Um contador a gás, com multifios, sensível à posição, para a detecção de raios X foi construído utilizando linhas de atraso integradas para leitura da posição. Seis linhas de atraso (50ns de atraso cada, frequência de corte de 40MHz) cobrem um comprimento sensível total de 150mm, possuindo uma razão do atraso total pelo tempo de subida dos sinais na linha adequadas para a detecção em posição raios X de 5,9keV do ANTIPOT. 55 Fe com alta resolução. Testes usando a forneceram uma não-linearidade linha de integral máxima menor que 0,1% e não-linearidade diferencial máxima de ±4,0%, com o detector utilizando a mistura 700torr. Testes similares foram feitos usando de Ar-CH IND 4 (90%-10%) a a linha de 8,04keV de um tubo de raios X de Cu. Uma resolução total de 330m, e as mesmas não-linearidades integral e diferencial foram obtidas. Com a finalidade de t.est.ar o comportamento do detector sob condições experimentais reais, duas diferentes amostras foram analisadas na região de espalhamento em baixo ângulo. As amostras analisadas foram o carvão vítreo e o dodecil sulfato de sódio (SLS). O feixe de raios X foi colimado por um conjunto de fendas, com 50,um cada uma delas e separadas de 98mm. A distância entre a amostra e o detector era de 404,5mm, fazendo com que a região sensível do detector cobrisse um ângulo de espalhamento de ±12 °. Foram obtidos um raio de giro de 22 Å para o carvão vítreo e um dos parâmetros da rede cristalina c de 39,1 Å para o SLS. Estes resultados estão de acordo com trabalhos anteriores obtidos com técnicas tradicionais de maior dispêndio de tempo que utilizam detectores de Nal(T1) e chapas fotográficas em uma câmara de Laue. / A multiware position sensitive gas counter for X-Ray detection was developed in our laboratory making use or commercial delay-lines for position sensing. Six delay-line chips (50ns delay each 40Mhz cut-off frequency) cover a total sensitive length of 190mm leading to a delay-risetime ratio that allows for a high-resolution position detection. Tests using the 5,9keV X-Ray line from a 55Fe source an integral linearity better than 0,1% and a maximum differential linearity or ±4,0% were obtained operating the detector with an Ar-CH 4 (90%-10%) gas mixture at 700torr. Similar tests were performed using the 8,04keV line from a Cu X-Ray tube. A total resolution or 330m, and the same integral and differential linearities were obtained. In order to check the detector performance under usual experimental conditions two different samples were analyzed in the low scattering-angle region. The samples analyzed were vitreous carbon and sodium dodecyl sulfate (SLS). The X-Rays were collimated by a set or slits each 50m wide separated by 98mm. The distance between the sample and the detector was 404,5mm, so that the detector covered a scattering angle of ±12°. A radius of gyration of 22Å for vitreous carbon and a crystallographic parameter of 39,1Å for SLS were obtained. These values are in good agreement with those obtained with the more time-consuming traditional techniques making use of a rotating NaI(T1) detector and photographic plates with a Laue camera.

