31,386 research outputs found
Differential image motion in the short exposure regime
Whole atmosphere seeing \beta_0 is the most important parameter in site
testing measurements. Estimation of the seeing from a variance of differential
image motion is always biased by a non-zero DIMM exposure, which results in a
wind smoothing. In the paper, the wind effects are studied within short
exposure approximation, i.e. when the wind shifts turbulence during exposure by
distance lesser than device aperture. The method of correction for this effect
on the base of image motion correlation between adjacent frames is proposed. It
is shown that the correlation can be used for estimation of the mean wind speed
V_2 and atmospheric coherence time \tau_0. Total power of longitudinal and
transverse image motion is suggested for elimination of dependence on the wind
direction. Obtained theoretical results were tested on the data obtained on
Mount Shatdjatmaz in 2007--2010 with MASS/DIMM device and good agreement was
found.Comment: 11 pages, 8 figures. Accepted for publication in MNRA
Testing general relativity with compact coalescing binaries: comparing exact and predictive methods to compute the Bayes factor
The second generation of gravitational-wave detectors is scheduled to start
operations in 2015. Gravitational-wave signatures of compact binary
coalescences could be used to accurately test the strong-field dynamical
predictions of general relativity. Computationally expensive data analysis
pipelines, including TIGER, have been developed to carry out such tests. As a
means to cheaply assess whether a particular deviation from general relativity
can be detected, Cornish et al. and Vallisneri recently proposed an approximate
scheme to compute the Bayes factor between a general-relativity
gravitational-wave model and a model representing a class of alternative
theories of gravity parametrised by one additional parameter. This approximate
scheme is based on only two easy-to-compute quantities: the signal-to-noise
ratio of the signal and the fitting factor between the signal and the manifold
of possible waveforms within general relativity. In this work, we compare the
prediction from the approximate formula against an exact numerical calculation
of the Bayes factor using the lalinference library. We find that, using
frequency-domain waveforms, the approximate scheme predicts exact results with
good accuracy, providing the correct scaling with the signal-to-noise ratio at
a fitting factor value of 0.992 and the correct scaling with the fitting factor
at a signal-to-noise ratio of 20, down to a fitting factor of 0.9. We
extend the framework for the approximate calculation of the Bayes factor which
significantly increases its range of validity, at least to fitting factors of
0.7 or higher.Comment: 13 pages, 4 figures, accepted for publication in Classical and
Quantum Gravit
Inference Under Convex Cone Alternatives for Correlated Data
In this research, inferential theory for hypothesis testing under general
convex cone alternatives for correlated data is developed. While there exists
extensive theory for hypothesis testing under smooth cone alternatives with
independent observations, extension to correlated data under general convex
cone alternatives remains an open problem. This long-pending problem is
addressed by (1) establishing that a "generalized quasi-score" statistic is
asymptotically equivalent to the squared length of the projection of the
standard Gaussian vector onto the convex cone and (2) showing that the
asymptotic null distribution of the test statistic is a weighted chi-squared
distribution, where the weights are "mixed volumes" of the convex cone and its
polar cone. Explicit expressions for these weights are derived using the
volume-of-tube formula around a convex manifold in the unit sphere.
Furthermore, an asymptotic lower bound is constructed for the power of the
generalized quasi-score test under a sequence of local alternatives in the
convex cone. Applications to testing under order restricted alternatives for
correlated data are illustrated.Comment: 31 page
From nucleon-nucleon interaction matrix elements in momentum space to an operator representation
Starting from the matrix elements of the nucleon-nucleon interaction in
momentum space we present a method to derive an operator representation with a
minimal set of operators that is required to provide an optimal description of
the partial waves with low angular momentum. As a first application we use this
method to obtain an operator representation for the Argonne potential
transformed by means of the unitary correlation operator method and discuss the
necessity of including momentum dependent operators. The resulting operator
representation leads to the same results as the original momentum space matrix
elements when applied to the two-nucleon system and various light nuclei. For
applications in fermionic and antisymmetrized molecular dynamics, where an
operator representation of a soft but realistic effective interaction is
indispensable, a simplified version using a reduced set of operators is given
New Analysis of the Delta I = 1/2 Rule in Kaon Decays and the B_K Parameter
We present a new analysis of the Delta I = 1/2 rule in K --> pi pi decays and
the B_K parameter. We use the 1/N_c expansion within the effective chiral
lagrangian for pseudoscalar mesons and compute the hadronic matrix elements at
leading and next-to-leading order in the chiral and the 1/N_c expansions.
