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De, Martino Danilo. "String inflationary models with non-monotonic slow-roll and detectable tensor modes." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/8391/.
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The first chapter of this work has the aim to provide a brief overview of the history of our Universe, in the context of string theory and considering inflation as its possible application to cosmological problems. We then discuss type IIB string compactifications, introducing the study of the inflaton, a scalar field candidated to describe the inflation theory. The Large Volume Scenario (LVS) is studied in the second chapter paying particular attention to the stabilisation of the Kähler moduli which are four-dimensional gravitationally coupled scalar fields which parameterise the size of the extra dimensions. Moduli stabilisation is the process through which these particles acquire a mass and can become promising inflaton candidates. The third chapter is devoted to the study of Fibre Inflation which is an interesting inflationary model derived within the context of LVS compactifications. The fourth chapter tries to extend the zone of slow-roll of the scalar potential by taking larger values of the field φ. Everything is done with the purpose of studying in detail deviations of the cosmological observables, which can better reproduce current experimental data. Finally, we present a slight modification of Fibre Inflation based on a different compactification manifold. This new model produces larger tensor modes with a spectral index in good agreement with the date released in February 2015 by the Planck satellite.
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Conigli, Alessandro. "Primordial tensor modes from inflation and their detectability with GW experiments." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18153/.
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L'obbiettivo di questa tesi è lo studio delle fluttuazioni quantistiche dei modi tensoriali primordiali prodotti durante l'inflazione, con particolare attenzione alla possibilità di rilevare tali modi come onde gravitazionali di background.
Una eventuale rilevazione confermerebbe ulteriormente la validità dei modelli inflazionari. Tuttavia, la densità di energia predetta per le onde gravitazionali di background è di gran lunga inferiore alla sensibilità degli attuali rivelatori. In questo lavoro noi andiamo oltre l'inflazione slow-roll standard e analizziamo nuovi modelli che ci permettono di amplificare le perturbazioni tensoriali su scale al di fuori dell'orizzonte.
Introduciamo un meccanismo che sfrutta una fase transitoria di evoluzione non-attractor per amplificare i modi tensoriali. Procediamo poi con lo studio della fenomenologia del modello, dimostrando la possibilità di amplificare la densità di energia delle onde gravitazionali fino alle scale accessibili dai rivelatori LISA, aLIGO e PTA. Calcoliamo poi il numero di e-folds di fase non-attractor necessari per assicurare la rivelazione di tali onde.
Successivamente, presentiamo un nuovo modello di bigravità, caratterizzato da un termine di accoppiamento tra un tensore privo di massa ed uno massivo.
Presentiamo un'analisi dettagliata della dinamica dei due campi tensoriali, derivando vincoli che la massa del campo deve soddisfare per poter amplificare le fluttuazioni prive di massa.
Infine, assumiamo che l'accoppiamento sia dominante per un certo numero di e-folds durante l'inflazione e diamo una stima di tale valore per i tre rivelatori sopracitati.
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Raghunathan, Srinivasan. "Experimental and theoretical challenges in the search for tensor B-modes." Tesis, Universidad de Chile, 2016. http://repositorio.uchile.cl/handle/2250/138002.
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Doctorado en Ciencias, Mención AstronomíaThis thesis describes the work that I performed to analyse the data from the Atacama B-mode Search (ABS) experiment. The ABS experiment observed the Cosmic Microwave Background (CMB) radiation for three years using polarisation sensitive detectors. The telescope is located at the Atacama desert in the north of Chile at an altitude of 5190 metres. The goal of the experiment is to detect the primordial gravitational waves which were supposed to have been generated during the initial phase of exponential expansion of the universe. These gravitational waves leave unique signatures on the polarised CMB called the tensor B-modes. Several experiments have been built over the last decade to observe them but the primordial tensor B-modes still remain undetected. If found, they will be a direct evidence for a process called Cosmic inflation which is responsible for the initial period of exponential expansion. The detection will also provide hints about the physics of inflation as the characterisation of tensor B-modes via the parameter called tensor-to-scalar ratio r is directly related to the energy scale of inflation O(10^16) GeV, comparable to the grand-unification-theory (GUT) energy scales. The ABS experiment was designed and led by the Physics department at Princeton University. The ABS observed the CMB at 145 GHz using polarisation sensitive transition-edge-sensor (TES) bolometers. There are two mirrors, 60 cms each arranged in a compact crossed-Dragone configuration. The ABS was the first ground-based CMB experiment to successfully implement the rapid polarisation modulation using a continuously rotating (warm) half-wave-plate (HWP). In this article, I present the observation strategy, data acquisition, instrument calibration, and the data selection techniques used to produce the CMB maps and power spectrum estimation. For completeness, I also briefly describe the work done by other members of the ABS project but clearly mention my contribution at the start of every chapter. The final power spectrum is not shown as the data selection techniques and the modelling of the galactic foregrounds are still being finalised. However, the results from detailed statistical assessment of the data using an exhaustive suite of null tests indicate that we are not affected by any significant systematic effects. The assessment of the ABS null tests will be the major result of this work. ### en español: Esta tesis describe el trabajo que he realizado para analizar los datos del experimento Atacama B-mode Search (ABS). Utilizando el telescopio de ABS, cuyos detectores son sensible a la polarización, durante un periodo de tres años se observa la radiación en microondas del fonda cósmico (CMB). El telescopio esta instalado en el desierto de Atacama, en el norte de Chile, a una altura de 5190 metros. El objetivo del experimento es detectar las ondas gravitationales primordiales supuestamente generadas durante la fase inicial de expansión exponencial del universo. Estas ondas gravitacionales dejan registros únicas en polarizacion del CMB llamados tensor B-modes. Durante la ultima decada se han realizado varios instrumentos para observar tensor B-modes, pero no se han detectado aun. Si se les detecta, serian una evidencia directa de un proceso llamado inflación cósmica que sera el período inicial de la expansión exponencial. La detección también proporcionará pistas sobre la física de la inflación como la caracterización de tensor B-modes vía el cuociente tensor-a-escalar llamado r, está directamente relacionada con la escala de energía de la inflación O(10^16) GeV, comparable a la gran unificación teoría (GUT) escalas de energía. El experimento ABS fue diseñado y dirigido por el departamento de Física de la Universidad de Princeton. El ABS observo la CMB en la frecuencia de 145 GHz utilizando bolometros sensibles a la polarizacio del tipo transition-edge-sensor (TES). Posee dos espejos, de 60 cms cada uno y dispuestos en una configuracion del tipo compact crossed-Dragone. El ABS fue el primer experimento de medicion de la CMB, situado en la Tierra, en implementar exitosamente la modulacion de polarizacion rápida mediante una placa de media-onda half-wave-plate (HWP) mantenida a temperatura ambiente y girando continuamente. En este reporte, presento la estrategia de observación, adquisición de datos, la calibración del instrumento, y las técnicas de selección de datos utilizados para producir los mapas de la CMB y estimación del Espectro de potencia de la CMB. Por completitud, también describo brevemente el trabajo realizado por otros miembros del proyecto ABS, pero menciono claramente mi contribución al comienzo de cada capítulo. El espectro de potencia final no se ha incluido debido a que tanto las técnicas de selección de datos y el modelado de la absorpcion debida a nuestra galaxia no están aun finalizadas. Sin embargo, los resultados de la evaluación estadística detallada de los datos utilizando un conjunto exhaustivo de pruebas de sesgo nulo (null tests) indican que nuestras medidas no estan afectadas significativamente por efectos sistemáticos. La evaluación de las pruebas de sesgo nulo de las observaciones llevadas a cabo con el telescopio ABS nulos, es el principal resultado de este trabajo. Este resultado posibilita una determinacion robusta del Espectro de Potencia de la CMB.
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Edwards, David Craig. "Theoretical considerations in the use of scalar-tensor theories of gravity in inflationary models." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31404.
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The inflationary paradigm is one which was designed to answer questions that arose from classical Hot Big Bang cosmology. The period of rapid expansion in the early Universe provides a mechanism to solve the flatness, horizon and relic problems. More importantly, since the theory was first introduced it has been realised that it also provides a mechanism to generate the initial perturbations from which structure in the Universe can grow. In the zoo of potential inflationary models there is a dominant class: slow-roll inflation. The idea that the energy density of the inflationary field is dominated by its potential highly simplifies the calculations required to predict observable quantities. This simplification relies on all the information required to know the subsequent dynamics of the field to be encoded in the space Φ-Φ̇; it must be an effective phase space. I show that Φ-Φ̇ can be considered to be such a space for the most general scalar-tensor theory which gives second-order equations of motion: Horndeski theory. There are theoretical issues associated with this reduction that are illuminated through specific examples in which they occur. A theoretical issue with inflation is that there is an overabundance of models, with some capable of predicting any value of the possible observables. The second block of work in this thesis looks at a particular set of models that make the same observational prediction. These 'attractor' models utilise a non-minimal coupling between the inflationary fields and gravity and are studied in depth, both in the case of one and several fields. Firstly, I examine the Universal Attractors, a single field subset of these models. I show, in detail, the observational prediction such a model makes in the case of a strong non-minimal coupling and then examine the constraints it would be possible to put on such a coupling if a confirmed detection of primordial gravitational waves was made. Despite the discussion existing in the literature there is a small deviation of the Universal Attractor models from the predictions of the Starobinsky model. Furthermore, the coupling, ξ is found to be constrained so that |ξ| < 1 in the case where there a level of detectable primordial tensor modes. While the attractor models have an effective one-field description in reality there are several other fields that are assumed to be fixed during the inflationary phase. This claim requires careful examination as the field-space of the models generally is not flat. This curvature can cause a destabilising effect with certain parameters and so I investigate how susceptible the α-attractors and related models are to the destabilisation. A key result of this chapter is to highlight how important it is to not rely on the slow-roll approximation when assessing the effect of the instability, as the region where the effect begins to become large corresponds with the region where slow-roll begins to break down. Assuming the slow-roll approximation is valid leads to an over-estimation of the effect that the instability mechanism has. Despite this, some of the models considered are seen to experience the instability for certain ranges of model parameters. Making the assumption that any occurrence of the instability will, at the very least, move the observational prediction of the model outside the currently constrained range allows a constraint on the model parameter in question which directly translates to a theoretical lower bound on the tensor-scalar ratio, r > 0.0005.
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Delepouve, Thibault. "Quartic Tensor Models." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS085/document.
