14,296 research outputs found
Higher-order Convergence Statistics for Three-dimensional Weak Gravitational Lensing
Weak gravitational lensing on a cosmological scales can provide strong
constraints both on the nature of dark matter and the dark energy equation of
state. Most current weak lensing studies are restricted to (two-dimensional)
projections, but tomographic studies with photometric redshifts have started,
and future surveys offer the possibility of probing the evolution of structure
with redshift. In future we will be able to probe the growth of structure in 3D
and put tighter constraints on cosmological models than can be achieved by the
use of galaxy redshift surveys alone. Earlier studies in this direction focused
mainly on evolution of the 3D power spectrum, but extension to higher-order
statistics can lift degeneracies as well as providing information on primordial
non-gaussianity. We present analytical results for specific higher-order
descriptors, the bispectrum and trispectrum, as well as collapsed multi-point
statistics derived from them, i.e. cumulant correlators. We also compute
quantities we call the power spectra associated with the bispectrum and
trispectrum, the Fourier transforms of the well-known cumulant correlators. We
compute the redshift dependence of these objects and study their performance in
the presence of realistic noise and photometric redshift errors.Comment: 21 page
Recommended from our members
Bayesian Estimation of Intensity Surfaces on the Sphere via Needlet Shrinkage and Selection
This paper describes an approach for Bayesian modeling in spherical datasets. Our method is based upon a recent construction called the needlet, which is a particular form of spherical wavelet with many favorable statistical and computational properties. We perform shrinkage and selection of needlet coefficients, focusing on two main alternatives: empirical-Bayes thresholding, and Bayesian local shrinkage rules. We study the performance of the proposed methodology both on simulated data and on two real data sets: one involving the cosmic microwave background radiation, and one involving the reconstruction of a global news intensity surface inferred from published Reuters articles in August, 1996. The fully Bayesian approach based on robust, sparse shrinkage priors seems to outperform other alternatives.Business Administratio
Large N (=3) Neutrinos and Random Matrix Theory
The large N limit has been successfully applied to QCD, leading to
qualitatively correct results even for N=3. In this work, we propose to treat
the number N=3 of Standard Model generations as a large number. Specifically,
we apply this idea to the neutrino anarchy scenario and study neutrino physics
using Random Matrix Theory, finding new results in both areas. For neutrino
physics, we obtain predictions for the masses and mixing angles as a function
of the generation number N. The Seesaw mechanism produces a hierarchy of order
1/N^3 between the lightest and heaviest neutrino, and a theta(13) mixing angle
of order 1/N, in parametric agreement with experimental data when N goes to 3.
For Random Matrix Theory, this motivates the introduction of a new type of
ensemble of random matrices, the "Seesaw ensemble." Basic properties of such
matrices are studied, including the eigenvalue density and the interpretation
as a Coulomb gas system. Besides its mathematical interest, the Seesaw ensemble
may be useful in random systems where two hierarchical scales exist.Comment: 20 pages, 6 figures, 1 table; accepted version for JHEP, references
adde
Higher-order Statistics of Weak Lensing Shear and Flexion
Owing to their more extensive sky coverage and tighter control on systematic
errors, future deep weak lensing surveys should provide a better statistical
picture of the dark matter clustering beyond the level of the power spectrum.
In this context, the study of non-Gaussianity induced by gravity can help
tighten constraints on the background cosmology by breaking parameter
degeneracies, as well as throwing light on the nature of dark matter, dark
energy or alternative gravity theories. Analysis of the shear or flexion
properties of such maps is more complicated than the simpler case of the
convergence due to the spinorial nature of the fields involved. Here we develop
analytical tools for the study of higher-order statistics such as the
bispectrum (or trispectrum) directly using such maps at different source
redshift. The statistics we introduce can be constructed from cumulants of the
shear or flexions, involving the cross-correlation of squared and cubic maps at
different redshifts. Typically, the low signal-to-noise ratio prevents recovery
of the bispectrum or trispectrum mode by mode. We define power spectra
associated with each multi- spectra which compresses some of the available
information of higher order multispectra. We show how these can be recovered
from a noisy observational data even in the presence of arbitrary mask, which
introduces mixing between Electric (E-type) and Magnetic (B-type) polarization,
in an unbiased way. We also introduce higher order cross-correlators which can
cross-correlate lensing shear with different tracers of large scale structures.Comment: 16 pages, 2 figure
Path Similarity Analysis: a Method for Quantifying Macromolecular Pathways
Diverse classes of proteins function through large-scale conformational
changes; sophisticated enhanced sampling methods have been proposed to generate
these macromolecular transition paths. As such paths are curves in a
high-dimensional space, they have been difficult to compare quantitatively, a
prerequisite to, for instance, assess the quality of different sampling
algorithms. The Path Similarity Analysis (PSA) approach alleviates these
difficulties by utilizing the full information in 3N-dimensional trajectories
in configuration space. PSA employs the Hausdorff or Fr\'echet path
metrics---adopted from computational geometry---enabling us to quantify path
(dis)similarity, while the new concept of a Hausdorff-pair map permits the
extraction of atomic-scale determinants responsible for path differences.
