3,087 research outputs found
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
(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.Comment: AAS Latex file, 44 pages, accepted for publication in Ap
A Multiresolution Census Algorithm for Calculating Vortex Statistics in Turbulent Flows
The fundamental equations that model turbulent flow do not provide much
insight into the size and shape of observed turbulent structures. We
investigate the efficient and accurate representation of structures in
two-dimensional turbulence by applying statistical models directly to the
simulated vorticity field. Rather than extract the coherent portion of the
image from the background variation, as in the classical signal-plus-noise
model, we present a model for individual vortices using the non-decimated
discrete wavelet transform. A template image, supplied by the user, provides
the features to be extracted from the vorticity field. By transforming the
vortex template into the wavelet domain, specific characteristics present in
the template, such as size and symmetry, are broken down into components
associated with spatial frequencies. Multivariate multiple linear regression is
used to fit the vortex template to the vorticity field in the wavelet domain.
Since all levels of the template decomposition may be used to model each level
in the field decomposition, the resulting model need not be identical to the
template. Application to a vortex census algorithm that records quantities of
interest (such as size, peak amplitude, circulation, etc.) as the vorticity
field evolves is given. The multiresolution census algorithm extracts coherent
structures of all shapes and sizes in simulated vorticity fields and is able to
reproduce known physical scaling laws when processing a set of voriticity
fields that evolve over time
A survey of parallel algorithms for fractal image compression
This paper presents a short survey of the key research work that has been undertaken in the application of parallel algorithms for Fractal image compression. The interest in fractal image compression techniques stems from their ability to achieve high compression ratios whilst maintaining a very high quality in the reconstructed image. The main drawback of this compression method is the very high computational cost that is associated with the encoding phase. Consequently, there has been significant interest in exploiting parallel computing architectures in order to speed up this phase, whilst still maintaining the advantageous features of the approach. This paper presents a brief introduction to fractal image compression, including the iterated function system theory upon
which it is based, and then reviews the different techniques that have been, and can be, applied in order to parallelize the compression algorithm
Spectral fluctuations of tridiagonal random matrices from the beta-Hermite ensemble
A time series delta(n), the fluctuation of the nth unfolded eigenvalue was
recently characterized for the classical Gaussian ensembles of NxN random
matrices (GOE, GUE, GSE). It is investigated here for the beta-Hermite ensemble
as a function of beta (zero or positive) by Monte Carlo simulations. The
fluctuation of delta(n) and the autocorrelation function vary logarithmically
with n for any beta>0 (1<<n<<N). The simple logarithmic behavior reported for
the higher-order moments of delta(n) for the GOE (beta=1) and the GUE (beta=2)
is valid for any positive beta and is accounted for by Gaussian distributions
whose variances depend linearly on ln(n). The 1/f noise previously demonstrated
for delta(n) series of the three Gaussian ensembles, is characterized by
wavelet analysis both as a function of beta and of N. When beta decreases from
1 to 0, for a given and large enough N, the evolution from a 1/f noise at
beta=1 to a 1/f^2 noise at beta=0 is heterogeneous with a ~1/f^2 noise at the
finest scales and a ~1/f noise at the coarsest ones. The range of scales in
which a ~1/f^2 noise predominates grows progressively when beta decreases.
Asymptotically, a 1/f^2 noise is found for beta=0 while a 1/f noise is the rule
for beta positive.Comment: 35 pages, 10 figures, corresponding author: G. Le Cae
On the efficient Monte Carlo implementation of path integrals
We demonstrate that the Levy-Ciesielski implementation of Lie-Trotter
products enjoys several properties that make it extremely suitable for
path-integral Monte Carlo simulations: fast computation of paths, fast Monte
Carlo sampling, and the ability to use different numbers of time slices for the
different degrees of freedom, commensurate with the quantum effects. It is
demonstrated that a Monte Carlo simulation for which particles or small groups
of variables are updated in a sequential fashion has a statistical efficiency
that is always comparable to or better than that of an all-particle or
all-variable update sampler. The sequential sampler results in significant
computational savings if updating a variable costs only a fraction of the cost
for updating all variables simultaneously or if the variables are independent.
In the Levy-Ciesielski representation, the path variables are grouped in a
small number of layers, with the variables from the same layer being
statistically independent. The superior performance of the fast sampling
algorithm is shown to be a consequence of these observations. Both mathematical
arguments and numerical simulations are employed in order to quantify the
computational advantages of the sequential sampler, the Levy-Ciesielski
implementation of path integrals, and the fast sampling algorithm.Comment: 14 pages, 3 figures; submitted to Phys. Rev.
