This PhD study, developed at Universitat Politècnica de València (UPV), aims to cover the first phase of the benchmark released by the expert group on Uncertainty Analysis in Modeling (UAM-LWR). The main contribution to the benchmark, made by the thesis' author, is the development of a MATLAB program requested by the benchmark organizers. This is used to generate neutronic libraries to distribute among the benchmark participants. The UAM benchmark pretends to determine the uncertainty introduced by coupled multi-physics and multi-scale LWR analysis codes. The benchmark is subdivided into three phases: 1. Neutronic phase: obtain collapsed and homogenized problem-dependent cross sections and criticality analyses. 2. Core phase: standalone thermohydraulic and neutronic codes. 3. System phase: coupled thermohydraulic and neutronic code. In this thesis the objectives of the first phase are covered. Specifically, a methodology is developed to propagate the uncertainty of cross sections and other neutronic parameters through a lattice physics code and core simulator. An Uncertainty and Sensitivity (U&S) analysis is performed over the cross sections contained in the ENDF/B-VII nuclear library. Their uncertainty is propagated through the lattice physics code SCALE6.2.1, including the collapse and homogenization phase, up to the generation of problem-dependent neutronic libraries. Afterward, the uncertainty contained in these libraries can be further propagated through a core simulator, in this study PARCSv3.2. The module SAMPLER -available in the latest release of SCALE- and DAKOTA 6.3 statistical tool are used for the U&S analysis. As a part of this process, a methodology to obtain neutronic libraries in NEMTAB format -to be used in a core simulator- is also developed. A code-to-code comparison with CASMO-4 is used as a verification. The whole methodology is tested using a Boiling Water Reactor (BWR) reactor type. Nevertheless, there is not any concern or limitation regarding its use in any other type of nuclear reactor. The Gesellschaft für Anlagen und Reaktorsicherheit (GRS) stochastic methodology for uncertainty quantification is used. This methodology makes use of the high-fidelity model and nonparametric sampling to propagate the uncertainty. As a result, the number of samples (determined using the revised Wilks' formula) does not depend on the number of input parameters but only on the desired confidence and uncertainty of output parameters. Moreover, the output Probability Distribution Functions (PDFs) are not subject to normality. The main disadvantage is that each input parameter must have a pre-defined PDF. If possible, input PDFs are defined using information found in the related literature. Otherwise, the uncertainty definition is based on expert judgment. A second scenario is used to propagate the uncertainty of different thermohydraulic parameters through the coupled code TRACE5.0p3/PARCSv3.0. In this case, a PWR reactor type is used and a transient control rod drop occurrence is simulated. As a new feature, the core is modeled chan-by-chan following a fully 3D discretization. No other study is found using a detailed 3D core. This U&S analysis also makes use of the GRS methodology and DAKOTA 6.3. / Este trabajo de doctorado, desarrollado en la Universitat Politècnica de València (UPV), tiene como objetivo cubrir la primera fase del benchmark presentado por el grupo de expertos Uncertainty Analysis in Modeling (UAM-LWR). La principal contribución al benchmark, por parte del autor de esta tesis, es el desarrollo de un programa de MATLAB solicitado por los organizadores del benchmark, el cual se usa para generar librerías neutrónicas a distribuir entre los participantes del benchmark. El benchmark del UAM pretende determinar la incertidumbre introducida por los códigos multifísicos y multiescala acoplados de análisis de reactores de agua ligera. El citado benchmark se divide en tres fases: 1. Fase neutrónica: obtener los parámetros neutrónicos y secciones eficaces del problema específico colapsados y homogenizados, además del análisis de criticidad. 2. Fase de núcleo: análisis termo-hidráulico y neutrónico por separado. 