Methods for increasing the computational efficiency of input-output and related large scale matrix operations /

Includes bibliographical references.

Direct Computation of Operational Matrices for Polynomial Bases

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

A linear algebra approach to OLAP

Inspired by the relational algebra of data processing, this paper addresses the foundations of data analytical processing from a linear algebra perspective. The paper investigates, in particular, how aggregation operations such as cross tabulations and data cubes essential to quantitative analysis of data can be expressed solely in terms of matrix multiplication, transposition and the Khatri–Rao variant of the Kronecker product. The approach offers a basis for deriving an algebraic theory of data consolidation, handling the quantitative as well as qualitative sides of data science in a natural, elegant and typed way. It also shows potential for parallel analytical processing, as the parallelization theory of such matrix operations is well acknowledged.

Tuning Performance of Multi-threaded programs

Diplomityö tarkastelee säikeistettyä ohjelmointia rinnakkaisohjelmoinnin ylemmällä hierarkiatasolla tarkastellen erityisesti hypersäikeistysteknologiaa. Työssä tarkastellaan hypersäikeistyksen hyviä ja huonoja puolia sekä sen vaikutuksia rinnakkaisalgoritmeihin. Työn tavoitteena oli ymmärtää Intel Pentium 4 prosessorin hypersäikeistyksen toteutus ja mahdollistaa sen hyödyntäminen, missä se tuo suorituskyvyllistä etua. Työssä kerättiin ja analysoitiin suorituskykytietoa ajamalla suuri joukko suorituskykytestejä eri olosuhteissa (muistin käsittely, kääntäjän asetukset, ympäristömuuttujat...). Työssä tarkasteltiin kahdentyyppisiä algoritmeja: matriisioperaatioita ja lajittelua. Näissä sovelluksissa on säännöllinen muistinkäyttökuvio, mikä on kaksiteräinen miekka. Se on etu aritmeettis-loogisissa prosessoinnissa, mutta toisaalta huonontaa muistin suorituskykyä. Syynä siihen on nykyaikaisten prosessorien erittäin hyvä raaka suorituskyky säännöllistä dataa käsiteltäessä, mutta muistiarkkitehtuuria rajoittaa välimuistien koko ja useat puskurit. Kun ongelman koko ylittää tietyn rajan, todellinen suorituskyky voi pudota murto-osaan huippusuorituskyvystä.

Solving large sparse linear systems over the field GF(2)

Nowadays problem of solving sparse linear systems over the field GF(2) remain as a challenge. The popular approach is to improve existing methods such as the block Lanczos method (the Montgomery method) and the Wiedemann-Coppersmith method. Both these methods are considered in the thesis in details: there are their modifications and computational estimation for each process. It demonstrates the most complicated parts of these methods and gives the idea how to improve computations in software point of view. The research provides the implementation of accelerated binary matrix operations computer library which helps to make the progress steps in the Montgomery and in the Wiedemann-Coppersmith methods faster.

A note on influence diagnostics in nonlinear mixed-effects elliptical models

This paper provides general matrix formulas for computing the score function, the (expected and observed) Fisher information and the A matrices (required for the assessment of local influence) for a quite general model which includes the one proposed by Russo et al. (2009). Additionally, we also present an expression for the generalized leverage on fixed and random effects. The matrix formulation has notational advantages, since despite the complexity of the postulated model, all general formulas are compact, clear and have nice forms. (C) 2010 Elsevier B.V. All rights reserved.

Ultrasonic density measurement cell design and simulation of non-ideal effects

This paper presents a theoretical analysis of a density measurement cell using an unidimensional model composed by acoustic and electroacoustic transmission lines in order to simulate non-ideal effects. The model is implemented using matrix operations, and is used to design the cell considering its geometry, materials used in sensor assembly, range of liquid sample properties and signal analysis techniques. The sensor performance in non-ideal conditions is studied, considering the thicknesses of adhesive and metallization layers, and the effect of residue of liquid sample which can impregnate on the sample chamber surfaces. These layers are taken into account in the model, and their effects are compensated to reduce the error on density measurement. The results show the contribution of residue layer thickness to density error and its behavior when two signal analysis methods are used. (c) 2006 Elsevier B.V. All rights reserved.

