Non-Gaussianity from Step Features in the Inflationary Potential

We provide analytic solutions for the power spectrum and bispectrum of curvature fluctuations produced by a step feature in the inflaton potential, valid in the limit that the step is short and sharp. In this limit, the bispectrum is strongly scale dependent and its effective non-linearity attains a large oscillatory amplitude. The perturbations to the curvature power spectrum, on the other hand, remain a small component on top of the usual spectrum of fluctuations generated by slow roll. We utilize our analytic solutions to assess the observability of the predicted non-Gaussian signatures and show that, if present, only very sharp steps on scales larger than ~ 2 Gpc are likely to be able to be detected by Planck. Such features are not only consistent with WMAP7 data, but can also improve its likelihood by 2 Delta ln L ~ 12 for two extra parameters, the step location and height. If this improvement were due to a slow roll violating step as considered here, a bispectrum or corresponding polarization power spectrum detection would provide definitive checks as to its primordial origin.Comment: Typos fixed, supersedes journal versio

Efficient numerical solution of the time fractional diffusion equation by mapping from its Brownian counterpart

The solution of a Caputo time fractional diffusion equation of order $0<\alpha<1$ is expressed in terms of the solution of a corresponding integer order diffusion equation. We demonstrate a linear time mapping between these solutions that allows for accelerated computation of the solution of the fractional order problem. In the context of an $N$-point finite difference time discretisation, the mapping allows for an improvement in time computational complexity from $O\left(N^2\right)$ to $O\left(N^\alpha\right)$, given a precomputation of $O\left(N^{1+\alpha}\ln N\right)$. The mapping is applied successfully to the least-squares fitting of a fractional advection diffusion model for the current in a time-of-flight experiment, resulting in a computational speed up in the range of one to three orders of magnitude for realistic problem sizes.Comment: 9 pages, 5 figures; added references for section

Structure/function Analyses Of Sex Hormone-binding Globulin

Sex hormone-binding globulin (SHBG) is a homodimeric glycoprotein that transports sex steroids in the blood and extravascular fluids, such as seminiferous tubule fluid, where it is often referred to as androgen-binding protein (ABP). A cDNA for the human SHBG precursor polypeptide was expressed in mammalian cell lines. Recombinant human SHBG bound steroids with the same affinity and specificity as natural SHBG, and was immunologically indistinguishable from its natural counterpart. Site-directed mutagenesis of the SHBG cDNA was used to introduce amino acid substitutions that selectively removed glycosylation sites from SHBG. Analysis of these glycosylation mutants demonstrated that carbohydrates are not involved in steroid binding, but the lack of both N-linked oligosaccharides reduced the level of SHBG secretion and/or production from CHO cells. In addition, the subunit size heterogeneity associated with SHBG is due to the differential utilization of the two consensus sites for N-glycosylation, and that subunits that comprise a given dimer are glycosylated and processed in the same way. An additional N-glycosylation site associated with an electrophoretic variant of SHBG was shown to be utilized and found not to affect steroid binding. Analyses of human SHBG/rat ABP chimeras and human SHBG C-terminal truncation mutants expressed in E. coli revealed that the steroid-binding domain is located within the N-terminal 205 amino acids of human SHBG. Specific amino acid substitutions in human SHBG produced mutants with altered steroid-binding specificity and demonstrated that Lys{dollar}\sp{lcub}134{rcub}{dollar}-Met{dollar}\sp{lcub}139{rcub}{dollar} interact with the A/B ring structures of steroids, and residues in a more N-terminal location may also contact steroid ligands. Human SHBG mutants with substitutions at residues Ile{dollar}\sp{lcub}138{rcub}{dollar}-Phe{dollar}\sp{lcub}148{rcub}{dollar} are defective in their ability to dimerize, especially in the absence of steroid and/or divalent cations, but readdition of these agents restores dimer formation. These data have led us to conclude that SHBG is a modular protein comprising an N-terminal steroid-binding and dimerization domain, and a C-terminal domain(s), which contains a phylogenetically conserved N-glycosylation site that may be required for other activities, such as recognition by a plasma membrane receptor