3. Fase de sistema: análisis termo-hidráulico y neutrónico acoplados. En esta tesis se completan los principales objetivos de la primera fase. Concretamente, se desarrolla una metodología para propagar la incertidumbre de secciones eficaces y otros parámetros neutrónicos a través de un código lattice y un simulador de núcleo. Se lleva a cabo un análisis de incertidumbre y sensibilidad para las secciones eficaces contenidas en la librería neutrónica ENDF/B-VII. Su incertidumbre se propaga a través del código lattice SCALE6.2.1, incluyendo las fases de colapsación y homogenización, hasta llegar a la generación de una librería neutrónica específica del problema. Luego, la incertidumbre contenida en dicha librería puede continuar propagándose a través de un simulador de núcleo, para este estudio PARCSv3.2. Para el análisis de incertidumbre y sensibilidad se ha usado el módulo SAMPLER -disponible en la última versión de SCALE- y la herramienta estadística DAKOTA 6.3. Como parte de este proceso, también se ha desarrollado una metodología para obtener librerías neutrónicas en formato NEMTAB para ser usadas en simuladores de núcleo. Se ha realizado una comparación con el código CASMO-4 para obtener una verificación de la metodología completa. Esta se ha probado usando un reactor de agua en ebullición del tipo BWR. Sin embargo, no hay ninguna preocupación o limitación respecto a su uso con otro tipo de reactor nuclear. Para la cuantificación de la incertidumbre se usa la metodología estocástica Gesellschaft für Anlagen und Reaktorsicherheit (GRS). Esta metodología hace uso del modelo de alta fidelidad y un muestreo no paramétrico para propagar la incertidumbre. Como resultado, el número de muestras (determinado con la fórmula revisada de Wilks) no depende del número de parámetros de entrada, sólo depende del nivel de confianza e incertidumbre deseados de los parámetros de salida. Además, las funciones de distribución de probabilidad no están limitadas a normalidad. El principal inconveniente es que se ha de disponer de las distribuciones de probabilidad de cada parámetro de entrada. Si es posible, las distribuciones de probabilidad de entrada se definen usando información encontrada en la literatura relacionada. En caso contrario, la incertidumbre se define en base a la opinión de un experto. Se usa un segundo escenario para propagar la incertidumbre de diferentes parámetros termo-hidráulicos a través del código acoplado TRACE5.0p3/PARCSv3.0. En este caso, se utiliza un reactor tipo PWR para simular un transitorio de una caída de barra. Como nueva característica, el núcleo se modela elemento a elemento siguiendo una discretización totalmente en 3D. No se ha encontrado ningún otro estudio que use un núcleo tan detallado en 3D. También se usa la metodología GRS y el DAKOTA 6.3 para este análisis de incertidumbre y sensibilidad. / Aquest treball de doctorat, desenvolupat a la Universitat Politècnica de València (UPV), té com a objectiu cobrir la primera fase del benchmark presentat pel grup d'experts Uncertainty Analysis in Modeling (UAM-LWR). La principal contribució al benchmark, per part de l'autor d'aquesta tesi, es el desenvolupament d'un programa de MATLAB sol¿licitat pels organitzadors del benchmark, el qual s'utilitza per a generar llibreries neutròniques a distribuir entre els participants del benchmark. El benchmark del UAM pretén determinar la incertesa introduïda pels codis multifísics i multiescala acoblats d'anàlisi de reactors d'aigua lleugera. El citat benchmark es divideix en tres fases: 1. Fase neutrònica: obtenir els paràmetres neutrònics i seccions eficaces del problema específic, col¿lapsats i homogeneïtzats, a més de la anàlisi de criticitat. 2. Fase de nucli: anàlisi termo-hidràulica i neutrònica per separat. 3. Fase de sistema: anàlisi termo-hidràulica i neutrònica acoblats. En aquesta tesi es completen els principals objectius de la primera fase. Concretament, es desenvolupa una metodologia per propagar la incertesa de les seccions eficaces i altres paràmetres neutrònics a través d'un codi lattice i un simulador de nucli. Es porta a terme una anàlisi d'incertesa i sensibilitat per a les seccions eficaces contingudes en la llibreria neutrònica ENDF/B-VII. La seua incertesa es propaga a través del codi lattice SCALE6.2.1, incloent les fases per col¿lapsar i homogeneïtzar, fins aplegar a la generació d'una llibreria neutrònica específica del problema. Després, la incertesa continguda en la esmentada llibreria pot continuar propagant-se a través d'un simulador de nucli, per a aquest estudi PARCSv3.2. Per a l'anàlisi d'incertesa i sensibilitat s'ha utilitzat el mòdul SAMPLER -disponible a l'última versió de SCALE- i la ferramenta estadística DAKOTA 6.3. Com a part d'aquest procés, també es desenvolupa una metodologia per a obtenir llibreries neutròniques en format