Nuevos métodos y algoritmos de altas prestaciones para el cálculo de funciones de matrices

Tesis por compendio[ES] El objetivo de esta tesis es el desarrollo de algoritmos e implementaciones innovadoras de altas prestaciones (HPC) para la computación de funciones de matrices basadas en series de polinomios matriciales. En concreto, se desarrollarán algoritmos para el cálculo de las funciones matriciales más utilizadas: la exponencial, el seno y el coseno. El estudio de los polinomios ortogonales matriciales es un campo emergente cuyo avance está alcanzando importantes resultados tanto desde el punto de vista teórico como práctico. Las ¿últimas investigaciones realizadas por el doctorando, junto a los miembros del grupo de investigación al que está vinculado, High Performance Scientific Computing (HiPerSC), revelan por qué los polinomios matriciales desempeñan un papel fundamental en la aproximación de funciones de matrices, proporcionando propiedades muy interesantes. En esta tesis se han desarrollado nuevos algoritmos de alto rendimiento basados en series polinomiales matriciales. En particular, se han implementado algoritmos para el cálculo de la exponencial, el seno y el coseno de una matriz usando las series matriciales polinomiales de Taylor y de Hermite. Además, se han proporcionado cotas del error cometido en las aproximaciones calculadas, proporcionando además los parámetros teóricos y experimentales óptimos de dichas aproximaciones. Los algoritmos finales han sido comparados con otras implementaciones del estado del arte para probar la mejora que presentan en cuanto a eficiencia y prestaciones. Los resultados obtenidos a lo largo de la investigación y presentados en esta memoria han sido publicados en varias revistas de alto nivel y se han presentado como ponencias en diversas ediciones del congreso internacional Mathematical Modelling in Engineering & Human Behaviour para dotarlas de la mayor difusión posible. Por otra parte, los códigos informáticos implementados han sido puestos a disposición de la comunidad científica internacional a través de nuestra página web http://hipersc.blogs.upv.es.[CA] L'objectiu d'aquesta Tesi és el desenvolupament d'algoritmes i implementacions innovadores d'altes prestacions (HPC) per a la computació de funcions de matrius basades en sèries de polinomis matricials. En concret, es desenvoluparan algoritmes per al càlcul de les funcions matricials més emprades: l'exponencial, el sinus i el cosinus. L'estudi dels polinomis ortogonals matricials és un camp emergent, el creixement del qual està aconseguint importants resultats tant des del punt de vista teòric com pràctic. Les últimes investigacions realitzades pel doctorand junt amb els membres del grup d'investigació on està vinculat, High Performance Scientific Computing (HiPerSC), revelen per què els polinomis matricials exerceixen un paper fonamental en l'aproximació de funcions de matrius, proporcionant propietats molt interessants. En aquesta Tesi s'han desenvolupat nous algoritmes d'alt rendiment basats en sèries polinomials matricials. En particular, s'han implementat algoritmes per al càlcul de l'exponencial, el sinus i el cosinus d'una matriu usant les sèries matricials polinomials de Taylor i d'Hermite. A més, s'han proporcionat cotes de l'error comès en les aproximacions calculades, proporcionant a més els paràmetres teòrics i experimentals òptims d'aquestes aproximacions. Els algoritmes finals han estat comparats amb altres implementacions de l'estat de l'art per a provar la millora que presenten en termes d'eficiència i prestacions. Els resultats obtinguts al llarg de la investigació i presentats en aquesta memòria han estat publicats en diverses revistes d'alt nivell i s'han presentat com a ponències en diferents edicions del congrés internacional Mathematical Modelling in Engineering \& Human Behaviour per a dotar-les de la major difusió possible. D'altra banda, s'han posat els codis informàtics implementats a disposició de la Comunitat Científica Internacional mitjançant la nostra pàgina web http://hipersc.blogs.upv.es.[EN] The aim of this thesis is the development of high performance computing (HPC) innovative algorithms and implementations for computing matrix functions based on matrix polynomials series. Specifically, algorithms for the calculation of the most commonly-used functions, the exponential, sine and cosine have been developed. The study of orthogonal matrix polynomials is an emerging field whose growth is achieving important results both theoretically and practically. The last investigations made by the doctoral student, together with the members of the research group, High Performance Scientific Computing (HiPerSC), he is linked, reveal why the matrix polynomials play a fundamental role in the approximation of matrix functions, providing very interesting properties.In this thesis new high-performance algorithms based on matrix polynomial series have been developed. In particular, algorithms for computing the exponential, sine and cosine of a matrix using Taylor and Hermite matrix polynomial series have been implemented.In addition, the error bounds for the approximations calculated have been provided and optimal theoretical and experimental parameters for such approximations have also been provided. Final algorithms have been compared to other state of the art implementations to test the improvement obtained in terms of efficiency and performance. The results obtained during the investigation and presented in this memory have been published in several high-level journals and presented as papers at various editions of the International Congress Mathematical Modelling in Engineering & Human Behaviour to give them the widest possible distribution. On the other hand, implemented computer codes have been made freely available to the international scientific community at our web page http://hipersc.blogs.upv.es.Ruiz Martínez, PA. (2020). Nuevos métodos y algoritmos de altas prestaciones para el cálculo de funciones de matrices [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/137035TESISCompendi

