L’effet isotopique cinétique (KIE) est un outil puissant pour obtenir un aperçu sur le mécanisme d'une grande variété réactions. Nous avons observé différentes mesures de l’effet isotopique cinétique primaire du 13C pour la formation des α-, et β-mannopyranosides et des α- et β-glucopyranosides, en partant du sulfoxyde de glycosyle protégé par le groupement 4,6-O-benzylidène, par la spectroscopie RMN à ultrahaut champ (13C à 200 MHz et 1H à 800 MHz). Nous avons aussi calculé les KIE pour ces réactions en collaboration avec le Prof. Pratt à l'Université d'Ottawa. Les valeurs expérimentale et calculée (B3LYP / 6-31G (d, p) avec un modèle de continuum polarisable) sont en bon accord sauf pour l’α-mannopyranoside. Trois cas (-mannopyanoside,  et -glucopyranosides) parmi les quatre ont montré un caractère “SN2-like“, mais la formation de l'-mannopyranoside suggère fortement un mécanisme dissociatif (SN1). Une telle différence de mécanisme nécessite une authentification par des mesures cinétiques. Nous avons ensuite porté notre attention sur le développement d'une réaction intramoléculaire, comme horloge intramoléculaire, afin d’évaluer la cinétique relative des réactions de glycosylation. La formation des produits tricycliques fournit une grande évidence de l'existence d'un ion mannosyloxocarbénium comme un intermédiaire transitoire. Les réactions de compétition avec de l'isopropanol et du méthallyltriméthylsilane sont interprétées comme indiquant que la β-O-mannosylation passe par un mécanisme associatif (SN2-like), tandis que l’α-O-mannosylation et le β-C-mannosylation sont dissociative (SN1-like). Ceci est en plein accord avec nos résultats expérimentaux sur l’effet isotopique cinétique. Cette approche de la détermination de la cinétique relative des réactions de glycosylation est une méthode directe et est potentiellement applicable à une large variété de donneurs de glycosyle. / Kinetic isotopic effects (KIEs) are powerful tools to obtain insight into the mechanism of a great range of reactions. We demonstrated differing primary 13C kinetic isotope effect (KIE) measurements for the formation of α-, β-mannopyranosides and α-, β-glucopyranosides from the 4,6-O-benzylidene protected mannosyl and glucosyl sulfoxides by NMR (13C at 200 MHz and 1H at 800 MHz). We have also calculated the KIEs in collaboration with the Pratt group at the University of Ottawa for these reactions. Experimental and calculated (B3LYP/ 6-31G (d,p) values with a polarizable continuum model) were in good agreement, except for the -mannopyranoside. Three of (-mannpyanoside and the -, -glupyranosides) four cases showed a SN2-like character. The formation of the -mannopyranoside on the other hand suggests a strongly dissociative mechanism (SN1). Such a difference in mechanism necessarily demands authentication by kinetic measurements. We turned then our attention to the development of an intramolecular clock reaction with which to probe the relative kinetics of glycosylation reactions and to the formation of the tricyclic products that provides strong evidence for the existence of a mannosyl oxocarbenium ion as a transient intermediate. Competition reactions with isopropanol and trimethylmethallylsilane are interpreted as indicating β-O-mannosylation to proceed via an associative SN2-like mechanism, whereas α-O-mannosylation and β-C-mannosylation are dissociative and SN1-like. This is in full agreement with our experimental KIE results. This approach to the determination of relative kinetics of glycosylation reactions, is straightforward and is potentially applicable to a broad range of glycosyl donors.

