Numerical methods and accurate computations with structured matrices

Esta tesis doctoral es un compendio de 11 artículos científicos. El tema principal de la tesis es el Álgebra Lineal Numérica, con énfasis en dos clases de matrices estructuradas: las matrices totalmente positivas y las M-matrices. Para algunas subclases de estas matrices, es posible desarrollar algoritmos para resolver numéricamente varios de los problemas más comunes en álgebra lineal con alta precisión relativa independientemente del número de condición de la matriz. La clave para lograr cálculos precisos está en el uso de una parametrización diferente que represente la estructura especial de la matriz y en el desarrollo de algoritmos adaptados que trabajen con dicha parametrización.Las matrices totalmente positivas no singulares admiten una factorización única como producto de matrices bidiagonales no negativas llamada factorización bidiagonal. Si conocemos esta representación con alta precisión relativa, se puede utilizar para resolver ciertos sistemas de ecuaciones y para calcular la inversa, los valores propios y los valores singulares con alta precisión relativa. Nuestra contribución en este campo ha sido la obtención de la factorización bidiagonal con alta precisión relativa de matrices de colocación de polinomios de Laguerre generalizados, de matrices de colocación de polinomios de Bessel, de clases de matrices que generalizan la matriz de Pascal y de matrices de q-enteros. También hemos estudiado la extensión de varias propiedades óptimas de las matrices de colocación de B-bases normalizadas (que en particular son matrices totalmente positivas). En particular, hemos demostrado propiedades de optimalidad de las matrices de colocación del producto tensorial de B-bases normalizadas.Si conocemos las sumas de filas y las entradas extradiagonales de una M-matriz no singular diagonal dominante con alta precisión relativa, entonces podemos calcular su inversa, determinante y valores singulares también con alta precisión relativa. Hemos buscado nuevos métodos para lograr cálculos precisos con nuevas clases de M-matrices o matrices relacionadas. Hemos propuesto una parametrización para las Z-matrices de Nekrasov con entradas diagonales positivas que puede utilizarse para calcular su inversa y determinante con alta precisión relativa. También hemos estudiado la clase denominada B-matrices, que está muy relacionada con las M-matrices. Hemos obtenido un método para calcular los determinantes de esta clase con alta precisión relativa y otro para calcular los determinantes de las matrices de B-Nekrasov también con alta precisión relativa. Basándonos en la utilización de dos matrices de escalado que hemos introducido, hemos desarrollado nuevas cotas para la norma infinito de la inversa de una matriz de Nekrasov y para el error del problema de complementariedad lineal cuando su matriz asociada es de Nekrasov. También hemos obtenido nuevas cotas para la norma infinito de las inversas de Bpi-matrices, una clase que extiende a las B-matrices, y las hemos utilizado para obtener nuevas cotas del error para el problema de complementariedad lineal cuya matriz asociada es una Bpi-matriz. Algunas clases de matrices han sido generalizadas al caso de mayor dimensión para desarrollar una teoría para tensores extendiendo la conocida para el caso matricial. Por ejemplo, la definición de la clase de las B-matrices ha sido extendida a la clase de B-tensores, dando lugar a un criterio sencillo para identificar una nueva clase de tensores definidos positivos. Hemos propuesto una extensión de la clase de las Bpi-matrices a Bpi-tensores, definiendo así una nueva clase de tensores definidos positivos que puede ser identificada en base a un criterio sencillo basado solo en cálculos que involucran a las entradas del tensor. Finalmente, hemos caracterizado los casos en los que las matrices de Toeplitz tridiagonales son P-matrices y hemos estudiado cuándo pueden ser representadas en términos de una factorización bidiagonal que sirve como parametrización para lograr cálculos con alta precisión relativa.<br /

