Dans la première partie de cette thèse, on formule deux méthodes pour le calcul d'une décomposition polyadique canonique avec facteurs matriciels linéairement structurés (tels que des facteurs de Toeplitz ou en bande): un algorithme de moindres carrés alternés contraint (CALS) et une solution algébrique dans le cas où tous les facteurs sont circulants. Des versions exacte et approchée de la première méthode sont étudiées. La deuxième méthode fait appel à la transformée de Fourier multidimensionnelle du tenseur considéré, ce qui conduit à la résolution d'un système d'équations monomiales homogènes. Nos simulations montrent que la combinaison de ces approches fournit un estimateur statistiquement efficace, ce qui reste vrai pour d'autres combinaisons de CALS dans des scénarios impliquant des facteurs non-circulants. La seconde partie de la thèse porte sur la récupération de tenseurs de rang faible et, en particulier, sur le problème de reconstruction tensorielle (TC). On propose un algorithme efficace, noté SeMPIHT, qui emploie des projections séquentiellement optimales par mode comme opérateur de seuillage dur. Une borne de performance est dérivée sous des conditions d'isométrie restreinte habituelles, ce qui fournit des bornes d'échantillonnage sous-optimales. Cependant, nos simulations suggèrent que SeMPIHT obéit à des bornes optimales pour des mesures Gaussiennes. Des heuristiques de sélection du pas et d'augmentation graduelle du rang sont aussi élaborées dans le but d'améliorer sa performance. On propose aussi un schéma d'imputation pour TC basé sur un seuillage doux du coeur du modèle de Tucker et son utilité est illustrée avec des données réelles de trafic routier / In the first part of this thesis, we formulate two methods for computing a canonical polyadic decomposition having linearly structured matrix factors (such as, e.g., Toeplitz or banded factors): a general constrained alternating least squares (CALS) algorithm and an algebraic solution for the case where all factors are circulant. Exact and approximate versions of the former method are studied. The latter method relies on a multidimensional discrete-time Fourier transform of the target tensor, which leads to a system of homogeneous monomial equations whose resolution provides the desired circulant factors. Our simulations show that combining these approaches yields a statistically efficient estimator, which is also true for other combinations of CALS in scenarios involving non-circulant factors. The second part of the thesis concerns low-rank tensor recovery (LRTR) and, in particular, the tensor completion (TC) problem. We propose an efficient algorithm, called SeMPIHT, employing sequentially optimal modal projections as its hard thresholding operator. Then, a performance bound is derived under usual restricted isometry conditions, which however yield suboptimal sampling bounds. Yet, our simulations suggest SeMPIHT obeys optimal sampling bounds for Gaussian measurements. Step size selection and gradual rank increase heuristics are also elaborated in order to improve performance. We also devise an imputation scheme for TC based on soft thresholding of a Tucker model core and illustrate its utility in completing real-world road traffic data acquired by an intelligent transportation

Nous nous intéressons dans cette thèse à certains modèles mathématiques permettant une description de systèmes ouverts classiques et quantiques. Dans l'étude de ces systèmes en interaction avec un environnement, nous montrons que la dynamique induite par l'environnement sur le système donne lieu à l'apparition de bruits. Dans une première partie de la thèse, dédiée aux systèmes classiques, le modèle décrit est le schéma d'interactions répétées. Etant à la fois hamiltonien et markovien, ce modèle en temps discret permet d'implémenter facilement la dissipation dans des systèmes physiques. Nous expliquons comment le mettre en place pour des systèmes physiques avant d'en étudier la limite en temps continu. Nous montrons la convergence Lp et presque sûre de l'évolution de certains systèmes vers la solution d'une équation différentielle stochastique, à travers l'étude de la limite de la perturbation d'un schéma d'Euler stochastique. Dans une seconde partie de la thèse sur les systèmes quantiques, nous nous intéressons dans un premier temps aux actions d'environnements quantiques sur des systèmes quantiques aboutissant à des bruits classiques. A cette fin, nous introduisons certains opérateurs unitaires appelés « classiques », que nous caractérisons à l'aide de variables aléatoires dites obtuses. Nous mettons en valeur comment ces variables classiques apparaissent naturellement dans ce cadre quantique à travers des 3-tenseurs possédant des symétries particulières. Nous prouvons notamment que ces 3-tenseurs sont exactement ceux diagonalisables dans une base