Les progrès de l’inférence variationnelle, tels que l’approche de variational autoencoder (VI) (Kingma and Welling (2013), Rezende et al. (2014)) et ses nombreuses modifications, se sont avérés très efficaces pour l’apprentissage des représentations latentes de données. Importance-weighted variational inference (IWVI) par Burda et al. (2015) améliore l’inférence variationnelle en utilisant plusieurs échantillons indépendants et répartis de manière identique pour obtenir des limites inférieures variationnelles plus strictes. Des articles récents tels que l’approche de hierarchical importance-weighted autoencoders (HIWVI) par Huang et al. (2019) et la modélisation de la distribution conjointe par Klys et al. (2018) démontrent l’idée de modéliser une distribution conjointe sur des échantillons pour améliorer encore l’IWVI en le rendant efficace pour l’échantillon. L’idée sous-jacente de ce mémoire est de relier les propriétés statistiques des estimateurs au resserrement des limites variationnelles. Pour ce faire, nous démontrons d’abord une borne supérieure sur l’écart variationnel en termes de variance des estimateurs sous certaines conditions. Nous prouvons que l’écart variationnel peut être fait disparaître au taux de O(1/n) pour une grande famille d’approches d’inférence variationelle. Sur la base de ces résultats, nous proposons l’approche de Conditional-IWVI (CIWVI), qui modélise explicitement l’échantillonnage séquentiel et conditionnel de variables latentes pour effectuer importance-weighted variational inference, et une approche connexe de Antithetic-IWVI (AIWVI) par Klys et al. (2018). Nos expériences sur les jeux de données d’analyse comparative, tels que MNIST (LeCun et al. (2010)) et OMNIGLOT (Lake et al. (2015)), démontrent que nos approches fonctionnent soit de manière compétitive, soit meilleures que les références IWVI et HIWVI en tant que le nombre d’échantillons augmente. De plus, nous démontrons que les résultats sont conformes aux propriétés théoriques que nous avons prouvées. En conclusion, nos travaux fournissent une perspective sur le taux d’amélioration de l’inference variationelle avec le nombre d’échantillons utilisés et l’utilité de modéliser la distribution conjointe sur des représentations latentes pour l’efficacité de l’échantillon. / Advances in variational inference, such as variational autoencoders (VI) (Kingma and Welling (2013), Rezende et al. (2014)) along with its numerous modifications, have proven highly successful for learning latent representations of data. Importance-weighted variational inference (IWVI) by Burda et al. (2015) improves the variational inference by using multiple i.i.d. samples for obtaining tighter variational lower bounds. Recent works like hierarchical importance-weighted autoencoders (HIWVI) by Huang et al. (2019) and joint distribution modeling by Klys et al. (2018) demonstrate the idea of modeling a joint distribution over samples to further improve over IWVI by making it sample efficient. The underlying idea in this thesis is to connect the statistical properties of the estimators to the tightness of the variational bounds. Towards this, we first demonstrate an upper bound on the variational gap in terms of the variance of the estimators under certain conditions. We prove that the variational gap can be made to vanish at the rate of O(1/n) for a large family of VI approaches. Based on these results, we propose the approach of Conditional-IWVI (CIWVI), which explicitly models the sequential and conditional sampling of latent variables to perform importance-weighted variational inference, and a related approach of Antithetic-IWVI (AIWVI) by Klys et al. (2018). Our experiments on the benchmarking datasets MNIST (LeCun et al. (2010)) and OMNIGLOT (Lake et al. (2015)) demonstrate that our approaches perform either competitively or better than the baselines IWVI and HIWVI as the number of samples increases. Further, we also demonstrate that the results are in accordance with the theoretical properties we proved. In conclusion, our work provides a perspective on the rate of improvement in VI with the number of samples used and the utility of modeling the joint distribution over latent representations for sample efficiency in VI.

