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This thesis investigates the mechanism of denitrification o f the Arctic lower stratosphere and the impact o f denitrification on ozone loss using the SLIMCAT chemical transport model. The development of a new microphysical model for the simulation of growth and sedimentation of large nitric acid trihydrate particles is also described. Model simulations of Arctic denitrification were carried out using thermodynamic equilibrium schemes based on the sedimentation of either nitric acid trihydrate or ice using different meteorological analyses. The severity and extent of denitrification in ice-based model runs was found to be highly sensitive to the meteorological analyses used whereas nitric acid trihydrate denitrification schemes exhibited considerably less sensitivity. The response of thermodynamic equilibrium and microphysical NAT-based denitrification to meteorological conditions has been studied in a series of short idealised simulations. It was found that microphysical denitrification was considerably more sensitive to the relative orientation of the polar vortex flow and the region of cold temperatures. A concentric vortex and cold region are required to promote the long particle growth times required for strong denitrification in the microphysical model. Reduced rates of denitrification were evident in the microphysical model at the highest altitudes. Results from the microphyical denitrification scheme were compared with in-situ and remote observations of denitrification for two recent cold Arctic winters. There was remarkable agreement between model and observations of both the magnitude and location of denitrification despite the simple volume-averaged nucleation rate used in the model. The limited range of observations did not allow further constraints to be placed on the microphysical model. Denitrification was found to enhance Arctic ozone loss by up to 30% during 1999/2000. Sensitivity studies o f the impact of denitrification on Arctic ozone loss were performed using thermodynamic nitric acid trihydrate denitrification schemes. Cumulative ozone depletion was found to increase non-linearly with increasing denitrification. Enhanced recovery of chlorine radicals to hydrogen chloride in strongly denitrified model runs offset reduced recovery to chlorine nitrate, limiting the impact of denitrification to the equivalent of 20 days additional ozone loss.

Water is the most important chemical component on Earth. Seawater distillation processes have a considerable promise as a technique suitable for producing large scale quantities of potable water from the seawater. Distillation process flowsheets consist of a number of interconnected units. The development of the mathematical model describing the behaviour of these units, and the subsequent solution of this model are fundamental steps in process flowsheeting. The first objective of this work is to develop a specialized flowsheeting program for performing design and simulation calculations for different types and configurations of seawater distillation processes. Many numerical methods have been used for solving linear and nonlinear sets of equations representing distillation processes. Most of these methods involve the direct manipulation of the mathematical model equations without exploiting the special properties, such as the sparsity and the weak nonlinearities, of these equations. The second aim of this study is to develop a new approach taking advantages of these properties. Hence, the model equations can be linearized, and grouped according to the variable type. These groups can then be solved by linear matrix technique. The performance of the developed program is investigated by solving many distillation process problems. The results from design and simulation calculations for large practical desalination plants are discussed. In addition to that the convergence characteristics of the new approach (such as stability. number of iterations. computing time. sensitivity to starting values, and general ease of use) are presented. Also. the validity of the approximation assumptions proposed to develop the new approach is examined.

This thesis is focused on sentiment analysis of unstructured text and its practical application on the real data downloaded from website Yelp.com The objectives of the theoretical part of this thesis is to sum up the information related to history, methods and possible applications of sentiment analysis. A reader is acquainted with important terms and processes of sentiment analysis. Theoretical part is focused on Naive Bayes classifier, that will be used in practical part of this thesis. In practical part there is detailed description of data set, construction and testing of model. At the end there are presented pros and cons of the chosen model and described some possibilities of its usage.

