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An interesting problem in proof theory is to find representations of proof that do not distinguish between proofs that are ‘morally’ the same. For many logics, the presentation of proofs in a traditional formalism, such as Gentzen’s sequent calculus, introduces artificial syntactic structure called ‘bureaucracy’; e.g., an arbitrary ordering of freely permutable inferences. A proof system that is free of bureaucracy is called canonical for a logic. In this dissertation two canonical proof systems are presented, for two logics: a notion of proof nets for additive linear logic with units, and ‘classical proof forests’, a graphical formalism for first-order classical logic. Additive linear logic (or sum–product logic) is the fragment of linear logic consisting of linear implication between formulae constructed only from atomic formulae and the additive connectives and units. Up to an equational theory over proofs, the logic describes categories in which finite products and coproducts occur freely. A notion of proof nets for additive linear logic is presented, providing canonical graphical representations of the categorical morphisms and constituting a tractable decision procedure for this equational theory. From existing proof nets for additive linear logic without units by Hughes and Van Glabbeek (modified to include the units naively), canonical proof nets are obtained by a simple graph rewriting algorithm called saturation. Main technical contributions are the substantial correctness proof of the saturation algorithm, and a correctness criterion for saturated nets. Classical proof forests are a canonical, graphical proof formalism for first-order classical logic. Related to Herbrand’s Theorem and backtracking games in the style of Coquand, the forests assign witnessing information to quantifiers in a structurally minimal way, reducing a first-order sentence to a decidable propositional one. A similar formalism ‘expansion tree proofs’ was presented by Miller, but not given a method of composition. The present treatment adds a notion of cut, and investigates the possibility of composing forests via cut-elimination. Cut-reduction steps take the form of a rewrite relation that arises from the structure of the forests in a natural way. Yet reductions are intricate, and initially not well-behaved: from perfectly ordinary cuts, reduction may reach unnaturally configured cuts that may not be reduced. Cutelimination is shown using a modified version of the rewrite relation, inspired by the game-theoretic interpretation of the forests, for which weak normalisation is shown, and strong normalisation is conjectured. In addition, by a more intricate argument, weak normalisation is also shown for the original reduction relation.

Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are widely-used mathematical models for decomposing multivariate data. They capture spatial relationships between variables, but ignore any temporal relationships that might exist between observations. Probabilistic PCA (PPCA) and Probabilistic CCA (ProbCCA) are versions of these two models that explain the statistical properties of the observed variables as linear mixtures of an alternative, hypothetical set of hidden, or latent, variables and explicitly model noise. Both the noise and the latent variables are assumed to be Gaussian distributed. This thesis introduces two new models, named PPCA-AR and ProbCCA-AR, that augment PPCA and ProbCCA respectively with autoregressive processes over the latent variables to additionally capture temporal relationships between the observations. To make PPCA-AR and ProbCCA-AR robust to outliers and able to model leptokurtic data, the Gaussian assumptions are replaced with infinite scale mixtures of Gaussians, using the Student-t distribution. Bayesian inference calculates posterior probability distributions for each of the parameter variables, from which we obtain a measure of confidence in the inference. It avoids the pitfalls associated with the maximum likelihood method: integrating over all possible values of the parameter variables guards against overfitting. For these new models the integrals required for exact Bayesian inference are intractable; instead a method of approximation, the variational Bayesian approach, is used. This enables the use of automatic relevance determination to estimate the model orders. PPCA-AR and ProbCCA-AR can be viewed as linear dynamical systems, so the forward-backward algorithm, also known as the Baum-Welch algorithm, is used as an efficient method for inferring the posterior distributions of the latent variables. The exact algorithm is tractable because Gaussian assumptions are made regarding the distribution of the latent variables. This thesis introduces a variational Bayesian forward-backward algorithm based on Student-t assumptions. The new models are demonstrated on synthetic datasets and on real remote sensing and EEG data.

