1,524 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
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
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
Quasi-local evolution of cosmic gravitational clustering in the weakly non-linear regime
We investigate the weakly non-linear evolution of cosmic gravitational
clustering in phase space by looking at the Zel'dovich solution in the discrete
wavelet transform (DWT) representation. We show that if the initial
perturbations are Gaussian, the relation between the evolved DWT mode and the
initial perturbations in the weakly non-linear regime is quasi-local. That is,
the evolved density perturbations are mainly determined by the initial
perturbations localized in the same spatial range. Furthermore, we show that
the evolved mode is monotonically related to the initial perturbed mode. Thus
large (small) perturbed modes statistically correspond to the large (small)
initial perturbed modes. We test this prediction by using QSO Ly
absorption samples. The results show that the weakly non-linear features for
both the transmitted flux and identified forest lines are quasi-localized. The
locality and monotonic properties provide a solid basis for a DWT
scale-by-scale Gaussianization reconstruction algorithm proposed by Feng & Fang
(Feng & Fang, 2000) for data in the weakly non-linear regime. With the
Zel'dovich solution, we find also that the major non-Gaussianity caused by the
weakly non-linear evolution is local scale-scale correlations. Therefore, to
have a precise recovery of the initial Gaussian mass field, it is essential to
remove the scale-scale correlations.Comment: 22 pages, 13 figures. Accepted for publication in the Astrophysical
Journa
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
Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: numerical study
We study scalar and vector modulation instabilities induced by the vacuum
fluctuations in birefringent optical fibers. To this end, stochastic coupled
nonlinear Schrodinger equations are derived. The stochastic model is equivalent
to the quantum field operators equations and allow for dispersion,
nonlinearity, and arbitrary level of birefringence. Numerical integration of
the stochastic equations is compared to analytical formulas in the case of
scalar modulation instability and non depleted pump approximation. The effect
of classical noise and its competition with vacuum fluctuations for inducing
modulation instability is also addressed.Comment: 33 pages, 5 figure
Time scales in nuclear giant resonances
We propose a general approach to characterise fluctuations of measured cross
sections of nuclear giant resonances. Simulated cross sections are obtained
from a particular, yet representative self-energy which contains all
information about fragmentations. Using a wavelet analysis, we demonstrate the
extraction of time scales of cascading decays into configurations of different
complexity of the resonance. We argue that the spreading widths of collective
excitations in nuclei are determined by the number of fragmentations as seen in
the power spectrum. An analytic treatment of the wavelet analysis using a
Fourier expansion of the cross section confirms this principle. A simple rule
for the relative life times of states associated with hierarchies of different
complexity is given.Comment: 5 pages, 4 figure
Parameter Estimation from Time-Series Data with Correlated Errors: A Wavelet-Based Method and its Application to Transit Light Curves
We consider the problem of fitting a parametric model to time-series data
that are afflicted by correlated noise. The noise is represented by a sum of
two stationary Gaussian processes: one that is uncorrelated in time, and
another that has a power spectral density varying as . We present
an accurate and fast [O(N)] algorithm for parameter estimation based on
computing the likelihood in a wavelet basis. The method is illustrated and
tested using simulated time-series photometry of exoplanetary transits, with
particular attention to estimating the midtransit time. We compare our method
to two other methods that have been used in the literature, the time-averaging
method and the residual-permutation method. For noise processes that obey our
assumptions, the algorithm presented here gives more accurate results for
midtransit times and truer estimates of their uncertainties.Comment: Accepted in ApJ. Illustrative code may be found at
http://www.mit.edu/~carterja/code/ . 17 page
Role of homeostasis in learning sparse representations
Neurons in the input layer of primary visual cortex in primates develop
edge-like receptive fields. One approach to understanding the emergence of this
response is to state that neural activity has to efficiently represent sensory
data with respect to the statistics of natural scenes. Furthermore, it is
believed that such an efficient coding is achieved using a competition across
neurons so as to generate a sparse representation, that is, where a relatively
small number of neurons are simultaneously active. Indeed, different models of
sparse coding, coupled with Hebbian learning and homeostasis, have been
proposed that successfully match the observed emergent response. However, the
specific role of homeostasis in learning such sparse representations is still
largely unknown. By quantitatively assessing the efficiency of the neural
representation during learning, we derive a cooperative homeostasis mechanism
that optimally tunes the competition between neurons within the sparse coding
algorithm. We apply this homeostasis while learning small patches taken from
natural images and compare its efficiency with state-of-the-art algorithms.
Results show that while different sparse coding algorithms give similar coding
results, the homeostasis provides an optimal balance for the representation of
natural images within the population of neurons. Competition in sparse coding
is optimized when it is fair. By contributing to optimizing statistical
competition across neurons, homeostasis is crucial in providing a more
efficient solution to the emergence of independent components
On Deterministic Sketching and Streaming for Sparse Recovery and Norm Estimation
We study classic streaming and sparse recovery problems using deterministic
linear sketches, including l1/l1 and linf/l1 sparse recovery problems (the
latter also being known as l1-heavy hitters), norm estimation, and approximate
inner product. We focus on devising a fixed matrix A in R^{m x n} and a
deterministic recovery/estimation procedure which work for all possible input
vectors simultaneously. Our results improve upon existing work, the following
being our main contributions:
* A proof that linf/l1 sparse recovery and inner product estimation are
equivalent, and that incoherent matrices can be used to solve both problems.
Our upper bound for the number of measurements is m=O(eps^{-2}*min{log n, (log
n / log(1/eps))^2}). We can also obtain fast sketching and recovery algorithms
by making use of the Fast Johnson-Lindenstrauss transform. Both our running
times and number of measurements improve upon previous work. We can also obtain
better error guarantees than previous work in terms of a smaller tail of the
input vector.
* A new lower bound for the number of linear measurements required to solve
l1/l1 sparse recovery. We show Omega(k/eps^2 + klog(n/k)/eps) measurements are
required to recover an x' with |x - x'|_1 <= (1+eps)|x_{tail(k)}|_1, where
x_{tail(k)} is x projected onto all but its largest k coordinates in magnitude.
* A tight bound of m = Theta(eps^{-2}log(eps^2 n)) on the number of
measurements required to solve deterministic norm estimation, i.e., to recover
|x|_2 +/- eps|x|_1.
For all the problems we study, tight bounds are already known for the
randomized complexity from previous work, except in the case of l1/l1 sparse
recovery, where a nearly tight bound is known. Our work thus aims to study the
deterministic complexities of these problems
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