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Les modèles de tenseurs sont des mesures de probabilité sur des espaces de tenseurs aléatoires. Ils généralisent les modèles de matrices et furent développés pour l’étude de la géométrie aléatoire en dimension arbitraire. De plus, ils sont fortement liés aux théories de gravité quantique car, en plus des modèles standards très simples, ils incluent les théories de champs sur groupes, qui constituent l’approche « intégrale fonctionnelle » de la gravité quantique à boucle. Dans cette thèse, nous étudions le cas restreint des modèles tensoriels quartiques, pour lesquels un plus grand nombre de résultats mathématiques rigoureux ont pu être démontrés. Grâce à la transformation de champ intermédiaire, les modèles quartiques peuvent être ré-écrits sous forme de modèles de matrices multiples, et leurs développements perturbatifs peuvent être indexés par des cartes combinatoires. En utilisant divers développement en cartes, nous démontrons d’importants résultats d’analycité ainsi que des bornes pour les cumulants du modèle tensoriel standard le plus général et de rang arbitraire, ainsi que du plus simple modèle renormalisable de rang 3. Ensuite, nous introduisons une nouvelle famille de modèles, les modèles améliorés, dont le développement perturbatif se comporte de manière nouvelle, différente du comportement « melonique » qui caractérise les modèles tensoriels précédemment étudiésTensor models are probability measures for random tensors. They generalise matrix models and were developed to study random geometry in arbitrary dimension. Moreover, they are strongly connected to quantum gravity theories as, additionally to the standard bare-bones models, they encompass the field theoretical approach to loop quantum gravity known as group field theory.In the present thesis, we focus on the restricted case of quartic tensor models, for which a far greater number of rigorous mathematical results have been proven. Quartic models can be re-written as multi-matrix models using the intermediate field representation, and their perturbative expansions can be written as series expansions over combinatorial maps. Using a variety of map expansions, we prove analyticity results and useful bounds for the cumulants of various tensor models : the most general standard quartic model at any rank and the simplest renormalisable tensor field theory at rank 3. Then, we introduce a new class of models, the enhanced models, which perturbative expansions display new behaviour, different to the so called melonic behaviour that characterise most known tensor models so far
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Da, Silva Caroline Dos Santos. "Cosmic strings and scalar tensor gravity." Thesis, Durham University, 1999. http://etheses.dur.ac.uk/4577/.
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This thesis is concerned with the study of cosmic strings. We studied the values for the Higgs mass and string coupling for which the gravitational effect of an infinite cosmic string in the context of the Einstein theory is not only locally but also globally weak. We conclude this happens for strings formed at scales less or equal to the Planck one with Higgs mass being less or equal to the boson vectorial mass. Then we examined the metric of an isolated self-gravitating abelian-Higgs vortex in dilatonic gravity for arbitrary coupling of the vortex fields to the dilaton. We looked for solutions in both massless and massive dilaton gravity. We compared our results to existing metrics for strings in Einstein and .Jordan-Brans-Dicke theories. We explored the generalisation of Bogomolnyi arguments for our vortices and commented on the effects on test particles. We then included the presence of an axion field and examined the metric of an isolated self-gravitating axionic-dilatonic string. Finally we studied dilatonic strings through black hole solutions in string theory. We concluded that the horizon of non-extreme charged black holes supports the long-range fields of the Nielsen-Olesen string that can be considered as black hole hair and whose gravitational effect is in general the production of a conical deficit into the metric of the black hole background. We also concluded that the effect of the dilaton on the horizon of these black holes is to generate an additional charge.
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Hou, Ming. "Tensor-based regression models and applications." Doctoral thesis, Université Laval, 2017. http://hdl.handle.net/20.500.11794/27787.
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Tableau d’honneur de la Faculté des études supérieures et postdoctorales, 2017-2018Avec l’avancement des technologies modernes, les tenseurs d’ordre élevé sont assez répandus et abondent dans un large éventail d’applications telles que la neuroscience informatique, la vision par ordinateur, le traitement du signal et ainsi de suite. La principale raison pour laquelle les méthodes de régression classiques ne parviennent pas à traiter de façon appropriée des tenseurs d’ordre élevé est due au fait que ces données contiennent des informations structurelles multi-voies qui ne peuvent pas être capturées directement par les modèles conventionnels de régression vectorielle ou matricielle. En outre, la très grande dimensionnalité de l’entrée tensorielle produit une énorme quantité de paramètres, ce qui rompt les garanties théoriques des approches de régression classique. De plus, les modèles classiques de régression se sont avérés limités en termes de difficulté d’interprétation, de sensibilité au bruit et d’absence d’unicité. Pour faire face à ces défis, nous étudions une nouvelle classe de modèles de régression, appelés modèles de régression tensor-variable, où les prédicteurs indépendants et (ou) les réponses dépendantes prennent la forme de représentations tensorielles d’ordre élevé. Nous les appliquons également dans de nombreuses applications du monde réel pour vérifier leur efficacité et leur efficacité.
With the advancement of modern technologies, high-order tensors are quite widespread and abound in a broad range of applications such as computational neuroscience, computer vision, signal processing and so on. The primary reason that classical regression methods fail to appropriately handle high-order tensors is due to the fact that those data contain multiway structural information which cannot be directly captured by the conventional vector-based or matrix-based regression models, causing substantial information loss during the regression. Furthermore, the ultrahigh dimensionality of tensorial input produces huge amount of parameters, which breaks the theoretical guarantees of classical regression approaches. Additionally, the classical regression models have also been shown to be limited in terms of difficulty of interpretation, sensitivity to noise and absence of uniqueness. To deal with these challenges, we investigate a novel class of regression models, called tensorvariate regression models, where the independent predictors and (or) dependent responses take the form of high-order tensorial representations. We also apply them in numerous real-world applications to verify their efficiency and effectiveness. Concretely, we first introduce hierarchical Tucker tensor regression, a generalized linear tensor regression model that is able to handle potentially much higher order tensor input. Then, we work on online local Gaussian process for tensor-variate regression, an efficient nonlinear GPbased approach that can process large data sets at constant time in a sequential way. Next, we present a computationally efficient online tensor regression algorithm with general tensorial input and output, called incremental higher-order partial least squares, for the setting of infinite time-dependent tensor streams. Thereafter, we propose a super-fast sequential tensor regression framework for general tensor sequences, namely recursive higher-order partial least squares, which addresses issues of limited storage space and fast processing time allowed by dynamic environments. Finally, we introduce kernel-based multiblock tensor partial least squares, a new generalized nonlinear framework that is capable of predicting a set of tensor blocks by merging a set of tensor blocks from different sources with a boosted predictive power.
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Ingalhalikar, Madhura Aditya Magnotta Vincent A. "Spatial normalization of diffusion models and tensor analysis." Iowa City : University of Iowa, 2009. http://ir.uiowa.edu/etd/299.
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Olness, James M. "The nucleon "tensor charges" and the Skyrme model." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/35421.
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Ingalhalikar, Madhura Aditya. "Spatial normalization of diffusion models and tensor analysis." Diss., University of Iowa, 2009. https://ir.uiowa.edu/etd/299.
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Diffusion tensor imaging provides the ability to study white matter connectivity and integrity noninvasively. The information contained in the diffusion tensors is very complex. Therefore a simple way of dealing with tensors is to compute rotationally invariant scalar quantities. These scalar indices have been used to perform population studies between controls and patients with neurological and psychiatric disorders. Implementing the scalar values may reduce the information contained in the whole tensor. A group analysis using the full tensors may give better estimate of white matter changes that occur in the diseased subjects. For spatial normalization of diffusion tensors, it is necessary to interpolate the tensor representation as well as rotate the diffusion tensors after transformation to keep the tensors consistent with the tissue reorientation. Existing reorientation methods cannot be directly used for higher order diffusion models (e.g. q-ball imaging). A novel technique called gradient rotation is introduced where the rotation is directly applied to the diffusion sensitizing gradients providing a voxel by voxel estimate of the diffusion gradients instead of a volume of by volume estimate. The technique is validated by comparing it with an existing method where the transformation is applied to the resulting diffusion tensors. For better matching of diffusion tensors a novel multichannel registration method is proposed based on a non-parametric diffeomorphic demons algorithm. The channels used for the registration include T1-weighted volume and tensor components. A fractional anisotropy (FA) channel is used for defining the contribution of each channel. Including the anatomical data together with the tensors, allows the registration to accurately match the global brain shape and the underlying white matter architecture simultaneously. Using this multichannel registration framework, 10 healthy controls and 9 patients of schizophrenia were spatially normalized. For the group analysis, the tensors were transformed to log-euclidean space. Linear regression analysis was performed on the transformed tensors. Results show that there is a significant difference in the anisotropy between patients and controls especially in the anterior regions that include genu of the corpus callosum and anterior and superior corona radiata, forceps minor and anterior limb on the internal capsule.
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Schorn, Scott A. "The evaluation of turbulence models using tensor visualization techniques." Thesis, This resource online, 1995. http://scholar.lib.vt.edu/theses/available/etd-12302008-063403/.
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Dartois, Stephane. "Random Tensor models : Combinatorics, Geometry, Quantum Gravity and Integrability." Thesis, Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCD104/document.
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Dans cette thèse nous explorons différentes facettes des modèles de tenseurs aléatoires. Les modèles de tenseurs aléatoires ont été introduits en physique dans le cadre de l'étude de la gravité quantique. En effet les modèles de matrices aléatoires, qui sont un cas particuliers de modèles de tenseurs, en sont une des origines. Ces modèles de matrices sont connus pour leur riche combinatoire et l'incroyable diversité de leurs propriétés qui les font toucher tous les domaines de l'analyse, la géométrie et des probabilités. De plus leur étude par les physiciens ont prouvé leur efficacité en ce qui concerne l'étude de la gravité quantique à deux dimensions. Les modèles de tenseurs aléatoires incarnent une généralisation possible des modèles de matrices. Comme leurs cousins, les modèles de matrices, ils posent questions dans les domaines de la combinatoire (comment traiter les cartes combinatoires d dimensionnelles ?), de la géométrie (comment contrôler la géométrie des triangulations générées ?) et de la physique (quel type d'espace-temps produisent-ils ? Quels sont leurs différentes phases ?). Cette thèse espère établir des pistes ainsi que des techniques d'études de ces modèles. Dans une première partie nous donnons une vue d'ensemble des modèles de matrices. Puis, nous discutons la combinatoire des triangulations en dimensions supérieures ou égales à trois en nous concentrant sur le cas tridimensionnelle (lequel est plus simple à visualiser). Nous définissons ces modèles et étudions certaines de leurs propriétés à l'aide de techniques combinatoires permettant de traiter les cartes d dimensionnelles. Enfin nous nous concentrons sur la généralisation de techniques issues des modèles de matrices dans le cas d'une famille particulières de modèles de tenseurs aléatoires. Ceci culmine avec le dernier chapitre de la thèse donnant des résultats partiels concernant la généralisation de la récurrence topologique de Eynard et Orantin à cette famille de modèles de tenseursIn this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short introduction to few aspects of random matrix models and recalling a physical motivation called Group Field Theory, we start exploring the world of random tensor models and its relation to geometry, quantum gravity and combinatorics. We first define these models in a natural way and discuss their geometry and combinatorics. After these first explorations we start generalizing random matrix methods to random tensors in order to describes the mathematical and physical properties of random tensor models, at least in some specific cases
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Zou, Haiyuan. "Tensor renormalization group methods for spin and gauge models." Diss., University of Iowa, 2014. https://ir.uiowa.edu/etd/1420.
