Los microproyectos de investigación como instrumento de aprendizaje en una asignatura de máster

[SPA]El proceso de Convergencia Europea de la educación superior implica un cambio profundo en las estrategias enseñanza-aprendizaje y plantea una renovación de las metodologías docentes universitarias. De manera que frente a los enfoques didácticos clásicos centrados en el aula y el profesor, hay que dejar paso a una enseñanza centrada en la actividad autónoma del estudiante, lo que conlleva un replanteamiento en la planificación de las técnicas y herramientas a utilizar en el desarrollo de las asignaturas. De acuerdo con esta idea, esta comunicación pretende dar a conocer la experiencia realizada en una asignatura de máster de la Facultad de Biología de la Universidad de Murcia, durante los cursos 2009/10 y 2010/11, utilizando como estrategia principal en el proceso de enseñanza-aprendizaje la planificación, desarrollo y presentación de microproyectos de investigación, realizados por pequeños grupos de alumnos. [ENG]The process of European convergence of higher education implies a profound change in teaching-learning strategies and proposes a renewal of university teaching methodologies. So in contrast with traditional teaching approaches that focus on the classroom and teacher, education should focus on students' independent activity, meaning to a rethink of planning techniques and the tools to used in developing subjects. In accordance with to this idea, this paper presents our experience in a subject forming part of a Master at the Faculty of Biology, University of Murcia, during the academic years 2009/10 and 2010/11, using as a main strategy in the teaching-learning process micro-research projects, and their planning, development and presentation carried by small groups of students.Campus Mare Nostrum, Universidad Politécnica de Cartagena, Universidad de Murcia, Región de Murci

Influence of the patients' sex, type of dental prosthesis and antagonist on residual bone resorption at the level of the premaxilla

Objectives: To analyze the height and width of the ridge at the level of the premaxilla in edentulous patients, eva-luating whether the sex of the patient, type of prosthetic rehabilitation and antagonist have an influence. Material and Method: We randomly selected a total of 89 patients, having an average age of 66.21 years old. A total of 308 measurements were made, all of them at the level of the premaxilla, in the intercanine area. As dependent variables, we analyzed the patients' sex, age and the antagonist: removable (dental) prostheses (RP), fixed (dental) prostheses (FD), natural dentition (ND). As independent variables, we measured the height and residual width in sagittal sections provided by tomographic studies using Dentascan®. Results: We observed a significantly smaller ridge in women versus in men, and in patients whose antagonist was a fixed prosthesis; whereas for the type of prosthesis, we did not observe significant differences between the two categories analyzed. Conclusions: Bone resorption at the level of the premaxilla is a variable process in which a smaller size is observed (height and width) in women and when the antagonist is a fixed prosthesis. © Medicina Oral S. L

Cattle mortality due to poisoning in Spain: a cross-sectional epidemiological study

La falta de un sistema público nacional de bases de datos sobre intoxicación en el ganado hace difícil investigar esta cuestión. Por lo tanto, hemos realizado un estudio epidemiológico utilizando los datos sobre intoxicación de ganado suministrado por una compañía de seguros (2000-2005), para determinar la tasa de mortalidad debido a la intoxicación en el ganado en España y valorar la influencia de las siguientes variables: tipo de agricultura, edad, sexo, época del año, año y región. Se observó una tasa de mortalidad de 23,25 por 100.000 animales en España con una tasa en el sector de la carne de ganado lechero (32,14 vs. 4,51 por 100.000 animales). También hubo diferencias en la tasa de mortalidad entre la cría de ganado y en el futuro, afectando a criadores de ganado vacuno de carne y leche de una manera diferente. En el ganado lechero, hemos encontrado diferencias entre los años analizados. En el ganado vacuno, la época del año con mayor riesgo de intoxicación fue el último trimestre (19,45 por 100.000 animales), mientras que la más baja tasa de mortalidad fue observada en el primer trimestre (1.33 por 100.000). Existen marcadas diferencias entre las regiones en el ganado vacuno, las diferencias no fueron significativas en el ganado lechero. Por último, en el ganado vacuno, no se encontraron diferencias entre sexos. En resumen, la tasa de mortalidad debido a la intoxicación en el ganado en España es bajo, y el riesgo de intoxicación es determinado por el sistema de cultivo, animales' estadio de desarrollo, época del año y la región.The lack of nationwide public databases on poisoning in cattle makes it difficult to investigate this issue. Hence, we conducted an epidemiological study using the data on cattle poisoning provided by an insurance company (2000-2005), to determine the mortality rate due to poisoning in cattle in Spain and to assess the influence of the following variables: type of farming, age, sex, time of year, year and region. We observed a mortality rate of 23.25 per 100,000 animals in Spain with a higher rate in beef than dairy cattle (32.14 vs. 4.51 per 100,000 animals). There were also differences in the mortality rate between breeding cattle and future breeders, affecting dairy and beef cattle in a different way. In dairy cattle, we found differences between the years analysed. In beef cattle, the time of year with highest risk of poisoning was the last quarter (19.45 per 100,000 animals), while the lowest mortality rate was observed in the first quarter (1.33 per 100,000). There were pronounced differences between regions in beef cattle, differences being non-significant in dairy cattle. Lastly, in beef cattle, no differences were found between sexes. In summary, the mortality rate due to poisoning in cattle in Spain is low, and the risk of poisoning is determined by the farming system, animals’ stage of development, time of year and region.peerReviewe

