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Desde el Instituto de Matemática Interdisciplinar (IMI), se propone la implantación de un nuevo método de gestión de la información relativa a las publicaciones científicas de los miembros del Instituto. Este procedimiento, basado en la creación de una base de datos que recoja los principales aspectos bibliométricos de las publicaciones, permitirá al Instituto llevar a cabo un seguimiento interno de la calidad de los trabajos científicos de los miembros del Instituto. Además, se busca ampliar la difusión de las publicaciones a través de los medios de los que dispone el Instituto: su web y el boletín semanal de noticias, llamado Boletín del IMI. Para poder llevar a cabo esta labor, se requiere un equipo y soporte informático adecuado que permita su constante actualización, lo cual supondría la principal parte del presupuesto solicitado. La parte restante se destinaría a maximizar la difusión de las publicaciones y actividades organizadas por el Instituto mediante la adquisición de material fungible y adquisición de DOIs. El equipo está conformado por dos PDI, los Profesores Ángel Manuel Ramos del Olmo, del dpto. de Análisis Matemático y Matemática Aplicada, y Begoña Vitoriano Villanueva, del dpto. de Estadística e Investigación Operativa; dos PAS, Tzveta Petkova Petkova y Fernando Porqueras Arabolaza; y dos estudiantes, Federico Herrero Hervás y Álvaro Salinas Trejo, siendo así de carácter interdisciplinar e interdepartamental, contando con miembros de cada categoría.

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

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

CRUE-CSIC (Acuerdos Transformativos 2023), In this work, we propose a novel methodology to identify parameters of compartmental epidemiological models. It is based on solving a multi-objective optimization problem that consists in fitting some of the model outputs to real observations. First, according to the available data of the considered epidemic, we define a multi-objective optimization problem where the model parameters are the optimization variables. Then, this problem is solved by considering a particular optimization algorithm called ParWASF-GA (Parallel Weighting Achievement Scalarizing Function Genetic Algorithm). Finally, the decision maker chooses, within the set of possible solutions, the values of parameters that better suit his/her preferences. In order to illustrate the benefit of using our approach, it is applied to estimate the parameters of a deterministic epidemiological model, called Be-CoDiS (Between-Countries Disease Spread), used to forecast the possible spread of human diseases within and between countries. We consider data from different Ebola outbreaks from 2014 up to 2019. In all cases, the proposed methodology helps to obtain reasonable predictions of the epidemic magnitudes with the considered model., Ministerio de Ciencia e Innovación (MICINN), Junta de Andalucía, Universidad Complutense de Madrid, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

The main goal of this work is to discuss a controllability approach to the image matching/shape identification problem, an important issue in many applications, medical ones in particular. The matching problem is formulated as an approximate controllability problem involving a cost functional whose gradient is computed using an adjoint equation based methodology. The time discrete version of the image matching problem is also discussed in this work., Dirección General de Universidades e Investigación de la Conserjería de Educación de la Comunidad de Madrid, Universidad Complutense de Madrid, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

t The goal of this paper is to find robust structures for a given main load and its perturbations. In the first part, we show the mathematical formulation of an original variance-expected compliance model used for structural optimization. In the second part, we study the interest of this model on two 3D benchmark test cases and compare the obtained results with those given by an expected compliance model, Comunidad de Madrid, Ministerio de Educación y Ciencia (España), Banco de Santander, Universidad Complutense de Madrid, FONDECYT, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

In this article, we focus on the design of code division multiple access filters (used in data transmission) composed of a particular optical fiber called sampled fiber Bragg grating (SFBG). More precisely, we consider an inverse problem that consists in determining the effective refractive index profile of an SFBG that produces a given reflected spectrum. In order to solve this problem, we use an original multi-layers semi-deterministic global optimization method based on the search of suitable initial conditions for a given optimization algorithm. The results obtained with our optimization algorithms are compared, in term of complexity and final design, with those given by an hybrid genetic algorithm (the method generally considered in the literature for designing SFBGs)., Comunidad de Madrid, Ministerio de Economía y Competitividad (España), Banco de Santander, Universidad Complutense, Unión Europea, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

