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Diseño de rúbricas destinadas a la evaluación de los trabajos de fin de grado y de fin de máster en la Facultad de Ciencias Matemáticas de la Universidad Complutense de Madrid. Se presentan modelos tanto para el tutor que dirige el trabajo como para el tribunal que debe evaluar la memoria realizada y su presentación.

In this work, we manage to disentangle the role of virus infectiousness and awarenessbased human behavior in the COVID-19 pandemic. Using Bayesian inference, we quantify the uncertainty of a state-space model whose propagator is based on an unusual SEIRtype model since it incorporates the effective population fraction as a parameter. Within the Markov Chain Monte Carlo (MCMC) algorithm, Unscented Kalman Filter (UKF) may be used to evaluate the likelihood approximately. UKF is a suitable strategy in many cases, but it is not well-suited to deal with non-negativity restrictions on the state variables. To overcome this difficulty, we modify the UKF, conveniently truncating Gaussian distributions, which allows us to deal with such restrictions. We use official infection notification records to analyze the first 22 weeks of infection spread in each of the 27 countries of the European Union (EU). It is known that such records are the primary source of information to assess the early evolution of the pandemic and, at the same time, usually suffer underreporting and backlogs. Our model explicitly accounts for uncertainty in the dynamic model parameters, the dynamic model adequacy, and the infection observation process. We argue that this modeling paradigm allows us to disentangle the role of the contact rate, the effective population fraction, and the infection observation probability across time and space with an imperfect first principles model. Our findings agree with phylogenetic evidence showing little variability in the contact rate, or virus infectiousness, across EU countries during the early phase of the pandemic, highlighting the advantage of incorporating the effective population fraction into pandemic modeling for heterogeneity in both human behavior and reporting. Finally, to evaluate the consistency of our data assimilation method, we performed a forecast that adequately fits the actual data. Statement of significance: Data-driven and model-based epidemiologic, Ministerio de Ciencia e Innovación, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

We consider space semi-discretizations of the 1 − d wave equation in a bounded interval with homogeneous Dirichlet boundary conditions. We analyze the problem of boundary observability,i.e., the problem of whether the total energy of solutions can be estimated uniformly in terms of the energy concentrated on the boundary as the net-spacing h ! 0. We prove that, due to the spurious modes that the numerical scheme introduces at high frequencies, there is no such a uniform bound. We prove however a uniform bound in a subspace of solutions generated by the low frequencies of the discrete system. When h ! 0 this nite-dimensional spaces increase and eventually cover the whole space. We thus recover the well-known observability property of the continuous system as the limit of discrete observability estimates as the mesh size tends to zero. We consider both nite-dierence and nite-element semi-discretizations., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Acuerdo transformativo, In recent years, the sustained increase in the worldwide demand for lithium batteries goes side by side with the need for reliable methods to assess battery performance. Of particular importance is assessing Lithium-Ion cell’s thermal behavior given its role on hazard and aging of batteries. An essential task towards developing battery management systems is the estimation of physical parameters and their uncertainties in terms of both models and observations. Consequently, this paper analyzes the uncertainty in a thermal single particle model for a lithium-ion cell. In the first part of the manuscript, we explore the model adequacy by analyzing the forward and backward uncertainty propagation in the model in terms of diffusion coefficients, reaction rate constants, and observations of cell voltage. In the second part of the manuscript, we infer the cell’s reversible heat given the energy balance equation and the cell’s temperature observations. We argue that the methods proposed here may be extended to analyze other more general lithium-ion models, Spanish Ministry of Science and Innovation, Research group MOMAT, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

High-pressure supported freezing processes need a more efficient refrigeration technique to be applied at industrial level. A cooling method consisting in the circulation of a refrigerant in ebullition around the product in the vessel has been tested on a lab-scale prototype built for that purpose. The cooling kinetic of a mixture of ethanol, ethylene glycol and water (a usual pressurizing medium) was followed, recording temperatures in the whole sample. A mathematical model has been developed to describe heat transfer during cooling of the sample in the vessel. The heat transfer coefficient between the refrigerant and the vessel was determined by a fitting procedure between the numerical simulation results and the experimental measurements. This model should be used to predict the cooling kinetics in other conditions (other products, larger vessels) and to optimise the process., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