L’hadronthérapie par ions carbone représente une modalité de radiothérapie alternative très attractive du fait des propriétés physiques et biologiques de ce type de particules. Les chondrosarcomes, tumeurs radio-résistantes à différentiation cartilagineuse, sont en première ligne pour le traitement par ions carbone. Cependant, les effets secondaires sur les tissus sains environnants sont peu ou mal connus. Ce projet a pour but l’étude des effets directs des ions accélérés dans un modèle 3D de cartilage sain et pathologique proche de l’homéostasie humaine et le développement de nouveaux outils de calculs d’efficacité biologique relative (EBR). Dans un premier temps, nous nous sommes intéressés aux séquelles radio-induites sur le cartilage articulaire dans un contexte d’hadronthérapie par ions carbone. En culture 2D physioxique (2% d’O2), l’efficacité biologique relative des ions carbone (transfert d’énergie linéique ou TEL intermédiaire) comparée aux rayons X a été évaluée à 2,6. Ceci a été corrélé à une plus forte induction de sénescence radio-induite. Cependant, cet effet différentiel n’a pas été retrouvé en utilisant un modèle 3D de cartilage articulaire. L’efficacité biologique relative des ions accélérés semble donc surévaluée, en utilisant des cultures en monocouche, par rapport à la 3D. Dans un deuxième temps, un modèle 3D de chondrosarcome a été développé pour des études d’hadronbiologie. Après plusieurs obstacles techniques, des méthodes d’extraction protéique et d’immunohistochimie ont été mises au point. Une nouvelle méthode d’évaluation de l’EBR en 3D basée sur la cinétique d’induction de la protéine γ-H2AX a été proposée. / Hadrontherapy using carbon ions has many advantages due to physical and biological properties of this type of particle. Chondrosarcoma, a cartilaginous radio-resistant tumor, has been successfully treated using carbon ions. However, potential side effects to the surrounding healthy tissues are still poorly known. This project aims to study the direct effects of carbon ions in a 3D model of healthy articular cartilage and chondrosarcoma close to human homeostasis, in order to provide new tools for the evaluation of the relative biological effectiveness (RBE).The first part of the project was dedicated to the evaluation of carbon ions-induced impact on articular cartilage in the context of chondrosarcoma treatment. Compared to X-rays, the relative biological effectiveness of intermediate-LET carbon ions scored 2.6 in 2D monolayer culture. This was correlated with a stronger induction of cellular senescence. However, this differential effect was not reproduced using a 3D model of articular cartilage. Thus, the relative biological effectiveness of accelerated ions is probably overestimated using monolayer cultures (2D), compared to 3D. In the second part of this work, we developed a 3D chondrosarcoma model for hadronbiology studies. Protein extraction and immunohistochemistry protocols were developed. A new RBE evaluation method based on γ -H2AX repair kinetic in 3D, was proposed.

Background: There are approximately 150.000 people with dementia living in Sweden, with 40 % living in nursing homes and the remaining 60 % living at home. Relatives caring for persons with dementia need support. The work is demanding and stressful. Caregiving is often carried out 24 hours a day, every day. Caregiver supporters offers support to relatives caring for persons with dementia. Aim: To describe caregiver supporters’ experience of caregiver support regarding dementia. Method: A qualitative interview study by manifest qualitative content analysis. Results: There are different types of caregiver support but according to caregiver supporters, relatives mainly want to be seen and heard based on their situation. With knowledge of dementia and the opportunity for relatives to talk with others in the same situation, the supporters feel that the relatives’ health and ability to care are improved. Collaboration between municipalities and the region is insufficient. The supporters feel that many nurses mediate contact, but it is pointed out that nursing education should contain more education about the subject. Conclusion: The accessibility of caregiver supporters in the municipality is important for relatives to receive support. Better cooperation between municipalities and the region could enable more relatives to have access to the caregiver support they need. To enhance this, nurses should have knowledge and education of dementia and caregiver support. / Bakgrund: Det finns omkring 150.000 demenssjuka personer i Sverige, endast 40 % bor på omvårdnadsboende, resterande 60 % bor hemma. Anhöriga som vårdar demenssjuka närstående behöver stöd, arbetet är tungt och stressande. Vårdandet utförs ofta 24 timmar om dygnet, varje dag. Anhörigstödjare erbjuder stöd till anhöriga som vårdar