Scale-scale Correlation Research Articles

Scale analysis of turbulent channel flow with varying pressure gradient

In this paper orthogonal wavelet transformations are applied to decompose experimental velocity signals in fully developed channel flows with varying pressure gradient into scales. We analyze the time series from turbulent data, to obtain the statistical characteristics, correlations between the adjacent scales and the principal scale of coherent structures in different scales by wavelet transformations. The results show that, in the counter gradient transport (CGT) region, skewness factors and flatness factors deviate strongly from the corresponding values of Gaussian distribution on certain scales. PDFs on each scale confirm this observation. Scale-scale correlations show further that the fluctuations on some certain special scales are more intermittent than nearby. Principal scale of coherent structure is coincident with the scales on which the statistical properties depart from Gaussian distribution. These features are the same for different families of wavelets, and it also shows some different features in the region between favorable pressure gradient and adverse pressure gradient.

PIH32 - Determinants of Non-Adherence to Medications Among Chronic Patients in Maccabi Health Care Services

were asked to complete Accept and MMAS-4 questionnaires at Month 1, 3 and 6 after having given their informed consent. The structure was explored through PCA, and confirmed with multi-trait analysis. Internal consistency reliability of dimensions was assessed through Cronbach’s alpha. Scale-scale correlations were calculated. RESULTS: After reduction, Accept was made of 25 items organised in 1 overall Acceptance score and 6 domain-specific scores (efficacy, tolerance, convenience, constraints, treatment duration, multiple medication). Cronbach’s alpha was 0,85 for overall Acceptance score, which met convergent and divergent validity criteria (both 100%). The domain-specific scores showed satisfactory to good results (Cronbach’s alpha ranging from 0,67 0,87, convegrent validity ranging from 63% to 100%, and divergent validity ranging from 33% 100%). Scale-scale correlations ranged from 0.02 to 0.58, confirming the multi-dimensional nature of the questionnaire. The good properties of Accept were stable over time. CONCLUSIONS: Accept is a brief, comprehensive, generic questionnaire focused on Acceptance. Initial validation in a population of patients with a wide range of long-term treatment showed promising results and confirmed the position of Acceptance. Further, disease-specific, large prospective study are needed to assess the ability of Accept to predict persistence to treatment.

Discriminating Dark Energy Models by Statistics of the Peak Count and Scale-scale Correlation of Weak Gravitational Lensing

In order to study the weak gravitational lensing effect under different cosmologicalmodels, the 2-dimensional κ-field samples are generated by using the ray-tracing method with high-resolution N-body simulation data. These samples correspond to three models with different parameters of dark-energy equation of state, i.e., ω = −0.8, ω = −1.0 and ω = −1.2, and have the same field of view of 3° × 3°. It is assumed that all galaxies, as background sources, are distributed on the plane of z = 1. The statistics of peak count and scale-scale correlation are performed on these samples. The statistical result of peak counts indicates that in the noisy κ field, some differences of peak distributions exist among various models. The noise has changed the distributions of the peaks with medium and low amplitudes, but has nearly no effect on high-amplitude peaks. However, after denoising the differences of high-amplitude peak distributions among various models become very clear. For the statistics of scale-scale correlation, the cumulative probability distribution functions of scale-scale correlation coefficients of different models are analyzed. It is found that the differences between the model of ω = −1.2 and the models of ω = −1.0 and ω = −0.8 can reach 20% and 30%, respectively. Hence the statistics of scale-scale correlation combining with the statistics of peak count can be taken as a new method to determine the dark energy equation-of-state parameter.

