Like the rest of the society modern health care has to deal with the ever increasing information flow. Imaging modalities such as CT, MRI, US, SPECT and PET just keep producing more and more data. Especially CT and MRI and their 3D image stacks cause problems in terms of how to effectively handle these data sets. Usually a PACS is used to manage the information flow. Since a PACS often is implemented with a server-client setup, the management of these large data sets requires an efficient representation of medical image stacks that minimizes the amount of data transmitted between server and client and that efficiently supports the workflow of a practitioner. In this thesis an efficient wavelet representation for large medical image stacks is proposed for the use in a PACS. The representation supports features such as lossless viewing, random access, ROI-viewing, scalable resolution, thick slab viewing and progressive transmission. All of these features are believed to be essential to form an efficient tool for navigation and reconstruction of an image stack. The proposed wavelet representation has also been implemented and found to be better in terms of memory allocation and amount of data transmitted between server and client when compared to prior solutions. Performance tests of the implementation has also shown the proposed wavelet representation to have a good computational performance.

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L’objet de cette thèse est de comprendre comment se généralise la théorie de la ramification pour des actions par des schémas en groupes affines avec un intérêt particulier pour la notion de modération. Comme contexte général pour ce résumé, considérons une base affine S := Spec(R) où R est un anneau unitaire, commutatif, X := Spec(B) un schéma affine sur S, G := Spec(A) un schéma en groupes affine, plat et de présentation finie sur S et une action de G sur X que nous noterons (X, G). Enfin, nous notons [X/G] le champ quotient associé à cette action et Y := Spec(BA) où BA est l’anneau des invariants pour l’action (X, G). Supposons de plus que le champ d’inertie soit fini.Comme point de référence, nous prenons la théorie classique de la ramification pour des anneaux munis d’une action par un groupe fini abstrait. Afin de comprendre comment généraliser cette théorie pour des actions par des schémas en groupes, nous considérons les actions par des schémas en groupes constants en se rappelant que la donnée de telles actions est équivalente à celle d’un anneau muni d’une action par un groupe fini abstrait nous ramenant au cas classique. Nous obtenons ainsi dans ce nouveau contexte des notions généralisant l’anneau des invariants en tant que quotient, les groupes d’inertie et toutes leurs propriétés. Le cas non ramifié se généralise naturellement avec les actions libres. En ce qui concerne le cas modéré, qui nous intéresse particulièrement pour cette thèse, deux généralisations sont proposées dans la littérature. Celle d’actions modérées par des schémas en groupes affines introduite par Chinburg, Erez, Pappas et Taylor dans l’article [CEPT96] et celle de champ modéré introduite par Abramovich, Olsson et Vistoli dans [AOV08]. Il a été alors naturel d’essayer de comparer ces deux notions et de comprendre comment se généralisent les propriétés classiques d’objets modérés à des actions par des schémas en groupes affines.Tout d’abord, nous avons traduit algébriquement la propriété de modération sur un champ quotient comme l’exactitude du foncteur des invariants. Ce qui nous a permis d’obtenir aisément à l’aide de [CEPT96] qu’une action modérée définit toujours un champ quotient modéré. Quant à la réciproque, nous avons réussi à l’obtenir seulement lorsque nous supposons de plus que G est fini et localement libre sur S et que X est plat sur Y . Nous pouvons voir que la notion de modération pour l’anneau B muni d’une action par un groupe fini abstrait Γ est équivalente au fait que tous les groupes d’inertie aux points topologiques sont linéairement réductifs si l’on considère l’action par le schéma en groupes constant correspondant à Γ sur X. Il a été donc naturel de se demander si cette propriété est encore vraie en général. Effectivement, l’article [AOV08] caractérise le fait que le champ quotient [X/G] est modéré par le fait que les groupes d’inertie aux points géométriques sont linéairement réductifs.