Recentemente a análise de capacidade do processo para dados com distribuição não normal começou a ser explorada, porém são raras as referências em língua portuguesa que abordem este assunto. Este trabalho apresenta os principais índices para análise da capacidade do processo com dados não normais encontrados na literatura, sendo o primeiro deles o método proposto por Clements em 1989, o segundo, proposto por Pearn e Chen (1997) e o terceiro método apresentado é o proposto por Chen e Ding em 2001. Os métodos de Clements (1989) e Pearn e Chen (1997) são parecidos em muitos aspectos, mas cada um deles apresenta uma novidade em relação ao cálculo dos índices de capacidade. Em comum, ambos os métodos apresentam índices semelhantes aos índices tradicionais, que supõem normalidade dos dados. O método de Chen e Ding (2001) traz como novidade o uso do índice proposto por eles para a estimação do número de itens não conformes apresentados pelo processo em estudo. Por fim, dois estudos de caso são apresentados neste trabalho. No primeiro deles tem-se a comparação entre os métodos de Clements (1989) e de Pearn e Chen (1997) para que se conclua sobre qual dos métodos é o melhor para o cálculo da capacidade do processo não normal. No segundo estudo de caso, todos os três métodos apresentados neste trabalho são aplicados em um conjunto de dados reais, obtidos de uma indústria metalúrgica. Para execução das análises nos estudos de caso, foi aplicado o software livre R versão 2.10. Os resultados apresentados mostram que o método proposto por Pearn e Chen (1997) é mais eficiente do que o proposto por Clements (1989) por considerar a assimetria do processo. Quanto ao processo da indústria metalúrgica observou-se que a etapa analisada é relativamente capaz. / The analysis of process capability for non-normal distribution data started to be explored recently, but is rare references that address this issue in Portuguese. This dissertation presents the main indices for process capability analysis for nonnormal data. The first method was proposed in 1989 by Clements, the second was proposed by Pearn e Chen (1997) and the third was proposed by Chen e Ding in 2001. The methods of Clements (1989) and Pearn e Chen (1997) are similar in many aspects, but each presents something new in the calculation of capability indices. In common, both methods have indices similar to the traditional indices, for normal data. The method proposed by Chen e Ding (2001) innovates using the index in the estimative of number of non-conforming in the process. Finally, two case studies are presented. The first compares the methods of Clement (1989) and Pearn e Chen (1997) to show the best method of calculation the capability of non-normal process. In the second, the three methods showing in this dissertation are applied in a metallurgical industry data. The R software version 2.10 was used in the analysis. The results show that the method proposed by Pearn and Chen (1997) is more efficient than that proposed by Clements (1989) for considering the asymmetry of the process. And the metallurgical process stage analyzed is relatively capable.

Recentemente a análise de capacidade do processo para dados com distribuição não normal começou a ser explorada, porém são raras as referências em língua portuguesa que abordem este assunto. Este trabalho apresenta os principais índices para análise da capacidade do processo com dados não normais encontrados na literatura, sendo o primeiro deles o método proposto por Clements em 1989, o segundo, proposto por Pearn e Chen (1997) e o terceiro método apresentado é o proposto por Chen e Ding em 2001. Os métodos de Clements (1989) e Pearn e Chen (1997) são parecidos em muitos aspectos, mas cada um deles apresenta uma novidade em relação ao cálculo dos índices de capacidade. Em comum, ambos os métodos apresentam índices semelhantes aos índices tradicionais, que supõem normalidade dos dados. O método de Chen e Ding (2001) traz como novidade o uso do índice proposto por eles para a estimação do número de itens não conformes apresentados pelo processo em estudo. Por fim, dois estudos de caso são apresentados neste trabalho. No primeiro deles tem-se a comparação entre os métodos de Clements (1989) e de Pearn e Chen (1997) para que se conclua sobre qual dos métodos é o melhor para o cálculo da capacidade do processo não normal. No segundo estudo de caso, todos os três métodos apresentados neste trabalho são aplicados em um conjunto de dados reais, obtidos de uma indústria metalúrgica. Para execução das análises nos estudos de caso, foi aplicado o software livre R versão 2.10. Os resultados apresentados mostram que o método proposto por Pearn e Chen (1997) é mais eficiente do que o proposto por Clements (1989) por considerar a assimetria do processo. Quanto ao processo da indústria metalúrgica observou-se que a etapa analisada é relativamente capaz. / The analysis of process capability for non-normal distribution data started to be explored recently, but is rare references that address this issue in Portuguese. This dissertation presents the main indices for process capability analysis for nonnormal data. The first method was proposed in 1989 by Clements, the second was proposed by Pearn e Chen (1997) and the third was proposed by Chen e Ding in 2001. The methods of Clements (1989) and Pearn e Chen (1997) are similar in many aspects, but each presents something new in the calculation of capability indices. In common, both methods have indices similar to the traditional indices, for normal data. The method proposed by Chen e Ding (2001) innovates using the index in the estimative of number of non-conforming in the process. Finally, two case studies are presented. The first compares the methods of Clement (1989) and Pearn e Chen (1997) to show the best method of calculation the capability of non-normal process. In the second, the three methods showing in this dissertation are applied in a metallurgical industry data. The R software version 2.10 was used in the analysis. The results show that the method proposed by Pearn and Chen (1997) is more efficient than that proposed by Clements (1989) for considering the asymmetry of the process. And the metallurgical process stage analyzed is relatively capable.

