Efficient evaluation of matrix polynomials

[EN] This paper presents a new family of methods for evaluating matrix polynomials more efficiently than the state-of-the-art Paterson-Stockmeyer method. Examples of the application of the methods to the Taylor polynomial approximation of matrix functions like the matrix exponential and matrix cosine are given. Their efficiency is compared with that of the best existing evaluation schemes for general polynomial and rational approximations, and also with a recent method based on mixed rational and polynomial approximants. For many years, the Paterson-Stockmeyer method has been considered the most efficient general method for the evaluation of matrix polynomials. In this paper we show that this statement is no longer true. Moreover, for many years rational approximations have been considered more efficient than polynomial approximations, although recently it has been shown that often this is not the case in the computation of the matrix exponential and matrix cosine. In this paper we show that in fact polynomial approximations provide a higher order of approximation than the state-of-the-art computational methods for rational approximations for the same cost in terms of matrix products. (C) 2017 Elsevier Inc. All rights reserved.This work has been supported by Spanish Ministerio de Economia y Competitividad and European Regional Development Fund (ERDF) grant TIN2014-59294-P. We thank the anonymous referee who revised this paper so thoroughly and carefully.Sastre, J. (2018). Efficient evaluation of matrix polynomials. Linear Algebra and its Applications. 539:229-250. https://doi.org/10.1016/j.laa.2017.11.010S22925053

ALIA ROMA : Propuesta didáctica interdisciplinar sobre textos latinos de época imperial.

En este Trabajo de Fin de Máster de Profesorado de Educación Secundaria Obligatoria y Bachillerato, Formación Profesional y Enseñanza de Idiomas se presenta un proyecto educativo consistente en una selección de textos de autores latinos con los que no suele trabajarse en las aulas de la materia de Latín y que, por tanto, son poco conocidos tanto para el alumnado de Secundaria como el de estudios superiores; la intención es mostrar, a través de ellos, qué aspectos de la cultura de Roma se pueden aprender y cotejar con la realidad actual, así como cuáles y en qué medida tienen hoy pervivencia. Con estos textos se pretende exponer una visión alternativa sobre el mundo de Roma: es decir, no se trata de explicar otra cultura de Roma distinta y que no se conozca, sino que se presenta la misma, pero de una manera diferente a como se suele hacer en las aulas, lo que explica el nombre del título Alia Roma. En lugar de basarse en frases sueltas, sean adaptadas o extraídas de cualquier texto latino, y en la traducción de textos de los autores “de siempre” (Julio César y Cicerón), como es el caso del curso de segundo de Bachillerato de Latín, lo que se propone es el empleo de textos latinos de autores menos “habituales” para el aprendizaje de la lengua, literatura y cultura romanas, y, además de ello, para observar cómo describen e interpretan dichos autores las ideas que tratan en sus testimonios. A su vez, puesto que en cada texto se tratan diferentes asuntos, se abarcan conocimientos de diferentes campos. De este modo, entra en juego la interdisciplinariedad, es decir, además de aprender la materia correspondiente a la lengua latina, se pueden desarrollar otros campos de estudio.Departamento de Filología ClásicaMáster en Profesor de Educación Secundaria Obligatoria y Bachillerato, Formación Profesional y Enseñanzas de Idioma

Efficient mixed rational and polynomial approximation of matrix functions

This paper presents an efficient method for computing approximations for general matrix functions based on mixed rational and polynomial approximations. A method to obtain this kind of approximation from rational approximations is given, reaching the highest efficiency when transforming nondiagonal rational approximations with a higher numerator degree than the denominator degree. Then, the proposed mixed rational and polynomial approximation can be successfully applied for matrix functions which have any type of rational approximation, such as Pade, Chebyshev, etc., with maximum efficiency for higher numerator degrees than the denominator degrees. The efficiency of the mixed rational and polynomial approximation is compared with the best existing evaluating schemes for general polynomial and rational approximations, providing greater theoretical accuracy with the same cost in terms of matrix multiplications. It is well known that diagonal rational approximants are generally more accurate than the corresponding nondiagonal rational approximants which have the same computational cost. Using the proposed mixed approximation we show that the above statement is no longer true, and nondiagonal rational approximants are in fact generally more accurate than the corresponding diagonal rational approximants with the same cost. (C) 2012 Elsevier Inc. All rights reserved.This work has been supported by Universitat Politecnica de Valencia grant PAID-06-011-2020.Sastre, J. (2012). Efficient mixed rational and polynomial approximation of matrix functions. Applied Mathematics and Computation. 218(24):11938-11946. https://doi.org/10.1016/j.amc.2012.05.064S11938119462182