NEMTAB per ser utilitzades en simuladors de nucli. S'ha realitzat una comparació amb el codi CASMO-4 per obtenir una verificació de la metodologia completa. Aquesta s'ha provat utilitzant un reactor d'aigua en ebullició del tipus BWR. Tanmateix, no hi ha cap preocupació o limitació respecte del seu ús amb un altre tipus de reactor nuclear. Per a la quantificació de la incertesa s'utilitza la metodologia estocàstica Gesellschaft für Anlagen und Reaktorsicherheit (GRS). Aquesta metodologia fa ús del model d'alta fidelitat i un mostreig no paramètric per propagar la incertesa. Com a resultat, el nombre de mostres (determinat amb la fórmula revisada de Wilks) no depèn del nombre de paràmetres d'entrada, sols depèn del nivell de confiança i incertesa desitjats dels paràmetres d'eixida. A més, las funcions de distribució de probabilitat no estan limitades a la normalitat. El principal inconvenient és que s'ha de disposar de les distribucions de probabilitat de cada paràmetre d'entrada. Si és possible, les distribucions de probabilitat d'entrada es defineixen utilitzant informació trobada a la literatura relacionada. En cas contrari, la incertesa es defineix en base a l'opinió d'un expert. S'utilitza un segon escenari per propagar la incertesa de diferents paràmetres termo-hidràulics a través del codi acoblat TRACE5.0p3/PARCSv3.0. En aquest cas, s'utilitza un reactor tipus PWR per simular un transitori d'una caiguda de barra. Com a nova característica, cal assenyalar que el nucli es modela element a element seguint una discretizació totalment 3D. No s'ha trobat cap altre estudi que utilitze un nucli tan detallat en 3D. També s'utilitza la metodologia GRS i el DAKOTA 6.3 per a aquesta anàlisi d'incertesa i sensibilitat.¿ / Mesado Melia, C. (2017). Uncertainty Quantification and Sensitivity Analysis for Cross Sections and Thermohydraulic Parameters in Lattice and Core Physics Codes. Methodology for Cross Section Library Generation and Application to PWR and BWR [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/86167

Causal models have been used in different areas of knowledge in order to comprehend the causal associations between variables. Over the past decades, the amount of studies using these models have been growing a lot, especially those related to biological systems where studying and learning causal relationships among traits are essential for predicting the consequences of interventions in such system. Graph analysis (GA) and structural equation modeling (SEM) are tools used to explore such associations. While GA allows searching causal structures that express qualitatively how variables are causally connected, fitting SEM with a known causal structure allows to infer the magnitude of causal effects. Also SEM can be viewed as multiple regression models in which response variables can be explanatory variables for others. In quantitative genetics studies, SEM aimed to study the direct and indirect genetic effects associated to individuals through information related to them, beyond the observed characteristics, such as the kinship relations. In those studies typically the assumptions of linear relationships among traits are made. However, in some scenarios, nonlinear relationships can be observed, which make unsuitable the mentioned assumptions. To overcome this limitation, this paper proposes to use a mixed effects polynomial structural equation model, second or superior degree, to model those nonlinear relationships. Two studies were developed, a simulation and an application to real data. The first study involved simulation of 50 data sets, with a fully recursive causal structure involving three characteristics in which linear and nonlinear causal relations between them were allowed. The second study involved the analysis of traits related to dairy cows of the Holstein breed. Phenotypic relationships between traits were calving difficulty, gestation length and also the proportion of perionatal death. We compare the model of multiple traits and polynomials structural equations models, under different polynomials degrees in order to assess the benefits of the SEM polynomial of second or higher degree. For some situations the inappropriate assumption of linearity results in poor predictions of the direct, indirect and total of the genetic variances and covariance, either overestimating, underestimating, or even assign opposite signs to covariances. Therefore, we conclude that the inclusion of a polynomial degree increases the SEM expressive