1,036 research outputs found

    Fast directional continuous spherical wavelet transform algorithms

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    We describe the construction of a spherical wavelet analysis through the inverse stereographic projection of the Euclidean planar wavelet framework, introduced originally by Antoine and Vandergheynst and developed further by Wiaux et al. Fast algorithms for performing the directional continuous wavelet analysis on the unit sphere are presented. The fast directional algorithm, based on the fast spherical convolution algorithm developed by Wandelt and Gorski, provides a saving of O(sqrt(Npix)) over a direct quadrature implementation for Npix pixels on the sphere, and allows one to perform a directional spherical wavelet analysis of a 10^6 pixel map on a personal computer.Comment: 10 pages, 3 figures, replaced to match version accepted by IEEE Trans. Sig. Pro

    General CMB bispectrum analysis using wavelets and separable modes

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    In this paper we combine partial-wave (`modal') methods with a wavelet analysis of the CMB bispectrum. Our implementation exploits the advantages of both approaches to produce robust, reliable and efficient estimators which can constrain the amplitude of arbitrary primordial bispectra. This will be particularly important for upcoming surveys such as \emph{Planck}. A key advantage is the computational efficiency of calculating the inverse covariance matrix in wavelet space, producing an error bar which is close to optimal. We verify the efficacy and robustness of the method by applying it to WMAP7 data, finding \fnllocal=38.4 \pm 23.6 and \fnlequil=-119.2 \pm 123.6

    Detection of the ISW effect and corresponding dark energy constraints made with directional spherical wavelets

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    Using a directional spherical wavelet analysis we detect the integrated Sachs-Wolfe (ISW) effect, indicated by a positive correlation between the first-year Wilkinson Microwave Anisotropy Probe (WMAP) and NRAO VLA Sky Survey (NVSS) data. Detections are made using both a directional extension of the spherical Mexican hat wavelet and the spherical butterfly wavelet. We examine the possibility of foreground contamination and systematics in the WMAP data and conclude that these factors are not responsible for the signal that we detect. The wavelet analysis inherently enables us to localise on the sky those regions that contribute most strongly to the correlation. On removing these localised regions the correlation that we detect is reduced in significance, as expected, but it is not eliminated, suggesting that these regions are not the sole source of correlation between the data. This finding is consistent with predictions made using the ISW effect, where one would expect weak correlations over the entire sky. In a flat universe the detection of the ISW effect provides direct and independent evidence for dark energy. We use our detection to constrain dark energy parameters by deriving a theoretical prediction for the directional wavelet covariance statistic for a given cosmological model. Comparing these predictions with the data we place constraints on the equation-of-state parameter ww and the vacuum energy density ΩΛ\Omega_\Lambda. We also consider the case of a pure cosmological constant, i.e. w=1w=-1. For this case we rule out a zero cosmological constant at greater than the 99.9% significance level. All parameter estimates that we obtain are consistent with the standand cosmological concordance model values.Comment: 16 pages, 13 figures; replaced to match version accepted by MNRA

    Tensor network and (pp-adic) AdS/CFT

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    We use the tensor network living on the Bruhat-Tits tree to give a concrete realization of the recently proposed pp-adic AdS/CFT correspondence (a holographic duality based on the pp-adic number field Qp\mathbb{Q}_p). Instead of assuming the pp-adic AdS/CFT correspondence, we show how important features of AdS/CFT such as the bulk operator reconstruction and the holographic computation of boundary correlators are automatically implemented in this tensor network.Comment: 59 pages, 18 figures; v3: improved presentation, added figures and reference

    Wavelet Methods in the Relativistic Three-Body Problem

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    In this paper we discuss the use of wavelet bases to solve the relativistic three-body problem. Wavelet bases can be used to transform momentum-space scattering integral equations into an approximate system of linear equations with a sparse matrix. This has the potential to reduce the size of realistic three-body calculations with minimal loss of accuracy. The wavelet method leads to a clean, interaction independent treatment of the scattering singularities which does not require any subtractions.Comment: 14 pages, 3 figures, corrected referenc

    Data-Adaptive Wavelets and Multi-Scale Singular Spectrum Analysis

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    Using multi-scale ideas from wavelet analysis, we extend singular-spectrum analysis (SSA) to the study of nonstationary time series of length NN whose intermittency can give rise to the divergence of their variance. SSA relies on the construction of the lag-covariance matrix C on M lagged copies of the time series over a fixed window width W to detect the regular part of the variability in that window in terms of the minimal number of oscillatory components; here W = M Dt, with Dt the time step. The proposed multi-scale SSA is a local SSA analysis within a moving window of width M <= W <= N. Multi-scale SSA varies W, while keeping a fixed W/M ratio, and uses the eigenvectors of the corresponding lag-covariance matrix C_M as a data-adaptive wavelets; successive eigenvectors of C_M correspond approximately to successive derivatives of the first mother wavelet in standard wavelet analysis. Multi-scale SSA thus solves objectively the delicate problem of optimizing the analyzing wavelet in the time-frequency domain, by a suitable localization of the signal's covariance matrix. We present several examples of application to synthetic signals with fractal or power-law behavior which mimic selected features of certain climatic and geophysical time series. A real application is to the Southern Oscillation index (SOI) monthly values for 1933-1996. Our methodology highlights an abrupt periodicity shift in the SOI near 1960. This abrupt shift between 4 and 3 years supports the Devil's staircase scenario for the El Nino/Southern Oscillation phenomenon.Comment: 24 pages, 19 figure
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