Beef cattle are continuously selected for different traits and the success in improving these traits has been remarkable. However, for certain traits, it is essential not only to improve the average performance, but also to control the variation around the mean. There is evidence that residual variance may be under genetic control, which opens the possibility of selecting for uniformity. In this sense, the objectives of the present dissertation were: 1) to investigate the extent of genetic heterogeneity of residual variance at the pedigree level in birth weight (BW), weaning weight (WW), yearling weight (YW), foot angle (FA), and claw set (CS) in American Angus cattle; 2) to compare the results of different genetic heterogeneity models; 3) to evaluate the effectiveness of Box-Cox transformation in continuous traits; and 4) to address limitations and explore alternative solutions for implementing genetic parameters for residual variance in genetic evaluations. The first study investigated the genetic heterogeneity of residual variances for BW, WW, and YW. Three models were compared: a homoscedastic residual variance model (M1), a double hierarchical generalized linear model (DHGLM, M2), and a genetically structured environmental variance model (MCMC, M3). The results showed significant genetic heterogeneity of residual variances in growth traits, suggesting the possibility of selection for uniformity. The genetic coefficient of variation for residual variance ranged from 0.90 to 0.92 in M2 and 0.31 to 0.38 in M3 for BW, 0.64 in M2 and 0.01 to 0.29 in M3 for WW, and 0.67 to 0.63 in M2 and 0.25 to 0.31 in M3 for YW. Low heritability estimates for residual variance were found, particularly in M2 (0.08 for BW, 0.06 for WW, and 0.09 for YW). The study identified both negative and positive genetic correlations between mean and residual variance, depending on the trait and data transformation. Negative correlations suggest the potential to increase trait means while decreasing residual variance. However, positive correlations indicate that the genetic response to selection for uniformity may be limited unless a selection index is used. Data transformation reduced skewness but did not eliminate genetic heterogeneity of residual variances. The Bayesian approach provided higher estimates of additive genetic variance for residual variance compared to DHGLM. Overall, the findings indicate the potential to reduce variability through selection and lay the groundwork for incorporating uniformity of growth traits into breeding goals. The second study focused on the genetic heterogeneity of residual variance for two foot conformation traits, FA and CS. Using 45,667 phenotypic records collected between 2009 and 2021, three models were compared: a traditional homoscedastic residual variance model (M1), a DHGLM (M2), and a genetically structured environmental variance model (M3). Results showed that heritability estimates for FA and CS means were within expected ranges, although lower in M2. Despite low heritability estimates for residual variance (0.07 for FA and 0.05 for CS in M2), significant genetic coefficients of variation were found, suggesting that selection on trait mean would also influence residual variance. Positive genetic correlations between mean and residual variance in M2 and M3 indicate that selection for uniformity is feasible, but may require additional strategies such as selection indices. The study highlights the potential of FA and CS as indicators for breeding programs aimed at improving production uniformity in beef cattle. Our findings suggest that selection for uniformity in growth and foot score traits in beef cattle may be limited by low heritability of residual variance and moderate to high positive genetic correlations between mean and residual variance. This was observed for most of the traits studied. To overcome these challenges, further research is needed, particularly to explore genomic information to improve the prediction accuracy of estimated breeding values (EBV) for residual variance. Although studies of uniformity using genomic data are limited, they have shown improved EBV accuracy for residual variance. Additionally, alternative methods for measuring uniformity, such as different uniformity or resilience indicators, should be considered, especially with advances in digital phenotyping. Precision livestock farming technologies that allow for extensive data collection on various production traits should be integrated into the development of new uniformity indicators. This dissertation provides valuable insights into the genetic heterogeneity of residual variance in American Angus cattle and highlights the complexity of selecting for uniformity while improving mean traits. Continued research with larger data sets, genomic information, and further methodological refinement will be critical to advance these findings to improve uniformity and productivity in beef cattle breeding. / Doctor of Philosophy / Uniformity in livestock breeding refers to the goal of reducing variability in certain traits within a livestock population to achieve more consistent and predictable outcomes. This is particularly important