates. Conclusion: Quadratic phase couplings during BSP increases in the time course depending on depth of sedation. The visually detected burst activity in BIP is only the temporarily observable EEG correlate of a hidden neural process. Time-variant bispectral approaches offer the possibility of a better characterization of underlying neural processes leading to improved diagnostic tools used in clinical routine.
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Sugiyama, Naonori S., Shun Saito, Florian Beutler, and Hee-Jong Seo. "Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space." Monthly Notices of the Royal Astronomical Society 497, no. 2 (2020): 1684–711. http://dx.doi.org/10.1093/mnras/staa1940.
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ABSTRACT In this paper, we predict the covariance matrices of both the power spectrum and the bispectrum, including full non-Gaussian contributions, redshift space distortions, linear bias effects, and shot-noise corrections, using perturbation theory (PT). To quantify the redshift-space distortion effect, we focus mainly on the monopole and quadrupole components of both the power and bispectra. We, for the first time, compute the 5- and 6-point spectra to predict the cross-covariance between the power and bispectra, and the autocovariance of the bispectrum in redshift space. We test the validity of our calculations by comparing them with the covariance matrices measured from the MultiDark-Patchy mock catalogues that are designed to reproduce the galaxy clustering measured from the Baryon Oscillation Spectroscopic Survey Data Release 12. We argue that the simple, leading-order PT works because the shot-noise corrections for the Patchy mocks are more dominant than other higher order terms we ignore. In the meantime, we confirm some discrepancies in the comparison, especially of the cross-covariance. We discuss potential sources of such discrepancies. We also show that our PT model reproduces well the cumulative signal-to-noise ratio of the power spectrum and the bispectrum as a function of maximum wavenumber, implying that our PT model captures successfully essential contributions to the covariance matrices.
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Chen, Yarong, Rui Zhu, Jianxin Guo, and Feng Wang. "High-Performance Computational Recognition of Communication Signals Based on Bispectral Quadratic Feature Model." Computational Intelligence and Neuroscience 2022 (April 26, 2022): 1–12. http://dx.doi.org/10.1155/2022/2773492.
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In response to the problems in the signal identification of radiation sources during the communication process, the bispectral quadratic feature model is applied to the identification algorithm for communication signals. According to the signal eigenvalues obtained from the bispectrum of the diagonal slices in the radiation source signals, the eigenvalues of the bispectrum diagonal slices can be extended from the frequency domain to the complex plane through the chirp-z operation in this paper, and the relevant data are obtained based on the bispectrum quadratic feature model of the signals by using the separation rules corresponding to the extended Babbitt distance. The bispectral quadratic feature model method is used to establish a sparse observation model, and the communication signal processing problem can be transformed into an estimation problem of signal motion parameters through the construction of a parametric database. At the same time, the high-resolution distance of communication signals is tested, and the communication signals are estimated by using the variational inference method. Finally, practical cases are analyzed, and the results indicate that the algorithm proposed in this paper can be used to identify different types of communication signals in accordance with simulated and measured data in the processing of communication signals in various environments, which has the certain anti-interference capacity to noise, can improve the identification rate of communication signals, and has verified the effectiveness and practicality of the algorithm proposed in this paper.
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Huang, Jin Ying, Hong Xia Pan, and Shi Hua Bi. "Your Bearing Fault Diagnosis Based on Bispectrum and Bispectrum Entropy Feature." Advanced Materials Research 159 (December 2010): 708–13. http://dx.doi.org/10.4028/www.scientific.net/amr.159.708.
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Fault feature extraction and application is the key technology of fault diagnosis. In this paper, a fault diagnosis method using bispectrum and bispectrum entropy as the fault feature parameters is put forward. Bispectrum entropy as the information entropy in bispectrum domain can reflect the complexity of information energy. When the structure is failed, the distribution of bispectrum will be changed. bispectrum entropy can reflect this change and achieve good separation of the different types of fault. Vibration signal in different bearing states of a secondary drive gearbox is compared and analyzed, bispectrum energy spetrum and bispectrum entropy are extracted. Feature vector is set up via bispectrum entropy for the fault pattern recognition and diagnosis by BP neural network. The analysis result proves that bispectrum entropy is more sensitive to fault characteristic and can separate the fault of bearing.
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Tiwari, Himanshu, Abinash Kumar Shaw, Suman Majumdar, Mohd Kamran, and Madhurima Choudhury. "Improving constraints on the reionization parameters using 21-cm bispectrum." Journal of Cosmology and Astroparticle Physics 2022, no. 04 (2022): 045. http://dx.doi.org/10.1088/1475-7516/2022/04/045.
