Esta tesis aborda la paralelización de los métodos de Krylov con reinicio para problemas de valores propios y valores singulares (SVD). Estos métodos son de naturaleza iterativa y resultan adecuados para encontrar unos pocos valores propios o singulares de problemas dispersos. El procedimiento de ortogonalización suele ser la parte más costosa de este tipo de métodos, por lo que ha recibido especial atención en esta tesis, proponiendo y validando nuevos algoritmos para mejorar sus prestaciones paralelas. La implementación se ha realizado en el marco de la librería SLEPc, que proporciona una interfaz orientada a objetos para la resolución iterativa de problemas de valores propios o singulares. SLEPc está basada en la librería PETSc, que dispone de implementaciones paralelas de métodos iterativos para la resolución de sistemas lineales, precondicionadores, matrices dispersas y vectores. Ambas librerías están optimizadas para su ejecución en máquinas paralelas de memoria distribuida y con problemas dispersos de gran dimensión. Esta implementación incorpora los métodos para valores propios de Arnoldi con reinicio explícito, de Lanczos (incluyendo variantes semiortogonales) con reinicio explícito, y versiones de Krylov-Schur (equivalente al reinicio implícito) para problemas no Hermitianos y Hermitianos (Lanczos con reinicio grueso). Estos métodos comparten una interfaz común, permitiendo su comparación de forma sencilla, característica que no está disponible en otras implementaciones. Las mismas técnicas utilizadas para problemas de valores propios se han adaptado a los métodos de Golub-Kahan-Lanczos con reinicio explícito y grueso para problemas de valores singulares, de los que no existe ninguna otra implementación paralela con paso de mensajes. Cada uno de los métodos se ha validado mediante una batería de pruebas con matrices procedentes de aplicaciones reales. Las prestaciones paralelas se han medido en máquinas tipo cluster, comprobando una buena escalabilidad inc / Tomás Domínguez, A. (2009). Implementación paralela de métodos de Krylov con reinicio para problemas de valores propios y singulares [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/5082 / Palancia

The purpose of this thesis is to implement algorithms of matrix eigendecomposition and pseudoinverse computation on a Field Programmable Gate Array (FPGA) platform. Firstly, there are described matrix decomposition methods that are broadly used in mentioned algorithms. Next section is focused on the basic theory and methods of computation eigenvalues and eigenvectors as well as matrix pseudoinverse. Several examples of implementation using Matlab are attached. The Vivado High-Level Synthesis tools and libraries were used for final implementation. After the brief introduction into the FPGA fundamentals the thesis continues with a description of implemented blocks. The results of each variant were compared in terms of timing and FPGA utilization. The selected block has been validated on the development board and its arithmetic precision was analyzed.

Introduction of this thesis is dedicated to the description of basic concepts and algorithms for image processing using sparse representation. Furthermore there is mentioned neural network model called Restricted Boltzmann machine, which is in the practical part of the thesis subject of behaving observation in the task of determining the optimal block size for extrapolation using K-SVD algorithm

The essence of face recognition within the image is generally computer vision, which provides methods and algorithms for the implementation. Some of them are described just in this work. Whole process is split in to three main phases. These are detection, aligning of detected faces and finally its recognition. Algorithms which are used to applied in given issue and which are still in progress from todays view are mentioned in every phase. Implementation is build up on three main algorithms, AdaBoost to obtain the classifier for detection, method of aligning face by principal features and method of Eigenfaces for recognizing. There are theoretically described except already mentioned algorithms neural networks for detection, ASM - Active Shape Models algorithm for aligning and AAM - Active Appearance Model for recognition. In the end there are tables of data retrieved by implemented system, which evaluated the main implementation.

No description available.

Many capacity and near-capacity achieving methods in multiple-input-multipleoutput (MIMO) wireless channels make use of the singular value decomposition (SVD) of the channel matrix. For the multi-user case, the SVD of the channel matrix for each user may result in right and left singular vectors that are similar between users. This proposes another descriptive characterization of the multi-user MIMO channel. Closely aligned singular vectors between any two users could reduce the achievable signaling rates of signal processing communication methods as one user would be more difficult to resolve in space-time from another. An examination into how this alignment can be described in realistic MIMO multipath channels using a two ring channel model is presented. The effects of correlation between singular vectors on achievable signaling rates is shown for one existing algorithm that approaches the sum capacity known as block-diagonalization. Analyzed is actual data collected in several indoor and outdoor experiments performed using newly constructed measurement hardware that extends the capabilities of an existing MIMO measurement system.