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The analysis of the error of perturbative series by comparing it to the exact solution is an important tool to understand the non-perturbative physics of statistical models. For some toy models, a new method can be used to calculate higher order weak coupling expansion and modified perturbation theory can be constructed. However, it is nontrivial to generalize the new method to understand the critical behavior of high dimensional spin and gauge models. Actually, it is a big challenge in both high energy physics and condensed matter physics to develop accurate and efficient numerical algorithms to solve these problems. In this thesis, one systematic way named tensor renormalization group method is discussed. The applications of the method to several spin and gauge models on a lattice are investigated. theoretically, the new method allows one to write an exact representation of the partition function of models with local interactions. E.g. O(N) models, Z2 gauge models and U(1) gauge models. Practically, by using controllable approximations, results in both finite volume and the thermodynamic limit can be obtained. Another advantage of the new method is that it is insensitive to sign problems for models with complex coupling and chemical potential. Through the new approach, the Fisher's zeros of the 2D O(2) model in the complex coupling plane can be calculated and the finite size scaling of the results agrees well with the Kosterlitz-Thouless assumption. Applying the method to the O(2) model with a chemical potential, new phase diagram of the models can be obtained. The structure of the tensor language may provide a new tool to understand phase transition properties in general.
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Lehebel, Antoine. "Objets astrophysiques compacts en gravité modifiée." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS204/document.
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Vingt années se sont écoulées depuis la découverte de l'expansion accélérée de l'Univers, ravivant l'intérêt pour les théories alternatives de la gravité. Ajouter un champ scalaire à la métrique habituelle de la relativité générale est l'une des manières les plus simples de modifier notre théorie de la gravité. En parallèle, nos connaissances sur les trous noirs et les étoiles à neutrons sont en plein essor, grâce notamment au développement de l'astronomie par ondes gravitationnelles. Cette thèse se situe au carrefour entre les deux domaines : elle étudie les propriétés des objets compacts dans les théories tenseur-scalaire généralisées. Je commence par rappeler les théorèmes d'unicité essentiels établis depuis les années soixante-dix. Après avoir présenté le théorème d'unicité pour les trous noirs en théorie de Horndeski, je l'étends aux étoiles. La deuxième partie de cette thèse détaille les différentes manières de contourner ce théorème. Parmi elles, je présente des solutions où la dépendance temporelle du champ scalaire permet de le raccorder à une solution cosmologique, mais aussi des trous noirs statiques et asymptotiquement plats. Dans la troisième partie, j'établis un critère important pour la stabilité de ces solutions, qui s'appuie sur leur structure causale. C'est aussi l'occasion d'étudier la propagation des ondes gravitationnelles au voisinage de trous noirs, et de sélectionner les théories dans lesquelles les ondes gravitationnelles se propagent à la même vitesse que la lumièreTwenty years have passed since the discovery of the accelerated expansion of the Universe, reviving the interest for alternative theories of gravity. Adding a scalar degree of freedom to the usual metric of general relativity is one of the simplest ways to modify our gravitational theory. In parallel, our knowledge about black holes and neutron stars is booming, notably thanks to the advent of gravitational wave astronomy. This thesis is at the crossroads between the two fields, investigating the properties of compact objects in extended scalar-tensor theories. I start by reviewing essential no-hair results established since the seventies. After discussing the no-hair theorem proposed for black holes in Horndeski theory, I present its extension to stars. The second part of the thesis investigates in detail the various ways to circumvent this theorem. These notably include solutions with a time-dependent scalar field in order to match cosmological evolution, but also static and asymptotically flat configurations. In a third part, I establish an important stability criterion for these solutions, based on their causal structure. It is also the occasion to study the propagation of gravitational waves in black hole environments, and to select the theories where gravitational waves travel at the same speed as light
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Ali, Mazen [Verfasser]. "Tensor approximation and adaptivity within model order reduction / Mazen Ali." Ulm : Universität Ulm, 2020. http://d-nb.info/1206248580/34.
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Nguyen, Viet anh. "Contributions to tensor models, Hurwitz numbers and Macdonald-Koornwinder polynomials." Thesis, Angers, 2017. http://www.theses.fr/2017ANGE0052/document.
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Dans cette thèse, j’étudie trois sujets reliés : les modèles de tenseurs, les nombres de Hurwitz et les polynômes de Macdonald-Koornwinder. Les modèles de tenseurs généralisent les modèles de matrices en tant qu’une approche à la gravité quantique en dimension arbitraire (les modèles de matrices donnent une version bidimensionnelle). J’étudie un modèle particulier qui s’appelle le modèle quartique mélonique. Sa spécialité est qu’il s’écrit en termes d’un modèle de matrices qui est lui-même aussi intéressant. En utilisant les outils bien établis, je calcule les deux premiers ordres de leur 1=N expansion. Parmi plusieurs interprétations, les nombres de Hurwitz comptent le nombre de revêtements ramifiés de surfaces de Riemann. Ils sont connectés avec de nombreux sujets en mathématiques contemporaines telles que les modèles de matrices, les équations intégrables et les espaces de modules. Ma contribution principale est une formule explicite pour les nombres doubles avec 3-cycles complétées d’une part. Cette formule me permet de prouver plusieurs propriétés intéressantes de ces nombres. Le dernier sujet de mon étude est les polynôme de Macdonald et Koornwinder, plus précisément les identités de Littlewood. Ces polynômes forment les bases importantes de l’algèbre des polynômes symétriques. Un des problèmes intrinsèques dans la théorie des fonctions symétriques est la décomposition d’un polynôme symétrique dans la base de Macdonald. La décomposition obtenue (notamment si les coefficients sont raisonnablement explicites et compacts) est nommée une identité de Littlewood. Dans cette thèse, j’étudie les identités démontrées récemment par Rains et Warnaar. Mes contributions incluent une preuve d’une extension d’une telle identité et quelques progrès partiels vers la généralisation d’une autreIn this thesis, I study three related subjects: tensor models, Hurwitz numbers and Macdonald-Koornwinder polynomials. Tensor models are generalizations of matrix models as an approach to quantum gravity in arbitrary dimensions (matrix models give a 2D version). I study a specific model called the quartic melonic tensor model. Its specialty is that it can be transformed into a multi-matrix model which is very interesting by itself. With the help of well-established tools, I am able to compute the first two leading orders of their 1=N expansion. Among many interpretations, Hurwitz numbers count the number of weighted ramified coverings of Riemann surfaces. They are connected to many subjects of contemporary mathematics such as matrix models, integrable equations and moduli spaces of complex curves. My main contribution is an explicit formula for one-part double Hurwitz numbers with completed 3-cycles. This explicit formula also allows me to prove many interesting properties of these numbers. The final subject of my study is Macdonald-Koornwinder polynomials, in particular their Littlewood identities. These polynomials form important bases of the algebra of symmetric polynomials. One of the most important problems in symmetric function theory is to decompose a symmetric polynomial into the Macdonald basis. The obtained decomposition (in particular, if the coefficients are explicit and reasonably compact) is called a Littlewood identity. In this thesis, I study many recent Littlewood identities of Rains and Warnaar. My own contributions include a proof of an extension of one of their identities and partial progress towards generalization of one another
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Parsons, Paul. "Scalar-field models of the early universe." Thesis, University of Sussex, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.390077.
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Cao, Zisheng, and 曹子晟. "Incremental algorithms for multilinear principal component analysis of tensor objects." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hdl.handle.net/10722/208151.
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In recent years, massive data sets are generated in many areas of science and business, and are gathered by using advanced data acquisition techniques. New approaches are therefore required to facilitate effective data management and data analysis in this big data era, especially to analyze multidimensional data for real-time applications. This thesis aims at developing generic and effective algorithms for compressing and recovering online multidimensional data, and applying such algorithms in image processing and other related areas.
Since multidimensional data are usually represented by tensors, this research uses multilinear algebra as the mathematical foundation to facilitate development. After reviewing the techniques of singular value decomposition (SVD), principal component analysis (PCA) and tensor decomposition, this thesis deduces an effective multilinear principal component analysis (MPCA) method to process such data by seeking optimal orthogonal basis functions that map the original tensor space to a tensor subspace with minimal reconstruction error. Two real examples, 3D data compression for positron emission tomography (PET) and offline fabric defect detection, are used to illustrate the tensor decomposition method and the deduced MPCA method, respectively. Based on the deduced MPCA method, this research develops an incremental MPCA (IMPCA) algorithm which targets at compressing and recovering online tensor objects.
To reduce computational complexity of the IMPCA algorithm, this research investigates the low-rank updates of singular values in the matrix and tensor domains, which leads to the development of a sequential low-rank update scheme similar to the sequential Karhunen-Loeve algorithm (SKL) for incremental matrix singular value decomposition, a sequential low-rank update scheme for incremental tensor decomposition, and a quick subspace tracking (QST) algorithm to further enhance the low-rank updates of singular values if the matrix is positive-symmetric definite. Although QST is slightly inferior to the SKL algorithm in terms of accuracy in estimating eigenvector and eigenvalue, the algorithm has lower computational complexity. Two fast incremental MPCA
(IMPCA) algorithms are then developed by incorporating the SKL algorithm and the QST algorithm separately into the IMPCA algorithm. Results obtained from applying the developed IMPCA algorithms to detect anomalies from online multidimensional data in a number of numerical experiments, and to track and reconstruct the global surface temperature anomalies over the past several decades clearly confirm the excellent performance of the algorithms.
This research also applies the developed IMPCA algorithms to solve an online fabric defect inspection problem. Unlike existing pixel-wise detection schemes, the developed algorithms employ a scanning window to extract tensor objects from fabric images, and to detect the occurrence of anomalies. The proposed method is unsupervised because no pre-training is needed. Two image processing techniques, selective local Gabor binary patterns (SLGBP) and multi-channel feature combination, are developed to accomplish the feature extraction of textile patterns and represent the features as tensor objects. Results of experiments conducted by using a real textile dataset confirm that the developed algorithms are comparable to existing supervised methods in terms of accuracy and computational complexity. A cost-effective parallel implementation scheme is developed to solve the problem in real-time.published_or_final_version
Industrial and Manufacturing Systems Engineering
Doctoral
Doctor of Philosophy
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Dailey, Natalie S., and Natalie S. Dailey. "Neurological Models of Dyslexia." Diss., The University of Arizona, 2016. http://hdl.handle.net/10150/622935.
