82,711 research outputs found
Principal Component Analysis of Weak Lensing Surveys
We study degeneracies between cosmological parameters and measurement errors
from cosmic shear surveys using a principal component analysis of the Fisher
matrix. We simulate realistic survey topologies with non-uniform sky coverage,
and quantify the effect of survey geometry, depth and noise from intrinsic
galaxy ellipticities on the parameter errors. This analysis allows us to
optimise the survey geometry. Using the shear two-point correlation functions
and the aperture mass dispersion, we study various degeneracy directions in a
multi-dimensional parameter space spanned by Omega_m, Omega_Lambda, sigma_8,
the shape parameter Gamma, the spectral index n_s, along with parameters that
specify the distribution of source galaxies. If only three parameters are to be
obtained from weak lensing data, a single principal component is dominant and
contains all information about the main parameter degeneracies and their
errors. The variance of the dominant principal component of the Fisher matrix
shows a minimum for survey strategies which have small cosmic variance and
measure the shear correlation up to several degrees [abridged].Comment: 13 pages, 17 figures. A&A in press, matches the version to be
publishe
Geometric methods for estimation of structured covariances
We consider problems of estimation of structured covariance matrices, and in
particular of matrices with a Toeplitz structure. We follow a geometric
viewpoint that is based on some suitable notion of distance. To this end, we
overview and compare several alternatives metrics and divergence measures. We
advocate a specific one which represents the Wasserstein distance between the
corresponding Gaussians distributions and show that it coincides with the
so-called Bures/Hellinger distance between covariance matrices as well. Most
importantly, besides the physically appealing interpretation, computation of
the metric requires solving a linear matrix inequality (LMI). As a consequence,
computations scale nicely for problems involving large covariance matrices, and
linear prior constraints on the covariance structure are easy to handle. We
compare this transportation/Bures/Hellinger metric with the maximum likelihood
and the Burg methods as to their performance with regard to estimation of power
spectra with spectral lines on a representative case study from the literature.Comment: 12 pages, 3 figure
Full metastable asymptotic of the Fisher information
We establish an expansion by Gamma-convergence of the Fisher information
relative to the reference measure exp(-beta V), where V is a generic multiwell
potential and beta goes to infinity. The expansion reveals a hierarchy of
multiple scales reflecting the metastable behavior of the underlying overdamped
Langevin dynamics: distinct scales emerge and become relevant depending on
whether one considers probability measures concentrated on local minima of V,
probability measures concentrated on critical points of V, or generic
probability measures on R^d. We thus fully describe the asymptotic behavior of
minima of the Fisher information over regular sets of probabilities. The
analysis mostly relies on spectral properties of diffusion operators and the
related semiclassical Witten Laplacian and covers also the case of a compact
smooth manifold as underlying space.Comment: 24 pages. Typos correcte
Weak value amplification: a view from quantum estimation theory that highlights what it is and what isn't
Weak value amplification (WVA) is a concept that has been extensively used in
a myriad of applications with the aim of rendering measurable tiny changes of a
variable of interest. In spite of this, there is still an on-going debate about
its true nature and whether is really needed for achieving high sensitivity.