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Abstract Radio interferometric experiments aim to constrain the reionization model parameters by measuring the 21-cm signal statistics, primarily the power spectrum. However the Epoch of Reionization (EoR) 21-cm signal is highly non-Gaussian, and this non-Gaussianity encodes important information about this era. The bispectrum is the lowest order statistic able to capture this inherent non-Gaussianity. Here we are the first to demonstrate that bispectra for large and intermediate length scales and for all unique k-triangle shapes provide tighter constraints on the EoR parameters compared to the power spectrum or the bispectra for a limited number of shapes of k-triangles. We use the Bayesian inference technique to constrain EoR parameters. We have also developed an Artificial Neural Network (ANN) based emulator for the EoR 21-cm power spectrum and bispectrum which we use to remarkably speed up our parameter inference pipeline. Here we have considered the sample variance and the system noise uncertainties corresponding to 1000 hrs of SKA-Low observations for estimating errors in the signal statistics. We find that using all unique k-triangle bispectra improves the constraints on parameters by a factor of 2 – 4 (depending on the stage of reionization) over the constraints that are obtained using power spectrum alone.
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Böning, Vincent G. A., Aaron C. Birch, Laurent Gizon, Thomas L. Duvall, and Jesper Schou. "Characterizing the spatial pattern of solar supergranulation using the bispectrum." Astronomy & Astrophysics 635 (March 2020): A181. http://dx.doi.org/10.1051/0004-6361/201937331.
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Context. The spatial power spectrum of supergranulation does not fully characterize the underlying physics of turbulent convection. For example, it does not describe the non-Gaussianity in the horizontal flow divergence. Aims. Our aim is to statistically characterize the spatial pattern of solar supergranulation beyond the power spectrum. The next-order statistic is the bispectrum. It measures correlations of three Fourier components and is related to the nonlinearities in the underlying physics. It also characterizes how a skewness in the dataset is generated by the coupling of three Fourier components. Methods. We estimated the bispectrum of supergranular horizontal surface divergence maps that were obtained using local correlation tracking (LCT) and time-distance helioseismology (TD) from one year of data from the helioseismic and magnetic imager on-board the solar dynamics observatory starting in May 2010. Results. We find significantly nonzero and consistent estimates for the bispectrum using LCT and TD. The strongest nonlinearity is present when the three coupling wave vectors are at the supergranular scale. These are the same wave vectors that are present in regular hexagons, which have been used in analytical studies of solar convection. At these Fourier components, the bispectrum is positive, consistent with the positive skewness in the data and consistent with supergranules preferentially consisting of outflows surrounded by a network of inflows. We use the bispectral estimates to generate synthetic divergence maps that are very similar to the data. This is done by a model that consists of a Gaussian term and a weaker quadratic nonlinear component. Using this method, we estimate the fraction of the variance in the divergence maps from the nonlinear component to be of the order of 4–6%. Conclusions. We propose that bispectral analysis is useful for understanding the dynamics of solar turbulent convection, for example for comparing observations and numerical models of supergranular flows. This analysis may also be useful to generate synthetic flow fields.
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Ramírez-Moreno, Mauricio A., Jesús G. Cruz-Garza, Akanksha Acharya, et al. "Brain-to-brain communication during musical improvisation: a performance case study." F1000Research 11 (September 1, 2022): 989. http://dx.doi.org/10.12688/f1000research.123515.1.
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Understanding and predicting others' actions in ecological settings is an important research goal in social neuroscience. Here, we deployed a mobile brain-body imaging (MoBI) methodology to analyze inter-brain communication between professional musicians during a live jazz performance. Specifically, bispectral analysis was conducted to assess the synchronization of scalp electroencephalographic (EEG) signals from three expert musicians during a three-part 45 minute jazz performance, during which a new musician joined every five minutes. The bispectrum was estimated for all musician dyads, electrode combinations, and five frequency bands. The results showed higher bispectrum in the beta and gamma frequency bands (13-50 Hz) when more musicians performed together, and when they played a musical phrase synchronously. Positive bispectrum amplitude changes were found approximately three seconds prior to the identified synchronized performance events suggesting preparatory cortical activity predictive of concerted behavioral action. Moreover, a higher amount of synchronized EEG activity, across electrode regions, was observed as more musicians performed, with inter-brain synchronization between the temporal, parietal, and occipital regions the most frequent. Increased synchrony between the musicians' brain activity reflects shared multi-sensory processing and movement intention in a musical improvisation task.
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Munshi, D., T. Namikawa, T. D. Kitching, et al. "The weak lensing bispectrum induced by gravity." Monthly Notices of the Royal Astronomical Society 493, no. 3 (2020): 3985–95. http://dx.doi.org/10.1093/mnras/staa296.