demenssjuka närstående. Syftet var att beskriva anhörigstödjares upplevelse av anhörigstöd vid demenssjukdom. Metod: En kvalitativ intervjustudie med manifest kvalitativ innehållsanalys. Resultat: Det finns olika sorters anhörigstöd, men enligt anhörigstödjarna verkar det viktigaste för anhöriga vara att bli sedda och hörda utifrån sin situation. Med kunskap om demenssjukdomar och möjligheten att samtala med andra anhöriga i samma situation upplever anhörigstödjarna att de anhörigas hälsa och förmåga att vårda sina demenssjuka närstående förbättras. Samverkan mellan kommuner och regionen är otillräcklig. Anhörigstödjarna upplever att grundutbildade sjuksköterskor förmedlar kontakt men det poängteras att sjuksköterskeutbildningen borde innehålla mer om ämnet. Slutsats: Anhörigstödjarnas tillgänglighet i kommunen har betydelse för att anhöriga ska få stöd. Bättre samarbete mellan kommuner och regionen skulle kunna möjliggöra att fler anhöriga får tillgång till anhörigstöd. För att främja detta bör sjuksköterskor ha kunskap om demenssjukdomar och anhörigstöd.

Ces dernières années, la quantité de données visuelles produites par divers types de capteurs est en augmentation permanente. L'interprétation et l'indexation automatique de telles données constituent des défis importants pour les domaines liés à la reconnaissance de formes et la vision par ordinateur. Dans ce contexte, la position relative des différents objets d'intérêt composant les images représente une information particulièrement importante pour interpréter leur contenu. Les relations spatiales sont en effet porteuses d'une sémantique riche, qui est fortement liée à la perception humaine. Les travaux de recherche présentés dans cette thèse proposent ainsi d'explorer différentes approches génériques de description de l'information spatiale, en vue de les intégrer dans des systèmes de reconnaissance et d'interprétation d'images de haut niveau. Tout d'abord, nous présentons une approche pour la description de configurations spatiales complexes, où les objets peuvent être imbriqués les uns dans les autres. Cette notion est formalisée par deux nouvelles relations spatiales, nommées enlacement et entrelacement. Nous proposons un modèle qui permet de décrire et de visualiser ces configurations avec une granularité directionnelle. Ce modèle est validé expérimentalement pour des applications en imagerie biomédicale, en télédétection et en analyse d'images de documents. Ensuite, nous présentons un cadre d'apprentissage de relations spatiales composites à partir d'ensembles d'images. Inspirée des approches par sacs de caractéristiques visuelles, cette stratégie permet de construire des vocabulaires de configurations spatiales apparaissant dans les images, à différentes échelles. Ces caractéristiques structurelles peuvent notamment être combinées avec des descriptions locales, conduisant ainsi à des représentations hybrides et complémentaires. Les résultats expérimentaux obtenus sur différentes bases d'images structurées permettent d'illustrer l'intérêt de cette approche pour la reconnaissance et la classification d'images. / In recent years, the amount of visual data produced by various types of sensors has been continuously increasing. The automatic interpretation and indexation of such data constitute an important challenge in the fields of pattern recognition and computer vision. In this context, the relative position of the different objects of interest depicted in images represents particularly important information for the interpretation of their content. Spatial relations indeed carry rich semantics that are strongly tied with human perception. The research work presented in this thesis thus proposes to explore different generic approaches to the description of spatial information, in order to integrate them in high-level image recognition and understanding systems. First, we present an approach for the description of complex spatial configurations, where objects can be imbricated in each other. This notion is formalized by two novel spatial relations, namely enlacement and interlacement. We propose a model to describe and to visualize these configurations with directional granularity. This model is experimentally validated for applications in biomedical imaging, remote sensing and document image analysis. Then, we present a framework for learning composite spatial relations from image datasets. Inspired by bags of visual features approaches, this strategy allows to build vocabularies of spatial configurations occurring across images, at different scales. These structural features can notably be combined with local descriptions, leading to hybrid and complementary representations. Experimental results obtained for different datasets of structured images highlight the interest of this approach for image recognition and classification tasks.

