Non-negative matrix decomposition approaches to frequency domain analysis of music audio signals

On étudie l’application des algorithmes de décomposition matricielles tel que la Factorisation Matricielle Non-négative (FMN), aux représentations fréquentielles de signaux audio musicaux. Ces algorithmes, dirigés par une fonction d’erreur de reconstruction, apprennent un ensemble de fonctions de base et un ensemble de coef- ficients correspondants qui approximent le signal d’entrée. On compare l’utilisation de trois fonctions d’erreur de reconstruction quand la FMN est appliquée à des gammes monophoniques et harmonisées: moindre carré, divergence Kullback-Leibler, et une mesure de divergence dépendente de la phase, introduite récemment. Des nouvelles méthodes pour interpréter les décompositions résultantes sont présentées et sont comparées aux méthodes utilisées précédemment qui nécessitent des connaissances du domaine acoustique. Finalement, on analyse la capacité de généralisation des fonctions de bases apprises par rapport à trois paramètres musicaux: l’amplitude, la durée et le type d’instrument. Pour ce faire, on introduit deux algorithmes d’étiquetage des fonctions de bases qui performent mieux que l’approche précédente dans la majorité de nos tests, la tâche d’instrument avec audio monophonique étant la seule exception importante.

Influence of Cu and Cr on the matrix decomposition of quenched Al-Zn-Mg alloy

The Inoue procedure is used to study the influence of Cr and Cu elements, jointly or individually, on the matrix decomposition of quenched Al-Zn-Mg alloys. The addition of copper and copper with chromium does not significantly change the limits of the temperatures of formation of Guinier-Preston zone and the range of the matrix decomposition. The control of the vacancy concentration in the alloys by different heat treatments and the addition of certain elements such as copper and chromium seems to play an important role in the nucleation rate and the kinetics of phase transformations.

On quantum integrability of the Landau-Lifshitz model

We investigate the quantum integrability of the Landau-Lifshitz (LL) model and solve the long-standing problem of finding the local quantum Hamiltonian for the arbitrary n-particle sector. The particular difficulty of the LL model quantization, which arises due to the ill-defined operator product, is dealt with by simultaneously regularizing the operator product and constructing the self-adjoint extensions of a very particular structure. The diagonalizibility difficulties of the Hamiltonian of the LL model, due to the highly singular nature of the quantum-mechanical Hamiltonian, are also resolved in our method for the arbitrary n-particle sector. We explicitly demonstrate the consistency of our construction with the quantum inverse scattering method due to Sklyanin [Lett. Math. Phys. 15, 357 (1988)] and give a prescription to systematically construct the general solution, which explains and generalizes the puzzling results of Sklyanin for the particular two-particle sector case. Moreover, we demonstrate the S-matrix factorization and show that it is a consequence of the discontinuity conditions on the functions involved in the construction of the self-adjoint extensions.

Análise do sinal cardíaco ECG através da técnica SVD

Este trabalho surge no âmbito da área Electromedicina, uma componente da Engenharia Electrotécnica cada vez mais influente e em permanente desenvolvimento, existindo nela uma constante inovação e tentativa de desenvolvimento e aplicação de novas tecnologias. Este projecto possui como principal objectivo o estudo aprofundado das aplicações da técnica SVD (Singular Value Decomposition), uma poderosa ferramenta matemática que permite a manipulação de sinais através da decomposição de matrizes, ao caso específico do sinal eléctrico obtido através de um electrocardiograma (ECG). Serão discriminados os princípios da operação do sistema eléctrico cardíaco, as principais componentes do sinal ECG (a onda P, o complexo QRS e a onda T) e os fundamentos da técnica SVD. A última fase deste trabalho consistirá na aplicação, em ambiente Matlab, da técnica SVD a sinais ECG concretos, com enfase na sua filtragem, para efeitos de remoção de ruído. De modo verificar as suas vantagens e desvantagens face a outras técnicas, os resultados da filtragem por SVD serão comparados com aqueles obtidos, em condições similares, através da aplicação de um filtro FIR de coeficientes estáticos e de um filtro adaptativo iterativo.

Correspondence analysis of two transition tables

The case of two transition tables is considered, that is two squareasymmetric matrices of frequencies where the rows and columns of thematrices are the same objects observed at three different timepoints. Different ways of visualizing the tables, either separatelyor jointly, are examined. We generalize an existing idea where asquare matrix is descomposed into symmetric and skew-symmetric partsto two matrices, leading to a decomposition into four components: (1)average symmetric, (2) average skew-symmetric, (3) symmetricdifference from average, and (4) skew-symmetric difference fromaverage. The method is illustrated with an artificial example and anexample using real data from a study of changing values over threegenerations.