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ABSTRACT Recent studies have demonstrated that secondary non-Gaussianity induced by gravity will be detected with a high signal-to-noise ratio (S/N) by future and even by on-going weak lensing surveys. One way to characterize such non-Gaussianity is through the detection of a non-zero three-point correlation function of the lensing convergence field, or of its harmonic transform, the bispectrum. A recent study analysed the properties of the squeezed configuration of the bispectrum, when two wavenumbers are much larger than the third one. We extend this work by estimating the amplitude of the (reduced) bispectrum in four generic configurations, i.e. squeezed, equilateral, isosceles and folded, and for four different source redshifts zs = 0.5, 1.0, 1.5, 2.0, by using an ensemble of all-sky high-resolution simulations. We compare these results against theoretical predictions. We find that, while the theoretical expectations based on widely used fitting functions can predict the general trends of the reduced bispectra, a more accurate theoretical modelling will be required to analyse the next generation of all-sky weak lensing surveys. The disagreement is particularly pronounced in the squeezed limit.
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Jiang, Ling Li, Yi Lun Liu, Xue Jun Li, and Anhua Chen. "Fault Diagnosis of Roller Bearing Based on Bispectrum Estimation and Fuzzy Cluster Analysis." Applied Mechanics and Materials 36 (October 2010): 129–34. http://dx.doi.org/10.4028/www.scientific.net/amm.36.129.
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Performing bispectrum analysis on the actual measured vibration signals of the roller bearing with different failure modes, it developed that the spectrum distribution regions are similar among the same failure modes, and distinguishable among the different failure modes, thus this character can be used to classify fault types. The binary images extracted from the bispectra are taken as the feature vectors. The fuzzy clustering analysis based on objective function is applied for pattern recognition, which makes use of the binary image to construct a core and a domain representing the common and scope of bispectrum distribution, respectively, then constructs the objective function as the classify to achieve pattern recognition and diagnosis. The roller bearing fault diagnosis is performed as an example to verify the feasibility of the proposed method.
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Shaw, Abinash Kumar, Somnath Bharadwaj, Debanjan Sarkar, Arindam Mazumdar, Sukhdeep Singh, and Suman Majumdar. "A fast estimator for quantifying the shape dependence of the 3D bispectrum." Journal of Cosmology and Astroparticle Physics 2021, no. 12 (2021): 024. http://dx.doi.org/10.1088/1475-7516/2021/12/024.
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Abstract The dependence of the bispectrum on the size and shape of the triangle contains a wealth of cosmological information. Here we consider a triangle parameterization which allows us to separate the size and shape dependence. We have implemented an FFT based fast estimator for the three dimensional (3D) bin averaged bispectrum, and we demonstrate that it allows us to study the variation of the bispectrum across triangles of all possible shapes (and also sizes). The computational requirement is shown to scale as ∼ N g 3 log N g 3 where N g is the number of grid points along each side of the volume. We have validated the estimator using a non-Gaussian field for which the bispectrum can be analytically calculated. The estimated bispectrum values are found to be in good agreement (< 10 % deviation) with the analytical predictions across much of the triangle-shape parameter space. We also introduce linear redshift space distortion, a situation where also the bispectrum can be analytically calculated. Here the estimated bispectrum is found to be in close agreement with the analytical prediction for the monopole of the redshift space bispectrum.
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Morita, Koh-Ichiro. "The Bispectrum analysis technique in millimeter interferometry." International Astronomical Union Colloquium 131 (1991): 197–201. http://dx.doi.org/10.1017/s0252921100013300.
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AbstractWe propose an application of the bispectrum analysis technique in millimeter interferometry, which is used in the speckle masking technique. For the millimeter interferometry, in which atmospheric phase fluctuations are very serious, not only bispectrum phase but also bispectrum amplitude is good observable. We have developed an algorithm to reconstruct images directly from bispectrum. We have made good maps with this algorithm in the case of both simple and compact sources.
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Nataraj, Sathees Kumar, Paulraj Murugesa Pandiyan, Sazali Bin Yaacob, and Abdul Hamid Bin Adom. "Intelligent robot chair with communication aid using TEP responses and higher order spectra band features." Informatics 17, no. 4 (2021): 92–103. http://dx.doi.org/10.37661/1816-0301-2020-17-4-92-103.
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In recent years, electroencephalography-based navigation and communication systems for differentially enabled communities have been progressively receiving more attention. To provide a navigation system with a communication aid, a customized protocol using thought evoked potentials has been proposed in this research work to aid the differentially enabled communities. This study presents the higher order spectra based features to categorize seven basic tasks that include Forward, Left, Right, Yes, NO, Help and Relax; that can be used for navigating a robot chair and also for communications using an oddball paradigm. The proposed system records the eight-channel wireless electroencephalography signal from ten subjects while the subject was perceiving seven different tasks. The recorded brain wave signals are pre-processed to remove the interference waveforms and segmented into six frequency band signals, i. e. Delta, Theta, Alpha, Beta, Gamma 1-1 and Gamma 2. The frequency band signals are segmented into frame samples of equal length and are used to extract the features using bispectrum estimation. Further, statistical features such as the average value of bispectral magnitude and entropy using the bispectrum field are extracted and formed as a feature set. The extracted feature sets are tenfold cross validated using multilayer neural network classifier. From the results, it is observed that the entropy of bispectral magnitude feature based classifier model has the maximum classification accuracy of 84.71 % and the value of the bispectral magnitude feature based classifier model has the minimum classification accuracy of 68.52 %.