Numerically, our calculation reproduces the dominant Delta I = 1/2 K --> pi pi
amplitude. Our result depends only moderately on the choice of the cutoff scale
in the chiral loops. The Delta I = 3/2 amplitude emerges sufficiently
suppressed but shows a significant dependence on the cutoff. The B_K parameter
turns out to be smaller than the value previously obtained in the 1/N_c
approach. It also shows a significant dependence on the choice of the cutoff
scale. Our results indicate that corrections from higher order terms and/or
higher resonances are large for the Delta I = 3/2 K --> pi pi amplitude and the
(|Delta S| = 2) K^0 -- anti K^0 transition amplitude.Comment: 50 pages, LaTeX, 13 eps figure
Testing an Optimised Expansion on Z_2 Lattice Models
We test an optimised hopping parameter expansion on various Z_2 lattice
scalar field models: the Ising model, a spin-one model and lambda (phi)^4. We
do this by studying the critical indices for a variety of optimisation
criteria, in a range of dimensions and with various trial actions. We work up
to seventh order, thus going well beyond previous studies. We demonstrate how
to use numerical methods to generate the high order diagrams and their
corresponding expressions. These are then used to calculate results numerically
and, in the case of the Ising model, we obtain some analytic results. We
highlight problems with several optimisation schemes and show for the best
scheme that the critical exponents are consistent with mean field results to at
least 8 significant figures. We conclude that in its present form, such
optimised lattice expansions do not seem to be capturing the non-perturbative
infra-red physics near the critical points of scalar models.Comment: 47 pages, some figures in colour but will display fine in B
Survey of Different Data Dependence Analysis Techniques
Dependency analysis is a technique to detect dependencies between tasks that prevent these tasks from running in parallel. It is an important aspect of parallel programming tools. Dependency analysis techniques are used to determine how much of the code is parallelizable.
Literature shows that number of data dependence test has been proposed for parallelizing loops in case of arrays with linear subscripts, however less work has been done for arrays with nonlinear subscripts. GCD test, Banerjee method, Omega test, I-test dependence decision algorithms are used for one-dimensional arrays under constant or variable bounds. However, these approaches perform well only for nested loop with linear array subscripts. The Quadratic programming (QP) test, polynomial variable interval (PVI) test, Range test are typical techniques for nonlinear subscripts. The paper presents survey of these different data dependence analysis tests
New Optimised Estimators for the Primordial Trispectrum
Cosmic microwave background studies of non-Gaussianity involving higher-order
multispectra can distinguish between early universe theories that predict
nearly identical power spectra. However, the recovery of higher-order
multispectra is difficult from realistic data due to their complex response to
inhomogeneous noise and partial sky coverage, which are often difficult to
model analytically. A traditional alternative is to use one-point cumulants of
various orders, which collapse the information present in a multispectrum to
one number. The disadvantage of such a radical compression of the data is a
loss of information as to the source of the statistical behaviour. A recent
study by Munshi & Heavens (2009) has shown how to define the skew spectrum (the
power spectra of a certain cubic field, related to the bispectrum) in an
optimal way and how to estimate it from realistic data. The skew spectrum
retains some of the information from the full configuration-dependence of the
bispectrum, and can contain all the information on non-Gaussianity. In the
present study, we extend the results of the skew spectrum to the case of two
degenerate power-spectra related to the trispectrum. We also explore the
relationship of these power-spectra and cumulant correlators previously used to
study non-Gaussianity in projected galaxy surveys or weak lensing surveys. We
construct nearly optimal estimators for quick tests and generalise them to
estimators which can handle realistic data with all their complexity in a
completely optimal manner. We show how these higher-order statistics and the
related power spectra are related to the Taylor expansion coefficients of the
potential in inflation models, and demonstrate how the trispectrum can
constrain both the quadratic and cubic terms.Comment: 19 pages, 2 figure
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