LOG-POISSON HIERARCHICAL CLUSTERING OF COSMIC NEUTRAL HYDROGEN AND Lyα TRANSMITTED FLUX OF QSO ABSORPTION SPECTRUM

we study, in this paper, the non-Gaussian features of the mass density field of neutral hydrogen fluid and the Ly-alpha transmitted flux of QSO absorption spectrum from the point-of-view of self-similar log-Poisson hierarchy. It has been shown recently that, in the scale range from the onset of nonlinear evolution to dissipation, the velocity and mass density fields of cosmic baryon fluid are extremely well described by the She-Leveque's scaling formula, which is due to the log-Poisson hierarchical cascade. Since the mass density ratio between ionized hydrogen to total hydrogen is not uniform in space, the mass density field of neutral hydrogen component is not given by a similar mapping of total baryon fluid. Nevertheless, we show, with hydrodynamic simulation samples of the concordance $\Lambda$CDM universe, that the mass density field of neutral hydrogen, is also well described by the log-Poisson hierarchy. We then investigate the field of Ly$\alpha$ transmitted flux of QSO absorption spectrum. Due to redshift distortion, Ly$\alpha$ transmitted flux fluctuations are no longer to show all features of the log-Poisson hierarchy. However, some non-Gaussian features predicted by the log-Poisson hierarchy are not affected by the redshift distortion. We test these predictions with the high resolution and high S/N data of quasars Ly$\alpha$ absorption spectra. All results given by real data, including $\beta$-hierarchy, high order moments and scale-scale correlation, are found to be well consistent with the log-Poisson hierarchy. We compare the log-Poisson hierarchy with the popular log-normal model of the Ly$\alpha$ transmitted flux. The later is found to yield too strong non-Gaussianity at high orders, while the log-Poisson hierarchy is in agreement with observed data.

Non‐Gaussianity of the Cosmic Baryon Fluid: Log‐Poisson Hierarchy Model

In the nonlinear regime of cosmic clustering, the mass density field of the cosmic baryon fluid is highly non-Gaussian. It shows different dynamical behavior from collisionless dark matter. Nevertheless, the evolved field of the baryon fluid is scale-covariant in the range from the Jeans length to a few tens of h−1 Mpc, within which the dynamical equations and initial perturbations are scale free. We show that in the scale-free range, the non-Gaussian features of the cosmic baryon fluid, governed by the Navier-Stokes equation in an expanding universe, can be well described by a log-Poisson hierarchical cascade. The log-Poisson scheme is a random multiplicative process (RMP), which causes non-Gaussianity and intermittency even when the original field is Gaussian. The log-Poisson RMP contains two dimensionless parameters: β for the intermittency and γ for the most singular structure. All the predictions given by the log-Poisson RMP model, including the hierarchical relation, the order dependence of the intermittent exponent, the moments, and the scale-scale correlation, are in good agreement with the results given by hydrodynamic simulations of the standard cold dark matter model. The intermittent parameter β decreases slightly at low redshift and indicates that the density field of the baryon fluid contains more singular structures at lower redshifts. The applicability of the model is addressed.

Constraining the parameters of the LN model with reconstructed power spectrum of Ly-α forest

A sample of three quasar spectra observed by the Keck telescope is selected to reconstruct the perturbations of mass density using the Gaussianization method, with a calculation of the corresponding wavelet power spectra. The two parameters in the lognormal (LN) model, namely the shape factor Γ and the Jeans smoothing factor r, are set as free parameters. Their most probable values are determined by comparing the result of statistical analysis on the observed sample with that on a simulated sample, and they are: Γ0.50 and r0.09. Non-Gaussian features in the quasar spectra can not be excluded using the traditional Gaussianization method. However, on the scales larger than 100 kpc, these features have little or no influence on our results described above. This argument has been verified by comparing the observed sample with the simulated sample as regards their skewness and kurtosis spectra, as well as their scale-scale correlations.

Statistical Features of 21 Centimeter Emission from the Epoch between Reionization and the Gunn‐Peterson Transparency

We investigate the 21 cm emission from the epoch between reionization z(r) and the Gunn-Peterson transparency z(GP). According to the lognormal model of the thermal history around reionization, hydrogen clouds in z(r) > z > z(GP) are hot and a predominant part of baryonic gas is ionized, but still opaque to Lyalpha photons. Therefore, 21 cm emission is a distinctive characteristic of this epoch. We show that the 21 cm emission comes from both uncollapsed and collapsing hydrogen clouds. The spatial distribution of the brightness temperature excess deltaT(b) is highly non-Gaussian. It consists of spikes with high deltaT(b) and a low deltaT(b) area between the spikes. The field has the following statistical features: ( 1) the one-point distributions of deltaT(b) are described approximately by power-law tailed probability distribution functions; (2) the nth-order moment of deltaT(b) is increasing much faster with n than that of a Gaussian field, but slower than that of a lognormal field; ( 3) the scale-scale correlation of the deltaT(b) field is significant for all scales larger than the Jeans length of the gas. These features would be useful for distinguishing the 21 cm emission of the early clustering from the noise of foreground contamination.