Un défi important en Biologie est de comprendre comment les organismes s’adaptent à des environnements fluctuants et de déterminer l’importance relative de la plasticité phénotypique et des mutations dans cette adaptation. Nous avons examiné la réponse d’un pathogène du blé (Zymoseptoria tritici) aux fluctuations de température grâce à des approches de transcriptomique, de phénotypage (fitness relative et pathogénie) et de génomique. Pour cela, une évolution expérimentale a été menée in vitro à partir de deux clones ayant évolué dans trois régimes thermiques : à 17°C, à 23°C et en température fluctuante. Le niveau d’expression de 11% du génome a évolué de manière distincte entre les deux génotypes fondateurs en conditions de fluctuations. Nous avons également observé une plus forte densité de gènes différentiellement exprimés dans des régions connues pour être riches en éléments transposables. L’évolution en conditions fluctuantes a favorisé la robustesse du transcriptome. La fitness relative estimée dans les conditions d’évolution a augmenté uniquement pour les lignées fluctuantes issues d’un des deux génotypes fondateurs. La différence de croissance entre les deux ancêtres en conditions de fluctuations et leur différent niveau de plasticité d’expression pourraient expliquer ces résultats différents. Enfin, nous avons observé : i). des pertes de pathogénie in planta suite à l’évolution à 17°C et en fluctuations, ii). aucune perte de chromosomes accessoires, iii). de nombreuses mutations dans le génome, dont des mutations codantes dans des effecteurs. Ces travaux apportent de nombreux éléments de compréhension des mécanismes évolutifs et moléculaires sous-jacents à l’évolution de Z. tritici dans des environnements variables. / An important challenge in Biology is to understand how organisms adapt to fluctuating environments and to determine the relative significance of phenotypic plasticity and mutations in this adaptation. We examined the response of a wheat pathogen (Zymoseptoria tritici) to temperature fluctuations using transcriptomics, phenotyping (relative fitness and disease level) and genomics. With this goal, we conducted an in vitro experimental evolution from two Z. tritici clones that evolved in three thermal conditions: at 17°C, at 23°C and under temperature fluctuations. Expression level of 11% of the genome evolved in a different way between the two founder genotypes that evolved under fluctuating conditions. We also observed a higher density of differentially expressed genes in regions known to be enriched in transposable elements. Evolution under fluctuating selection promoted robustness of the transcriptome. The relative fitness estimated in the same conditions as for the experimental evolution did increase for fluctuating lineages only for one of the founder genotypes. The difference of growth between the two ancestors in fluctuating conditions and their distinct level of expression plasticity could explain these opposite results. Finally we observed: i). in planta pathogenicity losses for lineages evolved at 17°C or under fluctuations ii). no accessory chromosome loss, iii). many de novo mutations, including coding mutations in effector genes. This work contributes to shade light on the evolutionary and molecular mechanisms underlying the evolution of Z. tritici in variable environments.

