Nonnegative matrix factorization (NMF) is an important data-analysis problem which concerns factoring a given d n matrix A with nonnegative entries into matrices B and C where B and C are d k and k n with nonnegative entries. It has numerous applications including Object recognition, Topic Modelling, Hyper-spectral imaging, Music transcription etc. In general, NMF is intractable and several heuristics exists to solve the problem of NMF. Recently there has been interest in investigating conditions under which NMF can be tractably recovered. We note that existing attempts make unrealistic assumptions and often the associated algorithms tend to be not scalable. In this thesis, we make three major contributions: First, we formulate a model of NMF with assumptions which are natural and is a substantial weakening of separability. Unlike requiring a bound on the error in each column of (A BC) as was done in much of previous work, our assumptions are about aggregate errors, namely spectral norm of (A BC) i.e. jjA BCjj2 should be low. This is a much weaker error assumption and the associated B; C would be much more resilient than existing models. Second, we describe a robust polynomial time SVD-based algorithm, UTSVD, with realistic provable error guarantees and can handle higher levels of noise than previous algorithms. Indeed, experimentally we show that existing NMF models, which are based on separability assumptions, degrade much faster than UTSVD, in the presence of noise. Furthermore, when the data has dominant features, UTSVD significantly outperforms existing models. On real life datasets we again see a similar outperformance of UTSVD on clustering tasks. Finally, under a weaker model, we prove a robust version of uniqueness of NMF, where again, the word \robust" refers to realistic error bounds.

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.

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]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/5082

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.