Dans le cadre discrétisé, la taille d'un ensemble à l'échelle δ est évaluée par son nombre de recouvrement par δ-boules (également connu sous le nom de l'entropie métrique). Dans cette thèse, nous étudions les propriétés combinatoires des ensembles discrétisés sous l'addition, la multiplication et les projections orthogonales. Il y a trois parties principales. Premièrement, nous démontrons un théorème somme-produit dans les algèbres de matrices, qui généralise un théorème somme-produit de Bourgain concernant l'anneau des réels. On améliore aussi des estimées somme-produit en dimension supérieure obtenues précédemment par Bougain et Gamburd. Deuxièmement, on étudie les projections orthogonales des sous-ensembles de l'espace euclidien et étend ainsi le théorème de projection discrétisé de Bourgain aux projections de rang supérieur. Enfin, dans un travail en commun avec Nicolas de Saxcé, nous démontrons un théorème produit dans les groupes de Lie parfaits. Ce dernier résultat généralise les travaux antérieurs de Bourgain-Gamburd et de Saxcé. / In the discretized setting, the size of a set is measured by its covering number by δ-balls (a.k.a. metric entropy), where δ is the scale. In this document, we investigate combinatorial properties of discretized sets under addition, multiplication and orthogonal projection. There are three parts. First, we prove sum-product estimates in matrix algebras, generalizing Bourgain's sum-product theorem in the ring of real numbers and improving higher dimensional sum-product estimates previously obtained by Bourgain-Gamburd. Then, we study orthogonal projections of subsets in the Euclidean space, generalizing Bourgain's discretized projection theorem to higher rank situations. Finally, in a joint work with Nicolas de Saxcé, we prove a product theorem for perfect Lie groups, generalizing previous results of Bourgain-Gamburd and Saxcé.

I detta kandidatarbete undersöker vi hur projection mapping (projicering på en yta) kan användas för att skapa en rumslig berättelse eller upplevelse. Utifrån vår egna tolkning av calm technologys (lugn teknologi) principer har vi skapat ett designperspektiv som syftar till att göra designen lugn, genom att teknologin inte ska bli störande för åskådaren. Till vår hjälp har vi använt oss utav Keri Smiths metoder till att utforska och experimentera med omgivningen och material. För att sedan kunna utöka kreativiteten och hitta nya idéer inom projection mapping har vi använt oss av metoder såsom brainstorming, moodboards och skisser. Vi har även utgått från Stolterman och Löwgrens syn på en designprocess. Detta resulterade till tre gestaltningar där alla utgår från naturens lugna atmosfär. Under detta arbete har vi kommit fram till att det finns många olika sätt att berätta med ytor, det behöver inte bara vara ett fysiskt rum med väggar och tak. Ytor kan bli rum genom att manipulera fysiska föremål med projektorer. Genom att lägga på ett extra lager på objekten som till exempel en animation så kan det förstärka objektet i sig eller få en helt ny karaktär. Med enkla medel som olika mönster, färger och ljus. / In this bachelor thesis we will examine how projection mapping (projection on a surface) can be used as a spatial experience. From our own interpretation of calm technology’s principles, will we create a design perspective that could keep the design calm with respect to the technology, and not be a disturbing moment for the viewer. To guide us through this we have taken Keri Smith’s methods to explore and experiment the environment and different materials. To expand the creativity to find new possibilities in projection mapping, we have used methods like brainstorming, moodboards and sketches. To help our process we based our project on Stolterman and Löwgren’s view of the design process. This led to a result of three figurations where all of them are inspired by the atmosphere of our nature. Through this project we have reached that there’s a lot of ways you can narrate with spaces, it doesn't need to be a physical room where you can stand in. Spaces can transform by manipulating physical artifacts. By adding an extra layer onto these artifacts like an animation it can amplify it’s meaning or give it a new character. Only with simple means like different patterns, colors and light.