for traits that affect productivity, economic efficiency, animal welfare, and product quality. By achieving greater uniformity, producers can optimize management practices, improve marketability, and enhance the overall efficiency of animal production systems. Residual variance refers to the variation in traits that is not explained by known genetic or environmental factors. Recent research suggests that residual variance may be under genetic control, meaning that it is possible to select animals that not only have desirable traits, but also have less variability in those traits. Therefore, this dissertation investigates the genetic control of residual variance that may allow selection for uniformity in traits. The research focused on American Angus cattle and aimed to 1) investigate genetic heterogeneity of residual variance in traits, such as birth weight, weaning weight, yearling weight, foot angle, and claw set; 2) compare different genetic models; 3) evaluate the effectiveness of data transformations; and 4) address limitations in genetic evaluations. The first study examined genetic heterogeneity in growth traits using three models. It revealed significant genetic variability, suggesting the potential for selection for uniformity. The study found both positive and negative genetic correlations between trait means and residual variance, indicating varying potential for reducing variance while improving trait means. Data transformations reduced skewness but did not eliminate genetic heterogeneity. A Bayesian approach provided higher estimates of genetic variance than other methods. The second study focused on foot conformation traits with over 45,000 records. The study showed that despite low heritability for residual variance, there was significant genetic variation, indicating the possibility of altering residual variance through selection. Positive genetic correlations suggested that additional strategies, such as selection indices, may be needed to achieve uniformity in practice. Overall, the findings highlight the complexity of selecting for uniformity while improving average traits and underscore the need for further research, particularly using genomic data, to improve prediction accuracy. Integrating precision livestock farming technologies could help develop new indicators of uniformity, improving productivity and uniformity in beef cattle breeding.

Social Capital and Open Innovation are important for organisational growth, as both of them influence Innovation, Learning and Job Satisfaction. The literature indicates that informal network measured as social capital and formal network measured as open innovation influences positively to organizational innovation performance, learning and job satisfaction. Most of the studies in this area have been carried out using univariate approaches, and only few dimensions of both Social Capital and Open Innovation have been considered. Current literature outlines the positive influence of Social Capital and Open Innovation on Learning, Innovation and Job Satisfaction. In this study, an attempt has been made to develop a multi-dimensional framework for Social Capital and Open Innovation, in order to better understand the nuances of Learning, Innovation and Job Satisfaction in an R&D setting. Another important factor influencing the R&D outcomes is Absorptive Capacity; it is the capacity of the organisation to identify and use external knowledge. The direct and moderating role of Absorptive Capacity has been examined. Both theoretical and conceptual models have been proposed, and a measurement scale in form of a questionnaire has been developed. Data was collected from 35 organisations across India operating in the field of defence R&D. The sample included Government-run R&D organisations, Public Sector Units (PSUs) and private firms, and total of 331 engineers/scientists responded to the survey. Data was analysed using statistical methods such as Exploratory Factor Analysis (EFA), Confirmatory Factor Analysis (CFA), Common Method Variance (CMV), and Analysis of Variance (ANOVA). Reliability and validity of the proposed scales for the constructs have been verified using appropriate techniques, and further inferences have been drawn by using regression techniques and Structural Equation Modeling (SEM) to assess the proposed relationships. It has been found that both Social Capital and Open Innovation have positive influence on Learning, Innovation and Job Satisfaction. Further, it was found that Absorptive Capacity had a positive association with both Innovation and Learning. However, Absorptive Capacity did not moderate the relationship of Social Capital with both Innovation and Learning, but was found to moderate the relationship between Open Innovation and Innovation, for both outbound and inbound approaches of Open Innovation. Bonding Social Capital had a relatively stronger positive association with Learning, while Bridging Social Capital was found to have a stronger relationship with Innovation. In summary, networking factors Social Capital and Open Innovation have strong positive association with R&D outcomes measured as innovation performance, learning and job satisfaction.