À nouveau, si l’on considère le cas des anneaux munis d’une action par un groupe fini abstrait, il est bien connu que l’action peut être totalement reconstruite à partir de l’action d’un groupe inertie. Lorsque l’on considère le cas des actions par les schémas en groupes constants, cela se traduit comme un théorème de slices, c’est-à-dire une description locale de l’action initiale par une action par un groupe d’inertie. Par exemple, lorsque G est fini, localement libre sur S, nous établissons que le fait qu’une action soit libre est une propriété locale pour la topologie fppf, ce qui peut se traduire comme un théorème de slices. Grâce à [AOV08], nous savons déjà qu’un champ quotient modéré [X/G] est localement isomorphe pour la topologie fppf à un champ quotient [X/H] où H est une extension du groupe d’inertie en un point de Y. Lorsque G est fini sur S, il nous a été possible de montrer que H est aussi un sous-groupe de G. / The purpose of this thesis is to understand how to generalize the ramification theory for actions by affine group schemes with a particular interest for the notion of tameness. As general context for this summary, we consider an affine basis S := Spec(R) where R is a commutative, unitary ring, an affine, finitely presented, Noetherian scheme X := Spec(B) over S, a flat, finitely presented, affine group scheme G := Spec(A) over S and an action of G on X that we denote by (X, G). Finally, we denote [X/G] the quotient stack associated to this action and we set Y := Spec(BA) where BA is the ring of invariants for the action (X, G). Moreover, we suppose that the inertia stack is finite.As reference point, we take the classical theory of ramification for rings endowed with an action of a finite, abstract group. In order to understand how to generalize this theory for actions of group schemes, we consider the actions of constant group schemes knowing that the data of such actions is equivalent to the data of rings endowed with an action of a finite abstract group, this being the classical case. We obtain thus in this new context notions generalizing the ring of invariants as a quotient, the inertia group and all their properties. The unramified case is generalized naturally by the free actions. For the tame case, which interests us particularly here, two generalizations are proposed in the literature: the one of tame actions of affine group schemes introduced by Chinburg, Erez, Pappas et Taylor in the article [CEPT96] and the one of tame stacks introduced by Abramovich, Olsson and Vistoli in [AOV08]. It was then natural to compare these two notions and to understand how to generalize the classical properties of tame objects for the actions of affine group schemes. First of all, we traduced algebraically the tameness property on a quotient stack as the exactness of the functor of invariants. This permits to obtain easily thanks to [CEPT96] that tame actions define always tame quotient stacks. For the converse, we only manage to prove it when we suppose G to be finite, locally free over S and X flat over Y . We are able to see that the notion of tameness for a ring endowed with an action of a finite, abstract group Γ is equivalent to the fact that all the inertia group schemes at the topological points are linearly reductive if we consider the action of the constant group scheme corresponding to Γ over X. It was thus natural to wonder if this property was also true in general. In fact, the article [AOV08] characterizes the fact that the quotient stack [X/G] is tame by the fact that the inertia group schemes at the geometric points are linearly reductive.Again, if we consider the case of rings endowed with an action of a finite, abstract group, it is well known that these actions can be totally reconstructed from an action involving an inertia group. When we consider actions by constant group schemes, this is translated as a slice theorem, that is, a local description of the initial action by an action involving an inertia group. For example, we establish that the fact that an action is free is a "local property" for the fppf topology and this can be translated also as a "local" slice theorem. Thanks to [AOV08], we already