orthonormée. Dans un second temps, nous étudions la limite en temps continu d'une variante des interactions répétées quantiques dans le cas particulier d'un système biparti, c'est-à-dire composé de deux systèmes isolés sans interaction entre eux. Nous montrons qu'à la limite du temps continu, une interaction entre ces sous-systèmes apparaît explicitement sous forme d'un hamiltonien d'interaction; cette interaction résulte de l'action de l'environnement et de l'intrication qu'il crée / This dissertation is dedicated to some mathematical models describing classical and quantum open systems. In the study of these systems interacting with an environment, we particularly show that the dynamics induced by the environment leads to the appearance of noises. In a first part of this thesis, devoted to classical open systems, the repeated interaction scheme is developed. This discrete-time model, being Hamiltonian and Markovian at the same time, has the advantage to easily implement the dissipation in physical systems. We explain how to set this scheme up in some physical examples. Then, we investigate the continuous-time limit of these repeated interactions. We show the Lp and almost sure convergences of the evolution of the system to the solution of a stochastic differential equation, by studying the limit of a perturbed Stochastic Euler Scheme. In a second part of this dissertation on quantum systems, we characterize in a first work classical actions of a quantum environment on a quantum system. In this study, we introduce some “classical” unitary operators representing these actions and we highlight a strong link between them and some random variables, called obtuse random variables. We explain how these random variables are naturally connected to some 3-tensors having some particular symmetries. We particularly show that these 3 tensors are exactly the ones that are diagonalizable in some orthonormal basis. In a second work of this part, we study the continuous-time limit of a variant of the repeated interaction scheme in a case of a bipartite system, that is, a system made of two isolated systems not interaction together. We prove that an explicit Hamiltonian interaction between them appears at the limit. This interaction is due to the action of the environment and the entanglement between the two systems that it creates

<p>Convolutional neural networks (CNNs) have become important workloads due to their<br> impressive accuracy in tasks like image classification and recognition. Convolution operations<br> are compute intensive, and this cost profoundly increases with newer and better CNN models.<br> However, convolutions come with characteristics such as sparsity which can be exploited. In<br> this dissertation, we propose three different works to capture sparsity for faster performance<br> and reduced energy. </p> <p><br></p> <p>The first work is an accelerator design called <em>SparTen</em> for improving two-<br> sided sparsity (i.e, sparsity in both filters and feature maps) convolutions with fine-grained<br> sparsity. <em>SparTen</em> identifies efficient inner join as the key primitive for hardware acceleration<br> of sparse convolution. In addition, <em>SparTen</em> proposes load balancing schemes for higher<br> compute unit utilization. <em>SparTen</em> performs 4.7x, 1.8x and 3x better than dense architecture,<br> one-sided architecture and SCNN, the previous state of the art accelerator. The second work<br> <em>BARISTA</em> scales up SparTen (and SparTen like proposals) to large-scale implementation<br> with as many compute units as recent dense accelerators (e.g., Googles Tensor processing<br> unit) to achieve full speedups afforded by sparsity. However at such large scales, buffering,<br> on-chip bandwidth, and compute utilization are highly intertwined where optimizing for<br> one factor strains another and may invalidate some optimizations proposed in small-scale<br> implementations. <em>BARISTA</em> proposes novel techniques to balance the three factors in large-<br> scale accelerators. <em>BARISTA</em> performs 5.4x, 2.2x, 1.7x and 2.5x better than dense, one-<br> sided, naively scaled two-sided and an iso-area two-sided architecture, respectively. The last<br> work, <em>EUREKA</em> builds an efficient tensor core to execute dense, structured and unstructured<br> sparsity with losing efficiency. <em>EUREKA</em> achieves this by proposing novel techniques to<br> improve compute utilization by slightly tweaking operand stationarity. <em>EUREKA</em> achieves a<br> speedup of 5x, 2.5x, along with 3.2x and 1.7x energy reductions over Dense and structured<br> sparse execution respectively. <em>EUREKA</em> only incurs area and power overheads of 6% and<br> 11.5%, respectively, over Ampere</p>

