2,209 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
Multiresolution analysis in statistical mechanics. II. The wavelet transform as a basis for Monte Carlo simulations on lattices
In this paper, we extend our analysis of lattice systems using the wavelet
transform to systems for which exact enumeration is impractical. For such
systems, we illustrate a wavelet-accelerated Monte Carlo (WAMC) algorithm,
which hierarchically coarse-grains a lattice model by computing the probability
distribution for successively larger block spins. We demonstrate that although
the method perturbs the system by changing its Hamiltonian and by allowing
block spins to take on values not permitted for individual spins, the results
obtained agree with the analytical results in the preceding paper, and
``converge'' to exact results obtained in the absence of coarse-graining.
Additionally, we show that the decorrelation time for the WAMC is no worse than
that of Metropolis Monte Carlo (MMC), and that scaling laws can be constructed
from data performed in several short simulations to estimate the results that
would be obtained from the original simulation. Although the algorithm is not
asymptotically faster than traditional MMC, because of its hierarchical design,
the new algorithm executes several orders of magnitude faster than a full
simulation of the original problem. Consequently, the new method allows for
rapid analysis of a phase diagram, allowing computational time to be focused on
regions near phase transitions.Comment: 11 pages plus 7 figures in PNG format (downloadable separately
Epoxidation of Allylic Alcohols with TiO2-SiO2: Hydroxy-Assisted Mechanism and Dynamic Structural Changes During Reaction
Epoxidation of allylic alcohols and cyclohexene with TBHP and titania-silica aerogels containing 1 and 5âwt% TiO2 has been studied. For the oxidation of geraniol and cyclohexenol, the regio- and diastereoselectivities and kinetic data indicate an OH-assisted mechanism involving a dative bond between the OH group and the Ti site. This mechanism is disabled in the oxidation of cyclooctenol due to steric hindrance. The moderate regio- and diastereoselectivities of the aerogels, compared with those of TS-1 and the homogeneous model Ti(OSiMe3)4, are attributed to the presence of non-isolated Ti sites and to a "silanol-assistedâ mechanism, according to which model the allylic alcohol is anchored to a neighboring SiOH group instead of the Ti-peroxo complex. Kinetic analysis of the initial transient period revealed rapid catalyst restructuring during the first few turnovers. A feasible explanation is the breaking of Si-O-Ti linkages of the carefully predried aerogels by water or TBHP, resulting in active Ti sites with remarkably different catalytic propertie
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
Multiresolution analysis in statistical mechanics. I. Using wavelets to calculate thermodynamic properties
The wavelet transform, a family of orthonormal bases, is introduced as a
technique for performing multiresolution analysis in statistical mechanics. The
wavelet transform is a hierarchical technique designed to separate data sets
into sets representing local averages and local differences. Although
one-to-one transformations of data sets are possible, the advantage of the
wavelet transform is as an approximation scheme for the efficient calculation
of thermodynamic and ensemble properties. Even under the most drastic of
approximations, the resulting errors in the values obtained for average
absolute magnetization, free energy, and heat capacity are on the order of 10%,
with a corresponding computational efficiency gain of two orders of magnitude
for a system such as a Ising lattice. In addition, the errors in
the results tend toward zero in the neighborhood of fixed points, as determined
by renormalization group theory.Comment: 13 pages plus 7 figures (PNG
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
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Numerical treatment of seismic accelerograms and of inelastic seismic structural responses using harmonic wavelets
The harmonic wavelet transform is employed to analyze various kinds of nonstationary signals common in aseismic design. The effectiveness of the harmonic wavelets for capturing the temporal evolution of the frequency content of strong ground motions is demonstrated. In this regard, a detailed study of important earthquake accelerograms is undertaken and smooth joint time-frequency spectra are provided for two near-field and two far-field records; inherent in this analysis is the concept of the mean instantaneous frequency. Furthermore, as a paradigm of usefulness for aseismic structural purposes, a similar analysis is conducted for the response of a 20-story steel frame benchmark building considering one of the four accelerograms scaled by appropriate factors as the excitation to simulate undamaged and severely damaged conditions for the structure. The resulting joint time-frequency representation of the response time histories captures the influence of nonlinearity on the variation of the effective natural frequencies of a structural system during the evolution of a seismic event. In this context, the potential of the harmonic wavelet transform as a detection tool for global structural damage is explored in conjunction with the concept of monitoring the mean instantaneous frequency of records of critical structural responses
Time domain study of frequency-power correlation in spin-torque oscillators
This paper describes a numerical experiment, based on full micromagnetic
simulations of current-driven magnetization dynamics in nanoscale spin valves,
to identify the origins of spectral linewidth broadening in spin torque
oscillators. Our numerical results show two qualitatively different regimes of
magnetization dynamics at zero temperature: regular (single-mode precessional
dynamics) and chaotic. In the regular regime, the dependence of the oscillator
integrated power on frequency is linear, and consequently the dynamics is well
described by the analytical theory of current-driven magnetization dynamics for
moderate amplitudes of oscillations. We observe that for higher oscillator
amplitudes, the functional dependence of the oscillator integrated power as a
function of frequency is not a single-valued function and can be described
numerically via introduction of nonlinear oscillator power. For a range of
currents in the regular regime, the oscillator spectral linewidth is a linear
function of temperature. In the chaotic regime found at large current values,
the linewidth is not described by the analytical theory. In this regime we
observe the oscillator linewidth broadening, which originates from sudden jumps
of frequency of the oscillator arising from random domain wall nucleation and
propagation through the sample. This intermittent behavior is revealed through
a wavelet analysis that gives superior description of the frequency jumps
compared to several other techniques.Comment: 11 pages, 4 figures to appear in PR
Delay-Coordinates Embeddings as a Data Mining Tool for Denoising Speech Signals
In this paper we utilize techniques from the theory of non-linear dynamical
systems to define a notion of embedding threshold estimators. More specifically
we use delay-coordinates embeddings of sets of coefficients of the measured
signal (in some chosen frame) as a data mining tool to separate structures that
are likely to be generated by signals belonging to some predetermined data set.
We describe a particular variation of the embedding threshold estimator
implemented in a windowed Fourier frame, and we apply it to speech signals
heavily corrupted with the addition of several types of white noise. Our
experimental work seems to suggest that, after training on the data sets of
interest,these estimators perform well for a variety of white noise processes
and noise intensity levels. The method is compared, for the case of Gaussian
white noise, to a block thresholding estimator
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
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