Multivariate Statistical Analysis Applied to X-Ray Spectra and X-Ray Mapping of Liver Cell Nuclei

Principal Components Analysis (PCA) and Factorial Analysis of Correspondence (FAC), two Multivariate Statistical Analyses (MSA), were applied to the analysis of X-ray data. MSA are descriptive methods which graphically display the correlations and anticorrelations between a large number of elements. Series of X-ray spectral data and X-ray maps obtained from rat liver were analyzed with reference to the diffusible elements Na, Mg, Cl, K and Ca and also P and S. By using an in situ precipitation method, the pyroantimonate method, it was found that the free, precipitable cations Na+, Mg2+, and Ca2+ are, in the nuclei, mainly distributed throughout the nucleoplasm. Images obtained from FAC allow those areas rich in nucleic acids to be displayed as areas with a strong anticorrelation between P and Sb. In cryoprocessed tissues, the evaluated wet mass-fraction of diffusible elements corresponds to physiological values of total amounts (free and complexed). PCA makes it possible to graphically display the correlation between P and K in chromatin and nucleolus, the correlation between K, Cl and S in cytoplasm and nucleoplasm and the observation of two populations of nuclei according to different Na, Mg and K concentrations. Factorial images obtained from FAC allow those areas rich in nucleic acids to be displayed as areas with a strong correlation between P and K. Similarly those areas rich in proteins are displayed as areas with a strong correlation between S and K

Linearizations of rational matrices

Mención Internacional en el título de doctorThis PhD thesis belongs to the area of Numerical Linear Algebra. Specifically, to the numerical solution of the Rational Eigenvalue Problem (REP). This is a type of eigenvalue problem associated with rational matrices, which are matrices whose entries are rational functions. REPs appear directly from applications or as approx imations to arbitrary Nonlinear Eigenvalue Problems (NLEPs). Rational matrices also appear in linear systems and control theory, among other applications. Nowa days, a competitive method for solving REPs is via linearization. This is due to the fact that there exist backward stable and efficient algorithms to solve the linearized problem, which allows to recover the information of the original rational problem. In particular, linearizations transform the REP into a generalized eigenvalue pro blem in such a way that the pole and zero information of the corresponding rational matrix is preserved. To recover the pole and zero information of rational matrices, it is fundamental the notion of polynomial system matrix, introduced by Rosenbrock in 1970, and the fact that rational matrices can always be seen as transfer functions of polynomial system matrices. This thesis addresses different topics regarding the problem of linearizing REPs. On the one hand, one of the main objectives has been to develop a theory of li nearizations of rational matrices to study the properties of the linearizations that have appeared so far in the literature in a general framework. For this purpose, a definition of local linearization of rational matrix is introduced, by developing as starting point the extension of Rosenbrock’s minimal polynomial system matrices to a local scenario. This new theory of local linearizations captures and explains rigor ously the properties of all the different linearizations that have been used from the 1970’s for computing zeros, poles and eigenvalues of rational matrices. In particu lar, this theory has been applied to a number of pencils that have appeared in some influential papers on solving numerically NLEPs through rational approximation. On the other hand, the work has focused on the construction of linearizations of rational matrices taking into account different aspects. In some cases, we focus on preserving particular structures of the corresponding rational matrix in the li nearization. The structures considered are symmetric (Hermitian), skew-symmetric (skew-Hermitian), among others. In other cases, we focus on the direct construc tion of the linearizations from the original representation of the rational matrix. The representations considered are rational matrices expressed as the sum of their polynomial and strictly proper parts, rational matrices written as general trans fer function matrices, and rational matrices expressed by their Laurent expansion around the point at infinity. In addition, we describe the recovery rules of the information of the original rational matrix from the information of the new lineari zations, including in some cases not just the zero and pole information but also the information about the minimal indices. Finally, in this dissertation we tackle one of the most important open problems related to linearizations of rational matrices. That is the analysis of the backward stability for solving REPs by running a backward stable algorithm on a linearization. On this subject, a global backward error analysis has been developed by considering the linearizations in the family of “block Kronecker linearizations”. An analysis of this type had not been developed before in the literature.Este trabajo ha sido desarrollado en el Departamento de Matemáticas de la Universidad Carlos III de Madrid (UC3M) bajo la dirección del profesor Froilán Martínez Dopico y codirección de la profesora Silvia Marcaida Bengoechea. Se contó durante cuatro años con un contrato predoctoral FPI, referencia BES-2016-076744, asociado al proyecto ALGEBRA LINEAL NUMERICA ESTRUCTURADA PARA MATRICES CONSTANTES, POLINOMIALES Y RACIONALES, referencia MTM2015-65798-P, del Ministerio de Economía y Competitividad, y cuyo investigador principal fue Froilán Martínez Dopico. Asociado a este contrato, se contó con una ayuda para realizar parte de este trabajo durante dos es tancias internacionales de investigación. La primera estancia de investigación se realizó del 30 de enero de 2019 hasta el 1 de marzo de 2019 en el Department of Mathematical En gineering, Université catholique de Louvain (Bélgica), bajo la supervisión del profesor Paul Van Dooren. La segunda estancia de investigación se realizó del 15 de septiembre de 2019 hasta el 19 de noviembre de 2019 en el Department of Mathematical Sciences, University of Montana (EEUU), bajo la supervisión del profesor Javier Pérez Alvaro. Dado que la entidad beneficiaria del contrato predoctoral es la UC3M mientras que el otro codirector de tesis, la profesora Silvia Marcaida Bengoechea, pertenece al Departamento de Matemáticas de la Universidad del País Vasco (UPV/EHU), el trabajo con la profesora Silvia Marcaida se reforzó mediante visitas a la UPV/EHU, financiadas por ayudas de la RED temática de Excelencia ALAMA (Algebra Lineal, Análisis Matricial y Aplicaciones) asociadas al los proyectos MTM2015-68805-REDT y MTM2017-90682-REDT.Programa de Doctorado en Ingeniería Matemática por la Universidad Carlos III de MadridPresidente: Ion Zaballa Tejada.- Secretario: Fernando de Terán Vergara.- Vocal: Vanni Noferin