Optics are a powerful probe of chemical structure that can often be linked to theoretical predictions, providing robustness as a measurement tool. Not only do optical interactions like second harmonic generation (SHG), single and two-photon excited fluorescence (TPEF), and infrared absorption provide chemical specificity at the molecular and macromolecular scale, but the ability to image enables mapping heterogeneous behavior across complex systems such as biological tissue. This thesis will discuss nonlinear and linear optics, leveraging theoretical predictions to provide frameworks for interpreting analytical measurement. In turn, the causal mechanistic understanding provided by these frameworks will enable structurally specific quantitative tools with a special emphasis on application in biological imaging. The thesis will begin with an introduction to 2nd order nonlinear optics and the polarization analysis thereof, covering both the Jones framework for polarization analysis and the design of experiment. Novel experimental architectures aimed at reducing 1/f noise in polarization analysis will be discussed, leveraging both rapid modulation in time through electro-optic modulators (Chapter 2), as well as fixed-optic spatial modulation approaches (Chapter 3). In addition, challenges in polarization-dependent imaging within turbid systems will be addressed with the discussion of a theoretical framework to model SHG occurring from unpolarized light (Chapter 4). The application of this framework to thick tissue imaging for analysis of collagen local structure can provide a method for characterizing changes in tissue morphology associated with some common cancers (Chapter 5). In addition to discussion of nonlinear optical phenomena, a novel mechanism for electric dipole allowed fluorescence-detected circular dichroism will be introduced (Chapter 6). Tackling challenges associated with label-free chemically specific imaging, the construction of a novel infrared hyperspectral microscope for chemical classification in complex mixtures will be presented (Chapter 7). The thesis will conclude with a discussion of the inherent disadvantages in taking the traditional paradigm of modeling and measuring chemistry separately and provide the multi-agent consensus equilibrium (MACE) framework as an alternative to the classic meet-in-the-middle approach (Chapter 8). Spanning topics from pure theoretical descriptions of light-matter interaction to full experimental work, this thesis aims to unify these two fronts. <br>

The present dissertation develops an invariant framework for 3D gesture comparison studies. 3D gesture comparison without Lagrangian models is challenging not only because of the lack of prediction provided by physics, but also because of a dual geometry representation, spatial dimensionality and non-linearity associated to 3D-kinematics. In 3D spaces, it is difficult to compare curves without an alignment operator since it is likely that discrete curves are not synchronized and do not share a common point in space. One has to assume that each and every single trajectory in the space is unique. The common answer is to assert the similitude between two or more trajectories as estimating an average distance error from the aligned curves, provided that the alignment operator is found. In order to avoid the alignment problem, the method uses differential geometry for position and orientation curves. Differential geometry not only reduces the spatial dimensionality but also achieves view invariance. However, the nonlinear signatures may be unbounded or singular. Yet, it is shown that pattern recognition between intrinsic signatures using correlations is robust for position and orientation alike. A new mapping for orientation sequences is introduced in order to treat quaternion and Euclidean intrinsic signatures alike. The new mapping projects a 4D-hyper-sphere for orientations onto a 3D-Euclidean volume. The projection uses the quaternion invariant distance to map rotation sequences into 3D-Euclidean curves. However, quaternion spaces are sectional discrete spaces. The significance is that continuous rotation functions can be only approximated for small angles. Rotation sequences with large angle variations can only be interpolated in discrete sections. The current dissertation introduces two multi-scale approaches that improve numerical stability and bound the signal energy content of the intrinsic signatures. The first is a multilevel least squares curve fitting method similar to Haar wavelet. The second is a geodesic distance anisotropic kernel filter. The methodology testing is carried out on 3D-gestures for obstetrics training. The study quantitatively assess the process of skill acquisition and transfer of manipulating obstetric forceps gestures. The results show that the multi-scale correlations with intrinsic signatures track and evaluate gesture differences between experts and trainees.