know that a tame quotient stack [X/G] is locally isomorphic for the fppf topology to a quotient stack [X/H], where H is an extension of the inertia group in a point of Y . When G is finite over S, it was possible to show that H is also a subgroup of G. In this thesis, it was not possible to obtain a slice theorem in this generality. However, when G is commutative, finite over S, it is possible to prove the existence of a torsor, if we suppose [X/G] to be tame. This permits to prove a slice theorem when G is commutative, finite over S and [X/G] is tame. / Lo scopo di questa tesi è capire come si generalizza la teoria della ramificazione per azioni di schemi in gruppi affini con un interesse particolare per la nozione di moderazione. Come contesto generale per questo riassunto, consideriamo una base affine S := Spec(R) dove R è un anello unitario e commutativo, X := Spec(B) uno schema affine, noetheriano e di presentazione finita su S, G := Spec(A) uno schema in gruppi affine, piatto e di presentazione finita su S e un’azione di G su X che denoteremo (X, G). Infine, denotiamo con [X/G] lo stack quoziente associato a questa azione e Y := Spec(BA) dove BA è l’anello degli invarianti per l’azione (X, G). Supponiamo inoltre che il campo d’inerzia sia finito.Come punto di riferimento prendiamo la teoria classica della ramificazione per anelli muniti d’un’azione d’un gruppo finito astratto. Al fine di comprendere come generalizzare questa teoria per azioni di schemi in gruppi, consideriamo le azioni di schemi in gruppi costanti ricordando che il dato di tali azioni è equivalente al dato d’un anello dotato d’un’azione d’un gruppo finito astratto, riconducendosi al caso classico. Otteniamo così in questo nuovo contesto delle nozioni che generalizzano l’anello degli invarianti in quanto quoziente, i gruppi d’inerzia e tutte le loro proprietà. Il caso non ramificato si generalizza in modo naturale con le azioni libere. Per qual che riguarda il caso moderato, al quale siamo particolarmente interessati in questa tesi, due generalizzazioni sono proposte nella letteratura: quella delle azioni moderate di schemi in gruppi affini introdotta da Chinburg, Erez, Pappas e Taylor nell’articolo [CEPT96] e quella di stack moderato introdotta da Abramovich, Olsson e Vistoli in [AOV08]. È stato quindi naturale cercare di confrontare queste due nozioni e capire come si generalizzano le proprietà classiche degli oggetti moderati ad azioni di schemi in gruppi affini.Per cominciare, abbiamo tradotto algebricamente la proprietà di moderazione su un stack quoziente come l’esattezza del funtore degli invarianti. Ciò ha permesso d’ottenere agevolmente, usando [CEPT96], che un’azione moderata definisce sempre uno stack quoziente moderato. Quanto al viceversa, siamo riusciti ad ottenerlo solamente sotto l’ulteriore ipotesi che G sia finito e localmente libero su S e che X sia piatto su Y . Possiamo vedere che la nozione di moderazione per l’anello B dotato d’un’azione d’un gruppo finito astratto Γ è equivalente al fatto che tutti i gruppi d’inerzia sui punti topologici siano linearmente riduttivi se si considera l’azione dello schema in gruppi costante corrispondente a Γ su X. È stato quindi naturale domandarsi se questa proprietà sia vera in generale. In effetti, l’articolo [AOV08] caratterizza il fatto che lo stack quoziente [X/G] è moderato tramite il fatto che i gruppi d’inerzia sui punti geometrici siano linearmente riduttivi.Di nuovo, se consideriamo il caso degli anelli muniti d’un’azione d’un gruppo finito astratto, è ben noto che quest’azione può essere totalmente ricostruita a partire da un’azione in cui interviene un gruppo d’inerzia. Quando consideriamo il caso delle azioni degli schemi in gruppi costanti, questo si traduce come un teorema di slices, cioè una descrizione locale dell’azione di partenza (X,G) tramite un’azione in cui interviene un gruppo d’inerzia. Per esempio quando G è finito e localmente libero su S, stabiliamo che il fatto che un’azione è libera è una proprietà locale per la topologia fppf, ciò si può interpretare come un teorema di slices. Grazie a [AOV08] sappiamo già che uno stack quoziente moderato [X/G] è localmente isomorfo per la topologia fppf a uno stack quoziente [X/H], dove H è un’estensione d’un gruppo d’inerzia in un punto di Y.

