O mecanismo de divisão mais comum entre procariotos é a divisão binária, na qual a célula- mãe reparte seu genoma e conteúdo citoplasmático de forma igual entre duas células filhas. Esse processo é mediado por um complexo protéico especializado, chamado divisoma, composto por cerca de 20 proteínas, que promovem a constrição da parede celular e membrana citoplasmática, formando o septo de divisão. O complexo é organizado em torno do anel Z, uma estrutura em anel composta pela proteína FtsZ, um homólogo de tubulina presente na maioria dos procariotos e em algumas organelas de eucariotos. Partindo de um levantamento detalhado da distribuição dos genes do divisoma em genomas completos de procariotos, aplicamos métodos de máxima verossimilhança para inferência de estados ancestrais e reconstruímos o conteúdo gênico do divisoma no ultimo ancestral comum das bactérias atuais. Estendendo essas análises com a aplicação de métodos filogenéticos, inferimos os eventos responsáveis pelas variações de composição deste complexo, observadas entre os diferentes grupos de bactérias. Nossos resultados mostram que o último ancestral comum de todas as bactérias já possuía a maior parte dos componentes conhecidos do divisoma, sugerindo a existência de uma parede de peptideoglicano e a presença de um aparato molecular tão ou mais complexo que o observado nas linhagens atuais, incluindo a presença de componentes considerados acessórios e de distribuição relativamente restrita, como as proteínas envolvidas na localização do anel Z (sistema Min) e alguns efetores positivos da polimerização de FtsZ. Observamos também que a evolução do complexo não foi muito afetada por eventos de transferência lateral, mas apresenta vários exemplos de perda de genes, em especial em linhagens com genoma reduzido, o que sugere a redundância de vários componentes já presentes no ancestral e a freqüente redução da complexidade, pelo menos dos componentes centrais do divisoma. Episódios de expansão de famílias de componentes do divisoma em linhagens específicas e os mecanismos evolutivos responsáveis pela incorporação de tais variações são discutidos. A caracterização da história evolutiva detalhada do divisoma, aqui apresentada, poderá servir como ponto de partida para novas análises evolutivas e como base para elaboração de experimentos funcionais. / The most common cell division mechanism among prokaryotes is binary fission, where a mother cell partitions its cytoplasm and genome equally among two daughter cells. This process is mediated by a specialized protein complex, known as the divisome, composed of around 20 proteíns, that promotes constriction of the cell wall and cytoplasmic membrane, thus forming the division septa. The complex is organized around the Z-ring, a ring-shaped struture composed by FtsZ, a tubulin homolog present in most prokaryotes and some eukaryotic organelles. After a detailed revision of the distribution of divisome genes among completely sequenced prokaryotic genomes, we applied maximum likelihood methods for the inference of ancestral states and reconstructed the gene content of the divisome in the last common ancestor of all extant bacteria. We then performed phylogeneticanalysis of all cell division genes and inferred the series of events responsible for the observed variations of the complex´s composition among bactérial lineages and their common ancestor. Our results show that the last common ancestor of all bacteria already possessed most of the known divisome components, thus suggesting the existence of a peptidoglycan cell wall and the presence of a molecular apparatus, perhaps more complex than those found in extant bacteria, including the presence of some accessory components with a somewhat restricted distribution, like the proteíns involved in the localization of the Z-ring (Min sistem) and some positive effectors os FtsZ polimerization. We also observed that the complex´s evolution was almost never the subject of horizontasl gene transfer events, but shows several examples of gene loss, specially in lineages displaying clear signs of genome reduction, thus suggesting the redundancy of several components in the ancestral divisome and a certain degree complexity reduction, at least for core components of the divisome. Lineage specific expansion of divisome component and the evolutionary mechanisms behind such processes are discussed. This characterization of the detailed evolutionary history of the divisome might serve as a starting point for new evolutionary analysis and as a basis for the design of functional experiments.

Tato diplomová práce se zabývá odhadováním matice intenzit Markovova pro- cesu se spojitým časem na základě diskrétně pozorovaných dat. Začátek práce je věnován jednoduššímu odhadu ze spojité trajektorie pomocí metody maximální věrohodnosti. Dále je zde popsán odhad z diskrétní trajektorie přes výpočet ma- tice pravděpodobností přechodu. Následně je velmi podrobně rozebrán EM al- goritmus, který předchozí odhad zpřesňuje. Na závěr teoretické části je uvedena metoda odhadu zvaná Monte Carlo Markov Chain. Všechny postupy jsou zároveň implementovány v počítačovém softwaru a prezentace jejich výsledk· je obsahem druhé části práce. V té jsou porovnané odhady pro denní, týdenní a měsíční po- zorování a také pro pětiletou a desetiletou pozorovanou trajektorii. K výsledk·m jsou připojeny odhady rozptyl· a intervaly spolehlivosti. 1

This work is devoted to seeking methods for analysis of survival data with the Aalen model under special circumstances. We supposed, that all regression functions and all covariates of the observed individuals were nonnegative and we named this class of models monotone Aalen models. To find estimators of the unknown regres- sion functions we considered three maximum likelihood based approaches, namely the nonparametric maximum likelihood method, the Bayesian analysis using Beta processes as the priors for the unknown cumulative regression functions and the Bayesian analysis using a correlated prior approach, where the regression functions were supposed to be jump processes with a martingale structure.

