2,367 research outputs found
General CMB and Primordial Trispectrum Estimation
We present trispectrum estimation methods which can be applied to general
non-separable primordial and CMB trispectra. We present a general optimal
estimator for the connected part of the trispectrum, for which we derive a
quadratic term to incorporate the effects of inhomogeneous noise and masking.
We describe a general algorithm for creating simulated maps with given
arbitrary (and independent) power spectra, bispectra and trispectra. We propose
a universal definition of the trispectrum parameter , so that the
integrated bispectrum on the observational domain can be consistently compared
between theoretical models. We define a shape function for the primordial
trispectrum, together with a shape correlator and a useful parametrisation for
visualizing the trispectrum. We derive separable analytic CMB solutions in the
large-angle limit for constant and local models. We present separable mode
decompositions which can be used to describe any primordial or CMB bispectra on
their respective wavenumber or multipole domains. By extracting coefficients of
these separable basis functions from an observational map, we are able to
present an efficient estimator for any given theoretical model with a
nonseparable trispectrum. The estimator has two manifestations, comparing the
theoretical and observed coefficients at either primordial or late times. These
mode decomposition methods are numerically tractable with order
operations for the CMB estimator and approximately order for the general
primordial estimator (reducing to order in both cases for a special class
of models). We also demonstrate how the trispectrum can be reconstructed from
observational maps using these methods.Comment: 38 pages, 9 figures. In v2 Figures 4-7 are altered slightly and some
extra references are included in the bibliography. v3 matches version
submitted to journal. Includes discussion of special case
Universal Non-Gaussian Initial Conditions for N-body Simulations
In this paper we present the implementation of an efficient formalism for the
generation of arbitrary non-Gaussian initial conditions for use in N-body
simulations. The methodology involves the use of a separable modal approach for
decomposing a primordial bispectrum or trispectrum. This approach allows for
the far more efficient generation of the non-Gaussian initial conditions
already described in the literature, as well as the generation for the first
time of non-separable bispectra and the special class of diagonal-free
trispectra. The modal approach also allows for the reconstruction of the
spectra from given realisations, a fact which is exploited to provide an
accurate consistency check of the simulations.Comment: 7 pages, 3 figure
Rapid Separable Analysis of Higher Order Correlators in Large Scale Structure
We present an efficient separable approach to the estimation and
reconstruction of the bispectrum and the trispectrum from observational (or
simulated) large scale structure data. This is developed from general CMB
(poly-)spectra methods which exploit the fact that the bispectrum and
trispectrum in the literature can be represented by a separable mode expansion
which converges rapidly (with terms). With an
effective grid resolution (number of particles/grid points
), we present a bispectrum estimator which requires only
operations, along with a
corresponding method for direct bispectrum reconstruction. This method is
extended to the trispectrum revealing an estimator which requires only operations. The complexity in
calculating the trispectrum in this method is now involved in the original
decomposition and orthogonalisation process which need only be performed once
for each model. However, for non-diagonal trispectra these processes present
little extra difficulty and may be performed in
operations. A discussion of how the methodology may be applied to the
quadspectrum is also given. An efficient algorithm for the generation of
arbitrary nonGaussian initial conditions for use in N-body codes using this
separable approach is described. This prescription allows for the production of
nonGaussian initial conditions for arbitrary bispectra and trispectra. A brief
outline of the key issues involved in parameter estimation, particularly in the
non-linear regime, is also given
Recommended from our members
Functional Imaging of the Outer Retinal Complex using High Fidelity Imaging Retinal Densitometry
We describe a new technique, high fidelity Imaging Retinal Densitometry (IRD), which probes the functional integrity of the outer retinal complex. We demonstrate the ability of the technique to map visual pigment optical density and synthesis rates in eyes with and without macular disease. A multispectral retinal imaging device obtained precise measurements of retinal reflectance over space and time. Data obtained from healthy controls and 5 patients with intermediate AMD, before and after photopigment bleaching, were used to quantify visual pigment metrics. Heat maps were plotted to summarise the topography of rod and cone pigment kinetics and descriptive statistics conducted to highlight differences between those with and without AMD. Rod and cone visual pigment synthesis rates in those with AMD (v = 0.043 SD 0.019 min-1 and v = 0.119 SD 0.046 min-1, respectively) were approximately half those observed in healthy controls (v = 0.079 SD 0.024 min-1 for rods and v = 0.206 SD 0.069 min-1 for cones). By mapping visual pigment kinetics across the central retina, high fidelity IRD provides a unique insight into outer retinal complex function. This new technique will improve the phenotypic characterisation, diagnosis and treatment monitoring of various ocular pathologies, including AMD
The CMB Bispectrum
We use a separable mode expansion estimator with WMAP data to estimate the
bispectrum for all the primary families of non-Gaussian models. We review the
late-time mode expansion estimator methodology which can be applied to any
non-separable primordial and CMB bispectrum model, and we demonstrate how the
method can be used to reconstruct the CMB bispectrum from an observational map.