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Nataraj, Sathees Kumar, Paulraj Murugesa Pandiyan, Sazali Bin Yaacob, and Abdul Hamid Bin Adom. "Intelligent robot chair with communication aid using TEP responses and higher order spectra band features." Informatics 17, no. 4 (2021): 92–103. http://dx.doi.org/10.37661/1816-0301-2020-17-4-92-103.
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In recent years, electroencephalography-based navigation and communication systems for differentially enabled communities have been progressively receiving more attention. To provide a navigation system with a communication aid, a customized protocol using thought evoked potentials has been proposed in this research work to aid the differentially enabled communities. This study presents the higher order spectra based features to categorize seven basic tasks that include Forward, Left, Right, Yes, NO, Help and Relax; that can be used for navigating a robot chair and also for communications using an oddball paradigm. The proposed system records the eight-channel wireless electroencephalography signal from ten subjects while the subject was perceiving seven different tasks. The recorded brain wave signals are pre-processed to remove the interference waveforms and segmented into six frequency band signals, i. e. Delta, Theta, Alpha, Beta, Gamma 1-1 and Gamma 2. The frequency band signals are segmented into frame samples of equal length and are used to extract the features using bispectrum estimation. Further, statistical features such as the average value of bispectral magnitude and entropy using the bispectrum field are extracted and formed as a feature set. The extracted feature sets are tenfold cross validated using multilayer neural network classifier. From the results, it is observed that the entropy of bispectral magnitude feature based classifier model has the maximum classification accuracy of 84.71 % and the value of the bispectral magnitude feature based classifier model has the minimum classification accuracy of 68.52 %.
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El-Morshedy, Mahmoud, Abd El-Moneim A. M. Teamah, Mohammed H. El-Menshawy, et al. "Some Asymptotic Properties of a Kernel Bispectum Estimate with Different Multitapers." Mathematics 10, no. 18 (2022): 3284. http://dx.doi.org/10.3390/math10183284.
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Assume X1,X2,…,XN are realizations of N observations from a real-valued discrete parameter third-order stationary process Xt,t=0±1,±2,…, with bispectrum fXXX(λ1,λ2) where “−π≤λ1,λ2≤π”. Based on the previous assumption, L different multitapered biperiodograms IXXX(mt)j(λ1,λ2);j=1,2,…,L on overlapped segments (Xt(j);1≤t<N) can be constructed. Further, the mean and variance of the average of these different multitapered biperiodograms can be expressed as asymptotic expressions. According to different bispectral windows/kernels (Wβ(j)(α1,α2), where “−π⩽α1,α2⩽π” andβ is the bandwidth) and IXXX(mt)j(λ1,λ2), the bispectrum fXXX(λ1,λ2) can be estimated. The asymptotic expressions of the first- and second-ordered moments as well as the integrated relative mean squared error (IMSE) of this estimate are derived. Finally, some estimation results based on numerically generated data from the selected process “DCGINAR(1)” are presented and discussed in detail.
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Pospelov, Boris, Evgenіy Rybka, Alexander Savchenko, et al. "Peculiarities of amplitude spectra of the third order for the early detection of indoor fires." Eastern-European Journal of Enterprise Technologies 5, no. 10 (119) (2022): 49–56. http://dx.doi.org/10.15587/1729-4061.2022.265781.
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The object of this study is the dynamics of hazardous parameters of the gas environment during the ignition of materials. The problem that was solved is the early detection of fires in the premises. The research results indicate the nonlinear nature of the dynamics of hazardous parameters of the gas environment in the absence and presence of materials ignition. It was established that the bispectrum amplitude, in contrast to the amplitude spectrum of the hazardous parameters of the gas medium, contains information on the reliable detection of fires. As such information, the value of the positive dynamic amplitude range of bispectrum is used. It was established that during the ignition of alcohol, the positive dynamics of the amplitude bispectrum of all dangerous parameters of the gas medium change. Significant changes are characteristic of smoke density (from 1 dB to 30 dB) and temperature (from 1 dB to 70 dB). The dynamic range of amplitude bispectrum for CO concentration is increased from 30 dB to 70 dB. Paper ignition was found to reduce the dynamic range of the amplitude bispectrum for smoke density from 40 dB to 20 dB. At the same time, the dynamic range of amplitude bispectrum for carbon monoxide concentration and temperature increases to 60 dB. The ignition of wood causes an increase in the dynamic range of the amplitude bispectrum relative to the concentration of carbon monoxide from 40 dB to 60 dB, and the temperature – from 30 dB to 40 dB. It was established that when textiles are ignited, the range of dynamics of the amplitude bispectrum for temperature increases from 10 dB to 60 dB. The results indicate that the dynamic characteristics of the amplitudes of the bispectrum of the gas medium can be used in practice for the early detection of fires in the premises
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Watkinson, Catherine A., Cathryn M. Trott, and Ian Hothi. "The bispectrum and 21-cm foregrounds during the Epoch of Reionization." Monthly Notices of the Royal Astronomical Society 501, no. 1 (2020): 367–82. http://dx.doi.org/10.1093/mnras/staa3677.