Central America is a region regularly affected by natural disasters, with most of them having a hydro-meteorological origin. Therefore, the understanding of annual changes of precipitation upon the region is relevant for planning and mitigation of natural disasters. This thesis focuses on studying the precipitation variability at annual scales in Central America within the framework of the Swedish Centre for Natural Disaster Science. The aims of this thesis are: i) to establish the main climate variability sources during the boreal winter, spring and summer by using different statistical techniques, and ii) to study the connection of sea surface temperature anomalies of the neighbouring oceans with extreme precipitation events in the region. Composites analysis is used to establish the variability sources during winter. Canonical correlation analysis is employed to explore the connection between the SST anomalies and extreme rainfall events during May-June and August-October. In addition, a global circulation model is used to replicate the results found with canonical correlation analysis, but also to study the relationship between the Caribbean Sea surface temperature and the Caribbean low-level jet. The results show that during winter both El Niño Southern Oscillation and the Pacific Decadal Oscillation, are associated with changes of the sea level pressure near the North Atlantic Subtropical High and the Aleutian low. In addition, the El Niño Southern Oscillation signal is intensified (destroyed) when El Niño and the Pacific Decadal Oscillation have the same (opposite) sign. Sea surface temperature anomalies have been related to changes in both the amount and temporal distribution of rainfall. Precipitation anomalies during May-June are associated with sea surface temperature anomalies over the Tropical North Atlantic region. Whereas, precipitation anomalies during August-September-October are associated with the sea surface temperature anomalies contrast between the Pacific Ocean and the Tropical North Atlantic region. Model outputs show no association between sea surface temperature gradients and the Caribbean low-level jet intensification. Canonical correlation analysis shows potential for prediction of extreme precipitation events, however, forecast validation shows that socio-economic variables must be included for more comprehensive natural disaster assessments.

Les études cliniques et in vitro suggèrent que la sclérose de l’os sous-chondral due aux ostéoblastes (Ob) anormaux est impliquée dans la progression de l’ostéoarthrose (OA). Les Ob OA humains isolés à partir d’os sous-chondral sclérosé montrent un phénotype altéré, un niveau réduit de signalisation Wnt/β-caténine canonique et une minéralisation in vitro réduite. Il existe également deux voies non-canoniques, Wnt/PKC et Wnt/PCP qui ont étés décrites dans la littérature. Cependant, il n’existe aucune étude qui traite de ces deux voies dans les Ob OA. Ces voies sont activées après qu’un ligand Wnt non-canonique tel que Wnt-5a se lie à un récepteur Wnt couplé à des corécepteurs de la voie non-canonique. Ceci enclenche, respectivement pour la voie Wnt/PKC-Ca2+ et Wnt/PCP, la phosphorylation de PKC (p-PKC) et la phosphorylation de JNK (p-JNK) et agit sur les cibles en aval. Nous avons voulu déterminer s’il était possible de constater des altérations dans les voies Wnt non-canoniques dans les Ob OA. Nous avons préparé des cultures primaires d’ostéoblastes sous-chondral humains à partir de plateaux tibiaux de patients OA subissant une arthroplastie totale du genou, ainsi qu’à partir de plateaux tibiaux recueillis à l’autopsie de patients « normaux ». L’expression des gènes impliqués dans les voies Wnt/PKC et Wnt/PCP a été évaluée par RT-qPCR et la production par Western Blot des protéines, ainsi que celle de p-PKC et p-JNK et que l’activité des facteurs NFAT et AP-1 utilisés par ces deux voies. L’activité phosphatase alcaline (ALPase) et la quantité d’ostéocalcine (OC) ont étés évaluées respectivement à l’aide d’hydrolyse de substrat et d’ELISA. Le niveau