>Magister Scientiae - MSc / Estimation of population distributions, from samples that are contaminated by measurement errors, is a common problem. This study considers the problem of estimating the population distribution of independent random variables Xi, from error-contaminated samples ~i (.j = 1, ... , n) such that Yi = Xi + f·.i, where E is the measurement error, which is assumed independent of X. The measurement error ( is also assumed to be normally distributed. Since the observed distribution function is a convolution of the error distribution with the true underlying distribution, estimation of the latter is often referred to as a deconvolution problem. A thorough study of the relevant deconvolution literature in statistics is reported. We also deal with the specific case when X is assumed to follow a truncated Pareto form. If observations are subject to Gaussian errors, then the observed Y is distributed as the convolution of the finite-support Pareto and Gaussian error distributions. The convolved probability density function (PDF) and cumulative distribution function (CDF) of the finite-support Pareto and Gaussian distributions are derived. The intention is to draw more specific connections bet.ween certain deconvolution methods and also to demonstrate the application of the statistical theory of estimation in the presence of measurement error. A parametric methodology for deconvolution when the underlying distribution is of the Pareto form is developed. Maximum likelihood estimation (MLE) of the parameters of the convolved distributions is considered. Standard errors of the estimated parameters are calculated from the inverse Fisher's information matrix and a jackknife method. Probability-probability (P-P) plots and Kolmogorov-Smirnov (K-S) goodnessof- fit tests are used to evaluate the fit of the posited distribution. A bootstrapping method is used to calculate the critical values of the K-S test statistic, which are not available. Simulated data are used to validate the methodology. A real-life application of the methodology is illustrated by fitting convolved distributions to astronomical data

Statistical inference is a tool for creating models that can accurately display real-world events. Special importance is given to the financial methods that model risk and large price movements. A parameter that describes tail heaviness, and risk overall, is α. This research finds a representative distribution that models α. The absolute value of standardized stock returns from the Center for Research on Security Prices are used in this research. The inference is performed using R. Approximations for α are found using the ptsuite package. The GAMLSS package employs maximum likelihood estimation to estimate distribution parameters using the CRSP data. The distributions are selected by using AIC and worm plots. The Skew t family is found to be representative for the parameter α based on subsets of the CRSP data. The Skew t type 2 distribution is robust for multiple subsets of values calculated from the CRSP stock return data.

This dissertation examines a number of issues related to Static and Dynamic Student t Regression Models. The Static Student t Regression Model is derived and transformed to an operational form. The operational form is then examined in a series of Monte Carlo experiments. The model is judged based on its usefulness for estimation and testing and its ability to model the heteroskedastic conditional variance. It is also compared with the traditional Normal Linear Regression Model. Subsequently the analysis is broadened to a dynamic setup. The Student t Autoregressive Model is derived and a number of its operational forms are considered. Three forms are selected for a detailed examination in a series of Monte Carlo experiments. The models’ usefulness for estimation and testing is evaluated, as well as their ability to model the conditional variance. The models are also compared with the traditional Dynamic Linear Regression Model. / Ph. D.