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ABSTRACT Numerous studies have established the theoretical potential of the 21-cm bispectrum to boost our understanding of the Epoch of Reionization (EoR). We take a first look at the impact of foregrounds (FGs) and instrumental effects on the 21-cm bispectrum and our ability to measure it. Unlike the power spectrum for which (in the absence of instrumental effects) there is a window clear of smooth-spectrum FGs in which it may be detectable, there is no such ‘EoR window’ for the bispectrum. For the triangle configurations and scales we consider, the EoR structures are completely swamped by those of the FGs, and the EoR + FG bispectrum is entirely dominated by that of the FGs. By applying a rectangular window function on the sky combined with a Blackman–Nuttall filter along the frequency axis, we find that spectral, or in our case scale, leakage (caused by FFTing non-periodic data) suppresses the FG contribution so that cross-terms of the EoR and FGs dominate. While difficult to interpret, these findings motivate future studies to investigate whether filtering can be used to extract information about the EoR from the 21-cm bispectrum. We also find that there is potential for instrumental effects to seriously corrupt the bispectrum. FG removal using GMCA (generalized morphological component analysis) is found to recover the EoR bispectrum to a reasonable level of accuracy for many configurations. Further studies are necessary to understand the error and/or bias associated with FG removal before the 21-cm bispectrum can be practically applied in analysis of future data.
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Lan, Xiaohong, and Domenico Marinucci. "The needlets bispectrum." Electronic Journal of Statistics 2 (2008): 332–67. http://dx.doi.org/10.1214/08-ejs197.
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Fergusson, J. R., M. Liguori, and E. P. S. Shellard. "The CMB bispectrum." Journal of Cosmology and Astroparticle Physics 2012, no. 12 (2012): 032. http://dx.doi.org/10.1088/1475-7516/2012/12/032.
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Zhang, Lanyue, Yang Wang, and Desen Yang. "Bispectrum and cross-bispectrum feature extraction based on vector hydrophone." Journal of the Acoustical Society of America 131, no. 4 (2012): 3485. http://dx.doi.org/10.1121/1.4709154.
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Delgado, Paola C. M., Ruth Durrer, and Nelson Pinto-Neto. "The CMB bispectrum from bouncing cosmologies." Journal of Cosmology and Astroparticle Physics 2021, no. 11 (2021): 024. http://dx.doi.org/10.1088/1475-7516/2021/11/024.
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Abstract In this paper we compute the CMB bispectrum for bouncing models motivated by Loop Quantum Cosmology. Despite the fact that the primordial bispectrum of these models is decaying exponentially above a large pivot scale, we find that the cumulative signal-to-noise ratio of the bispectrum induced in the CMB from scales ℓ<30 is larger than 10 in all cases of interest and therefore can, in principle, be detected in the Planck data.
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Somia Alfatih, M. S., M. Salman Leong, and L. M. Hee. "Experimental Investigation on the Use of Bispectral Analysis in Detecting Nonlinear Faults in Hydraulic Machines." Applied Mechanics and Materials 606 (August 2014): 147–51. http://dx.doi.org/10.4028/www.scientific.net/amm.606.147.
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Bispectral analysis is one of the relatively more recent tools in signal processing used for detection and identification of higher harmonics in a signal. It is also acknowledged to be one of Higher Order Spectral Analysis (HOSA) effective tools for detecting nonlinear behavior in mechanical systems. In this study, vibration sources in a hydraulic machine which may have features of nonlinear behavior were investigated. An experimental study was undertaken to formulate a more sensitive and effective method using Bispectral analysis to diagnose cavitation in a centrifugal pump facility. Cavitation was induced on the suction side of the pump. The cavitation signal was analyzed with and without induced cavitation conditions at different locations on the pump, and analyzed using FFT and bispectrum methods. It was observed that bispectral analysis could be used as an early indicator of cavitation with changes for severity of cavitation.
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Vanhoff, Barry, and Steve Elgar. "Simulating Quadratically Nonlinear Random Processes." International Journal of Bifurcation and Chaos 07, no. 06 (1997): 1367–74. http://dx.doi.org/10.1142/s0218127497001084.