de minéralisation a été évalué par la coloration au rouge Alizarine. Nos résultats montrent que l’expression et la production de Wnt-5a étaient augmentées dans les Ob OA comparées aux Ob N et LGR5 était significativement plus élevée. De plus, l’expression de LGR5 est directement régulée via la stimulation ou la diminution de Wnt-5a, à la fois au niveau de l’ARNm et des protéines. Par ailleurs, Wnt-5a a stimulé la phosphorylation de JNK et de PKC ainsi que l’activité NFAT et AP-1. Les niveaux de minéralisation ainsi que d’activité ALPase et de sécrétion d’OC ont aussi été affectés par les changements du niveau de Wnt-5a. Ces résultats suggèrent que Wnt-5a, qui est augmentée dans les OA Ob, peut stimuler les voies Wnt non-canoniques et affecter le phénotype et la minéralisation des OA Ob humains. / Clinical and in vitro studies suggest that subchondral bone sclerosis due to abnormal osteoblasts (Ob) is involved in the progression and/or onset of osteoarthritis (OA). Human Ob isolated from sclerotic subchondral OA bone tissue show an altered phenotype, a decreased canonical Wnt/ß-catenin signaling pathway (cWnt), and a reduced mineralization in vitro. Besides the cWnt pathway, at least two non-canonical signaling pathways, the Wnt/PKC and Wnt/PCP pathway have been described. These pathways are activated when a non-canonical Wnt ligand like Wnt-5a binds to a Wnt receptor coupled with non-canonical co-receptors. This activates, respectively for Wnt/PKC-Ca2+ and Wnt/PCP, the phosphorylation of PKC (pPKC) and the phosphorylation of JNK (pJNK) and their effect on downstream targets. However, there are no reports of either pathway in OA Ob. Here, we studied if alterations of the non-canonical pathways could be observed in OA Ob. We prepared primary human subchondral Ob using the tibial plateaus of OA patients undergoing total knee arthroplasty, or from tibial plateaus of normal individuals at autopsy. The expression of genes involved in Wnt/PKC and Wnt/PCP was evaluated by RT-qPCR and their protein production by Western blot analysis, in addition to p-PKC and p-PCP and NFAT and AP-1 activity with luciferase. Alkaline phosphatase activity and osteocalcin levels were evaluated respectively by substrate hydrolysis and ELISA respectively, and mineralization levels were evaluated with Alizarin red staining. OA Ob showed an increased alkaline phosphatase activity and osteocalcin release. The expression of Wnt5a was increased in OA Ob compared to normal. The expression of LGR5 was significantly increased in these cells. Moreover, the expression and production of LGR5 is directly modulated via the stimulation or inhibition of Wnt5a. However, Wnt5a did not stimulate the expression of LGR4. Wnt5a increased the phosphorylation of PKC and JNK as well as NFAT and AP-1 activity. Mineralization levels as well as alkaline phosphatase activity and osteocalcin secretion levels were also linked with changes in Wnt-5a levels. These data indicate that Wnt5a, which is increased in OA Ob, can directly stimulate the Wnt/PKC and Wnt/PCP pathways and this can affect the phenotype and mineralization observed in human OA Ob.

This study investigated the impact of three edaphic factors on the distribution of forest plants in Sweden. Based on 2657 plots with 22 common species, Canonical Correspondence Analysis (CCA) and Generalized-linear-model (GLM) were performed with pH measurements in the top layer of the soil, latitude and deciduous tree proportion as explanatory variables. Variation of the species occurrence could to a substantial degree be explained by pH, latitude and proportion of timber volume of deciduous tree species. Furthermore, the majority of species were affected by the studied environmental variables. Therefore, these factors have an important role in the ecological interactions in the forest. All species also showed broad pH-niches with many occurrences spread out within the species entire pH-range. Finally, the study relates to educational science through designing a meaningful excursion for secondary school when teaching ecology.