On adaptive wavelet estimation of a class of weighted densities
We investigate the estimation of a weighted density taking the form
, where denotes an unknown density, the associated
distribution function and is a known (non-negative) weight. Such a class
encompasses many examples, including those arising in order statistics or when
is related to the maximum or the minimum of (random or fixed)
independent and identically distributed (\iid) random variables. We here
construct a new adaptive non-parametric estimator for based on a plug-in
approach and the wavelets methodology. For a wide class of models, we prove
that it attains fast rates of convergence under the risk with
(not only for corresponding to the mean integrated squared
error) over Besov balls. The theoretical findings are illustrated through
several simulations
Multiscale 3D Shape Analysis using Spherical Wavelets
©2005 Springer. The original publication is available at www.springerlink.com:
http://dx.doi.org/10.1007/11566489_57DOI: 10.1007/11566489_57Shape priors attempt to represent biological variations within a population. When variations are global, Principal Component Analysis (PCA) can be used to learn major modes of variation, even from a limited training set. However, when significant local variations exist, PCA typically cannot represent such variations from a small training set. To address this issue, we present a novel algorithm that learns shape variations from data at multiple scales and locations using spherical wavelets and spectral graph partitioning. Our results show that when the training set is small, our algorithm significantly improves the approximation of shapes in a testing set over PCA, which tends to oversmooth data
Selective Principal Component Extraction and Reconstruction: A Novel Method for Ground Based Exoplanet Spectroscopy
Context: Infrared spectroscopy of primary and secondary eclipse events probes
the composition of exoplanet atmospheres and, using space telescopes, has
detected H2O, CH4 and CO2 in three hot Jupiters. However, the available data
from space telescopes has limited spectral resolution and does not cover the
2.4 - 5.2 micron spectral region. While large ground based telescopes have the
potential to obtain molecular-abundance-grade spectra for many exoplanets,
realizing this potential requires retrieving the astrophysical signal in the
presence of large Earth-atmospheric and instrument systematic errors. Aims:
Here we report a wavelet-assisted, selective principal component extraction
method for ground based retrieval of the dayside spectrum of HD 189733b from
data containing systematic errors. Methods: The method uses singular value
decomposition and extracts those critical points of the Rayleigh quotient which
correspond to the planet induced signal. The method does not require prior
knowledge of the planet spectrum or the physical mechanisms causing systematic
errors. Results: The spectrum obtained with our method is in excellent
agreement with space based measurements made with HST and Spitzer (Swain et al.
2009b; Charbonneau et al. 2008) and confirms the recent ground based
measurements (Swain et al. 2010) including the strong 3.3 micron emission.Comment: 4 pages, 3 figures; excepted for publication by A&
Deep Regionlets for Object Detection
In this paper, we propose a novel object detection framework named "Deep
Regionlets" by establishing a bridge between deep neural networks and
conventional detection schema for accurate generic object detection. Motivated
by the abilities of regionlets for modeling object deformation and multiple
aspect ratios, we incorporate regionlets into an end-to-end trainable deep
learning framework. The deep regionlets framework consists of a region
selection network and a deep regionlet learning module. Specifically, given a
detection bounding box proposal, the region selection network provides guidance
on where to select regions to learn the features from. The regionlet learning
module focuses on local feature selection and transformation to alleviate local
variations. To this end, we first realize non-rectangular region selection
within the detection framework to accommodate variations in object appearance.
Moreover, we design a "gating network" within the regionlet leaning module to
enable soft regionlet selection and pooling. The Deep Regionlets framework is
trained end-to-end without additional efforts. We perform ablation studies and
conduct extensive experiments on the PASCAL VOC and Microsoft COCO datasets.
The proposed framework outperforms state-of-the-art algorithms, such as
RetinaNet and Mask R-CNN, even without additional segmentation labels.Comment: Accepted to ECCV 201
Measurements design and phenomena discrimination
The construction of measurements suitable for discriminating signal
components produced by phenomena of different types is considered. The required
measurements should be capable of cancelling out those signal components which
are to be ignored when focusing on a phenomenon of interest. Under the
hypothesis that the subspaces hosting the signal components produced by each
phenomenon are complementary, their discrimination is accomplished by
measurements giving rise to the appropriate oblique projector operator. The
subspace onto which the operator should project is selected by nonlinear
techniques in line with adaptive pursuit strategies
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