In recent years, the interest in flying multiple Unmanned Aerial Vehicles (UAVs) in formation has increased. One challenging aspect of achieving this is the relative positioning within the swarm. This thesis evaluates two different methods for estimating the relative position and orientation between two fixed wing UAVs by fusing range measurements from Ultra-wideband (UWB) sensors and orientation estimates from Inertial Measurement Units (IMUs). To investigate the problem of estimating the relative position and orientation using range measurements, the performance of the UWB nodes regarding the accuracy of the measurements is evaluated. The resulting information is then used to develop a simulation environment where two fixed wing UAVs fly in formation. In this environment, the two estimation solutions are developed. The first solution to the estimation problem is based on the Extended Kalman Filter (EKF) and the second solution is based on Factor Graph Optimization (FGO). In addition to evaluating these methods, two additional areas of interest are investigated: the impact of varying the placement and number of UWB sensors, and if using additional sensors can lead to an increased accuracy of the estimates. To evaluate the EKF and the FGO solutions, multiple scenarios are simulated at different distances, with different amounts of changes in the relative position, and with different accuracies of the range measurements. The results from the simulations show that both solutions successfully estimate the relative position and orientation. The FGO-based solution performs better at estimating the relative position, while both algorithms perform similarly when estimating the relative orientation. However, both algorithms perform worse when exposed to more realistic range measurements. The thesis concludes that both solutions work well in simulation, where the Root Mean Square Error (RMSE) of the position estimates are 0.428 m and 0.275 m for the EKF and FGO solutions, respectively, and the RMSE of the orientation estimates are 0.016 radians and 0.013 radians respectively. However, to perform well on hardware, the accuracy of the UWB measurements must be increased. It is also concluded that by adding more sensors and by placing multiple UWB sensors on each UAV, the accuracy of the estimates can be improved. In simulation, the lowest RMSE is achieved by fusing barometer data from both UAVs in the FGO algorithm, resulting in an RMSE of 0.229 m for the estimated relative position.

No description available.

O princípio de reconhecimento de espaços de $\\infty$-laços é que o funtor $\\Omega^\\infty:\\textttightarrow \\mathcal E^\\infty[\\texttt]$ dado por $\\Omega^\\infty Y_\\bullet=\\text_{\\bullet\\shortrightarrow\\infty}\\Omega^\\bullet Y_\\bullet$ induz uma equivalência entre a categoria homotópica de espectros conectivos e a categoria homotópica de $\\mathcal E^\\infty$-álgebras grouplike para qualquer resolução cofibrante $\\mathcal E^\\infty$ do operad $\\mathcal Com$ de monóides comutativos. Nesta tese é provado um princípio de reconhecimento de 2-espaços de $N$-laços para $2<N\\leq\\infty$. Quando $N=\\infty$ esse princípio afirma o seguinte: Um espectro relativo é um par de espectros $B_\\bullet$ e $Y_\\bullet$ equipados com uma sequências de aplicações pontuadas $\\iota_\\bullet:B_\\bulletightarrow Y_{\\bullet+1}$ compatíveis com as estruturas de espectros. Um espectro relativo é conectivo se o par de espectros subjacentes forem conectivos. Denotamos a categoria de espectros relativos por $\\texttt^ earrow$ e de espectros relativos conectivos por $\\texttt^ earrow_0$. Um $2E_\\infty$-operad é uma resolução cofibrante $\\mathcal