Some results about randomized binary Markov chains: Theory, computing and applications

[EN] This paper is addressed to give a generalization of the classical Markov methodology allowing the treatment of the entries of the transition matrix and initial condition as random variables instead of deterministic values lying in the interval [0,1]. This permits the computation of the first probability density function (1-PDF) of the solution stochastic process taking advantage of the so-called Random Variable Transformation technique. From the 1-PDF relevant probabilistic information about the evolution of Markov models can be calculated including all one-dimensional statistical moments. We are also interested in determining the computation of distribution of some important quantities related to randomized Markov chains (steady state, hitting times, etc.). All theoretical results are established under general assumptions and they are illustrated by modelling the spread of a technology using real data.This work has been partially supported by the Ministerio de Economía y Competitividad [grant MTM2017-89664-P]. Ana Navarro Quiles acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigación y Desarrollo (PAID), Universitat Politècnica de ValènciaCortés, J.; Navarro-Quiles, A.; Romero, J.; Roselló, M. (2020). Some results about randomized binary Markov chains: Theory, computing and applications. International Journal of Computer Mathematics. 97(1-2):141-156. https://doi.org/10.1080/00207160.2018.1440290S141156971-

Full solution of random autonomous first-order linear systems of difference equations. Application to construct random phase portrait for planar systems

[EN] This paper deals with the explicit determination of the first probability density function of the solution stochastic process to random autonomous first-order linear systems of difference equations under very general hypotheses. This finding is applied to extend the classical stability classification of the zero-equilibrium point based on phase portrait to the random scenario. An example illustrates the potentiality of the theoretical results established and their connection with their deterministic counterpart.This work has been partially supported by the Ministerio de Economia y Competitividad grant MTM2013-41765-P. Ana Navarro Quiles acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigation y Desarrollo (PAID), Universitat Politecnica de Valencia.Cortés, J.; Navarro-Quiles, A.; Romero, J.; Roselló, M. (2017). Full solution of random autonomous first-order linear systems of difference equations. Application to construct random phase portrait for planar systems. Applied Mathematics Letters. 68:150-156. https://doi.org/10.1016/j.aml.2016.12.0151501566

Introducing randomness in the analysis of chemical reactions: An analysis based on random differential equations and probability density function

This is the peer reviewed version of the following article: Cortés, J-C, Navarro-Quiles, A, Romero, J-V, Roselló, M-D. Introducing randomness in the analysis of chemical reactions: An analysis based on random differential equations and probability density functions. Comp and Math Methods. 2021; 3:e1141, which has been published in final form at https://doi.org/10.1002/cmm4.1141. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.[EN] In this work we consider a particular randomized kinetic model for reaction-deactivation of hydrogen peroxide decomposition. We apply the Random Variable Transformation technique to obtain the first probability density function of the solution stochastic process under general conditions. From the rst probability density function, we can obtain fundamental statistical information, such as the mean and the variance of the solution, at every instant time. The transformation considered in the application of the Random Variable Transformation technique is not unique. Then, the first probability density function can take different expressions, although essentially equivalent in terms of computing probabilistic information. To motivate this fact, we consider in our analysis two different mappings. Several numerical examples show the capability of our approach and of the obtained results as well. We show, through simulations, that the choice of the transformation, that permits computing the first probability density function, is a crucial issue regarding the computational time.This work has been supported by the Spanish Ministerio de Economía, Industria y Competitividad (MINECO), the Agencia Estatal de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER UE) grant MTM2017-89664-P. Computations have been carried thanks to the collaboration of Raúl San Julián Garcés and Elena López Navarro granted by European Union through the Operational Program of the European Regional Development Fund (ERDF)/European Social Fund (ESF) of the Valencian Community 2014-2020, grants GJIDI/2018/A/009 and GJIDI/2018/A/010, respectively.Cortés, J.; Navarro-Quiles, A.; Romero, J.; Roselló, M. (2021). Introducing randomness in the analysis of chemical reactions: An analysis based on random differential equations and probability density function. Computational and Mathematical Methods. 3(6):1-10. https://doi.org/10.1002/cmm4.1141S1103