Here we aim at solving the puzzle, using some basic concepts from quantum
estimation theory, highlighting what the use of the WVA concept can offer and
what it can not. While WVA cannot be used to go beyond some fundamental
sensitivity limits that arise from considering the full nature of the quantum
states, WVA can notwithstanding enhance the sensitivity of real detection
schemes that are limited by many other things apart from the quantum nature of
the states involved, i.e. technical noise. Importantly, it can do that in a
straightforward and easily accessible manner.Comment: 2 pages, 5 figure
Recommended from our members
Spectral filtering as a method of visualising and removing striped artefacts in digital elevation data
Spectral filtering was compared with traditional mean spatial filters to assess their ability to identify and remove striped artefacts in digital elevation data. The techniques were applied to two datasets: a 100 m contour derived digital elevation model (DEM) of southern Norway and a 2 m LiDAR DSM of the Lake District, UK. Both datasets contained diagonal data artefacts that were found to propagate into subsequent terrain analysis. Spectral filtering used fast Fourier transformation (FFT) frequency data to identify these data artefacts in both datasets. These were removed from the data by applying a cut filter, prior to the inverse transform. Spectral filtering showed considerable advantages over mean spatial filters, when both the absolute and spatial distribution of elevation changes made were examined. Elevation changes from the spectral filtering were restricted to frequencies removed by the cut filter, were small in magnitude and consequently avoided any global smoothing. Spectral filtering was found to avoid the smoothing of kernel based data editing, and provided a more informative measure of data artefacts present in the FFT frequency domain. Artefacts were found to be heterogeneous through the surfaces, a result of their strong correlations with spatially autocorrelated variables: landcover and landsurface geometry. Spectral filtering performed better on the 100 m DEM, where signal and artefact were clearly distinguishable in the frequency data. Spectrally filtered digital elevation datasets were found to provide a superior and more precise representation of the landsurface and be a more appropriate dataset for any subsequent geomorphological applications
Time Dilation from Spectral Feature Age Measurements of Type Ia Supernovae
We have developed a quantitative, empirical method for estimating the age of
Type Ia supernovae (SNe Ia) from a single spectral epoch. The technique
examines the goodness of fit of spectral features as a function of the temporal
evolution of a large database of SNe Ia spectral features. When a SN Ia
spectrum with good signal-to-noise ratio over the rest frame range 3800 to 6800
A is available, the precision of a spectral feature age (SFA) is (1-sigma) ~
1.4 days. SFA estimates are made for two spectral epochs of SN 1996bj (z=0.574)
to measure the rate of aging at high redshift. In the 10.05 days which elapsed
between spectral observations, SN 1996bj aged 3.35 3.2 days, consistent
with the 6.38 days of aging expected in an expanding Universe and inconsistent
with no time dilation at the 96.4 % confidence level. The precision to which
individual features constrain the supernova age has implications for the source
of inhomogeneities among SNe Ia.Comment: 14 pages (LaTex), 7 postscript figures to Appear in the Astronomical
Journa
Quantum-limited time-frequency estimation through mode-selective photon measurement
By projecting onto complex optical mode profiles, it is possible to estimate
arbitrarily small separations between objects with quantum-limited precision,
free of uncertainty arising from overlapping intensity profiles. Here we extend
these techniques to the time-frequency domain using mode-selective
sum-frequency generation with shaped ultrafast pulses. We experimentally
resolve temporal and spectral separations between incoherent mixtures of
single-photon level signals ten times smaller than their optical bandwidths
with a ten-fold improvement in precision over the intensity-only Cram\'er-Rao
bound.Comment: Six pages, three figures. Comments welcome
Constraining Inflation
Slow roll reconstruction is derived from the Hamilton-Jacobi formulation of
inflationary dynamics. It automatically includes information from sub-leading
terms in slow roll, and facilitatesthe inclusion of priors based on the
duration on inflation. We show that at low inflationary scales the
Hamilton-Jacobi equations simplify considerably. We provide a new
classification scheme for inflationary models, based solely on the number of
parameters needed to specify the potential, and provide forecasts for likely
bounds on the slow roll parameters from future datasets. A minimal running of
the spectral index, induced solely by the first two slow roll parameters
(\epsilon and \eta) appears to be effectively undetectable by realistic Cosmic
Microwave Background experiments. However, we show that the ability to detect
this signal increases with the lever arm in comoving wavenumber, and we
conjecture that high redshift 21 cm data may allow tests of second order
consistency conditions on inflation. Finally, we point out that the second
order corrections to the spectral index are correlated with the inflationary
scale, and thus the amplitude of the CMB B-mode.Comment: 32 pages. v
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