Data from insect studies may present different features. Univariate responses may be analyzed using generalized linear models (continuous and discrete data), survival models (time until event data), mixed effects models (longitudinal data), among other methods. These models may be used to analyse data from experiments which assess complex ecological processes, such as competition and predation. In that sense, computational tools are useful for researchers in several fields, e.g., insect biology and physiology, applied ecology and biological control. Using different datasets from entomology as motivation, as well as other types of datasets for illustration purposes, this work intended to develop new modelling frameworks and goodness-of-fit assessment tools. We propose accelerated failure rate mixed models with simultaneous location and scale modelling with regressors to analyse time-until-attack data from a choice test experiment. We use the exponential, Weibull and exponentiated-Weibull models, and assess goodness-of-fit using half-normal plots with simulation envelopes. These plots are the subject of an entire Chapter on an R package, called hnp, developed to implement them. We use datasets from different types of experiments to illustrate the use of these plots and the package. A bivariate extension to the N-mixture modelling framework is proposed to analyse longitudinal count data for two species from the same food web that may interact directly or indirectly, and example datasets from ecological studies are used. An advantage of this modelling framework is the computation of an asymmetric correlation coefficient, which may be used by ecologists to study the degree of association between species. The jointNmix R package was also developed to implement the estimation process for these models. Finally, we propose a goodness-of-fit assessment tool for bivariate models, analogous to the half-normal plot with a simulation envelope, and illustrate the approach with simulated data and insect competition data. This tool is also implemented in an R package, called bivrp. All software developed in this thesis is made available freely on the Comprehensive R Archive Network. / Dados provenientes de estudos com insetos podem apresentar características diferentes. Respostas univariadas podem ser analisadas utilizando-se modelos lineares generalizados (dados contínuos e discretos), modelos de análise de sobrevivência (dados de tempo até ocorrência de um evento), modelos de efeitos mistos (dados longitudinais), dentre outros métodos. Esses modelos podem ser usados para analisar dados provenientes de experimentos que avaliam processos ecológicos complexos, como competição e predação. Nesse sentido, ferramentas computacionais são úteis para pesquisadores em diversos campos, por exemplo, biologia e fisiologia de insetos, ecologia aplicada e controle biológico. Utilizando diferentes conjuntos de dados entomológicos como motivação, assim como outros tipos de dados para ilustrar os métodos, este trabalho teve como objetivos desenvolver novos modelos e ferramentas para avaliar a qualidade do ajuste. Foram propostos modelos de tempo de vida acelerado mistos, com modelagem simultânea dos parâmetros de locação e de escala com regressores, para analisar dados de tempo até ataque de um experimento que avaliou escolha de predadores. Foram utilizados modelos exponencial, Weibull e Weibull-exponenciado, e a qualidade do ajuste foi avaliada utilizando gráficos meio-normais com envelope de simulação. Esses gráficos são o assunto de um Capítulo inteiro sobre um pacote para o software R, chamado hnp, desenvolvido para implementá-los. Foram utilizados conjuntos de dados de diferentes tipos de experimentos para ilustrar o uso desses gráficos e do pacote. Uma extensão bivariada para os modelos chamados \"N-mixture\" foi proposta para analisar dados longitudinais de contagem para duas espécies pertencentes à mesma teia trófica, que podem interagir direta e indiretamente, e conjuntos de dados provenientes de estudos ecológicos são usados para ilustrar a abordagem. Uma vantagem dessa estratégica de modelagem é a obtenção de um coeficiente de correlação assimétrico, que pode ser utilizado por ecologistas para inferir acerca do grau de associação entre espécies. O pacote jointNmix foi desenvolvido para implemetar o processo de estimação para esses modelos. Finalmente, foi proposta uma ferramenta de avaliação de qualidade do ajuste para modelos bivariados, análoga ao gráfico meio-normal com envelope de simulação, e a metodologia _e ilustrada com dados simulados e dados de competição de insetos. Essa ferramenta está também implementada em um pacote para o R, chamado bivrp. Todo o software desenvolvido nesta tese está disponível, gratuitamente, na Comprehensive R Archive Network (CRAN).