Randomizing the parameters of a Markov chain to model the stroke disease: A technical generalization of established computational methodologies towards improving real applications

[EN] Classical Markov models are defined through a stochastic transition matrix, i.e., a matrix whose columns (or rows) are deterministic values representing transition probabilities. However, in practice these quantities could often not be known in a deterministic manner, therefore, it is more realistic to consider them as random variables. Following this approach, this paper is aimed to give a technical generalization of classical Markov methodology in order to improve modelling of stroke disease when dealing with real data. With this goal, we randomize the entries of the transition matrix of a Markov chain with three states (susceptible, reliant and deceased) that has been previously proposed to model the stroke disease. This randomization of the classical Markov model permits the computation of the first probability density function of the solution stochastic process taking advantage of the so-called Random Variable Transformation technique. Afterwards, punctual and probabilistic predictions are computed from the first probability density function. In addition, the probability density functions of the time instants until a certain proportion of the total population remains susceptible, reliant and deceased are also computed. The study is completed showing the usefulness of our computational approach to determine, from a probabilistic point of view, key quantities in medical decision making, such as the cost-effectiveness ratio.This work has been partially supported by the Ministerio de Economia y Competitividad grant MTM2013-41765-P. Ana Navarro-Quiles acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia. Authors would like to thank Prof. Dr. Javier Mar for providing them medical data about stroke disease from his research.Cortés, J.; Navarro-Quiles, A.; Romero, J.; Roselló, M. (2017). Randomizing the parameters of a Markov chain to model the stroke disease: A technical generalization of established computational methodologies towards improving real applications. Journal of Computational and Applied Mathematics. 324:225-240. https://doi.org/10.1016/j.cam.2017.04.040S22524032

Solving second-order linear differential equations with random analytic coefficients about regular-singular points