Introdução: As técnicas mais comumente empregadas em análise de sobrevida que utilizam dados censurados são o estimador produto limite de Kaplan-Meier (KM) e o modelo de riscos proporcionais de Cox. Estas técnicas têm como suposição que a causa da perda de seguimento seja independente do tempo de sobrevida. Objetivo: O presente estudo visa a analisar o efeito das perdas de seguimento nestas duas técnicas. Material e Métodos: O estudo foi realizado utilizando-se o banco de dados dos pacientes cadastrados no Registro Hospitalar do Hospital do Câncer de São Paulo em 1994. Foram elaborados 28 bancos de dados simulando perdas informativas e não informativas. A perda informativa foi simulada transformando os óbitos em vivos, na proporção de 5 a 50%. A perda não informativa foi simulada através do sorteio de 5 a 50% do total do banco. O estimador de Kaplan-Meier (KM) foi utilizado para estimar a sobrevida acumulada no primeiro, terceiro e quinto ano de seguimento, e o modelo de riscos proporcionais de Cox para estimar as hazard ratio (HR). Todas as estimativas obtidas no KM e as HR's foram comparadas com os resultados do banco de dados original. Resultados: Houve maior proporção de perda nos pacientes com maior escolaridade, admitidos por convênio e particular e os menos graves (estádio I ou II). Quanto maior a proporção de perda informativa, maior a diferença alcançada nas estimativas realizadas pelo KM, verificando-se que a perda de seguimento superior a 15% acarretou diferenças superiores a 20% nas estimativas da probabilidade de sobrevida. As HR's foram menos afetadas, e proporções superiores a 20% de perda de seguimento acarretaram variações de cerca de 10% nas estimativas. Quando as perdas foram não informativas não houve diferenças significativas nas estimativas pelo KM e nas HR's em relação ao banco original. Conclusões: É importante avaliar se as perdas ocorridas em estudos de coorte são informativas ou não, pois se forem podem acarretar distorções principalmente nas estimativas feitas pelo método de KM. / Introduction: The Kaplan Meier product limit estimator (KM) and the Cox proportional hazard (HR) model are the most used tools in survival analysis. These two methods have the key assumption that censoring must be independent from the survival time. Objective: To analyze the consequences of loss to follow up in these two methods. Methods: The study has utilized the data of the Cancer Registry of the patients of Hospital do Cancer in São Paulo of 1994. The informative censure was simulated transforming the death by 5 to 50% into alive. Besides 5 to 50% was spared at random simulating the non-informative censoring. The survival probability and was calculated to the first, third and fifth year of follow –up. All the estimated probabilities and HR’s were compared with the results of the original data. Results: Patients with greater scholars, lower stages and admitted by health plans or private had more losses to follow up. The maximum proportion of accepted loss to follow –up is 10% to 15% when using the KM estimator, and the HR are less affected by the loss to follow-up and one can afford having 20% of it. When the losses were non informative there were no differences between the original probabilities. Conclusions: The possibility of over or under estimated probability must be analyzed in the presence of the losses to follow- up when using the KM and HR in survival analyses.

Title: Exponential control of homogeneous Markov processes Author: Pavol Stanek Department: Department of Probability and Mathematical Statistics, MFF UK Supervisor: Mgr. Peter Dostál Ph.D., Department of Probability and Mathematical Statistics, MFF UK Abstract: This master thesis concerns exponential control of Markov decision chains. An iterative alghorithm for finding a control, that maximizes a long term growth rate of expected utility is developed. The utility is measured by exponential utility function. The algorithm is derived for both discrete time and continuous time chain. Subsequently, the results are applied on the problem of optimally managing port- folio with proportional transaction costs. The dynamics of the investor's position is derived and the consequent process is approximated by Markov chain. Using the iterative alghorithm, the optimal trading strategy is numerically found. Keywords: exponential control, Markov chain, portfolio optimization, proportional transaction costs 1

Diante da importância do sistema financeiro para a economia de um país, faz-se necessária sua constante fiscalização. Nesse sentido, a identificação de problemas existentes no cenário bancário apresenta-se fundamental, visto que as crises bancárias ocorridas mundialmente ao longo da história mostraram que a falta de credibilidade bancária e a instabilidade do sistema financeiro geram enormes custos financeiros e sociais. Os modelos de previsão de insolvência bancária são capazes de identificar a condição financeira de um banco devido ao valor correspondente da sua probabilidade de insolvência. Dessa forma, o presente trabalho teve como objetivo identificar os principais indicadores característicos da insolvência de bancos privados no Brasil. Para isso, foi utilizada a técnica de análise de sobrevivência em uma amostra de 70 bancos privados no Brasil, sendo 33 bancos insolventes e 37 bancos solventes. Foi possível identificar os principais indicadores financeiros que apresentaram-se significativos para explicar a insolvência de bancos privados no Brasil e analisar a relação existente entre estes indicador e esta probabilidade. O resultado deste trabalho permitiu a realização de importantes constatações para explicar o fenômeno da insolvência de bancos privados no Brasil, bem como, permitiu constatar alguns aspectos característicos de bancos em momentos anteriores à sua insolvência. / The financial system is very important to the economy of a country, than its supervision is necessary. Accordingly, the identification of problems in the banking scenario is fundamental, since the banking crisis occurring worldwide throughout history have shown that and instability of the financial system generates huge financial and social costs. The banking failure prediction models are able to identify the financial condition of a bank based on the value of its probability of insolvency. Thus, this study aimed to identify the main financial ratios that can explain the insolvency of private banks in Brazil. For this, it was used the survival analysis to analize a sample of 70 private banks in Brazil, with 33 solvent banks and 37 insolvent banks. It was possible to identify the key financial indicators that were significantly to explain the bankruptcy of private banks in Brazil and it was possible to examine the relationship between these financial ratios and the probability of bank failure. The result of this work has enabled the achievement of important findings to explain the phenomenon of the bankruptcy of private banks in Brazil, and has seen some characteristic of banks in times prior to its insolvency.