This work focuses on the optimization of some high-pressure and temperature food treatments. When dealing with real--life multi-objective optimization problems, the computational cost of evaluating the considered objective functions is usually quite high. Therefore, only a reduced number of iterations is affordable for the optimization algorithm. However, using fewer iterations can lead to inaccurate solutions far from the real Pareto optimal front. In this work, we analyze and compare different mechanisms to improve the convergence of a preference-based multi-objective optimization algorithm called Weighting Achievement Scalarizing Function Genetic Algorithm. The combination of these techniques has been applied for optimizing a particular food treatment process. In particular, the proposed method based on the introduction of an advanced population achieves important improvements in the considered quality indicator measures., Ministerio de Economía y Competitividad (MINECO), Junta de Andalucía, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Climate change is affecting the ecosystem and many of the factors associated with human and animal diseases. In particular, significant changes in insect-borne diseases have been shown. The clearest example is found in Europe regarding the bluetongue virus (BTV), a disease of ruminants transmitted by insects (Culicoides spp.). Traditionally this disease was distributed below the 40th parallel, but since 2006 spread to northern Europe where the situation is now endemic. This spread of BTV has been produced by several factors. First, there is a direct relationship between the increased of temperature and the presence of Culicoides. It is also important to highlight the role of the wind in the movement of insects, and could be a significant mode of transmission of vector-borne diseases (such as bluetongue) from endemic areas to free areas. In Spain, the introduction of Culicoides by the wind has not formally been proved, but many experts and epidemiological data has hypothesized it, especially in the first outbreaks occurred in 2004 in the Iberian Peninsula. The objective of the model described here has been, first, to predict the number of Culicoides introduced by the wind and its potential survival in Spain and, secondly, to assess the impact that a potential increase in temperature could have on the distribution and survival Culicoides in Spain. This model will help to identify locations and time periods at highest risk for mosquitoes introduction and survival, and will help to optimize efforts and better prevent and control future outbreaks of bluetongue in the country., El cambio climático está afectando al ecosistema y con ello a muchos de los factores asociados con enfermedades humanas y animales. En particular, se ha demostrado cambios importantes en las enfermedades transmitidas por insectos. El ejemplo más claro se encuentra en Europa referente al virus de la lengua azul, enfermedad de los rumiantes transmitida por insectos (Culicoides spp.). Tradicionalmente esta enfermedad se distribuía por debajo del paralelo 40, pero desde 2006 se ha difundido hacia el norte de Europa y desde entonces la situación es endémica. Esta difusión se ha podido producir por varios factores. En primer lugar, existe una relación directa entre el aumento de temperatura y la presencia de Culicoides. Además, es importante destacar el papel del viento en el movimiento de los insectos, y podría ser un modo de transmisión importante de enfermedades como la lengua azul desde zonas endémicas a las zonas libres. 121 Cianci, C et al. Revista Complutense. En España, la introducción de Culicoides por el viento no está formalmente demostrada, pero hay muchos expertos y datos epidemiológicos que lo sugieren, sobre todo en los primeros brotes que se produjeron en 2004 en la Península Ibérica. El objetivo del modelo aquí descrito ha sido, en primer lugar, predecir el número de Culicoides introducidos por el viento y su potencial supervivencia en España y, en segundo lugar, evaluar el impacto que un potencial incremento de temperatura podría tener en la distribución y supervivencia de Culicoides en España. Este modelo permitirá la identificación de lugares y períodos de tiempo con mayor riesgo de introducción de los mosquitos y de su supervivencia, y ayudará a optimizar los esfuerzos de prevención y control de futuras epidemias de lengua azul en el país., Ministerio de Educación y Ciencia (España), Banco de Santander, Universidad Complutense, Comunidad de Madrid”, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

This article is concerned with the numerical solution of multiobjective control problems associated with nonlinear partial differential equations and more precisely the Burgers equation. For this kind of problems, we look for the Nash equilibrium, which is the solution to a noncooperative game. To compute the solution of the problem, we use a combination of finite-difference methods for the time discretization, finite-element methods for the space discretization, and a quasi-Newton BFGS algorithm for the iterative solution of the discrete control problem. Finally, we apply the above methodology to the solution of several tests problems. To be able to compare our results with existing results in the literature, we discuss first a single-objective control problem, already investigated by other authors. Finally, we discuss the multiobjective case., Universidad Complutense de Madrid, Texas Higher Education Coordinating Board, DGES, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