E_2^\\infty$ do 2-operad $\\mathcal Com^\\shortrightarrow$ de homomorfismos de monóides comutativos. Uma $\\mathcal E^\\infty_2$-álgebra $(X_c,X_o)$ é grouplike se $X_c$ e $X_o$ forem grouplike. Denotamos a categoria de $\\mathcal E^\\infty_2$-álgebras por $\\mathcal E^\\infty_2[\\texttt]$ e a categoria de $\\mathcal E^\\infty_2$-álgebras grouplike por $\\mathcal E^\\infty_2[\\texttt]_$. O 2-espaço de $\\infty$-laços de um espectro relativo é o par de espaços $\\Omega^\\infty_2\\iota_\\bullet:=\\text_{\\bullet\\shortrightarrow\\infty}(\\Omega^\\bullet Y_\\bullet,\\Omega^{\\bullet}_{\\text} \\iota_\\bullet)$. Temos que as imagens do funtor $\\Omega^\\infty_2$ admitem uma estrutura natural de $\\mathcal E^\\infty_2$-álgebra, logo $\\Omega^\\infty_2$ define um funtor $\\texttt^ earrowightarrow \\mathcal E^\\infty_2[\\texttt]$. Existe um funtor $B^\\infty_2:\\mathcal E^\\infty_2[\\texttt]ightarrow \\texttt^ earrow$ e uma adjunção $(\\mathbb L B^\\infty_2\\dashv\\mathbb R\\Omega^\\infty_2)$ entre as categorias homotópicas $\\mathcal Ho\\mathcal E^\\infty_2[\\texttt]$ e $\\mathcal Ho\\texttt^ earrow$ que induzem uma equivalência entre as categorias homotópicas $\\mathcal Ho\\mathcal E^\\infty_2[\\texttt]_$ e $\\mathcal Ho\\texttt^ earrow_0$. / The recognition principle of $\\infty$-loop spaces is that the functor $\\Omega^\\infty:\\textttightarrow \\mathcal E^\\infty[\\texttt]$ defined by $\\Omega^\\infty Y_\\bullet=\\text_{\\bullet\\shortrightarrow\\infty}\\Omega^\\bullet Y_\\bullet$ induces an equivalence between the homotopy category of connective spectra and the homotopy category of grouplike $\\mathcal E^\\infty$-algebras for any cofibrant resolution $\\mathcal E^\\infty$ of the commutative monoid operad $\\mathcal Com$. In this thesis a relative recognition principle of $N$-loop 2-spaces is proved for $2<N\\leq\\infty$. For $N=\\infty$ this principle states the following: A relative spectrum is a pair of spectra $B_\\bullet$ and $Y_\\bullet$ equipped with a sequence of pointed maps $\\iota_\\bullet:B_\\bulletightarrow Y_{\\bullet+1}$ compatible with the spectrum structures. A relative spectrum is connective if the underlying pair of spectra are connective. The category of relative spectra is denoted by $\\texttt^ earrow$ and the category of connective relative spectra by $\\texttt^ earrow_0$. A $2E_\\infty$-operad is a cofibrant resolution $\\mathcal E_2^\\infty$ of the commutative monoid homomorphism 2-operad $\\mathcal Com^\\shortrightarrow$. An $\\mathcal E^\\infty_2$-algebra $(X_c,X_o)$ is grouplike if $X_c$ and $X_o$ are grouplike. The category of $\\mathcal E^\\infty_2$-algebras is denoted by $\\mathcal E^\\infty_2[\\texttt]$ and the category of grouplike $\\mathcal E^\\infty_2$-algebras by $\\mathcal E^\\infty_2[\\texttt]_$. The $\\infty$-loop 2-space of a relative spectrum is the pair of pointed spaces $\\Omega^\\infty_2\\iota_\\bullet:=\\text_{\\bullet\\shortrightarrow\\infty}(\\Omega^\\bullet Y_\\bullet,\\Omega_{\\text}^{\\bullet} \\iota_\\bullet)$. The images of the functor $\\Omega^\\infty_2$ admit an $\\mathcal E^\\infty_2$-algebra structure, therefore $\\Omega^\\infty_2$ defines a functor $\\texttt^ earrowightarrow \\mathcal E^\\infty_2[\\texttt]$. The infinite relative recognition principle is that there is a functor $B^\\infty_2:\\mathcal E^\\infty_2[\\texttt]ightarrow \\texttt^ earrow$ and a derived adjunction $(\\mathbb L B^\\infty_2\\dashv\\mathbb R\\Omega^\\infty_2)$ between the homotopy categories $\\mathcal Ho\\mathcal E^\\infty_2[\\texttt]$ and $\\mathcal Ho\\texttt^ earrow$ that induce an equivalence beteween the homotopy categories $\\mathcal Ho\\mathcal E^\\infty_2[\\texttt]_$ and $\\mathcal Ho\\texttt^ earrow_0$.