<p>This thesis consists of four papers about the assumption of proportional hazards for the Cox model in survival analysis. </p><p>The <b>first paper </b>compares the hazard ratio estimated from the Cox model to an exact calculation of the geometric average of the hazard ratio when the underlying assumption of proportional hazards is false, i.e. when the hazards are not proportional. The estimates are evaluated in a simulation study.</p><p>The <b>second paper</b> describes and compares six of the most common numerical procedures to check the assumption of proportional hazards for the Cox model. The tests are evaluated in a simulation study.</p><p>Six graphical procedures to check the same assumption of proportional hazards for the Cox model are described and compared in the <b>third paper</b>. A criterion for rejection is derived for each procedure, to make it possible to compare the results of the different methods. The procedures are evaluated in a simulation study.</p><p>In the <b>fourth paper </b>the effects of covariate measurement error on testing the assumption of proportional hazards is investigated. Three of the most common numerical procedures to check the assumption of proportional hazards for the Cox model are evaluated in a simulation study. </p>

<p>In drug development clinical trials are designed to investigate whether a new treatment is safe and has the desired effect on the disease in the target patient population. Categorical endpoints, for example different ranking scales or grading of adverse events, are commonly used to measure effects in the trials. </p><p>Pharmacokinetic/Pharmacodynamic (PK/PD) models are used to describe the plasma concentration of a drug over time and its relationship to the effect studied. The models are utilized both in drug development and in discussions with drug regulating authorities. Methods for incorporation of ordered categorical data in PK/PD models were studied using a non-linear mixed effects modelling approach as implemented in the software NONMEM. The traditionally used proportional odds model was used for analysis of a 6-grade sedation scale in acute stroke patients and for analysis of a T-cell receptor expression in patients with Multiple Sclerosis, where the results also were compared with an analysis of the data on a continuous scale. Modifications of the proportional odds model were developed to enable analysis of a spontaneously reported side-effect and to analyze situations where the scale used is heterogeneous or where the drug affects the different scores in the scale in a non-proportional way. The new models were compared with the proportional odds model and were shown to give better predictive performances in the analyzed situations. </p><p>The results in this thesis show that categorical data obtained in clinical trials with different design and different categorical endpoints successfully can be incorporated in PK/PD models. The models developed can also be applied to analyses of other ordered categorical scales than those presented.</p>

Effects of drugs are in clinical trials often measured on categorical scales. These measurements are increasingly being analyzed using mixed-effects logistic regression. However, the experience with such analyzes is limited and only a few models are used. The aim of this thesis was to investigate the performance and improve the use of models and methods for mixed-effects categorical data analysis. The Laplacian method was shown to produce biased parameter estimates if (i) the data variability is large or (ii) the distribution of the responses is skewed. Two solutions are suggested; the Gaussian quadrature method and the back-step method. Two assumptions made with the proportional odds model have also been investigated. The assumption with proportional odds for all categories was shown to be unsuitable for analysis of data arising from a ranking scale of effects with several underlying causes. An alternative model, the differential odds model, was developed and shown to be an improvement, in regard to statistical significance as well as predictive performance, over the proportional odds model for such data. The appropriateness of the likelihood ratio test was investigated for an analysis where dependence between observations is ignored, i.e. performing the analysis using the proportional odds model. The type I error was found to be affected; thus assessing the actual critical value is prudent in order to verify the statistical significance level. An alternative approach is to use a Markov model, in which dependence between observations is incorporated. In the case of polychotomous data such model may involve considerable complexity and thus, a strategy for the reduction of the time-consuming model building with the Markov model and sleep data is presented. This thesis will hopefully contribute to a more confident use of models for categorical data analysis within the area of pharmacokinetic and pharmacodynamic modelling in the future.

