non-Gaussian Properties Research Articles

Axial symmetries in WMAP ILC data

A test of the Gaussianity of the background signal in the zones located symmetrically with respect to the Galactic equator is proposed. The test is based on the analysis of the dominating harmonics in symmetric zones and the distribution of the correlation coefficients as a function of the number of selected multipole. Zones located symmetrically in the Galactic and ecliptical coordinate systems are chosen and analyzed for the presence of an antisymmetric signal. Nongaussian properties are found in the distribution of the correlation coefficients for several zones

Virtual evolution for visual search in natural images results in behavioral receptive fields with inhibitory surrounds

The neural mechanisms driving perception and saccades during search use information about the target but are also based on an inhibitory surround not present in the target luminance profile (e.g., Eckstein et al., 2007). Here, we ask whether these inhibitory surrounds might reflect a strategy that the brain has adapted to optimize the search for targets in natural scenes. To test this hypothesis, we sought to estimate the best linear template (behavioral receptive field), built from linear combinations of Gabor channels representing V1 simple cells in search for an additive Gaussian target embedded in natural images. Statistically nonstationary and non-Gaussian properties of natural scenes preclude calculation of the best linear template from analytic expressions and require an iterative optimization method such as a virtual evolution via a genetic algorithm. Evolved linear receptive fields built from linear combinations of Gabor functions include substantial inhibitory surround, larger than those found in humans performing target search in white noise. The inhibitory surrounds were robust to changes in the contrast of the signal, generalized to a larger calibrated natural image data set, and tasks in which the signal occluded other objects in the image. We show that channel nonlinearities can have strong effects on the observed linear behavioral receptive field but preserve the inhibitory surrounds. Together, the results suggest that the apparent suboptimality of inhibitory surrounds in human behavioral receptive fields when searching for a target in white noise might reflect a strategy to optimize detection of signals in natural scenes. Finally, we contend that optimized linear detection of spatially compact signals in natural images might be a new possible hypothesis, distinct from decorrelation of visual input and sparse representations (e.g., Graham et al., 2006), to explain the evolution of center-surround organization of receptive fields in early vision.

Statistical properties of deep ocean noise.

The various arrays sea test (VAST) was conducted in July 1989 in the northeast Pacific Ocean. A 3000-m-long, 200-element hydrophone array was suspended for an 11-day period from R/P FLIP, moored about halfway between San Diego and Hawaii (34N, 140W). Simultaneously, 12 neutrally buoyant, freely drifting Swallow floats equipped with both infrasonic hydrophones and three-component geophones were deployed at various depths 150 km off the California coast (35N, 122W). The statistical properties of deep ocean noise recorded by these sensor systems, both single element and beam level, are examined quantitatively under a variety of conditions, including wind-dominated (15–18 kt), distant air gun operations, and marine mammal vocalizations. Non-parametric statistical tests applied to narrow band complex time series of the data include the Wald–Wolfowitz run test for mutual independence of the data samples, the Kolmogorov–Smirnov two-sample test for stationarity, and the Kolmogorov–Smirnov one-sample test for Gaussianity. Results are presented over a broad range in frequencies and time scales and show that the noise field at times and in certain directions displays non-stationary and non-Gaussian properties. In a few cases, these statistical characteristics can be associated with specific physical processes. [Work supported by the Office of Naval Research.]

DROPOUTS IN SOLAR ENERGETIC PARTICLES: ASSOCIATED WITH LOCAL TRAPPING BOUNDARIES OR CURRENT SHEETS?