Les travaux portent sur l’estimation de la variance dans le cas d’une non- réponse partielle traitée par une procédure d’imputation. Traiter les valeurs imputées comme si elles avaient été observées peut mener à une sous-estimation substantielle de la variance des estimateurs ponctuels. Les estimateurs de variance usuels reposent sur la disponibilité des probabilités d’inclusion d’ordre deux, qui sont parfois difficiles (voire impossibles) à calculer. Nous proposons d’examiner les propriétés d’estimateurs de variance obtenus au moyen d’approximations des probabilités d’inclusion d’ordre deux. Ces approximations s’expriment comme une fonction des probabilités d’inclusion d’ordre un et sont généralement valides pour des plans à grande entropie. Les résultats d’une étude de simulation, évaluant les propriétés des estimateurs de variance proposés en termes de biais et d’erreur quadratique moyenne, seront présentés. / Variance estimation in the case of item nonresponse treated by imputation is the main topic of this work. Treating the imputed values as if they were observed may lead to substantial under-estimation of the variance of point estimators. Classical variance estimators rely on the availability of the second-order inclusion probabilities, which may be difficult (even impossible) to calculate. We propose to study the properties of variance estimators obtained by approximating the second-order inclusion probabilities. These approximations are expressed in terms of first-order inclusion probabilities and are usually valid for high entropy sampling designs. The results of a simulation study evaluating the properties of the proposed variance estimators in terms of bias and mean squared error will be presented.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

Ce mémoire de thèse présente une étude fondamentale enrichie par des contributions qui sont articulées autour de la modélisation de processus ainsi qu'un diagnostic de défauts en utilisant l'analyse en composantes principales (ACP). Dans l'objectif d'un choix optimal du modèle ACP, une étude comparative de quelques critères connus dans la littérature nous a permis de conclure que le problème rencontré est souvent lié à une ignorance des variables indépendantes et quasi-indépendantes. Dans ce cadre, nous avons réalisé deux démonstrations mettant en évidence les limitations de deux critères en particulier la variance non reconstruite (VNR). En s'appuyant sur le principe d'une telle variance, nous avons proposé trois nouveaux critères. Parmi eux, deux ont été considérés comme étant empiriques car seule l'expérience permettra de prouver leur efficacité. Le troisième critère noté VNRVI représente un remède à la limitation du critère VNR. Une étude de sa consistance théorique a permis d'établir les conditions garantissant l'optimalité de son choix. Les résultats de simulation ont validé une telle théorie en prouvant ainsi que le critère VNRVI étant plus efficace que ceux étudiés dans cette thèse. Dans le cadre d'un diagnostic de défauts par ACP, l'approche de reconstruction des indices de détection ainsi que celle des contributions ont été utilisées. A travers une étude de généralisation, nous avons étendu le concept d'isolabilité de défauts par reconstruction à tout indice quadratique. / This thesis presents a fundamental study enhanced by some contributions that are focused on process modelling and fault diagnosis using principal components analysis (PCA). In order to find an optimal PCA model, we have concluded through a comparative study of some popular criteria that the problem is often related to an ignorance of the independent and quasi-independent variables. In this framework, we have performed two demonstrations highlighting the limitations of two selection criteria in particular the unreconstructed variance (VNR). Based on the principle of VNR approach, we have proposed three new criteria, among them two methods were considered as empirical criteria because only the experience will prove their effectiveness. However the third one which is noted VNRVI represents a cure for the limitation of the classical VNR criterion. Thus, the conditions that ensure an optimal selection were derived according to a theoretical consistency study of the VNRVI approach. The simulation results have successfully validated the VNRVI criterion by proving that is more effective than the other studied criteria in the present thesis. The reconstruction and contributions approaches were used for fault diagnosis using PCA. According to a unified study, we have extended the fault isolability concept based on the reconstruction method to any detection index which has a quadratic form. Such generalization has allowed us to develop a theoretical fault isolability analysis based on the reconstruction of the combined index versus those of SPE and T2 indices. This analysis has highlighted the advantage of using the combined index for fault isolation.