Dans [PRID], Pridham a montré que tout n-champs d'Artin M admet une présentation en tant que schéma simplicial X. → M, telle que le schéma simplicial X satisfait à certaines propriétés notées par G.Pn,k de [GROTH]. Dans la présentation (…→ X2 → X1 → X0 → M), le schéma X1 représente une carte pour X0 x MX0. Donc, la lissité de X0 → M est équivalente à la lissité des deux projections ә0,ә1 : X1 → X0. Ce sont les deux premières parties de la condition de Grothendieck-Pridham, notées G.P1,0 et G.P1,1. Dans [BENZ12] nous avons introduit un n-champ d'Artin M des éléments de Maurer-Cartan d'une dg-catégorie. On a construit une carte, et on a déjà fait la preuve des premières conditions de lissité explicitement. Pour tout n et tout 0 ≤ k ≤ n Pridham considère un schéma noté MatchΛkn(X) avec un morphisme Xn → MatchΛkn(X). On construira explicitement le schéma simplicial de Grothendieck-Pridham X, on montrera la lissité formelle de cette carte précédente, ainsi que M est un n-champ géométrique. / In [PRID], Pridham has shown that any Artin n-stack M has a presentation as a simplicial scheme X. → M such that the simplicial scheme X satisfies certain properties denoted G.Pn,k of [GROTH]. In the presentation (…→ X2 → X1 → X0 → M), the scheme X1 represents a chart for X0 x MX0. Thus, the smoothness of X0 → M is equivalent to the smoothness of the two projections ә0,ә1 : X1 → X0. These are the first two parts of the Grothendieck-Pridham condition, denoted G.P1,0 and G.P1,1. In [BENZ12] we introduced an Artin n-stack M of Maurer-Cartan elements of a dg-category. We constructed a chart, and have already proven the first smoothness conditions explicitly. For any n and any 0 ≤ k ≤ n Pridham considers a scheme denoted MatchΛkn(X) with a morphism Xn → MatchΛkn(X). We will construct explicitly the Grothendieck-Pridham simplicial scheme and show the smoothness of the preceding map, therefore M is a geometric n-stack.

Bolted cores made of coated silicon steel sheets constitute a vital part of heavy electrical equipment for transformers, motors and turbogenerators. Bolted laminates are eminently suitable for facilitating smooth magnetic flux paths, but, unfortunately, they are unable to suppress interlaminate shearing caused by flexural vibration generating noise levels often exceeding 100 dB during operation. The resulting din and cacophony in the surrounding has become a major environmental concern. This thesis makes an attempt to develop theoretical, experimental and numerical models for evolving an effective stiffness approach enhancing the design and analysis underlying nonlinear flexure of bolted laminates. While large machine cores contain thousands of thin sheets bolted together along with end plates, this thesis reports the results obtained on two different assemblies. Two 375 mm long 60 mm wide and 10 mm thick plates assembled with 3, 4 or 5 bolts constitute the first configuration. The second one which is much more realistic comprises 80 coated 270 micron silicon steel sheets with end plates of 2 or 4 mm thickness held together by 3 or 5 bolts. Static 3 point bend tests on these bolted assemblies are followed by instrumented impact tests. Static bending tests highlight the role of frictional nonlinearity inducing a drop in the stiffness due to sliding between the plates. An experimentally determined effective modulus in the initial linear range is utilized for static and dynamic finite element simulations. Nonlinear response of bolted plates is simulated using contact elements in between the sliding plates, plates and the bolts heads. Since the first fundamental mode of vibration dominates the tribomechanical vibration induced noise, the primary focus is on the fundamental frequency in bending. There is generally a good overall agreement in all the results obtained through theory, experiment and FE simulation. Experiments, however, unveil quite complex nonlinear effects induced by friction and plasticity outside the scope of this thesis. However, the low amplitude response of bolted laminates which is reasonably well captured in this thesis represents the starting point for initiating a more elaborate effort for addressing large amplitude nonlinear flexure in bolted laminates. These findings shed light on estimating and controlling noise and vibration levels in heavy electric machines.