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Master of Science / Department of Agricultural Economics / Kevin C. Dhuyvetter / Structural change within the industry, improved management, and volatility in commodity markets are reasons to evaluate and monitor the dairy industry in the future. The dairy industry has shifted concentration of production between regions over time. The Southern High Plains region, including the states of Colorado, Kansas, Oklahoma, New Mexico, and Texas, has undergone cow inventory growth in the past ten years. Dairies have become more concentrated, management has become more refined, and the commodity markets have become more volatile. Education and tools are readily available to producers with issues on reducing production, animal health, and feed losses. Financial risk is a key area producers have limited knowledge and resources. Mitigating this risk is essential in today‟s marketplace to maximize gains and margins as well as create opportunities for the operation to succeed and be financially sound. There are several resources which approximate returns based on either a point in time reference or complete user input. This study allows users to reflect on 21 years of historical data, 1990-2010, as well as plug in their own data or use default market data to estimate projected returns over the next 12 months. This study also builds a modeling framework that will allow historical dairy returns to be estimated and future returns projected on a regular basis. Over time average herd size has grown to reduce cost per head and producers are more efficient, milk production per cow has increased to over 70 pounds per day. Historically prices have increased over time, but the spread between highs and lows has escalated. This model solidifies that milk price and production are key revenue drivers while feed, replacement costs, and labor are large cost components at 39, 17, and 6 percent, respectively. Additionally, changing market prices can intensify the gain or loss an operation will incur over the short term, the projection model shows 2011 just below breakeven due to strong commodity markets. Dairy operations in the Southern High Plains region have shown positive returns in 108 of 252, 43 percent, months with greatest negative annual returns 2006 and 2009.

Published Article / The role of the Projection Principle within Chomsky's Government-Binding (GB) Theory is to preserve the subcategorisation properties of lexical items at all levels of syntactic representation, viz. D-structure, S-structure, and Lexical Form. Arguments have been made that the Projection Principle is a new concept that is simply an extension of theTransformational Component (XFM) and Emonds' Structure-Preserving Constraint (SPC), and that it does not deserve the high status it has been accorded in GB theory. This paper provides evidence, based on sentences involving movement operations, that the Projection Principle is innovative and that it convincingly addresses what theXFMandSPChave failed to address.

Depuis leurs premières applications par la NASA dans les années 60, les procédés aux plasmas thermiques se sont de plus en plus orientés vers la fabrication de matériaux spécialisés et à haute valeur ajoutée, comme les nano-poudres, les produits sphéroïdisés et les céramiques. La projection de suspension par plasma est l'une des techniques les plus récentes dans ce domaine et elle permet de traiter thermiquement une grande variété de réactifs et de réaliser des revêtements dont les propriétés physico-chimiques dépendent des produits de départ, des phénomènes en vol (lors du traitement thermique) ainsi que des phénomènes liés à la formation du revêtement projeté. Ce travail s'intéresse à la projection de suspensions de nickel dans un réacteur de projection par plasma inductif afin de vérifier et d'estimer la relation qui existe entre des paramètres opératoires choisis et une propriété physique des produits finis: la porosité. Cette étude consiste à réaliser des dépôts de nickel sur un substrat choisi et à observer la morphologie du revêtement métallique obtenu. La revue bibliographique des travaux réalisés dans les mêmes laboratoires a permis de mettre en exergue les principaux paramètres affectant la qualité du revêtement. Des tests préliminaires séparés ont été réalisés pour choisir la composition de la suspension et les paramètres d'atomisation optimaux avant de les intégrer au procédé de revêtement en question. Les échantillons fabriqués sont analysés par traitement d'images obtenues par microscopie à balayage d'électrons ainsi que par une méthode d'immersion. Une approche combinatoire permettra d'évaluer l'effet de la combinaison de certains réactifs et de post-traitements sur la porosité des revêtements de nickel obtenus. Les résultats obtenus montrent que les paramètres tels que la puissance utilisée et la méthode de refroidissement affectent les propriétés du revêtement et les porosités obtenues pour les conditions opératoires choisies varient entre 10% et 50%.

