A Comparative Study of Coq and HOL

This paper illustrates the differences between the style of theory mechanisation of Coq and of HOL. This comparative study is based on the mechanisation of fragments of the theory of computation in these systems. Examples from these implementations are given to support some of the arguments discussed in this paper. The mechanisms for specifying definitions and for theorem proving are discussed separately, building in parallel two pictures of the different approaches of mechanisation given by these systems

Cosmic Shear Systematics: Software-Hardware Balance

Cosmic shear measurements rely on our ability to measure and correct the Point Spread Function (PSF) of the observations. This PSF is measured using stars in the field, which give a noisy measure at random points in the field. Using Wiener filtering, we show how errors in this PSF correction process propagate into shear power spectrum errors. This allows us to test future space-based missions, such as Euclid or JDEM, thereby allowing us to set clear engineering specifications on PSF variability. For ground-based surveys, where the variability of the PSF is dominated by the environment, we briefly discuss how our approach can also be used to study the potential of mitigation techniques such as correlating galaxy shapes in different exposures. To illustrate our approach we show that for a Euclid-like survey to be statistics limited, an initial pre-correction PSF ellipticity power spectrum, with a power-law slope of -3 must have an amplitude at l =1000 of less than 2 x 10^{-13}. This is 1500 times smaller than the typical lensing signal at this scale. We also find that the power spectrum of PSF size \dR^2) at this scale must be below 2 x 10^{-12}. Public code available as part of iCosmo at http://www.icosmo.orgComment: 5 pages, 3 figures. Submitted to MNRA

Optimal PSF modeling for weak lensing: complexity and sparsity

We investigate the impact of point spread function (PSF) fitting errors on cosmic shear measurements using the concepts of complexity and sparsity. Complexity, introduced in a previous paper, characterizes the number of degrees of freedom of the PSF. For instance, fitting an underlying PSF with a model with low complexity will lead to small statistical errors on the model parameters, however these parameters could suffer from large biases. Alternatively, fitting with a large number of parameters will tend to reduce biases at the expense of statistical errors. We perform an optimisation of scatters and biases by studying the mean squared error of a PSF model. We also characterize a model sparsity, which describes how efficiently the model is able to represent the underlying PSF using a limited number of free parameters. We present the general case and illustrate it for a realistic example of PSF fitted with shapelet basis sets. We derive the relation between complexity and sparsity of the PSF model, signal-to-noise ratio of stars and systematic errors on cosmological parameters. With the constraint of maintaining the systematics below the statistical uncertainties, this lead to a relation between the required number of stars to calibrate the PSF and the sparsity. We discuss the impact of our results for current and future cosmic shear surveys. In the typical case where the biases can be represented as a power law of the complexity, we show that current weak lensing surveys can calibrate the PSF with few stars, while future surveys will require hard constraints on the sparsity in order to calibrate the PSF with 50 stars.Comment: accepted by A&A, 9 pages, 6 figure

Deriving Matrix Concentration Inequalities from Kernel Couplings

This paper derives exponential tail bounds and polynomial moment inequalities for the spectral norm deviation of a random matrix from its mean value. The argument depends on a matrix extension of Stein's method of exchangeable pairs for concentration of measure, as introduced by Chatterjee. Recent work of Mackey et al. uses these techniques to analyze random matrices with additive structure, while the enhancements in this paper cover a wider class of matrix-valued random elements. In particular, these ideas lead to a bounded differences inequality that applies to random matrices constructed from weakly dependent random variables. The proofs require novel trace inequalities that may be of independent interest.Comment: 29 page

Volume and surface propellant heating in an electrothermal radio-frequency plasma micro-thruster

The temporal evolution of neutral gas temperature over the first 5 min of operation for an electrothermal radio-frequency micro-thruster with nitrogen (N2) propellant was measured using rovibrational band matching of the second positive N2 system. Three distinct periods of gas heating were identified with time constants of τ 1 = 8 × 10⁻⁵ s, τ 2 = 8 s, and τ 3 = 100 s. The fast heating (τ 1) is attributed to volumetric heating processes within the discharge driven by ion-neutral collisions. The slow heating (τ 3) is from ion neutralization and vibrational de-excitation on the walls creating wall heating. The intermediate heating mechanism (τ 2) is yet to be fully identified although some theories are suggested.This research was partially funded by the Australian Space Research Program (APT project) and the Australian Research Council Discovery Project (No. DP140100571)