In recent observations by the Advanced Composition Explorer, the intensity of solar energetic particles exhibits sudden, large changes known as dropouts. These have been explained in terms of turbulence or a flux tube structure in the solar wind. Dropouts are believed to indicate filamentary magnetic connection to a localized particle source near the solar surface, and computer simulations of a random-phase model of magnetic turbulence have indicated a spatial association between dropout features and local trapping boundaries (LTBs) defined for a two-dimensional (2D) + slab model of turbulence. Previous observations have shown that dropout features are not well associated with sharp magnetic field changes, as might be expected in the flux tube model. Random-phase turbulence models do not properly treat sharp changes in the magnetic field, such as current sheets, and thus cannot be tested in this way. Here, we explore the properties of a more realistic magnetohydrodynamic (MHD) turbulence model (2D MHD), in which current sheets develop and the current and magnetic field have characteristic non-Gaussian statistical properties. For this model, computer simulations that trace field lines to determine magnetic connection from a localized particle source indicate that sharp particle gradients should frequently be associated with LTBs, sometimes with strong 2D magnetic fluctuations, and infrequently with current sheets. Thus, the 2D MHD + slab model of turbulent fluctuations includes some realistic features of the flux tube view and is consistent with the lack of an observed association between dropouts and intense magnetic fields or currents.

Limits on isocurvature perturbations from non-Gaussianity inWMAPtemperature anisotropy

We study the effect of primordial isocurvature perturbations on non-Gaussian properties of cosmic microwave background (CMB) temperature anisotropies. We consider generic forms of the non-linearity of isocurvature perturbations which can be applied to a wide range of theoretical models. We derive analytical expressions for the bispectrum and the Minkowski Functionals for CMB temperature fluctuations to describe the non-Gaussianity from isocurvature perturbations. We find that the isocurvature non-Gaussianity in the quadratic isocurvature model, where the isocurvature perturbation S is written as a quadratic function of the Gaussian variable σ, S = σ 2 ― , can give the same signal-to-noise ratio as f NL = 30 even if we impose the current observational limit on the fraction of isocurvature perturbations contained in the primordial power spectrum α. We give constraints on isocurvature non-Gaussianity from Minkowski Functionals using the Wilkinson Microwave Anisotropy Probe (WMAP) 5-year data. We do not find a significant signal of isocurvature non-Gaussianity. For the quadratic isocurvature model, we obtain a stringent upper limit on the isocurvature fraction α < 0.070 (95 per cent CL) for a scale-invariant spectrum which is comparable to the limit obtained from the power spectrum.

Modelling non-Gaussianity from foreground contaminants

We introduce a general class of models for characterizing the non-Gaussian properties of foreground contaminants in the cosmic microwave background with view towards the removal of the non-primordial non-Gaussian signal from the primordial one. This is important not only for treating temperature maps but also for characterizing the nature and origin of the primordial cosmological perturbations and thus establishing a theory of the early universe.

Validation of large eddy simulation method for study of flatness and skewness of decaying compressible magnetohydrodynamic turbulence

In the present work we study potential applicability of large eddy simulation (LES) method for prediction of flatness and skewness of compressible magnetohydrodynamic (MHD) turbulence. The knowledge of these quantities characterizes non-Gaussian properties of turbulence and can be used for verification of hypothesis on Gaussianity for the turbulent flow under consideration. Prediction accuracy of these quantities by means of LES method directly determines efficiency of reconstruction of probability density function (PDF) that depends on used subgrid-scale (SGS) parameterizations. Applicability of LES approach for studying of PDF properties of turbulent compressible magnetic fluid flow is investigated and potential feasibilities of five SGS parameterizations by means of comparison with direct numerical simulation results are explored. The skewness and the flatness of the velocity and the magnetic field components under various hydrodynamic Reynolds numbers, sonic Mach numbers, and magnetic Reynolds numbers are studied. It is shown that various SGS closures demonstrate the best results depending on change of similarity numbers of turbulent MHD flow. The case without any subgrid modeling yields sufficiently good results as well. This indicates that the energy pile-up at the small scales that is characteristic for the model without any subgrid closure, does not significantly influence on determination of PDF. It is shown that, among the subgrid models, the best results for studying of the flatness and the skewness of velocity and magnetic field components are demonstrated by the Smagorinsky model for MHD turbulence and the model based on cross-helicity for MHD case. It is visible from the numerical results that the influence of a choice subgrid parametrization for the flatness and the skewness of velocity is more essential than for the same characteristics of magnetic field.

IS THE UNIVERSE ROTATING?