Wavelets andWilkinson Microwave Anisotropy ProbeNon‐Gaussianity

We study the statistical properties of the 1st year WMAP data on different scales using the spherical mexican hat wavelet transform. Consistent with the results of Vielva et al. (2003) we find a deviation from Gaussianity in the form of kurtosis of wavelet coefficients on $3-4^\circ$ scales in the southern Galactic hemisphere. This paper extends the work of Vielva et al. as follows. We find that the non-Gaussian signal shows up more strongly in the form of a larger than expected number of cold pixels and also in the form of scale-scale correlations amongst wavelet coefficients. We establish the robustness of the non-Gaussian signal under more wide-ranging assumptions regarding the Galactic mask applied to the data and the noise statistics. This signal is unlikely to be due to the usual quadratic term parametrized by the non-linearity parameter $f_{NL}$. We use the skewness of the spherical mexican hat wavelet coefficients to constrain $f_{NL}$ with the 1st year WMAP data. Our results constrain $f_{NL}$ to be $50\pm 80$ at 68% confidence, and less than 280 at 99% confidence.

Topology of the Universe fromCOBE-DMR - a wavelet approach

In this paper, we pursue a new technique to search for evidence of a finite universe, making use of a spherical Mexican Hat wavelet decomposition of the microwave background fluctuations. Using the information provided by the wavelet coefficients at several scales, we test whether compact orientable flat topologies are consistent with the COBE-DMR data. We consider topological sizes ranging from half to twice the horizon size. A scale-scale correlation test indicates that non-trivial topologies with appropriate topological sizes are as consistent with the COBE-DMR data as an infinite universe. Among the finite models, the data seems to prefer a universe which is about the size of the horizon for all but the hypertorus and the triple-twist torus. For the latter, the wavelet technique does not seem a good discriminator of scales for the range of topological sizes considered here, while a hypertorus has a preferred size which is 80 per cent of the horizon. This analysis allows us to find a best fit topological size for each model, although cosmic variance might limit our ability to distinguish some of the topologies.

Construct Validity of the Scores of the Chinese Version of the Need for Closure Scale

This study evaluated the construct validity of the scores of the Chinese version of the Need for Closure Scale (NFCS) as administered to a sample of Hong Kong college students who also completed the Personal Need for Structure Scale (PNS) and the Personal Fear of Invalidity Scale (PFI). The scale-scale and scale-facet correlations were similar to those of the original English versions. Factor analyses confirmed that the scores of the Chinese NFCS have a bidimensional structure in which the facets preference for order, preference for predictability, and discomfort with ambiguity constitute a factor together with the PNS and the facet decisiveness and the reverse-scored PFI constitute another orthogonal factor. The facet closed mindedness, however, needs further development. The two factors showed satisfactory internal consistency and divergent validity.

Probing the Statistics of the Temperature-Density Relation of the Intergalactic Medium

Gravitational instability induces a simple correlation between the large- and small-scale fluctuations of the Lyα flux spectrum. However, nongravitational processes involved in structure formation and evolution will alter such a correlation. In this Letter, we explore how scatter in the temperature-density relation of the intergalactic medium reduces the gravitationally induced scale-scale correlation. By examining whether or not observations of the correlation are close to that predicted by pure gravity, we put constraints on the scatter in the ρ-T relation and in turn on any physical process that would lead to scatter, e.g., strong fluctuations in the UV background or radiative transfer effects. By applying this method to high-resolution Keck spectra of Q1422+231 and HS 1946+7658, we find the predicted correlation signal induced by gravity and the diminishing of this correlation signal at small scales. This suggests extra physics affects the small-scale structure of the forest, and we can constrain the scatter in the ρ-T relation to a conservative 20% upper limit. A crude model suggests, if there is any spatial correlation of temperature, the coherence length scale must be smaller than ~0.3 h-1 Mpc to be consistent with the Keck data.

Spherical Mexican hat wavelet: an application to detect non-Gaussianity in theCOBE-DMR maps

The spherical Mexican Hat wavelet is introduced in this paper, with the aim of testing the Gaussianity of the Cosmic Microwave Background temperature fluctuations. Using the information given by the wavelet coefficients at several scales, we have performed several statistical tests on the COBE-DMR maps to search for evidence of non-Gaussianity. Skewness, kurtosis, scale-scale correlations (for two and three scales) and Kolmogorov-Smirnov tests indicate that the COBE-DMR data are consistent with a Gaussian distribution. We have extended the analysis to compare temperature values provided by COBE-DMR data with distributions (obtained from Gaussian simulations) at each pixel and at each scale. The number of pixels with temperature values outside the 95% and the 99% is consistent with that obtained from Gaussian simulations, at all scales. Moreover, the extrema values for COBE-DMR data (maximum and minimum temperatures in the map) are also consistent with those obtained from Gaussian simulations.

