B-type supergiants in the Small Magellanic Cloud: rotational velocities and implications for evolutionary models

High-resolution spectra for 24 SMC and Galactic B-type supergiants have been analysed to estimate the contributions of both macroturbulence and rotation to the broadening of their metal lines. Two different methodologies are considered, viz. goodness-of-fit comparisons between observed and theoretical line profiles and identifying zeros in the Fourier transforms of the observed profiles. The advantages and limitations of the two methods are briefly discussed with the latter techniques being adopted for estimating projected rotational velocities ( v sin i) but the former being used to estimate macroturbulent velocities. The projected rotational velocity estimates range from approximately 20 to 60 kms(-1), apart from one SMC supergiant, Sk 191, with a v sin i similar or equal to 90 km s(-1). Apart from Sk 191, the distribution of projected rotational velocities as a function of spectral type are similar in both our Galactic and SMC samples with larger values being found at earlier spectral types. There is marginal evidence for the projected rotational velocities in the SMC being higher than those in the Galactic targets but any differences are only of the order of 5 - 10 km s(-1), whilst evolutionary models predict differences in this effective temperature range of typically 20 to 70 km s(-1). The combined sample is consistent with a linear variation of projected rotational velocity with effective temperature, which would imply rotational velocities for supergiants of 70 kms(-1) at an effective temperature of 28 000 K ( approximately B0 spectral type) decreasing to 32 km s(-1) at 12 000 K (B8 spectral type). For all targets, the macroturbulent broadening would appear to be consistent with a Gaussian distribution ( although other distributions cannot be discounted) with an 1/e half-width varying from approximately 20 km s(-1) at B8 to 60 km s(-1) at B0 spectral types.

The VLT-FLAMES survey of massive stars: stellar parameters and rotational velocities in NGC 3293, NGC 4755 and NGC 6611

An analysis is presented of VLT-FLAMES spectroscopy for three Galactic clusters, NGC3293, NGC4755 and NGC6611. Non-LTE model atmosphere calculations have been used to estimate effective temperatures (from either the helium spectrum or the silicon ionization equilibrium) and gravities (from the hydrogen spectrum). Projected rotational velocities have been deduced from the helium spectrum (for fast and moderate rotators) or the metal line spectrum (for slow rotators). The origin of the low gravity estimates for apparently near main sequence objects is discussed and is related to the stellar rotational velocity. The atmospheric parameters have been used to estimate cluster distances (which are generally in good agreement with previous determinations) and these have been used to estimate stellar luminosities and evolutionary masses. The observed Hertzsprung-Russell diagrams are compared with theoretical predictions and some discrepancies including differences in the main sequence luminosities are discussed. Cluster ages have been deduced and evidence for non-coeval star formation is found for all three of the clusters. Projected rotational velocities for targets in the older clusters, NGC3293 and NGC4755, have been found to be systematically larger than those for the field, confirming recent results in other similar age clusters. The distribution of projected rotational velocities are consistent with a Gaussian distribution of intrinsic rotational velocities. For the relatively unevolved targets in the older clusters, NGC3293 and NGC4755, the peak of the velocity distribution would be 250 km s(-1) with a full-width-half-maximum of approximately 180 km s(-1). For NGC6611, the sample size is relatively small but implies a lower mean rotational velocity. This may be evidence for the spin-down effect due to angular momentum loss through stellar winds, although our results are consistent with those found for very young high mass stars. For all three clusters we deduce present day mass functions with Gamma-values in the range of -1.5 to -1.8, which are similar to other young stellar clusters in the Milky Way.

Barrier height variations and interface properties of PtSi/Si structures

To study some of the interfacial properties of PtSi/Si diodes, Schottky structures were fabricated on (100) crystalline silicon substrates by conventional thermal evaporation of Pt on Si followed by annealing at different temperatures (from 400 degrees C to 700 degrees C) to form PtSi. The PtSi/n-Si diodes, all yielded Schottky barrier (SB) heights that are remarkably temperature dependent. The temperature range (20-290 K) over which the I-V characteristics were measured in the present study is broader with a much lower limit (20 K), than what is usually reported in literature. These variations in the barrier height are adequately interpreted by introducing spatial inhomogeneity into the barrier potential with a Gaussian distribution having a mean barrier of 0.76 eV and a standard deviation of 30 meV. Multi-frequency capacitance-voltage measurements suggest that the barrier is primarily controlled by the properties of the silicide-silicon interface. The forward C-V characteristics, in particular, show small peaks at low frequencies that can be ascribed to interface states rather than to a series resistance effect.