This work deals with some numerical experiments regarding the distributed control of semilinear parabolic equations of the type y(t) - y(xx) + f (y) = u(Xw), in (0, 1) x (0, T), with Neumann and initial auxiliary conditions, where w is an open subset of (0, 1), f is a C-1 nondecreasing real function, a is the output control and T > 0 is (arbitrarily) fixed. Given a target state y(T) we study the associated approximate controllability problem (given epsilon > 0, find u is an element of L-2(0, T), such that parallel toy(T; u) - y(T)parallel to(L2(0,1)) less than or equal to epsilon) by passing to the limit (when k --> infinity) in the penalized optimal control problem. (find u(k) as the minimum of J(k)(u) = 1/2 parallel touparallel to(L2)(2) ((0,T)) + (k/2)parallel toy(T; u) -y(T)parallel to(L2)(2) ((0,1))). In the superlinear case (e.g., f (y) = \y\(n-1)y, n > 1) the existence of two obstruction functions Y+/-infinity shows that the approximate controllability is only possible if Y-infinity (x,T) +/- y(T)(x) less than or equal to Y-infinity(x,T) for a.e. x is an element of (0, 1). We carry out some numerical experiments showing that, for a fixed k, the "minimal cost" J(k)(u) (and the norm of the optimal control u(k)) for a superlinear function f becomes much larger when this condition is not satisfied. We also compare the values of J(k)(u) (and the norm of the optimal control u(k)) for a fixed y(T) associated with two nonlinearities: one sublinear and the other one superlinear., European project, Ministerio de Ciencia y Tecnologfa of Spain. “Ramón y Cajal, MCYT, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

High-pressure freezing processes are a novel emerging technology in food processing, offering significant improvements to the quality of frozen foods. To be able to simulate plateau times and thermal history under different conditions, in this work, we present a generalized enthalpy model of the high-pressure shift freezing process. The model includes the effects of pressure on conservation of enthalpy and incorporates the freezing point depression of non-dilute food samples. In addition, the significant heat-transfer effects of convection in the pressurizing medium are accounted for by solving the two-dimensional Navier-Stokes equations. We run the model for several numerical tests where the food sample is agar gel, and find good agreement with experimental data from the literature., Ministerio de Ciencias e Inovación, MOMAT, Comunidad de Madrid, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

This article is concerned with the numerical solution of multiobjective control problems associated with linear partial differential equations. More precisely, for such problems, we look for the Nash equilibrium, which is the solution to a noncooperative game. First, we study the continuous case. Then, to compute the solution of the problem, we combine finite-difference methods for the time discretization, finite-element methods for the space discretization, and conjugate-gradient algorithms for the iterative solution of the discrete control problems. Finally, we apply the above methodology to the solution of several tests problems., DGES, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

3rd International Congress on Industrial and Applied Mathematics (ICIAM 95), In this communication we develop and improve some of the results of [4] on the approximate controllability of several semilinear parabolic boundary value problems where the nonlinear term appears either at the second order parabolic equation or at the put boundary condition. We also distinguish the cases where the control function acts on the interior of the parabolic set Q := R x (0, T) from the one in which the control acts on the boundary Sigma := partial derivative Omega x (0, T). Most of our results will concern to control problems with final observation i.e. our goal is to prove that the set {y(T, : v)} generated by the value of solutions at time T is dense in L(2)(Omega) when v runs through the set of controls. Nevertheless we also consider a control problem with a boundary observation. In that case we shall prove that if Sigma(1) subset of Sigma then the set {y(.,.:v}/(Sigma 1)} generated by the trace of solutions on Sigma(1) is a dense subset of L(2)(Sigma(1)) when v runs through the set of controls., DGICYT (Spain), Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We prove the approximate controllability of several nonlinear parabolic boundary-value problems by means of two different methods: the first one can be called a Cancellation method and the second one uses the Kakutani fixed-point theorem., DGICYT (Spain), Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Special Issue: One World, One Health, One Virology — Selected papers from the IXth International Congress of Veterinary Virology, organized by the European Society for Veterinary Virology, The study presented here is one of the very first aimed at exploring the potential spread of classical swine fever (CSF)from backyard pigs to other domestic pigs. Specifically, we used a spatial stochastic spread model, called Be-FAST, to evaluate the potential spread of CSF virus (CSFV) in Bulgaria, which holds a large number of backyards (96% of the total number of pig farms) and is one of the very few countries for which backyard pigs and farm counts are available. The model revealed that, despite backyard pigs being very likely to become infected, infections from backyard pigs to other domestic pigs were rare. In general, the magnitude and duration of the CSF simulated epidemics were small, with a median [95% PI] number of infected farms per epidemic of 1 [1,4] and a median [95% PI] duration of the epidemic of 44 [17,101] days. CSFV transmission occurs primarily (81.16%) due to indirect contacts (i.e. vehicles, people and local spread) whereas detection of infected premises was mainly (69%) associated with the observation of clinical signs on farm rather than with implementation of tracing or zoning. Methods and results of this study may support the implementation of risk-based strategies more cost-effectively to prevent, control and, ultimately, eradicate CSF from Bulgaria. The model may also be easily adapted to other countries in which the backyard system is predominant. It can also be used to simulate other similar diseases such as African swine fever, Unión Europea. FP7, Comunidad de Madrid, Ministerio de Ciencia e Innovación (España), Fundación Caja Madrid, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Ebola virus disease is a lethal human and primate disease that currently requires a particular attention from the international health authorities due to important outbreaks in some Western African countries and possible spread to other continents, which has already occurred in the USA and Spain. Regarding the emergency of this situation, there is a need of development of decision tools to assist the authorities to focus their efforts in important factors to eradicate Ebola. In particular, mathematical modelling can help to predict the possible evolution of the Ebola outbreaks and to give some recommendations about surveillance. In this work, we propose a novel spatial and temporal model, called Be-CoDiS (BetweenCOuntries Disease Spread), to study the evolution of human diseases between countries. The goal is to simulate the spread of a particular disease and identify risk zones worldwide. The main interesting characteristics of Be-CoDiS are the consideration of the migratory flux between countries and control measure effects and the use of time dependent coefficients adapted to each country. First, we focus on the mathematical formulation of each component of the model. Next, in order to validate our approach, we consider various numerical experiments regarding the 2014 Ebola epidemic. In particular, we study the ability of the model in predicting the EVD evolution at 30 days and until the end of the epidemic. The results are compared to real data and other models outputs found in the literature. Finally, a brief parameter sensitivity analysis is done., Ministerio de Economia y Competitividad (España), Junta de Andalucía, European Regional Development Fund (ERDF), Banco de Santander, Universidad Complutense de Madrid, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, FALSE, submitted