O princípio de reconhecimento de espaços de $\\infty$-laços é que o funtor $\\Omega^\\infty:\\textttightarrow \\mathcal E^\\infty[\\texttt]$ dado por $\\Omega^\\infty Y_\\bullet=\\text_{\\bullet\\shortrightarrow\\infty}\\Omega^\\bullet Y_\\bullet$ induz uma equivalência entre a categoria homotópica de espectros conectivos e a categoria homotópica de $\\mathcal E^\\infty$-álgebras grouplike para qualquer resolução cofibrante $\\mathcal E^\\infty$ do operad $\\mathcal Com$ de monóides comutativos. Nesta tese é provado um princípio de reconhecimento de 2-espaços de $N$-laços para $2<N\\leq\\infty$. Quando $N=\\infty$ esse princípio afirma o seguinte: Um espectro relativo é um par de espectros $B_\\bullet$ e $Y_\\bullet$ equipados com uma sequências de aplicações pontuadas $\\iota_\\bullet:B_\\bulletightarrow Y_{\\bullet+1}$ compatíveis com as estruturas de espectros. Um espectro relativo é conectivo se o par de espectros subjacentes forem conectivos. Denotamos a categoria de espectros relativos por $\\texttt^ earrow$ e de espectros relativos conectivos por $\\texttt^ earrow_0$. Um $2E_\\infty$-operad é uma resolução cofibrante $\\mathcal E_2^\\infty$ do 2-operad $\\mathcal Com^\\shortrightarrow$ de homomorfismos de monóides comutativos. Uma $\\mathcal E^\\infty_2$-álgebra $(X_c,X_o)$ é grouplike se $X_c$ e $X_o$ forem grouplike. Denotamos a categoria de $\\mathcal E^\\infty_2$-álgebras por $\\mathcal E^\\infty_2[\\texttt]$ e a categoria de $\\mathcal E^\\infty_2$-álgebras grouplike por $\\mathcal E^\\infty_2[\\texttt]_$. O 2-espaço de $\\infty$-laços de um espectro relativo é o par de espaços $\\Omega^\\infty_2\\iota_\\bullet:=\\text_{\\bullet\\shortrightarrow\\infty}(\\Omega^\\bullet Y_\\bullet,\\Omega^{\\bullet}_{\\text} \\iota_\\bullet)$. Temos que as imagens do funtor $\\Omega^\\infty_2$ admitem uma estrutura natural de $\\mathcal E^\\infty_2$-álgebra, logo $\\Omega^\\infty_2$ define um funtor $\\texttt^ earrowightarrow \\mathcal E^\\infty_2[\\texttt]$. Existe um funtor $B^\\infty_2:\\mathcal E^\\infty_2[\\texttt]ightarrow \\texttt^ earrow$ e uma adjunção $(\\mathbb L B^\\infty_2\\dashv\\mathbb R\\Omega^\\infty_2)$ entre as categorias homotópicas $\\mathcal Ho\\mathcal E^\\infty_2[\\texttt]$ e $\\mathcal Ho\\texttt^ earrow$ que induzem uma equivalência entre as categorias homotópicas $\\mathcal Ho\\mathcal E^\\infty_2[\\texttt]_$ e $\\mathcal Ho\\texttt^ earrow_0$. / The recognition principle of $\\infty$-loop spaces is that the functor $\\Omega^\\infty:\\textttightarrow \\mathcal E^\\infty[\\texttt]$ defined by $\\Omega^\\infty Y_\\bullet=\\text_{\\bullet\\shortrightarrow\\infty}\\Omega^\\bullet Y_\\bullet$ induces an equivalence between the homotopy category of connective spectra and the homotopy category of grouplike $\\mathcal E^\\infty$-algebras for any cofibrant resolution $\\mathcal E^\\infty$ of the commutative monoid operad $\\mathcal Com$. In this thesis a relative recognition principle of $N$-loop 2-spaces is proved for $2<N\\leq\\infty$. For $N=\\infty$ this principle states the following: A relative spectrum is a pair of spectra $B_\\bullet$ and $Y_\\bullet$ equipped with a sequence of pointed maps $\\iota_\\bullet:B_\\bulletightarrow Y_{\\bullet+1}$ compatible with the spectrum structures. A relative spectrum is connective if the underlying pair of spectra are connective. The category of relative spectra is denoted by $\\texttt^ earrow$ and the category of connective relative spectra by $\\texttt^ earrow_0$. A $2E_\\infty$-operad is a cofibrant resolution $\\mathcal E_2^\\infty$ of the commutative monoid homomorphism 2-operad $\\mathcal Com^\\shortrightarrow$. An $\\mathcal E^\\infty_2$-algebra $(X_c,X_o)$ is