O uso das técnicas de análise multivariada está reservado aos grandes centros de pesquisa, µas grandes empresas e ao ambiente acad^emico. Essas técnicas s~ao muito interessantes porque utilizam simultaneamente todas as variáveis respostas na interpretação teórica do conjunto de dados, levando em conta as correlações existentes entre elas. Uma das principais barreiras para a utilização dessas técnicas é o seu desconhecimento pelos pesquisadores interessados na pesquisa quantitativa. A outra dificuldade é que a grande maioria de softwares que permitem esse tipo de análise (SAS, MINITAB, BMDP, STATISTICA, S-PLUS, SYSTAT, etc.) não são de domínio público. A disseminação do uso das técnicas multivariadas pode melhorar a qualidade das pesquisas, proporcionar uma economia relativa de tempo e de custo, e facilitar a interpretação das estruturas dos dados, diminuindo a perda de informação. Neste trabalho, foram confirmadas algumas vantagens das técnicas multivariadas sobre as univariadas na análise de dados de expe- rimentos agropecuários. As análises foram realizadas com o auxílio do software R, um software aberto, \"amigável\" e gratuito, com inúmeros recursos disponíveis. / The use of the techniques of multivariate analysis is restricted to large centers of research, the higher companies and the academic environment. These techniques are very inte- resting because of the use of all answers variables simultaneously in theoretical interpretation of the data set, considering the correlations between them. One of the main obstacle to the usage of these techniques is that researchers interested in the quantitative research do not know them. The other di±culty is that most of the software that allow this type of analysis (SAS, MINITAB, BMDP, STATISTICA, S-PLUS, SYSTAT etc.) are not in public domain. Publishing the use of Multivariate techniques can improve the quality of the research, decrease the time spend and the cost, and make easy the interpretation of the structures of the data without cause damage of the information. In this report, were con¯rmed some advantages of the multivariate techniques in a univariate analysis for data of agricultural experiments. The analysis were taken with R software, a open software, \"friendly\" and free, with many statistical resources available.

A principal fonte de proteína na nutrição dos ruminantes é a proteína de origem microbiana, sintetizada no processo fermentativo de degradação ruminal a partir de proteína dietética ou microbiana. Logo o conhecimento deste processo é de grande importância em estudos de avaliação de alimentos para estes animais. Modelos não lineares são amplamente utilizados nestes estudos, buscando estimar os parâmetros da cinética de degradação ruminal através de métodos clássicos de análise univariada. Como estes ensaios envolvem medidas repetidas, propõem-se o uso de modelos não lineares mistos que permitem que a função de regressão não linear dependa de efeitos fixos e aleatórios, o que pode resolver os problemas de correlação entre as medidas repetidas e heterogeneidade de variâncias das respostas. Neste trabalho foram utilizadas duas alternativas comuns de análise de dados de digestibilidade, e seus resultados foram comparados com os da abordagem que utiliza modelos não lineares mistos. Utilizou-se o modelo não linear de Orskov e McDonald (1979) para explicar a cinética de degradação ruminal da matéria seca (MS) e da fibra em detergente neutro (FDN) do feno de capim-Tifton 85, em novilhos alimentados com seis rações experimentais compostas por três diferentes combinações de volumoso(Vo):concentrado(Co) (70:30, 50:50 e 30:70%). Como volumoso foram utilizados fenos de capim-Tifton 85 de diferentes qualidades (4% e 10% de proteína bruta) e como concentrado, casca de soja, milho moído e farelo de girassol. A degradabilidade foi determinada pela técnica in situ e os dez tempos