power. / Modelos causais têm sido muitos utilizados em estudos em diferentes áreas de conhecimento, a fim de compreender as associações ou relações causais entre variáveis. Durante as últimas décadas, o uso desses modelos têm crescido muito, especialmente estudos relacionados à sistemas biológicos, uma vez que compreender as relações entre características são essenciais para prever quais são as consequências de intervenções em tais sistemas. Análise do grafo (AG) e os modelos de equações estruturais (MEE) são utilizados como ferramentas para explorar essas relações. Enquanto AG nos permite buscar por estruturas causais, que representam qualitativamente como as variáveis são causalmente conectadas, ajustando o MEE com uma estrutura causal conhecida nos permite inferir a magnitude dos efeitos causais. Os MEE também podem ser vistos como modelos de regressão múltipla em que uma variável resposta pode ser vista como explanatória para uma outra característica. Estudos utilizando MEE em genética quantitativa visam estudar os efeitos genéticos diretos e indiretos associados aos indivíduos por meio de informações realcionadas aos indivíduas, além das característcas observadas, como por exemplo o parentesco entre eles. Neste contexto, é tipicamente adotada a suposição que as características observadas são relacionadas linearmente. No entanto, para alguns cenários, relações não lineares são observadas, o que torna as suposições mencionadas inadequadas. Para superar essa limitação, este trabalho propõe o uso de modelos de equações estruturais de efeitos polinomiais mistos, de segundo grau ou seperior, para modelar relações não lineares. Neste trabalho foram desenvolvidos dois estudos, um de simulação e uma aplicação a dados reais. O primeiro estudo envolveu a simulação de 50 conjuntos de dados, com uma estrutura causal completamente recursiva, envolvendo 3 características, em que foram permitidas relações causais lineares e não lineares entre as mesmas. O segundo estudo envolveu a análise de características relacionadas ao gado leiteiro da raça Holandesa, foram utilizadas relações entre os seguintes fenótipos: dificuldade de parto, duração da gestação e a proporção de morte perionatal. Nós comparamos o modelo misto de múltiplas características com os modelos de equações estruturais polinomiais, com diferentes graus polinomiais, a fim de verificar os benefícios do MEE polinomial de segundo grau ou superior. Para algumas situações a suposição inapropriada de linearidade resulta em previsões pobres das variâncias e covariâncias genéticas diretas, indiretas e totais, seja por superestimar, subestimar, ou mesmo atribuir sinais opostos as covariâncias. Portanto, verificamos que a inclusão de um grau de polinômio aumenta o poder de expressão do MEE.

<p>Air pollutants pose a high risk for humans, and the environment, and this pollution is one of the major environmental problems facing modern society. Active air sampling is the technique that has been traditionally used to monitor nonpolar aromatic air pollutants. However, active high volume samplers (HiVols) require a power supply, maintenance and specialist operators, and the equipment is often expensive. Thus, there is a need to develop new, less complicated sampling techniques that can increase the monitoring frequency, the geographical distribution of the measurements, and the number of sites used in air monitoring programs. In the work underlying this thesis, the use of semipermeable membrane devices (SPMDs) as tools for monitoring gas phase concentrations of nonpolar aromatic compound was evaluated using the compound classes polychlorinated biphenyls (PCBs), polycyclic aromatic hydrocarbons (PAHs), alkylated PAHs (alkyl-PAHs) and nitrated PAHs (nitro-PAHs) as test compounds. </p><p>High wind-speeds increased the uptake and release in SPMDs of PAHs and PCBs with log K_OA values > 7.9, demonstrating that the uptake of most nonpolar aromatic compounds is controlled by the boundary layer at the membrane-air interface. The use of a metal umbrella to shelter the SPMDs decreased the uptake of PAHs and PCBs by 38 and 55 percent, respectively, at high wind/turbulence, and thus reduced the wind effect. Further, the use of performance reference compounds (PRCs) to assess the site effect of wind on the uptake in SPMDs reduced the between-site differences to less than 50 percent from as much as three times differences in uptake of PCBs and PAHs. However, analytical interferences reduced the precision of some PRCs, showing the importance of using robust analytical quality control.