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The reading network is only partially understood and even less is known regarding how the network functions when reading is impaired. Dyslexia is characterized by poor phonological processing and affects roughly 5-12% of the population. The Dorsal-Ventral and Cerebellar-Deficit models propose distinct behavioral and structural differences in young adults with dyslexia. Behavioral assessments were used to determine if deficits for young adults with dyslexia were restricted to the literacy domain or dispersed among reading and associated behavioral domains. Diffusion tensor imaging (DTI) was used determine the extent to which white matter pathways and gray matter regions differ structurally in young adults with dyslexia. The present study also investigated whether brain-behavior relationships exist and are consistent with the theoretical models of reading in this population. Findings show that young adults with dyslexia exhibited deficits in both literacy and associated behavioral domains, including verbal working memory and motor function. Structural findings showed increased fractional anisotropy in the left anterior region (the aslant) and decreased fractional anisotropy in left posterior regions (inferior occipital fasciculus and vertical occipital fasciculus) of the reading network for young adults with dyslexia. Brain-behavior associations were found between the right inferior frontal gyrus and decoding for those with dyslexia. These findings provide support for the use of an altered reading network by young adults with dyslexia, as outlined by the Dorsal-Ventral model of reading. Limited structural and behavior findings support of the Cerebellar-Deficit model of reading, findings that warrant additional investigation.
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Chen, Cong. "High-Dimensional Generative Models for 3D Perception." Diss., Virginia Tech, 2021. http://hdl.handle.net/10919/103948.
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Modern robotics and automation systems require high-level reasoning capability in representing, identifying, and interpreting the three-dimensional data of the real world. Understanding the world's geometric structure by visual data is known as 3D perception. The necessity of analyzing irregular and complex 3D data has led to the development of high-dimensional frameworks for data learning. Here, we design several sparse learning-based approaches for high-dimensional data that effectively tackle multiple perception problems, including data filtering, data recovery, and data retrieval. The frameworks offer generative solutions for analyzing complex and irregular data structures without prior knowledge of data.
The first part of the dissertation proposes a novel method that simultaneously filters point cloud noise and outliers as well as completing missing data by utilizing a unified framework consisting of a novel tensor data representation, an adaptive feature encoder, and a generative Bayesian network. In the next section, a novel multi-level generative chaotic Recurrent Neural Network (RNN) has been proposed using a sparse tensor structure for image restoration. In the last part of the dissertation, we discuss the detection followed by localization, where we discuss extracting features from sparse tensors for data retrieval.Doctor of Philosophy
The development of automation systems and robotics brought the modern world unrivaled affluence and convenience. However, the current automated tasks are mainly simple repetitive motions. Tasks that require more artificial capability with advanced visual cognition are still an unsolved problem for automation. Many of the high-level cognition-based tasks require the accurate visual perception of the environment and dynamic objects from the data received from the optical sensor. The capability to represent, identify and interpret complex visual data for understanding the geometric structure of the world is 3D perception. To better tackle the existing 3D perception challenges, this dissertation proposed a set of generative learning-based frameworks on sparse tensor data for various high-dimensional robotics perception applications: underwater point cloud filtering, image restoration, deformation detection, and localization. Underwater point cloud data is relevant for many applications such as environmental monitoring or geological exploration. The data collected with sonar sensors are however subjected to different types of noise, including holes, noise measurements, and outliers. In the first chapter, we propose a generative model for point cloud data recovery using Variational Bayesian (VB) based sparse tensor factorization methods to tackle these three defects simultaneously. In the second part of the dissertation, we propose an image restoration technique to tackle missing data, which is essential for many perception applications. An efficient generative chaotic RNN framework has been introduced for recovering the sparse tensor from a single corrupted image for various types of missing data. In the last chapter, a multi-level CNN for high-dimension tensor feature extraction for underwater vehicle localization has been proposed.
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Mimoso, Jose Pedro. "Cosmological models of the early universe." Thesis, University of Sussex, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358557.
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Braglia, Matteo. "Initial conditions for cosmological perturbations in scalar-tensor dark-energy models." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13860/.
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We discuss the evolution and imprints of isocurvature initial conditions for the scalar field in scalar tensor extensions of Einstein gravity. We consider the simplest models of scalar tensor theories, as Induced gravity (IG, which can be recasted in form of Jordan-Brans-Dicke theory by a redefinition of the scalar field) or non-minimally coupled (NMC) scalar fields in which the acceleration of the Universe is connected to a variation of the effective Planck mass. After introducing the fundamental ideas of cosmological perturbation theory and scalar tensor theories of gravity, we give the evolution equations for matter, metric and scalar field fluctuations in synchronous gauge. We use this set of equations for both the IG and the NMC models to find a new isocurvature solution in which the scalar field fluctuations compensate for the relativistic components respectively. We also show how we can generalize the well known isocurvature modes in Einstein GR to these models. We show the different evolution of cosmological fluctuations for these isocurvature initial conditions compared to the standard adiabatic one. After that, we compute the CMB angular power spectrum for these solutions in the IG model, with the help of a modified Einstein-Boltzmann CLASS code. In particular the CMB power spectrum is computed separately for adiabatic and isocurvature initial conditions, i.e. for totally uncorrelated modes, and with arbitrary correlations leading to an interesting explanation of the lack of power in the low multipoles region of the CMB temperature power spectrum. Finally we show how a simple model of double inflation in IG could explain the generation of the new isocurvature mode.
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Shelton, Joel A. "Consensus Model of Families of Images using Tensor-based Fourier Analysis." Digital Commons @ East Tennessee State University, 2016. https://dc.etsu.edu/etd/3038.
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A consensus model is a statistical approach that uses a family of signals or in our case, a family of images to generate a predictive model. In this thesis, we consider a family of images that are represented as tensors. In particular, our images are (2,0)-tensors. The consensus model is produced by utilizing the quantum Fourier transform of a family of images as tensors to transform images to images. We write a quantum Fourier transform in the numerical computation library for Python, known as Theano to produce the consensus spectrum. From the consensus spectrum, we produce the consensus model via the inverse quantum Fourier transform. Our method seeks to improve upon the phase reconstruction problem when transforming images to images under a 2-dimensional consensus model by considering images as (2,0)-tensors.
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MacDonald, C. S. "Efficient moving mesh methods for Q-tensor models of liquid crystals." Thesis, University of Strathclyde, 2018. http://digitool.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=29525.
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As devices using liquid crystals become ever smaller and increasingly complex, there is a commensurate increase in the need for more effective numerical modelling tools in the area. In this thesis, an adaptive finite element method is used to solve a non-linear singularly perturbed boundary value problem which arises from a one dimensional Q-tensor model of liquid crystals. The adaptive non-uniform mesh is generated by equidistribution of a selection of strictly positive monitor functions. By an appropriate selection of the monitor function parameters, it is shown that the computed numerical solution converges at an optimal rate with respect to the mesh density and that the solution accuracy is robust to the size of the singular perturbation parameter. A robust and efficient numerical scheme is then used to solve the system of six coupled partial differential equations which arises from Q-tensor theory. The key novel feature is the use of a full moving mesh partial differential equation (MMPDE) approach to generate an adaptive mesh which accurately resolves important solution features. This includes the use of a new monitor function based on a local measure of biaxiality. The behaviour of the method is illustrated on a one-dimensional time-dependent problem in a π-cell geometry with an applied electric field. The numerical results show that, as well as achieving optimal rates of convergence in space and time, higher levels of solution accuracy and a considerable improvement in computational efficiency are obtained compared to other moving mesh methods used by previous authors on similar problems. The numerical scheme is then extended to tackle a two-dimensional π-cell problem. It is shown that the adaptive moving mesh method copes well with the presence of moving defects, with the mesh adapting and relaxing to capture the motion, growth and annihilation of the defects.
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Åström, Freddie. "Variational Tensor-Based Models for Image Diffusion in Non-Linear Domains." Doctoral thesis, Linköpings universitet, Datorseende, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-114279.
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This dissertation addresses the problem of adaptive image filtering. Although the topic has a long history in the image processing community, researchers continuously present novel methods to obtain ever better image restoration results. With an expanding market for individuals who wish to share their everyday life on social media, imaging techniques such as compact cameras and smart phones are important factors. Naturally, every producer of imaging equipment desires to exploit cheap camera components while supplying high quality images. One step in this pipeline is to use sophisticated imaging software including, e.g., noise reduction to reduce manufacturing costs, while maintaining image quality. This thesis is based on traditional formulations such as isotropic and tensor-based anisotropic diffusion for image denoising. The difference from main-stream denoising methods is that this thesis explores the effects of introducing contextual information as prior knowledge for image denoising into the filtering schemes. To achieve this, the adaptive filtering theory is formulated from an energy minimization standpoint. The core contributions of this work is the introduction of a novel tensor-based functional which unifies and generalises standard diffusion methods. Additionally, the explicit Euler-Lagrange equation is derived which, if solved, yield the stationary point for the minimization problem. Several aspects of the functional are presented in detail which include, but are not limited to, tensor symmetry constraints and convexity. Also, the classical problem of finding a variational formulation to a given tensor-based partial differential equation is studied. The presented framework is applied in problem formulation that includes non-linear domain transformation, e.g., visualization of medical images. Additionally, the framework is also used to exploit locally estimated probability density functions or the channel representation to drive the filtering process. Furthermore, one of the first truly tensor-based formulations of total variation is presented. The key to the formulation is the gradient energy tensor, which does not require spatial regularization of its tensor components. It is shown empirically in several computer vision applications, such as corner detection and optical flow, that the gradient energy tensor is a viable replacement for the commonly used structure tensor. Moreover, the gradient energy tensor is used in the traditional tensor-based anisotropic diffusion scheme. This approach results in significant improvements in computational speed when the scheme is implemented on a graphical processing unit compared to using the commonly used structure tensor.VIDI
NACIP
GARNICS
EMC^2
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Câmara, Amanda Souza. "Uma transição assimétrica entre estados simétricos: o alosterismo da Glucosamina 6-fosfato Desaminase." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/76/76132/tde-18042013-101101/.