A new stochastic and spatial model was developed to evaluate the potential spread of classical swine fever virus (CSFV) within- and between-farms, and considering the specific farm-to-farm contact network. Within-farm transmission was simulated using a modified SI model. Between-farm transmission was assumed to occur by direct contacts (i.e. animal movement) and indirect contacts (i.e. local spread, vehicle and person contacts) and considering the spatial location of farms. Control measures dictated by the European legislation (i.e. depopulation of infected farms, movement restriction, zoning, surveillance, contact tracing) were also implemented into the model. Model experimentation was performed using real data from Segovia, one of the provinces with highest density of pigs in Spain, and results were presented using the mean, 95% probability intervals [95% PI] and risk maps. The estimated mean [95% PI] number of infected, quarantined and depopulated farms were 3 [1,17], 23 [0,76] and 115 [0,318], respectively. The duration of the epidemic was 63 [26,177] days and the most important way of transmission was associated with local spread (61.4% of the infections). Results were consistent with the spread of previous CSFV introductions into the study region. The model and results presented here may be useful for the decision making process and for the improvement of the prevention and control programmes for CSFV., Ministerio de Ciencia e Innovación (España), Universidad Complutense, Junta de Castillla y León, Ministerio de Medio Ambiente y Medio Rural y Marino (España), Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

In this work, we study the mathematical analysis of a coupled system of two reaction-diffusion-advection equations and Danckwerts boundary conditions, which models the interaction between a microbial population (e.g., bacterias) and a diluted substrate (e.g., nitrate) in a continuous flow bioreactor. This type of bioreactor can be used, for instance, for water treatment. First, we prove the existence and uniqueness of solution, under the hypothesis of linear reaction by using classical results for linear parabolic boundary value problems. Next, we prove the existence and uniqueness of solution for some nonlinear reactions by applying \textit{Schauder Fixed Point Theorem} and the theorem obtained for the linear case. Results about the nonnegativeness and boundedness of the solution are also proved here., Ministry of Science and Innovation, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

In this paper, we focus in developing a stochastic model for topology optimization. The principal objective of such a model is to find robust structures for a given main load having a stochastic behavior. In the first part, we present the expected compliance formulation and some results in topology optimization. Then, in order to illustrate the interest of our approach, we consider a preliminary 3D cantilever benchmark experiment and compare the obtained results with the one given by a single load approach., Comunidad de Madrid, Ministerio de Educación y Ciencia (España), Universidad de los Andes, FONDECYT, UCM, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

This paper has two objectives. We introduce a new global optimization algorithm reformulating optimization problems in terms of boundary-value problems. Then, we apply this algorithm to a pointwise control problem of the viscous Burgers equation, where the control weight coefficient is progressively decreased. The results are compared with those obtained with a genetic algorithm and an LM-BFGS algorithm in order to check the efficiency of our method and the necessity of using global optimization techniques., Ministerio de Educación y Ciencia, Dirección General e Investigación de la Conserjería de Educación de la Comunidad de Madrid, Universidad Complutense de Madrid, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