Non-invasive Quantification of Alveolar Morphometry Measurements in Older Never-smokers

Diffusion-weighted noble gas pulmonary magnetic resonance imaging (MRI) provides in vivo images with a contrast uniquely sensitive to molecular displacement at cellular and sub-cellular length scales. We estimated the external airway radius (R) and internal airway radius (r) of the alveolar dimensions to evaluate potential differences in acinar duct morphometries in healthy older never-smokers and compared those with a group of ex-smokers. The acinar duct and alveolar MRI morphometry results were within the physiologically-valid range of parameters. Estimated values of internal (r) and external (R) airway radius as well as alveolar sheath (h) and mean linear intercept (Lm) for individual subjects were similar with low variance. Results showed that MRI measurements of lung air space size in healthy older never-smokers were elevated compared to previous results reported in younger never-smokers, and lower than in age-matched ex-smokers (p\u3c.05). Specifically, older never-smokers had significantly lower external and internal airway radius and mean linear intercept, but higher alveolar sheath thickness, alveolar density and surface area-to-volume ratio than ex-smokers (p\u3c.05). Such results are compatible with the senile emphysematous changes to healthy parenchyma that accompany aging. These results demonstrate the potential MRI has with regards to replacing histology and lung stereology as the gold standard for measuring pulmonary acinus microstructure

The Dark UNiverse Explorer (DUNE): Proposal to ESA's Cosmic Vision

The Dark UNiverse Explorer (DUNE) is a wide-field space imager whose primary goal is the study of dark energy and dark matter with unprecedented precision. For this purpose, DUNE is optimised for the measurement of weak gravitational lensing but will also provide complementary measurements of baryonic accoustic oscillations, cluster counts and the Integrated Sachs Wolfe effect. Immediate auxiliary goals concern the evolution of galaxies, to be studied with unequalled statistical power, the detailed structure of the Milky Way and nearby galaxies, and the demographics of Earth-mass planets. DUNE is an Medium-class mission which makes use of readily available components, heritage from other missions, and synergy with ground based facilities to minimise cost and risks. The payload consists of a 1.2m telescope with a combined visible/NIR field-of-view of 1 deg^2. DUNE will carry out an all-sky survey, ranging from 550 to 1600nm, in one visible and three NIR bands which will form a unique legacy for astronomy. DUNE will yield major advances in a broad range of fields in astrophysics including fundamental cosmology, galaxy evolution, and extrasolar planet search. DUNE was recently selected by ESA as one of the mission concepts to be studied in its Cosmic Vision programme.Comment: Accepted in Experimental Astronom

Microlensing towards M31 with MDM data

We report the final analysis of a search for microlensing events in the direction of the Andromeda galaxy, which aimed to probe the MACHO composition of the M31 halo using data collected during the 1998-99 observational campaign at the MDM observatory. In a previous paper, we discussed the results from a first set of observations. Here, we deal with the complete data set, and we take advantage of some INT observations in the 1999-2000 seasons. This merging of data sets taken by different instruments turns out to be very useful, the study of the longer baseline available allowing us to test the uniqueness characteristic of microlensing events. As a result, all the candidate microlensing events previously reported turn out to be variable stars. We further discuss a selection based on different criteria, aimed at the detection of short--duration events. We find three candidates whose positions are consistent with self--lensing events, although the available data do not allow us to conclude unambiguously that they are due to microlensing.Comment: Accepted for publication in Astronomy and Astrophysic

Studies of CO oxidation on Pt/SnO2 catalyst in a surrogate CO2 laser facility

Samples of 1% Pt/SnO2 catalyst were exposed to a stoichiometric gas mixture of 1% CO and 1.2% O2 in helium over a range of flowrates from 5 to 15 sccm and temperatures from 338 to 394 Kelvin. Reaction rate constants for the catalytic oxidation of carbon monoxide and their temperature dependence were determined and compared with previous literature values