Nous interagissons quotidiennement avec une multitude de matériaux et nous pouvons sans effort identifier les différents matériaux. Nous qualifions facilement des caractéristiques à des matériaux particuliers comme matte, doux, dur, lisse, brillant, par exemple. Ces caractéristiques sont basées sur l’aspect visuel du matériau et les estimations des propriétés physiques sous-jacentes du système visuel. Cependant, la perception est un problème mathématiquement sous-constraint. La quantité de lumière atteignant notre œil dépend des propriétés de réflectance de la matière, l’éclairage de la scène et la géométrie des objets. Estimer les propriétés intrinsèques des matériaux nécessite une clarification de ces différents éléments les uns des autres. Pour estimer propriétés, intrinsèques des matériaux, il faut les étudier indépendamment les uns des autres. Dans cette thèse, j’étudie l’influence d’une propriété intrinsèque particulière : les réflexions spéculaires. J’étudie l’influence du contexte sur la brillance perçue et le rôle des autres matériaux dans la scène observée. D’autres matériaux pourraient fournir des informations supplémentaires sur les caractéristiques de la scène qui guident et façonnent le percept final. Nos résultats expérimentaux confirment que : 1. La perception de la brillance est influencée par le point de vue et la direction d’illumination. La brillance perçue est bien corrélée avec les propriétés des réflexions spéculaires sur la surface. 2. La brillance perçue est largement affectée par d’autres matériaux sur la surface indiquant que les participants prennent les informations d’autres matériaux en compte. 3. La procédure d’estimation conjointe du maximum de vraisemblance peut être utilisées pour quantifier précisément les effets contextuels dans la perception matérielle. La luminance et interagissent brillant physique et en même temps une influence sur la perception de l’autre. En conclusion, cette thèse met en évidence l’importance du contexte sur la brillance perçue. Je soutiens que la définition de constance de brillance néglige largement l’influence du contexte. La capacité du système visuel pour récupérer la réflectance de surface a été largement testée et une absence de constance de brillance ont été trouvé. Cependant, le jugement d’une seule surface dans l’isolement ne correspond pas à une tâche naturelle. D’autres matériaux et objets de la scène apportent des informations supplémentaires sur l’environnement au système visuel. Le percept final de la brillance est formé par des informations disponibles à partir de ces matériaux dans la même scène. / We interact with a multitude of different materials on a daily basis and we can effortless identify different materials. We easily add labels to particular materials like soft, hard, smooth, shiny, matte, for example. These labels are based on the visual appearances of the materials and the visual system's estimations of the underlying physical properties. However, mathematically material perception is an underconstrained problem. The light reaching our eye depends on the reflectance properties of the material, the illumination in the scene and the object's geometry. Estimating the intrinsic properties of materials requires to disambiguate these different factors from one another. In this thesis I will focus on one particular intrinsic property: Gloss. I will focus on the influence of the context onto perceived gloss and the role of other materials in the observed scene. Additional materials might provide supplementary information about the scene characteristics that guide and shape the final percept. Our experimental results confirm that: 1. Gloss perception is influenced by the viewpoint and the illumination direction. Perceived gloss correlates well with simple highlight properties on the surface. 2. Perceived gloss is largely influenced by other materials on the surface. Surfaces with two materials generate contrasting perceptual effects. 3. Maximum likelihood conjoint measurements can be used to precisely quantify contextual effects in material perception. Both, luminance and physical gloss interact and simultaneously influence each other. In conclusion, this thesis highlights the importance of the context onto perceived gloss. I argue that the definition of gloss constancy broadly neglects the influence of the context. The visual system's ability to recover the surface reflectance has extensively been tested and lacks of gloss constancy have been found. However, the judgement of a single surface in isolation does not correspond to a natural task. Other materials and objects in the scene provide the visual system with rich information about the environment (e.g. the illumination) and the final percept of the surface is formed by the additional information from these materials in the same scene.

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Ku-band dual-polarization radar backscatter measurements from the SeaWinds on QuikScat scatterometer and microwave radiometer measurements from the Special Sensor Microwave/Imager (SSM/I) are used to determine periods of surface melt and freeze in the Antarctic ice-shelves. The normalized radar backscatter (sigma-0) and backscatter polarization ratio (PR) are used in the maximum likelihood estimation of the ice-state. This method is used to infer the daily ice-surface conditions for 25 selected study points located on the Ronne, Ross, Larsen, Fimbul, Amery, and Shackleton Ice-shelves. The temporal and spatial variations of the radar response are also observed for various neighborhood sizes surrounding each given point during the study period. Criteria for determining the dates of melt-onset and freeze-up for each Austral summer are also presented. Validation of the ice-state and melt-onset date estimates is performed by analyzing corresponding brightness temperature (Tb) measurements from radiometers. QuikScat sigma-0 measurements from 1999 through 2003 are analyzed and it is shown that Ku-band scatterometers are very useful for determining periods of melt in Antarctic ice-sheets and provide high temporal and spatial resolution ice-state estimates. These estimates can be important for long-term studies of the climatic effects of the seasonal and inter-annual melting of the Antarctic ice-sheets. The SeaWinds on QuikScat (QuikScat) and SeaWinds on ADEOS-2 (SeaWinds) scatterometers are identical radar sensors on different spaceborne platforms traversing similar orbits. QuikSCAT and SeaWinds data are used to infer near-surface wind vectors, polar sea-ice extent, polar-ice melt events, among others. In order to verify the relative calibration of these two sensors a simple cross-calibration method is implemented based on land measurements. A first-order polynomial model for the incidence angle dependence of sigma-0 is used to account for biases in the sigma-0 measurements. This model is applied to selected regions of the Amazon rainforest and the Sahara desert. It is shown that the two sensors are well calibrated. Additionally, evidence of a previously presumed diurnal cycle in the Amazon rainforest backscatter is given.