Classical Swine Fever is a viral disease of pigs that causes severe restrictions on the movement of pigs and pig products in the affected areas. The knowledge of its spread patterns and risk factors would help to implement specific measures for controlling future outbreaks. In this article, we describe in detail a spatial hybrid model, called Be-FAST, based on the combination of a stochastic Individual-Based model (modeling the interactions between the farms, considered as individuals) for between-farm spread with a Susceptible-Infected model for within-farm spread, to simulate the spread of this disease and identify risk zones in a given region. First, we focus on the mathematical formulation of each component of the model. Then, in order to validate Be-FAST, we perform various numerical experiments considering the Spanish province of Segovia. Obtained results are compared with the ones given by two other Individual-Based models and real outbreaks data from Segovia and The Netherlands, Comunidad de Madrid, Ministerio de Ciencia e Innovación (España), Banco de Santander, Universidad Complutense de Madrid (Ref. 910480), Fondo Social Europeo, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

The objective of this article is to discuss the modelling and simulation of the motion of oil spots in the open sea, and the effect on the pollutant concentration when a polluted water pumping ship follows a pre-assigned trajectory to remove the pollutant. We assume here that the oil spots motion is due to the coupling of diffusion, the transport from the wind, sea currents and pumping process and the reaction due to the extraction of oil, implying that the mathematical model will be of advection-reaction-diffusion type. Our discussion includes the description of a parallelization of the selected numerical procedure. We present some results of numerical experiments showing that indeed the parallelization makes the model evaluation more efficient, Spanish Ministry of Science and Innovation, MOMAT, Scientific Computing Advanced Training, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

In this paper, we develop a stochastic model for topology optimization. We find robust structures that minimize the compliance for a given main load having a stochastic behavior. We propose a model that takes into account the expected value of the compliance and its variance. We show that, similarly to the case of truss structures, these values can be computed with an equivalent deterministic approach and the stochastic model can be transformed into a nonlinear programming problem, reducing the complexity of this kind of problems. First, we obtain an explicit expression (at the continuous level) of the expected compliance and its variance, then we consider a numerical discretization (by using a finite element method) of this expression and finally we use an optimization algorithm. This approach allows to solve design problems which include point, surface or volume loads with dependent or independent perturbations. We check the capacity of our formulation to generate structures that are robust to main loads and their perturbations by considering several 2D and 3D numerical examples. To this end, we analyze the behavior of our model by studying the impact on the optimized solutions of the expected-compliance and variance weight coefficients, the laws used to describe the random loads, the variance of the perturbations and the dependence/independence of the perturbations. Then, the results are compared with similar ones found in the literature for a different modeling approach., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, inpress

We study an optimal control problem for a semilinear elliptic boundary value problem giving rise to a free boundary. Here, the free boundary is generated due to the fact that the nonlinear term of the state equation is not differentiable. The new aspect considered in this paper, with respect to other control problems involving free boundaries, is that here the cost functional explicitly depends on the location of the free boundary. The main difficulty is to show the continuous dependence (in measure) of the free boundary with respect to the control function. The crucial tool to get such continuous dependence is to know how behaves the state solution near the free boundary, as in previous works by L.A. Caffarelli and D. Phillips among other authors. Here we improved previous results in the literature thanks to a suitable application of the Fleming-Rishel formula., Unión Europea. FP7, Comunidad de Madrid, UCM, DGISPI, Spain, AMR, Fundación Caja Madrid, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We present a method to factorize a second-order boundary value problem in a cylindrical domain in a system of uncoupled first-order initial value problems, together with a nonlinear Riccati-type equation for functional operators. This uncoupling is obtained by a space invariant embedding technique along the axis of the cylinder. This method can be viewed as an infinite-dimensional generalization of the block Gauss LU factorization., Ministerio de Ciencia y Tecnología of Spain, Ramón y Cajal, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), 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 objetivo de esta tesis es el diseño e implementación de un algoritmo numérico para la solución de juegos diferenciales, tanto deterministas como estocásticos, en equilibrios de Nash en bucle cerrado ya horizonte infinito. Estos juegos son de especial relevancia puesto que, en la literatura, suelen ser los más comunes debido a sus amplias aplicaciones. Este algoritmo se denomina RaBVItG (Radial Basis and Value Iteration for Games) dadas las principales características de su diseño. Desde nuestro punto de vista, este algoritmo puede considerarse innovador, puesto que en la literatura no hemos encontrado un competidor que resuelva tanto juegos deterministas como estocásticos. Además, cuenta con un diseño "sin mallado", de tal forma que pueden resolverse juegos con N jugadores, donde N es mucho mayor que 2 (en la literatura suelen plantearse algoritmos para mallados con 2 jugadores). En este trabajo, utilizaremos los artículos [13] (en el caso determinista) y [76] (en el caso estocástico) como dos referencias con las que poder compararnos siempre que sea posible. Los principales resultados se enmarcan, por un lado, en la eficiencia del algoritmo. Comparado, por ejemplo, con [13], RaBVItG presenta menor tiempo de cálculo y menor error, en general, debido a la ventaja que supone no tener que usar un mallado. Otro conjunto de resultados de interés son las aplicaciones del algoritmo a dos casos prácticos de dos áreas de conocimiento: marketing y psicología matemática. Estos dos campos, a su vez, están abriendo líneas futuras de investigación donde poder usar el algoritmo y sus sucesivas mejoras..., The goal of this thesis is the design and implementation of a numerical algorithm for solving deterministic and stochastic infinite horizon differential games in closed-loop Nash equilibria. These games are specially relevant since, in the Literature, are the most commonly used due to their wide range of applications. We call the algorithm RaBVItG (Radial Basis and Value Iteration for Games) trying to specify the main characteristics of its design.The algorithm introduced here can be considered innovative because, as far as we know, we have not found a competitor solving both deterministic and stochastic cases. Additionally, the algorithm has a "mesh-free" design, so that it is possible to solve games with N players, where N is considerably greater than 2. We use the reference papers [13] in the deterministic case and [76] in the stochastic, as two main works to compare with our results.Our remarkable results are twofold. On the one hand, the algorithm’s efficiency: Comparing with [13], RaBVItG outperforms needing less computational time and lower errors. This is possible, in general, due to the advantages of the "mesh-free" computational design. On the other hand, we apply our algorithm to two problems borrowed from two scientific fields such as Marketing and Mathematical Psychology. Both contributions are opening future researching lines to use the algorithm and its future improvements...

