This thesis presents a comparison between two factorization techniques { Probabilistic Latent Component Analysis (PLCA) and Non-Negative Least Squares (NNLSQ) { for the problem of detecting note events played by a vibraphone, using a microphone for sound acquisition in the context of live performance. Ambient noise is reduced by using specifi c dictionary codewords to model the noise. The results of the factorization are analyzed by two causal onset detection algorithms: a rule-based algorithm and a trained machine learning based classi fier. These onset detection algorithms yield decisions on when note events happen. Comparative results are presented, considering a database of vibraphone recordings with di fferent levels of noise, showing the conditions under which the event detection is reliable. / Graduate

Thesis (M.A.)--The University of North Carolina at Greensboro, 2010. / Directed by Paul Duvall; submitted to the Dept. of Mathematics and Statistics. Title from PDF t.p. (viewed Jul. 16, 2010). Includes bibliographical references (p. 39-40).

We give explicit factorizations of $a$-cyclotomic polynomials of order $2^m 3$, $Q_{2^m3,a}(x)$, over a finite field $F_q$ with $q$ elements where $q$ is a prime power, $m$ is a nonnegative integer and $a$ is a nonnegative element of $F_q$. We use the relation between usual cyclotomic polynomials and $a$-cyclotomic polynomials. Factorizations split into eight categories according to $q \equiv \pm1$ (mod 4), $a$ and $-3$ are square in $F_q$. We find that the coefficients of irreducible factors are primitive roots of unity and in some cases that are related with Dickson polynomials.

We define morphism (E, M)-structures in an abstract category, develop their basic properties and present some examples. We also consider the existence of such factorization structures, and find conditions under which they can be extended to factorization structures for certain classes of sources. There is a Galois correspondence between the collection of all subclasses of X-morphisms and the collection of all subclasses of X-objects. A-epimorphisms diagonalize over A-regular morphisms. Given an (E, M)-factorization structure on a finitely complete category, E-separated objects are those for which diagonal morphisms lie in M. Other characterizations of E-separated objects are given. We give a bijective correspondence between the class of all (E, M)factorization structures with M contained in the class of all X-embeddings and the class of all strong limit operators. We study M-preserving morphisms, M-perfect morphisms and M-compact objects in a morphism (E, M)-hereditary construct, and prove some of their properties which are analogous to the topological ones. / Mathematical Sciences / M. Sc. (Mathematics)

This thesis deals with collecting facts and making the complete analysis of SQUFOF algorithm. In the beginning you can find a short hystorical re- view and then it continues with desribing how the binary quadratic forms, which represents the number N, continued fractions of √ N, ideals in the ring Z( √ N) and lattices in Q( √ N) are related. This thesis offers the tools usable to switch between these structures and finally it uses these tools to show, how the algorithm SQUFOF works. 1

Block-structured matrices arise in several contexts in circuit simulation problems. These matrices typically inherit the pattern of sparsity from the circuit connectivity. However, they are also characterized by dense spots or blocks. Direct factorization of those matrices has emerged as an attractive approach if the host memory is sufficiently large to store the block-structured matrix. The approach proposed in this thesis aims to accelerate the direct factorization of general block-structured matrices by leveraging the power of multiple OpenCL accelerators such as Graphical Processing Units (GPUs). The proposed approach utilizes the notion of a Directed Acyclic Graph representing the matrix in order to schedule its factorization on multiple accelerators. This thesis also describes memory management techniques that enable handling large matrices while minimizing the amount of memory transfer over the PCIe bus between the host CPU and the attached devices. The results demonstrate that by using two GPUs the proposed approach can achieve a nearly optimal speedup when compared to a single GPU platform.