grouplike if $X_c$ and $X_o$ are grouplike. The category of $\\mathcal E^\\infty_2$-algebras is denoted by $\\mathcal E^\\infty_2[\\texttt]$ and the category of grouplike $\\mathcal E^\\infty_2$-algebras by $\\mathcal E^\\infty_2[\\texttt]_$. The $\\infty$-loop 2-space of a relative spectrum is the pair of pointed spaces $\\Omega^\\infty_2\\iota_\\bullet:=\\text_{\\bullet\\shortrightarrow\\infty}(\\Omega^\\bullet Y_\\bullet,\\Omega_{\\text}^{\\bullet} \\iota_\\bullet)$. The images of the functor $\\Omega^\\infty_2$ admit an $\\mathcal E^\\infty_2$-algebra structure, therefore $\\Omega^\\infty_2$ defines a functor $\\texttt^ earrowightarrow \\mathcal E^\\infty_2[\\texttt]$. The infinite relative recognition principle is that there is a functor $B^\\infty_2:\\mathcal E^\\infty_2[\\texttt]ightarrow \\texttt^ earrow$ and a derived adjunction $(\\mathbb L B^\\infty_2\\dashv\\mathbb R\\Omega^\\infty_2)$ between the homotopy categories $\\mathcal Ho\\mathcal E^\\infty_2[\\texttt]$ and $\\mathcal Ho\\texttt^ earrow$ that induce an equivalence beteween the homotopy categories $\\mathcal Ho\\mathcal E^\\infty_2[\\texttt]_$ and $\\mathcal Ho\\texttt^ earrow_0$.

We study minimization problems with respect to a one-parameter family of generalized relative entropies. These relative entropies, which we call relative -entropies (denoted I (P; Q)), arise as redundancies under mismatched compression when cumulants of compression lengths are considered instead of expected compression lengths. These parametric relative entropies are a generalization of the usual relative entropy (Kullback-Leibler divergence). Just like relative entropy, these relative -entropies behave like squared Euclidean distance and satisfy the Pythagorean property. We explore the geometry underlying various statistical models and its relevance to information theory and to robust statistics. The thesis consists of three parts. In the first part, we study minimization of I (P; Q) as the first argument varies over a convex set E of probability distributions. We show the existence of a unique minimizer when the set E is closed in an appropriate topology. We then study minimization of I on a particular convex set, a linear family, which is one that arises from linear statistical constraints. This minimization problem generalizes the maximum Renyi or Tsallis entropy principle of statistical physics. The structure of the minimizing probability distribution naturally suggests a statistical model of power-law probability distributions, which we call an -power-law family. Such a family is analogous to the exponential family that arises when relative entropy is minimized subject to the same linear statistical constraints. In the second part, we study minimization of I (P; Q) over the second argument. This minimization is generally on parametric families such as the exponential family or the - power-law family, and is of interest in robust statistics ( > 1) and in constrained compression settings ( < 1). In the third part, we show an orthogonality relationship between the -power-law family and an associated linear family. As a consequence of this, the minimization of I (P; ), when the second argument comes from an -power-law family, can be shown to be equivalent to a minimization of I ( ; R), for a suitable R, where the first argument comes from a linear family. The latter turns out to be a simpler problem of minimization of a quasi convex objective function subject to linear constraints. Standard techniques are available to solve such problems, for example, via a sequence of convex feasibility problems, or via a sequence of such problems but on simpler single-constraint linear families.