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In dieser Arbeit werden das Wachstum mittels Molekularstrahlepitaxie und die Eigenschaften der Ferromagneten Fe und Fe_3Si auf niedrig-symmetirschen GaAs(113)A-Substraten studiert. Drei wichtige Aspekte werden untersucht: (i) Wachstum und strukturelle Charakterisierung, (ii) magnetische Eigenschaften und (iii) Magnetotransporteigenschaften der Fe und Fe_3Si Schichten auf GaAs(113)A-Substraten. Das Wachstum der Fe- und Fe_3Si-Schichten wurde bei einer Wachstumstemperatur von = bzw. 250 °C optimiert. Bei diesen Wachstumstemperaturen zeigen die Schichten eine hohe Kristallperfektion und glatte Grenz- und Oberflächen analog zu [001]-orientierten Schichten. Weiterhin wurde die Stabilität der Fe_(3+x)Si_(1-x) Phase über einen weiten Kompositionsbereich innerhalb der Fe_3Si-Stoichiometry demonstriert. Die Abhängigkeit der magnetischen Anisotropie innerhalb der Schichtebene von der Schichtdicke weist zwei Bereiche auf: einen Beresich mit dominanter uniaxialer Anisotropie für Fe-Schichten = 70 MLs. Weiterhin wird eine magnetische Anisotropie senkrecht zur Schichtebene in sehr dünnen Schichten gefunden. Der Grenzflächenbeitrag sowohl der uniaxialen als auch der senkrechten Anisotropiekonstanten, die aus der Dickenabhängigkeit bestimmt wurden, sind unabhängig von der [113]-Orientierung und eine inhärente Eigenschaft der Fe/GaAs-Grenzfläche. Die anisotrope Bindungskonfiguration zwischen den Fe und den As- oder Ga-Atomen an der Grenzfläche wird als Ursache für die uniaxiale magnetische Anisotropie betrachtet. Die magnetische Anisotropie der Fe_3Si-Schichten auf GaAs(113)A-Substraten zeigt ein komplexe Abhängigkeit von der Wachstumsbedingungen und der Komposition der Schichten. In den Magnetotransportuntersuchungen tritt sowohl in Fe(113)- als auch in Fe_3Si(113)-Schichten eine antisymmetrische Komponente (ASC) im planaren Hall-Effekt (PHE) auf. Ein phänomenologisches Modell, dass auf der Kristallsymmetrie basiert, liefert ein gute Beschreibung sowohl der ASC im PHE als auch des symmetrischen, anisotropen Magnetowiderstandes. Das Modell zeigt, dass die beobachtete ASC als Hall-Effekt zweiter Ordnung beschreiben werden kann. / In this work, the molecular-beam epitaxial growth and properties of ferromagnets, namely Fe and Fe_3Si are studied on low-symmetric GaAs(113)A substrates. Three important aspects are investigated: (i) growth and structural characterization, (ii) magnetic properties, and (iii) magnetotransport properties of Fe and Fe_3Si films on GaAs(113)A substrates. The growth of Fe and Fe_3Si films is optimized at growth temperatures of 0 and 250 degree Celsius, respectively, where the layers exhibit high crystal quality and a smooth interface/surface similar to the [001]-oriented films. The stability of Fe_(3+x)Si_(1-x) phase over a range of composition around the Fe_3Si stoichiometry is also demonstrated. The evolution of the in-plane magnetic anisotropy with film thickness exhibits two regions: a uniaxial magnetic anisotropy (UMA) for Fe film thicknesses = 70 MLs. The existence of an out-of-plane perpendicular magnetic anisotropy is also detected in ultrathin Fe films. The interfacial contribution of both the uniaxial and the perpendicular anisotropy constants, derived from the thickness-dependent study, are found to be independent of the [113] orientation and are hence an inherent property of the Fe/GaAs interface. The origin of the UMA is attributed to anisotropic bonding between Fe and As or Ga at the interface, similarly to Fe/GaAs(001). The magnetic anisotropy in Fe_3Si on GaAs(113)A exhibits a complex dependence on the growth conditions and composition. Magnetotransport measurements of both Fe(113) and Fe_3Si(113) films shows the striking appearance of an antisymmetric component (ASC) in the planar Hall effect (PHE). A phenomenological model based on the symmetry of the crystal provides a good explanation to both the ASC in the PHE as well as the symmetric anisotropic magnetoresistance. The model shows that the observed ASC component can be ascribed to a second-order Hall effect.