Gauge-Fixing and Residual Symmetries in Gauge/Gravity Theories with Extra Dimensions

We study compactified pure gauge/gravitational theories with gauge-fixing terms and show that these theories possess quantum mechanical SUSY-like symmetries between unphysical degrees of freedom. These residual symmetries are global symmetries and generated by quantum mechanical N=2 supercharges. Also, we establish new one-parameter family of gauge choices for higher-dimensional gravity, and calculate as a check of its validity one graviton exchange amplitude in the lowest tree-level approximation. We confirm that the result is indeed $\xi$-independent and the cancellation of the $\xi$-dependence is ensured by the residual symmetries. We also give a simple interpretation of the vDVZ-discontinuity, which arises in the lowest tree-level approximation, from the supersymmetric point of view.Comment: REVTeX4, 17 pages, 1 figur

Dynamical Shakeup of Planetary Systems II. N-body simulations of Solar System terrestrial planet formation induced by secular resonance sweeping

We revisit the "dynamical shakeup" model of Solar System terrestrial planet formation, wherein the whole process is driven by the sweeping of Jupiter's secular resonance as the gas disk is removed. Using a large number of 0.5 Gyr-long N-body simulations, we investigate the different outcomes produced by such a scenario. We confirm that in contrast to existing models, secular resonance sweeping combined with tidal damping by the disk gas can reproduce the low eccentricities and inclinations, and high radial mass concentration, of the Solar System terrestrial planets. At the same time, this also drives the final assemblage of the planets on a timescale of several tens of millions of years, an order of magnitude faster than inferred from previous numerical simulations which neglected these effects, but possibly in better agreement with timescales inferred from cosmochemical data. In addition, we find that significant delivery of water-rich material from the outer Asteroid Belt is a natural byproduct.Comment: To appear in Ap

On inversions and Doob hh-transforms of linear diffusions

Let $X$ be a regular linear diffusion whose state space is an open interval $E\subseteq\mathbb{R}$. We consider a diffusion $X^*$ which probability law is obtained as a Doob $h$-transform of the law of $X$, where $h$ is a positive harmonic function for the infinitesimal generator of $X$ on $E$. This is the dual of $X$ with respect to $h(x)m(dx)$ where $m(dx)$ is the speed measure of $X$. Examples include the case where $X^*$ is $X$ conditioned to stay above some fixed level. We provide a construction of $X^*$ as a deterministic inversion of $X$, time changed with some random clock. The study involves the construction of some inversions which generalize the Euclidean inversions. Brownian motion with drift and Bessel processes are considered in details.Comment: 19 page

Spectral properties on a circle with a singularity

We investigate the spectral and symmetry properties of a quantum particle moving on a circle with a pointlike singularity (or point interaction). We find that, within the U(2) family of the quantum mechanically allowed distinct singularities, a U(1) equivalence (of duality-type) exists, and accordingly the space of distinct spectra is U(1) x [SU(2)/U(1)], topologically a filled torus. We explore the relationship of special subfamilies of the U(2) family to corresponding symmetries, and identify the singularities that admit an N = 2 supersymmetry. Subfamilies that are distinguished in the spectral properties or the WKB exactness are also pointed out. The spectral and symmetry properties are also studied in the context of the circle with two singularities, which provides a useful scheme to discuss the symmetry properties on a general basis.Comment: TeX, 26 pages. v2: one reference added and two update

Regulation of Calcium-Permeable TRPV2 Channel by Insulin in Pancreatic β-Cells

OBJECTIVE—Calcium-permeable cation channel TRPV2 is expressed in pancreatic β-cells. We investigated regulation and function of TRPV2 in β-cells

The Photoeccentric Effect and Proto-Hot Jupiters I. Measuring photometric eccentricities of individual transiting planets

Exoplanet orbital eccentricities offer valuable clues about the history of planetary systems. Eccentric, Jupiter-sized planets are particularly interesting: they may link the "cold" Jupiters beyond the ice line to close-in hot Jupiters, which are unlikely to have formed in situ. To date, eccentricities of individual transiting planets primarily come from radial velocity measurements. Kepler has discovered hundreds of transiting Jupiters spanning a range of periods, but the faintness of the host stars precludes radial velocity follow-up of most. Here we demonstrate a Bayesian method of measuring an individual planet's eccentricity solely from its transit light curve using prior knowledge of its host star's density. We show that eccentric Jupiters are readily identified by their short ingress/egress/total transit durations -- part of the "photoeccentric" light curve signature of a planet's eccentricity --- even with long-cadence Kepler photometry and loosely-constrained stellar parameters. A Markov Chain Monte Carlo exploration of parameter posteriors naturally marginalizes over the periapse angle and automatically accounts for the transit probability. To demonstrate, we use three published transit light curves of HD 17156 b to measure an eccentricity of e = 0.71 +0.16/-0.09, in good agreement with the discovery value e = 0.67+/-0.08 based on 33 radial-velocity measurements. We present two additional tests using actual Kepler data. In each case the technique proves to be a viable method of measuring exoplanet eccentricities and their confidence intervals. Finally, we argue that this method is the most efficient, effective means of identifying the extremely eccentric, proto hot Jupiters predicted by Socrates et al. (2012).Comment: ApJ, 756, 122. Received 2012 April 5; accepted 2012 July 9; published 2012 August 2