Combined with clustering techniques, PSA facilitates the comparison of many
paths, including collections of transition ensembles. We use the closed-to-open
transition of the enzyme adenylate kinase (AdK)---a commonly used testbed for
the assessment enhanced sampling algorithms---to examine multiple microsecond
equilibrium molecular dynamics (MD) transitions of AdK in its substrate-free
form alongside transition ensembles from the MD-based dynamic importance
sampling (DIMS-MD) and targeted MD (TMD) methods, and a geometrical targeting
algorithm (FRODA). A Hausdorff pairs analysis of these ensembles revealed, for
instance, that differences in DIMS-MD and FRODA paths were mediated by a set of
conserved salt bridges whose charge-charge interactions are fully modeled in
DIMS-MD but not in FRODA. We also demonstrate how existing trajectory analysis
methods relying on pre-defined collective variables, such as native contacts or
geometric quantities, can be used synergistically with PSA, as well as the
application of PSA to more complex systems such as membrane transporter
proteins.Comment: 9 figures, 3 tables in the main manuscript; supplementary information
includes 7 texts (S1 Text - S7 Text) and 11 figures (S1 Fig - S11 Fig) (also
available from journal site
Wavelets, ridgelets and curvelets on the sphere
We present in this paper new multiscale transforms on the sphere, namely the
isotropic undecimated wavelet transform, the pyramidal wavelet transform, the
ridgelet transform and the curvelet transform. All of these transforms can be
inverted i.e. we can exactly reconstruct the original data from its
coefficients in either representation. Several applications are described. We
show how these transforms can be used in denoising and especially in a Combined
Filtering Method, which uses both the wavelet and the curvelet transforms, thus
benefiting from the advantages of both transforms. An application to component
separation from multichannel data mapped to the sphere is also described in
which we take advantage of moving to a wavelet representation.Comment: Accepted for publication in A&A. Manuscript with all figures can be
downloaded at http://jstarck.free.fr/aa_sphere05.pd
Foreground component separation with generalised ILC
The 'Internal Linear Combination' (ILC) component separation method has been
extensively used to extract a single component, the CMB, from the WMAP
multifrequency data. We generalise the ILC approach for separating other
millimetre astrophysical emissions. We construct in particular a
multidimensional ILC filter, which can be used, for instance, to estimate the
diffuse emission of a complex component originating from multiple correlated
emissions, such as the total emission of the Galactic interstellar medium. The
performance of such generalised ILC methods, implemented on a needlet frame, is
tested on simulations of Planck mission observations, for which we successfully
reconstruct a low noise estimate of emission from astrophysical foregrounds
with vanishing CMB and SZ contamination.Comment: 11 pages, 6 figures (2 figures added), 1 reference added,
introduction expanded, V2: version accepted by MNRA
Modification of Decay Constants of Superstring Axions: Effects of Flux Compactification and Axion Mixing
We study possibilities for lowering the decay constants of superstring
axions. In the heterotic Calabi-Yau compactification, a localized
model-dependent axion can appear at a nearly collapsing 2-cycle. The effect of
flux can be used for generating warp factor suppression of the axion decay
constant. We also point out that the hidden sector instanton potential much
higher than the QCD instanton potential picks up the larger effective axion
decay constant as that of the QCD axion. We show that this can be converted by
introducing many hidden-sector quarks so that the decay constant of the QCD
axion turns out to be much smaller than the string scale.Comment: 6 pages with 3 figures, revtex; figure added,section of axion mixing
modifie
- …