Performance Analysis of Randomized Distributed Space-Time Codes over Composite Gamma/Lognormal Fading Channels

This work investigates the end-to-end performance of randomized distributed space-time codes with complex Gaussian distribution, when employed in a wireless relay network. The relaying nodes are assumed to adopt a decode-and-forward strategy and transmissions are affected by small and large scale fading phenomena. Extremely tight, analytical approximations of the end-to-end symbol error probability and of the end-to-end outage probability are derived and successfully validated through Monte-Carlo simulation. For the high signal-to-noise ratio regime, a simple, closed-form expression for the symbol error probability is further provided.

Barrier characteristics of PtSi/p-Si schottky diodes as determined from I-V-T measurements

The current-voltage-temperature characteristics of PtSi/p-Si Schottky barrier diodes were measured in the temperature range 60-115 K. Deviation of the ideality factor from unity below 80 K may be modelled using the so-called T-0 parameter with T-0 = 18 K. It is also shown that the curvature in the Richardson plots may be remedied by using the flatband rather than the zero-bias saturation current density. Physically, the departure from ideality is interpreted in terms of an inhomogeneous Schottky contact. Here we determine a mean barrier height at T = 0 K, phi(b)(-0) = 223 mV, with an (assumed) Gaussian distribution of standard deviation sigma(phi) = 12.5 mV. These data are correlated with the zero-bias barrier height, phi(j)(0) = 192 mV (at T = 90 K), the photoresponse barrier height, phi(ph) = 205 mV, and the flatband barrier height, phi(fb) = 214 mV. Finally, the temperature coefficient of the flatband barrier was found to be -0.121 mV K-1, which is approximately equal to 1/2(dE(g)(i)/dT), thus suggesting that the Fermi level at the interface is pinned to the middle of the band gap.

Polarization effects in fiber-optic communication systems

In this thesis we perform a detailed analysis of the state of polarization (SOP) of light scattering process using a concatenation of ber-coil based polarization controllers (PCs). We propose a polarization-mode dispersion (PMD) emulator, built through the concatenation of bercoil based PCs and polarization-maintaining bers (PMFs), capable of generate accurate rst- and second-order PMD statistics. We analyze the co-propagation of two optical waves inside a highbirefringence ber. The evolution along the ber of the relative SOP between the two signals is modeled by the de nition of the degree of co-polarization parameter. We validate the model for the degree of co-polarization experimentally, exploring the polarization dependence of the four-wave mixing e ect into a ber with high birefringence. We also study the interaction between signal and noise mediated by Kerr e ect in optical bers. A model accurately describing ampli ed spontaneous emission noise in systems with distributed Raman gain is derived. We show that the noise statistics depends on the propagation distance and on the signal power, and that for distances longer than 120 km and signal powers higher than 6 mW it deviates signi catively from the Gaussian distribution. We explore the all-optical polarization control process based on the stimulated Raman scattering e ect. Mapping parameters like the degree of polarization (DOP), we show that the preferred ampli cation of one particular polarization component of the signal allows a polarization pulling over a wavelength range of 60 nm. The e ciency of the process is higher close to the maximum Raman gain wavelength, where the DOP is roughly constant for a wavelength range of 15 nm. Finally, we study the polarization control in quantum key distribution (QKD) systems with polarization encoding. A model for the quantum bit error rate estimation in QKD systems with time-division multiplexing and wavelength-division multiplexing based polarization control schemes is derived.

Classification of incomplete feature vectors by radial basis function networks

The paper describes the use of radial basis function neural networks with Gaussian basis functions to classify incomplete feature vectors. The method uses the fact that any marginal distribution of a Gaussian distribution can be determined from the mean vector and covariance matrix of the joint distribution.

Practical simulation of GNSS signals in the presence of ionospheric scintillaton

We propose a low complexity technique to generate amplitude correlated time-series with Nakagami-m distribution and phase correlated Gaussian-distributed time-series, which is useful in the simulation of ionospheric scintillation effects during the transmission of GNSS signals. The method requires only the knowledge of parameters S4 (scintillation index) and σΦ (phase standard deviation) besides the definition of models for the amplitude and phase power spectra. The Zhang algorithm is used to produce Nakagami-distributed signals from a set of Gaussian autoregressive processes.

