7,701 research outputs found
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
Visual Analysis of Variability and Features of Climate Simulation Ensembles
This PhD thesis is concerned with the visual analysis of time-dependent scalar field ensembles as occur in climate simulations.
Modern climate projections consist of multiple simulation runs (ensemble members) that vary in parameter settings and/or initial values, which leads to variations in the resulting simulation data.
The goal of ensemble simulations is to sample the space of possible futures under the given climate model and provide quantitative information about uncertainty in the results.
The analysis of such data is challenging because apart from the spatiotemporal data, also variability has to be analyzed and communicated.
This thesis presents novel techniques to analyze climate simulation ensembles visually.
A central question is how the data can be aggregated under minimized information loss.
To address this question, a key technique applied in several places in this work is clustering.
The first part of the thesis addresses the challenge of finding clusters in the ensemble simulation data.
Various distance metrics lend themselves for the comparison of scalar fields which are explored theoretically and practically.
A visual analytics interface allows the user to interactively explore and compare multiple parameter settings for the clustering and investigate the resulting clusters, i.e. prototypical climate phenomena.
A central contribution here is the development of design principles for analyzing variability in decadal climate simulations, which has lead to a visualization system centered around the new Clustering Timeline.
This is a variant of a Sankey diagram that utilizes clustering results to communicate climatic states over time coupled with ensemble member agreement.
It can reveal
several interesting properties of the dataset, such as:
into how many inherently similar groups the ensemble can be divided at any given time,
whether the ensemble diverges in general,
whether there are different phases in the time lapse, maybe periodicity, or outliers.
The Clustering Timeline is also used to compare multiple climate simulation models and assess their performance.
The Hierarchical Clustering Timeline is an advanced version of the above.
It introduces the concept of a cluster hierarchy that may group the whole dataset down to the individual static scalar fields into clusters of various sizes and densities recording the nesting relationship between them.
One more contribution of this work in terms of visualization research is, that ways are investigated how to practically utilize a hierarchical clustering of time-dependent scalar fields to analyze the data.
To this end, a system of different views is proposed which are linked through various interaction possibilities.
The main advantage of the system is that a dataset can now be inspected at an arbitrary level of detail without having to recompute a clustering with different parameters.
Interesting branches of the simulation can be expanded to reveal smaller differences in critical clusters or folded to show only a coarse representation of the less interesting parts of the dataset.
The last building block of the suit of visual analysis methods developed for this thesis aims at a robust, (largely) automatic detection and tracking of certain features in a scalar field ensemble.
Techniques are presented that I found can identify and track super- and sub-levelsets.
And I derive “centers of action” from these sets which mark the location of extremal climate phenomena that govern the weather (e.g. Icelandic Low and Azores High).
The thesis also presents visual and quantitative techniques to evaluate the temporal change of the positions of these centers; such a displacement would be likely to manifest in changes in weather.
In a preliminary analysis with my collaborators, we indeed observed changes in the loci of the centers of action in a simulation with increased greenhouse gas concentration as compared to pre-industrial concentration levels
Stable Clustering Ansatz, Consistency Relations and Gravity Dual of Large-Scale Structure
Gravitational clustering in the nonlinear regime remains poorly understood.
Gravity dual of gravitational clustering has recently been proposed as a means
to study the nonlinear regime. The stable clustering ansatz remains a key
ingredient to our understanding of gravitational clustering in the highly
nonlinear regime. We study certain aspects of violation of the stable
clustering ansatz in the gravity dual of Large Scale Structure (LSS). We extend
the recent studies of gravitational clustering using AdS gravity dual to take
into account possible departure from the stable clustering ansatz and to
arbitrary dimensions. Next, we extend the recently introduced consistency
relations to arbitrary dimensions. We use the consistency relations to test the
commonly used models of gravitational clustering including the halo models and
hierarchical ans\"atze. In particular we establish a tower of consistency
relations for the hierarchical amplitudes: etc. as a
functions of the scaled peculiar velocity . We also study the variants of
popular halo models in this context. In contrast to recent claims, none of
these models, in their simplest incarnation, seem to satisfy the consistency
relations in the soft limit.Comment: 21 pages, 4 figure
Source-lens clustering and intrinsic-alignment bias of weak-lensing estimators
We estimate the amplitude of the source-lens clustering bias and of the
intrinsic-alignment bias of weak lensing estimators of the two-point and
three-point convergence and cosmic-shear correlation functions. We use a linear
galaxy bias model for the galaxy-density correlations, as well as a linear
intrinsic-alignment model. For the three-point and four-point density
correlations, we use analytical or semi-analytical models, based on a
hierarchical ansatz or a combination of one-loop perturbation theory with a
halo model. For two-point statistics, we find that the source-lens clustering
bias is typically several orders of magnitude below the weak lensing signal,
except when we correlate a very low-redshift galaxy (z_2 \la 0.05) with a
higher redshift galaxy (z_1 \ga 0.5), where it can reach of the signal
for the shear. For three-point statistics, the source-lens clustering bias is
typically of order of the signal, as soon as the three galaxy source
redshifts are not identical. The intrinsic-alignment bias is typically about
of the signal for both two-point and three-point statistics. Thus, both
source-lens clustering bias and intrinsic-alignment bias must be taken into
account for three-point estimators aiming at a better than accuracy.Comment: 27 page
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
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