This research investigates how shifts in perception might be brought about through the development of visual imagery created by the use of virtual environment technology. Through a discussion of historical uses of immersion in art, this thesis will explore how immersion functions and why immersion has been a goal for artists throughout history. It begins with a discussion of ancient cave drawings and the relevance of Plato’s Allegory of the Cave. Next it examines the biological origins of “making special.” The research will discuss how this concept, combined with the ideas of “action” and “reaction,” has reinforced the view that art is fundamentally experiential rather than static. The research emphasizes how present-day virtual environment art, in providing a space that engages visitors in computer graphics, expands on previous immersive artistic practices. The thesis examines the technical context in which the research occurs by briefly describing the use of computer science technologies, the fundamentals of visual arts practices, and the importance of aesthetics in new media and provides a description of my artistic practice. The aim is to investigate how combining these approaches can enhance virtual environments as artworks. The computer science of virtual environments includes both hardware and software programming. The resultant virtual environment experiences are technologically dependent on the types of visual displays being used, including screens and monitors, and their subsequent viewing affordances. Virtual environments fill the field of view and can be experienced with a head mounted display (HMD) or a large screen display. The sense of immersion gained through the experience depends on how tracking devices and related peripheral devices are used to facilitate interaction. The thesis discusses visual arts practices with a focus on how illusions shift our cognition and perception in the visual modalities. This discussion includes how perceptual thinking is the foundation of art experiences, how analogies are the foundation of cognitive experiences and how the two intertwine in art experiences for virtual environments. An examination of the aesthetic strategies used by artists and new media critics are presented to discuss new media art. This thesis investigates the visual elements used in virtual environments and prescribes strategies for creating art for virtual environments. Methods constituting a unique virtual environment practice that focuses on visual analogies are discussed. The artistic practice that is discussed as the basis for this research also concentrates on experiential moments and shifts in perception and cognition and references Douglas Hofstadter, Rudolf Arnheim and John Dewey. iv Virtual environments provide for experiences in which the imagery generated updates in real time. Following an analysis of existing artwork and critical writing relative to the field, the process of inquiry has required the creation of artworks that involve tracking systems, projection displays, sound work, and an understanding of the importance of the visitor. In practice, the research has shown that the visitor should be seen as an interlocutor, interacting from a first-person perspective with virtual environment events, where avatars or other instrumental intermediaries, such as guns, vehicles, or menu systems, do not to occlude the view. The aesthetic outcomes of this research are the result of combining visual analogies, real time interactive animation, and operatic performance in immersive space. The environments designed in this research were informed initially by paintings created with imagery generated in a hypnopompic state or during the moments of transitioning from sleeping to waking. The drawings often emphasize emotional moments as caricatures and/or elements of the face as seen from a number of perspectives simultaneously, in the way of some cartoons, primitive artwork or Cubist imagery. In the imagery, the faces indicate situations, emotions and confrontations which can offer moments of humour and reflective exploration. At times, the faces usurp the space and stand in representation as both face and figure. The power of the placement of the caricatures in the paintings become apparent as the imagery stages the expressive moment. The placement of faces sets the scene, establishes relationships and promotes the honesty and emotions that develop over time as the paintings are scrutinized. The development process of creating virtual environment imagery starts with hand drawn sketches of characters, develops further as paintings on “digital canvas”, are built as animated, three-dimensional models and finally incorporated into a virtual environment. The imagery is generated while drawing, typically with paper and pencil, in a stream of consciousness during the hypnopompic state. This method became an aesthetic strategy for producing a snappy straightforward sketch. The sketches are explored further as they are worked up as paintings. During the painting process, the figures become fleshed out and their placement on the page, in essence brings them to life. These characters inhabit a world that I explore even further by building them into three dimensional models and placing them in computer generated virtual environments. The methodology of developing and placing the faces/figures became an operational strategy for building virtual environments. In order to open up the range of art virtual environments, and develop operational strategies for visitors’ experience, the characters and their facial features are used as navigational strategies, signposts and methods of wayfinding in order to sustain a stream of consciousness type of navigation. Faces and characters were designed to represent those intimate moments of self-reflection and confrontation that occur daily within ourselves and with others. They sought to reflect moments of wonderment, hurt, curiosity and humour that could subsequently be relinquished for more practical or purposeful endeavours. They were intended to create conditions in which visitors might reflect upon their emotional state, v enabling their understanding and trust of their personal space, in which decisions are made and the nature of world is determined. In order to extend the split-second, frozen moment of recognition that a painting affords, the caricatures and their scenes are given new dimensions as they become characters in a performative virtual reality. Emotables, distinct from avatars, are characters confronting visitors in the virtual environment to engage them in an interactive, stream of consciousness, non-linear dialogue. Visitors are also situated with a role in a virtual world, where they were required to adapt to the language of the environment in order to progress through the dynamics of a drama. The research showed that imagery created in a context of whimsy and fantasy could bring ontological meaning and aesthetic experience into the interactive environment, such that emotables or facially expressive computer graphic characters could be seen as another brushstroke in painting a world of virtual reality.