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Sistemas alostéricos são característicos de proteínas com um ou mais estados de equilíbrio. Nesse sentido, uma enzima passa por modificações de sua atividade quando um substrato cooperativo se liga a um estado ou outro (1). Estes estados são reconhecidos por possuírem uma conformação mais estável e coexistirem num ensemble. Este trabalho sustenta que tais proteínas oscilem naturalmente entre esses estados. Experimentos de difração de raios-X e RMN, que proporcionam parâmetros de deslocamento anisotrópicos e tempos de relaxação de spin nuclear, já demonstram a coexistência de ambos estados em solução e descrevem o movimento como uma mudança de equilíbrio populacional dos confórmeros (2). Também é possível desenvolver métodos numéricos, como o cálculo de modos normais e a simulação de dinâmica molecular, para associar a geometria proteica a um movimento sobre determinado potencial de campos de força. O sistema adotado para o desenvolvimento desses estudos é a enzima alostérica Glucosamina-6-fosfato Desaminase. Características que defendem seu uso são sua reversibilidade catalítica, rápido equilíbrio cinético e muito baixa afinidade do estado T por ligantes. Sua estrutura também já foi resolvida por experimentos de cristalografia, identificando ambos estados alostéricos. E a caracterização das mudanças estruturais entre os estados T e R está bem estabelecida, identificando diferentes subunidades a distintos graus de rotação e prevendo uma oscilação de baixa frequência entre eles (3). Resultados obtidos neste projeto constituem: (a) uma dinâmica de 100ns partindo do estado T de toda a proteína (hexamérica) solvatada explicitamente, formando um ensemble NVT de 92000 átomos através do programa NAMD, usando o campo de forças CHARMM; (b) análise de componentes principais aproveitando esta dinâmica e usando algoritmos do programa Gromacs; (c) e análise de modos normais, em que os cálculos de minimização de energia foram feitos pelo programa Gromacs sob o campo de forças ENCADV, no vácuo. Análises desses resultados envolvem cálculos de RMSDs e flutuações, trajetórias calculadas para os autovetores oriundos de NMA ou de PCA, fatores de Debye-Waller e a confirmação visual (e gráficos de distância entre resíduos) de aproximação a um estado ou outro. Como a prévia caracterização da movimentação alostérica, identificava duas regiões para cada monômero como representativas de corpos rígidos, também é desenvolvida uma análise por tensores de inércia. Espera-se que, ao longo do tempo, essas subunidades se comportem como corpos quase rígidos e os movimentos destas regiões rígidas correspondam a uma maior representatividade da transição alostérica. Assim, a caracterização dos tensores seria capaz de filtrar movimentos de mais alta frequência que constituem ruído em relação a movimentos funcionais da proteína. - Algoritmos para cálculos matriciais dos tensores foram escritos em Fortran e em TCl.Allosteric systems are characteristic of proteins with one or more equilibrium states. Such an enzyme experiences a modification of its activity when a cooperative substrate binds to a state or another, thus, establishing a change in population equilibrium (1). These states are recognized by having a more stable conformation, and they coexist in an ensemble. X-ray diffraction and NMR experiments already demonstrated this dynamic equilibrium, and simulation methods, as molecular dynamics and normal mode analysis, generally provide a more complete proof (2).The allosteric enzyme Glucosamine-6-Phosphate Deaminase appeared to be a good model to better understand the equilibrium dynamics as essential to the protein function, given its reversibility of the catalysis and rapid-equilibrium kinetic mechanism. It also has the structure elucidated for both its conformers (3). A computational approach would now give better perspective on how the conformational changes occur. A set of results of this latter kind were obtained: (a) a 100ns dynamic starting at the hexameric T conformer, explicitly solvated, building a NVT ensemble using NAMD program and CHARMM force field; (b) a principal components analysis making use of the calculated dynamic and of the Gromacs algorithms; (c) and normal mode analysis of the T conformer structure (pdb code 1fsf) minimized with Gromacs program using ENCADV vacuum force field. Not only the conventional analyses for these results (fluctuations and projections) were taken, but also an inertia tensor analysis was developed. As the allosteric conformational change, for this protein, was described by the displacement of only two rigid body subunits³, its description by inertia tensors should act as a filter for the high frequency and functionally uninteresting motions, which normally constitute only noise.
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Kang, Kingston. "ESTIMATING THE RESPIRATORY LUNG MOTION MODEL USING TENSOR DECOMPOSITION ON DISPLACEMENT VECTOR FIELD." VCU Scholars Compass, 2018. https://scholarscompass.vcu.edu/etd/5254.
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Modern big data often emerge as tensors. Standard statistical methods are inadequate to deal with datasets of large volume, high dimensionality, and complex structure. Therefore, it is important to develop algorithms such as low-rank tensor decomposition for data compression, dimensionality reduction, and approximation.
With the advancement in technology, high-dimensional images are becoming ubiquitous in the medical field. In lung radiation therapy, the respiratory motion of the lung introduces variabilities during treatment as the tumor inside the lung is moving, which brings challenges to the precise delivery of radiation to the tumor. Several approaches to quantifying this uncertainty propose using a model to formulate the motion through a mathematical function over time. [Li et al., 2011] uses principal component analysis (PCA) to propose one such model using each image as a long vector. However, the images come in a multidimensional arrays, and vectorization breaks the spatial structure. Driven by the needs to develop low-rank tensor decomposition and provided the 4DCT and Displacement Vector Field (DVF), we introduce two tensor decompositions, Population Value Decomposition (PVD) and Population Tucker Decomposition (PTD), to estimate the respiratory lung motion with high levels of accuracy and data compression. The first algorithm is a generalization of PVD [Crainiceanu et al., 2011] to higher order tensor. The second algorithm generalizes the concept of PVD using Tucker decomposition. Both algorithms are tested on clinical and phantom DVFs. New metrics for measuring the model performance are developed in our research. Results of the two new algorithms are compared to the result of the PCA algorithm.
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Benger, Werner. "Visualization of general relativistic tensor fields via a fiber bundle data model /." Berlin : Lehmanns Media-LOB.de, 2005. http://deposit.ddb.de/cgi-bin/dokserv?id=2669729&prov=M&dok_var=1&dok_ext=htm.
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Zniyed, Yassine. "Breaking the curse of dimensionality based on tensor train : models and algorithms." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS330.
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Le traitement des données massives, communément connu sous l’appellation “Big Data”, constitue l’un des principaux défis scientifiques de la communauté STIC.Plusieurs domaines, à savoir économique, industriel ou scientifique, produisent des données hétérogènes acquises selon des protocoles technologiques multi-modales. Traiter indépendamment chaque ensemble de données mesurées est clairement une approche réductrice et insatisfaisante. En faisant cela, des “relations cachées” ou des inter-corrélations entre les données peuvent être totalement ignorées.Les représentations tensorielles ont reçu une attention particulière dans ce sens en raison de leur capacité à extraire de données hétérogènes et volumineuses une information physiquement interprétable confinée à un sous-espace de dimension réduite. Dans ce cas, les données peuvent être organisées selon un tableau à D dimensions, aussi appelé tenseur d’ordre D.Dans ce contexte, le but de ce travail et que certaines propriétés soient présentes : (i) avoir des algorithmes de factorisation stables (ne souffrant pas de probème de convergence), (ii) avoir un faible coût de stockage (c’est-à-dire que le nombre de paramètres libres doit être linéaire en D), et (iii) avoir un formalisme sous forme de graphe permettant une visualisation mentale simple mais rigoureuse des décompositions tensorielles de tenseurs d’ordre élevé, soit pour D > 3.Par conséquent, nous nous appuyons sur la décomposition en train de tenseurs (TT) pour élaborer de nouveaux algorithmes de factorisation TT, et des nouvelles équivalences en termes de modélisation tensorielle, permettant une nouvelle stratégie de réduction de dimensionnalité et d'optimisation de critère des moindres carrés couplés pour l'estimation des paramètres d'intérêts nommé JIRAFE.Ces travaux d'ordre méthodologique ont eu des applications dans le contexte de l'analyse spectrale multidimensionelle et des systèmes de télécommunications à relaisMassive and heterogeneous data processing and analysis have been clearly identified by the scientific community as key problems in several application areas. It was popularized under the generic terms of "data science" or "big data". Processing large volumes of data, extracting their hidden patterns, while preforming prediction and inference tasks has become crucial in economy, industry and science.Treating independently each set of measured data is clearly a reductiveapproach. By doing that, "hidden relationships" or inter-correlations between thedatasets may be totally missed. Tensor decompositions have received a particular attention recently due to their capability to handle a variety of mining tasks applied to massive datasets, being a pertinent framework taking into account the heterogeneity and multi-modality of the data. In this case, data can be arranged as a D-dimensional array, also referred to as a D-order tensor.In this context, the purpose of this work is that the following properties are present: (i) having a stable factorization algorithms (not suffering from convergence problems), (ii) having a low storage cost (i.e., the number of free parameters must be linear in D), and (iii) having a formalism in the form of a graph allowing a simple but rigorous mental visualization of tensor decompositions of tensors of high order, i.e., for D> 3.Therefore, we rely on the tensor train decomposition (TT) to develop new TT factorization algorithms, and new equivalences in terms of tensor modeling, allowing a new strategy of dimensionality reduction and criterion optimization of coupled least squares for the estimation of parameters named JIRAFE.This methodological work has had applications in the context of multidimensional spectral analysis and relay telecommunications systems
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Gong, Xue. "Dynamical Systems in Cell Division Cycle, Winnerless Competition Models, and Tensor Approximations." Ohio University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1458303716.
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Arciniega, Aleman Roman Augusto. "On a tensor-based finite element model for the analysis of shell structures." Texas A&M University, 2005. http://hdl.handle.net/1969.1/3156.
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In the present study, we propose a computational model for the linear and nonlinear
analysis of shell structures. We consider a tensor-based finite element formulation which
describes the mathematical shell model in a natural and simple way by using curvilinear
coordinates. To avoid membrane and shear locking we develop a family of high-order
elements with Lagrangian interpolations.
The approach is first applied to linear deformations based on a novel and consistent
third-order shear deformation shell theory for bending of composite shells. No
simplification other than the assumption of linear elastic material is made in the
computation of stress resultants and material stiffness coefficients. They are integrated
numerically without any approximation in the shifter. Therefore, the formulation is valid
for thin and thick shells. A conforming high-order element was derived with 0 C
continuity across the element boundaries.
Next, we extend the formulation for the geometrically nonlinear analysis of
multilayered composites and functionally graded shells. Again, Lagrangian elements
with high-order interpolation polynomials are employed. The flexibility of these
elements mitigates any locking problems. A first-order shell theory with seven
parameters is derived with exact nonlinear deformations and under the framework of the Lagrangian description. This approach takes into account thickness changes and,
therefore, 3D constitutive equations are utilized. Finally, extensive numerical
simulations and comparisons of the present results with those found in the literature for
typical benchmark problems involving isotropic and laminated composites, as well as
functionally graded shells, are found to be excellent and show the validity of the
developed finite element model. Moreover, the simplicity of this approach makes it
attractive for future applications in different topics of research, such as contact
mechanics, damage propagation and viscoelastic behavior of shells.