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A technique to generate realizations of quadratically nonlinear non-Gaussian time series with a desired ("target") power spectrum and bispectrum is presented. Specifically, by generating a Gaussian time series (using amplitude information from the target power spectrum and random phases) and passing it through a quadratic filter (that uses phase information from the target bispectrum), a realization of a quadratically nonlinear random process with a specified power spectrum and bispectrum can be produced. Second- and third-order statistics from many realizations of simulated nonlinear time series compare well to those from the original time series providing the target power spectrum and bispectrum, with deviations consistent with theory. The simulation technique is shown to simulate accurately ocean waves in shallow water, which are well known to be quadratically nonlinear.
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Bartolo, Nicola, Giovanni Battista Carollo, Sabino Matarrese, Luigi Pilo, and Rocco Rollo. "The physical content of long tensor modes in cosmology." Journal of Cosmology and Astroparticle Physics 2022, no. 11 (2022): 034. http://dx.doi.org/10.1088/1475-7516/2022/11/034.
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Abstract We analyze the physical content of squeezed bispectra involving long-wavelength tensor perturbations, showing that these modes cannot be gauged away, except for the exact (unphysical) limit of infinite wavelength, k = 0. This result has a direct implication on the validity of the Maldacena consistency relation, respected by a subclass of inflationary models. Consequently, in the squeezed limit, as in the case of the scalar-scalar-scalar bispectrum, squeezed mixed correlators could be observed by future experiments, remaining a key channel to study Early Universe physics and discriminate among different models of inflation.
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Agrawal, Aniket. "Non-Gaussianity of inflationary gravitational waves from the field equation." International Journal of Modern Physics D 28, no. 02 (2019): 1950036. http://dx.doi.org/10.1142/s0218271819500366.
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We demonstrate equivalence of the in–in formalism and Green’s function method for calculating the bispectrum of primordial gravitational waves generated by vacuum fluctuations of the metric. The tree-level bispectrum from the field equation, [Formula: see text], agrees with the results obtained previously using the in–in formalism exactly. Characterizing non-Gaussianity of the fluctuations using the ratio [Formula: see text] in the equilateral configuration, where [Formula: see text] is the power spectrum of scale-invariant gravitational waves, we show that it is much weaker than in models with spectator gauge fields. We also calculate the tree-level bispectrum of two right-handed and one left-handed gravitational wave using Green’s function, reproducing the results from in–in formalism, and show that it can be as large as the bispectrum of three right-handed gravitational waves.
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He, Guang Jin, Jin Fang Cheng, and Wei Zhang. "The Research on Bispectrum Detection of Underwater Target in Frequency Domain." Applied Mechanics and Materials 182-183 (June 2012): 1761–65. http://dx.doi.org/10.4028/www.scientific.net/amm.182-183.1761.
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As the non-Gaussianity of ship-radiated noise reduces fast when the Signal-to-Noise Ratio (SNR) becomes low, a bispectrum detector in the frequency domain is proposed to ease the problem. First, FFT method is applied on the received data to calculate the power spectrum. Second, the non-Gaussianity of the power spectrum series is tested by Hinich-Wilson Gaussian Test rule. Last, the bispectrum detector based on non-Gaussianity is used to determine whether there are ship-radiated signals. The bispectrum detector in frequency domain is applied to detect simulated noise and real ship-radiated noise. The results are compared with the detector which is in the signal’s time domain. The comparison illustrates that the bispectrum detector based on the power spectrum series(in frequency domain) is much better in detecting low SNR signals, which is very valuable in far distance detection.
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Mondal, Rajesh, Garrelt Mellema, Abinash Kumar Shaw, Mohd Kamran, and Suman Majumdar. "The Epoch of Reionization 21-cm bispectrum: the impact of light-cone effects and detectability." Monthly Notices of the Royal Astronomical Society 508, no. 3 (2021): 3848–59. http://dx.doi.org/10.1093/mnras/stab2900.
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ABSTRACT We study the spherically averaged bispectrum of the 21-cm signal from the Epoch of Reionization (EoR). This metric provides a quantitative measurement of the level of non-Gaussianity of the signal, which is expected to be high. We focus on the impact of the light-cone (LC) effect on the bispectrum and its detectability with the future SKA-Low telescope. Our investigation is based on a single reionization LC model and an ensemble of 50 realizations of the 21-cm signal to estimate the cosmic variance errors. We calculate the bispectrum with a new, optimized direct estimation method, DviSukta, which calculates the bispectrum for all possible unique triangles. We find that the LC effect becomes important on scales $k_1 \lesssim 0.1\, {\rm Mpc}^{-1}$, where, for most triangle shapes, the cosmic variance errors dominate. Only for the squeezed limit triangles, the impact of the LC effect exceeds the cosmic variance. Combining the effects of system noise and cosmic variance we find that ∼3σ detection of the bispectrum is possible for all unique triangle shapes around a scale of $k_1 \sim 0.2\, {\rm Mpc}^{-1}$, and cosmic variance errors dominate above and noise errors below this length-scale. Only the squeezed limit triangles are able to achieve a more than 5σ significance over a wide range of scales, $k_1\lesssim 0.8\, {\rm Mpc}^{-1}$. Our results suggest that among all the possible triangle combinations for the bispectrum, the squeezed limit one will be the most measurable and hence useful.
