A Stein characterisation of the generalized hyperbolic distribution

The generalized hyperbolic (GH) distributions form a five parameter family of probability distributions that includes many standard distributions as special or limiting cases, such as the generalized inverse Gaussian distribution, Student's $t$-distribution and the variance-gamma distribution, and thus the normal, gamma and Laplace distributions. In this paper, we consider the GH distribution in the context of Stein's method. In particular, we obtain a Stein characterisation of the GH distribution that leads to a Stein equation for the GH distribution. This Stein equation reduces to the Stein equations from the current literature for the aforementioned distributions that arise as limiting cases of the GH superclass.Comment: 19 pages, to appear in ESAIM: Probability and Statistics, 2017

Commodity Trading Advisor Indexes And Alpha Generation Relationships

This research investigates the trend following relationships between Commodity Trading Advisor (CTA) Indexes and a widely known trend following proxy Index using a database covering 21 years with 24 CTA, Managed Futures, and Hedge Fund (that can trade CTA-like) Indexes.  The trend following relationships are tested using a modification of the Methodology employed by Baesel, Gonzalez-Heres, Chen, & Shin (2012).  A unique Alpha adjustment is proposed to include the traditional Alpha plus or minus a reward or penalty for displaying relationships to the larger positive and negative returns of the trend following Index proxy.  Results for the first sample period show evidence of at least some association of the returns of the trend following proxy to those of the individual CTA Indexes; however, most of the Indexes showed little to no statistical support for much traditional or adjusted Total Alpha generation.  For the second sample period the regression results show that almost none of the Indexes had a statistically significant association with the monthly total returns of the trend following proxy Index.  Instead, generally all of the Indexes showed the impact of the larger monthly returns of the trend following proxy Index such that the Alpha adjustments overall were positive and, on average, generated approximately 50% of the Total Alpha of the individual CTA Indexes

The M33 Globular Cluster System with PAndAS Data: The Last Outer Halo Cluster?

We use CFHT/MegaCam data to search for outer halo star clusters in M33 as part of the Pan-Andromeda Archaeological Survey (PAndAS). This work extends previous studies out to a projected radius of 50 kpc and covers over 40 square degrees. We find only one new unambiguous star cluster in addition to the five previously known in the M33 outer halo (10 kpc <= r <= 50 kpc). Although we identify 2440 cluster candidates of various degrees of confidence from our objective image search procedure, almost all of these are likely background contaminants, mostly faint unresolved galaxies. We measure the luminosity, color and structural parameters of the new cluster in addition to the five previously-known outer halo clusters. At a projected radius of 22 kpc, the new cluster is slightly smaller, fainter and redder than all but one of the other outer halo clusters, and has g' ~ 19.9, (g'-i') ~ 0.6, concentration parameter c ~ 1.0, a core radius r_c ~ 3.5 pc, and a half-light radius r_h ~ 5.5 pc. For M33 to have so few outer halo clusters compared to M31 suggests either tidal stripping of M33's outer halo clusters by M31, or a very different, much calmer accretion history of M33.Comment: 37 pages, 9 figures. Accepted by the Astrophysical Journa

The large-scale structure of the halo of the Andromeda Galaxy Part I: global stellar density, morphology and metallicity properties

We present an analysis of the large-scale structure of the halo of the Andromeda galaxy, based on the Pan-Andromeda Archeological Survey (PAndAS), currently the most complete map of resolved stellar populations in any galactic halo. Despite copious substructure, the global halo populations follow closely power law profiles that become steeper with increasing metallicity. We divide the sample into stream-like populations and a smooth halo component. Fitting a three-dimensional halo model reveals that the most metal-poor populations ([Fe/H]<-1.7) are distributed approximately spherically (slightly prolate with ellipticity c/a=1.09+/-0.03), with only a relatively small fraction (42%) residing in discernible stream-like structures. The sphericity of the ancient smooth component strongly hints that the dark matter halo is also approximately spherical. More metal-rich populations contain higher fractions of stars in streams (86% for [Fe/H]>-0.6). The space density of the smooth metal-poor component has a global power-law slope of -3.08+/-0.07, and a non-parametric fit shows that the slope remains nearly constant from 30kpc to 300kpc. The total stellar mass in the halo at distances beyond 2 degrees is 1.1x10^10 Solar masses, while that of the smooth component is 3x10^9 Solar masses. Extrapolating into the inner galaxy, the total stellar mass of the smooth halo is plausibly 8x10^9 Solar masses. We detect a substantial metallicity gradient, which declines from [Fe/H]=-0.7 at R=30kpc to [Fe/H]=-1.5 at R=150kpc for the full sample, with the smooth halo being 0.2dex more metal poor than the full sample at each radius. While qualitatively in-line with expectations from cosmological simulations, these observations are of great importance as they provide a prototype template that such simulations must now be able to reproduce in quantitative detail.Comment: 21 pages, 17 figures, accepted for publication in the Astrophysical Journa

