Rising global antibiotic resistance has caused concerns over sources and pathways for the spread of contributing factors. Majority of the antimicrobials used in the U.S. are involved in veterinary medicine, primarily with livestock rearing. Animal manure land application integrates livestock farming and agroecosystems. This manure contains antibiotic resistant elements (AREs) (resistant bacteria, resistance genes, and veterinary antibiotics) that contribute towards antimicrobial resistance. Altering manure application techniques can reduce surface runoff of other contaminants such as excess N and P, pesticides, and hormones, that can impact water quality. Conventional tillage practices in the U.S. has reduced or stopped, making subsurface injection of manure a promising option when compared to surface application. Our research compared manure application methods, manure application seasons, cropping system, and manure-rainfall time gaps to gauge the impact on AREs in the environment. Two field-scale rainfall simulation studies were conducted along with one laboratory study. Using the injection method lowered concentrations of manure associated AREs entering surface runoff. When manure was surface applied and rainfall occurred 7 d after application, 9-30 times less resistant fecal coliform bacteria (FCB) entered surface runoff when compared to 1 d time gap for that broadcast method. Within a day of manure application, antibiotic resistance gene (ARG) profiles in soil began to differ from each other based on manure application and soil ARG richness in all manure-amended soil increased compared to the background. Runoff from injection plots contained 52 ARGs with higher abundance compared to runoff from surface applied plots. ARGs in the former were more correlated to soil and more correlated to manure in the latter. The highest antibiotic concentrations were in the injection slit soil of those plots. Antibiotic concentrations in samples corresponded positively to concentrations of resistant FCB and ARGs, and there was a positive correlation between resistant FCB and their associated ARGs (Spearman's ρ = 0.43-0.63). A CRIISPR-Cas12a assay for quantification of ARGs in environmental samples was just as precise as conventional methods. There is also potential for in-situ detection. These combined results can hopefully help farmers improve manure management practices that mitigate spread of AREs to surrounding water, crops, and soil. / Doctor of Philosophy / Rising global antibiotic resistance cause concerns over sources and pathways for the spread of contributing factors. Most of the antimicrobials used in the U.S. are involved in veterinary medicine, especially with livestock rearing. Overuse of antibiotics that are medically important to human medicine compromises the effectiveness of our medicines. Animal manure contains antibiotic resistant elements (AREs) such as resistant bacteria, resistance genes, and antibiotics) that contribute towards resistance issues. Once these AREs enter the environment, they can be taken up by crops, runoff into surface water or leached into ground water, or even reside within the animal products we consume. Altering manure application techniques is beneficial for nutrient conservation but also potentially for reducing ARE spread. With our research, we compared manure application methods, manure application seasons, cropping systems, and manure-rainfall time gaps to find ways to balance the need for manure application and the spread of resistance. We used two field-scale rainfall simulation studies along with one laboratory study. Overall, using the injection method resulted in significantly lower concentrations of manure associated AREs entering surface runoff. When manure was surface applied and rainfall occurred 7 d after application, less resistant fecal coliform bacteria (FCB) entered surface runoff when compared to the 1 d time gap for broadcast methods. Within a day of manure application, antibiotic resistance gene (ARG) profiles in soil began to differ from each other and soil ARG totals in all manure applied soil increased compared to the background. Runoff from injection plots contained more soil ARGs and runoff from surface applied plots containing more manure associated ARGs. The subsurface injection method also caused highest antibiotic concentrations in the injection slit soil of those plots. High antibiotic concentrations in samples generally meant high concentrations of resistant FCB and ARGs, and resistant FCB were also found with their associated ARGs as well. A CRISPR-Cas12a assay for quantification of ARGs in environmental samples was just as precise as conventional methods. There is also potential for onsite detection. These combined results can hopefully help farmers improve manure management practices that mitigate spread of AREs to surrounding water, crops, and soil.

Cette thèse porte sur l'étude de la modélisation et estimation de la dépendance des portefeuilles de risques et l'estimation du risque agrégé. Dans le Chapitre 2, nous proposons une nouvelle méthode pour estimer les quantiles de haut niveau pour une somme de risques. Elle est basée sur l'estimation du rapport entre la VaR de la somme et la VaR du maximum des risques. Nous utilisons des résultats sur les fonctions à variation régulière. Nous comparons l'efficacité de notre méthode avec quelques estimations basées sur la théorie des valeurs extrêmes, sur plusieurs modèles. Notre méthode donne de bons résultats lors de l'approximation de la VaR à des niveaux élevés lorsque les risques sont fortement dépendants et au moins l'un des risques est à queue épaisse. Dans le Chapitre 3, nous proposons une procédure d'estimation pour la distribution d'un risque agrégé basée sur la copule échiquier. Elle permet d'obtenir de bonnes estimations à partir d'un petit échantillon de la loi multivariée et une connaissance complète des lois marginales. Cette situation est réaliste pour de nombreuses applications. Les estimations peuvent être améliorées en incluant dans la copule échiquier des informations supplémentaires (sur la loi d'un sous-vecteur ou sur des probabilités extrêmes). Notre approche est illustrée par des exemples numériques. Finalement, dans le Chapitre 4, nous proposons un estimateur de la mesure spectrale basé sur l'estimation à noyau de la densité de la mesure spectrale d'une distribution à variation régulière bivariée. Une extension de notre méthode permet d'estimer la mesure spectrale discrète. Certaines propriétés de convergence sont obtenues / This thesis comprises three essays on estimation methods for the dependence between risks and its aggregation. In the first essay we propose a new method to estimate high level quantiles of sums of risks. It is based on the estimation of the ratio between the VaR (or TVaR) of the sum and the VaR (or TVaR) of the maximum of the risks. We use results on regularly varying functions. We compare the efficiency of our method with classical ones, on several models. Our method gives good results when approximating the VaR or TVaR in high levels on strongly dependent risks where at least one of the risks is heavy tailed. In the second essay we propose an estimation procedure for the distribution of an aggregated risk based on the checkerboard copula. It allows to get good estimations from a (quite) small sample of the multivariate law and a full knowledge of the marginal laws. This situation is realistic for many applications. Estimations may be improved by including in the checkerboard copula some additional information (on the law of a sub-vector or on extreme probabilities). Our approach is illustrated by numerical examples. In the third essay we propose a kernel based estimator for the spectral measure density of a bivariate distribution with regular variation. An extension of our method allows to estimate discrete spectral measures. Some convergence properties are obtained