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Liguori, Michele, Emiliano Sefusatti, James R. Fergusson, and E. P. S. Shellard. "Primordial Non-Gaussianity and Bispectrum Measurements in the Cosmic Microwave Background and Large-Scale Structure." Advances in Astronomy 2010 (2010): 1–64. http://dx.doi.org/10.1155/2010/980523.
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The most direct probe of non-Gaussian initial conditions has come from bispectrum measurements of temperature fluctuations in the Cosmic Microwave Background and of the matter and galaxy distribution at large scales. Such bispectrum estimators are expected to continue to provide the best constraints on the non-Gaussian parameters in future observations. We review and compare the theoretical and observational problems, current results, and future prospects for the detection of a nonvanishing primordial component in the bispectrum of the Cosmic Microwave Background and large-scale structure, and the relation to specific predictions from different inflationary models.
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Jhang, Kyung Young, Kimio Sasaki, Job Ha, and Hiroaki Tanaka. "Advanced Technologies for Estimation of Nonlinear Ultrasonic Parameter." Key Engineering Materials 326-328 (December 2006): 673–76. http://dx.doi.org/10.4028/www.scientific.net/kem.326-328.673.
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This paper proposes an advanced signal processing technique for the precise estimation of a nonlinear ultrasonic parameter, based on power spectral and bispectral analysis. The power spectrum and bispectrum estimation of the pulse-like ultrasonic signal used in the commercial SAM (scanning acoustic microscopy) equipment is especially considered in this study. The usefulness of the proposed estimation is confirmed by experiments for a Newton ring with a continuous air gap and a real semiconductor sample with local delaminations. The results show that the nonlinear parameter obtained by the proposed method had a good correlation with the delamination.
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O’Brien, Michael J., Blakesley Burkhart, and Michael J. Shelley. "Studying Interstellar Turbulence Driving Scales Using the Bispectrum." Astrophysical Journal 930, no. 2 (2022): 149. http://dx.doi.org/10.3847/1538-4357/ac6502.
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Abstract We demonstrate the utility of the bispectrum, the Fourier three-point correlation function, for studying driving scales of magnetohydrodynamic (MHD) turbulence in the interstellar medium. We calculate the bispectrum by implementing a parallelized Monte Carlo direct measurement method, which we have made publicly available. In previous works, the bispectrum has been used to identify nonlinear scaling correlations and break degeneracies in lower-order statistics like the power spectrum. We find that the bicoherence, a related statistic which measures phase coupling of Fourier modes, identifies turbulence-driving scales using density and column density fields. In particular, it shows that the driving scale is phase-coupled to scales present in the turbulent cascade. We also find that the presence of an ordered magnetic field at large scales enhances phase coupling as compared to a pure hydrodynamic case. We therefore suggest the bispectrum and bicoherence as tools for searching for non-locality for wave interactions in MHD turbulence.
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Chakraborty, Priyesh, Shu-Fan Chen, and Cora Dvorkin. "Skewing the CMB×LSS: a fast method for bispectrum analysis." Journal of Cosmology and Astroparticle Physics 2022, no. 07 (2022): 038. http://dx.doi.org/10.1088/1475-7516/2022/07/038.
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Abstract Upcoming cosmic microwave background (CMB) lensing measurements and tomographic galaxy surveys are expected to provide us with high-precision data sets in the coming years, thus paving the way for fruitful cross-correlation analyses. In this paper we study the information content of the weighted skew-spectrum, a nearly-optimal estimator of the angular bispectrum amplitude, as a means to extract non-Gaussian information on both bias and cosmological parameters from the bispectra of galaxies cross-correlated with CMB lensing, while gaining significantly on speed. Our results show that for the combination of the Planck satellite and the Dark Energy Spectroscopic Instrument (DESI), the difference in the constraints on bias and cosmological parameters from the skew-spectrum and the bispectrum is at most 17%. We further compare and find agreement between our theoretical skew-spectra and those estimated from N-body simulations, for which it is important to include gravitational non-linearities beyond perturbation theory and the post-Born effect for CMB lensing. We define an algorithm to apply the skew-spectrum estimator to the data and, as a preliminary step, we use the skew-spectra to constrain bias parameters and the amplitude of shot noise from the simulations through a Markov chain Monte Carlo likelihood analysis, finding that it may be possible to reach percent-level estimates for the linear bias parameter b 1.
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Fang, Teng Fei, and Guo Fu Li. "Condition Feature Extraction of Machine Tools Based on Wavelet Packet Energy Spectrum Analysis and Bispectrum Analysis of Current Signal." Applied Mechanics and Materials 101-102 (September 2011): 847–50. http://dx.doi.org/10.4028/www.scientific.net/amm.101-102.847.