</p><p>SPMDs were shown to be efficient samplers of gas phase nonpolar aromatic compounds, and were able to determine local, continental and indoor spatial distributions of PAHs, alkyl- PAHs and nitro-PAHs. In addition, the use of the SPMDs, which do not require electricity, made sampling possible at remote/rural areas where the infrastructure was limited. SPMDs were also used to determine the source of PAH pollution, and different approaches were discussed. Finally, SPMDs were used to estimate the importance of the gas phase exposure route to the uptake of PAHs in plants. The results demonstrate that SPMDs have several advantages compared with HiVols, including integrative capacity over long times, reduced costs, and no need of special operators, maintenance or power supply for sampling. However, calibration data of SPMDs in air are limited, and spatial differences are often only semi-quantitatively determined by comparing amounts and profiles in the SPMDs, which have limited their use in air monitoring programs. In future work, it is therefore important that SPMDs are properly sheltered, PRCs are used in the sampling protocols, and that calibrated sampling rate data, or the SPMD-air partition data, of specific compounds are further developed to make determination of time weighted average (TWA) concentrations possible.</p>

Air pollutants pose a high risk for humans, and the environment, and this pollution is one of the major environmental problems facing modern society. Active air sampling is the technique that has been traditionally used to monitor nonpolar aromatic air pollutants. However, active high volume samplers (HiVols) require a power supply, maintenance and specialist operators, and the equipment is often expensive. Thus, there is a need to develop new, less complicated sampling techniques that can increase the monitoring frequency, the geographical distribution of the measurements, and the number of sites used in air monitoring programs. In the work underlying this thesis, the use of semipermeable membrane devices (SPMDs) as tools for monitoring gas phase concentrations of nonpolar aromatic compound was evaluated using the compound classes polychlorinated biphenyls (PCBs), polycyclic aromatic hydrocarbons (PAHs), alkylated PAHs (alkyl-PAHs) and nitrated PAHs (nitro-PAHs) as test compounds. High wind-speeds increased the uptake and release in SPMDs of PAHs and PCBs with log KOA values &gt; 7.9, demonstrating that the uptake of most nonpolar aromatic compounds is controlled by the boundary layer at the membrane-air interface. The use of a metal umbrella to shelter the SPMDs decreased the uptake of PAHs and PCBs by 38 and 55 percent, respectively, at high wind/turbulence, and thus reduced the wind effect. Further, the use of performance reference compounds (PRCs) to assess the site effect of wind on the uptake in SPMDs reduced the between-site differences to less than 50 percent from as much as three times differences in uptake of PCBs and PAHs. However, analytical interferences reduced the precision of some PRCs, showing the importance of using robust analytical quality control. SPMDs were shown to be efficient samplers of gas phase nonpolar aromatic compounds, and were able to determine local, continental and indoor spatial distributions of PAHs, alkyl- PAHs and nitro-PAHs. In addition, the use of the SPMDs, which do not require electricity, made sampling possible at remote/rural areas where the infrastructure was limited. SPMDs were also used to determine the source of PAH pollution, and different approaches were discussed. Finally, SPMDs were used to estimate the importance of the gas phase exposure route to the uptake of PAHs in plants. The results demonstrate that SPMDs have several advantages compared with HiVols, including integrative capacity over long times, reduced costs, and no need of special operators, maintenance or power supply for sampling. However, calibration data of SPMDs in air are limited, and spatial differences are often only semi-quantitatively determined by comparing amounts and profiles in the SPMDs, which have limited their use in air monitoring programs. In future work, it is therefore important that SPMDs are properly sheltered, PRCs are used in the sampling protocols, and that calibrated sampling rate data, or the SPMD-air partition data, of specific compounds are further developed to make determination of time weighted average (TWA) concentrations possible.