We explore the paradigm shift in quantum computing and quantum information science, emphasizing the synergy between hardware advancements and algorithm development. Only now have the recent advances in quantum computing hardware, despite a century of quantum mechanics, unveiled untapped potential, requiring innovative algorithms for full utilization. Project 1 addresses quantum applications in radiative reactions, overcoming challenges in many-fermion physics due to imaginary time evolution, stochastic methods like Monte Carlo simulations, and the associated sign problem. The methodology introduces the Electromagnetic Transition System and a general two-level system for computing radiative capture reactions. Project 2 utilizes Variational Quantum Eigensolver (VQE) to address the difficulties in adiabatic quantum computations, highlighting Singular Value Decomposition (SVD) in quantum computing. Results demonstrate an accurate ground state wavefunction match with only a 0.016% energy error. These projects advance quantum algorithm design, error mitigation, and SVD integration, showcasing quantum computing’s transformative potential in computational science.

Die Strukturen in Lösung dreier unterschiedlich modifizierter DNA Doppelstränge wurden mittels NMR Spektroskopie gelöst. Sie alle besitzen polare Sonden im Zentrum der Helix, welche sensitiv für die nähere Umgebung sind. Ihr Schmelzverhalten wurde mit Hilfe einer neuen Methode charakterisiert, welche komplette Absorptionsspektren in Kombination mit Singularwertzerlegung (SVD) nutzt. Letztere erlaubt die Analyse der Spektren als Ganzes, die notwendig ist um der Blauverschiebung des Sondensignals zu folgen, welche durch die zuvor genannte Sensitivität zur Umgebung verursacht wird. Auf diese Weise kann der Schmelzprozess des Duplex lokal und global beschrieben werden. Die erste Modifikation, 2-Hydroxy-7-Carboxyfluoren (HCF), wurde gegenüber einer abasischen Seite platziert, um sterische Spannungen zu vermeiden. Die NMR Spektroskopie deckte zwei gleichverteilte Konformationen auf, da die Rotation des HCF Chromophors nur durch die Stapelwechselwirkung innerhalb der Helix unterbunden wird. Der zweite Doppelstrang enthält ein über R-Glycerol gebundenes 6-Hydroxychinolinium (6HQ) gegenüber Cytosin. Der Einbau von 6HQ als Mononukleotid einer Glykolnukleinsäure (GNA) ist ein strukturelles Alleinstellungsmerkmal. Bisher sind nur Kristallstrukturen von vollständiger GNA bekannt, daher ist die Struktur in Lösung dieses Doppelstranges von generellem Interesse. Die geringe Größe von R-Glycerol stört das Rückgrat des 6HQ-Stranges, welche eine von der helikalen Achse abweichende Stapelachse für die drei zentralen Basen verursacht. Die letzte Modifikation ist ein künstliches Basenpaar bestehend aus 4-Aminophthalimid (4AP) und 2,4-Diaminopyrimidin (DAP). Anstatt der gewünschten drei Wasserstoffbrücken wurden zwei Strukturen, die entweder eine oder zwei Wasserstoffbrücken beinhalten, beobachtet, welche durch die Verbindung von 4AP zur 2’-Deoxyribofuranose erklärt werden können. / The solution structures of three differently modified DNA double strands were solved by NMR spectroscopy. They all incorporate polarity probes in the center of the helix that are sensitive to the immediate environment. Their melting behavior was characterized by a new method that utilizes complete absorption spectra in combination with Singular Value Decomposition (SVD). The latter allows to analyze the spectra in their entirety, which is required to follow the blue shift of the probe signal that is caused by the aforementioned sensitivity to the environment. In this way the duplex melting process is characterized in local and global terms.The first modification, 2-hydroxy-7-carboxyfluorene (HCF), is placed opposite an abasic site to avoid steric strain. NMR spectroscopy revealed two equally distributed conformations, since rotation of the HCF chromophore is only hindered by stacking interactions inside the helix. The second double strand comprises R-glycerol linked 6-hydroxyquinolinium (6HQ) opposite cytosine. The incorporation of 6HQ as glycol nucleic acid (GNA) mononucleotide is a unique structural feature. Until now, only crystal structures of full GNA backbone duplexes are known, so the solution structure of this double strand is of general interest. The small size of R-glycerol disturbs the backbone of the 6HQ strand, which causes a stacking axis that differs from the helical long axis for the three central bases. The last modification is an artificial base pair made of 4-aminophthalimide (4AP) and 2,4-diaminopyrimidine (DAP). Instead of the desired three hydrogen bonds, two structures containing either a single or two hydrogen bonds are observed that can be explained by the linkage of 4AP to 2’-deoxyribofuranose.