de incubação foram de: 3, 6, 12, 24, 48, 60, 72, 84, 96 e 120 horas. Originalmente o experimento foi delineado em quadrado latino (6×6) com seis novilhos mestiços fistulados (linhas), seis períodos (colunas) e seis tratamentos, em que nas parcelas tem-se uma estrutura de parcelas subdivididas, sendo as subparcelas, os tempos de incubação. O uso de modelos não lineares mistos na análise de dados de digestibilidade in situ é bastante atraente principalmente quando a pesquisa tem por objetivo entender o comportamento do processo de digestibilidade ao longo dos tempos de incubação. Além disso, quanto maior a variabilidade dos dados, a abordagem mista se torna mais indicada, reduzindo os erros padrão das estimativas dos parâmetros. Mesmo não incluindo a estrutura de delineamento experimental, os modelos não lineares mistos conseguem explicar bem a variabilidade extra, provocada pelos efeitos dos fatores associados ao delineamento, com a inclusão de efeitos aleatórios nos parâmetros do modelo de Orskov e McDonald (1979). O pacote estatístico nlme do R mostrou-se ágil e eficiente no ajuste dos modelos não lineares mistos e as suas ferramentas gráficas foram importantes na avaliação da qualidade dos ajustes e na escolha de modelos. / The main source of protein in ruminant nutrition is the protein of microbial origin, synthesized in the fermentation process of ruminal degradation starting from dietetics or microbial protein. Then, the knowledge of this process is of great importance in evaluation studies of food for these animals. Nonlinear models are widely used in these studies to estimate the parameters of ruminal degradation kinetics through the classical methods of univariate analysis. As these trials involve repeated measurements, we propose the use of nonlinear mixed models which allows that the nonlinear regression function depends on fixed and random effects, which can solve the problems of correlation between the repeated measurements and heterogeneity of variances of the responses. In this work, we used two common alternatives of digestibility data analysis, and their results were compared with the approach which uses nonlinear mixed model. We used the nonlinear model of Orskov and McDonald (1979) to explain the kinetics of ruminal degradation of dry matter (MS) and neutral detergent fiber (FDN) of the hay grass-Tifton 85, in steers fed experimental with six diets composed of three different combinations of forage(Vo):concentrate(Co) (70:30, 50:50 and 30:70%). As forage, we used hay grass-Tifton 85 of different qualities (4% and 10% crude protein) and as concentrate, soybean hulls, corn and sunflower meal. The degradability was determined by the in situ technique and the incubation times were 3, 6, 12, 24, 48, 60, 72, 84, 96 and 120 hours. Originally the experiment was designed as a Latin square (6 × 6) with six fistulated crossbred steers (lines), six periods (columns) and six treatments, in which the plots have a splitplot structure where the subplots were considered the times of incubation. The use of nonlinear mixed models in the analysis of the in situ digestibility data is quite attractive especially when the research aims to understand the process behavior digestibility over the incubation times. Moreover, the higher the variability of the data, the mixed approach becomes more suitable, reducing standard errors of the estimated parameters. Even excluding the structure of experimental design, the linear mixed models can explain well the extra variability caused by the effects of the factors associated with the design, with the inclusion of random effects in the model parameters of Orskov and McDonald (1979). The R statistical package nlme proved to be agile and efficient for the adjustment of nonlinear mixed models and its graphical tools were important in evaluating the quality of the adjustments and the choice of models.

