1,036 research outputs found
Fast directional continuous spherical wavelet transform algorithms
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
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
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 and the vacuum energy density .
We also consider the case of a pure cosmological constant, i.e. . 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 (-adic) AdS/CFT
We use the tensor network living on the Bruhat-Tits tree to give a concrete
realization of the recently proposed -adic AdS/CFT correspondence (a
holographic duality based on the -adic number field ). Instead
of assuming the -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
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
Using multi-scale ideas from wavelet analysis, we extend singular-spectrum
analysis (SSA) to the study of nonstationary time series of length 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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