Youth participation in development planning: case study of Sayausí (Rural Parish) Cuenca-Ecuador

Young people now represent the highest percentage of the world population. Soon, they will be seniors and they will take decisions for a more orderly and equitable world. For this reason, the participation of young people in development planning is very important and many countries are trying to promote it through various measures. This article analyzes the trajectory of youth participation in the Latin American region and specifically the profile of youth participation in Ecuador, country in which the Constitution recognizes the strategic role of youth in development. The case study of Sayausí rural parish in canton Cuenca is analyzed, through surveys, interviews and an Empowerment Evaluation workshop to young people and decentralized government. The results obtained allow to propose strategies to help improve the participation of youth in the community

Efficient Evaluation of Matrix Polynomials beyond the Paterson-Stockmeyer Method

[EN] Recently, two general methods for evaluating matrix polynomials requiring one matrix product less than the Paterson-Stockmeyer method were proposed, where the cost of evaluating a matrix polynomial is given asymptotically by the total number of matrix product evaluations. An analysis of the stability of those methods was given and the methods have been applied to Taylor-based implementations for computing the exponential, the cosine and the hyperbolic tangent matrix functions. Moreover, a particular example for the evaluation of the matrix exponential Taylor approximation of degree 15 requiring four matrix products was given, whereas the maximum polynomial degree available using Paterson-Stockmeyer method with four matrix products is 9. Based on this example, a new family of methods for evaluating matrix polynomials more efficiently than the Paterson-Stockmeyer method was proposed, having the potential to achieve a much higher efficiency, i.e., requiring less matrix products for evaluating a matrix polynomial of certain degree, or increasing the available degree for the same cost. However, the difficulty of these family of methods lies in the calculation of the coefficients involved for the evaluation of general matrix polynomials and approximations. In this paper, we provide a general matrix polynomial evaluation method for evaluating matrix polynomials requiring two matrix products less than the Paterson-Stockmeyer method for degrees higher than 30. Moreover, we provide general methods for evaluating matrix polynomial approximations of degrees 15 and 21 with four and five matrix product evaluations, respectively, whereas the maximum available degrees for the same cost with the Paterson-Stockmeyer method are 9 and 12, respectively. Finally, practical examples for evaluating Taylor approximations of the matrix cosine and the matrix logarithm accurately and efficiently with these new methods are given.This research was partially funded by the European Regional Development Fund (ERDF) and the Spanish Ministerio de Economia y Competitividad grant TIN2017-89314-P, and by the Programa de Apoyo a la Investigacion y Desarrollo 2018 of the Universitat Politecnica de Valencia grant PAID-06-18-SP20180016.Sastre, J.; Ibáñez González, JJ. (2021). Efficient Evaluation of Matrix Polynomials beyond the Paterson-Stockmeyer Method. Mathematics. 9(14):1-23. https://doi.org/10.3390/math9141600S12391

La enseñanza del inglés a través de la literatura en la Educación Española. Propuesta experimental para la enseñanza de la lengua extranjera: inglés a través de la literatura inglesa

La enseñanza de las lenguas extranjeras en nuestro país ha ido cambiando y evolucionando a lo largo de los años, y más concretamente la enseñanza del inglés. Se analizará la perspectiva de la literatura en las lenguas extranjeras, y en concreto de la literatura inglesa, en las últimas leyes educativas españolas. Además, se propondrá una guía para que el profesor elabore materiales y utilice la literatura inglesa en la enseñanza del inglés, desde una perspectiva oral, en los primeros cursos de Educación Primaria. Una manera útil y entretenida de abordar tanto la lengua inglesa como la literatura inglesa.Grado en Educación Primari

Determination of biosorption mechanism in biomass of agave, using spectroscopic and microscopic techniques for the purification of contaminated water

