Submitted by Aline Batista (alinehb.ufpel@gmail.com) on 2018-06-18T19:35:11Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertacao_Marcos_Bueno.pdf: 1090005 bytes, checksum: 8a09f779933fec0b08f15123be48ec93 (MD5) / Approved for entry into archive by Aline Batista (alinehb.ufpel@gmail.com) on 2018-06-18T19:47:25Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertacao_Marcos_Bueno.pdf: 1090005 bytes, checksum: 8a09f779933fec0b08f15123be48ec93 (MD5) / Made available in DSpace on 2018-06-18T19:47:32Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertacao_Marcos_Bueno.pdf: 1090005 bytes, checksum: 8a09f779933fec0b08f15123be48ec93 (MD5) Previous issue date: 2018-02-26 / Sem bolsa / Este trabalho tratou do uso de geotecnologias no manejo da água em terras baixas do Rio Grande do Sul e foi constituído por dois capitulo. O primeiro teve como titulo “Demarcação de taipas em lavouras de arroz irrigado: Nível laser versus GNSS-RTK”. O objetivo foi comparar o desempenho dos sistemas Nível Laser e GNSS-RTK aplicados na demarcação de taipas. O trabalho foi realizado em uma área experimental de 27 ha pertencente a Granja Bretanhas S/A, localizada no município de Jaguarão/RS. A área experimental foi subdividida, em função da declividade, em três subáreas, denominadas como: i) plana (0,16%); ii) intermediaria (0,36%); e iii) suavemente ondulada (1,3%). Para avaliar os sistemas de demarcação de taipas foram realizadas analises do comportamento vertical e horizontal das taipas, bem como uma análise espacial da lâmina de água aplicada proporcionada pelas taipas em cada um dos sistemas. Concluiu-se que: (i) as taipas demarcadas pelo sistema GNSS-RTK apresentaram maior precisão que as taipas demarcadas pelo sistema NL, principalmente na zona plana; (ii) na zona plana o sistema de demarcação GNSS-RTK permite diminuir o número de taipas, aumentar a equidistância vertical entre taipas, ou ainda diminuir a altura das mesmas e; (iii) o comprimento das taipas para todas as zonas foi menor no sistema GNSS-RTK. O segundo capítulo teve como titulo “Avaliação de modelos de sistematização com declividade variada nas terras baixas”. O objetivo foi avaliar os novos modelos de sistematização com declividade variada em áreas de terras baixas do RS tendo como base o modelo de sistematização com declividade uniforme. Para tal foram escolhidas aleatoriamente sete áreas experimentais, na região “Litoral Sul” do RS, com relevo típico dessa região. Foi elaborado o modelo digital de elevação das áreas e elaborados os projetos de sistematização segundo três modelos: com declividade uniforme (testemunha, DU); com declividade variada - drenagem (DVD) e; com declividade variada - irrigação (DVI). A comparação do desempenho entre os diferentes modelos de sistematização foi avaliada pelos impactos sobre o movimento de solo, corte máximo em 99% da área, comprimento e numero de taipas. Concluiu-se que: (i) os novos modelos de sistematização com declividade variada representam um avanço tecnológico em relação ao modelo com declividade uniforme devido a que diminuem o custo e agridem menos o solo; (ii) o modelo de sistematiza com declividade variada - drenagem apresenta de forma geral menor movimento de solo e corte que o modelo com declividade variada – irrigação; (iii) o modelo de sistematização com declividade variada - irrigação apresenta melhor desempenho que o com declividade variada - drenagem com relação ao comprimento e número de taipas. / This work dealt with the use of geotechnologies in the management of water in the lowlands of Rio Grande do Sul and was constituted by two chapters. The first one was entitled "Demarcation of levees in irrigated rice crops: Laser level versus GNSS-RTK". The objective was to compare the performance of Laser Level and GNSS-RTK systems applied in the demarcation of levees. The work was carried out in an experimental area of 27 ha belonging to Granja Bretanhas S / A, located in the count of Jaguarão/RS. The experimental area was subdivided, as a function of slope, in three subareas, denominated as: i) flat (0.16%); ii) intermediary (0.36%); and iii) gently undulated (1.3%). To evaluate the levee demarcation systems, the vertical and horizontal behavior of the levee were analyzed, as well as a spatial analysis of the applied water depth provided by the levee in each of the systems. It was concluded that: (i) the levees demarcated by the GNSS-RTK system presented higher precision than the tails demarcated by the NL system, mainly in the flat zone; (ii) in the flat zone the GNSS-RTK demarcation system allows to reduce the number of levees, to increase the vertical equidistance between levees, or to decrease their