Cette thèse s’articule autour des espaces de modules de représentations de carquois arbitraires, c’est-à-dire possédant d’éventuelles boucles. Nous obtenons trois types de résultats. Le premier concerne la base canonique de Lusztig, dont la définition est étendue à notre cadre, notamment en introduisant une algèbre de Hopf généralisant les groupes quantiques usuels (i.e. associés aux algèbres de Kac-Moody symétriques). On démontre au passage une conjecture faite par Lusztig en 1993, portant sur la catégorie de faisceaux pervers qu’il définit sur les variétés de représentations de carquois.Le second type de résultats, également inspiré par le travail de Lusztig, concerne la base semi- canonique et la variété Lagrangienne nilpotent de Lusztig. Pour un carquois arbitraire, on définit des sous-variétés de représentations semi-nilpotentes Λ(α), et nous montrons qu’elles sont Lagrangiennes. La démonstration repose sur l’existence de fibrations affines partielles entre diverses composantes de Λ(α), contrôlées par une combinatoire précise. Nous définissons une algèbre de convolution de fonctions constructibles sur ⊔Λ(α), et montrons qu’elle possède une base formée de fonctions quasi- caractéristiques des composantes irréductibles des Λ(α). La structure combinatoire qui se dégage ici est analogue à celle obtenue sur les faisceaux pervers de Lusztig, et fait apparaître des opérateurs plus généraux que ceux décrits par les cristaux de Kashiwara.Le troisième thème considéré est celui des variétés carquois de Nakajima, dont l’étude géomé- trique menée ici permet, conjointement avec ce qui est fait précédemment, de donner une définition de cristaux de Kashiwara généralisés. On définit à nouveau des sous-variétés Lagrangiennes, ainsi qu’un produit tensoriel sur leurs composantes irréductibles, comme fait dans le cas classique par Nakajima. / This thesis is about the moduli spaces of representations of arbitrary quivers, i.e. possibly carrying loops. We obtain three types of results. The first one deals with the Lusztig canonical basis, whose definition is here extended to our framework, thanks in particular to the definition of a Hopf algebra generalizing the usual quantum groups (i.e. associated to symmetric Kac-Moody algebras). We also prove a conjecture raised by Lusztig in 1993, which concerns the category of perverse sheaves he defines on varieties of representations of quivers.The second type of results, also inspired by the work of Lusztig, concerns the semicanonical basis. For an arbitrary quiver, we define subvarieties of seminilpotent representations Λ(α), and we show that they are Lagrangian. The proof relies on the existence of partial affine fibrations between some irreducible components of Λ(α), controled by a precise combinatorial structure. We define a convolution algebra of constructible functions on ⊔Λ(α), and show it is equipped with a basis of quasi-characteristic functions of the irreducible components of the Λ(α). The combinatorial structure arising from this construction is analogous to the one obtained on Lusztig perverse sheaves, and yields operators more general than the ones described by Kashiwara crystals.The third considered topic is the one of Nakajima quiver varieties, whose geometric study in this thesis allows, along with the previous (also geometric) work, to define generalized Kashiwara crystals. We define, again, Lagrangian subvarieties, and a tensor product of their irreducible components, as done by Nakajima on the classical case.

Com o objetivo de compreender quais fatores abióticos determinam a ocorrência das diferentes formações florestais na região de Batatais, entre as coordenadas 20038S e 20058S e 47037W e 47028W, foram escolhidas três propriedades agrícolas (Fazenda Monte Belo, em Restinga, SP e Fazenda Magnólia e Sítio Pratinha, em Batatais, SP), que apresentavam remanescentes florestais representativos da região (floresta ribeirinha paludícula, floresta estacional semidecídua ribeirinha e cerradão). Para descrever a composição florística e a estrutura da comunidade arbórea foram amostradas 05 parcelas de 10 x 10 m ao redor de cada estação tensiométrica. Para o estudo dos fatores abióticos foram determinados os parâmetros físicos e químicos dos solos e as curvas de retenção de água nos solos e piezometria. A discriminação das variáveis abióticas e de vegetação foi feita através da análise de componentes principais (PCA) e, na correlação entre a abundância de espécies e fatores abióticos, foram feitas análises diretas de gradiente por meio de Análise de Correlação Canônica (CCA). A textura dos solos (teores de argila, silte e areia) e a posição no terreno (cota), foram as variáveis ambientais mais importantes na distribuição das espécies e nas variações das fisionomias florestais, com influência na retenção hídrica e nos índices de fertilidade dos solos. Essas diferenças nos teores de argila em profundidade ao longo do declive, com influência direta na retenção de umidade dos solos ou mesmo na formação de ambientes paludículos, determinaram grupos distintos de espécies e fisionomias florestais: (i) um grupo de espécies de ocorrência