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Giesbrecht, Eugenie [Verfasser], and R. [Akademischer Betreuer] Studer. "Distributional Tensor Space Model of Natural Language Semantics / Eugenie Giesbrecht. Betreuer: R. Studer." Karlsruhe : KIT-Bibliothek, 2014. http://d-nb.info/1064003044/34.
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Mohamed, Shakir. "Generalised Bayesian matrix factorisation models." Thesis, University of Cambridge, 2011. https://www.repository.cam.ac.uk/handle/1810/237246.
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Factor analysis and related models for probabilistic matrix factorisation are of central importance to the unsupervised analysis of data, with a colourful history more than a century long. Probabilistic models for matrix factorisation allow us to explore the underlying structure in data, and have relevance in a vast number of application areas including collaborative filtering, source separation, missing data imputation, gene expression analysis, information retrieval, computational finance and computer vision, amongst others. This thesis develops generalisations of matrix factorisation models that advance our understanding and enhance the applicability of this important class of models. The generalisation of models for matrix factorisation focuses on three concerns: widening the applicability of latent variable models to the diverse types of data that are currently available; considering alternative structural forms in the underlying representations that are inferred; and including higher order data structures into the matrix factorisation framework. These three issues reflect the reality of modern data analysis and we develop new models that allow for a principled exploration and use of data in these settings. We place emphasis on Bayesian approaches to learning and the advantages that come with the Bayesian methodology. Our port of departure is a generalisation of latent variable models to members of the exponential family of distributions. This generalisation allows for the analysis of data that may be real-valued, binary, counts, non-negative or a heterogeneous set of these data types. The model unifies various existing models and constructs for unsupervised settings, the complementary framework to the generalised linear models in regression. Moving to structural considerations, we develop Bayesian methods for learning sparse latent representations. We define ideas of weakly and strongly sparse vectors and investigate the classes of prior distributions that give rise to these forms of sparsity, namely the scale-mixture of Gaussians and the spike-and-slab distribution. Based on these sparsity favouring priors, we develop and compare methods for sparse matrix factorisation and present the first comparison of these sparse learning approaches. As a second structural consideration, we develop models with the ability to generate correlated binary vectors. Moment-matching is used to allow binary data with specified correlation to be generated, based on dichotomisation of the Gaussian distribution. We then develop a novel and simple method for binary PCA based on Gaussian dichotomisation. The third generalisation considers the extension of matrix factorisation models to multi-dimensional arrays of data that are increasingly prevalent. We develop the first Bayesian model for non-negative tensor factorisation and explore the relationship between this model and the previously described models for matrix factorisation.
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Delporte, Nicolas. "Tensor Field Theories : Renormalization and Random Geometry." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASP011.
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Cette thèse se scinde en deux volets, avec vue sur la renormalisation de théorie quantique des champs.Le premier volet traite de trois modèles tensoriels en trois dimensions, un quartique fermionique de rang 3 et deux sextiques bosonique, de rangs 3 et 5. On se base sur l'expansion melonique à grand N des théories tensorielles. Pour le premier modèle, invariant sous le groupe U(N)³, on calcule le flot du groupe de renormalisation des deux couplages meloniques et on dresse le diagramme des phases du vide de la théorie, en étudiant sa reformulation par un champ intermédiaire matriciel diagonalisable. Observant une brisure spontanée de la symétrie discrète chirale, la comparaison avec le modèle de Gross-Neveu tri-dimensionel est faite. Au-delà de la phase symétrique U(N)³ sans masse, on note aussi une phase massive de même symétrie et une autre où la symétrie est brisée vers U(N²) x U(N/2) x U(N/2). Un modèle matriciel de symétrie U(N) x U(N²), présentant les mêmes caractéristiques, est aussi considéré.Dans les deux autres modèles tensoriels, de groupes de symétrie U(N)³ et O(N)⁵, un couplage non-melonique (la ``roue") adjoint d'une puissance de N optimale nous conduit à une expansion melonique généralisée. Les termes cinétiques sont pris de courte ou longue portée et on étudie, à grand N, perturbativement les différents groupes de renormalisation des couplages d'ordre 6, jusqu'à quatre boucles. Tandis que le modèle de rang 5 ne présente pas de point fixe non-trivial, celui de rang 3 possède deux points fixes non-triviaux réels de type Wilson-Fisher dans le cas à courte portée et une ligne de points fixes dans l'autre. On obtient enfin les dimensions conformes réelles des opérateurs primaires bilinéaires en le champ fondamental.Le second volet établit les premiers résultats de renormalisation constructive multi-échelle pour un modèle scalaire quartique sur des arbres de Galton-Watson critiques, avec un terme cinétique à longue portée. Au point critique, l'émergence d'une spine infinie fournit un espace de dimension effective 4/3 sur lequel calculer des fonctions de corrélations moyennées. Cela formalise la notion de théorie des champs sur une géométrie aléatoire. Nous utilisons dans notre approche des bornes probabilistes sur le noyau de la chaleur dans un graphe aléatoire. On esquisse pour terminer l'extension du formalisme à des fermions et à une spine compactifiéeThis thesis divides into two parts, focusing on the renormalization of quantum field theories. The first part considers three tensor models in three dimensions, a fermionic quartic with tensors of rank-3 and two bosonic sextic, of ranks 3 and 5. We rely upon the large-N melonic expansion of tensor models. For the first model, invariant under U(N)³, we compute the renormalization group flow of the two melonic couplings and establish the vacuum phase diagram, from a reformulation with a diagonalizable matrix intermediate field. Noting a spontaneous symmetry breaking of the discrete chiral symmetry, the comparison with the three-dimensional Gross-Neveu model is made. Beyond the massless U(N)³ symmetric phase, we also observe a massive phase of same symmetry and another where the symmetry breaks into U(N²) x U(N/2) x U(N/2). A matrix model invariant under U(N) x U(N²), sharing the same properties, is also studied.For the two other tensor models, with symmetry groups U(N)³ and O(N)⁵, a non-melonic coupling (the ``wheel") with an optimal scaling in N drives us to a generalized melonic expansion. The kinetic terms are taken of short and long range, and we analyze perturbatively, at large-N, the renormalization group flows of the sextic couplings up to four loops. While the rank-5 model doesn't present any non-trivial fixed point, that of rank 3 displays two real non-trivial Wilson-Fisher fixed points in the short-range case and a line of fixed points in the other. We finally obtain the real conformal dimensions of the primary operators bilinear in the fundamental field.In the second part, we establish the first results of constructive multi-scale renormalization for a quartic scalar field on critical Galton-Watson trees, with a long-range kinetic term. At the critical point, an emergent infinite spine provides a space of effective dimension 4/3 on which to compute averaged correlation fonctions. This approach formalizes the notion of a quantum field theory on a random geometry. We use known probabilistic bounds on the heat-kernel on a random graph. At the end, we sketch the extension of the formalism to fermions and to a compactified spine
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Nunez, Ian Louis. "Centrifuge model tension piles in clay." Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.316783.
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Piatkowski, Jakub Przemyslaw. "Probing the brain's white matter with diffusion MRI and a tissue dependent diffusion model." Thesis, University of Edinburgh, 2014. http://hdl.handle.net/1842/8850.
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While diffusion MRI promises an insight into white matter microstructure in vivo, the axonal pathways that connect different brain regions together can only partially be segmented using current methods. Here we present a novel method for estimating the tissue composition of each voxel in the brain from diffusion MRI data, thereby providing a foundation for computing the volume of different pathways in both health and disease. With the tissue dependent diffusion model described in this thesis, white matter is segmented by removing the ambiguity caused by the isotropic partial volumes: both grey matter and cerebrospinal fluid. Apart from the volume fractions of all three tissue types, we also obtain estimates of fibre orientations for tractography as well as diffusivity and anisotropy parameters which serve as proxy indices of pathway coherence. We assume Gaussian diffusion of water molecules for each tissue type. The resulting three-tensor model comprises one anisotropic (white matter) compartment modelled by a cylindrical tensor and two isotropic compartments (grey matter and cerebrospinal fluid). We model the measurement noise using a Rice distribution. Markov chain Monte Carlo sampling techniques are used to estimate posterior distributions over the model’s parameters. In particular, we employ a Metropolis Hastings sampler with a custom burn-in and proposal adaptation to ensure good mixing and efficient exploration of the high-probability region. This way we obtain not only point estimates of quantities of interest, but also a measure of their uncertainty (posterior variance). The model is evaluated on synthetic data and brain images: we observe that the volume maps produced with our method show plausible and well delineated structures for all three tissue types. Estimated white matter fibre orientations also agree with known anatomy and align well with those obtained using current methods. Importantly, we are able to disambiguate the volume and anisotropy information thus alleviating partial volume effects and providing measures superior to the currently ubiquitous fractional anisotropy. These improved measures are then applied to study brain differences in a cohort of healthy volunteers aged 25-65 years. Lastly, we explore the possibility of using prior knowledge of the spatial variability of our parameters in the brain to further improve the estimation by pooling information among neighbouring voxels.
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Stamile, Claudio. "Unsupervised Models for White Matter Fiber-Bundles Analysis in Multiple Sclerosis." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE1147/document.