Uncertainty in Inverted Pendulum Thrust Measurements

An uncertainty analysis of a common configuration of electric propulsion thrust stand is presented. The analysis applies to inverted pendulum thrust stands operating in a null-coil configuration with in-situ calibration. Several sources of bias and precision uncertainty are discussed, propagated, and combined to form conservative estimates of the relative and absolute thrust uncertainties. A case study of the NASA Glenn Research Center Vacuum Facility 6 thrust stand is presented. For the thruster investigated, the uncertainty was estimated to be 6.9mN over the entire span of thrust. This uncertainty represents a maximum instrument bias introduced by the thrust stand. The paper does not address repeatability of actual thrust measurements, as this is generally beyond the influence of the thrust stand and can be dependent on a large number of factors

Molecular Distributions in Gene Regulatory Dynamics

We show how one may analytically compute the stationary density of the distribution of molecular constituents in populations of cells in the presence of noise arising from either bursting transcription or translation, or noise in degradation rates arising from low numbers of molecules. We have compared our results with an analysis of the same model systems (either inducible or repressible operons) in the absence of any stochastic effects, and shown the correspondence between behaviour in the deterministic system and the stochastic analogs. We have identified key dimensionless parameters that control the appearance of one or two steady states in the deterministic case, or unimodal and bimodal densities in the stochastic systems, and detailed the analytic requirements for the occurrence of different behaviours. This approach provides, in some situations, an alternative to computationally intensive stochastic simulations. Our results indicate that, within the context of the simple models we have examined, bursting and degradation noise cannot be distinguished analytically when present alone.Comment: 14 pages, 12 figures. Conferences: "2010 Annual Meeting of The Society of Mathematical Biology", Rio de Janeiro (Brazil), 24-29/07/2010. "First International workshop on Differential and Integral Equations with Applications in Biology and Medicine", Aegean University, Karlovassi, Samos island (Greece), 6-10/09/201

Observing the Reionization Epoch Through 21 Centimeter Radiation

We study the observability of the reionization epoch through the 21 cm hyperfine transition of neutral hydrogen. We use a high-resolution cosmological simulation (including hydrodynamics) together with a fast radiative transfer algorithm to compute the evolution of 21 cm emission from the intergalactic medium (IGM) in several different models of reionization. We show that the mean brightness temperature of the IGM drops from dT_b~25 mK to dT_b~0.01 mK during overlap (over a frequency interval of ~25 MHz), while the root mean square brightness temperature fluctuations on small scales drop abruptly from ~10 mK before overlap to ~0.1 mK at the end of overlap. We show that 21 cm observations can efficiently discriminate models with a single early reionization epoch from models with two distinct reionization episodes.Comment: 10 pages, 7 figures, submitted to MNRA

PAndAS in the mist: The stellar and gaseous mass within the halos of M31 and M33

Large scale surveys of the prominent members of the Local Group have provided compelling evidence for the hierarchical formation of massive galaxies, revealing a wealth of substructure that is thought to be the debris from ancient and on-going accretion events. In this paper, we compare two extant surveys of the M31-M33 subgroup of galaxies; the Pan-Andromeda Archaeological Survey (PAndAS) of the stellar structure, and a combination of observations of the HI gaseous content, detected at 21cm. Our key finding is a marked lack of spatial correlation between these two components on all scales, with only a few potential overlaps between stars and gas.The paucity of spatial correlation significantly restricts the analysis of kinematic correlations, although there does appear to the HI kinematically associated with the Giant Stellar Stream where it passes the disk of M31. These results demonstrate that that different processes must significantly influence the dynamical evolution of the stellar and HI components of substructures, such as ram pressure driving gas away from a purely gravitational path. Detailed modelling of the offset between the stellar and gaseous substructure will provide a determination of the properties of the gaseous halo of M31 and M33.Comment: 11 pages, 6 figures. Accepted for publication in the Astrophysical Journal. Figure quality reduced. High quality version available at http://www.physics.usyd.edu.au/~gfl/Arxiv_Papers/PAndAS_Mist