Exact Skewness-Kurtosis Tests for Multivariate Normality and Goodness-of-fit in Multivariate Regressions with Application to Asset Pricing Models

We study the problem of testing the error distribution in a multivariate linear regression (MLR) model. The tests are functions of appropriately standardized multivariate least squares residuals whose distribution is invariant to the unknown cross-equation error covariance matrix. Empirical multivariate skewness and kurtosis criteria are then compared to simulation-based estimate of their expected value under the hypothesized distribution. Special cases considered include testing multivariate normal, Student t; normal mixtures and stable error models. In the Gaussian case, finite-sample versions of the standard multivariate skewness and kurtosis tests are derived. To do this, we exploit simple, double and multi-stage Monte Carlo test methods. For non-Gaussian distribution families involving nuisance parameters, confidence sets are derived for the the nuisance parameters and the error distribution. The procedures considered are evaluated in a small simulation experi-ment. Finally, the tests are applied to an asset pricing model with observable risk-free rates, using monthly returns on New York Stock Exchange (NYSE) portfolios over five-year subperiods from 1926-1995.

Environnement local des défauts structurels et ordre à moyenne portée dans le silicium amorphe

Malgré une vaste littérature concernant les propriétés structurelles, électroniques et ther- modynamiques du silicium amorphe (a-Si), la structure microscopique de ce semi-cond- ucteur covalent échappe jusqu’à ce jour à une description exacte. Plusieurs questions demeurent en suspens, concernant par exemple la façon dont le désordre est distribué à travers la matrice amorphe : uniformément ou au sein de petites régions hautement déformées ? D’autre part, comment ce matériau relaxe-t-il : par des changements homo- gènes augmentant l’ordre à moyenne portée, par l’annihilation de défauts ponctuels ou par une combinaison de ces phénomènes ? Le premier article présenté dans ce mémoire propose une caractérisation des défauts de coordination, en terme de leur arrangement spatial et de leurs énergies de formation. De plus, les corrélations spatiales entre les défauts structurels sont examinées en se ba- sant sur un paramètre qui quantifie la probabilité que deux sites défectueux partagent un lien. Les géométries typiques associées aux atomes sous et sur-coordonnés sont extraites du modèle et décrites en utilisant les distributions partielles d’angles tétraédriques. L’in- fluence de la relaxation induite par le recuit sur les défauts structurels est également analysée. Le second article porte un regard sur la relation entre l’ordre à moyenne portée et la relaxation thermique. De récentes mesures expérimentales montrent que le silicium amorphe préparé par bombardement ionique, lorsque soumis à un recuit, subit des chan- gements structuraux qui laissent une signature dans la fonction de distribution radiale, et cela jusqu’à des distances correspondant à la troisième couche de voisins.[1, 2] Il n’est pas clair si ces changements sont une répercussion d’une augmentation de l’ordre à courte portée, ou s’ils sont réellement la manifestation d’un ordonnement parmi les angles dièdres, et cette section s’appuie sur des simulations numériques d’implantation ionique et de recuit, afin de répondre à cette question. D’autre part, les corrélations entre les angles tétraédriques et dièdres sont analysées à partir du modèle de a-Si.

Computationally Efficient Bootstrap Prediction Intervals for Returns and Volatilities in ARCH and GARCH Processes

We propose a novel, simple, efficient and distribution-free re-sampling technique for developing prediction intervals for returns and volatilities following ARCH/GARCH models. In particular, our key idea is to employ a Box–Jenkins linear representation of an ARCH/GARCH equation and then to adapt a sieve bootstrap procedure to the nonlinear GARCH framework. Our simulation studies indicate that the new re-sampling method provides sharp and well calibrated prediction intervals for both returns and volatilities while reducing computational costs by up to 100 times, compared to other available re-sampling techniques for ARCH/GARCH models. The proposed procedure is illustrated by an application to Yen/U.S. dollar daily exchange rate data.