CRUE-CSIC (Acuerdos Transformativos 2021), The continuous mutation of SARS-CoV-2 opens the possibility of the appearance of new variants of the virus with important differences in its spreading characteristics, mortality rates, etc. On 14 December 2020, the United Kingdom reported a potentially more contagious coronavirus variant, present in that country, which is referred to as VOC 202012/01. On 18 December 2020, the South African government also announced the emergence of a new variant in a scenario similar to that of the UK, which is referred to as variant 501.V2. Another important milestone regarding this pandemic was the beginning, in December 2020, of vaccination campaigns in several countries. There are several vaccines, with different characteristics, developed by various laboratories and research centers. A natural question arises: what could be the impact of these variants and vaccines on the spread of COVID-19? Many models have been proposed to simulate the spread of COVID-19 but, to the best of our knowledge, none of them incorporates the effects of potential SARS-CoV-2 variants together with the vaccines in the spread of COVID-19. We develop here a -SVEIHQRD mathematical model able to simulate the possible impact of this type of variants and of the vaccines, together with the main mechanisms influencing the disease spread. The model may be of interest for policy makers, as a tool to evaluate different possible future scenarios. We apply the model to the particular case of Italy (as an example of study case), showing different outcomes. We observe that the vaccines may reduce the infections, but they might not be enough for avoiding a new wave, with the current expected vaccination rates in that country, if the control measures are relaxed. Furthermore, a more contagious variant could increase significantly the cases, becoming the most common way of infection. We show how, even with the pandemic cases slowing down (with an effective reproduction number less than 1) and the disease seeming to be u, Ministerio de Ciencia, Innovación y Universidades (España), Universidad Complutense de Madrid, Fondo Europeo de Desarrollo Regional, Junta de Andalucía, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

Since the start of the COVID-19 pandemic in China many models have appeared in the literature, trying to simulate its dynamics. Focusing on modeling the biological and sociological mechanisms which influence the disease spread, the basic reference example is the SIR model. However, it is too simple to be able to model those mechanisms (including the three main types of control measures: social distancing, contact tracing and health system measures) to fit real data and to simulate possible future scenarios. A question, then, arises: how much and how do we need to complexify a SIR model? We develop a -SEIHQRD model, which may be the simplest one satisfying the mentioned requirements for arbitrary territories and can be simplified in particular cases. We show its very good performance in the Italian case and study different future scenarios., Depto. de Economía Financiera y Actuarial y Estadística, Depto. de Análisis Matemático y Matemática Aplicada, Instituto de Matemática Interdisciplinar (IMI), Fac. de Ciencias Económicas y Empresariales, Fac. de Ciencias Matemáticas, FALSE, pub

Preparar al profesorado novel de matemáticas para una docencia universitaria de calidad, en el desarrollo de competencias y conocimiento estratégico para aprender a enseñar Matemáticas. Ejemplificaciones e instrumentos de evaluación para el aula., To prepare new mathematics lecturers for quality university teaching, in the development of strategic knowledge and skills to learn how to teach Mathematics. Exemplifications and evaluation instruments for the classroom.