“This is an Accepted Manuscript of an article published by Taylor & Francis in Inverse Problems in Science and Engineering on 26-jun-2019, available online: https://www.tandfonline.com/doi/full/10.1080/17415977.2019.1632841.”, In this paper we introduce a method to estimate a pressure dependent thermal conductivity coefficient arising in a heat diffusion model with applications in food technology. The strong smoothing effect of the corresponding direct problem renders the inverse problem under consideration severely ill-posed. Thus specially tailored methods are necessary in order to obtain a stable solution. Consequently, we model the uncertainty of the conductivity coefficient as a hierarchical Gaussian Markov random field (GMRF) restricted to uniqueness conditions for the solution of the inverse problem established in Fraguela et al. [1]. Furthermore, we propose a Single Variable Exchange Metropolis-Hastings algorithm (SVEMH) to sample the corresponding conditional probability distribution of the conductivity coefficient given observations of the temperature. Sensitivity analysis of the direct problem suggests that large integration times are necessary to identify the thermal conductivity coefficient. Numerical evidence indicates that a signal to noise ratio of roughly 10 cubed suffices to reliably retrieve the thermal conductivity coefficient., Ministerio de Economía y Competitividad (MINECO), Universidad Complutense de Madrid, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

High Pressure (HP) Processing has turned out to be very e®ective in prolonging the shelf life of some food. This paper deals with the modelling and simulation of the e®ect of the combination of high pressure and thermal treatments on food processing, focusing on the inactivation of certain enzymes. The behavior and stability of the proposed models are checked by various numerical examples. Furthermore, various simpli¯ed versions of these models are presented and compared with each other in terms of accuracy and computational time. The models developed in this paper provide a useful tool to design suitable industrial equipments and optimize the processes., Ministry of Education and Science[MTM2007-64540, MTM2007-04621/MTM]; Ingenio Matematica (i-MATH)[CSD2006, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

El proyecto de innovación ha consistido en el diseño de un modelo de garantía de calidad para los títulos de formación permanente de la Universidad Complutense de Madrid, especialmente centrado en los programas de máster de formación permanente, capaz de garantizar la calidad y el rigor académico y científico de los títulos, alineado con los Criterios y directrices para el Aseguramiento de la Calidad en el Espacio Europeo de Educación Superior (ESG) y con las orientaciones realizadas por Red Española de Agencias de Calidad (REACU) para el aseguramiento de la calidad de los títulos de formación permanente.

Este proyecto de innovación docente de la Universidad Complutense de Madrid ha desarrollado una serie de contenidos online con elementos interactivos, integrados en la plataforma libretext.org, que permita a los estudiantes el aprendizaje de los fundamentos matemáticos de la inteligencia artificial de una manera autónoma, clara y sencilla.

This document provides a detailed methodology for designing and evaluating InquiryBased Mathematics Evaluation in university education. In this sense, our objective is twofold: on the one hand, it must be useful for designing teaching activities coherent with Inquiry-based teaching, focusing in both the evaluation with respect to the learning and engagement of students and the evaluation of the design and implementation of the task itself. On the other hand, it helps lectures to develop schemes for learning outcomes and mathematical competence, as well as to monitor and assess students’ engagement in Inquiry-based activities. This methodology is composed of three stages: before, during, and after the inquiry. These stages include different subtasks that lecturers must follow in order to fulfil the objectives described above. Finally, these guidelines are exemplified by a collection of experiences that illustrate how they can be used in different contexts. Lecturers can follow these examples when designing their own activities.

Informe del proyecto de innovación docente para el diseño de una metodología b-learning en distintos grupos de las asignaturas de segundo curso del programa de grados de la Facultad de Matemáticas y desarrollo de materiales de autoaprendizaje y prácticas virtuales.

Resumen del proyecto PIMCD 232 (2017) que presenta el diseño y uso de un sistema de seguimiento de egresados en la Facultad de Matemáticas para análisis de empleabilidad así como para información que valga para la mejora de las titulaciones.

In this paper, we identify a time-dependent thermal expansion function when some information about the temperature is known. This inverse problem is motivated by models that arise in food engineering. In particular, the model studied here describes high-pressure processes and it is governed by the heat equation with Robin boundary conditions in a cylindrical spatial domain. We study the inverse problem, proving a uniqueness result and obtaining a numerical scheme to compute the thermal expansion function. Several numerical examples are shown., Spanish ‘Ministry of Economy and Competitiveness’, Comunidad de Madrid, European Social Fund, Universidad Complutense de Madrid, Banco de Santander, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, inpress

This paper deals with the problem of determining the time-dependent thermal diffusivity coefficient of a medium, when the evolution of the temperature in a part of it is known. Such situations arise in the context of food technology, when thermal processes at high pressures are used for extending the shelf life of the food, in order to preserve its nutritional and organoleptic properties (Infante et al 2009 On the Modelling and Simulation of High Pressure Processes and Inactivation of Enzymes in Food Engineering pp 2203–29 and Otero et al 2007 J. Food Eng. 78 1463–70). The phenomenon is modeled by the heat equation involving a term which depends on the source temperature and pressure increase, and appropriate initial and boundary conditions. We study the inverse problem of determining time-dependent thermal diffusivities k, when some temperature measurements at the border and inside the medium are known. We prove the uniqueness of the inverse problem solution under suitable a priori assumptions on regularity, size and growth of k., Comunidad de Madrid, Ministerio de Educación, Cultura y Deporte, Ministerio de Economía y Competitividad (MINECO), Fundacion Caja Madrid, European Social Fund, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