Análise de estruturas reticuladas utilizando o software excel pelo método dos elementos finitos

Pós-graduação em Engenharia Mecânica - FEG

Generación de una librería RVC – CAL para la etapa de determinación de endmembers en el proceso de análisis de imágenes hiperespectrales

El análisis de imágenes hiperespectrales permite obtener información con una gran resolución espectral: cientos de bandas repartidas desde el espectro infrarrojo hasta el ultravioleta. El uso de dichas imágenes está teniendo un gran impacto en el campo de la medicina y, en concreto, destaca su utilización en la detección de distintos tipos de cáncer. Dentro de este campo, uno de los principales problemas que existen actualmente es el análisis de dichas imágenes en tiempo real ya que, debido al gran volumen de datos que componen estas imágenes, la capacidad de cómputo requerida es muy elevada. Una de las principales líneas de investigación acerca de la reducción de dicho tiempo de procesado se basa en la idea de repartir su análisis en diversos núcleos trabajando en paralelo. En relación a esta línea de investigación, en el presente trabajo se desarrolla una librería para el lenguaje RVC – CAL – lenguaje que está especialmente pensado para aplicaciones multimedia y que permite realizar la paralelización de una manera intuitiva – donde se recogen las funciones necesarias para implementar dos de las cuatro fases propias del procesado espectral: reducción dimensional y extracción de endmembers. Cabe mencionar que este trabajo se complementa con el realizado por Raquel Lazcano en su Proyecto Fin de Grado, donde se desarrollan las funciones necesarias para completar las otras dos fases necesarias en la cadena de desmezclado. En concreto, este trabajo se encuentra dividido en varias partes. La primera de ellas expone razonadamente los motivos que han llevado a comenzar este Proyecto Fin de Grado y los objetivos que se pretenden conseguir con él. Tras esto, se hace un amplio estudio del estado del arte actual y, en él, se explican tanto las imágenes hiperespectrales como los medios y las plataformas que servirán para realizar la división en núcleos y detectar las distintas problemáticas con las que nos podamos encontrar al realizar dicha división. Una vez expuesta la base teórica, nos centraremos en la explicación del método seguido para componer la cadena de desmezclado y generar la librería; un punto importante en este apartado es la utilización de librerías especializadas en operaciones matriciales complejas, implementadas en C++. Tras explicar el método utilizado, se exponen los resultados obtenidos primero por etapas y, posteriormente, con la cadena de procesado completa, implementada en uno o varios núcleos. Por último, se aportan una serie de conclusiones obtenidas tras analizar los distintos algoritmos en cuanto a bondad de resultados, tiempos de procesado y consumo de recursos y se proponen una serie de posibles líneas de actuación futuras relacionadas con dichos resultados. ABSTRACT. Hyperspectral imaging allows us to collect high resolution spectral information: hundred of bands covering from infrared to ultraviolet spectrum. These images have had strong repercussions in the medical field; in particular, we must highlight its use in cancer detection. In this field, the main problem we have to deal with is the real time analysis, because these images have a great data volume and they require a high computational power. One of the main research lines that deals with this problem is related with the analysis of these images using several cores working at the same time. According to this investigation line, this document describes the development of a RVC – CAL library – this language has been widely used for working with multimedia applications and allows an optimized system parallelization –, which joins all the functions needed to implement two of the four stages of the hyperspectral imaging processing chain: dimensionality reduction and endmember extraction. This research is complemented with the research conducted by Raquel Lazcano in her Diploma Project, where she studies the other two stages of the processing chain. The document is divided in several chapters. The first of them introduces the motivation of the Diploma Project and the main objectives to achieve. After that, we study the state of the art of some technologies related with this work, like hyperspectral images and the software and hardware that we will use to parallelize the system and to analyze its performance. Once we have exposed the theoretical bases, we will explain the followed methodology to compose the processing chain and to generate the library; one of the most important issues in this chapter is the use of some C++ libraries specialized in complex matrix operations. At this point, we will expose the results obtained in the individual stage analysis and then, the results of the full processing chain implemented in one or several cores. Finally, we will extract some conclusions related with algorithm behavior, time processing and system performance. In the same way, we propose some future research lines according to the results obtained in this document