Using a multiple stage age of infection model, we derive an expression for the basic reproduction number, Ro. We apply this method to find Ro in analogous treatment models. We find, in the model without treatment, Ro depends only on the mean infective period, and not on the infective distribution. In treatment models, Ro depends on the mean infective and mean treatment period, as well as the distribution of the infective period, but not on the distribution of the treatment period. With an explicit formula for Ro and the final size relation, we provide a practical alternative to evaluating the effect of treatment and other control measures. We compare our models to previous models of SARS and TB. / Science, Faculty of / Mathematics, Department of / Graduate

Cross validation (CV) is widely used for model assessment and comparison. In this thesis, we first review and compare three v-fold CV strategies: best single CV, repeated and averaged CV and double CV. The mean squared errors of the CV strategies in estimating the best predictive performance are illustrated by using simulated and real data examples. The results show that repeated and averaged CV is a good strategy and outperforms the other two CV strategies for finite samples in terms of the mean squared error in estimating prediction accuracy and the probability of choosing an optimal model. In practice, when we need to compare many models, conducting repeated and averaged CV strategy is not computational feasible. We develop an efficient sequential methodology for model comparison based on CV. It also takes into account the randomness in CV. The number of models is reduced via an adaptive, multiplicity-adjusted sequential algorithm, where poor performers are quickly eliminated. By exploiting matching of individual observations, it is sometimes even possible to establish the statistically significant inferiority of some models with just one execution of CV. This adaptive and computationally efficient methodology is demonstrated on a large cheminformatics data set from PubChem. Cross validated mean squared error (CVMSE) is widely used to estimate the prediction mean squared error (MSE) of statistical methods. For linear models, we show how CVMSE depends on the number of folds, v, used in cross validation, the number of observations, and the number of model parameters. We establish that the bias of CVMSE in estimating the true MSE decreases with v and increases with model complexity. In particular, the bias may be very substantial for models with many parameters relative to the number of observations, even if v is large. These results are used to correct CVMSE for its bias. We compare our proposed bias correction with that of Burman (1989), through simulated and real examples. We also illustrate that our method of correcting for the bias of CVMSE may change the results of model selection. / Science, Faculty of / Statistics, Department of / Graduate

From option pricing using the Black and Scholes model, to determining the signi cance of regression coe cients in a capital asset pricing model (CAPM), the assumption of normality was pervasive throughout the eld of nance. This was despite evidence that nancial returns were non-normal, skewed and heavy- tailed. In addition to non-normality, there remained questions about the e ect of rm size on returns. Studies examining these di erences were limited to ex- amining the mean return, with respect to an asset pricing model, and did not consider higher moments. Janse van Rensburg, Sharp and Friskin (in press) attempted to address both the problem of non-normality and size simultaneously. They (Janse van Rens- burg et al in press) tted a mixture of two normal distributions, with common mean but di erent variances, to a small capitalisation portfolio and a large cap- italisation portfolio. Comparison of the mixture distributions yielded valuable insight into the di erences between the small and large capitalisation portfolios' risk. Janse van Rensburg et al (in press), however, identi ed several shortcom- ings within their work. These included data problems, such as survivorship bias and the exclusion of dividends, and the questionable use of standard statistical tests in the presence of non-normality. This study sought to correct the problems noted in the paper by Janse van Rensburg et al (in press) and to expand upon their research. To this end survivorship bias was eliminated and an e ective dividend was included into the return calculations. Weekly data were used, rather than the monthly data of Janse van Rensburg et al (in press). More portfolios, over shorter holding periods, were considered. This allowed the authors to test whether Janse van Rensburg et al's (in press) ndings remained valid under conditions di erent to their original study. Inference was also based on bootstrapped statistics, in order to circumvent problems associated with non-normality. Additionally, several di erent speci cations of the normal mixture distribution were considered, as opposed to only the two-component scale mixture. In the following, Chapter 2 provided a literature review of previous studies on return distributions and size e ects. The data, data preparation and portfolio formation were discussed in Chapter 3. Chapter 4 gave an overview of the statistical methods and tests used throughout the study. The empirical results of these tests, prior to risk adjustment, were presented in Chapter 5. The impact of risk adjustment on the distribution of returns was documented in Chapter 6. The study ended, Chapter 7, with a summary of the results and suggestions for future research.

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