Scale-Scale Correlation as Discriminant Among the BiasedGalaxy Formation Models

Using the mock galaxy catalogues created from the N-bodysimulations, various biasing prescriptions for modelling therelative distribution between the galaxies and the underlying darkmatter are statistically tested by using scale-scale correlation.We found that the scale-scale correlation is capable of breakingthe model degeneracy indicated by the low-order clusteringstatistics, and could be taken as an effective discriminant amonga variety of biasing models. Particularly, comparing with the APMbright galaxy catalogue, we infer that the two parameterLagrangian biasing model gives the best fit to the observedclustering features.

The Local Power Spectrum and Correlation Hierarchy of the Cosmic Mass Field

We analyze the power spectrum of a QSO's Lyα-transmitted flux in the discrete wavelet transform (DWT) representation. Although the mean DWT power spectrum is consistent with its counterpart in Fourier representation, the spatial distribution of the local power varies greatly; i.e., the local DWT power spectra show remarkably spiky structures on small scales. To measure these spiky features, we introduce the quantities roughness of the local power spectrum and correlation between spikes on different scales. We then test the predictions made by the correlation hierarchy model on the roughness and the scale-scale correlations of the local power spectrum. Using the Lyα-transmitted flux of the QSO HS 1700, we find that the underlying cosmic mass field of the transmitted flux at redshift around z 2.2 can be described by the hierarchical clustering model on physical scales from 2.5 h-1 Mpc to a few tens h-1 kpc in an Einstein-de Sitter universe. However, the nonlinear features of the clustering show differences on different scale ranges: (1) On physical scales larger than ~1.3 h-1 Mpc, the field is almost Gaussian. (2) On scales 1.3-0.3 h-1 Mpc, the field is consistent with the correlation hierarchy with a constant value for the coefficient Q4. (3) On scales less than 300 h-1 kpc, the field is no longer Gaussian but essentially intermittent. In this case, the field can still be fitted by the correlation hierarchy, but the coefficient, Q4, should be scale dependent. These three points are strongly supported by the following result: the scale dependencies of Q4 given by two statistically independent measures, i.e., Q by roughness and Q by scale-scale correlation, are the same in the entire scale range considered.

Quasi‐local Evolution of Cosmic Gravitational Clustering in a Weakly Nonlinear Regime

We investigate the weakly non-linear evolution of cosmic gravitational clustering in phase space by looking at the Zel'dovich solution in the discrete wavelet transform (DWT) representation. We show that if the initial perturbations are Gaussian, the relation between the evolved DWT mode and the initial perturbations in the weakly non-linear regime is quasi-local. That is, the evolved density perturbations are mainly determined by the initial perturbations localized in the same spatial range. Furthermore, we show that the evolved mode is monotonically related to the initial perturbed mode. Thus large (small) perturbed modes statistically correspond to the large (small) initial perturbed modes. We test this prediction by using QSO Ly$\alpha$ absorption samples. The results show that the weakly non-linear features for both the transmitted flux and identified forest lines are quasi-localized. The locality and monotonic properties provide a solid basis for a DWT scale-by-scale Gaussianization reconstruction algorithm proposed by Feng & Fang (Feng & Fang, 2000) for data in the weakly non-linear regime. With the Zel'dovich solution, we find also that the major non-Gaussianity caused by the weakly non-linear evolution is local scale-scale correlations. Therefore, to have a precise recovery of the initial Gaussian mass field, it is essential to remove the scale-scale correlations.

Testing the Gaussianity of the COBE DMR data with spherical wavelets

We investigate the Gaussianity of the 4-year COBE-DMR data (in HEALPix pixelisation) using an analysis based on spherical Haar wavelets. We use all the pixels lying outside the Galactic cut and compute the skewness, kurtosis and scale-scale correlation spectra for the wavelet coefficients at each scale. We also take into account the sensitivity of the method to the orientation of the input signal. We find a detection of non-Gaussianity at $> 99$ per cent level in just one of our statistics. Taking into account the total number of statistics computed, we estimate that the probability of obtaining such a detection by chance for an underlying Gaussian field is 0.69. Therefore, we conclude that the spherical wavelet technique shows no strong evidence of non-Gaussianity in the COBE-DMR data.