típica nas fisionomias de Cerrado e fortemente associado às cotas mais elevadas (solos menos férteis, bem drenados e porcentagens mais baixas de argila e silte nas camadas mais profundas), entre as quais: Matayba juglandifolia, Trichilia pallida, Lithraea molleoides, Anadenanthera falcata, Myrcia tomentosa, Copaifera langsdorffii, Erytrhoxylum pelleteranum, Platipodium elegans, Chrysophyllum marginatum, Luehea divaricata, entre outras e (ii) um grupo com espécies indicadoras de Florestas Paludículas ou de ocorrência comum nestas fisionomias, associado aos solos das cotas mais baixas (Gleissolos), com porcentagens altas de argila e silte nas camadas superficiais, mais férteis e maior retenção hídrica: Cecropia pachystachya, Citronella gongonha, Rapanea guianensis, Talauma ovata e Tapirira guianensis. Pode-se considerar um terceiro grupo de transição entre Floresta Estacional Semidecídua e Cerradão, nas cotas intermediárias e menos úmidas (espécies amostradas em parcelas localizadas nas bordas das Florestas Paludículas), onde ocorreram espécies tanto de ambiente de Cerradão, como de Floresta Estacional Semidecídua, e algumas poucas de ambiente paludículo. As porcentagens mais elevadas de Areia nos solos do Sítio Pratinha, com influência na menor retenção hídrica e também nos índices de fertilidade (solos álicos, com maior acidez e os menos férteis), podem explicar algumas diferenças na composição e abundância das espécies entre fisionomias florestais iguais. O Cerradão da Fazenda Monte Belo, mostrou-se diferente floristicamente do Cerradão do Sítio Pratinha. Esta mesma diferença ocorreu em relação às Florestas Paludículas da Fazenda Magnólia e a do Sítio Pratinha. As poucasespécies de ocorrência comum tiveram populações diferentes. A CCA evidenciou também correlações de algumas espécies com determinadas variáveis de solo. / In order to understand what abiotic factors determine the occurrence of different forest formations in the region of Batatais, coordinated between 20038\'S and 20058\'S and 47037\'W and 47028\'W, three agricultural properties were chosen (Monte Belo, in the city of Restinga, SP and Magnolia and Pratinha in Batatais, SP, Brazil), which had forests representative of the region (swamp forest, semi-deciduous riverine forest and forested savanna). To describe the floristic composition and structure of the arboreal community, 05 plots of 10 x 10 meters around each tensiometric station were sampled. For the study of abiotic factors, the physico-chemical characteristics of the soils, the soil-water-retention curves and the groundwater fluctuation were determined. The discrimination of the environmental variables and arboreal species were made through the Principal Components Analysis (PCA), and in the correlation between the abundance of species and abiotic factors, direct analyses of gradient through Canonical Correspondence Analysis (CCA) were made. The texture of the soil (levels of clay, silt and sand) and the position on the ground (altitude) were the most important environmental variables in the distribution of species and variations of forest physiognomies, with influence in the retention rates of water and soil fertility. These differences in levels of clay in depth along the slope, with direct influence on the retention of soil moisture and even in the development of swampy environment, determined distinct groups of species and forest physiognomies: (i) a group of species of typical occurrence in physiognomies of Forested Savanna and strongly associated with higher altitude (less fertile, well-drained soil and lower percentages of clay and silt in the deeper layers), including: Matayba juglandifolia, Trichilia pallida, Lithraea molleoides, Anadenanthera falcata, Myrcia tomentosa, Copaifera langsdorffii, Erytrhoxylum pelleteranum, Platipodium elegans, Chrysophyllum marginatum, Luehea divaricata, among others, and (ii) a group with indicator species of Swamp Forests or common occurrence in these physiognomies, associated with lower altitude (Gleisoil), with high percentages of clay and silt in the upper and more fertile layers, and greater water retention: Cecropia pachystachya, Citronella gongonha, Rapanea guianensis, Talauma ovata and Tapirira guianensis. A third group of transition between Semi-deciduous Forest and Forested Savanna, in intermediate altitude and soils less humid (species sampled in plots located at the edges of Swamp Forests), occurred both in the Forested Savanna and in Semi-deciduous Forest and a few in swampy environment. The highest percentages of sand in the soil of Pratinha, with less influence on water retention and also on the rates of fertility (alic soils, with greater acidity and less fertile), may explain some differences in the composition and abundance of species of forest physiognomies equal. The forested Savanna of Monte Belo, has proved floristically different from the Forested Savanna of Pratinha. This same difference occurred in swamp forests of Magnolia and Pratinha. The few species of common occurrence had differentpopulations. The CCA also revealed correlations of some species with certain variables of soil.