Diseño e implementación de un sistema de medida de gases con Arduino

En el mercado existen aparatos para la medición de la concentración de gases, pero son muy costosos económicamente. Así, en este proyecto se estudia la posibilidad de usar Arduino para construir y sistema de detección de gases y medición de temperatura que sea accesible y que sirva para aplicaciones en interiores. Además el sistema es capaz de registrar los datos medidos por los sensores. Finalmente, se evalúa la viabilidad económica con respecto a otras alternativas existentes

Computation of the eigenvalues of convexity preserving matrices

AbstractA direct method using O(kn2) elementary operations to compute the k largest eigenvalues of an r-convexity preserving n×n matrix, for all r=0,1,…,k, is presented

Diseño de una instalación experimental para el análisis de intercambiadores de calor agua-emulsión de materiales de cambio de fase

El presente TFG forma parte de un proyecto de I+D Retos del Ministerio de Economía y Empresa que está llevando a cabo el grupo de investigación en Ingeniería Térmica y Sistemas Energéticos, perteneciente al Instituto de Investigación en Ingeniería de Aragón de la Universidad de Zaragoza. El objetivo es el diseño de una instalación experimental en la que se puedan ensayar intercambiadores de calor por los que circulará por un lado agua y por el otro una emulsión de materiales de cambio de fase con el fin de estudiar la transferencia de calor entre ambos. Para ello se han determinado en primer lugar las propiedades termofísicas y reológicas de la emulsión de materiales de cambio de fase. Para la caracterización de la curva entalpíatemperatura se ha utilizado una instalación de la metodología T-history y un calorímetro diferencial de barrido. La caracterización de las propiedades reológicas se ha realizado mediante un reómetro de esfuerzo controlado. Tras ello, se ha dimensionado un intercambiador de calor adecuado para el estudio del cambio de fase del material de cambio de fase de la emulsión y por último, se han seleccionado el resto los componentes de la instalación experimental

Comparative analysis of some modeal reconstruction methods of the cornea from corneal elevation data

Purpose. A comparative study of the ability of some modal schemes to reproduce corneal shapes of varying complexity is performed, using both standard radial polynomials and the radial basis functions (RBF). Our claim is that the correct approach in the case of highly irregular corneas should combine several bases. Methods. Standard approaches of reconstruction by Zernike and other types of radial polynomials are compared with the discrete least squares fit (LSF) by the RBF in three theoretical surfaces, synthetically generated by computer algorithms in the lack of measurement noise. For the reconstruction by polynomials the maximal radial order 6 was chosen, which corresponds to the first 28 Zernike polynomials or the first 49 Bhatia-Wolf polynomials. The fit with the RBF has been carried out using a regular grid of centers. Results. The quality of fit was assessed by computing for each surface the mean square errors (MSE) of the reconstruction by LSF, measured at the same nodes where the heights were collected. Another criterion of the fitting quality used was the accuracy in recovery of the Zernike coefficients, especially in the case of incomplete data. Conclusions. The Zernike (and especially, the Bhatia-Wolf) polynomials constitute a reliable reconstruction method of a non-severely aberrated surface with a small surface regularity index (SRI). However, they fail to capture small deformations of the anterior surface of a synthetic cornea. The most promising is a combined approach that balances the robustness of the Zernike fit with the localization of the RBF

Comparative Analysis of Some Modal Reconstruction Methods of the Shape of the Cornea from Corneal Elevation Data