Le substrat SOI (Silicon-On-Insulator) constitue aujourd’hui le support de choix pour la fabrication de fonctions optiques compactes. Cette plateforme commune avec la micro-électronique favorise l’intégration de circuits photoniques avec des circuits CMOS. Néanmoins, si le silicium peut être utilisé de manière très avantageuse pour la fabrication de composants optiques passifs, il présente l’inconvénient d’être un très mauvais émetteur de lumière. Ceci constitue un obstacle majeur au développement de sources d’émission laser, briques de constructions indispensables à la fabrication d’un circuit photonique. La solution exploitée dans le cadre de cette thèse consiste à reporter sur SOI des épitaxies laser III-V par collage direct SiO2-SiO2. L’objectif est de réaliser sur SOI des sources lasers à cavité horizontale permettant d’injecter au moins 1mW de puissance dans un guide d’onde silicium inclus dans le SOI. Notre démarche est de transférer un maximum des fonctions du laser vers le silicium, dont les procédés sont familiers au monde de la micro-électronique. Dans l’idéal, le III-V ne devrait être utilisé que comme matériau à gain ; la cavité laser pouvant être fabriquée dans le silicium. Mais cette ligne de conduite n’est pas forcément aisée à mettre en œuvre. En effet, les photons sont produits dans le III-V mais doivent être injectés dans un guide silicium placé sous l’épitaxie. La difficulté est que les deux matériaux sont séparés par plus d’une centaine de nanomètres d’oxyde de collage faisant obstacle au transfert de photons. Le développement de lasers III-V couplés à un guide d’onde SOI demande alors de nouvelles conceptions du système laser dans son ensemble. Notre travail a donc consisté à concevoir un laser hybride III-IV / silicium se pliant aux contraintes technologiques du collage. En s’appuyant sur la théorie des modes couplés et les concepts des cristaux photoniques, nous avons imaginé, réalisé, puis caractérisé un laser à contre-réaction distribuée hybride (en anglais : « distributed feedback laser », laser DFB). Son fonctionnement optique original, permet à la fois un maximum de gain et d’efficacité de couplage grâce à une circulation en boucle des photons du guide III-V au guide SOI. Sur ces dispositifs, nous montrons une émission laser monomode (SMSR de 35 dB) à température ambiante en pompage optique et électrique pulsé. Comme attendu, la longueur d’onde d’émission est dépendante du pas de réseau DFB. Les lasers fonctionnent avec une épaisseur de collage de silice de 200 nm, ce qui offre une grande souplesse quant au procédé d’intégration. Tous les lasers fonctionnent jusqu’à des longueurs de 150 μm (la plus petite longueur prévue sur le masque). Malgré les faibles niveaux de puissances récoltés dans la fibre lors des caractérisations, la prise en compte des pertes optiques induites pas les coupleurs fibres nous indique que la puissance réellement injectée dans le guide silicium dépasse le milliwatt. Notre objectif de ce point de vue est donc rempli. Malheureusement le fonctionnement des lasers en injection électrique continue n’a pas pu être obtenu dans les délais impartis. Cependant, les faibles densités de courant de seuil mesurées en injection pulsée (300A / cm2 à température ambiante sur les lasers de 550 μm de long) laissent présager un fonctionnement prochain en courant continu. / Silicon-On-Insulator (SOI) is today the utmost platform for the fabrication of compact optical functions. This common platform with microelectronics favors the integration of photonic circuits with CMOS circuits. Nevertheless, if silicon allows for the fabrication of compact passive photonic functions, its poor light emission properties constitute a major obstacle to the development of an integrated laser source. The solution used within the framework of this thesis consists in integrating III-IV laser stacks on 200 mm SOI wafers by the mean of SiO2-SiO2 direct bonding. The aim of this work is to demonstrate a III-V on SOI laser that couples at least 1mW to a silicon waveguide. Our approach is to transfer a maximum of the laser complexity to the silicon, which processes are familiar to microelectronics. Ideally, III-V should be just used as a gain material ; the laser cavity being made out of silicon. However, this approach is not so easy to put into practice. Indeed, photons are generated by the III-V waveguide but have to be transferred into the silicon waveguide located under the stack. The difficulty is that both waveguides are separated by a low index bonding layer, which thickness ranges from one hundred to several hundreds of nanometres. The development of a III-V on SOI laser then requires a new thinking of the whole laser system. Therefore, our work has consisted in designing a III-V on silicon hybrid laser that takes into consideration the specific constraints of the integration technology. Based on the coupled mode theory and on the photonic crystals concepts, we have designed, fabricated and characterized an hybrid Distributed Feedback Laser (DFB). Its original work principle allows for both a high amount of gain and coupling efficiency, thanks to a continuous circulation of photons from the III-V to the SOI waveguide. On these devices, we show a monomode laser emission at room temperature (with a side mode suppression ratio of 35dB) under pulsed optical and electrical pumping. As expected, the lasing wavelength is function of the DFB grating pitch. The lasers work with a bonding layer as thick as 200nm, that greatly relaxes the constraints of the bonding technology. Lasers work down to a minimum length of 150 μm, which is the shortest laser lenght of the mask. Despite the low power levels collected by the fibre during the characterizations, accounting for the high optical losses due to the fiber couplers, the optical power effectively injected to the silicon waveguide should be in the miliwatt range. Unfortunately, the low threshold current densities measured under pulsed operation (300 A / cm2 at room temperature) suggest that the continuous-wave regime should be reached in a very near future.