height and; (iii) the length of the levees for all zones was lower in the GNSS-RTK system. The second chapter was entitled "Evaluation of land forming models with varied slope in the lowlands". The objective was to evaluate the new models of systematization with varied slope in lowland areas of RS based on the land level model with uniform slope. For this, seven experimental areas were selected, in the "South Coast" region of RS, with typical relief of this region. The digital elevation model of the areas was created and the systematization projects were elaborated according to three models: with uniform slope (control, DU); with varied slope to drainage (DVD) and; with varied slope to irrigation (DVI). The performance comparison between the different models of systematization was evaluated by the impacts on soil movement, maximum cut in 99% of the area, length and number of levees. It was concluded that: (i) the new models of land forming with varied slope represent a technological advance in relation to the model with uniform slope because they reduce the cost and less cut of the soil; (ii) the model of land forming with varied slope - drainage presents, in general, less movement of soil and cut than the model with varied slope to irrigation; (iii) the land forming model with varied slope - irrigation presents better performance than the one with varied slope to drainage with respect to the length and number of levees.

Cette thèse a pour but le développement de certains aspects de la modélisation de la dépendance dans la gestion des risques en dimension plus grande que un. Le premier chapitre est constitué d'une introduction générale. Le deuxième chapitre est constitué d'un article s'intitulant « Estimating Bivariate Tail : a copula based approach », soumis pour publication. Il concerne la construction d'un estimateur de la queue d'une distribution bivariée. La construction de cet estimateur se fonde sur une méthode de dépassement de seuil (Peaks Over Threshold method) et donc sur une version bivariée du Théorème de Pickands-Balkema-de Haan. La modélisation de la dépendance est obtenue via la Upper Tail Dependence Copula. Nous démontrons des propriétés de convergence pour l'estimateur ainsi construit. Le troisième chapitre repose sur un article: « A multivariate extension of Value-at-Risk and Conditional-Tail-Expectation», soumis pour publication. Nous abordons le problème de l'extension de mesures de risque classiques, comme la Value-at-Risk et la Conditional-Tail-Expectation, dans un cadre multidimensionnel en utilisant la fonction de Kendall multivariée. Enfin, dans le quatrième chapitre de la thèse, nous proposons un estimateur des courbes de niveau d'une fonction de répartition bivariée avec une méthode plug-in. Nous démontrons des propriétés de convergence pour les estimateurs ainsi construits. Ce chapitre de la thèse est lui aussi constitué d'un article, s'intitulant « Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory», accepté pour publication dans la revue ESAIM:Probability and Statistics. / In this PhD thesis we consider different aspects of dependence modeling with applications in multivariate risk theory. The first chapter is constituted by a general introduction. The second chapter is essentially constituted by the article “Estimating Bivariate Tail: a copula based approach”, actually submitted for publication. It deals with the problem of estimating the tail of a bivariate distribution function. We develop a general extension of the POT (Peaks-Over-Threshold) method, mainly based on a two-dimensional version of the Pickands-Balkema-de Haan Theorem. The dependence structure between the marginals in the upper tails is described by the Upper Tail Dependence Copula. Then we construct a two-dimensional tail estimator and study its asymptotic properties. The third chapter of this thesis is based on the article “A multivariate extension of Value-at-Risk and Conditional-Tail-Expectation” and submitted for publication. We propose a multivariate generalization of risk measures as Value-at-Risk and Conditional-Tail-Expectation and we analyze the behavior of these measures in terms of classical properties of risk measures. We study the behavior of these measures with respect to different risk scenarios and stochastic ordering of marginals risks. Finally in the fourth chapter we introduce a consistent procedure to estimate level sets of an unknown bivariate distribution function, using a plug-in approach in a non-compact setting. Also this chapter is constituted by the article “Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory”, accepted for publication in ESAIM: Probability and Statistics journal.