Models of a rotating universe have been studied widely since G{\"o}del \cite{1}, who showed an example that is consistent with General Relativity (GR). By now, the possibility of a rotating universe has been discussed comprehensively in the framework of some types of Bianchi's models, such as Type V, VII and IX \cite{2,3}, and different approaches have been proposed to constrain the rotation. Recent discoveries of some non-Gaussian properties of the Cosmic Microwave Background Anisotropies (CMBA) \cite{nG1,nG2,nG3,nG4,nG5,nG6,nG7}, such as the suppression of the quadrupole and the alignment of some multipoles draw attention to some Bianchi models with rotation \cite{bi1,bi2}. However, cosmological data, such as those of the CMBA, strongly prefer a homogeneous and isotropic model. Therefore, it is of interest to discuss the rotation of the universe as a perturbation of the Robertson-Walker metric, to constrain the rotating speed by cosmological data and to discuss whether it could be the origin of the non-Gaussian properties of the CMBA mentioned above. Here, we derive the general form of the metric (up to 2nd-order perturbations) which is compatible with the rotation perturbation in a flat $\Lambda$-CDM universe. By comparing the 2nd-order Sachs-Wolfe effect \cite{4,5,6,7,8} due to rotation with the CMBA data, we constrain the angular speed of the rotation to be less than $10^{-9}$ rad yr$^{-1}$ at the last scattering surface. This provides the first constraint on the shear-free rotation of a $\Lambda$CDM universe.

Observation of Non-Gaussian and Generation-Recombination Noise in n-Type GaAs/AlGaAs Multiple Quantum Wells

Observation of Non-Gaussian and Generation-Recombination Noise in n-Type GaAs/AlGaAs Multiple Quantum Wells Youngsang Kim, Joo-Yoo Hong and Heejun Jeong Department of Applied Physics, Hanyang University, Ansan 426-791 (Received 21 January 2009) The time trace and the noise spectrum of the dark current are measured to probe the nonGaussian properties and the generation-recombination noise in n-type GaAs/AlGaAs quantum well infrared photodetectors. We observed that time-dependent random telegraph signals showed a non-Gaussian two-level random uctuation of the current amplitude arising from trapping and detrapping of carriers by a quantum well. A change in the carrier lifetime, which corresponds to capture in a well, is also observed at low bias by measuring the low-frequency noise spectrum. We investigated a relation between the two-level random uctuation and the carrier lifetime or the capture probability. PACS numbers: 72.20.Jv, 73.21.Fg

Nonlinear dynamic analysis of frames with stochastic non-Gaussian material properties

The efficient prediction of the nonlinear dynamic response of structures with uncertain system properties poses a major challenge in the field of computational stochastic mechanics. In order to investigate realistic problems of structures subjected to transient seismic actions, an efficient approach is introduced. The presented methodology is used to assess the response of a steel frame modeled with a mixed fiber-based, beam–column element. The adopted modeling provides increased accuracy compared to traditional displacement-based elements and offers significant computational advantages for the analysis of systems with stochastic properties. The uncertain parameters considered are the Young’s modulus and the yield stress, both described by homogeneous non-Gaussian translation stochastic fields. The frame is subjected to natural seismic records that correspond to three levels of increasing seismic intensity as well as to spectrum-compatible artificial accelerograms. Under the assumption of a pre-specified power spectral density function of the stochastic fields that describe the two uncertain parameters, the response variability is computed using Monte Carlo simulation. A parametric investigation is carried out providing useful conclusions regarding the influence of different non-Gaussian distributions (lognormal and beta) and of the spectral characteristics of the stochastic fields on the response variability.

Virtual evolution for visual search in natural images results in behavioral receptive fields with inhibitory surrounds