Computer-assisted radiographic calculation of spinal curvature in brachycephalic "screw-Tailed" dog breeds with congenital thoracic vertebral malformations: reliability and clinical evaluation

The objectives of this study were: To investigate computer-assisted digital radiographic measurement of Cobb angles in dogs with congenital thoracic vertebral malformations, to determine its intra- and inter-observer reliability and its association with the presence of neurological deficits. Medical records were reviewed (2009–2013) to identify brachycephalic screw-tailed dog breeds with radiographic studies of the thoracic vertebral column and with at least one vertebral malformation present. Twenty-eight dogs were included in the study. The end vertebrae were defined as the cranial end plate of the vertebra cranial to the malformed vertebra and the caudal end plate of the vertebra caudal to the malformed vertebra. Three observers performed the measurements twice. Intraclass correlation coefficients were used to calculate the intra- and inter-observer reliabilities. The intraclass correlation coefficient was excellent for all intra- and inter-observer measurements using this method. There was a significant difference in the kyphotic Cobb angle between dogs with and without associated neurological deficits. The majority of dogs with neurological deficits had a kyphotic Cobb angle higher than 35°. No significant difference in the scoliotic Cobb angle was observed. We concluded that the computer assisted digital radiographic measurement of the Cobb angle for kyphosis and scoliosis is a valid, reproducible and reliable method to quantify the degree of spinal curvature in brachycephalic screw-tailed dog breeds with congenital thoracic vertebral malformations

Quadrature formulae of Euler-Maclaurin type based on generalized Euler polynomials of level m

This article deals with some properties -which are, to the best of our knowledge, new- of the generalized Euler polynomials of level m. These properties include a new recurrence relation satisfied by these polynomials and quadrature formulae of Euler-Maclaurin type based on them. Numerical examples are also given.The work of the first author (YQ) has been supported by Decanato de Investigación y Desarrollo, Universidad Simón Bolívar, grant DID-USB (S1-IC-CB-003-16). Also, the first author thanks the hospitality of Coordinación de Matemáticas of Universidad del Atlántico during her visit for the Fall Semester 2016. The work of the second author (AU) has been supported by Universidad del Atlántico, Colombia, grant Impacto Caribe (IC-002627-2015)

Estonian education system vs Spanish education system

When Estonia regained its independence from the Soviet regime, and as a consequence of the reform of its educational system, taking as a reference what they did in their neighbouring country Finland. Some analysts have defined it as the educational miracle in Estonia, being ratified for the results achieved in the PISA reports. The factors that have been identified as successful in the Estonian Educational System are equal opportunities for all of their young people, the great concern in families for students to have quality training, access to technology from a very early age at schools. Besides, the stability of the education legislation have achieved PISA results, where students stand out for not having low grades, rather than for having some students with very high grades, that is, there is little dispersion. On the other hand, it is interesting to know which innovations are being used by some schools in Estonia, focusing on those that are being incorporated into the Peetri Lasteaed Pohikool School in Tallinn