Experiencia con la herramienta de virtualización VNUML para la enseñanza de redes de computadores

La virtualización permite disponer y configurar infraestructuras de red con un coste asumible para un laboratorio y, a diferencia de los simuladores, muestra un comportamiento real del sistema. Este artículo presenta la metodología que seguimos en la asignatura de Redes de la Facultad de Informática de la Universidad de Murcia para la enseñanza práctica de conceptos tales como encaminamiento, movilidad IP, balanceo de carga y alta disponibilidad por medio de la herramienta de virtualización de código abierto VNUML. Para mostrar estos conceptos hemos añadido diversas utilidades al sistema de ficheros utilizado en VNUML. Gracias a estas herramientas, los alumnos han podido mejorar el aprendizaje de estos conceptos como lo refutan las encuestas realizadas.Peer Reviewe

VNUML vs GNS3 en el desarrollo de laboratorios de redes virtuales

El aprendizaje práctico de redes de computadores es reconocido como un proceso crítico que permite a los estudiantes consolidar los conceptos introducidos en las lecciones teóricas. En este sentido, las tecnologías de virtualización están adquiriendo gran relevancia debido a que permiten desarrollar laboratorios de redes de computadores con un reducido coste de despliegue y gestión. Este artículo presenta un análisis comparativo entre GNS3 y VNUML, que son herramientas de virtualización open-source que han sido empleadas para el desarrollo de laboratorios de red virtuales para llevar a cabo el proceso de enseñanza-aprendizaje en las asignaturas Arquitectura de Redes y Arquitectura de Redes Avanzadas del Grado en Ingeniería Informática impartido en la Universidad de Murcia. El estudio presenta las principales ventajas y/o deficiencias de cada herramienta tanto para profesores como alumnos y se identifican los escenarios en los que parece más adecuada su utilización.SUMMARY -- The practical learning of computer networks is known to be a critical process in order to allow students to consolidate the concepts introduced in theoretical lessons. In this sense, virtualization technologies are becoming popular since they allow to set up a computer network laboratory with a reduced deployment and management cost. This paper presents a comparative analysis performed between GNS3 and VNUML, which are open-source tools for virtualization that have been used for developing virtual network laboratories that support the teaching-learning process in the Networks Architecture and Advanced Networks Architecture subjects of the Computer Engineering degree at the University of Murcia. The study presents the main advantages and/or deficiencies of each tool not only for professors but also for students and identifies the scenarios where the use of each tool seems to be more appropriate.Peer Reviewe

On the influence of psychrometric ambient conditions on cooling tower drift deposition

Water drift emitted from cooling towers is objectionable for several reasons, mainly due to human health reasons. A numerical model to study the influence of sychrometric ambient conditions on cooling tower drift deposition was developed. The mathematical model presented, consisting of two coupled sets of conservation equations for the continuous and discrete phases, was incorporated in the general purpose CFD code Fluent. Both experimental plume performance and drift deposition were employed to validate the numerical results. This study shows the influence of variables like ambient dry bulb temperature, ambient absolute humidity and droplet exit temperature from cooling tower on the drift evaporation (and therefore deposition) and on the zone affected by the cooling tower. The stronger effect detected corresponds to the ambient dry bulb temperature. When a higher ambient temperature was present, deposition was lower (evaporation was therefore higher) and the zone affected by the cooling tower was smaller. The influence of the other two variables included in the study was weaker than the one corresponding to the dry bulb ambient temperature. A high level of ambient absolute humidity increased drift deposition and also the size of the zone affected by the cooling tower. Finally, a high level of droplet exit temperature decreased deposition and increased the zone affected by the cooling tower

Solving initial value problems for ordinary differential equations by two approaches: BDF and Piecewise-linearized methods