The neural mechanisms driving perception and saccades during search use information about the target but are also based on an inhibitory surround not present in the target luminance profile (e.g., Eckstein et al., 2007). Here, we ask whether these inhibitory surrounds might reflect a strategy that the brain has adapted to optimize the search for targets in natural scenes. To test this hypothesis, we sought to estimate the best linear template (behavioral receptive field), built from linear combinations of Gabor channels representing V1 simple cells in search for an additive Gaussian target embedded in natural images. Statistically nonstationary and non-Gaussian properties of natural scenes preclude calculation of the best linear template from analytic expressions and require an iterative optimization method such as a virtual evolution via a genetic algorithm. Evolved linear receptive fields built from linear combinations of Gabor functions include substantial inhibitory surround, larger than those found in humans performing target search in white noise. The inhibitory surrounds were robust to changes in the contrast of the signal, generalized to a larger calibrated natural image data set, and tasks in which the signal occluded other objects in the image. We show that channel nonlinearities can have strong effects on the observed linear behavioral receptive field but preserve the inhibitory surrounds. Together, the results suggest that the apparent suboptimality of inhibitory surrounds in human behavioral receptive fields when searching for a target in white noise might reflect a strategy to optimize detection of signals in natural scenes. Finally, we contend that optimized linear detection of spatially compact signals in natural images might be a new possible hypothesis, distinct from decorrelation of visual input and sparse representations (e.g., Graham et al., 2006), to explain the evolution of center-surround organization of receptive fields in early vision.

Multifractal detrended fluctuation analysis of analog random multiplicative processes

We investigate non-Gaussian statistical properties of stationary stochastic signals generated by an analog circuit that simulates a random multiplicative process with weak additive noise. The random noises are originated by thermal shot noise and avalanche processes, while the multiplicative process is generated by a fully analog circuit. The resulting signal describes stochastic time series of current interest in several areas such as turbulence, finance, biology and environment, which exhibit power-law distributions. Specifically, we study the correlation properties of the signal by employing a detrended fluctuation analysis and explore its multifractal nature. The singularity spectrum is obtained and analyzed as a function of the control circuit parameter that tunes the asymptotic power-law form of the probability distribution function.

Noise Reduction in Side Channel Attack Using Fourth-Order Cumulant

Side channel attacks exploit physical information leaked during the operation of a cryptographic device (e.g., a smart card). The confidential data, which can be leaked from side channels, are timing of operations, power consumption, and electromagnetic emanation. In this paper, we propose a preprocessing method based on the fourth-order cumulant, which aims to improve the performance of side channel attacks. It takes advantages of the Gaussian and nonGaussian properties, that respectively characterize the noise and the signal, to remove the effects due to Gaussian noise coupled into side channel signals. The proposed method is then applied to analyze the electromagnetic signals of a synthesized application-specific integrated circuit during a data encryption standard operation. The theoretical and experimental results show that our method significantly reduces the number of side channel signals needed to detect the encryption key.

Measured Statistics of Multicomponent Gust Patterns in Atmospheric Turbulence

Non-Gaussian statistical properties of severe atmospheric turbulence, recorded at both high and low altitudes, are illustrated by analyzing the outputs of linear filters tuned to respond to multicomponent gust patterns comprising sequences of velocity increments, or ramp gusts. The measured probability distributions of filter outputs typically have strong tails which can be fitted by a model of exponential form. Although it is known that exponential distributions can be reproduced by considering sequences of Gaussian patches, as assumed in the power-spectral-density method for gust-loads prediction, it is demonstrated, by comparing the outputs of pairs of filters which are tuned to respond to gust patterns comprising different numbers of component increments, that the measured severe turbulence has non-Gaussian properties that cannot be reproduced in this way. In particular, the ratio of the response of a filter tuned to a complex gust pattern to that of a filter tuned to a single-ramp gust varies as a function of gust amplitude, reducing as the amplitude increases. This result is consistent with the hypothesis that the more severe gusts, associated with the tails of the distributions, tend to occur in short bursts and is in conflict with the result predicted by the power-spectral-density method, which is that the above ratio is independent of the amplitude. Reference is made to the representation of the burst phenomenon in the statistical-discrete-gust model of extreme turbulence.

