2,246 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 Theory for Multiresolution Signal Decomposition: The Wavelet Representation
It is now well admitted in the computer vision literature that a multi-resolution decomposition provides a useful image representation for vision algorithms. In this paper we show that the wavelet theory recently developed by the mathematician Y. Meyer enables us to understand and model the concepts of resolution and scale. In computer vision we generally do not want to analyze the images at each resolution level because the information is redundant. After processing the signal at a resolution r0, it is more efficient to analyze only the additional details which are available at a higher resolution rl. We prove that this difference of information can be computed by decomposing the signal on a wavelet orthonormal basis and that it can be efficiently calculated with a pyramid transform. This can also be interpreted as a division of the signal in a set of orientation selective frequency channels. Such a decomposition is particularly well adapted for computer vision applications such as signal coding, texture discrimination, edge detection, matching algorithms and fractal analysis
What is a preferred angiotensin II receptor blocker-based combination therapy for blood pressure control in hypertensive patients with diabetic and non-diabetic renal impairment?
Hypertension has a major associated risk for organ damage and mortality, which is further heightened in patients with prior cardiovascular (CV) events, comorbid diabetes mellitus, microalbuminuria and renal impairment. Given that most patients with hypertension require at least two antihypertensives to achieve blood pressure (BP) goals, identifying the most appropriate combination regimen based on individual risk factors and comorbidities is important for risk management. Single-pill combinations (SPCs) containing two or more antihypertensive agents with complementary mechanisms of action offer potential advantages over free-drug combinations, including simplification of treatment regimens, convenience and reduced costs. The improved adherence and convenience resulting from SPC use is recognised in updated hypertension guidelines. Despite a wide choice of SPCs for hypertension treatment, clinical evidence from direct head-to-head comparisons to guide selection for individual patients is lacking. However, in patients with evidence of renal disease or at greater risk of developing renal disease, such as those with diabetes mellitus, microalbuminura and high-normal BP or overt hypertension, guidelines recommend renin-angiotensin system (RAS) blocker-based combination therapy due to superior renoprotective effects compared with other antihypertensive classes. Furthermore, RAS inhibitors attenuate the oedema and renal hyperfiltration associated with calcium channel blocker (CCB) monotherapy, making them a good choice for combination therapy. The occurrence of angiotensin-converting enzyme (ACE) inhibitor-induced cough supports the use of angiotensin II receptor blockers (ARBs) for RAS blockade rather than ACE inhibitors. In this regard, ARB-based SPCs are available in combination with the diuretic, hydrochlorothiazide (HCTZ) or the calcium CCB, amlodipine. Telmisartan, a long-acting ARB with preferential pharmacodynamic profile compared with several other ARBs, and the only ARB with an indication for the prevention of CV disease progression, is available in two SPC formulations, telmisartan/HCTZ and telmisartan/amlodipine. Clinical studies suggest that in CV high-risk patients and those with evidence of renal disease, the use of an ARB/CCB combination may be preferred to ARB/HCTZ combinations due to superior renoprotective and CV benefits and reduced metabolic side effects in patients with concomitant metabolic disorders. However, selection of the most appropriate antihypertensive combination should be dependent on careful review of the individual patient and appropriate consideration of drug pharmacology
Dyadic Wavelets Energy Zero-Crossings
An important problem in signal analysis is to define a general purpose signal representation which is well adapted for developing pattern recognition algorithms. In this paper we will show that such a representation can be defined from the position of the zero-crossings and the local energy values of a dyadic wavelet decomposition. This representation is experimentally complete and admits a simple distance for pattern matching applications. It provides a multiscale decomposition of the signal and at each scale characterizes the locations of abrupt changes in the signal. We have developed a stereo matching algorithm to illustrate the application of this representation to pattern matching
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
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
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
Discrepancy between sub-critical and fast rupture roughness: a cumulant analysis
We study the roughness of a crack interface in a sheet of paper. We
distinguish between slow (sub-critical) and fast crack growth regimes. We show
that the fracture roughness is different in the two regimes using a new method
based on a multifractal formalism recently developed in the turbulence
literature. Deviations from monofractality also appear to be different in both
regimes
One-point Statistics of the Cosmic Density Field in Real and Redshift Spaces with A Multiresolutional Decomposition
In this paper, we develop a method of performing the one-point statistics of
a perturbed density field with a multiresolutional decomposition based on the
discrete wavelet transform (DWT). We establish the algorithm of the one-point
variable and its moments in considering the effects of Poisson sampling and
selection function. We also establish the mapping between the DWT one-point
statistics in redshift space and real space, i.e. the algorithm for recovering
the DWT one-point statistics from the redshift distortion of bulk velocity,
velocity dispersion, and selection function. Numerical tests on N-body
simulation samples show that this algorithm works well on scales from a few
hundreds to a few Mpc/h for four popular cold dark matter models.
Taking the advantage that the DWT one-point variable is dependent on both the
scale and the shape (configuration) of decomposition modes, one can design
estimators of the redshift distortion parameter (beta) from combinations of DWT
modes. When the non-linear redshift distortion is not negligible, the beta
estimator from quadrupole-to-monopole ratio is a function of scale. This
estimator would not work without adding information about the scale-dependence,
such as the power-spectrum index or the real-space correlation function of the
random field. The DWT beta estimators, however, do not need such extra
information. Numerical tests show that the proposed DWT estimators are able to
determine beta robustly with less than 15% uncertainty in the redshift range 0
< z < 3.Comment: 39 pages, 12 figures, ApJ accepte
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
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