Kationinvaihtohartsien hapetuskestävyys

Hyvin puhdasta vettä vaativissa sovelluksissa käytettävät kationinvaihtohartsit eivät saisi vuotaa puhdistettavaan veteen mitään vieraita aineita. Todellisuudessa hartsit kuitenkin vuotavat hyvin pieniä määriä erilaisia yhdisteitä käytön aikana. Aineet, joita kationinvaihtohartsi päästää veteen, ovat osaksi hartsin polymerointireaktion aikana sen rungon sisään jääneitä yhdisteitä. Nämä voidaan suurimmaksi osaksi poistaa pesemällä hartsia. Osittain niitä syntyy myös hartsin polystyreenidivinyylibentseenirungon (PS-DVB) hapettuessa. Hapettumisen seurauksena syntyneet yhdisteet ovat pääosin orgaanisia sulfonaatteja. Tämä työ koskee ydinvoimalaitoksissa käytettäviä pulverihartseja, joita käytetään primääripiirissä kiertävän lauhdeveden puhdistukseen ja jotka joutuvat siellä alttiiksi hapettumiselle. Yleensä hapettuminen on hidasta ja se johtuu veteen liuenneesta hapesta. Hapettuminen nopeutuu huomattavasti, jos vedessä on läsnä hapettimia tai siirtymämetalli-ioneja. Tällaisia hapettimia ovat esimerkiksi vetyperoksidi, otsoni, vapaa kloori, typpihappo ja kromi. Vetyperoksidin vaikutuksesta hartsin runkoon muodostuu hydroperoksidiryhmä, jonka hajoamisesta alkaa reaktioiden sarja, joka lopulta johtaa hartsin polymeerirungon katkeamiseen. Siirtymämetalli-ionit katalysoivat peroksidien hajoamista. Tavallisimpia hapetusta katalysoivia metalli-ioneja ovat rauta ja kupari, joiden katalyyttinen aktiivisuus on suuri. Tässä työssä pyrittiin selvittämään, onko mahdollista valmistaa hartseja, jotka kestävät hapettumista paremmin kuin nykyisin käytössä olevat hartsit. Sen tutkimiseksi tehtiin kiihdytettyjä hapetuskokeita käyttäen hapettimena vetyperoksidia ilman siirtymämetalli-ioni katalyyttejä. Hapetuskokeet tehtiin kaupallisesti saatavilla hartseilla ja uusilla työtä varten syntetisoiduilla koehartseilla. Hapetuskokeiden etenemistä seurattiin mittaamalla veteen liuenneiden orgaanisten aineiden kokonaismäärää (TOC-analyysi) ja liuoksessa esiintyvien orgaanisten sulfonaattien määrää johtokykymittauksin. Saadut tulokset antoivat viitteitä siitä, että hartsin synteesiolosuhteilla voi olla suurempi vaikutus sen hapetuskestävyyteen kuin synteesissä käytetyillä raaka-aineilla.

Um modelo de linha de transmissão bifásica desenvolvido diretamente no domínio das fases

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Uso das rotações de givens modificadas como um método direto para obtenção e atualização das soluções em sistemas com acumulação seqüencial de dados

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Direct determination of chromium in empty medicine capsules by tungsten coil atomic emission spectrometry

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Low rank subspace clustering (LRSC)

We consider the problem of fitting a union of subspaces to a collection of data points drawn from one or more subspaces and corrupted by noise and/or gross errors. We pose this problem as a non-convex optimization problem, where the goal is to decompose the corrupted data matrix as the sum of a clean and self-expressive dictionary plus a matrix of noise and/or gross errors. By self-expressive we mean a dictionary whose atoms can be expressed as linear combinations of themselves with low-rank coefficients. In the case of noisy data, our key contribution is to show that this non-convex matrix decomposition problem can be solved in closed form from the SVD of the noisy data matrix. The solution involves a novel polynomial thresholding operator on the singular values of the data matrix, which requires minimal shrinkage. For one subspace, a particular case of our framework leads to classical PCA, which requires no shrinkage. For multiple subspaces, the low-rank coefficients obtained by our framework can be used to construct a data affinity matrix from which the clustering of the data according to the subspaces can be obtained by spectral clustering. In the case of data corrupted by gross errors, we solve the problem using an alternating minimization approach, which combines our polynomial thresholding operator with the more traditional shrinkage-thresholding operator. Experiments on motion segmentation and face clustering show that our framework performs on par with state-of-the-art techniques at a reduced computational cost.