We extend the previous validation of the general estimator using local map
simulations. We apply the estimator to the coadded WMAP 5-year data,
reconstructing the WMAP bispectrum using multipoles and
orthonormal 3D eigenmodes. We constrain all popular nearly scale-invariant
models, ensuring that the theoretical bispectrum is well-described by a
convergent mode expansion. Constraints from the local model \fnl=54.4\pm
29.4 and the equilateral model \fnl=143.5\pm 151.2 (\Fnl = 25.1\pm 26.4)
are consistent with previously published results. (Here, we use a nonlinearity
parameter \Fnl normalised to the local case, to allow more direct comparison
between different models.) Notable new constraints from our method include
those for the constant model \Fnl = 35.1 \pm 27.4 , the flattened model \Fnl
= 35.4\pm 29.2, and warm inflation \Fnl = 10.3\pm 27.2. We investigate
feature models surveying a wide parameter range in both the scale and phase,
and we find no significant evidence of non-Gaussianity in the models surveyed.
We propose a measure \barFnl for the total integrated bispectrum and find
that the measured value is consistent with the null hypothesis that CMB
anisotropies obey Gaussian statistics. We argue that this general bispectrum
survey with the WMAP data represents the best evidence for Gaussianity to date
and we discuss future prospects, notably from the Planck satellite
Platelet-rich plasmapheresis in cardiac surgery: A meta-analysis of the effect on transfusion requirements
AbstractObjective:Our purpose was to determine whether intraoperative platelet-rich plasmapheresis in cardiac surgery is effective in reducing the proportion of patients exposed to allogeneic red cell transfusions. Methods: A systematic search for prospective, randomized trials of platelet-rich plasmapheresis in cardiac surgery, using MEDLINE, HEALTHSTAR, Current Contents, “Biological Abstracts,” and EMBASE/Excerpta Medica up to August 1997, was completed. Trials were included if they reported either the proportion of patients exposed to allogeneic red cells or the units of allogeneic red cells transfused. Trials were abstracted by 2 independent investigators and the quality of trial design was assessed with the use of a validated scale. Results: Seventeen references met the inclusion criteria (1369 patients [675 control: 694 platelet-rich plasmapheresis]). Platelet-rich plasmapheresis reduced the likelihood of exposure to allogeneic red cells in cardiac surgery (odds ratio 0.44; 95% confidence interval 0.27, 0.72, P = .001). Platelet-rich plasmapheresis had a small but statistically significant effect on both the volume of blood lost in the first 24 hours (weighted mean difference –102 mL; 95% confidence interval –148, –55 mL, P < .0001) and the mean units transfused (weighted mean difference –0.33 units; 95% confidence interval –0.43, –0.23, P < .0001). However, platelet-rich plasmapheresis was only marginally effective (odds ratio 0.83, 95% confidence interval 0.34, 2.01, P = .68) for “good” quality trials, whereas it appeared very effective in trials with poor methodologic quality (odds ratio 0.33, 95% confidence interval 0.17, 0.62, P = .0007). Conclusions: Although platelet-rich plasmapheresis appeared effective in decreasing the proportion of patients receiving transfusions after cardiac operations, the quality of most of the supporting trials was low and the benefit was small in trials of good quality. Further clinical trials should be completed. (J Thorac Cardiovasc Surg 1998;116:641-7
Oscillations in the bispectrum
There exist several models of inflation that produce primordial bispectra
that contain a large number of oscillations. In this paper we discuss these
models, and aim at finding a method of detecting such bispectra in the data. We
explain how the recently proposed method of mode expansion of bispectra might
be able to reconstruct these spectra from separable basis functions. Extracting
these basis functions from the data might then lead to observational
constraints on these models.Comment: 6 pages, 2 figures, submitted to JOP: Conference Series, PASCOS 201
The Trans-Pacific Partnership Agreement: Looking Ahead to the Next Steps
Pressure has been building for the conclusion of the 12-country Trans-Pacific Partnership (TPP) negotiations. Getting the deal done is important, but the TPP is not just another free trade agreement (FTA). It represents the chance to set a trade agenda for the future across a wide range of topics for countries throughout the Asia-Pacific region. This means that the agreement should not be settled in haste. More importantly, it also means that key decisions need to be reached about broader issues related to the institutional structure of the TPP. These decisions must be made now, before the deal is closed, on issues such as how to create the TPP as a living agreement, the formation of a TPP Secretariat, and the clarification of entry conditions for future members such as the People’s Republic of China (PRC). These choices must be made deliberately and carefully even while officials are struggling with reaching closure on the most highly sensitive issues still remaining in the agreement. It will not be easy, but wise decisions are necessary now to ensure the long-term success of the TPP
- …