Measuring the Galaxy Power Spectrum and Scale‐Scale Correlations with Multiresolution‐decomposed Covariance. I. Method

We present a method of measuring galaxy power spectrum based on the multiresolution analysis of the discrete wavelet transformation (DWT). Since the DWT representation has strong capability of suppressing the off-diagonal components of the covariance for selfsimilar clustering, the DWT covariance for popular models of the cold dark matter cosmogony generally is diagonal, or $j$(scale)-diagonal in the scale range, in which the second scale-scale correlations are weak. In this range, the DWT covariance gives a lossless estimation of the power spectrum, which is equal to the corresponding Fourier power spectrum banded with a logarithmical scaling. In the scale range, in which the scale-scale correlation is significant, the accuracy of a power spectrum detection depends on the scale-scale or band-band correlations. This is, for a precision measurements of the power spectrum, a measurement of the scale-scale or band-band correlations is needed. We show that the DWT covariance can be employed to measuring both the band-power spectrum and second order scale-scale correlation. We also present the DWT algorithm of the binning and Poisson sampling with real observational data. We show that the alias effect appeared in usual binning schemes can exactly be eliminated by the DWT binning. Since Poisson process possesses diagonal covariance in the DWT representation, the Poisson sampling and selection effects on the power spectrum and second order scale-scale correlation detection are suppressed into minimum. Moreover, the effect of the non-Gaussian features of the Poisson sampling can be calculated in this frame.

Non‐Gaussianity and the Recovery of the Mass Power Spectrum from the Lyα Forest

We investigate the eUect of non-Gaussianity on the reconstruction of the initial mass —eld from the Lya forest. We show that the transmitted —ux of QSO absorption spectra are highly non-Gaussian in terms of the statistics, the kurtosis spectrum, and the scale-scale correlation. These non-Gaussianities cannot be completely removed by the conventional algorithm of Gaussianization, and the scale-scale correlations are largely retained in the mass —eld recovered by the Gaussian mapping. Therefore, the mass power spectrum recovered by the conventional algorithm is systematically lower than the initial mass spectrum on scales at which the local scale-scale correlation is substantial. To reduce the non- Gaussian contamination, we present two methods. The —rst is to perform the Gaussianization scale-by- scale using the discrete wavelet transform (DWT) decomposition. We show that the non-Gaussian features of the Lya forest basically will no longer exist in the scale-by-scale Gaussianized mass —eld. The second method is to choose a proper orthonormal basis (representation) to suppress the eUect of the non-Gaussian correlations. In the quasi-linear regime of cosmic structure formation, the DWT power spectrum is efficient for suppressing the non-Gaussian contamination. These two methods signi—cantly improve the recovery of the mass power spectrum from the Lya forest. Subject headings: cosmology: theorydark matterlarge-scale structure of universe ¨ quasars: absorption lines

Breaking Degeneracy of Dark Matter Models by the Scale‐Scale Correlations of Galaxies

Recently, scale-scale correlations have been detected in the distributions of quasars' Lyα absorption lines and the maps of cosmic temperature fluctuations. This paper investigates the scale-scale correlations in galaxy distributions. Using samples of mass field given by N-body simulation, we first show that the scale-scale correlation of two-dimensional and three-dimensional mass distributions at present day are capable of breaking the degeneracy between the SCDM (standard cold dark matter model) and OCDM (open CDM model) or LCDM (flat CDM model) and even show the difference between the OCDM and LCDM. Using biased galaxy samples produced in an appropriate bias model, we show that the scale-scale correlation of galaxy distribution at zero redshift is still a powerful tool to break the degeneracy in the parameter space, including both cosmological and biasing parameters. We analyze the scale-scale correlations of the APM bright galaxy catalog and compare it with the mock catalog in the SCDM, OCDM, and LCDM models. We find that all the spectra of local and nonlocal scale-scale correlations predicted by the OCDM model are in excellent agreement with those of the APM-BGC sample, while the SCDM and LCDM mock catalog appear to have somewhat weaker scale-scale correlations than the observation.

Evidence for Scale-Scale Correlations in the Cosmic Microwave Background Radiation

We perform a discrete wavelet analysis of the Cosmic Background Explorer differential microwave radiometer (DMR) 4-yr sky maps and find a significant scale-scale correlation on angular scales from about 11\ifmmode^\circ\else\textdegree\fi{} to 22\ifmmode^\circ\else\textdegree\fi{}, only in the DMR face centered on the north galactic pole. This non-Gaussian signature does not arise either from the known foregrounds or the correlated noise maps, nor is it consistent with upper limits on the residual systematic errors in the DMR maps. Either the scale-scale correlations are caused by an unknown foreground contaminate or systematic errors on angular scales as large as 22\ifmmode^\circ\else\textdegree\fi{}, or the standard inflation plus cold dark matter paradigm is ruled out at the $>99%$ confidence level.