Fast Update of Conditional Simulation Ensembles

Gaussian random field (GRF) conditional simulation is a key ingredient in many spatial statistics problems for computing Monte-Carlo estimators and quantifying uncertainties on non-linear functionals of GRFs conditional on data. Conditional simulations are known to often be computer intensive, especially when appealing to matrix decomposition approaches with a large number of simulation points. This work studies settings where conditioning observations are assimilated batch sequentially, with one point or a batch of points at each stage. Assuming that conditional simulations have been performed at a previous stage, the goal is to take advantage of already available sample paths and by-products to produce updated conditional simulations at mini- mal cost. Explicit formulae are provided, which allow updating an ensemble of sample paths conditioned on n ≥ 0 observations to an ensemble conditioned on n + q observations, for arbitrary q ≥ 1. Compared to direct approaches, the proposed formulae proveto substantially reduce computational complexity. Moreover, these formulae explicitly exhibit how the q new observations are updating the old sample paths. Detailed complexity calculations highlighting the benefits of this approach with respect to state-of-the-art algorithms are provided and are complemented by numerical experiments.

Quantifying and Modeling the Influence of Forest on the Magnitude and Duration of Mountain Snow Storage in the Pacific Northwest, USA

Thesis (Ph.D.)--University of Washington, 2016-08

Model selection and the vectorial misspecification-resistant information criterion in multivariate time series

The thesis deals with the problem of Model Selection (MS) motivated by information and prediction theory, focusing on parametric time series (TS) models. The main contribution of the thesis is the extension to the multivariate case of the Misspecification-Resistant Information Criterion (MRIC), a criterion introduced recently that solves Akaike’s original research problem posed 50 years ago, which led to the definition of the AIC. The importance of MS is witnessed by the huge amount of literature devoted to it and published in scientific journals of many different disciplines. Despite such a widespread treatment, the contributions that adopt a mathematically rigorous approach are not so numerous and one of the aims of this project is to review and assess them. Chapter 2 discusses methodological aspects of MS from information theory. Information criteria (IC) for the i.i.d. setting are surveyed along with their asymptotic properties; and the cases of small samples, misspecification, further estimators. Chapter 3 surveys criteria for TS. IC and prediction criteria are considered for: univariate models (AR, ARMA) in the time and frequency domain, parametric multivariate (VARMA, VAR); nonparametric nonlinear (NAR); and high-dimensional models. The MRIC answers Akaike’s original question on efficient criteria, for possibly-misspecified (PM) univariate TS models in multi-step prediction with high-dimensional data and nonlinear models. Chapter 4 extends the MRIC to PM multivariate TS models for multi-step prediction introducing the Vectorial MRIC (VMRIC). We show that the VMRIC is asymptotically efficient by proving the decomposition of the MSPE matrix and the consistency of its Method-of-Moments Estimator (MoME), for Least Squares multi-step prediction with univariate regressor. Chapter 5 extends the VMRIC to the general multiple regressor case, by showing that the MSPE matrix decomposition holds, obtaining consistency for its MoME, and proving its efficiency. The chapter concludes with a digression on the conditions for PM VARX models.

Numerical computation of an analytic singular value decomposition of a matrix valued function

This paper extends the singular value decomposition to a path of matricesE(t). An analytic singular value decomposition of a path of matricesE(t) is an analytic path of factorizationsE(t)=X(t)S(t)Y(t) T whereX(t) andY(t) are orthogonal andS(t) is diagonal. To maintain differentiability the diagonal entries ofS(t) are allowed to be either positive or negative and to appear in any order. This paper investigates existence and uniqueness of analytic SVD's and develops an algorithm for computing them. We show that a real analytic pathE(t) always admits a real analytic SVD, a full-rank, smooth pathE(t) with distinct singular values admits a smooth SVD. We derive a differential equation for the left factor, develop Euler-like and extrapolated Euler-like numerical methods for approximating an analytic SVD and prove that the Euler-like method converges.

Decomposition of the B2-type matrix

The microstructural stability of aluminide diffusion coatings, prepared by means of a two-stage pack-aluminization treatment on single-crystal nickel-base superalloy substrates, is considered in this article. Edge-on specimens of coated superalloy are studied using transmission electron microscopy (TEM). The effects of coating thickness and post-coating heat treatment (duration, temperature, and atmosphere) on coating microstructure are examined. The article discusses the partial transformation of the matrix of the coating, from a B2-type phase (nominally NiAl) to a L12 phase (nominally Ni3(Al, Ti)), during exposure at temperatures of 850 °C and 950 °C in air and in vacuum for up to 138 hours. Three possible processes that can account for decom- position of the coating matrix are investigated, namely, interdiffusion between the coating and the substrate, oxidation of the coating surface, and aging of the coating. Of these processes, aging of the coating is shown to be the predominant factor in the coating transformation under the conditions considered. © 1992 The Minerals, Metals and Materials Society, and ASM International.