El objetivo de esta tesis es el diseño e implementación de un algoritmo numérico para la solución de juegos diferenciales, tanto deterministas como estocásticos, en equilibrios de Nash en bucle cerrado ya horizonte infinito. Estos juegos son de especial relevancia puesto que, en la literatura, suelen ser los más comunes debido a sus amplias aplicaciones. Este algoritmo se denomina RaBVItG (Radial Basis and Value Iteration for Games) dadas las principales características de su diseño. Desde nuestro punto de vista, este algoritmo puede considerarse innovador, puesto que en la literatura no hemos encontrado un competidor que resuelva tanto juegos deterministas como estocásticos. Además, cuenta con un diseño "sin mallado", de tal forma que pueden resolverse juegos con N jugadores, donde N es mucho mayor que 2 (en la literatura suelen plantearse algoritmos para mallados con 2 jugadores). En este trabajo, utilizaremos los artículos [13] (en el caso determinista) y [76] (en el caso estocástico) como dos referencias con las que poder compararnos siempre que sea posible. Los principales resultados se enmarcan, por un lado, en la eficiencia del algoritmo. Comparado, por ejemplo, con [13], RaBVItG presenta menor tiempo de cálculo y menor error, en general, debido a la ventaja que supone no tener que usar un mallado. Otro conjunto de resultados de interés son las aplicaciones del algoritmo a dos casos prácticos de dos áreas de conocimiento: marketing y psicología matemática. Estos dos campos, a su vez, están abriendo líneas futuras de investigación donde poder usar el algoritmo y sus sucesivas mejoras...

Preparar al profesorado novel de matemáticas para una docencia universitaria de calidad, mediante el desarrollo de competencias y conocimiento estratégico para aprender a enseñar Matemáticas. Se desarrollan ejemplificaciones para ser implementadas.

This work focuses on the optimization of some high-pressure and temperature food treatments. When dealing with real--life multi-objective optimization problems, the computational cost of evaluating the considered objective functions is usually quite high. Therefore, only a reduced number of iterations is affordable for the optimization algorithm. However, using fewer iterations can lead to inaccurate solutions far from the real Pareto optimal front. In this work, we analyze and compare different mechanisms to improve the convergence of a preference-based multi-objective optimization algorithm called Weighting Achievement Scalarizing Function Genetic Algorithm. The combination of these techniques has been applied for optimizing a particular food treatment process. In particular, the proposed method based on the introduction of an advanced population achieves important improvements in the considered quality indicator measures., Ministerio de Economía y Competitividad (MINECO), Junta de Andalucía, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Preparar al profesorado novel de matemáticas para una docencia universitaria de calidad, mediante el desarrollo de competencias y conocimiento estratégico para aprender a enseñar Matemáticas. Se desarrollan ejemplificaciones para ser implementadas.

En esta tesis se han aplicado diversas herramientas matemáticas con el objetivo de estudiar dos fenómenos diferentes en el ámbito de los fluidos. Los modelos matemáticos propuestos para ambos problemas están principalmente basados en Ecuaciones Diferenciales Ordinarias y Ecuaciones en Derivadas Parciales. Para llevar a cabo el análisis matemático de los modelos propuestos, hemos estudiado la existencia y unicidad de solución, junto con resultados de no negatividad y acotación, utilizando entre otros el Teorema de Punto Fijo de Schauder y técnicas variacionales. Hemos realizado un análisis dimensional de los modelos resultantes, el cual nos ha dado una pista de las escalas temporales características de los procesos y ha facilitado la reducción del número de parámetros de los modelos. En aquellos casos en los que los modelos resultantes se veían afectados por la presencia de parámetros o bien muy grandes o bien muy pequeños, hemos obtenido soluciones aproximadas del modelo aplicando técnicas de análisis asintótico. Además, se ha estudiado el comportamiento asintótico de los modelos, desarrollando el análisis de estabilidad de los estados estacionarios vía métodos de linealización. Finalmente, hemos definido dos problemas de optimización y los hemos abordado utilizando un Algoritmo Genético Híbrido. Descontaminación de agua utilizando reactores biológicos Con el objetivo de afrontar de forma precisa el problema de descontaminación de agua, primero hemos tratado de entender el comportamiento de un biorreactor continuo, un tanque donde tienen lugar reacciones biológicas, que puede ser utilizado para tratar agua contaminada. En el Capítulo 1 se introducen algunos conceptos básicos en la teoría de biorreactores, y se repasan resultados previos relacionados con el uso de biorreactores en procesos de descontaminación de agua. En el Capítulo 2 se proponen dos modelos diferentes, los cuales describen respectivamente el comportamiento de biorreactores mezclados y no mezclados.