Many scientific and engineering problems are described using Ordinary Differential Equations (ODEs), where the analytic solution is unknown. Much research has been done by the scientific community on developing numerical methods which can provide an approximate solution of the original ODE. In this work, two approaches have been considered based on BDF and Piecewise-linearized Methods. The approach based on BDF methods uses a Chord–Shamanskii iteration for computing the nonlinear system which is obtained when the BDF schema is used. Two approaches based on piecewise-linearized methods have also been considered. These approaches are based on a theorem proved in this paper which allows to compute the approximate solution at each time step by means of a block-oriented method based on diagonal Padé approximations. The difference between these implementations is in using or not using the scale and squaring technique. Five algorithms based on these approaches have been developed. MATLAB and Fortran versions of the above algorithms have been developed, comparing both precision and computational costs. BLAS and LAPACK libraries have been used in Fortran implementations. In order to compare in equality of conditions all implementations, algorithms with fixed step have been considered. Four of the five case studies analyzed come from biology and chemical kinetics stiff problems. Experimental results show the advantages of the proposed algorithms, especially when they are integrating stiff problems.Ibáñez González, JJ.; Hernández García, V.; Arias, E.; Ruíz Martínez, PA. (2009). Solving initial value problems for ordinary differential equations by two approaches: BDF and Piecewise-linearized methods. Computer Physics Communications. 180(5):712-723. doi:10.1016/j.cpc.2008.11.013S712723180

Accurate and efficient matrix exponential computation

[EN] This work gives a new formula for the forward relative error of matrix exponential Taylor approximation and proposes new bounds for it depending on the matrix size and the Taylor approximation order, providing a new efficient scaling and squaring Taylor algorithm for the matrix exponential. A Matlab version of the new algorithm is provided and compared with Pad´e state-of-the-art algorithms obtaining higher accuracy in the majority of tests at similar or even lower cost.This work has been supported by the Programa de Apoyo a la Investigacion y el Desarrollo of the Universitat Politecnica de Valencia grant PAID-06-11-2020Sastre, J.; Ibáñez González, JJ.; Ruiz Martínez, PA.; Defez Candel, E. (2014). Accurate and efficient matrix exponential computation. International Journal of Computer Mathematics. 91(1):97-112. https://doi.org/10.1080/00207160.2013.791392S97112911Al-Mohy, A. H., & Higham, N. J. (2010). A New Scaling and Squaring Algorithm for the Matrix Exponential. SIAM Journal on Matrix Analysis and Applications, 31(3), 970-989. doi:10.1137/09074721xArioli, M., Codenotti, B., & Fassino, C. (1996). The Padé method for computing the matrix exponential. Linear Algebra and its Applications, 240, 111-130. doi:10.1016/0024-3795(94)00190-1S. Blackford and J. Dongarra,Installation guide for LAPACK, LAPACK Working Note 411, Department of Computer Science, University of Tenessee, 1999.Dieci, L., & Papini, A. (2000). Padé approximation for the exponential of a block triangular matrix. Linear Algebra and its Applications, 308(1-3), 183-202. doi:10.1016/s0024-3795(00)00042-2Dieci, L., & Papini, A. (2001). Numerical Algorithms, 28(1/4), 137-150. doi:10.1023/a:1014071202885Dolan, E. D., & Moré, J. J. (2002). Benchmarking optimization software with performance profiles. Mathematical Programming, 91(2), 201-213. doi:10.1007/s101070100263C. Fassino,Computation of matrix functions, Ph.D. thesis TD-7/93, Università di Pisa, Genova, 1993.Higham, N. J. (2002). Accuracy and Stability of Numerical Algorithms. doi:10.1137/1.9780898718027Higham, N. J. (2005). The Scaling and Squaring Method for the Matrix Exponential Revisited. SIAM Journal on Matrix Analysis and Applications, 26(4), 1179-1193. doi:10.1137/04061101xHigham, N. J. (2008). Functions of Matrices. doi:10.1137/1.9780898717778Higham, N. J., & Tisseur, F. (2000). A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra. SIAM Journal on Matrix Analysis and Applications, 21(4), 1185-1201. doi:10.1137/s0895479899356080Moler, C., & Van Loan, C. (2003). Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later. SIAM Review, 45(1), 3-49. doi:10.1137/s00361445024180Paterson, M. S., & Stockmeyer, L. J. (1973). On the Number of Nonscalar Multiplications Necessary to Evaluate Polynomials. SIAM Journal on Computing, 2(1), 60-66. doi:10.1137/0202007Sastre, J., Ibáñez, J., Defez, E., & Ruiz, P. (2011). Accurate matrix exponential computation to solve coupled differential models in engineering. Mathematical and Computer Modelling, 54(7-8), 1835-1840. doi:10.1016/j.mcm.2010.12.04

