On Determining Minimal Spectrally Arbitrary Patterns

In this paper we present a new family of minimal spectrally arbitrary patterns which allow for arbitrary spectrum by using the Nilpotent-Jacobian method. The novel approach here is that we use the Intermediate Value Theorem to avoid finding an explicit nilpotent realization of the new minimal spectrally arbitrary patterns.Comment: 8 page

Simultaneous capacitive probe and planar laser-induced fluorescence measurements in downwards gas-liquid annular flow

Various experimental techniques are available to analyse two-phase flows. The measurement concept and the applicability can however vary greatly. Prime examples from the opposite spectrum are planar laser-induced measurements (PLIF) versus capacitive probes. PLIF is an optical technique, it is non-intrusive but optical access is necessary. PLIF based measurements are known for their high temporal and spatial resolution but require a costly set-up. In contrast, the capacitive probe is another non-intrusive technique but doesn’t require optical access. It is fairly easy to set up, robust, and is cheap to construct. To rigorously compare both techniques, simultaneous PLIF and capacitive probe measurements are made in this work. As the void fraction is one of the key parameters to classify flow regimes, both techniques are compared on the determination of the void fraction. This is done for a limited set of six annular flows. The experiments were performed in a downward annular-flow facility with demineralized water - air as working medium. The first results indicate that both techniques give similar volume averaged void fractions. The mean absolute percentage error and the maximum relative error between both techniques are 0.30% and 0.54%, respectively. The PLIF measurements confirm however to have a better spatial resolution

Constraining the Atmospheric Composition of the Day-Night Terminators of HD 189733b : Atmospheric Retrieval with Aerosols

A number of observations have shown that Rayleigh scattering by aerosols dominates the transmission spectrum of HD 189733b at wavelengths shortward of 1 $\mu$m. In this study, we retrieve a range of aerosol distributions consistent with transmission spectroscopy between 0.3-24 $\mu$m that were recently re-analyzed by Pont et al. (2013). To constrain the particle size and the optical depth of the aerosol layer, we investigate the degeneracies between aerosol composition, temperature, planetary radius, and molecular abundances that prevent unique solutions for transit spectroscopy. Assuming that the aerosol is composed of MgSiO$_3$, we suggest that a vertically uniform aerosol layer over all pressures with a monodisperse particle size smaller than about 0.1 $\mu$m and an optical depth in the range 0.002-0.02 at 1 $\mu$m provides statistically meaningful solutions for the day/night terminator regions of HD 189733b. Generally, we find that a uniform aerosol layer provide adequate fits to the data if the optical depth is less than 0.1 and the particle size is smaller than 0.1 $\mu$m, irrespective of the atmospheric temperature, planetary radius, aerosol composition, and gaseous molecules. Strong constraints on the aerosol properties are provided by spectra at wavelengths shortward of 1 $\mu$m as well as longward of 8 $\mu$m, if the aerosol material has absorption features in this region. We show that these are the optimal wavelengths for quantifying the effects of aerosols, which may guide the design of future space observations. The present investigation indicates that the current data offer sufficient information to constrain some of the aerosol properties of HD189733b, but the chemistry in the terminator regions remains uncertain.Comment: Transferred to ApJ and accepted. 11 pages, 10 figures, 1 tabl

On the potential of the EChO mission to characterise gas giant atmospheres

Space telescopes such as EChO (Exoplanet Characterisation Observatory) and JWST (James Webb Space Telescope) will be important for the future study of extrasolar planet atmospheres. Both of these missions are capable of performing high sensitivity spectroscopic measurements at moderate resolutions in the visible and infrared, which will allow the characterisation of atmospheric properties using primary and secondary transit spectroscopy. We use the NEMESIS radiative transfer and retrieval tool (Irwin et al. 2008, Lee et al. 2012) to explore the potential of the proposed EChO mission to solve the retrieval problem for a range of H2-He planets orbiting different stars. We find that EChO should be capable of retrieving temperature structure to ~200 K precision and detecting H2O, CO2 and CH4 from a single eclipse measurement for a hot Jupiter orbiting a Sun-like star and a hot Neptune orbiting an M star, also providing upper limits on CO and NH3. We provide a table of retrieval precisions for these quantities in each test case. We expect around 30 Jupiter-sized planets to be observable by EChO; hot Neptunes orbiting M dwarfs are rarer, but we anticipate observations of at least one similar planet.Comment: 22 pages, 30 figures, 4 tables. Accepted for publication in MNRA

Hypotheses Testing from Complex Survey Data Using Bootstrap Weights: A Unified Approach

Standard statistical methods that do not take proper account of the complexity of survey design can lead to erroneous inferences when applied to survey data due to unequal selection probabilities, clustering, and other design features. In particular, the actual type I error rates of tests of hypotheses based on standard tests can be much bigger than the nominal significance level. Methods that take account of survey design features in testing hypotheses have been proposed, including Wald tests and quasi-score tests that involve the estimated covariance matrices of parameter estimates. Bootstrap methods designed for survey data are often applied to estimate the covariance matrices, using the data file containing columns of bootstrap weights. Standard statistical packages often permit the use of survey weighted test statistics, and it is attractive to approximate their distributions under the null hypothesis by their bootstrap analogues computed from the bootstrap weights supplied in the data file. In this paper, we present a unified approach to the above method by constructing bootstrap approximations to weighted likelihood ratio statistics and weighted quasi-score statistics and establish the asymptotic validity of the proposed bootstrap tests. In addition, we also consider hypothesis testing from categorical data and present a bootstrap procedure for testing simple goodness of fit and independence in a two-way table. In the simulation studies, the type I error rates of the proposed approach are much closer to their nominal level compared with the naive likelihood ratio test and quasi-score test. An application to data from an educational survey under a logistic regression model is also presented

A model for correlations in stock markets

We propose a group model for correlations in stock markets. In the group model the markets are composed of several groups, within which the stock price fluctuations are correlated. The spectral properties of empirical correlation matrices reported in [Phys. Rev. Lett. {\bf 83}, 1467 (1999); Phys. Rev. Lett. {\bf 83}, 1471 (1999.)] are well understood from the model. It provides the connection between the spectral properties of the empirical correlation matrix and the structure of correlations in stock markets.Comment: two pages including one EPS file for a figur