Statistical evaluation of texture analysis from the biocrystallization method

The consumers are becoming more concerned about food quality, especially regarding how, when and where the foods are produced (Haglund et al., 1999; Kahl et al., 2004; Alföldi, et al., 2006). Therefore, during recent years there has been a growing interest in the methods for food quality assessment, especially in the picture-development methods as a complement to traditional chemical analysis of single compounds (Kahl et al., 2006). The biocrystallization as one of the picture-developing method is based on the crystallographic phenomenon that when crystallizing aqueous solutions of dihydrate CuCl2 with adding of organic solutions, originating, e.g., from crop samples, biocrystallograms are generated with reproducible crystal patterns (Kleber & Steinike-Hartung, 1959). Its output is a crystal pattern on glass plates from which different variables (numbers) can be calculated by using image analysis. However, there is a lack of a standardized evaluation method to quantify the morphological features of the biocrystallogram image. Therefore, the main sakes of this research are (1) to optimize an existing statistical model in order to describe all the effects that contribute to the experiment, (2) to investigate the effect of image parameters on the texture analysis of the biocrystallogram images, i.e., region of interest (ROI), color transformation and histogram matching on samples from the project 020E170/F financed by the Federal Ministry of Food, Agriculture and Consumer Protection(BMELV).The samples are wheat and carrots from controlled field and farm trials, (3) to consider the strongest effect of texture parameter with the visual evaluation criteria that have been developed by a group of researcher (University of Kassel, Germany; Louis Bolk Institute (LBI), Netherlands and Biodynamic Research Association Denmark (BRAD), Denmark) in order to clarify how the relation of the texture parameter and visual characteristics on an image is. The refined statistical model was accomplished by using a lme model with repeated measurements via crossed effects, programmed in R (version 2.1.0). The validity of the F and P values is checked against the SAS program. While getting from the ANOVA the same F values, the P values are bigger in R because of the more conservative approach. The refined model is calculating more significant P values. The optimization of the image analysis is dealing with the following parameters: ROI(Region of Interest which is the area around the geometrical center), color transformation (calculation of the 1 dimensional gray level value out of the three dimensional color information of the scanned picture, which is necessary for the texture analysis), histogram matching (normalization of the histogram of the picture to enhance the contrast and to minimize the errors from lighting conditions). The samples were wheat from DOC trial with 4 field replicates for the years 2003 and 2005, “market samples”(organic and conventional neighbors with the same variety) for 2004 and 2005, carrot where the samples were obtained from the University of Kassel (2 varieties, 2 nitrogen treatments) for the years 2004, 2005, 2006 and “market samples” of carrot for the years 2004 and 2005. The criterion for the optimization was repeatability of the differentiation of the samples over the different harvest(years). For different samples different ROIs were found, which reflect the different pictures. The best color transformation that shows efficiently differentiation is relied on gray scale, i.e., equal color transformation. The second dimension of the color transformation only appeared in some years for the effect of color wavelength(hue) for carrot treated with different nitrate fertilizer levels. The best histogram matching is the Gaussian distribution. The approach was to find a connection between the variables from textural image analysis with the different visual criteria. The relation between the texture parameters and visual evaluation criteria was limited to the carrot samples, especially, as it could be well differentiated by the texture analysis. It was possible to connect groups of variables of the texture analysis with groups of criteria from the visual evaluation. These selected variables were able to differentiate the samples but not able to classify the samples according to the treatment. Contrarily, in case of visual criteria which describe the picture as a whole there is a classification in 80% of the sample cases possible. Herewith, it clearly can find the limits of the single variable approach of the image analysis (texture analysis).

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Exercise sheet 8

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Stochastic modelling of rainfall from satellite data

Satellite-based rainfall monitoring is widely used for climatological studies because of its full global coverage but it is also of great importance for operational purposes especially in areas such as Africa where there is a lack of ground-based rainfall data. Satellite rainfall estimates have enormous potential benefits as input to hydrological and agricultural models because of their real time availability, low cost and full spatial coverage. One issue that needs to be addressed is the uncertainty on these estimates. This is particularly important in assessing the likely errors on the output from non-linear models (rainfall-runoff or crop yield) which make use of the rainfall estimates, aggregated over an area, as input. Correct assessment of the uncertainty on the rainfall is non-trivial as it must take account of • the difference in spatial support of the satellite information and independent data used for calibration • uncertainties on the independent calibration data • the non-Gaussian distribution of rainfall amount • the spatial intermittency of rainfall • the spatial correlation of the rainfall field This paper describes a method for estimating the uncertainty on satellite-based rainfall values taking account of these factors. The method involves firstly a stochastic calibration which completely describes the probability of rainfall occurrence and the pdf of rainfall amount for a given satellite value, and secondly the generation of ensemble of rainfall fields based on the stochastic calibration but with the correct spatial correlation structure within each ensemble member. This is achieved by the use of geostatistical sequential simulation. The ensemble generated in this way may be used to estimate uncertainty at larger spatial scales. A case study of daily rainfall monitoring in the Gambia, west Africa for the purpose of crop yield forecasting is presented to illustrate the method.