Die Auswertung von Mehrschleifen-Feynman-Integralen ist eine der größten Herausforderungen bei der Berechnung präziser theoretischer Vorhersagen für die am LHC gemessenen Wirkungsquerschnitte. In den vergangenen Jahren hat sich die Nutzung von Differentialgleichungen bei der Berechnung von Feynman-Integralen als sehr erfolgreich erwiesen. Es wurde dabei beobachtet, dass die von den Feynman-Integralen erfüllte Differentialgleichung oftmals in eine sogenannte kanonische Form transformiert werden kann, welche die Integration der Differentialgleichung mittels iterierter Integrale wesentlich vereinfacht. Das zentrale Ergebnis der vorliegenden Arbeit ist ein Algorithmus zur Berechnung rationaler Transformationen von Differentialgleichungen von Feynman-Integralen in eine kanonische Form. Neben der Existenz einer solchen rationalen Transformation stellt der Algorithmus keinerlei weitere Bedingungen an die Differentialgleichung. Insbesondere ist der Algorithmus auf Mehrskalenprobleme anwendbar und erlaubt eine rationale Abhängigkeit der Differentialgleichung vom dimensionalen Regulator. Bei der Anwendung des Algorithmus wird zunächst das Transformationsgesetz im dimensionalen Regulator entwickelt, um Differentialgleichungen für die Koeffizienten in der Entwicklung der Transformation herzuleiten. Diese Differentialgleichungen werden dann mit einem rationalen Ansatz für die gesuchte Transformation gelöst. Es wird zudem eine Implementation des Algorithmus in dem Mathematica Paket CANONICA vorgestellt, welches das erste veröffentlichte Programm dieser Art ist, das auf Mehrskalenprobleme anwendbar ist. CANONICAs Potential für moderne Mehrschleifenrechnungen wird anhand mehrerer nicht trivialer Mehrschleifen-Integraltopologien demonstriert. Die gezeigten Topologien hängen von bis zu drei Variablen ab und umfassen auch vormals ungelöste Topologien, die zu Korrekturen höherer Ordnung zum Wirkungsquerschnitt der Produktion einzelner Top-Quarks am LHC beitragen. / The evaluation of multi-loop Feynman integrals is one of the main challenges in the computation of precise theoretical predictions for the cross sections measured at the LHC. In recent years, the method of differential equations has proven to be a powerful tool for the computation of Feynman integrals. It has been observed that the differential equation of Feynman integrals can in many instances be transformed into a so-called canonical form, which significantly simplifies its integration in terms of iterated integrals. The main result of this thesis is an algorithm to compute rational transformations of differential equations of Feynman integrals into a canonical form. Apart from requiring the existence of such a rational transformation, the algorithm needs no further assumptions about the differential equation. In particular, it is applicable to problems depending on multiple kinematic variables and also allows for a rational dependence on the dimensional regulator. First, the transformation law is expanded in the dimensional regulator to derive differential equations for the coefficients of the transformation. Using an ansatz in terms of rational functions, these differential equations are then solved to determine the transformation. This thesis also presents an implementation of the algorithm in the Mathematica package CANONICA, which is the first publicly available program to compute transformations to a canonical form for differential equations depending on multiple variables. The main functionality and its usage are illustrated with some simple examples. Furthermore, the package is applied to state-of-the-art integral topologies appearing in recent multi-loop calculations. These topologies depend on up to three variables and include previously unknown topologies contributing to higher-order corrections to the cross section of single top-quark production at the LHC.

Anotation This diploma thesis "Reflection of the Canonical Approach of Brevard S. Childs" deals with the charakteristic focuses and postulates of the canonical approach of Brevard S. Childs with focusing on his two important publications: Introduction to the Old Testament as Scripture (1979) and Biblical Theology of the Old and New Testaments (1993). It shows a short intersection of his longterm academic exploratory work and with respect to the interpretative emphasis describes a brief overview of history of the canon exploration from the Reformation to the so called New Biblical Theology. The content centre of the diploma thesis is to introduce the main methological foundations of Childs'canonical approach with regard to its central postulates - for example: canonical intentionality, final form of the text, etc. and to those hermeneutical elements which are applicable in practical pastoral work of the church. At the end of the diploma thesis there is a short practical guide to the theological exegesis based on the main hermeneutical principles of the Childs'canonical approach.