A avicultura é uma das principais atividades agropecuárias do Brasil, em 2011 o país produziu 12.230 toneladas de carne de frango, sendo o 3º maior produtor de frango do mundo, apenas atrás dos EUA e China. Parte deste êxito se deve principalmente ao melhoramento genético animal implantado nas últimas décadas. Os objetivos nesse estudo foram: 1º - Comparar as funções das curvas de crescimento: von Bertalanffy, Gompertz, Logística, Richards e Brody, pelo método dos Mínimos Quadrados Ordinários (QMO) e Quadrados Mínimos Ponderados (QMP) a dados de peso vivo para as linhagens experimentais de frango caipira (7P, Caipirão da ESALQ, Caipirinha da ESALQ e Carijó Barbado) e selecionar uma curva de crescimento que melhor descreva o padrão de crescimento para cada linhagem, e estimar os componentes genéticos (herdabilidades e correlações genéticas) dos parâmetros destas funções sob análise bicaracterística; 2º - Comparar modelos com diferentes ordens de ajuste por meio de funções polinomiais de Legendre, sob modelos de regressão aleatória, com variância residual heterogênea, para a estimação dos componentes de (co) variância e avaliação genética de linhagens experimentais de frango caipira (7P, Caipirão da ESALQ, Caipirinha da ESALQ e Carijó Barbado). O modelo que melhor se adequou a curva de crescimento para as linhagens estudadas foi à função de Gompertz ajustado pelo método dos Quadrados Mínimos Ponderados (QMP). Os parâmetros genéticos estimados para as medidas e dos modelos Gompertz ponderado podem ser utilizados como critérios de seleção, pois parecem ter efeito genético considerável para estas características. No entanto, deve-se haver cautela na utilização do parâmetro como critério de seleção para a linhagem Carijó Barbado devido a baixa herdabilidade. As correlações genéticas e fenotípicas entre as características e foram negativas e altas. Indicando que quanto maior o peso assintótico menor a taxa de crescimento. Dentre os modelos de Regressão Aleatória estudados o polinômio de 3ª ordem foi o que melhor se adequou para descrever as curvas de crescimento das linhagens estudadas. As estimativas de variâncias, herdabilidades foram afetadas pela modelagem da variância residual. Em geral as herdabilidades estimadas para as idades de 1 a 84 dias variaram de moderadas a altas para as linhagens estudadas, indicando que qualquer idade pode ser utilizada como critério de seleção. A seleção aos 42 dias de idade pode ser mantida como critério de seleção. / Aviculture is one of the main agribusiness activities in Brazil, in 2011 the country produced 12,230 tons of broiler meat, was the 3rd largest producer of broiler in the world, only behind the USA and China. Part of this success is mainly due to animal genetic improvement implemented in recent decades. In this study, our objectives were: 1 - to compare the functions of the Von Bertalanffy, Gompertz, Logistic, Richards and Brody growth curves by the Ordinary Least Squares and Weighted Least Squares method, from data for body weight from experimental free-range chicken lines (7P, Caipirão da ESALQ, Caipirinha da ESALQ and Carijó Barbado) and select a growth curve that best describes their growth. From this, estimates of the genetic components (heritability and genetic correlations) of the parameters of these functions under bivariate analysis; 2 - Comparing models with different orders of adjustment by means of Legendre polynomial functions under random regression models with heterogeneous residual variance for the estimation of (co) variance and genetic evaluation of experimental free-range chicken lines (7P, Caipirão da ESALQ, Caipirinha da ESALQ and Carijó Barbado). The model that best adapted the growth curve for all lines studied was the Gompertz function adjusted using weighted least squares. Genetic parameters for measurements and can be used as selection criteria because they seem to have considerable genetic effects for these characteristics. There should be caution in using the parameter as a selection criterion for the Carijó Barbado line due to low heritability. The genetic and phenotypic correlations between traits and were negative and high, indicating that the higher the asymptotic weight, the lower the growth rate. Among the Random Regression models studied the 3rd order polynomial was best adapted to describe the growth curves of the lines studied. Estimates of variances and heritabilities were affected by residual variance modeling. Overall heritability estimates between 1 to 84 days of age ranged from moderate to high for all lines, indicating that any age can be used as a selection criterion, including maintaining the current selection at 42 days of age.