L’Accident Vasculaire Cérébral (AVC) est une maladie grave pour laquelle des critères très stricts encadrent l’administration du traitement curatif en phase aigüe. Ces critères limitent drastiquement l’accès à ce traitement : on estime que seuls 10% des patients atteints d’un AVC en bénéficient. L’objectif de ce travail est de proposer un modèle prédictif de l’évolution de l’AVC qui permette d’identifier le volume de tissu à risque de chaque patient. Ce volume, qui correspond au bénéfice potentiel du traitement, permettra de mieux orienter le médecin dans sa décision de traiter. Pour répondre à cet objectif nous nous intéressons aux problématiques d’évaluation de modèles prédictifs dans un contexte de faible prévalence, de modélisation prédictive sur données spatiales, de prédiction volumique en fonction de l’option de traitement et de segmentation d’images en présence d’artefacts. Les outils développés ont été rassemblés au sein d’une librairie de fonctions du logiciel R nommée MRIaggr / Stroke is a serious disease that needs emergency health care. Due to potential side effects, the patients must fulfil very restrictive criteria for eligibility to the curative treatment. These criteria limit drastically the accessibility to treatment : currently, an estimated 10% of stroke patients are treated. The purpose of this work was to develop a statistical framework for stroke predictive models. We deal with assessing predictive models in a low-prevalence context, building predictive models for spatial data, making volumic predictions depending on the treatement option, and performing image segmentation in presence of image artefacts. Tools developed in this thesis have been collected in an R package named MRIaggr

The aim of this work was to present the issue of neural network, which is still, despite the fact it exist and has been applied for several years, remains quite unknown for a considerably big part of public and academical environment. The aim of the practical part was to verify via practical application if neural network are truly a better instrument of statistical analysis, than the commonly used ones, especially when the goal is to analyze and describe complex processes and relationships between them. Further aim of the work was to investigate and describe the relationships between the development of trading volumes of Apple shares and the shares of competitive companies regarding the market of smart phones such as Google, HTC, Nokia, Samsung using neural network models. The attainment of these goals was realized through a rather extensive description of neural networks theory as well as the presentation of valuable theoretical tools for avoiding the frequent barriers occurring during the practical implementation. This practical application was realized via software called R, which has widely spread lately due to its availability and a vast range of flexibility, which is provided to users. The value of this work is familiarization and the creation of an integrated knowledge within readers about the issue of neural networks and the deliverance of a proof, that neural networks are indeed a better tool compared to the commonly used ones (ARMA models, linear regression). The author of the work gained a lot of useful knowledge about neural networks, learned how to use them in practice especially in the environment of R software, by which he shifted his proficiency with the current software to a whole new level.

No description available.

The agricultural sector is one of the largest consumers of fresh water. With the ever-increasing problem of water scarcity, urbanization, over-population, and climate change, fresh water resources used by agriculture could be put to better use by redirecting it for drinking water purposes. In this context, many countries reuse treated urban waste water for irrigation, to overcome this problem. While this is a sustainable practice, the reuse of urban wastewater could facilitate the spread of pathogenic bacteria (or antibiotic resistant bacteria) in the subsoil region and consequently the groundwater. Since groundwater is one of the main sources of drinking water, the contaminants could pose a risk to human health. Furthermore, obtaining scientific data for emerging contaminants during water reuse is the need of the hour. The objective of this work is to build a mechanistic model that can aid in the development of large-scale risk assessment models; thus facilitating the setup of water reuse regulations for the relevant pathogenic organisms. In the present study, process based models were developed and evaluated using lab scale results. Then, the relative time scales of the processes are compared, and the relative importance of the various process studies are assessed. When assessing time scales of the processes, it is kept in mind that processes with relatively fast time scales can be approximated using equilibrium models, relatively slow processes can be neglected, and only the rate limiting processes can neither be neglected or further simplified in further model development. Therefore, an idea of the rate limiting processes assessed in lab scale can serve as important tools facilitating model simplification when evaluating larger scale models. A combined experimental and modelling approach has been used to study relevant transport and reactive processes during bacteria transport through sandy sediments. The mechanistic model contained transport processes which were implemented using the advective dispersive equation. An additional straining process was added using non-linear rate law. The biological processes of decay, respiration, attachment, and growth were expressed using linear rate laws. This mechanistic model was verified using data from fully water saturated, sediment packed lab-scale column experiments. Continuous