This article deals with an inverse problem concerning the identification of the heat exchange coefficient H (assumed depending on the temperature and/or pressure) between a certain material with the external environment, when only experimental measurements of the temperature are supposed to be known. The main difficulties are that we consider the case of functions H depending on the solution of the state equation and we use experimental data that may have errors. We develop rigorous mathematical strategies for this identification. We separately consider pressure and temperature dependence and, in both cases, we set several scenarios for the inverse problem. For each scenario, we know the initial and ambient temperatures, we identify function H through different methods and we obtain error bounds in adequate norms (uniform and square integrable). Finally, we perform numerical tests in order to compare the results obtained with these algorithms and with some classical regularization algorithms., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

Se modeliza el tratamiento a altas presiones de alimentos, haciendo especial énfasis en su simulación computacional, para diseñar metodologías que contribuyan a la optimización de los procesos. Los modelos que se utilizan son complejos y requieren sofisticadas herramientas numéricas para su resolución aproximada. Pero además, en las ecuaciones aparecen parámetros físicos característicos de los materiales que son sensibles a los cambios de presión y temperatura y no suelen ser conocidos para presiones distintas de la atmosférica. En la primera parte se presenta un modelo matemático que permite trabajar con fluidos compresible cuya simulación numérica describe el comportamiento térmico y fluidodinámico de la muestra de alimento, cuando es sometida a un tratamiento a altas presiones. Este modelo se acopla con ecuaciones cinéticas que modelizan la actividad degradante de diversas enzimas; su resolución numérica permite estimar la inactivación de estas enzimas tras el uso de diversos tratamientos. El resto de la memoria está motivada por la mencionada falta de información relativa a los parámetros físicos de este tipo de problemas. Se pretende identificar los valores que, para cada material en concreto, toman esos coeficientes en un rango de temperaturas y presiones dados, partiendo de una cantidad (lo menor posible) de mediciones de la temperatura. Esto nos coloca en el contexto de los problemas inversos, y en él se diseñan algoritmos numéricos mediante los que se consigue identificar dos de estos parámetros: para un modelo simplificado planteado como un problema de valor inicial en dimensión uno, el coeficiente de intercambio de calor, que puede depender de la presión y/o de la temperatura (que es la incógnita de la ecuación diferencial ordinaria); y para un segundo modelo simplificado que se plantea como una ecuación en derivadas parciales con condiciones de contorno mixtas, el coeficiente de conductividad térmica (dependiente de la presión).

This paper deals with an inverse problem concerning the identification of the heat exchange coefficient H (assumed depending on the temperature) between a certain material with the external environment (see, e.g., [2], [4] for real applications modelled with equations involving this coefficient). Only experimental measurements of the temperature are supposed to be known. The goal is to identify H in order to get a solution for the corresponding model, approximating same given temperature measurements. We begin by setting several scenarios for the inverse problem. For each scenario, we know the initial and ambient temperatures, identify function H through different methods and obtain error bounds in adequate norms (uniform and square integrable). Finally, we study the inverse problem in the framework of the classical theory for Hilbert spaces. Several methods are used (Tikhonov, Morozov, Landweber,...) and the approximations obtained, as well as the one provided by the previous algorithm, are shown.

A model for the simulation of thermal exchanges in a high-pressure equip-ment prototype is developed. Good agreement between simulated and experimental time-temperature profiles is found during different tests. The model allows to study the effectof the different variables implied in it and its variation in order to have a better ther-mal control in the treatments performed. This work involves an important advance inoptimization of high-pressure processes in food industry

We introduce a full approximation storage (FAS) multigrid algorithm to find the finite element solution for a class of nonlinear monotone elliptic problems. Since the solution of the problem is equivalent to minimize a strictly convex functional, we use a Polak-Ribiere conjugate gradient method as the nonlinear smoother in our algorithm. The advantage in so doing is that we do not have to calculate derivatives of operators. We prove local convergence of our algorithm and illustrate its performance by solving benchmark problems., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

We consider the finite-difference and finite-element space discretization of the 1 - d wave equation with homogeneous Dirichlet boundary conditions in a bounded interval. We analyze the problem of estimating the total energy of solutions in terms of the energy concentrated on the boundary, uniformly as the net-spacing h --> 0. We prove that there is no such a uniform bound due to spurious high frequencies. We prove however an uniform bound in suitable subspaces of solutions that eventually cover the whole energy space., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub