DNA microarray technology has been extensively utilized in the biomedical field, becoming a standard in identifying gene expression signatures for disease diagnosis/prognosis and pharmaceutical practices. Although cancer research has benefited from this technology, challenges such as large-scale data size, few replicates and complex heterogeneous data types remain; thus the biomarkers identified by various studies have a small proportion of overlap because of molecular heterogeneity. However, it is desirable in cancer research to consider robust and consistent biomarkers for drug development as well as diagnosis/prognosis. Although cancer is a highly heterogeneous disease, some mechanism common to developing cancers is believed to exist; integrating datasets from multiple experiments increases the accuracy of predictions because increasing the sample size improves and enhances biomarkers detection. Therefore, integrative study is required for compiling multiple cancer data sets when searching for the common mechanism leading to cancers. Some critical challenges of integration analysis remain despite many successful methods introduced. Few is able to work on data sets with different dimensionalities. More seriously, when the replicate number is small, most existing algorithms cannot deliver robust predictions through an integrative study. In fact, as modern high-throughput technology matures to provide increasingly precise data, and with well-designed experiments, variance across replicates is believed to be small for us to consider a mean pattern model. This model assumes that all the genes (or metabolites, proteins or DNA copies) are random samples of a hidden (mean pattern) model. The study implements this model using a hierarchical modelling structure. As the primary component of the system, a multi-scale Gaussian (MSG) model, designed to identify robust differentially-expressed genes to be integrated, was developed for predicting differentially expressed genes from microarray expression data of small replicate numbers. To assure the validity of the mean pattern hypothesis, a bimodality detection method that was a revision of the Bimodality index was proposed.

Title: Stochastic Catastrophe Model Cusp Author: Jan Voříšek Department: Department of Probability and Mathematical Statistics Supervisor: Prof. Ing. Miloslav Vošvrda, CSc., Czech Academy of Sciences, Institute of Information Theory and Automation Abstract: The goal of this thesis is to analyze the stochastic cusp model. This task is divided into two main topics. The first of them concentrates on the stationary density of the cusp model and statistical testing of its bimodality, where power and size of the proposed tests are simulated and compared with the dip test of unimodality. The second main topic deals with the transition density of the stochastic cusp model. Comparison of approximate maximum likelihood approach with traditional finite difference and numerical simulations indicates its advantage in terms of speed of estimation. An approximate Fisher information matrix of general stochastic process is derived. An application of the cusp model to the exchange rate with time-varying parameters is estimated, the extension of the cusp model into stochastic bimodality model is proposed, and the measure of probability of intrinsic crash of the cusp model is suggested. Keywords: stochastic cusp model, bimodality testing, transition density ap- proximation

The goal of galaxy classification is to understand the physical basis for the wide range in shapes and structures exhibited by galaxies in the local and high redshift universe. We present a catalog of visually classified galaxies from the Sloan Digital Sky Survey with detailed morphological classifications including bars, rings, lenses, tails, warps, dustlanes, arm flocculence and multiplicity (so called ’fine structure’). This thesis explores the importance of galaxy morphology by probing its relationship to physical properties. Our analysis includes an investigation of correlations between fine structures and AGN activity. This sample defines a comprehensive local galaxy sample which we use to study the low redshift universe both qualitatively and quantitatively. We find the stellar mass appears to be a defining characteristic of a galaxy. The break in most correlations of physical properties with morphology is due to a lack of late type, massive disk galaxies. Our analysis of the size-mass relations of galaxies as a function of morphology (T-Type) has revealed many interesting connections. We find the size-mass relation of Sa, Sab, Sb, and Sbc galaxies bifurcates into two families of objects as one moves down the sequence such that the high concentration branch exhibits a similar slope to low concentration early type (E) galaxies suggesting a closer than expected physical (possibly evolutionary) connection between the two populations. We find bar fraction is bimodal with respect to mass (at 3 x 10^10 M) and color (at g - r ∼ 0.55). The dependence is seen to intimately depend on central concentration such that objects below the transition mass with low concentrations have a higher bar fraction than objects above the transition mass which have high bar fractions for high concentration systems. In addition we find the presence of an AGN alters the behavior and abundance of barred/ringed galaxies in the high mass peak such that the bar/ring fractions increase with mass in nonactive galaxies whereas they decrease with mass in active galaxies. AGN fractions are also decreasing in the same mass range possibly implying a positive correlation between fine structure and ring formation.