injection of tracer, microspheres, and Enterococci (in water environments with and without dissolved oxygen and nutrients) was performed. The experiment was verified for three flow velocities (0.13, 0.08 and 0.02 cm/min), and the parameter values were compared for these flow velocities using dimensionless numbers. The linear rate coefficients were converted to a dimensionless form (Peclet and Damkoehler numbers respectively) to facilitate the comparison of processes across the various flow velocities. The results indicate that the processes of attachment and growth are flow dependent. Furthermore, in the presence of dissolved oxygen, attachment of bacteria to sediment was the most influential process. Sensitivity analysis showed that the parameters representing growth and respiration were influential, and care must be taken when using the results for field-scale experiments or models. These processes and parameters add new knowledge on the impact of urban wastewater reuse on the spread of pathogenic bacteria (especially resilient species like Enterococci), and emphasizes the importance of research in this area. Future work could focus on obtaining data from culture independent methods and extension of the model framework, and include (where necessary) non-linear rate laws. This will provide a critical pathway to developing a decision support framework for use by regulatory frameworks, policy makers, stakeholders, local and global environmental agencies, World Health Organization, or the United Nations.:List of Figures vii List of Tables xi List of Abbreviations xiii List of Symbols xv Summary xvii Zussamenfassung xix 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Broad Scope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Hypotheses and Research objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Outline of the work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Concepts, terminologies, and methodology 7 2.1 Concepts and terminologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.2 The vadose zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 Porosity and pore models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.4 Darcy’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Bacteria strain used and Processes Studied . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.1 Enterococcus faecalis JH2-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.2 Advection and Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2.3 Straining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.4 Microbial Decay and Respiration . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.5 Microbial Attachment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2.6 Microbial Growth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.7 Dimensionless numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3 Experimental design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4 Model setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3 Reactive-transport modelling of Enterococcus faecalis JH2-2 passage through water saturated sediment columns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2.1 Experimental study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2.2 Modeling and data analysis procedure. . . . . . . . . . . . . . . . . . . . . . . . 40 3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.3.1 Determination of hydraulic and non-reactive transport parameters (experiments E1 and E2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.3.2 Determination of parameters related to the bacteria transport (E3 series) . . . 45 3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.4.1 Physical processes (E1 and E2) . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.4.2 Biological Processes (E3 series) . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.5 Conclusions and Outlook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.6 Supplementary material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4 Determining the impact of flow velocities on reactive processes associated with Enterococcus faecalis JH2-2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.2.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.2.2 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.3.1 Tracer and microsphere experiments. . . . . . . . . . . . . . . . . . . . . . . . . 74 4.3.2 Bacteria experiments - comparison of processes. . . . . . . . . . . . . . . . . . . 75 4.4 Conclusions and Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.5 Supplementary material 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.6 Supplementary Material 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5 Synthesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.1 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.2 Critical review, pathways towards future work . . . . . . . . . . . . . . . . . . . . . . . 91 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Note on the commencement of the doctoral procedure. . . . . . . . . . . . . . . . . . . . 107 Übereinstimmungserklärung. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 List of Publications and conference presentations. . . . . . . . . . . . . . . . . . . . . . . . 