In dieser Arbeit untersuchen wir drei Fragestellungen. Zwei beschäftigen sich mit Divisoren auf Modulräumen von Kurven mit Levelstruktur, die dritte handelt von Stabilitätseigenschaften der Normalenbündel von kanonischen Kurven. Die erste Frage, die in Kapitel 2 studiert wird, beschäftigt sich mit der Kodairadimension des Modulraums R15,2 von Prym-Varietäten vom Geschlecht 15. Wir studieren einen neuen Divisor auf diesem Modulraum und berechnen seine Klasse in der Standardbasis der Picardgruppe. Mit Hilfe dieser Klasse können wir schlussfolgern, dass R15,2 von allgemeinem Typ ist. In Kapitel 3 setzen wir unsere Untersuchung von Kurven mit Levelstruktur fort und untersuchen für jede Primzahl l Theta-Divisoren auf den Modulräumen R6,l und R8,l. Die Divisoren werden mit Hilfe der Mukai-Bündel von Kurven vom Geschlecht 6 beziehungsweise 8 definiert. Diese Bündel liefern kanonische Einbettungen unserer Kurven in Grassmann-Varietäten und beschreiben fundamentale geometrische Aspekte von Kurven dieser Geschlechter. Indem wir die Klasse des Divisors für g = 8 und l = 3 berechnen, können wir zeigen, dass R8,3 ebenfalls von allgemeinem Typ ist. Schließlich studieren wir in Kapitel 4 die Stabilität des Normalenbündels kanonischer Kurven vom Geschlecht 8 und beweisen, dass das Bündel auf einer generischen Kurve stabil ist. Für kanonische Kurven vom Geschlecht 9 beweisen wir die Stabilität zumindest im Bezug auf Unterbündel von niedrigem Rang. Ebenfalls liefern wir zusätzliche Hinweise für die Vermutung von M. Aprodu, G. Farkas und A. Ortega, die besagt, dass eine generische kanonische Kurve jedes Geschlechts g >= 7 ein stabiles Normalenbündel besitzt. / In this thesis we investigate three questions. Two are about divisors on moduli spaces of level curves, and about the consequences for the birational geometry of these spaces. The third asks about the stability properties of normal bundles of canonical curves. The first question, to be studied in Chapter 2, is about the Kodaira dimension of the moduli space R15,2 of Prym varieties of genus 15. We study a new divisor on this space and calculate its class in terms of the standard basis of the Picard group. This allows us to conclude that R15,2 is of general type. Continuing the study of level curves in Chapter 3, we investigate, for every l, theta divisors on R6,l and R8,l defined in terms of the Mukai bundle of genus 6 and 8 curves, respectively. These bundles provide canonical embeddings of our curves in Grassmann varieties and describe fundamental aspects of the geometry of curves of these genera. Using the class of the divisor for g = 8 and l = 3, we are able to prove that R8,3 is of general type as well. Finally, in Chapter 4 we study the stability of the normal bundle of canonical genus 8 curves and prove that on a general curve the bundle is stable. For canonical genus 9 curves we prove stability at least with respect to subbundles of low ranks. We also provide some more evidence for the conjecture of M. Aprodu, G. Farkas, and A. Ortega that a a general canonical curve of every genus g >= 7 has stable normal bundle.