This work discusses the effect of erasing rules to the generative power of regulated grammars, which is a big open problem in the theory of regulated rewriting. It studies the possibility of removal of erasing rules from regulated grammars by aggregation of current, up-to-date results concerning this elimination and by presentation of a new condition, called k-limited erasing, under which all erasing rules can be always removed from regularly controlled context-free grammars without affecting their generative power. This result partially solves the abovementioned problem. Moreover, a new algorithm for elimination of erasing rules from context-free grammars is presented. This algorithm does not require any predetermination of so called epsilon-nonterminals (in contrast to the standard algorithm used in textbooks). In the conclusion, a significance of these results concerning syntactical analysis is discussed.

This thesis studies regulated grammars, their fundamentals and expressing power regarding Chomsky hierarchy of languages. Programmed grammars are investigated in more depth considering a few types of leftmost derivations. A variant of deterministic syntax analysis of programmed grammars is introduced. This analysis works similarly as LL(k) parsing. Transformations of matrix grammars into programmed grammars without changing their expressing power are introduced. The syntax analysis by regularly controlled grammars partly using programmed grammars are presented. In the end, cooperating distributed grammars with left permitting grammars as components are mentioned. Their deterministic syntax analysis uses predictive table or exhaustive exploration of the whole state space.

Wird der Äquator-Pol-Energietransfer als Wärmediffusion berücksichtigt, so gehen Energiebilanzmodelle in Reaktions-Diffusionsgleichungen über, deren Modellfall die (deterministische) Chafee-Infante-Gleichung darstellt. Ihre Lösung besitzt zwei stabile Zustände und mehrere instabile auf der separierenden Mannigfaltigkeit (Separatrix) der stabilen Anziehungsgebiete. Es wird bewiesen, dass die Lösung auf geeignet verkleinerten Anziehungsgebieten mit Minimalabstand zur Separatrix innerhalb von Zeitskalen relaxiert, die höchstens logarithmisch darin anwachsen. Motiviert durch statistische Belege aus grönländischen Zeitreihen wird diese partielle Differentialgleichung unter Störung mit unendlichdimensionalem, Hilbertraum-wertigen, regulär variierenden Lévy''schen reinen Sprungrauschen mit index alpha und Intensität epsilon untersucht. Ein kanonisches Beispiel dieses Rauschens ist alpha-stabiles Rauschen im Hilbertraum. Durch Erweiterung einer Methode von Imkeller und Pavlyukevich auf stochastische partielle Differentialgleichungen wird unter milden Bedingungen bewiesen, dass im Gegensatz zu Gauß''schem Rauschen die erwarteten Austritts- und übertrittszeiten zwischen Anziehungsgebieten polynomiell mit Ordnung in der inversen Intensität für kleine Rauschintensität anwachsen. In Kapitel 6 wird eine zusätzliche natürliche “Separatrixhypothese” über das Sprungmaß, eingeführt, die eine obere Schranke für die Austrittszeiten aus einer Umgebung der Separatrix impliziert. Dies ermöglicht den Nachweis einer oberen Schranke für die Austrittszeiten, welche gleichmäßig für Anfangsbedingungen in dem ganzen Anziehungsgebiet gilt. Es folgen zwei Lokalisierungsergebnisse. Schließlich wird gezeigt, dass die Lösung metastabiles Verhalten aufweist. Unter der “Separatrixhypothese” wird dies auf ein Ergebnis erweitert, welches gleichmäßig im Raum gilt. / If equator-to-pole energy transfer by heat diffusion is taken into account, Energy Balance Models turn into reaction-diffusion equations, whose prototype is the (deterministic) Chafee-Infante equation. Its solution has two stable states and several unstable ones on the separating manifold (separatrix) of the stable domains of attraction. We show, that on appropriately reduced domains of attraction of a minimal distance to the separatrix the solution relaxes in time scales increasing only logarithmically in it. Motivated by the statistical evidence from Greenland ice core time series, we consider this partial differential equation perturbed by an infinite-dimensional Hilbert space-valued regularly varying (pure jump) Lévy noise of index alpha and intensity epsilon. A proto-type of this noise is alpha-stable noise in the Hilbert space. Extending a method developed by Imkeller and Pavlyukevich to the SPDE setting we prove under mild conditions that in contrast to Gaussian perturbations the expected exit and transition times between the domains of attraction increase polynomially in the inverse intensity. In Chapter 6 we introduce an additional natural separatrix hypothesis on the jump measure that implies an upper bound on the exit time of a neighborhood of the separatrix. This allows to obtain an upper bound for the asymptotic exit time uniform for the initial positions inside the entire domain of attraction. It is followed by two localization results. Finally we prove that the solution exhibits metastable behavior. Under the separatrix hypothesis we can extend this to a result that holds uniformly in space.