Exploiting Nonlinear Recurrence and Fractal Scaling Properties for Voice Disorder Detection

Abstract Background: Voice disorders affect patients profoundly, and acoustic tools can potentially measure voice function objectively. Disordered sustained vowels exhibit wide-ranging phenomena, from nearly periodic to highly complex, aperiodic vibrations, and increased "breathiness". Modelling and surrogate data studies have shown significant nonlinear and non-Gaussian random properties in these sounds. Nonetheless, existing tools are limited to analysing voices displaying near periodicity, and do not account for this inherent biophysical nonlinearity and non-Gaussian randomness, often using linear signal processing methods insensitive to these properties. They do not directly measure the two main biophysical symptoms of disorder: complex nonlinear aperiodicity, and turbulent, aeroacoustic, non-Gaussian randomness. Often these tools cannot be applied to more severe disordered voices, limiting their clinical usefulness. Methods: This paper introduces two new tools to speech analysis: recurrence and fractal scaling, which overcome the range limitations of existing tools by addressing directly these two symptoms of disorder, together reproducing a "hoarseness" diagram. A simple bootstrapped classifier then uses these two features to distinguish normal from disordered voices. Results: On a large database of subjects with a wide variety of voice disorders, these new techniques can distinguish normal from disordered cases, using quadratic discriminant analysis, to overall correct classification performance of 91.8% plus or minus 2.0%. The true positive classification performance is 95.4% plus or minus 3.2%, and the true negative performance is 91.5% plus or minus 2.3% (95% confidence). This is shown to outperform all combinations of the most popular classical tools. Conclusions: Given the very large number of arbitrary parameters and computational complexity of existing techniques, these new techniques are far simpler and yet achieve clinically useful classification performance using only a basic classification technique. They do so by exploiting the inherent nonlinearity and turbulent randomness in disordered voice signals. They are widely applicable to the whole range of disordered voice phenomena by design. These new measures could therefore be used for a variety of practical clinical purposes.

Development of stochastic models for turbulence

Subgrid scale interactions in forced homogeneous turbulence are decomposed into components correlated and uncorrelated with the resolved velocity field. The correlated part is well known to be equivalent to a spectral eddy viscosity. The mean energy transfer can be predicted even if the uncorrelated remainder is ignored, but statistics pertaining to the fluctuations of the nonlinear term require a model for the remainder, which is found to have a strongly non-Gaussian probability density. Some implications of including these non-Gaussian properties in stochastic models are described.

Coherence oscillations in dephasing by non-Gaussian shot noise

A non-perturbative treatment is developed for the dephasing produced by the shot noise of a one-dimensional electron channel. It is applied to two systems: a charge qubit and the electronic Mach–Zehnder interferometer (MZI), both of them interacting with an adjacent partitioned electronic channel acting as a detector. We find that the visibility (interference contrast) can display oscillations as a function of detector voltage and interaction time. This is a unique consequence of the non-Gaussian properties of the shot noise, and only occurs in the strong coupling regime, when the phase contributed by a single electron exceeds π. The resulting formula reproduces the recent surprising experimental observations reported in (I Neder et al 2006 Preprint cond-mat/0610634), and indicates a general explanation for similar visibility oscillations observed earlier in the MZI at large bias voltage. We explore in detail the full pattern of oscillations as a function of coupling strength, voltage and time, which might be observable in future experiments.

Statistical properties of dust far-infrared emission

Context. Far-infrared dust emission has a self-similar structure which reveals the complex dynamical processes that shape the interstellar medium. The description of the statistical properties of this emission gives important constraints on the physics of the interstellar medium but it is also a useful way to estimate the contamination of diffuse interstellar emission in the cases where it is considered a nuisance. Aims. The main goals of this analysis of the power spectrum and non-Gaussian properties of far-infrared dust emission are 1) to estimate the power spectrum of interstellar matter density in three dimensions; 2) to review and extend previous estimates of the cirrus noise due to dust emission; and 3) to produce simulated dust emission maps that reproduce the observed statistical properties. Methods. To estimate the statistical properties of dust emission we analyzed the power spectrum and wavelet decomposition of 100 μ m IRIS data (an improved version of the IRAS data) over 55% of the sky. The simulation of realistic infrared emission maps is based on modified Gaussian random fields. Results. The main results are the following. 1) The cirrus noise level as a function of brightness has been previously overestimated. It is found to be proportional to $\langle I\rangle $ instead of $\langle I\rangle^{1.5}$, where $\langle I\rangle $ is the local average brightness at 100 μ m. This scaling is in accordance with the fact that the brightness fluctuation level observed at a given angular scale on the sky is the sum of fluctuations of increasing amplitude with distance on the line of sight. 2) The spectral index of dust emission at scales between 5 arcmin and 12.5° is $\langle\gamma\rangle=-2.9$ on average but shows significant variations over the sky. Bright regions have systematically steeper power spectra than diffuse regions. 3) The skewness and kurtosis of brightness fluctuations are high, indicative of strong non-Gaussianity. Unlike the standard deviation of the fluctuations, the skewness and kurtosis do not depend significantly on brightness, except in bright regions (>10 MJy sr -1 ) where they are systematically higher, probably due to contrasted structures related to star formation activity. 4) Based on our characterization of the 100 μ m power spectrum we provide a prescription of the cirrus confusion noise as a function of wavelength and scale. 5) Finally we present a method based on a modification of Gaussian random fields to produce simulations of dust maps which reproduce the power spectrum and non-Gaussian properties of interstellar dust emission.