Regression with Gaussian processes

The Bayesian analysis of neural networks is difficult because the prior over functions has a complex form, leading to implementations that either make approximations or use Monte Carlo integration techniques. In this paper I investigate the use of Gaussian process priors over functions, which permit the predictive Bayesian analysis to be carried out exactly using matrix operations. The method has been tested on two challenging problems and has produced excellent results.

Gaussian processes for regression

The Bayesian analysis of neural networks is difficult because a simple prior over weights implies a complex prior distribution over functions. In this paper we investigate the use of Gaussian process priors over functions, which permit the predictive Bayesian analysis for fixed values of hyperparameters to be carried out exactly using matrix operations. Two methods, using optimization and averaging (via Hybrid Monte Carlo) over hyperparameters have been tested on a number of challenging problems and have produced excellent results.

EXPRESSION OF MEMBRANE TYPE 1 MATRIX METALLOPROTEINASE IN MEDULLARY THYROID CARCINOMA: PROGNOSTIC IMPLICATIONS

Background. Clinical and pathologic examinations cannot always provide a prognosis for patients with medullary thyroid carcinoma. Membrane type 1 matrix metalloproteinase (MT1-MMP) can act directly on carcinogenesis and takes part in 1 of the processes of metalloproteinase 2 activation, an enzyme related to prognostic impairment of patients with such tumor. Methods. Thirty-five patients who were submitted to surgery were followed up for an average of 74 months, Postoperative and final medical conditions were characterized for comparison with MT1-MMP immunostainings, performed in surgical paraffin blocks. A value of p < .05 was considered statistically significant. Results. Proposed index (association of proportion and intensity of immunostaining) and proportion of immunostained cells in primary specimens were correlated with cure or persistence after initial operations (p = .0216 and p = .0098, respectively). Conclusion. MT1-MMP immunostaining in primary tumor specimens is a new and complementary prognostic predictor in patients with medullary thyroid carcinomas. (C) 2009 Wiley Periodicals, Inc. Head Neck 32: 58-67, 2010

Analysis of Some Queueing Models Related To N-Policy: Operations Research

This study is about the analysis of some queueing models related to N-policy.The optimal value the queue size has to attain in order to turn on a single server, assuming that the policy is to turn on a single server when the queue size reaches a certain number, N, and turn him off when the system is empty.The operating policy is the usual N-policy, but with random N and in model 2, a system similar to the one described here.This study analyses “ Tandem queue with two servers”.Here assume that the first server is a specialized one.In a queueing system,under N-policy ,the server will be on vacation until N units accumulate for the first time after becoming idle.A modified version of the N-policy for an M│M│1 queueing system is considered here.The novel feature of this model is that a busy service unit prevents the access of new customers to servers further down the line.It is deals with a queueing model consisting of two servers connected in series with a finite intermediate waiting room of capacity k.Here assume that server I is a specialized server.For this model ,the steady state probability vector and the stability condition are obtained using matrix – geometric method.

Matrix based Cryptographic Procedure for Efficient Image Encryption

In this paper we propose a cryptographic transformation based on matrix manipulations for image encryption. Substitution and diffusion operations, based on the matrix, facilitate fast conversion of plaintext and images into ciphertext and cipher images. The paper describes the encryption algorithm, discusses the simulation results and compares with results obtained from Advanced Encryption Standard (AES). It is shown that the proposed algorithm is capable of encrypting images eight times faster than AES.