Esse trabalho teve como objetivo comparar métodos de estimação de componentes de variância e parâmetros genéticos, considerando tanto o delineamento estatístico fatorial instalado em látice quadrado como o delineamento genético III. Como referência, foram utilizados três conjuntos de dados reais, em melhoramento genético de milho, relativos aos caracteres de produção de grãos (gramas por parcela), altura da folha bandeira ao chão (centímetros) e o número de folhas entre a primeira espiga e o pendão; sendo que a altura da folha bandeira e o número de folhas foram obtidos pela média entre cinco plantas competitivas para cada parcela. O método da Análise da Variância (ANOVA), conforme indicado pelo Delineameno III, foi utilizado na análise dos dados e estimação dos componentes de variância relativos ao modelo matemático, variâncias genéticas, coeficiente de herdabilidade e grau médio de dominância para cada um dos três caracteres estudados. Essas estimativas foram utilizadas na simulação de 1000 conjuntos de dados com características semelhantes a cada um dos conjuntos de dado reais considerados. Os métodos da ANOVA e da máxima verossimilhança restrita (REML) foram utilizados na predição dos parâmetros já mencionados para cada um dos conjuntos de dados simulados dentro de cada caráter. As 1000 estimativas obtidas por cada método, para cada caráter estudado, foram utilizadas no cálculo de estatísticas descritivas (média, desvio-padrão e acurácia relativa) e na montagem de gráficos de Box-plot. Utilizando as informações obtidas a partir das estimativas fornecidas por cada método e em posse dos valores reais que essas estimativas deveriam prever (valor utilizado na simulação dos dados) foi possível comparar ambos os métodos quanto à eficiência das estimativas por eles fornecidas. Ambos os métodos apresentaram características semelhantes na predição da maioria dos componentes de variância relativos ao modelo matemático, sendo que as maiores disparidades se deram para os componentes relativos aos efeitos de progênie (?p2) e as interações entre progênie e linhagem (?pt2) e entre progênie, linhagem e ambiente (?pta2); os quais são os componentes de maior peso no cálculo das variâncias e parâmetros genéticos. O método da ANOVA foi o bastante eficiente na predição de ?p2, sendo que o método da REML se aproxima dos resultados obtidos pelo método da ANOVA conforme diminuem os valores de referência para esse componente; para ?pt2 o método da REML se mostrou mais eficiente conforme maior é o valor de referência, porém, perde eficiência e se aproxima do método da ANOVA conforme o valor de referência do componente diminui. Ambos os métodos se mostraram ineficientes na predição de ?pta2, porém o método da REML foi o menos eficiente. O melhor desempenho do método da ANOVA na predição dos componentes de variância de maior peso no cálculo das variâncias genéticas levou a um melhor desempenho desse método na predição de todos os parâmetros genéticos, com exceção da variância de dominância, a qual depende unicamente de ?pt2. Porém, foi observada uma tendência no método da ANOVA, em média, na superestimação do grau médio de dominância em cerca de 45% do seu valor de referência, independentemente do caráter estudado. / This work aimed to compare estimation methods for variance components and genetic parameters, considering the factorial statistical design set in randomized blocks and the genetic Design III. As reference, three sets of real data were used, on maize genetic improvement, related to the characters: grain yield (grams by plot), plant height, measured from the ground to the °ag leaf in centimeters, and the number of leaves above the uppermost ear. The analysis of variance method (ANOVA), accordingly to the proposed by the Design III, was used on the analysis of the data and estimation of the variance components derived from the mathematical model, genetic variances, heritability and average degree of dominance for each of the studied characters. This estimatives were used on the simulation of 1000 data sets with similar characteristics to the real data analyzed. The ANOVA and restricted maximum likelihood (REML) methods were used on the prediction of the already mentioned parameters for each of the simulated data sets within each character. The 1000 estimatives obtained by each method, for each studied character, were used on the calculation of descriptive statistics (mean, standard deviation and relative accuracy) and for the ¯tting of box-plot graphics. Through the information obtained from the estimatives given by each method and in possession of the actual values that they should predict (values used in the simulation of the data sets) it was possible to compare both methods as to the e±ciency of the estimatives given by them. Both methods presented similar characteristics on the prediction of most of the variance components derived from the mathematical model, being that most di®erences were pertinent to the components related to the e®ects of progeny (¾2 p) and to the interactions between progeny and parental inbred (¾2 pt) and between progeny, parental inbred and environment (¾2 pta); which are the components of greater importance on the calculation of the genetic parameters. The ANOVA method was very e±cient on the prediction of ¾2 p, being that the smaller the reference value for this component, more the REML method approached the results obtained by the ANOVA method; for larger values of ¾2 pt the most e±cient was the REML method, but its e±ciency decayed and approached the ANOVA method for smaller reference values for this component. Both methods were poorly e±cient on the prediction of ¾2 pta, but the REML method was the least e±cient. The better performance of the ANOVA method on the prediction of the variance components of greater importance on the calculation of the genetic variances lead to a better performance of the ANOVA method on the prediction of all genetic parameters, with exception to the dominance variance, which depended solely on ¾2 pt. However, it was observed a tendency on the ANOVA method, in average, on the overestimation of the average degree of dominance of around 45% of the actual reference value, independently of the studied character.