The goal of galaxy classification is to understand the physical basis for the wide range in shapes and structures exhibited by galaxies in the local and high redshift universe. We present a catalog of visually classified galaxies from the Sloan Digital Sky Survey with detailed morphological classifications including bars, rings, lenses, tails, warps, dustlanes, arm flocculence and multiplicity (so called ’fine structure’). This thesis explores the importance of galaxy morphology by probing its relationship to physical properties. Our analysis includes an investigation of correlations between fine structures and AGN activity. This sample defines a comprehensive local galaxy sample which we use to study the low redshift universe both qualitatively and quantitatively. We find the stellar mass appears to be a defining characteristic of a galaxy. The break in most correlations of physical properties with morphology is due to a lack of late type, massive disk galaxies. Our analysis of the size-mass relations of galaxies as a function of morphology (T-Type) has revealed many interesting connections. We find the size-mass relation of Sa, Sab, Sb, and Sbc galaxies bifurcates into two families of objects as one moves down the sequence such that the high concentration branch exhibits a similar slope to low concentration early type (E) galaxies suggesting a closer than expected physical (possibly evolutionary) connection between the two populations. We find bar fraction is bimodal with respect to mass (at 3 x 10^10 M) and color (at g - r ∼ 0.55). The dependence is seen to intimately depend on central concentration such that objects below the transition mass with low concentrations have a higher bar fraction than objects above the transition mass which have high bar fractions for high concentration systems. In addition we find the presence of an AGN alters the behavior and abundance of barred/ringed galaxies in the high mass peak such that the bar/ring fractions increase with mass in nonactive galaxies whereas they decrease with mass in active galaxies. AGN fractions are also decreasing in the same mass range possibly implying a positive correlation between fine structure and ring formation.

Em análise de dados que apresentam certo grau de assimetria, curtose ou bimodalidade, a suposição de normalidade não é válida, sendo necessários modelos que capturem estas características dos dados. Neste contexto, uma nova classe de distribuições bimodais assimétricas gerada por um mecanismo de mistura é proposta neste trabalho. Algumas propriedades para o caso particular que inclui a distribuição normal como família base desta classe são estudadas e apresentadas, tal caso resulta no chamado Modelo Mistura de Potência Normal (MPN). Dois algoritmos de simulação são desenvolvidos com a finalidade de obter variáveis aleatórias com esta distribuição. A abordagem frequentista é empregada para a inferência dos parâmetros do modelo proposto. São realizados estudos de simulação com o objetivo de avaliar o comportamento das estimativas de máxima verossimilhança dos parâmetros. Adicionalmente, um modelo de regressão para dados bimodais é proposto, utilizando a distribuição MPN como variável resposta nos modelos Generalizados Aditivos para Posição, Escala e Forma, cuja sigla em inglês é GAMLSS. Para este modelo de regressão estudos de simulação também são realizados. Em ambos os casos estudados, o modelo proposto é ilustrado utilizando um conjunto de dados reais referente à pontuação de jogadores na Super Liga Brasileira de Voleibol Masculino 2014/2015. Com relação a este conjunto de dados, o modelo MPN apresenta melhor ajuste quando comparado à modelos já existentes na literatura para dados bimodais. / In analysis of data that present a certain degree of asymmetry, kurtosis or bimodality, the assumption of normality is not valid and models that capture these characteristics of the data are required. In this context, a new class of bimodal asymmetric distributions generated by a mixture mechanism is proposed. Some properties for the particular case that includes the normal distribution as the base family of this class are studied and presented, such case results in the so-called Power Normal Mixture Model. Two simulation algorithms are developed with the purpose of obtaining random variables with this new distribution. The frequentist approach is used to the inference of the model parameters. Simulation studies are carried out with the aim of assessing the behavior of the maximum likelihood estimates of the parameters. In addition, the power normal mixture distribution is introduced as the response variable for the Generalized Additives Models for Location, Scale and Shape (GAMLSS). For this regression model, simulation studies are also performed. In both cases studied, the proposed model is illustrated using a data set on players\' scores in the Male Brazilian Volleyball Superliga 2014/2015. With respect to this dataset, the power normal mixture model presents better fit when compared to models already existing in the literature to bimodal data.