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Based on the study of the characteristics of load current signal, this article develops a method to extract features that can be use to distinguish the different working status of machine tools in real-time manner. The features are extracted from wavelet packet energy spectrum and bispectrum of the load current signal, and thus can take advantages of both wavelet packet transforms and bispectrum in signal analysis. Experimental results show that, compared with the features extracted from wavelet packet energy spectrum or bispectrum alone, the features extracted by applying the proposed method can provide better performance in term of identifying the machine working status.
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Gualdi, Davide, Héctor Gil-Marín, Marc Manera, Benjamin Joachimi, and Ofer Lahav. "GEOMAX: beyond linear compression for three-point galaxy clustering statistics." Monthly Notices of the Royal Astronomical Society 497, no. 1 (2020): 776–92. http://dx.doi.org/10.1093/mnras/staa1941.
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ABSTRACT We present the GEOMAX algorithm and its python implementation for a two-step compression of bispectrum measurements. The first step groups bispectra by the geometric properties of their arguments; the second step then maximizes the Fisher information with respect to a chosen set of model parameters in each group. The algorithm only requires the derivatives of the data vector with respect to the parameters and a small number of mock data, producing an effective, non-linear compression. By applying GEOMAX to bispectrum monopole measurements from BOSS DR12 CMASS redshift-space galaxy clustering data, we reduce the 68 per cent credible intervals for the inferred parameters (b1, b2, f, σ8) by 50.4, 56.1, 33.2, and 38.3 per cent with respect to standard MCMC on the full data vector. We run the analysis and comparison between compression methods over 100 galaxy mocks to test the statistical significance of the improvements. On average, GEOMAX performs ∼15 per cent better than geometrical or maximal linear compression alone and is consistent with being lossless. Given its flexibility, the GEOMAX approach has the potential to optimally exploit three-point statistics of various cosmological probes like weak lensing or line-intensity maps from current and future cosmological data sets such as DESI, Euclid, PFS, and SKA.
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Fiorini, Bartolomeo, Kazuya Koyama, and Albert Izard. "Studying large-scale structure probes of modified gravity with COLA." Journal of Cosmology and Astroparticle Physics 2022, no. 12 (2022): 028. http://dx.doi.org/10.1088/1475-7516/2022/12/028.
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Abstract We study the effect of two Modified Gravity (MG) theories, f(R) and nDGP, on three probes of large-scale structure, the real space power spectrum estimator Q 0, bispectrum and voids, and validate fast approximate COLA simulations against full N-body simulations for the prediction of these probes. We find that using the first three even multipoles of the redshift space power spectrum to estimate Q 0 is enough to reproduce the MG boost factors of the real space power spectrum for both halo and galaxy catalogues. By analysing the bispectrum and reduced bispectrum of Dark Matter (DM), we show that the strong MG signal present in the DM bispectrum is mainly due to the enhanced power spectrum. We warn about adopting screening approximations in simulations as this neglects non-linear contributions that can source a significant component of the MG bispectrum signal at the DM level, but we argue that this is not a problem for the bispectrum of galaxies in redshift space where the signal is dominated by the non-linear galaxy bias. Finally, we search for voids in our mock galaxy catalogues using the ZOBOV watershed algorithm. To apply a linear model for Redshift-Space Distortion (RSD) in the void-galaxy cross-correlation function, we first examine the effects of MG on the void profiles entering into the RSD model. We find relevant MG signals in the integrated-density, velocity dispersion and radial velocity profiles in the nDGP theory. Fitting the RSD model for the linear growth rate, we recover the linear theory prediction in an nDGP model, which is larger than the ΛCDM prediction at the 3σ level. In f(R) theory we cannot naively compare the results of the fit with the linear theory prediction as this is scale-dependent, but we obtain results that are consistent with the ΛCDM prediction.
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Jung, Gabriel, Filippo Oppizzi, Andrea Ravenni, and Michele Liguori. "The integrated angular bispectrum." Journal of Cosmology and Astroparticle Physics 2020, no. 06 (2020): 035. http://dx.doi.org/10.1088/1475-7516/2020/06/035.
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Heavens, Alan, Mario Santos, and Pedro Ferreira. "The bispectrum of MAXIMA." New Astronomy Reviews 47, no. 8-10 (2003): 815–20. http://dx.doi.org/10.1016/j.newar.2003.07.009.
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Magueijo, João, and João Medeiros. "On the bispectrum ofCOBEandWMAP." Monthly Notices of the Royal Astronomical Society 351, no. 1 (2004): L1—L4. http://dx.doi.org/10.1111/j.1365-2966.2004.07912.x.
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Hirlekar, S. G., R. S. Holambe, and T. K. Basu. "Phase Recovery from Bispectrum." IETE Journal of Research 46, no. 3 (2000): 139–45. http://dx.doi.org/10.1080/03772063.2000.11416149.
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