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L’imagerie de résonance magnétique de diffusion (dMRI) est une technique très sensible pour la tractographie des fibres de substance blanche et la caractérisation de l’intégrité et de la connectivité axonale. A travers la mesure des mouvements des molécules d’eau dans les trois dimensions de l’espace, il est possible de reconstruire des cartes paramétriques reflétant l’organisation tissulaire. Parmi ces cartes, la fraction d’anisotropie (FA) et les diffusivités axiale (λa), radiale (λr) et moyenne (MD) ont été largement utilisés pour caractériser les pathologies du système nerveux central. L’emploi de ces cartes paramétriques a permis de mettre en évidence la survenue d’altérations micro structurelles de la substance blanche (SB) et de la substance grise (SG) chez les patients atteints d’une sclérose en plaques (SEP). Cependant, il reste à déterminer l’origine de ces altérations qui peuvent résulter de processus globaux comme la cascade inflammatoire et les mécanismes neurodégénératifs ou de processus plus localisés comme la démyélinisation et l’inflammation. De plus, ces processus pathologiques peuvent survenir le long de faisceaux de SB afférents ou efférents, conduisant à une dégénérescence antero- ou rétrograde. Ainsi, pour une meilleure compréhension des processus pathologiques et de leur progression dans l’espace et dans le temps, une caractérisation fine et précise des faisceaux de SB est nécessaire. En couplant l’information spatiale de la tractographie des fibres aux cartes paramétriques de diffusion, obtenues grâce à un protocole d’acquisitions longitudinal, les profils des faisceaux de SB peuvent être modélisés et analysés. Une telle analyse des faisceaux de SB peut être effectuée grâce à différentes méthodes, partiellement ou totalement non-supervisées. Dans la première partie de ce travail, nous dressons l’état de l’art des études déjà présentes dans la littérature. Cet état de l’art se focalisera sur les études montrant les effets de la SEP sur les faisceaux de SB grâce à l’emploi de l’imagerie de tenseur de diffusion. Dans la seconde partie de ce travail, nous introduisons deux nouvelles méthodes,“string-based”, l’une semi-supervisée et l’autre non-supervisée, pour extraire les faisceaux de SB. Nous montrons comment ces algorithmes permettent d’améliorer l’extraction de faisceaux spécifiques comparé aux approches déjà présentes dans la littérature. De plus, dans un second chapitre, nous montrons une extension de la méthode proposée par le couplage du formalisme “string-based” aux informations spatiales des faisceaux de SB. Dans la troisième et dernière partie de ce travail, nous décrivons trois algorithmes automatiques permettant l’analyse des changements longitudinaux le long des faisceaux de SB chez des patients atteints d’une SEP. Ces méthodes sont basées respectivement sur un modèle de mélange Gaussien, la factorisation de matrices non-négatives et la factorisation de tenseurs non-négatifs. De plus, pour valider nos méthodes, nous introduisons un nouveau modèle pour simuler des changements longitudinaux réels, base sur une fonction de probabilité Gaussienne généralisée. Des hautes performances ont été obtenues avec ces algorithmes dans la détection de changements longitudinaux d’amplitude faible le long des faisceaux de SB chez des patients atteints de SEP. En conclusion, nous avons proposé dans ce travail des nouveaux algorithmes non supervisés pour une analyse précise des faisceaux de SB, permettant une meilleure caractérisation des altérations pathologiques survenant chez les patients atteints de SEPDiffusion Magnetic Resonance Imaging (dMRI) is a meaningful technique for white matter (WM) fiber-tracking and microstructural characterization of axonal/neuronal integrity and connectivity. By measuring water molecules motion in the three directions of space, numerous parametric maps can be reconstructed. Among these, fractional anisotropy (FA), mean diffusivity (MD), and axial (λa) and radial (λr) diffusivities have extensively been used to investigate brain diseases. Overall, these findings demonstrated that WM and grey matter (GM) tissues are subjected to numerous microstructural alterations in multiple sclerosis (MS). However, it remains unclear whether these tissue alterations result from global processes, such as inflammatory cascades and/or neurodegenerative mechanisms, or local inflammatory and/or demyelinating lesions. Furthermore, these pathological events may occur along afferent or efferent WM fiber pathways, leading to antero- or retrograde degeneration. Thus, for a better understanding of MS pathological processes like its spatial and temporal progression, an accurate and sensitive characterization of WM fibers along their pathways is needed. By merging the spatial information of fiber tracking with the diffusion metrics derived obtained from longitudinal acquisitions, WM fiber-bundles could be modeled and analyzed along their profile. Such signal analysis of WM fibers can be performed by several methods providing either semi- or fully unsupervised solutions. In the first part of this work, we will give an overview of the studies already present in literature and we will focus our analysis on studies showing the interest of dMRI for WM characterization in MS. In the second part, we will introduce two new string-based methods, one semi-supervised and one unsupervised, to extract specific WM fiber-bundles. We will show how these algorithms allow to improve extraction of specific fiber-bundles compared to the approaches already present in literature. Moreover, in the second chapter, we will show an extension of the proposed method by coupling the string-based formalism with the spatial information of the fiber-tracks. In the third, and last part, we will describe, in order of complexity, three different fully automated algorithms to perform analysis of longitudinal changes visible along WM fiber-bundles in MS patients. These methods are based on Gaussian mixture model, nonnegative matrix and tensor factorisation respectively. Moreover, in order to validate our methods, we introduce a new model to simulate real longitudinal changes based on a generalised Gaussian probability density function. For those algorithms high levels of performances were obtained for the detection of small longitudinal changes along the WM fiber-bundles in MS patients. In conclusion, we propose, in this work, a new set of unsupervised algorithms to perform a sensitivity analysis of WM fiber bundle that would be useful for the characterisation of pathological alterations occurring in MS patients
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Nogueira, Pedro Henrique Fusco. "Modelos para partículas massivas de spin-2 via tensor simétrico." Universidade Estadual Paulista (UNESP), 2018. http://hdl.handle.net/11449/152896.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Neste trabalho buscamos encontrar a teoria mais geral para partículas massivas de spin-2 via tensor simétrico. Começamos expondo o caminho que seguiremos para calcular a amplitude de dois pontos saturada por fontes e obter o conteúdo físico de uma dada teoria livre. Como primeira tentativa partimos de uma teoria semelhante a teoria de Fierz-Pauli, mas com termo de massa generalizado. Após isto exploramos uma densidade lagrangiana mais geral, com no máximo duas derivadas. Em ambos os casos retornamos a teoria de Fierz-Pauli como a única viável. Em busca de maior generalidade, posteriormente, propomos uma densidade lagrangiana com coeficientes arbitrários e com potência arbitrária nas derivadas, relacionamos os coeficientes desta teoria com os coeficientes da densidade lagrangiana encontrada anteriormente na literatura via imersão de Euler das equações de Fierz Pauli, o propósito foi verificar se existe uma teoria mais geral que esta última. Por último, a fim de complementar o assunto tratado neste trabalho, verificaremos as consequências de uma dada simetria local no conteúdo físico de uma teoria, de spin-2 massiva.
In this project we seek to find the most general theory for massive particles of spin-2 through symmetric tensor. We begin by the path we will follow to calculate the amplitude of two points, saturated by sources, and obtain physical contente of a free theory. As first attempt, we started with a theory similar to the Fierz-Pauli’s theory, but with a generalized mass term. After this we explored a more general Lagrangian density, with two derivatives in the most. In both cases we return to the Fierz-Pauli’s theory as the only viable one. In search of a greater generality, we later propoused a Lafrangian density with arbitrary coefficients and arbitrary power in the derivatives. We related the coefficients of this theory with the Lagrangian density’s coefficients found previously in the literature through imersão de Euler of the Fierz-Pauli’s equations. The purpose was to verify if there is a more general theory than this last one. Finally, in order to complemente the subject discussed in this paper, we will verify the consequences of a certain local symmetry on the physical contente of a massive spin-2 theory
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Sokolov, Aleksandr. "Tension stiffening model for reinforced concrete beams." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2010. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2010~D_20100803_110628-45999.
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Modelling behaviour of cracked tensile concrete is a complicated issue. Due to bond with reinforcement, the cracked concrete between cracks carries a certain amount of tensile force normal to the cracked plane. Concrete adheres to rein-forcement bars and contributes to overall stiffness of the structure. The phe-nomenon, called tension-stiffening, has significant influence on the results of short-term deformational analysis. Assumption of a tension-stiffening law has great influence on numerical results of load – deflection behaviour of reinforced concrete members subjected to short – term loading. Under wrong assumption of this law, errors in calculated deflections, particularly for lightly members, may exceed 100 %. Most known tension-stiffening relationships relate average stresses to average strains. However, some experimental and theoretical investi-gations have shown that tension-stiffening may be affected by other parameters. The scientific supervisor of the thesis has proposed a tension-stiffening model depending on reinforcement ratio. This model has been developed using experi-mental data reported in the literature. Besides, concrete shrinkage effect was not taken into account. The main objective of this PhD dissertation is to propose a tension-stiffening law for bending RC members subjected to short-term loading with eliminated concrete shrinkage effect.Gelžbetonis yra kompozitinė medžiaga, kurios komponentai yra betonas ir plieninė armatūra. Kaip žinoma, betono stipris tempiant yra 10-20 kartų mažesnis nei stipris gniuždant. Atrodytų, kad tempiamojo betono įtaka, atlaikant įrąžas skerspjūvyje, yra nereikšminga. Iš tiesų, nustatant lenkiamųjų elementų stiprumą normaliniame pjūvyje, tempiamo betono įtempių galima nevertinti. Kita vertus, skaičiuojant įlinkius, neįvertinus tempiamojo betono įtakos, gali būti daroma didesnė nei 100 % paklaida. Adekvatus supleišėjusio tempiamojo betono įtakos įvertinimas, nustatant trumpalaike apkrova veikiamų gelžbetoninių elementų deformacijas, yra bene svarbiausia ir sudėtingiausia problema. Plyšio vietoje betonas negali atlaikyti tempimo įtempių, todėl visą įrąžą atlaiko armatūra. Kadangi plyšyje ir gretimuose pjūviuose armatūra praslysta betono atžvilgiu, kontakto zonoje atsiranda tangentiniai įtempiai. Šie įtempiai perduodami betonui, todėl jis atlaiko tempimo įtempius. Armatūros ir betono sąveika ruožuose tarp plyšių standina gelžbetoninį elementą. Supleišėjusio betono gebėjimas atlaikyti tempimo įtempius vadinama tempimo sustandėjimu (angl. tension stiffening). Šis efektas dažniausiai modeliuojamas supleišėjusio betono įtempių ir deformacijų diagrama, taikant vidutinių plyšių koncepciją. Tuomet neatsižvelgiama į diskrečius plyšius, o supleišėjęs betonas traktuojamas kaip ortotropinė medžiaga su pakitusiomis savybėmis. Dauguma tempimo sustandėjimo modelių įvertina betono įtempių... [toliau žr. visą tekstą]
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Farbood, Morwaread Mary. "A quantitative, parametric model of musical tension." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/34182.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts and Sciences, 2006.Includes bibliographical references (leaves [125]-132).
This thesis presents a quantitative, parametric model for describing musical tension. While the phenomenon of tension is evident to listeners, it is difficult to formalize due to its subjective and multi-dimensional nature. The model is therefore derived from empirical data. Two experiments with contrasting approaches are described. The first experiment is an online test with short musical excerpts and multiple choice answers. The format of the test makes it possible to gather large amounts of data. The second study requires fewer subjects and collects real-time responses to musical stimuli. Both studies present test subjects with examples that take into account a number of musical parameters including harmony, pitch height, melodic expectation, dynamics, onset frequency, tempo, and rhythmic regularity. The goal of the first experiment is to confirm that the individual musical parameters contribute directly to the listener's overall perception of tension. The goal of the second experiment is to explore linear and nonlinear models for predicting tension given descriptions of the musical parameters for each excerpt. The resulting model is considered for potential incorporation into computer-based applications. Specifically, it could be used as part of a computer-assisted composition environment. One such application, Hyperscore, is described and presented as a possible platform for integration.
by Morwaread M. Farbood.