111 Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 / Der Agrarsektor ist einer der größten Verbraucher von Süßwasser. Angesichts der zunehmenden Wasserknappheit, der Verstädterung, der Überbevölkerung und des Klimawandels könnten die von der Landwirtschaft genutzten Süßwasserressourcen besser genutzt werden, indem sie für Trinkwasserzwecke umgewidmet werden. In diesem Zusammenhang verwenden viele Länder aufbereitetes kommunales Abwasser für die Bewässerung, um dieses Problem zu lösen. Dies ist zwar eine nachhaltige Praxis, aber die Wiederverwendung von kommunalem Abwasser könnte die Ausbreitung pathogener Bakterien (oder antibiotikaresistenter Bakterien) im Untergrund und damit im Grundwasser fördern. Da das Grundwasser eine der Hauptquellen für Trinkwasser ist, könnten diese Schadstoffe eine Gefahr für die menschliche Gesundheit darstellen. Darüber hinaus ist es ein Gebot der Stunde, wissenschaftliche Daten über neu auftretende Verunreinigungen bei der Wasserwiederverwendung zu gewinnen. Ziel dieser Arbeit ist es, ein mechanistisches Modell zu erstellen, das bei der Entwicklung groß angelegter Risikobewertungsmodelle behilflich sein kann und somit die Aufstellung von Vorschriften für die Wiederverwendung von Wasser für die relevanten pathogenen Organismen erleichtert. In der vorliegenden Studie wurden prozessbasierte Modelle entwickelt und anhand von Ergebnissen im Labormaßstab bewertet. Anschließend werden die relativen Zeitskalen der Prozesse verglichen und die relative Bedeutung der verschiedenen Prozessstudien bewertet. Bei der Bewertung der Zeitskalen der Prozesse wird berücksichtigt, dass Prozesse mit relativ schnellen Zeitskalen durch Gleichgewichtsmodelle angenähert werden können, relativ langsame Prozesse können vernachlässigt werden, und nur die ratenbegrenzenden Prozesse dürfen in der weiteren Modellentwicklung weder vernachlässigt noch vereinfacht werden. Daher kann eine Vorstellung von den ratenbegrenzenden Prozessen, die im Labormaßstab bewertet werden, als wichtiges Instrument zur Vereinfachung des Modells bei der Bewertung von Modellen in größerem Maßstab dienen. Ein kombinierter experimenteller und modellierender Ansatz wurde verwendet, um relevante Transport- und reaktive Prozesse während des Bakterientransports durch sandige Sedimente zu untersuchen. Das mechanistische Modell enthielt Transportprozesse, die mit Hilfe der Advektions-Dispersions-Gleichung implementiert wurden. Ein zusätzlicher Filtrationsprozess ('straining') wurde mit Hilfe nichtlinearer Ratengesetze hinzugefügt. Die biologischen Prozesse des Zerfalls, der Atmung, der Anhaftung und des Wachstums wurden durch lineare Ratengesetze ausgedrückt. Dieses mechanistische Modell wurde anhand von Daten aus vollständig wassergesättigten, sedimentgefüllten Säulenexperimenten im Labormaßstab verifiziert. Kontinuierliche Injektion von Tracer, Mikrosphären und Enterokokken (in Wasserumgebungen mit und ohne gelösten Sauerstoff und Nährstoffe) wurde durchgeführt. Das Experiment wurde für drei Strömungsgeschwindigkeiten (0,13, 0,08 und 0,02 cm/min) verifiziert, und die Parameterwerte wurden für diese Strömungsgeschwindigkeiten anhand dimensionsloser Zahlen verglichen. Die linearen Ratengesetze wurden in eine dimensionslose Form umgewandelt (Peclet- bzw. Damköhler-Zahlen), um den Vergleich der Prozesse bei den verschiedenen Strömungsgeschwindigkeiten zu erleichtern. Die Konzentrationen wurden in regelmäßigen Abständen sowohl am Einlass als auch am Auslass der Kolonnen gemessen. Die überprüften Prozesse waren Advektion, Dispersion, Filtration, Zerfall, Atmung, Wachstum und Anhaftung. Der Versuch wurde für drei Strömungsgeschwindigkeiten (0,13, 0,08 und 0,02 cm/min) wiederholt, und die verifizierten Parameterwerte wurden für diese Strömungsgeschwindigkeiten verglichen. Die Ergebnisse zeigen, dass die Prozesse der Anhaftung und des Wachstums strömungsabhängig sind. Darüber hinaus war bei Vorhandensein von gelöstem Sauerstoff die Anhaftung der Bakterien an das Sediment der einflussreichste Prozess. Die Sensitivitätsanalyse zeigte, dass die Parameter, die das Wachstum und die Atmung repräsentieren, einflussreich sind, so dass bei der Verwendung der Ergebnisse für Experimente oder Modelle im Feldmaßstab Vorsicht geboten ist. Diese Prozesse und Parameter liefern neue Erkenntnisse über die Auswirkungen der Wiederverwendung von kommunalem Abwasser auf die Ausbreitung pathogener Bakterien (insbesondere widerstandsfähiger Arten wie Enterokokken) und unterstreichen die Bedeutung der Forschung in diesem Bereich. Zukünftige Arbeiten könnten sich auf die Gewinnung von Daten aus kulturunabhängigen Methoden und die Erweiterung des Modellrahmens konzentrieren und (wo nötig) nichtlineare Parameter einbeziehen. Dies wird einen entscheidenden Weg zur Entwicklung eines Rahmens für die Entscheidungsfindung darstellen, der von Regulierungsbehörden, politischen Entscheidungsträgern, Interessengruppen sowie lokalen und globalen Umweltbehörden, der Weltgesundheitsorganisation oder den Vereinten Nationen genutzt werden kann.:List of Figures vii List of Tables xi List of Abbreviations xiii List of Symbols xv Summary xvii Zussamenfassung xix 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Broad Scope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Hypotheses and Research objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Outline of the work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Concepts, terminologies, and methodology 7 2.1 Concepts and terminologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.2 The vadose zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 Porosity and pore models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.4 Darcy’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Bacteria strain used and Processes Studied . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.1 Enterococcus faecalis JH2-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.2 Advection and Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2.3 Straining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.4 Microbial Decay and Respiration . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.5 Microbial Attachment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2.6 Microbial Growth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.7 Dimensionless numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3 Experimental design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4 Model setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3 Reactive-transport modelling of Enterococcus faecalis JH2-2 passage through water saturated sediment columns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2.1 Experimental study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2.2 Modeling and data analysis procedure. . . . . . . . . . . . . . . . . . . . . . . . 40 3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.3.1 Determination of hydraulic and non-reactive transport parameters (experiments E1 and E2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.3.2 Determination of parameters related to the bacteria transport (E3 series) . . . 45 3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.4.1 Physical processes (E1 and E2) . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.4.2 Biological Processes (E3 series) . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.5 Conclusions and Outlook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.6 Supplementary material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4 Determining the impact of flow velocities on reactive processes associated with Enterococcus faecalis JH2-2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.2.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.2.2 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.3.1 Tracer and microsphere experiments. . . . . . . . . . . . . . . . . . . . . . . . . 74 4.3.2 Bacteria experiments - comparison of processes. . . . . . . . . . . . . . . . . . . 75 4.4 Conclusions and Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.5 Supplementary material 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.6 Supplementary Material 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5 Synthesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.1 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.2 Critical review, pathways towards future work . . . . . . . . . . . . . . . . . . . . . . . 91 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Note on the commencement of the doctoral procedure. . . . . . . . . . . . . . . . . . . . 107 Übereinstimmungserklärung. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 List of Publications and conference presentations. . . . . . . . . . . . . . . . . . . . . . . . 111 Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

The Birnbaum-Saunders (BS) distribution is the most popular model used to describe lifetime process under fatigue. Throughout the years, this distribution has received a wide ranging of applications, demanding some more flexible extensions to solve more complex problems. One of the most well-known extensions of the BS distribution is the generalized Birnbaum- Saunders (GBS) family of distributions that includes the Birnbaum-Saunders special-case (BSSC) and the Birnbaum-Saunders generalized t (BSGT) models as special cases. Although the BS-SC distribution was previously developed in the literature, it was never deeply studied and hence, in this thesis, we provide a full Bayesian study and develop a tool to generate random numbers from this distribution. Further, we develop a very flexible regression model, that admits different degrees of skewness and kurtosis, based on the BSGT distribution using the generalized additive models for location, scale and shape (GAMLSS) framework. We also introduce a new extension of the BS distribution called the Birnbaum-Saunders power (BSP) family of distributions, which contains several special or limiting cases already published in the literature, including the GBS family. The main feature of the new family is that it can produce both unimodal and bimodal shapes depending on its parameter values. We also introduce this new family of distributions into the GAMLSS framework, in order to model any or all the parameters of the distribution using parametric linear and/or nonparametric smooth functions of explanatory variables. Throughout this thesis we present five different applications in real data sets in order to illustrate the developed theoretical results. / A distribuição Birnbaum-Saunders (BS) é o modelo mais popular utilizado para descrever processos de fadiga. Ao longo dos anos, essa distribuição vem recebendo aplicações nas mais diversas áreas, demandando assim algumas extensões mais flexíveis para resolver problemas mais complexos. Uma das extensões mais conhecidas na literatura é a família de distribuições Birnbaum-Saunders generalizada (GBS), que inclui as distribuições Birnbaum-Saunders casoespecial (BS-SC) e Birnbaum-Saunders t generalizada (BSGT) como modelos especiais. Embora a distribuição BS-SC tenha sido previamente desenvolvida na literatura, nunca foi estudada mais profundamente e, assim, nesta tese, um estudo bayesiano é desenvolvido acerca da mesma além de um novo gerador de números aleatórios dessa distribuição ser apresentado. Adicionalmente, um modelo de regressão baseado na distribuição BSGT é desenvolvido utilizando-se os modelos aditivos generalizados para locação, escala e forma (GAMLSS), os quais apresentam grande flexibilidade tanto para a assimetria como para a curtose. Uma nova extensão da distribuição BS também é apresentada, denominada família de distribuições Birnbaum-Saunders potência (BSP), que contém inúmeros casos especiais ou limites já publicados na literatura, incluindo a família GBS. A principal característica desta nova família é que ela é capaz de produzir formas tanto uni como bimodais dependendo do valor de seus parâmetros. Esta nova família também é introduzida na estrutura dos modelos GAMLSS para fornecer uma ferramenta capaz de modelar todos os parâmetros da distribuição como funções lineares e/ou não-lineares suavizadas de variáveis explicativas. Ao longo desta tese são apresentadas cinco diferentes aplicações em conjuntos de dados reais para ilustrar os resultados teóricos obtidos.