Exploiting Nonlinear Recurrence and Fractal Scaling Properties for Voice Disorder Detection

BackgroundVoice disorders affect patients profoundly, and acoustic tools can potentially measure voice function objectively. Disordered sustained vowels exhibit wide-ranging phenomena, from nearly periodic to highly complex, aperiodic vibrations, and increased "breathiness". Modelling and surrogate data studies have shown significant nonlinear and non-Gaussian random properties in these sounds. Nonetheless, existing tools are limited to analysing voices displaying near periodicity, and do not account for this inherent biophysical nonlinearity and non-Gaussian randomness, often using linear signal processing methods insensitive to these properties. They do not directly measure the two main biophysical symptoms of disorder: complex nonlinear aperiodicity, and turbulent, aeroacoustic, non-Gaussian randomness. Often these tools cannot be applied to more severe disordered voices, limiting their clinical usefulness.MethodsThis paper introduces two new tools to speech analysis: recurrence and fractal scaling, which overcome the range limitations of existing tools by addressing directly these two symptoms of disorder, together reproducing a "hoarseness" diagram. A simple bootstrapped classifier then uses these two features to distinguish normal from disordered voices.ResultsOn a large database of subjects with a wide variety of voice disorders, these new techniques can distinguish normal from disordered cases, using quadratic discriminant analysis, to overall correct classification performance of 91.8 ± 2.0%. The true positive classification performance is 95.4 ± 3.2%, and the true negative performance is 91.5 ± 2.3% (95% confidence). This is shown to outperform all combinations of the most popular classical tools.ConclusionGiven the very large number of arbitrary parameters and computational complexity of existing techniques, these new techniques are far simpler and yet achieve clinically useful classification performance using only a basic classification technique. They do so by exploiting the inherent nonlinearity and turbulent randomness in disordered voice signals. They are widely applicable to the whole range of disordered voice phenomena by design. These new measures could therefore be used for a variety of practical clinical purposes.

Three‐dimensional characterization of non‐gaussian water diffusion in humans using diffusion kurtosis imaging

Conventional diffusion tensor imaging (DTI) measures water diffusion parameters based on the assumption that the spin displacement distribution is a Gaussian function. However, water movement in biological tissue is often non-Gaussian and this non-Gaussian behavior may contain useful information related to tissue structure and pathophysiology. Here we propose an approach to directly measure the non-Gaussian property of water diffusion, characterized by a four-dimensional matrix referred to as the diffusion kurtosis tensor. This approach does not require the complete measurement of the displacement distribution function and, therefore, is more time efficient compared with the q-space imaging technique. A theoretical framework of the DK calculation is established, and experimental results are presented for humans obtained within a clinically feasible time of about 10 min. The resulting kurtosis maps are shown to be robust and reproducible. Directionally-averaged apparent kurtosis coefficients (AKC, a unitless parameter) are 0.74 +/- 0.03, 1.09 +/- 0.01 and 0.84 +/- 0.02 for gray matter, white matter and thalamus, respectively. The three-dimensional kurtosis angular plots show tissue-specific geometry for different brain regions and demonstrate the potential of identifying multiple fiber structures in a single voxel. Diffusion kurtosis imaging is a useful method to study non-Gaussian diffusion behavior and can provide complementary information to that of DTI.