Philosophiae Doctor - PhD / The major result of this thesis is the development of a framework for the application of pair-mixtures of copulas to model asymmetric dependencies in bivariate data. The main motivation is the inadequacy of mixtures of bivariate Gaussian models which are commonly fitted to data. Mixtures of rotated single parameter Archimedean and Gaussian copulas are fitted to real data sets. The method of maximum likelihood is used for parameter estimation. Goodness-of-fit tests performed on the models giving the highest log-likelihood values show that the models fit the data well. We use mixtures of univariate Gaussian models and mixtures of regression models to investigate the existence of bimodality in the distribution of the widths of autocorrelation functions in a sample of 119 gamma-ray bursts. Contrary to previous findings, our results do not reveal any evidence of bimodality. We extend a study by Genest et al. (2012) of the power and significance levels of tests of copula symmetry, to two copula models which have not been considered previously. Our results confirm that for small sample sizes, these tests fail to maintain their 5% significance level and that the Cramer-von Mises-type statistics are the most powerful.

Archamoebae is a small group of anaerobic protists belonging to the eukaryotic supergroup Amoebozoa. Historically, they were regarded as primitively amitochondriate. However, a mitochondrial remnant has been found in some archamoebae. Phylogenetic analyses showed that Archamoebae are closely related to the aerobic slime moulds (Mycetozoa). Trophozoites of archamoebae are amoeboflagellates or aflagellated amoebae. The group includes both parasitic (Entamoeba, Endolimax and, possibly, Endamoeba and Iodamoeba) and free-living (Mastigamoeba, Mastigella, Pelomyxa) genera. The genus Mastigina comprises both endozoic and free-living representatives. Flagellated genera Mastigina, Mastigamoeba, Mastigella and Pelomyxa possess a single basal body associated with a microtubular cone which may or may not be associated with nucleus. The cone is a common feature for Archamoebae and mycetozoan slime moulds. The phylogeny of Archamoebae has not been fully elucidated yet and the taxonomy of free-living representatives is confusing. In the present study, we obtained 42 stable isolates of free-living Archamoebae. We sequenced and analyzed SSU rDNA of 15 of them. The Archamoebae split into five lineages. Based on TEM, we were able to recognize genera Mastigamoeba and Mastigella. The isolate IND8 probably represents a new...

The goal of the present thesis is to introduce on a Riemannian Spin- manifold a system of partial differential equations for spinor-valued differ- ential forms called Killing equations. We study basic properties of several types of Killing fields and relationships among them. We provide a simple construction of Killing spinor-valued forms from Killing spinors and Killing forms. We also review the construction of metric cone and discuss the re- lationship between Killing spinor-valued forms on the base manifold and parallel spinor-valued forms on the metric cone.