O delineamento III foi proposto para estimar as variâncias aditivas e de dominância e o grau médio de dominância de caracteres quantitativos. Com o advento dos marcadores moleculares, Cockerham & Zeng (1996) desenvolveram uma metodologia genético-estatística associando o delineamento III com marcadores moleculares. Esta metodologia foi proposta visando estimar, com o uso de quatro contrastes ortogonais, os efeitos aditivos, dominantes e epistáticos dos QTLs ligados a marcadores moleculares. O objetivo desta pesquisa foi usar ambas as metodologias para análise genética da produção de grãos, componentes da produção e número de ramificações do pendão em uma população referência F2 de milho. Duzentos e cinqüenta progênies F2:3 foram retrocruzadas com ambas linhagens genitoras, dando origem a 500 progênies de retrocruzamento. Estas progênies foram alocadas em cinco látices 10x10 e avaliadas em seis ambientes em três estações experimentais próximas a Piracicaba, SP, com duas repetições por ambientes. Estimativas de variância aditiva e de dominância, assim como o grau médio de dominância dos caracteres avaliados, apresentaram magnitudes similares às reportadas em populações de milho temperado para todos os caracteres. Estimativas do grau médio de dominância foram inferiores a um para o diâmetro da espiga, número de fileiras, peso de 500 grãos e número de ramificações do pendão, mostrando que os efeitos aditivos foram mais importantes que os efeitos de dominância para estes caracteres. Para prolificidade, comprimento da espiga e número de grãos por fileira, o grau médio de dominância não diferiu de dominância completa, sugerindo que os efeitos de dominância foram importantes para estes caracteres. Para produção de grãos, o resultado do grau médio de dominância sugeriu sobredominância. Porém, como é conhecido, o desequilíbrio de ligação causa viéses nas estimativas de grau médio de dominância e, conseqüentemente, estas estimativas podem ser menores, sendo que, provavelmente tenha ocorrido pseudo-sobredominância para produção de grãos. A análise do delineamento III com marcadores moleculares mostrou que os QTLs estão distribuídos em todos os cromossomos para todos caracteres. As somas em módulo dos efeitos dos QTLs mostraram que para produção de grãos, prolificidade, comprimento da espiga, e número de grãos por fileira, os efeitos de dominância foram superiores aos efeitos aditivos, e estes superiores aos efeitos epistáticos; para diâmetro da espiga, peso de 500 grãos, número de fileiras, e número ramificações do pendão, os efeitos aditivos foram maiores que os efeitos de dominância, e estes superiores aos efeitos epistáticos, exceto para número de fileiras em que os efeitos epistáticos foram maiores que os efeitos de dominância. Os efeitos epistáticos foram detectados para todos caracteres e contribuíram mais para os componentes da produção que para a produção de grãos per se. A análise clássica do delineamento III e a associada a marcadores moleculares forneceram resultados de grande utilidade, mas o delineamento III com marcadores permitiu a estimação dos efeitos genéticos de regiões específicas do genoma e sugeriu que os efeitos epistáticos foram muito importantes na expressão e na herança dos caracteres analisados. / The Design III was proposed to estimate additive and dominance variances, and the average levels of dominance of quantitative traits. With the advent of the molecular markers, Cockerham & Zeng (1996) developed a genetic-statistical procedure using the Design III with molecular markers. This procedure was designed to estimate additive, dominance and epistatic effects of the QTLs linked to molecular markers from four orthogonal contrasts. The objectives of this research were to use both methodologies for the genetic analysis of grain yield, yield components, and number of tassel branches in an F2 reference maize population. Two-hundred and fifty F2:3 progenies were backcrossed to the two parental inbred lines, which gave rise to 500 backcrossed