Ph.D.
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Palli, Gianluca <1977>. "Model and control of tendon actuated robots." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2007. http://amsdottorato.unibo.it/341/.
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The use of tendons for the transmission of the forces and the movements in robotic devices
has been investigated from several researchers all over the world. The interest in
this kind of actuation modality is based on the possibility of optimizing the position of
the actuators with respect to the moving part of the robot, in the reduced weight, high reliability,
simplicity in the mechanic design and, finally, in the reduced cost of the resulting
kinematic chain.
After a brief discussion about the benefits that the use of tendons can introduce in
the motion control of a robotic device, the design and control aspects of the UB Hand 3
anthropomorphic robotic hand are presented. In particular, the tendon-sheaths transmission
system adopted in the UB Hand 3 is analyzed and the problem of force control and
friction compensation is taken into account.
The implementation of a tendon based antagonistic actuated robotic arm is then investigated.
With this kind of actuation modality, and by using transmission elements with
nonlinear force/compression characteristic, it is possible to achieve simultaneous stiffness
and position control, improving in this way the safety of the device during the operation
in unknown environments and in the case of interaction with other robots or with humans.
The problem of modeling and control of this type of robotic devices is then considered
and the stability analysis of proposed controller is reported.
At the end, some tools for the realtime simulation of dynamic systems are presented.
This realtime simulation environment has been developed with the aim of improving the
reliability of the realtime control applications both for rapid prototyping of controllers
and as teaching tools for the automatic control courses.
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Umiltà, Caterina. "Cosmological predictions for a scalar tensor dark energy model by a dedicated Einstein-Boltzmann code." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/6580/.
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Donner, Stefanie, Manfred Strecker, Dirk Rößler, Abdolreza Ghods, Frank Krüger, Angela Landgraf, and Paolo Ballato. "Earthquake source models for earthquakes in Northern Iran." Universität Potsdam, 2009. http://opus.kobv.de/ubp/volltexte/2009/3258/.
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The complex system of strike-slip and thrust faults in the Alborz Mountains, Northern Iran, are not well understood yet. Mainly structural and geomorphic data are available so far. As a more extensive base for seismotectonic studies and seismic hazard analysis we plan to do a comprehensive seismic moment tensor study also from smaller magnitudes (M < 4.5) by developing a new algorithm. Here, we present first preliminary results.
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Balaji, R. "Collisions of tension leg platforms with ships." Thesis, University of Southampton, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.380192.
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Jenkyn, Thomas Richard. "Biomechanics of the ankle joint complex using a muscle model assisted optimisation model." Thesis, University of Strathclyde, 2001. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=21444.
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A seven segment model of the right leg and foot was developed with segments: thigh, lower leg, talus, hindfoot, midfoot and lateral and medial forefoot. Three-dimensional mapping of internal structures was made from CT scans and anatomical photographs (Visible Human Project). Twelve healthy subjects performed level walking and medial walking turns at slow, preferred and fast speed. Equilibrium about the two joints of the ankle complex (ankle and subtalar), was solved using Muscle Model Assisted Optimisation (MMAO). A three component, Hill-type muscle model determined tensions in eight muscles of the lower leg using EMG. Linear optimisation then corrected muscle tensions and solved for ligament tensions and articular surface compression. MMAO was successful in modeling ankle complex equilibrium during walking and walking turn. External forces acting on the right foot were similar for all subjects. Despite similar external loading, subjects employed different muscle tension strategies to produce equilibrium about the ankle and subtalar joints. For all subjects, triceps surae muscle tensions were largest. Peak tension in achilles tendon was 7.9xBW during walking and 8.0xBW during walking turn. The two heads of gastrocnernius behaved as distinct muscles performing different roles during stance. Peroneus brevis produced movement about the subtalar joint while peroneus longus had a stabilising role. The dorsi-flexors were significantly active during stance phase, antagonistic to triceps surae muscle group. This antagonism has not been predicted by previous models. Ligaments acted in an all-or-nothing manner when constraining the ankle complex. Ligaments were either slack or tensed at constant tension. Maximum ligament tension was 1.75xBW in the lateral ligaments of the ankle joint during walking turn. No difference between the walking and walking turn was seen in compressive loading of articular surfaces. Maximum compression of ankle joint was 10.0xBW and of subtalar joint was 8.0xBW.
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Mickel, Walter. "Geometry controlled phase behavior in nanowetting and jamming." Phd thesis, Université Claude Bernard - Lyon I, 2011. http://tel.archives-ouvertes.fr/tel-00868861.
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This thesis is devoted to several aspects of geometry and morphology in wetting problems and hard sphere packings. First, we propose a new method to simulate wetting and slip on nanostructured substrates: a phase field model associated with a dynamical density theory approach. We showed omniphobicity, meaning repellency, no matter the chemical properties of the liquid on monovalued surfaces, i.e. surfaces without overhangs, which is in contradiction with the macroscopic Cassie-Baxter-Wenzel theory, can produce so-called We checked systematically the impact of the surface parameters on omniphobic repellency, and we show that the key ingredient are line tensions, which emerge from needle shaped surface structures. Geometrical effects have also an important influence on glassy or jammed systems, for example amorphous hard sphere systems in infinite pressure limit. Such hard sphere packings got stuck in a so-called jammed phase, and we shall demonstrate that the local structure in such systems is universal, i.e. independent of the protocol of the generation. For this, robust order parameters - so-called Minkowski tensors - are developed, which overcome robustness deficiencies of widely used order parameters. This leads to a unifying picture of local order parameters, based on geometrical principles. Furthermore, we find with the Minkowski tensor analysis crystallization in jammed sphere packs at the random closed packing point
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Wang, Silun, and 王思倫. "Diffusion tensor MR imaging as a biomarker for the evaluation of whitematter injury in rodent models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B43085416.
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Bsoul, Mohammad. "Economic scheduling in Grid computing using Tender models." Thesis, Loughborough University, 2007. https://dspace.lboro.ac.uk/2134/3094.
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Economic scheduling needs to be considered for Grid computing environment, because it gives an incentive for resource providers to supply their resources. Moreover, it enforces efficient use of resources, because the users have to pay for their use. Tendering is a suitable model for Grid scheduling because users start the negotiations for finding suitable resources for executing their jobs. Furthermore, the users specify their job requirements with their requests and therefore the resources reply with bids that are based on the cost of taking on the job and the availability of their processors. In this thesis, a framework for economic Grid scheduling using tendering is proposed. The framework entities such as users, brokers and resources employ tender/contract-net model to negotiate the prices and deadlines. The brokers' role is acting on behalf of users. During the negotiations, the entities aim to maximise their performance which is measured by a number of metrics. In order to evaluate the entities' performance under different scenarios, a Java- based simulator, called MICOSim, supporting event-driven simulation of economic Grid scheduling is presented. MICOSim can perform a simulation of more than one hundred entities faster than real time. It is concluded from the evaluation that users who are interested in increasing the job success rate and paying less for executing their jobs have to consider received prices to select the most appropriate bids, while users who are interested in improving the job average satisfaction rate have to consider either received completion time or both price and completion time to select the most suitable bids when the submission of jobs is static. The best broker strategy is the one that doesn't take into account meeting the job deadlines in the bids it sends to job owners. Finally, the resource strategy that considers the price to determine if to reply to a request or not is superior to other resource strategies. The only exception is employing this strategy with price that is too low. However, there is a tiny difference between the performances of different user strategies in dynamic submission. It is also concluded from the evaluation that broker strategies have the best performance when the revenue they target from the users is reasonable. Thus, the broker's aim has to be receiving reasonable revenue (neither too low nor too high) from acting on behalf of users. It is observed from the results that the strategy performance is influenced by the behaviour of other entities such as the submission time of user jobs. Finally, it is observed that the characteristics of entities have an effect on the performance of strategies. For example, the two user strategies that consider the received completion time and both price and completion time to determine if to accept a broker bid have similar performance, because of the existence of resources with various prices from cheap to expensive and existence of resources which don't care about the price paid for the execution. So, the price threshold doesn't have a large effect on the performance.
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JUNCOSA, LAURA NATALIA. "DESIGN PARAMETERS FOR TISSUE ENGINEERED IMPLANTS FOR RABBIT PATELLAR TENDON AND ACHILLES TENDON REPAIRS." University of Cincinnati / OhioLINK, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1022080022.
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Hamilton, Nicholas Michael. "Anisotropy of the Reynolds Stress Tensor in the Wakes of Counter-Rotating Wind Turbine Arrays." PDXScholar, 2014. https://pdxscholar.library.pdx.edu/open_access_etds/1848.
Full textAbstract:
A wind turbine array was constructed in the wind tunnel at Portland State University in a standard Cartesian arrangement. Configurations of the turbine array were tested with rotor blades set to rotate in either a clockwise or counter-clockwise sense. Measurements of velocity were made with stereo particle-image velocimetry. Mean statistics of velocities and Reynolds stresses clearly show the effect of direction of rotation of rotor blades for both entrance and exit row turbines. Rotational sense of the turbine blades is visible in the mean spanwise velocity W and the Reynolds shear stress -[macron over vw]. The normalized anisotropy tensor was decomposed yielding invariants [lowercase eta] and [lowercase xi], which are plotted onto the Lumley triangle. Invariants of the normalized Reynolds stress anisotropy tensor indicate that distinct characters of turbulence exist in regions of the wake following the nacelle and the rotor blade tips. Eigendecomposition of the tensor yields principle components and corresponding coordinate system transformations. Characteristic spheroids are composed with the eigenvalues from the decomposition yielding shapes predicted by the Lumley triangle. Rotation of the coordinate system defined by the eigenvectors demonstrates streamwise trends, especially trailing the top rotor tip and below the hub of the rotors. Direction of rotation of rotor blades is evidenced in the orientation of characteristic spheroids according to principle axes. The characteristic spheroids of the anisotropy tensor and their relate alignments varies between cases clearly seen in the inflows to exit row turbines. There the normalized Reynolds stress anisotropy tensor shows cumulative effects of the rotational sense of upstream turbines. Comparison between the invariants of the Reynolds stress anisotropy tensor and terms from the mean mechanical energy equation indicate a correlation between the degree of anisotropy and the regions of the wind turbine wakes where turbulence kinetic energy is produced. The flux of kinetic energy into the momentum-deficit area of the wake from above the canopy is associated with prolate characteristic spheroids. Flux upward into the wake from below the rotor area is associate with oblate characteristic spheroids. Turbulence in the region of the flow directly following the nacelle of the wind turbines demonstrates more isotropy compared to the regions following the rotor blades. The power and power coefficients for wind turbines indicate that flow structures on the order of magnitude of the spanwise turbine spacing that increase turbine efficiency depending on particular array configuration.