針對金融時序資料變異數不齊一的性質，隨機波動模型除了提供於ARCH族外的另一選擇；且由於其設定隱含波動本身亦為一個隨機波動函數，藉由設定隨時間改變且自我相關的條件變異數，使得隨機波動模型較ARCH族來得有彈性且符合實際。傳統上處理隨機波動模型的參數估計往往需要面對到複雜的多維積分，此問題可藉由貝氏分析裡的馬可夫鏈蒙地卡羅法解決。本文主要的探討標的，即在於利用馬可夫鏈蒙地卡羅法估計美元/新台幣匯率隨機波動模型參數。除原始模型之外，模型的擴充分為三部分：其一為隱含波動的二階自我回歸模型；其二則為藉由基本模型的修改，檢測匯率市場上的槓桿效果；最後，我們嘗試藉由加入scale mixture的方式以驗證金融時序資料中常見的厚尾分配。

設二個隨機變數X1 和X2，所可能的發生值分別為{1,…,I}和{1,…,J}。條件機率分配模型為二個I × J 的矩陣A 和B，分別代表在X2 給定的條件下X1的條件機率分配和在X1 給定的條件下X2的條件機率分配。若存在一個聯合機率分配，而且它的二個條件機率分配剛好就是A 和B，則稱A和B相容。我們透過圖形表示法，提出新的二個離散條件機率分配會相容的充分必要條件。另外，我們證明，二個相容的條件機率分配會有唯一的聯合機率分配的充分必要條件為:所對應的圖形是相連的。我們也討論馬可夫鏈與相容性的關係。 / For two discrete random variables X1 and X2 taking values in {1,…,I} and {1,…,J}, respectively, a putative conditional model for the joint distribution of X1 and X2 consists of two I × J matrices representing the conditional distributions of X1 given X2 and of X2 given X1. We say that two conditional distributions (matrices) A and B are compatible if there exists a joint distribution of X1 and X2 whose two conditional distributions are exactly A and B. We present new versions of necessary and sufficient conditions for compatibility of discrete conditional distributions via a graphical representation. Moreover, we show that there is a unique joint distribution for two given compatible conditional distributions if and only if the corresponding graph is connected. Markov chain characterizations are also presented.

Causal models have been used in different areas of knowledge in order to comprehend the causal associations between variables. Over the past decades, the amount of studies using these models have been growing a lot, especially those related to biological systems where studying and learning causal relationships among traits are essential for predicting the consequences of interventions in such system. Graph analysis (GA) and structural equation modeling (SEM) are tools used to explore such associations. While GA allows searching causal structures that express qualitatively how variables are causally connected, fitting SEM with a known causal structure allows to infer the magnitude of causal effects. Also SEM can be viewed as multiple regression models in which response variables can be explanatory variables for others. In quantitative genetics studies, SEM aimed to study the direct and indirect genetic effects associated to individuals through information related to them, beyond the observed characteristics, such as the kinship relations. In those studies typically the assumptions of linear relationships among traits are made. However, in some scenarios, nonlinear relationships can be observed, which make unsuitable the mentioned assumptions. To overcome this limitation, this paper proposes to use a mixed effects polynomial structural equation model, second or superior degree, to model those nonlinear relationships. Two studies were developed, a simulation and an application to real data. The first study involved simulation of 50 data sets, with a fully recursive causal structure involving three characteristics in which linear and nonlinear causal relations between them were allowed. The second study involved the analysis of traits related to dairy cows of the Holstein breed. Phenotypic relationships between traits were calving difficulty, gestation length and also the proportion of perionatal death. We compare the model of multiple traits and polynomials structural equations models, under different polynomials degrees in order to assess the benefits of the SEM polynomial of second or higher degree. For some situations the inappropriate assumption of linearity results in poor predictions of the direct, indirect and total of the genetic variances and covariance, either overestimating, underestimating, or even assign opposite signs to covariances. Therefore, we conclude that the inclusion of a polynomial degree increases the SEM expressive power. / Modelos causais têm sido muitos utilizados em estudos em diferentes áreas de conhecimento, a fim de compreender as associações ou relações causais entre variáveis. Durante as últimas décadas, o uso desses modelos têm crescido muito, especialmente estudos relacionados à sistemas biológicos, uma vez que compreender as relações entre características são essenciais para prever quais são as consequências de intervenções em tais sistemas. Análise do grafo (AG) e os modelos de equações estruturais (MEE) são utilizados como ferramentas para explorar essas relações. Enquanto AG nos permite buscar por estruturas causais, que representam qualitativamente como as variáveis são causalmente conectadas, ajustando o MEE com uma estrutura causal conhecida nos permite inferir a magnitude dos efeitos causais. Os MEE também podem ser vistos como modelos de regressão múltipla em que uma variável resposta pode ser vista como explanatória para uma outra característica. Estudos utilizando MEE em genética quantitativa visam estudar os efeitos genéticos diretos e indiretos associados aos indivíduos por meio de informações realcionadas aos indivíduas, além das característcas observadas, como por exemplo o parentesco entre eles. Neste contexto, é tipicamente adotada a suposição que