progenies. These progenies were allocated in five 10x10 lattices design, and evaluated in six environments in three experimental stations near Piracicaba, SP, with two replications per environment. Estimates of additive and dominance variances, as well as the average levels of dominance for the traits evaluated, had magnitudes similar to those already reported for temperate maize populations for all traits. Estimates of the average level of dominance were lower than one for ear diameter, kernel row number, weight of 500 kernels, and tassel branches number, showing that the additive effects were more important than the dominance effects for these traits. For prolificacy, ear length, and kernels per row number, the average levels of dominance did not differ from complete dominance, suggesting that the dominance effects were important for these traits. For grain yield, the result suggested overdominance as the average level of dominance. However, as is well-known, linkage disequilibrium causes biases in the estimates of the average levels of dominance and, therefore, these estimates could be lower, and probably for grain yield a pseudo-overdominance was detected. The analysis of the Design III with molecular markers showed that QTLs were distributed in all chromosomes for all traits. The sum in module of the QTLs effects showed that for grain yield, prolificacy, ear length, and kernels per row number, dominance effect was greater than additive effect, and the latter greater than epistatic effect; whereas for ear diameter, weight of 500 kernels, kernel row number, and tassel branches number, additive effect was greater than dominance effect, and the latter greater than epistatic effect, except for kernel row number where epistatic effect was greater than dominance effect. Epistatic effects were detected for all traits, and had higher contribution for the yield components than for yield per se. Both traditional and QTL analysis of the Design III presented very useful results, but the Design III with molecular markers allowed the estimation of the genetic effects from specific genomic regions, and suggested that the epistatic effects play a very important role for the expression and inheritance of the traits assessed.

Interessado em fazer com que o seu capital gere lucros, o investidor ao optar por negociar ativos, fica sujeito aos riscos econômicos de qualquer negociação, pois não existe uma certeza quanto a valorização ou desvalorização de um ativo. Eis que surge o mercado futuro, em que é possível negociar contratos a fim de se proteger (hedge) dos riscos de perdas ou ganhos excessivos, fazendo com que a compra ou venda de ativos, seja justa para ambas as partes. O objetivo deste trabalho consiste em estudar os processos de Lévy de puro salto de atividade finita, também conhecido como modelo de Poisson composto, e suas aplicações. Proposto pelo matemático francês Paul Pierre Lévy, os processos de Lévy tem como principal característica admitir saltos em sua trajetória, o que é frequentemente observado no mercado financeiro. Determinaremos uma estratégia de hedging no modelo de mercado com o processo de Poisson composto via o conceito de mean-variance hedging e princípio da programação dinâmica. / The investor, that negotiate assets, is subject to economic risks of any negotiation because there is no certainty regarding the appreciation or depreciation of an asset. Here comes the futures market, where contracts can be negotiated in order to protect (hedge) the risk of excessive losses or gains, making the purchase or sale assets, fair for both sides. The goal of this work consist in study Lévy pure-jump process with finite activity, also known as compound Poisson process, and its applications. Discovered by the French mathematician Paul Pierre Lévy, the Lévy processes admits jumps in paths, which is often observed in financial markets. We will define a hedging strategy for a market model with compound Poisson process using mean-variance hedging and dynamic programming.