On s'intéresse à une compactification, due à Ekedahl, Lando, Shapiro et Vainshtein, du champ des courbes lisses munies de fonctions méromorphes d'ordres fixés. Celle-ci est obtenue comme une adhérence du champ de départ dans un champ propre. On commence par en donner deux constructions alternatives et on étudie les déformations de ses points. On la relie par la suite à la compactification à la Harris-Mumford par les revêtements admissibles et on donne une interprétation modulaire des points du bord. / We study a compactification, due to Ekedahl, Lando, Shapiro and Vainshtein, of the stack of smooth curves endowed with meromorphic functions having fixed orders. The original compactification is obtained as the closure of the initial stack in a proper substack. We start by giving two alternative constructions of the E.L.S.V compactification and by studying the deformation theory of its points. We finally link it to the Harris-Mumford compactification by admissible covers and give a modular interpretation of boundary points.

Recent efforts to classify off-shell representations of supersymmetry without a central charge have focused upon directed, supermultiplet graphs of hypercubic topology known as Adinkras. These encodings of Super Poincare algebras, depict every generator of a chosen supersymmetry as a node-pair transformtion between fermionic bosonic component fields. This research thesis is a culmination of investigating novel diagrammatic sums of gauge-quotients by supersymmetric images of other Adinkras, and the correlated building of field theoretic worldline Lagrangians to accommodate both classical and quantum venues. We find Ref [40], that such gauge quotients do not yield other stand alone or "proper" Adinkras as afore sighted, nor can they be decomposed into supermultiplet sums, but are rather a connected "Adinkraic network". Their iteration, analogous to Weyl's construction for producing all finite-dimensional unitary representations in Lie algebras, sets off chains of algebraic paradigms in discrete-graph and continuous-field variables, the links of which feature distinct, supersymmetric Lagrangian templates. Collectively, these Adiankraic series air new symbolic genera for equation to phase moments in Feynman path integrals. Guided in this light, we proceed by constructing Lagrangians actions for the N = 3 supermultiplet YI /(iDI X) for I = 1, 2, 3, where YI and X are standard, Salam-Strathdee superfields: YI fermionic and X bosonic. The system, bilinear in the component fields exhibits a total of thirteen free parameters, seven of which specify Zeeman-like coupling to external background (magnetic) fluxes. All but special subsets of this parameter space describe aperiodic oscillatory responses, some of which are found to be surprisingly controlled by the golden ratio, [phi] = 1.61803, Ref [52]. It is further determined that these Lagrangians allow an N = 3 - > 4 supersymmetric extension to the Chiral-Chiral and Chiral-twistedChiral multiplet, while a subset admits two inequivalent such extensions. In a natural proiii gression, a continuum of observably and usefully inequivalent, finite-dimensional off-shell representations of worldline N = 4 extended supersymmetry are explored, that are variate from one another but in the value of a tuning parameter, Ref [53]. Their dynamics turns out to be nontrivial already when restricting to just bilinear Lagrangians. In particular, we find a 34-parameter family of bilinear Lagrangians that couple two differently tuned supermultiplets to each other and to external magnetic fluxes, where the explicit parameter dependence is unremovable by any field redefinition and is therefore observable. This offers the evaluation of X-phase sensitive, off-shell path integrals with promising correlations to group product decompositions and to deriving source emergences of higher-order background flux-forms on 2-dimensional manifolds, the stacks of which comprise space-time volumes. Application to nonlinear sigma models would naturally follow, having potential use in M- and F- string theories.