Purpose: A comparative study of the ability of some modal schemes to reproduce corneal shapes of varying complexity was performed, by using both standard radial polynomials and radial basis functions (RBFs). The hypothesis was that the correct approach in the case of highly irregular corneas should combine several bases. Methods: Standard approaches of reconstruction by Zernike and other types of radial polynomials were compared with the discrete least-squares fit (LSF) by the RBF in three theoretical surfaces, synthetically generated by computer algorithms in the absence of measurement noise. For the reconstruction by polynomials, the maximal radial order 6 was chosen, which corresponds to the first 28 Zernike polynomials or the first 49 Bhatia-Wolf polynomials. The fit with the RBF was performed by using a regular grid of centers. Results: The quality of fit was assessed by computing for each surface the mean square errors (MSEs) of the reconstruction by LSF, measured at the same nodes where the heights were collected. Another criterion of the fit quality used was the accuracy in recovery of the Zernike coefficients, especially in the case of incomplete data. Conclusions: The Zernike (and especially, the Bhatia-Wolf) polynomials constitute a reliable reconstruction method of a nonseverely aberrated surface with a small surface regularity index (SRI). However, they fail to capture small deformations of the anterior surface of a synthetic cornea. The most promising approach is a combined one that balances the robustness of the Zernike fit with the localization of the RBF

Point-of-care lung ultrasound assessment for risk stratification and therapy guiding in COVID-19 patients. A prospective non-interventional study.

Background Lung ultrasound is feasible for assessing lung injury caused by coronavirus disease 2019 (COVID-19). However, the prognostic meaning and time-line changes of lung injury assessed by lung ultrasound in COVID-19 hospitalised patients are unknown. Methods Prospective cohort study designed to analyse prognostic value of lung ultrasound in COVID-19 patients by using a quantitative scale (lung ultrasound Zaragoza (LUZ)-score) during the first 72 h after admission. The primary end-point was in-hospital death and/or admission to the intensive care unit. Total length of hospital stay, increase of oxygen flow and escalation of medical treatment during the first 72 h were secondary end-points. Results 130 patients were included in the final analysis; mean±sd age was 56.7±13.5 years. Median (interquartile range) time from the beginning of symptoms to admission was 6 (4–9) days. Lung injury assessed by LUZ-score did not differ during the first 72 h (21 (16–26) points at admission versus 20 (16–27) points at 72 h; p=0.183). In univariable logistic regression analysis, estimated arterial oxygen tension/inspiratory oxygen fraction ratio (PAFI) (hazard ratio 0.99, 95% CI 0.98–0.99; p=0.027) and LUZ-score >22 points (5.45, 1.42–20.90; p=0.013) were predictors for the primary end-point. Conclusions LUZ-score is an easy, simple and fast point-of-care ultrasound tool to identify patients with severe lung injury due to COVID-19, upon admission. Baseline score is predictive of severity along the whole period of hospitalisation. The score facilitates early implementation or intensification of treatment for COVID-19 infection. LUZ-score may be combined with clinical variables (as estimated by PAFI) to further refine risk stratification

Proyección social y profesionalización en el ámbito del aprendizaje de la Sociología

La red ha tenido como objetivo planificar y ejecutar acciones de apoyo y orientación a los/as estudiantes de Sociología en su proceso de formación académica y profesional. Para ello se han implementado diferentes acciones como la jornada “Día de la Sociología en la Universidad de Alicante”, presentación de resultados de investigación, charlas a estudiantes de secundaria, difusión de información para orientadores de centros de secundaria, planificación de la participación en las conferencias-coloquio sobre titulaciones que organiza la Universidad de Alicante y avances en la articulación con otras titulaciones de Sociología en España

CARB-ES-19 Multicenter Study of Carbapenemase-Producing Klebsiella pneumoniae and Escherichia coli From All Spanish Provinces Reveals Interregional Spread of High-Risk Clones Such as ST307/OXA-48 and ST512/KPC-3.