as características observadas são relacionadas linearmente. No entanto, para alguns cenários, relações não lineares são observadas, o que torna as suposições mencionadas inadequadas. Para superar essa limitação, este trabalho propõe o uso de modelos de equações estruturais de efeitos polinomiais mistos, de segundo grau ou seperior, para modelar relações não lineares. Neste trabalho foram desenvolvidos dois estudos, um de simulação e uma aplicação a dados reais. O primeiro estudo envolveu a simulação de 50 conjuntos de dados, com uma estrutura causal completamente recursiva, envolvendo 3 características, em que foram permitidas relações causais lineares e não lineares entre as mesmas. O segundo estudo envolveu a análise de características relacionadas ao gado leiteiro da raça Holandesa, foram utilizadas relações entre os seguintes fenótipos: dificuldade de parto, duração da gestação e a proporção de morte perionatal. Nós comparamos o modelo misto de múltiplas características com os modelos de equações estruturais polinomiais, com diferentes graus polinomiais, a fim de verificar os benefícios do MEE polinomial de segundo grau ou superior. Para algumas situações a suposição inapropriada de linearidade resulta em previsões pobres das variâncias e covariâncias genéticas diretas, indiretas e totais, seja por superestimar, subestimar, ou mesmo atribuir sinais opostos as covariâncias. Portanto, verificamos que a inclusão de um grau de polinômio aumenta o poder de expressão do MEE.

The aim of the present study has been to investigate how titles of social rank used in Tudor and Stuart England are modified by attributive adjectives in pre-adjacent position and the implications that become possible to observe. Using the Corpus of Early English Correspondence Sampler (CEECS) the present work set out to examine adjectival modification, gender perspectives and MI (Mutual Information) scores in order to gain a deeper understanding of how and why titles were modified in certain ways. The titles under scrutiny are Lord, Lady, Sir, Dame, Madam, Master and Mistress and these have been analysed following theories and frameworks pertaining to the scientific discipline of sociohistorical linguistics.    The findings of the present study suggest that male titles were modified more frequently than, and differently from, female titles. The adjectives used as pre-modifiers, in turn, stem from different semantic domains which reveals differences in attitudes from the language producers towards the referents and in what traits are described regarding the holders of the titles. Additionally, a type/token ratio investigation reveals that the language producers were keener on using a more varied vocabulary when modifying female titles and less so when modifying male titles. The male terms proved to be used more formulaically than the female terms, as well. Lastly, an analysis of MI scores concludes that the most frequent collocations are not necessarily the most relevant ones.    A discussion regarding similarities and differences to other studies is carried out, as well, which, further, is accompanied by suggestions for future research.

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Genome-wide association studies have greatly improved our understanding of the contribution of common variants to the genetic architecture of complex traits. However, two major limitations have been highlighted. First, common variant associations typically do not identify the causal variant and/or the gene that it is exerting its effect on to influence a trait. Second, common variant associations usually consist of variants with small effects. As a consequence, it is more challenging to harness their translational impact. Association studies of rare variants and complex traits may be able to help address these limitations. Empirical population genetic data shows that deleterious variants are rare. More specifically, there is a very strong depletion of common protein truncating variants (PTVs, commonly referred to as loss-of-function variants) in the genome, a group of variants that have been shown to have large effect on gene function, are enriched for severe disease-causing mutations, but in other instances may actually be protective against disease. This thesis is divided into three parts dedicated to the study of protein truncating variants, their medical relevance, and their functional consequences. First, I present statistical, bioinformatic, and computational methods developed for the study of protein truncating variants and their association to complex traits, and their functional consequences. Second, I present application of the methods to a number of case-control and quantitative trait studies discovering new variants and genes associated to breast and ovarian cancer, type 1 diabetes, lipids, and metabolic traits measured with NMR spectroscopy. Third, I present work on improving annotation of protein truncating variants by studying their functional consequences. Taken together, these results highlight the utility of interrogating protein truncating variants in medical and functional genomic studies.