[Abstract] Lead (Pb2+) and copper (Cu2+) are polluting metals due to their toxicity; however, the extraction of these metals is essential for economic development, so it is important to look for efficient and low-cost alternatives that can remove heavy metals from the various bodies of water. One of the alternatives used in this work is biosorption, for which an agroindustrial waste (epidermis from Agave atrovirens) was used to evaluate the affinity of removal of lead and copper in aqueous solutions; in addition, spectroscopy and microscopy techniques were used to elucidate and corroborate the removal and affinity capacity of the agave epidermis for both metals studied. The optimal pH value for the removal of both metals was 3. The adsorption isotherms yielded a qmax of 25.7 and 8.6 mg/g for lead and copper, respectively. Adjusting to the Langmuir-Freundlich model, the adsorption kinetics were pseudo-second order, and it was found that the equilibrium time was at 140 min. The spectroscopy and microscopy analyses corroborated the affinity between metals and functional groups of the agave, as well as with the elemental analysis, which reported 17.38% of lead and 4.25% of copper.[Resumen] El plomo (Pb2+) y el cobre (Cu2+) son metales contaminantes debido a su toxicidad; sin embargo, la extracción de estos metales es indispensable para el desarrollo económico, por lo que es importante buscar alternativas eficientes y de bajo costo que puedan remover metales pesados de los diversos cuerpos de agua. Una de las alternativas utilizadas en este trabajo es la biosorción, para la cual se utilizó un residuo agroindustrial (epidermis de Agave atrovirens), para evaluar la afinidad de remoción del plomo y cobre en soluciones acuosas; adicionalmente, se emplearon técnicas de espesctroscopía y microscopía que permitieron elucidar y corroborar la capacidad de remoción y afinidad que tuvo la epidermis de A. atrovirens para ambos metales estudiados. El valor óptimo de pH para la remoción de ambos metales fue 3. Las isotermas de adsorción arrojaron una qmax de 25.7 y 8.6 mg/g para el plomo y cobre, respectivamente. Ajustando al modelo de Langmuir-Freundlich, las cinéticas de adsorción resultaron de pseudo-segundo orden, se encontró que el tiempo de equilibrio es a los 140 min. El análisis espectroscópico y microscópico, corroboró la afinidad entre metales y grupos funcionales del agave, así como con el análisis elemental, el cual reportó 17.38% de plomo y 4.25% de cobre

Boosting the computation of the matrix exponential

[EN] This paper presents new Taylor algorithms for the computation of the matrix exponential based on recent new matrix polynomial evaluation methods. Those methods are more efficient than the well known Paterson-Stockmeyer method. The cost of the proposed algorithms is reduced with respect to previous algorithms based on Taylor approximations. Tests have been performed to compare the MATLAB implementations of the new algorithms to a state-of-the-art Pade algorithm for the computation of the matrix exponential, providing higher accuracy and cost performances.This work has been supported by Spanish Ministerio de Economia y Competitividad and European Regional Development Fund (ERDF) grant TIN2014-59294-P.Sastre, J.; Ibáñez González, JJ.; Defez Candel, E. (2019). Boosting the computation of the matrix exponential. Applied Mathematics and Computation. 340:206-220. https://doi.org/10.1016/j.amc.2018.08.017S20622034

Growing underground: Development of thermogenesis in pups of the fossorial rodent Ctenomys talarum

In mammals, during the pup’s development and adult life, integrated requirements of all activities of the individual must conform to a sustained rate of metabolism. Thus, partitioning the available energy according to short-term priorities at a specific moment allows animals to survive and optimize long-term reproductive success. In altricial rodents, thermal balance is a key factor for survival. When no exogenous source of heat is present, altricial pups rapidly lose heat, reaching ambient temperature (Ta). Fossorial rodents showed a strong dependence on burrows, where Ta remains relatively stable within narrow ranges. Pups of the fossorial rodent Ctenomys talarum are altricial, making them an excellent model to evaluate the development of thermogenic capacity. In this study, the ontogeny of the thermogenic capacity of pups of C. talarum was evaluated. Using respirometry techniques, non-shivering thermogenesis (NST), total thermogenic capacity (cold-induced maximum metabolic rate, MMR), and resting metabolic rate (RMR) in pups until post-weaning age (day 60) were analyzed. No NST was present in pups until day 60 despite the presence of molecular markers for NST in brown adipose tissue deposits, which became functional in adults. Although pups are altricial at birth, they maintain their thermal balance behaviorally during lactation. Total thermogenic capacity became fixed at an early age, indicating an improvement in shivering thermogenesis (ST) efficiency after day 10, which might be related to the development of musculature related to digging. Before the aboveground dispersal period (~day 60), pups gradually reached adult Tb by improving ST and thermal isolation, allowing them to confront climatic fluctuations on the surface.Fil: Luna, Facundo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Marinas y Costeras. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Marinas y Costeras; ArgentinaFil: Sastre Serra, Jorge. Instituto de Salud Carlos III; EspañaFil: Oliver, Jordi. Instituto de Salud Carlos III; EspañaFil: Antenucci, Carlos Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Marinas y Costeras. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Marinas y Costeras; Argentin