4,403 research outputs found
Effect of detrending on multifractal characteristics
Different variants of MFDFA technique are applied in order to investigate
various (artificial and real-world) time series. Our analysis shows that the
calculated singularity spectra are very sensitive to the order of the
detrending polynomial used within the MFDFA method. The relation between the
width of the multifractal spectrum (as well as the Hurst exponent) and the
order of the polynomial used in calculation is evident. Furthermore, type of
this relation itself depends on the kind of analyzed signal. Therefore, such an
analysis can give us some extra information about the correlative structure of
the time series being studied.Comment: Presented by P. O\'swi\k{e}cimka at FENS2012 conference, 17 pages, 9
figure
On Pairs of Difference Operators Satisfying: [P,Q] = Id
Different finite difference replacements for the derivative are analyzed in
the context of the Heisenberg commutation relation. The type of the finite
difference operator is shown to be tied to whether one can naturally consider
and to be self-adjoint and skew self-adjoint or whether they have to be
viewed as creation and annihilation operators. The first class, generalizing
the central difference scheme, is shown to give unitary equivalent
representations. For the second case we construct a large class of examples,
generalizing previously known difference operator realizations of .Comment: 32 pages, plain Te
Testing physical models for dipolar asymmetry with CMB polarization
The cosmic microwave background (CMB) temperature anisotropies exhibit a
large-scale dipolar power asymmetry. To determine whether this is due to a
real, physical modulation or is simply a large statistical fluctuation requires
the measurement of new modes. Here we forecast how well CMB polarization data
from \Planck\ and future experiments will be able to confirm or constrain
physical models for modulation. Fitting several such models to the \Planck\
temperature data allows us to provide predictions for polarization asymmetry.
While for some models and parameters \Planck\ polarization will decrease error
bars on the modulation amplitude by only a small percentage, we show,
importantly, that cosmic-variance-limited (and in some cases even \Planck)
polarization data can decrease the errors by considerably better than the
expectation of based on simple -space arguments. We project
that if the primordial fluctuations are truly modulated (with parameters as
indicated by \Planck\ temperature data) then \Planck\ will be able to make a
2 detection of the modulation model with 20--75\% probability,
increasing to 45--99\% when cosmic-variance-limited polarization is considered.
We stress that these results are quite model dependent. Cosmic variance in
temperature is important: combining statistically isotropic polarization with
temperature data will spuriously increase the significance of the temperature
signal with 30\% probability for \Planck.Comment: 18 pages, 11 figures, 2 tables. Version updated to match PRD versio
Measuring Planck beams with planets
Aims. Accurate measurement of the cosmic microwave background (CMB) anisotropy requires precise knowledge of the instrument beam. We explore how well the Planck beams will be determined from observations of planets, developing techniques that are also appropriate for other experiments.
Methods. We simulate planet observations with a Planck-like scanning strategy, telescope beams, noise, and detector properties. Then we employ both parametric and non-parametric techniques, reconstructing beams directly from the time-ordered data. With a faithful parameterization of the beam shape, we can constrain certain detector properties, such as the time constants of the detectors, to high precision. Alternatively, we decompose the beam using an orthogonal basis. For both techniques, we characterize the errors in the beam reconstruction with Monte Carlo realizations. For a simplified scanning strategy, we study the impact on estimation of the CMB power spectrum. Finally, we explore the consequences for measuring cosmological parameters, focusing on the spectral index of primordial scalar perturbations, n_s.
Results. The quality of the power spectrum measurement will be significantly influenced by the optical modeling of the telescope. In our most conservative case, using no information about the optics except the measurement of planets, we find that a single transit of Jupiter across the focal plane will measure the beam window functions to better than 0.3% for the channels at 100–217 GHz that are the most sensitive to the CMB. Constraining the beam with optical modeling can lead to much higher quality reconstruction.
Conclusions. Depending on the optical modeling, the beam errors may be a significant contribution to the measurement systematics for n_s
The two-and three-point correlation functions of the polarized five-year WMAP sky maps
We present the two- and three-point real space correlation functions of the
five-year WMAP sky maps, and compare the observed functions to simulated LCDM
concordance model ensembles. In agreement with previously published results, we
find that the temperature correlation functions are consistent with
expectations. However, the pure polarization correlation functions are
acceptable only for the 33GHz band map; the 41, 61, and 94 GHz band correlation
functions all exhibit significant large-scale excess structures. Further, these
excess structures very closely match the correlation functions of the two
(synchrotron and dust) foreground templates used to correct the WMAP data for
galactic contamination, with a cross-correlation statistically significant at
the 2sigma-3sigma confidence level. The correlation is slightly stronger with
respect to the thermal dust template than with the synchrotron template.Comment: 10 pages, 5 figures, published in ApJ. v2: New title, minor changes
to appendix, and fixed some typos. v3: Matches version published in Ap
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 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.Comment: latex file 7 pages, 6 figures, submitted to MNRA
Digging for Dark Matter: Spectral Analysis and Discovery Potential of Paleo-Detectors
Paleo-detectors are a recently proposed method for the direct detection of
Dark Matter (DM). In such detectors, one would search for the persistent damage
features left by DM--nucleus interactions in ancient minerals. Initial
sensitivity projections have shown that paleo-detectors could probe much of the
remaining Weakly Interacting Massive Particle (WIMP) parameter space. In this
paper, we improve upon the cut-and-count approach previously used to estimate
the sensitivity by performing a full spectral analysis of the background- and
DM-induced signal spectra. We consider two scenarios for the systematic errors
on the background spectra: i) systematic errors on the normalization only, and
ii) systematic errors on the shape of the backgrounds. We find that the
projected sensitivity is rather robust to imperfect knowledge of the
backgrounds. Finally, we study how well the parameters of the true WIMP model
could be reconstructed in the hypothetical case of a WIMP discovery.Comment: 14 pages, 5 figures, code available at
https://github.com/tedwards2412/paleo_detectors/ . v2: Added additional
analysis theory details, matches version published in PR
Optimized Large-Scale CMB Likelihood And Quadratic Maximum Likelihood Power Spectrum Estimation
We revisit the problem of exact CMB likelihood and power spectrum estimation
with the goal of minimizing computational cost through linear compression. This
idea was originally proposed for CMB purposes by Tegmark et al.\ (1997), and
here we develop it into a fully working computational framework for large-scale
polarization analysis, adopting \WMAP\ as a worked example. We compare five
different linear bases (pixel space, harmonic space, noise covariance
eigenvectors, signal-to-noise covariance eigenvectors and signal-plus-noise
covariance eigenvectors) in terms of compression efficiency, and find that the
computationally most efficient basis is the signal-to-noise eigenvector basis,
which is closely related to the Karhunen-Loeve and Principal Component
transforms, in agreement with previous suggestions. For this basis, the
information in 6836 unmasked \WMAP\ sky map pixels can be compressed into a
smaller set of 3102 modes, with a maximum error increase of any single
multipole of 3.8\% at , and a maximum shift in the mean values of a
joint distribution of an amplitude--tilt model of 0.006. This
compression reduces the computational cost of a single likelihood evaluation by
a factor of 5, from 38 to 7.5 CPU seconds, and it also results in a more robust
likelihood by implicitly regularizing nearly degenerate modes. Finally, we use
the same compression framework to formulate a numerically stable and
computationally efficient variation of the Quadratic Maximum Likelihood
implementation that requires less than 3 GB of memory and 2 CPU minutes per
iteration for , rendering low- QML CMB power spectrum
analysis fully tractable on a standard laptop.Comment: 13 pages, 13 figures, accepted by ApJ
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