No description available.

La multiplication des projets HVDC de par le monde démontre l'engouement toujours croissant pour cette technologie de transport de l'électricité. La grande majorité de ces transmissions HVDC correspondent à des liaisons point-à-point et se basent sur des convertisseurs AC/DC de type LCC ou VSC à 2 ou 3 niveaux. Les travaux de cette thèse se focalisent sur l'étude, le contrôle et la commande de systèmes HVDC de type multi-terminal (MTDC), avec des convertisseurs de type VSC classique ou modulaire multi-niveaux. La première étape consiste à obtenir les modèles moyens du VSC classique et du MMC. La différence fondamentale entre ces deux convertisseurs, à savoir la possibilité pour le MMC de stocker et de contrôler l'énergie des condensateurs des sous-modules, est détaillée et expliquée. Ces modèles et leurs commandes sont ensuite linéarisés et mis sous forme de représentations d'état, puis validés en comparant leur comportement à ceux de modèles de convertisseurs plus détaillés à l'aide de logiciels de type EMT. Une fois validés, les modèles d'état peuvent être utilisés afin de générer le modèle d'état de tout système de transmissions HVDC, qu'il soit point-à-point ou MTDC. La comparaison d'une liaison HVDC à base de VSCs classiques puis de MMCs est alors réalisée. Leurs valeurs propres sont étudiées et comparées, et les modes ayant un impact sur la tension DC sont identifiés et analysés. Cette étude est ensuite étendue à un système MTDC à 5 terminaux, et son analyse modale permet à la fois d'étudier la stabilité du système, mais aussi de comprendre l'origine de ses valeurs propres ainsi que leur impact sur la dynamique du système. La méthode de décomposition en valeurs singulières permet ensuite d'obtenir un intervalle de valeurs possibles pour le paramètre de"voltage droop", permettant ainsi le contrôle du système MTDC tout en s'assurant qu'il soit conforme à des contraintes bien définies, comme l'écart maximal admissible en tension DC. Enfin, une proposition de "frequency droop" (ou "statisme"), permettant aux convertisseurs de participer au réglage de la fréquence des réseaux AC auxquels ils sont connectés, est étudiée. Le frequency droop est utilisé conjointement avec le voltage droop afn de garantir le bon fonctionnement de la partie AC et de la partie DC. Cependant, l'utilisation des deux droop génère un couplage indésirable entre les deux commandes. Ces interactions sont mathématiquement quantifiées et une correction à apporter au paramètre de frequency droop est proposée. Ces résultats sont ensuite validés par des simulations EMT et par des essais sur la plate-forme MTDC du laboratoire L2EP. / HVDC transmission systems are largely used worldwide, mostly in the form of back-to-back and point-to-point HVDC, using either thyristor-based LCC or IGBT-based VSC. With the recent deployment of the INELFE HVDC link between France and Spain, and the commissioning in China of a three-terminal HVDC transmission system using Modular Multilevel Converters (MMCs), a modular design of voltage source converters, the focus of the scientific community has shifted onto the analysis and control of MMC-based HVDC transmission systems. In this thesis, the average value models of both a standard 2-level VSC and an MMC are proposed and the most interesting difference between the two converter technologies -the control of the stored energy in the MMC- is emphasised and explained. These models are then linearised, expressed in state-space form and validated by comparing their behaviour to more detailed models under EMT programs. Afterwards, these state-space representations are used in the modelling of HVDC transmission systems, either point-to-point or Multi-Terminal HVDC (MTDC). A modal analysis is performed on an HVDC link, for both 2-level VSCs and MMCs. The modes of these two systems are specifed and compared and the independent control of the DC voltage and the DC current in the case of an MMC is illustrated. This analysis is extended to the scope of a 5-terminal HVDC system in order to perform a stability analysis, understand the origin of the system dynamics and identify the dominant DC voltage mode that dictates the DC voltage response time. Using the Singular Value Decomposition method on the MTDC system, the proper design of the voltage-droop gains of the controllers is then achieved so that the system operation is ensured within physical constraints, such as the maximum DC voltage deviation and the maximum admissible current in the power electronics. Finally, a supplementary droop "the frequency-droop control" is proposed so that MTDC systems also participate to the onshore grids frequency regulation. However, this controller interacts with the voltage-droop controller. This interaction is mathematically quantified and a corrected frequency-droop gain is proposed. This control is then illustrated with an application to the physical converters of the Twenties project mock-up.