Synthetic aperture radar is an important tool in a wide range of civilian and military imaging applications. This is primarily due to its ability to image in all weather conditions, during both the day and the night, unlike optical imaging systems. A synthetic aperture radar system contains a step which is not present in an optical imaging system, this is image formation. This is required because the acquired data from the radar sensor does not directly correspond to the image. Instead, to form an image, the system must solve an inverse problem. In conventional scenarios, this inverse problem is relatively straight forward and a matched lter based algorithm produces an image of suitable image quality. However, there are a number of interesting scenarios where this is not the case. Scenarios where standard image formation algorithms are unsuitable include systems with data undersampling, errors in the system observation model and data that is corrupted by radio frequency interference. Image formation in these scenarios will form the topics of this thesis and a number of iterative algorithms are proposed to achieve image formation. The motivation for these proposed algorithms is primarily from the eld of compressed sensing, which considers the recovery of signals with a low-dimensional structure. The rst contribution of this thesis is the development of fast algorithms for the system observation model and its adjoint. These algorithms are required by large-scale gradient based iterative algorithms for image formation. The proposed algorithms are based on existing fast back-projection algorithms, however, a new decimation strategy is proposed which is more suitable for some applications. The second contribution is the development of a framework for iterative near- eld image formation, which uses the proposed fast algorithms. It is shown that the framework can be used, in some scenarios, to improve the visual quality of images formed from fully sampled data and undersampled data, when compared to images formed using matched lter based algorithms. The third contribution concerns errors in the system observation model. Algorithms that correct these errors are commonly referred to as autofocus algorithms. It is shown that conventional autofocus algorithms, which work as a post-processor on the formed image, are unsuitable for undersampled data. Instead an autofocus algorithm is proposed which corrects errors within the iterative image formation procedure. The proposed algorithm is provably stable and convergent with a faster convergence rate than previous approaches. The nal contribution is an algorithm for ultra-wideband synthetic aperture radar image formation. Due to the large spectrum over which the ultra-wideband signal is transmitted, there is likely to be many other users operating within the same spectrum. These users can produce signi cant radio frequency interference which will corrupt the received data. The proposed algorithm uses knowledge of the RFI spectrum to minimise the e ect of the RFI on the formed image.

Compressed Sensing (CS) is an emerging paradigm in which signals are recovered from undersampled nonadaptive linear measurements taken at a rate proportional to the signal's true information content as opposed to its ambient dimension. The resulting problem consists in finding a sparse solution to an underdetermined system of linear equations. It has now been established, both theoretically and empirically, that certain optimization algorithms are able to solve such problems. Iterative Hard Thresholding (IHT) (Blumensath and Davies, 2007), which is the focus of this thesis, is an established CS recovery algorithm which is known to be effective in practice, both in terms of recovery performance and computational efficiency. However, theoretical analysis of IHT to date suffers from two drawbacks: state-of-the-art worst-case recovery conditions have not yet been quantified in terms of the sparsity/undersampling trade-off, and also there is a need for average-case analysis in order to understand the behaviour of the algorithm in practice. In this thesis, we present a new recovery analysis of IHT, which considers the fixed points of the algorithm. In the context of arbitrary matrices, we derive a condition guaranteeing convergence of IHT to a fixed point, and a condition guaranteeing that all fixed points are 'close' to the underlying signal. If both conditions are satisfied, signal recovery is therefore guaranteed. Next, we analyse these conditions in the case of Gaussian measurement matrices, exploiting the realistic average-case assumption that the underlying signal and measurement matrix are independent. We obtain asymptotic phase transitions in a proportional-dimensional framework, quantifying the sparsity/undersampling trade-off for which recovery is guaranteed. By generalizing the notion of xed points, we extend our analysis to the variable stepsize Normalised IHT (NIHT) (Blumensath and Davies, 2010). For both stepsize schemes, comparison with previous results within this framework shows a substantial quantitative improvement. We also extend our analysis to a related algorithm which exploits the assumption that the underlying signal exhibits tree-structured sparsity in a wavelet basis (Baraniuk et al., 2010). We obtain recovery conditions for Gaussian matrices in a simplified proportional-dimensional asymptotic, deriving bounds on the oversampling rate relative to the sparsity for which recovery is guaranteed. Our results, which are the first in the phase transition framework for tree-based CS, show a further significant improvement over results for the standard sparsity model. We also propose a dynamic programming algorithm which is guaranteed to compute an exact tree projection in low-order polynomial time.