This thesis consists of four papers about the assumption of proportional hazards for the Cox model in survival analysis. The <b>first paper </b>compares the hazard ratio estimated from the Cox model to an exact calculation of the geometric average of the hazard ratio when the underlying assumption of proportional hazards is false, i.e. when the hazards are not proportional. The estimates are evaluated in a simulation study. The <b>second paper</b> describes and compares six of the most common numerical procedures to check the assumption of proportional hazards for the Cox model. The tests are evaluated in a simulation study. Six graphical procedures to check the same assumption of proportional hazards for the Cox model are described and compared in the <b>third paper</b>. A criterion for rejection is derived for each procedure, to make it possible to compare the results of the different methods. The procedures are evaluated in a simulation study. In the <b>fourth paper </b>the effects of covariate measurement error on testing the assumption of proportional hazards is investigated. Three of the most common numerical procedures to check the assumption of proportional hazards for the Cox model are evaluated in a simulation study.

This thesis presents various studies on energy efficient design of wireless networks. It starts with a survey on recent shortest path based energy efficient routing algorithms developed for ad hoc and sensor networks, making a comprehensive classification for these algorithms. In addition to energy efficient design, sustainable and environmentally friendly deployment of wireless networks demands increased use of renewable energy. However, this calls for novel design principles to efficiently utilize the variation in the availability of the energy. The thesis continues with an investigation of state-of-the-art resource management and scheduling algorithms developed for energy harvesting wireless sensor networks. Building on the stateof- the-art, the main contribution of this thesis is to formulate and solve a utility maximizing scheduling problem in a multiuser broadcast channel with an energy harvesting transmitter. The goal is to determine the optimal power and time allocations to users between energy arrivals. The structural properties of the problem are analyzed, and its biconvexity is proved. A Block Coordinate Descent (BCD) based algorithm is developed to obtain the optimal solution. Two simple and computationally scalable heuristics, PTF and ProNTO, which mimic the characteristics of the optimal policy, are proposed. Finally, an online algorithm, PTF-On,that will bypass the need for offline knowledge about the energy harvesting statistics, is developed. PTF-On uses a Kalman filter based energy harvesting prediction algorithm, developed in this thesis, to predict the energy that will arrive in the future.

Le problème principalement étudié dans ce manuscrit est la stabilisation d'orbites périodiques de systèmes dynamiques non linéaires à l'aide d'une commande de rétroaction (feedback). Le but des méthodes de contrôle proposées ici est d'obtenir une oscillation périodique stable. Ces méthodes de contrôle sont appliquées à des systèmes présentant des orbites périodiques instables dans l'espace d'état, et ces dernières sont les orbites destinées à être stabilisées. Les méthodes proposées ici sont telles que l'oscillation stable qui en résulte est obtenue avec un effort de contrôle faible, et que la valeur de la commande tend vers zéro lorsque la trajectoire tend vers l'orbite stabilisée. La stabilité locale des orbites périodiques est analysée par l'étude de la stabilité des systèmes linéaires périodiques à l'aide de la théorie de Floquet. Ces systèmes linéaires sont obtenus par linéarisation des trajectoires au voisinage de l'orbite périodique. Les méthodes de contrôle utilisées ici pour la stabilisation des orbites périodiques sont une loi de commande proportionnelle, une loi de commande de rétroaction retardée et une loi de commande de rétroaction basée sur une prédiction. Ces méthodes sont appliquées aux systèmes en temps discret et aux systèmes en temps continu avec les modifications nécessaires. Les contributions principales de cette thèse sont associées à ces méthodes, proposant une méthode alternative de design de gain, une nouvelle loi de commande et des résultats associés.