[EN] In this contribution, we construct approximations for the density associated with the solution of second-order linear differential equations whose coefficients are analytic stochastic processes about regular-singular points. Our analysis is based on the combination of a random Fröbenius technique together with the random variable transformation technique assuming mild probabilistic conditions on the initial conditions and coefficients. The new results complete the ones recently established by the authors for the same class of stochastic differential equations, but about regular points. In this way, this new contribution allows us to study, for example, the important randomized Bessel differential equation.This work was partially funded by the Ministerio de Economia y Competitividad Grant MTM2017-89664-P. Ana Navarro Quiles acknowledges the funding received from Generalitat Valenciana through a postdoctoral contract (APOSTD/2019/128). Computations were carried out thanks to the collaboration of Raul San Julian Garces and Elena Lopez Navarro granted by the European Union through the Operational Program of the European Regional Development Fund (ERDF)/European Social Fund (ESF) of the Valencian Community 2014-2020, Grants GJIDI/2018/A/009 and GJIDI/2018/A/010, respectivelyCortés, J.; Navarro-Quiles, A.; Romero, J.; Roselló, M. (2020). Solving second-order linear differential equations with random analytic coefficients about regular-singular points. Mathematics. 8(2):1-20. https://doi.org/10.3390/math8020230S12082Hussein, A., & Selim, M. M. (2012). Solution of the stochastic radiative transfer equation with Rayleigh scattering using RVT technique. Applied Mathematics and Computation, 218(13), 7193-7203. doi:10.1016/j.amc.2011.12.088Dorini, F. A., Cecconello, M. S., & Dorini, L. B. (2016). On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density. Communications in Nonlinear Science and Numerical Simulation, 33, 160-173. doi:10.1016/j.cnsns.2015.09.009Santos, L. T., Dorini, F. A., & Cunha, M. C. C. (2010). The probability density function to the random linear transport equation. Applied Mathematics and Computation, 216(5), 1524-1530. doi:10.1016/j.amc.2010.03.001Hussein, A., & Selim, M. M. (2019). A complete probabilistic solution for a stochastic Milne problem of radiative transfer using KLE-RVT technique. Journal of Quantitative Spectroscopy and Radiative Transfer, 232, 54-65. doi:10.1016/j.jqsrt.2019.04.034Cortés, J.-C., Navarro-Quiles, A., Romero, J.-V., & Roselló, M.-D. (2018). Solving second-order linear differential equations with random analytic coefficients about ordinary points: A full probabilistic solution by the first probability density function. Applied Mathematics and Computation, 331, 33-45. doi:10.1016/j.amc.2018.02.051Cortés, J.-C., Jódar, L., Camacho, F., & Villafuerte, L. (2010). Random Airy type differential equations: Mean square exact and numerical solutions. Computers & Mathematics with Applications, 60(5), 1237-1244. doi:10.1016/j.camwa.2010.05.046Calbo, G., Cortés, J.-C., & Jódar, L. (2011). Random Hermite differential equations: Mean square power series solutions and statistical properties. Applied Mathematics and Computation, 218(7), 3654-3666. doi:10.1016/j.amc.2011.09.008Calbo, G., Cortés, J.-C., Jódar, L., & Villafuerte, L. (2011). Solving the random Legendre differential equation: Mean square power series solution and its statistical functions. Computers & Mathematics with Applications, 61(9), 2782-2792. doi:10.1016/j.camwa.2011.03.045Cortés, J.-C., Villafuerte, L., & Burgos, C. (2017). A Mean Square Chain Rule and its Application in Solving the Random Chebyshev Differential Equation. Mediterranean Journal of Mathematics, 14(1). doi:10.1007/s00009-017-0853-6Cortés, J.-C., Jódar, L., & Villafuerte, L. (2017). Mean square solution of Bessel differential equation with uncertainties. Journal of Computational and Applied Mathematics, 309, 383-395. doi:10.1016/j.cam.2016.01.034Khudair, A. R., Haddad, S. A. M., & Khalaf, S. L. (2016). Mean Square Solutions of Second-Order Random Differential Equations by Using the Differential Transformation Method. Open Journal of Applied Sciences, 06(04), 287-297. doi:10.4236/ojapps.2016.64028Qi, Y. (2018). A Very Brief Introduction to Nonnegative Tensors from the Geometric Viewpoint. Mathematics, 6(11), 230. doi:10.3390/math6110230Ragusa, M. A., & Tachikawa, A. (2016). Boundary regularity of minimizers of p(x)-energy functionals. Annales de l’Institut Henri Poincaré C, Analyse non linéaire, 33(2), 451-476. doi:10.1016/j.anihpc.2014.11.003Ragusa, M. A., & Tachikawa, A. (2019). Regularity for minimizers for functionals of double phase with variable exponents. Advances in Nonlinear Analysis, 9(1), 710-728. doi:10.1515/anona-2020-0022Braumann, C. A., Cortés, J.-C., Jódar, L., & Villafuerte, L. (2018). On the random gamma function: Theory and computing. Journal of Computational and Applied Mathematics, 335, 142-155. doi:10.1016/j.cam.2017.11.04

Solving fully randomized higher-order linear control differential equations: Application to study the dynamics of an oscillator

This is the peer reviewed version of the following article: Cortés, J-C, Navarro-Quiles, A, Romero, J-V, Roselló, M-D. Solving fully randomized higher-order linear control differential equations: Application to study the dynamics of an oscillator. Comp and Math Methods. 2021; 3:e1163, which has been published in final form at https://doi.org/10.1002/cmm4.1163. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.[EN] In this work, we consider control problems represented by a linear differential equation assuming that all the coefficients are random variables and with an additive control that is a stochastic process. Specifically, we will work with controllable problems in which the initial condition and the final target are random variables. The probability density function of the solution and the control has been calculated. The theoretical results have been applied to study, from a probabilistic standpoint, a damped oscillator.European Social Fund, Grant/Award Numbers: GJIDI/2018/A/009, GJIDI/2018/A/010; Spanish Ministerio de Economía, Industria y Competitividad (MINECO), the Agencia Estatal de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER UE), Grant/Award Number: MTM2017-89664-P.Cortés, J.; Navarro-Quiles, A.; Romero, J.; Roselló, M. (2021). Solving fully randomized higher-order linear control differential equations: Application to study the dynamics of an oscillator. Computational and Mathematical Methods. 3(6):1-15. https://doi.org/10.1002/cmm4.1163S1153