In this dissertation, we examine atomicity in rings with zero divisions. We begin by examining the relationship between a ring’s level of atomicity and the highest level of irreducibility shared by the ring’s irreducible elements. Later, we chose one of the higher forms of atomicity and identify ways of building large classes of examples of rings that rise to this level of atomicity but no higher. Characteristics of the various types of irreducible elements will also be examined. Next, we extend our view to include polynomial extensions of rings with zero divisors. In particular, we focus on properties of the three forms of maximal common divisors and how a ring’s classification as an MCD, SMCD, or VSMCD ring affects its atomicity. To conclude, we identify some unsolved problems relating to the topics discussed in this dissertation.

Cette thèse introduit des nouveaux modèles de signaux musicaux informés par la physique des instruments. Alors que les communautés de l'acoustique instrumentale et du traitement du signal considèrent la modélisation des sons instrumentaux suivant deux approches différentes (respectivement, une modélisation du mécanisme de production du son, opposée à une modélisation des caractéristiques "morphologiques" générales du son), cette thèse propose une approche collaborative en contraignant des modèles de signaux génériques à l'aide d'information basée sur l'acoustique. L'effort est ainsi porté sur la construction de modèles spécifiques à un instrument, avec des applications aussi bien tournées vers l'acoustique (apprentissage de paramètres liés à la facture et à l'accord) que le traitement du signal (transcription de musique). En particulier nous nous concentrons sur l'analyse de musique pour piano, instrument pour lequel les sons produits sont de nature inharmonique. Cependant, l'inclusion d'une telle propriété dans des modèles de signaux est connue pour entraîner des difficultés d'optimisation, allant jusqu'à endommager les performances (en comparaison avec un modèle harmonique plus simple) dans des tâches d'analyse telles que la transcription. Un objectif majeur de cette thèse est d'avoir une meilleure compréhension des difficultés liées à l'inclusion explicite de l'inharmonicité dans des modèles de signaux, et d'étudier l'influence de l'apport de cette information sur les performances d'analyse, en particulier dans une tâche de transcription. / This thesis introduces new models of music signals informed by the physics of the instruments. While instrumental acoustics and audio signal processing target the modeling of musical tones from different perspectives (modeling of the production mechanism of the sound vs modeling of the generic "morphological'' features of the sound), this thesis aims at mixing both approaches by constraining generic signal models with acoustics-based information. Thus, it is here intended to design instrument-specific models for applications both to acoustics (learning of parameters related to the design and the tuning) and signal processing (transcription). In particular, we focus on piano music analysis for which the tones have the well-known property of inharmonicity. The inclusion of such a property in signal models however makes the optimization harder, and may even damage the performance in tasks such as music transcription when compared to a simpler harmonic model. A major goal of this thesis is thus to have a better understanding about the issues arising from the explicit inclusion of the inharmonicity in signal models, and to investigate whether it is really valuable when targeting tasks such as polyphonic music transcription.

Note:

<p> For 30 years the Lempel-Ziv factorization LZx of a string x = x[1..n] has been a fundamental data structure of string processing, especially valuable for string compression and for computing all the repetitions (runs) in x. When the Internet came in, a huge need for Lempel-Ziv factorization was created. Nowadays it has become a basic efficient data transmission format on the Internet.</p> <p> Traditionally the standard method for computing LZx was based on O(n)-time processing of the suffix tree STx of x. Ukkonen's algorithm constructs suffix tree online and so permits LZ to be built from subtrees of ST; this gives it an advantage, at least in terms of space, over the fast and compact version of McCreight's STCA [37] due to Kurtz [24]. In 2000 Abouelhoda, Kurtz & Ohlebusch proposed a O(n)-time Lempel-Ziv factorization algorithm based on an "enhanced" suffix array - that is, a suffix array SAx together with other supporting data structures.</p> <p> In this thesis we first examine some previous algorithms for computing Lempel-Ziv factorization. We then analyze the rationale of development and introduce a collection of new algorithms for computing LZ-factorization. By theoretical proof and experimental comparison based on running time and storage usage, we show that our new algorithms appear either in their theoretical behavior or in practice or both to be superior to those previously proposed. In the last chapter the conclusion of our new algorithms are given, and some open problems are pointed out for our future research.</p> / Thesis / Master of Science (MSc)