Natural boundaries for the Smoluchowski equation and affiliated diffusion processes

The Schr\"{o}dinger problem of deducing the microscopic dynamics from the input-output statistics data is known to admit a solution in terms of Markov diffusions. The uniqueness of solution is found linked to the natural boundaries respected by the underlying random motion. By choosing a reference Smoluchowski diffusion process, we automatically fix the Feynman-Kac potential and the field of local accelerations it induces. We generate the family of affiliated diffusions with the same local dynamics, but different inaccessible boundaries on finite, semi-infinite and infinite domains. For each diffusion process a unique Feynman-Kac kernel is obtained by the constrained (Dirichlet boundary data) Wiener path integration.As a by-product of the discussion, we give an overview of the problem of inaccessible boundaries for the diffusion and bring together (sometimes viewed from unexpected angles) results which are little known, and dispersed in publications from scarcely communicating areas of mathematics and physics.Comment: Latex file, Phys. Rev. E 49, 3815-3824, (1994

A novel targeted/untargeted GC-Orbitrap metabolomics methodology applied to Candida albicans and Staphylococcus aureus biofilms

Introduction: Combined infections from Candida albicans and Staphylococcus aureus are a leading cause of death in the developed world. Evidence suggests that Candida enhances the virulence of Staphylococcus—hyphae penetrate through tissue barriers, while S. aureus tightly associates with the hyphae to obtain entry to the host organism. Indeed, in a biofilm state, C. albicans enhances the antimicrobial resistance characteristics of S. aureus. The association of these microorganisms is also associated with significantly increased morbidity and mortality. Due to this tight association we hypothesised that metabolic effects were also in evidence. Objectives: To explore the interaction, we used a novel GC-Orbitrap-based mass spectrometer, the Q Exactive GC, which combines the high peak capacity and chromatographic resolution of gas chromatography with the sub-ppm mass accuracy of an Orbitrap system. This allows the capability to leverage the widely available electron ionisation libraries for untargeted applications, along with expanding accurate mass libraries and targeted matches based around authentic standards. Methods: Optimised C. albicans and S. aureus mono- and co-cultured biofilms were analysed using the new instrument in addition to the fresh and spent bacterial growth media. Results: The targeted analysis experiment was based around 36 sugars and sugar phosphates, 22 amino acids and five organic acids. Untargeted analysis resulted in the detection of 465 features from fresh and spent medium and 405 from biofilm samples. Three significantly changing compounds that matched to high scoring library fragment patterns were chosen for validation. Conclusion: Evaluation of the results demonstrates that the Q Exactive GC is suitable for metabolomics analysis using a targeted/untargeted methodology. Many of the results were as expected: e.g. rapid consumption of glucose and fructose from the medium regardless of the cell type. Modulation of sugar-phosphate levels also suggest that the pentose phosphate pathway could be enhanced in the cells from co-cultured biofilms. Untargeted metabolomics results suggested significant production of cell-wall biosynthesis components and the consumption of non-proteinaceous amino-acids

No cosmological domain wall problem for weakly coupled fields

After inflation occurs, a weakly coupled scalar field will in general not be in thermal equilibrium but have a distribution of values determined by the inflationary Hubble parameter. If such a field subsequently undergoes discrete symmetry breaking, then the different degenerate vacua may not be equally populated so the domain walls which form will be `biased' and the wall network will subsequently collapse. Thus the cosmological domain wall problem may be solved for sufficiently weakly coupled fields in a post-inflationary universe. We quantify the criteria for determining whether this does happen, using a Higgs-like potential with a spontaneously broken $Z_2$ symmetry.Comment: 17 pages, 4 figures (Revtex), clarifying Comments added in Introduction; to appear in Phys. Rev

The Doppler Shadow of WASP-3b: A tomographic analysis of Rossiter-McLaughlin observations

Hot-Jupiter planets must form at large separations from their host stars where the temperatures are cool enough for their cores to condense. They then migrate inwards to their current observed orbital separations. Different theories of how this migration occurs lead to varying distributions of orbital eccentricity and the alignment between the rotation axis of the star and the orbital axis of the planet. The spin-orbit alignment of a transiting system is revealed via the Rossiter-McLaughlin effect, which is the anomaly present in the radial velocity measurements of the rotating star during transit due to the planet blocking some of the starlight. In this paper we aim to measure the spin-orbit alignment of the WASP-3 system via a new way of analysing the Rossiter-McLaughlin observations. We apply a new tomographic method for analysing the time variable asymmetry of stellar line profiles caused by the Rossiter-McLaughlin effect. This new method eliminates the systematic error inherent in previous methods used to analyse the effect. We find a value for the projected stellar spin rate of v sin i = 13.9 \pm 0.03 km/s which is in agreement with previous measurements but has a much higher precision. The system is found to be well aligned which favours an evolutionary history for WASP-3b involving migration through tidal interactions with a protoplanetary disc. Using gyrochronology we estimate the age of the star to be ~300 Myr with an upper limit of 2 Gyr from comparison with isochrones.Comment: Accepted for publication in A&A, 8 pages, 4 figures, 2 table