The cold gas dynamic spray process developed in the middle of the 80’s reached the industrial stage in development. Even so, many scientific investigations still go on. The nature of the bond between the coating and the substrate is the subject of some controversy. The development of the process will be improved by understanding how the properties of the powder and the mechanical properties of the substrate influence the bonding process. This study analyses the basic dynamics of the process when copper is sprayed. • The one dimensional isentropic model of the gas behaviour in a Laval type nozzle allows evaluating the effect of the gas stagnation pressure P0 and temperature T0 on the impact velocity and temperature of the powder particle. • The analysis of single splats on two substrates (aluminium and steel) shows the influence of the substrate on the deformation of single particles and the influence of the impact speed on the impact shape. • Coatings are made of with powders with a specific size distribution. Two copper powders with a different size distribution are compared based on the deposition efficiency (D.E.) and the mechanical properties of the coating. The mechanical properties tested are the microhardness, the bond strength and the nanohardness. • X-ray diffraction will show that the two powders have an initial very different microstructure. The consequence of this is a different deformation mechanism during the coating build up. • An Auger analysis of the interface has shown the presence of diffusion zone when copper was sprayed on the Al and TA6V substrate. It appears that the size distribution will determine the final impact conditions of the powder. The microstructure of the powder and the oxide content of the powder yield different deformation processes and may explain the differences in D.E. and mechanical properties. The Auger analysis of the interface has yielded diffusion zone that were not expected but some mechanisms under impact loading can explain their presence./ Le procédé de projection thermique à froid a été développé dans le milieu des années 80 et il arrive au stade industriel. Néanmoins, plusieurs développements scientifiques sont encore en cours. La nature du lien entre la poudre et le substrat est toujours l’objet de certaines controverses. Le développement futur du procédé nécessite une bonne compréhension de l’influence de la poudre et des propriétés du substrat sur le mécanisme d’adhérence. Cette étude va mettre en évidence les principaux facteurs influençant la projection de cuivre. • Le modèle unidimensionnel isentropique du gaz parfait dans une buse convergente/ divergente permet de déterminer l’influence de la pression de stagnation et de la température de stagnation sur la vitesse et la température d’impact des particules de poudre. • L’analyse d’impact unique sur les substrats d’acier et d’alliage d’Al (AA2014) montre l’influence du substrat sur la déformation des particules de poudre. La vitesse d’impact a une conséquence importante sur la forme d’une particule projetée sur une surface. . • Les revêtements sont fabriqués à partir de poudre avec une granulométrie donnée. Deux poudres avec une distribution de taille différente sont comparées par leur rendement de déposition et les propriétés mécaniques des revêtements obtenus. Les propriétés mécaniques testées sont la microdureté, l’adhérence et la nanodureté. • La diffraction par rayons-X montre que les deux poudres ont initialement une microstructure très différente. Lors de l’impact, les deux poudres vont se déformer de manière différente et ceci se traduit dans la microstructure. • La spectroscopie Auger montre qu’une zone de diffusion s’est formée à l’interface entre le cuivre et les deux substrats d’Al et de TA6V. La distribution de taille des poudres a une influence considérable sur la vitesse et la température d’impact des particules de poudres mais il apparaît que d’autres facteurs ont aussi énormément d’influence. Le taux d’oxyde dans la poudre a une influence très importante sur le rendement et l’adhérence du dépôt. Les deux poudres projetées ont une microstructure initiale très différente et ceci se traduit par une déformation différente des particules de poudre dans le revêtement.