Dans ce travail, les propriétés des oxydes de titane mésoporeux organisés ont été étudiées en détail. La synthèse de ces matériaux a été mise au point auparavant au laboratoire à l’aide d’une méthode combinant le mécanisme transcriptif à partir des cristaux liquides du copolymère bloc P123 et la méthode EISA. Tout d’abord, une optimisation des conditions d’élimination du tensioactif a été effectuée en testant des méthodes d’extraction à partir de solvant et des méthodes thermiques. L’élimination du P123 par l’eau suivie d’un rinçage à l’acétone est efficace, simple et rapide et en même temps favorise la formation de la phase anatase du TiO2. Par contre, les propriétés photocatalytiques de ces TiO2 extraits à l’eau sont médiocres et ne sont améliorées qu’après calcination. En combinant une extraction du P123 à l’eau avec une calcination les oxydes de titane mésoporeux possédent une meilleure activité photocatalytique que celle de l’anatase commercial. Dans un second temps l’incorporation du zinc et du tungstène dans les TiO2 mésoporeux organisés a été investie dans le but d’améliorer leur activité photocatalytique. L’introduction de faibles quantités de zinc (<10% mol) augmente la surface spécifique ; au-delà la mésostructuration est perdue. L’incorporation du tungstène dans le TiO2 mésoporeux n’a pas d’influence sur l’organisation des mésopores, mais des agrégats de WO3 orthorhombique coexistent avec le réseau mésoporeux de TiO2 anatase. Même si la présence d’oxyde de zinc ou de tungstène dans la matrice TiO2 mésoporeux diminue bien l’énergie bandgap, l’activité photocatalytique ne s’en trouve pas améliorée. D’autre part, la synthèse de matériaux à porosité bimodale, en utilisant deux systèmes mixtes de tensioactifs hydrogéné/fluoré, CTABr/RF8(EO)9 et P123/ RF8(EO)9, a été explorée. Sur la base des diagrammes de phase de ces deux systèmes dans l’eau, les solutions micellaires et les cristaux liquides ont été investis pour préparer des silices mésoporeuses en utilisant les deux mécanismes CTM et LCT. Quand le CTABr est présent une seule taille de pores dans le domaine mésoporeux est observée, toutefois il est possible qu’une bimodalité de type micro-mésopores existe. Par contre, l’utilisation de la phase hexagonale du système P123/RF8(EO)9 permet d’obtenir des matériaux à deux tailles de pores distincts dans le domaine mésoporeux. / In this work we will study in detail the properties of the mesoporous TiO2 materials, for which the preparation was developed previously via a method combining Liquid Crystal Templating (LCT) and EISA mechanisms, using P123 as template. We have tested, in the first time, extraction and thermal methods efficiency to eliminate surfactant in order to optimize the P123 elimination step. Removal of P123 using water followed by washing with acetone is effective, easy and promotes the formation of the anatase phase of TiO2. Otherwise, the photocatalytic properties of the obtained TiO2 are not important and can be improved after calcination. Combining extraction using water and calcination give rise to mesoporous TiO2 with better photocatalytic activity than that of commercial anatase. The incorporation of zinc and tungsten in the mesoporous well-ordered TiO2 has been investigated in the third time, in order to improve their photocatalytic activity. The introduction of small amounts of zinc (<10 mol%) increases the surface area; beyond this amount the mesostructure is lost. The incorporation of tungsten in the mesoporous TiO2 does not affect the mesopores organization, and orthorhombic WO3 aggregates are formed beside the mesoporous network of anatase TiO2. Although, the presence of zinc or tungsten oxides in the matrix decreases the bandgap of mesoporous TiO2, the photocatalytic activity is not improved. In the third time, the synthesis of bimodal porosity materials, using a mixed surfactant systems hydrogenated/fluorinated, CTABr/RF8(EO)9 and P123/RF8(EO)9, was explored. Based on the phase diagrams of these two systems in water, micellar solutions and liquid crystals have been investigated to prepare mesoporous silicas using two mechanisms CTM and LCT. When CTABr is present, pores of one size in the mesoporous range are observed, however, it is possible that bimodal type micro-mesopores exist. The use of the hexagonal liquid crystal phase of P123/RF8(EO)9 provides two separate pore sizes materials in the mesoporous range.

