Cosmic String Power Spectrum, Bispectrum and Trispectrum

We use analytic calculations of the post-recombination gravitational effects of cosmic strings to estimate the resulting CMB power spectrum, bispectrum and trispectrum. We place a particular emphasis on multipole regimes relevant for forthcoming CMB experiments, notably the Planck satellite. These calculations use a flat sky approximation, generalising previous work by integrating string contributions from last scattering to the present day, finding the dominant contributions to the correlators for multipoles l > 50. We find a well-behaved shape for the string bispectrum (without divergences) which is easily distinguishable from the inflationary bispectra which possess significant acoustic peaks. We estimate that the nonlinearity parameter characterising the bispectrum is approximately f_NL \sim -20 (given present string constraints from the CMB power spectrum. We also apply these unequal time correlator methods to calculate the trispectrum for parrallelogram configurations, again valid over a large range of angular scales relevant for WMAP and Planck, as well as on very small angular scales. We find that, unlike the bispectrum which is suppressed by symmetry considerations, the trispectrum for cosmic strings is large. Our current estimate for the trispectrum parameter is tau_NL \sim 10^5, which may provide one of the strongest constraints on the string model as estimators for the trispectrum are developed

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 $T_{NL}$, 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 $l^5$ operations for the CMB estimator and approximately order $l^6$ for the general primordial estimator (reducing to order $l^3$ 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

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 $n_\textrm{max}={\cal{O}}(30)$ terms). With an effective grid resolution $l_\textrm{max}$ (number of particles/grid points $N=l_\textrm{max}^3$), we present a bispectrum estimator which requires only ${\cal O}(n_\textrm{max} \times l_\textrm{max}^3)$ operations, along with a corresponding method for direct bispectrum reconstruction. This method is extended to the trispectrum revealing an estimator which requires only ${\cal O}(n_\textrm{max}^{4/3} \times l_\textrm{max}^3)$ 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 ${\cal O}(l_\textrm{max}^4)$ 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

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

Oral contraceptives, hormone replacement therapy, thrombophilias and risk of venous thromboembolism: a systematic review The Thrombosis: Risk and Economic Assessment of Thrombophilia Screening (TREATS) Study

Combined oral contraceptives,oral hormone replacement therapy and thrombophilias are recognised risk factors for venous thromboembolism in women.The objective of this study was to assess the risk of thromboembolism among women with thrombophilia who are taking oral contraceptives or hormone replacement therapy, conducting a systematic review and metaanalysis. Of 201 studies identified, only nine met the inclusion criteria. Seven studies included pre-menopausal women on oral contraceptives and two studies included peri-menopausal women on hormone replacement therapy. For oral contraceptive use, significant associations of the risk of venous thromboembolism were found in women with factor V Leiden (OR 15.62; 95%CI 8.66 to 28.15); deficiencies of antithrombin (OR 12.60; 95%CI 1.37 to 115.79), protein C (OR 6.33; 95%CI 1.68 to 23.87), or protein S (OR 4.88; 95%CI 1.39 to 17.10), elevated levels of factor VIIIc (OR 8.80; 95%CI 4.13 to 18.75); and factor V Leiden and prothrombin G20210A (OR 7.85; 95%CI 1.65 to 37.41). For hormone replacement therapy, a significant association was found in women with factor V Leiden (OR 13.16; 95%CI 4.28 to 40.47).Although limited by the small number of studies, the findings of this study support the presence of interaction between thrombophilia and venous thromboembolism among women taking oral contraceptives. However, further studies are required to establish with greater confidence the associations of these, and other, thrombophilias with venous thromboembolism among hormone users

Optimization of optical data transmitters for 40-Gb/s lightwave systems using frequency resolved optical gating

The measurement technique of frequency resolved optical gating has been used to optimize the phase of a 40-GHz train of optical pulses generated using a continuous-wave laser gated with an external modulator. This technique will be vital for optimization of optical transmitters to be used in systems operating at 40 Gb/s and beyond, as standard measurement techniques will not suffice to optimize such high-speed systems

A Case Study of the Development of an eCoach

Internship is a critical feature of teacher preparation programs and can be one of the most influential experiences for teacher candidates. New technologies, such as eCoaching, demonstrate promising results in providing richer experiences to teacher candidates during internship. eCoaching allows university supervisors to provide real-time feedback on instruction and has proven effective at improving teacher change. However, eCoaching is different from traditional university supervision. In this case study, we describe the evolution of a traditional university supervisor using eCoaching for the first time and the support she needs to be effective. Implications are discussed