CARB-ES-19 is a comprehensive, multicenter, nationwide study integrating whole-genome sequencing (WGS) in the surveillance of carbapenemase-producing K. pneumoniae (CP-Kpn) and E. coli (CP-Eco) to determine their incidence, geographical distribution, phylogeny, and resistance mechanisms in Spain. Methods: In total, 71 hospitals, representing all 50 Spanish provinces, collected the first 10 isolates per hospital (February to May 2019); CPE isolates were first identified according to EUCAST (meropenem MIC > 0.12 mg/L with immunochromatography, colorimetric tests, carbapenem inactivation, or carbapenem hydrolysis with MALDI-TOF). Prevalence and incidence were calculated according to population denominators. Antibiotic susceptibility testing was performed using the microdilution method (EUCAST). All 403 isolates collected were sequenced for high-resolution single-nucleotide polymorphism (SNP) typing, core genome multilocus sequence typing (cgMLST), and resistome analysis. Results: In total, 377 (93.5%) CP-Kpn and 26 (6.5%) CP-Eco isolates were collected from 62 (87.3%) hospitals in 46 (92%) provinces. CP-Kpn was more prevalent in the blood (5.8%, 50/853) than in the urine (1.4%, 201/14,464). The cumulative incidence for both CP-Kpn and CP-Eco was 0.05 per 100 admitted patients. The main carbapenemase genes identified in CP-Kpn were bla OXA-48 (263/377), bla KPC-3 (62/377), bla VIM-1 (28/377), and bla NDM-1 (12/377). All isolates were susceptible to at least two antibiotics. Interregional dissemination of eight high-risk CP-Kpn clones was detected, mainly ST307/OXA-48 (16.4%), ST11/OXA-48 (16.4%), and ST512-ST258/KPC (13.8%). ST512/KPC and ST15/OXA-48 were the most frequent bacteremia-causative clones. The average number of acquired resistance genes was higher in CP-Kpn (7.9) than in CP-Eco (5.5). Conclusion: This study serves as a first step toward WGS integration in the surveillance of carbapenemase-producing Enterobacterales in Spain. We detected important epidemiological changes, including increased CP-Kpn and CP-Eco prevalence and incidence compared to previous studies, wide interregional dissemination, and increased dissemination of high-risk clones, such as ST307/OXA-48 and ST512/KPC-3

The CARBA-MAP study: national mapping of carbapenemases in Spain (2014–2018)

Introduction:Infections caused by carbapenem-resistant Enterobacterales (CRE) and carbapenem-resistant Pseudomonas aeruginosa, including isolates producing acquired carbapenemases, constitute a prevalent health problem worldwide. The primary objective of this study was to determine the distribution of the different carbapenemases among carbapenemase-producing Enterobacterales (CPE, specifically Escherichia coli, Klebsiella pneumoniae, Enterobacter cloacae complex, and Klebsiella aerogenes) and carbapenemase-producing P. aeruginosa (CPPA) in Spain from January 2014 to December 2018.Methods: A national, retrospective, cross-sectional multicenter study was performed. The study included the first isolate per patient and year obtained from clinical samples and obtained for diagnosis of infection in hospitalized patients. A structured questionnaire was completed by the participating centers using the REDCap platform, and results were analyzed using IBM SPSS Statistics 29.0.0.Results: A total of 2,704 carbapenemase-producing microorganisms were included, for which the type of carbapenemase was determined in 2692 cases: 2280 CPE (84.7%) and 412 CPPA (15.3%), most often using molecular methods and immunochromatographic assays. Globally, the most frequent types of carbapenemase in Enterobacterales and P. aeruginosa were OXA-48-like, alone or in combination with other enzymes (1,523 cases, 66.8%) and VIM (365 cases, 88.6%), respectively. Among Enterobacterales, carbapenemase-producing K. pneumoniae was reported in 1821 cases (79.9%), followed by E. cloacae complex in 334 cases (14.6%). In Enterobacterales, KPC is mainly present in the South and South-East regions of Spain and OXA-48-like in the rest of the country. Regarding P. aeruginosa, VIM is widely distributed all over the country. Globally, an increasing percentage of OXA-48-like enzymes was observed from 2014 to 2017. KPC enzymes were more frequent in 2017–2018 compared to 2014–2016.Discussion: Data from this study help to understand the situation and evolution of the main species of CPE and CPPA in Spain, with practical implications for control and optimal treatment of infections caused by these multi-drug resistant organisms