In this work was proposed a new distributions, called log-sinh Cauchy, with has bimodal shapes and can be used as alternative to the mixture models. Based in the proposed distribution, the following models were proposed: Regression model based in the GAMLSS framework; models with cure rate based in the mixture and promotion time models; semiparametric models, modeling the parameters using penalized splies; semiparametric models, using the penalized splines to model the non-linear effects present in the cure rate. For all proposed models, the computational codes were implemented in the R software, with is available along of the document as well as some brief introduction on how to use them. / Nesse trabalho foi proposto uma nova distribuição, denominada de exponentiated log-sinh Cauchy, a qual possui densidades bimodais e pode ser utilizada como alternativa aos modelos de mistura. Com base na nova distribuição, foram propostos: modelos de regressão baseados nos modelos GAMLSS; modelos com fração de cura baseados em modelos de mistura e tempo de promoção; modelo semi-paramétrico modelando os parâmetros com splines penalizados; modelo semi-paramétrico com fração de cura utilizando splines para modelar efeitos não lineares na proporção de curados. Para todos os modelos propostos, toda parte computacional foi implementada no software R, sendo disponibilizada ao longo do documento assim como breve descrições de uso.

Náplní této práce je teoretický úvod a následné praktické zpracování tématu Molekulární signatura jako optimální multi-objektivní funkce s aplikací v predikci v onkogenomice. Úvodní kapitoly jsou zaměřeny na téma rakovina, zejména pak rakovina prsu a její podtyp triple negativní rakovinu prsu. Následuje literární přehled z oblasti optimalizačních metod, zejména se zaměřením na metaheuristické metody a problematiku strojového učení. Část se odkazuje na onkogenomiku a principy microarray a také na statistiku a s důrazem na výpočet p-hodnoty a bimodálního indexu. Praktická část je pak zaměřena na konkrétní průběh výzkumu a nalezené závěry, vedoucí k dalším krokům výzkumu. Implementace vybraných metod byla provedena v programech Matlab a R, s využitím dalších programovacích jazyků a to konkrétně programů Java a Python.

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Les rythmes biologiques aident les organismes vivants à programmer la plupart des processus comportementaux dans la fenêtre temporelle la plus appropriée. Les données de la littérature sur la rythmicité du chat domestique sont rares et conflictuelles. Pour approfondir nos connaissances sur le sujet, nous avons utilisé de récentes technologies de télémétrie pour enregistrer et caractériser les rythmes journaliers d'activité locomotrice et de prises alimentaire chez des chats en fonction des saisons et des conditions d’hébergement. Les rythmes des chats étaient modifiés par la photopériode et la présence humaine. Suivant une périodicité de 24 heures, ils ont affiché une bimodalité dans leurs rythmes quotidiens, avec des creux d'activité locomotrice et de consommation au milieu de la journée et de la nuit. Les deux périodes principales d'activité/alimentaires correspondaient à l'aube et au crépuscule à chaque saison, indépendamment de leur horaire, confirmant la nature intrinsèque crépusculaire de l'espèce. Le rythme alimentaire des chats était plus variable au cours du cycle que celui de leur activité locomotrice, rappelant ainsi le caractère opportuniste de ce prédateur. Les chats ont présenté une plasticité comportementale caractérisée par des rythmes plus faibles et un comportement d'exploration plus nocturne en milieu extérieur qu’en milieu intérieur, au sein duquel ils étaient plus enclins à la routine. Nos résultats ouvrent la voie au développement de solutions nutritionnelles et des recommandations d’hébergement adaptées aux rythmes du chat en respectant les besoins physiologiques de l’animal. / Biological rhythms are of importance for living organisms as they help to schedule most behavioural processes within the most suitable temporal window. Literature on daily rhythmicity is scarce and conflicting regarding domestic cats. To sharpen our knowledge on the subject, we used advanced telemetry technologies to record and characterise the daily rhythms of locomotor activity and feeding in cats according to the seasons and housing conditions. The cats were sensitive to photoperiod and to human presence. Along 24-hour periodicity, they displayed bimodality in their daily patterns, with mid-day and mid-night troughs of locomotor activity and food consumption. The two main activity/eating periods corresponded to dawn and dusk at each season, regardless of the twilight timings, confirming the crepuscular intrinsic nature of the species. The feeding rhythm of the cats was more variable daily than their locomotor activity one, recalling the opportunistic character of this predator. Cats displayed plasticity in their behaviour, such as weaker daily rhythms and more nocturnal exploratory behaviour outdoors, compared to indoors where they were more prone to routine. Our results open new avenues for developing nutritional and housing guidelines fitted to the rhythms of the cats according to their way of life.