Experiencia con la herramienta de virtualización VNUML para la enseñanza de redes de computadores

La virtualización permite disponer y configurar infraestructuras de red con un coste asumible para un laboratorio y, a diferencia de los simuladores, muestra un comportamiento real del sistema. Este artículo presenta la metodología que seguimos en la asignatura de Redes de la Facultad de Informática de la Universidad de Murcia para la enseñanza práctica de conceptos tales como encaminamiento, movilidad IP, balanceo de carga y alta disponibilidad por medio de la herramienta de virtualización de código abierto VNUML. Para mostrar estos conceptos hemos añadido diversas utilidades al sistema de ficheros utilizado en VNUML. Gracias a estas herramientas, los alumnos han podido mejorar el aprendizaje de estos conceptos como lo refutan las encuestas realizadas.Este trabajo ha sido parcialmente financiado por el “Programa de Ayuda a los Grupos de Excelencia de la Fundación Séneca 04552/GERM/06” y por el proyecto CICYT TIN2008-06441-C02-02

Humoral response (IgG) of goats experimentally infected with Fasciola hepatica against cysteine proteinases of adult fluke

The use of cysteine proteinases from Fasciola hepatica adult flukes for the serodiagnosis of caprine fasciolosis by means of an indirect ELISA test was studied. Two proteolytic fractions from adult fluke homogenates, with apparent molecular weights of 28 and 34 kDa (P28 and P34 respectively), were characterised as cysteine proteinases using azocasein assays and gelatin gel analysis. Both P28 and P34 fractions were electroluted and used as antigens in two different indirect ELISA tests. Serum IgG levels against P28 and P34 in goats given an experimental primary infection with 200 metacercariae or in goats given two experimental infections with 200 metacercariae were determined and compared with those observed in an uninfected control group. ELISA tests using both cysteine proteases showed a rapid and consistent detection of specific IgG in all experimentally infected goats. The IgG response to P28 was the first to be detected as early as 2–3 weeks post-infection and remained elevated throughout the experiment. The response to P34 was detected later (4–6 wpi) and disappeared in some animals at 18 wpi, while flukes were still present in the bile ducts. No significant differences were observed between the anti-P28 and anti-P34 IgG responses between animals receiving a primary or a challenge infection. The results of our study, although preliminary, are promising since the P28 ELISA described here may be a reliable method for the immunodiagnosis of F. hepatica infection in goats

Adaptative ECT System Based on Reconfigurable Electronics

In this work we present a novel scheme for the design of electrical capacitance tomography systems that is based on the use of reconfigurable electronics. The objective of this strategy is to generate an adaptable and portable prototype for the processing electronics, i.e., an instrument suitable to be easily transported and applied to different ECT sensors and scenarios with no need of hardware redesign. In order to show the benefits of this approach, a prototype of the processing electronics for the readings of the inter-electrode capacitance values has been implemented using a Programmable System on Chip (PSoC) that allows configuring both analog and digital blocks included in the design. The result is a compact and portable instrument that can work with any ECT sensor up to 8 electrodes. The measurements are sent through a wireless Bluetooth link to an external smart-device such as smartphone, where the permittivity distribution is reconstructed using a custom-developed Android application.Junta de Andalucía (University Professor and Researcher Training Program – FPDI grant)EI BIOTiC under project MPTIC1

Numerical study of the behavior of an air pre-cooler

Introducing an air pre-cooler step before an air cooler system have been proved to improve the global efficiency of a cooling setup. Several authors have studied the mass and the heat exchanges of an air stream and the water sprayed inside an adiabatic cooling pad. However, these previous studies present their results and correlations as functions of experimental dependent parameters. Therefore, the aim of this study is to develop a numerical modeling capable of characterizing the behavior of an air pre-cooling stage without the need of previous experimental tests, allowing an accurate initial study when designing an air cooler installation. Several numerical models and simulation tests have been developed by our researching group in order to get a proper approximation of the problem, and the employment of previous experimental data allowed the model validation in terms of pressure drop and air cooling efficiency. As a result, a numerical model is defined, validated, and compared with existing empirical correlations models as a first step to determine the best possible cooling pad configuration in every air cooling setup as a function of the pad geometry, air and water flow rates, with an only numerical simulation.The authors acknowledge the financial support received from the Spanish Government, through Projects ENE2013-48696-C2-1-R and C2-2-R as well as by the FEDER (FondoEuropeo de Desarrollo Regional