We study the static equilibria of a simplified Leslie–Ericksen model for a unidirectional uniaxial nematic flow in a prototype microfluidic channel, as a function of the pressure gradient G and inverse anchoring strength, B. We numerically find multiple static equilibria for admissible pairs (G,B) and classify them according to their winding numbers and stability. The case G=0 is analytically tractable and we numerically study how the solution landscape is transformed as G increases. We study the one-dimensional dynamical model, the sensitivity of the dynamic solutions to initial conditions and the rate of change of G and B. We provide a physically interesting example of how the time delay between the applications of G and B can determine the selection of the final steady state., Ministerio de Economía y Competitividad (MINECO), Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

The demand of highest quality foods in terms of taste and their properties preservation without the use of additives is constantly increasing. Consequently, new approaches to food processing have been developed, as for example high-pressure technology which has proven to be very valuable because it allows to maintain good properties of food like some vitamins and, at the same time, to reduce some undesirable bacteria. This technology avoids the use of high temperatures during the process (not like Pasteurization), which may have adverse effect on some nutritional properties of the food, its flavour, etc. The models for some enzymatic inactivations, which depend on the pressure and temperature profiles are presented. This work deals with the optimization of the inactivation of certain enzymes when high pressure treatment on food processing is applied. The optimization algorithms will minimize the inactivation not only of a certain isolated enzyme but also to several enzymes that can be involved simultaneously in the high-pressure process.

We discuss the well-posedness of a mathematical model that is used in the literature for the simulation of lithium-ion batteries. First, a mathematical model based on a macrohomogeneous approach is presented, following previous work. Then it is shown, from a physical and a mathematical point of view, that a boundary condition widely used in the literature is not correct. Although the errors could be just sign typos (which can be explained as carelessness in the use of d/dx versus d/dn, with n the outward unit vector) and authors using this model probably use the correct boundary condition when they solve it in order to do simulations, readers should be aware of the right choice. Therefore, the deduction of the correct boundary condition is done here, and a mathematical study of the well-posedness of the corresponding problem is presented., Ministerio de Economía y Competitividad (MINECO), Banco Santander and Universidad Complutense de Madrid, Junta de Andalucía and the European Regional Development Fund, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Ministerio de Ciencia e Innovación (MICINN), Junta de Andalucía, European Regional Development Fund (ERDF), Universidad Complutense de Madrid, Banco de Santander, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

In this work, we study the mathematical analysis of a coupled system of two reaction-diffusion-advection equations and Danckwerts boundary conditions, which models the interaction between a microbial population (e.g., bacterias) and a diluted substrate (e.g., nitrate) in a continuous flow bioreactor. This type of bioreactor can be used, for instance, for water treatment. First, we prove the existence and uniqueness of solution, under the hypothesis of linear reaction by using classical results for linear parabolic boundary value problems. Next, we prove the existence and uniqueness of solution for some nonlinear reactions by applying \textit{Schauder Fixed Point Theorem} and the theorem obtained for the linear case. Results about the nonnegativeness and boundedness of the solution are also proved here., Ministry of Science and Innovation, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

En esta tesis se han aplicado diversas herramientas matemáticas con el objetivo de estudiar dos fenómenos diferentes en el ámbito de los fluidos. Los modelos matemáticos propuestos para ambos problemas están principalmente basados en Ecuaciones Diferenciales Ordinarias y Ecuaciones en Derivadas Parciales. Para llevar a cabo el análisis matemático de los modelos propuestos, hemos estudiado la existencia y unicidad de solución, junto con resultados de no negatividad y acotación, utilizando entre otros el Teorema de Punto Fijo de Schauder y técnicas variacionales. Hemos realizado un análisis dimensional de los modelos resultantes, el cual nos ha dado una pista de las escalas temporales características de los procesos y ha facilitado la reducción del número de parámetros de los modelos. En aquellos casos en los que los modelos resultantes se veían afectados por la presencia de parámetros o bien muy grandes o bien muy pequeños, hemos obtenido soluciones aproximadas del modelo aplicando técnicas de análisis asintótico. Además, se ha estudiado el comportamiento asintótico de los modelos, desarrollando el análisis de estabilidad de los estados estacionarios vía métodos de linealización. Finalmente, hemos definido dos problemas de optimización y los hemos abordado utilizando un Algoritmo Genético Híbrido. Descontaminación de agua utilizando reactores biológicos Con el objetivo de afrontar de forma precisa el problema de descontaminación de agua, primero hemos tratado de entender el comportamiento de un biorreactor continuo, un tanque donde tienen lugar reacciones biológicas, que puede ser utilizado para tratar agua contaminada. En el Capítulo 1 se introducen algunos conceptos básicos en la teoría de biorreactores, y se repasan resultados previos relacionados con el uso de biorreactores en procesos de descontaminación de agua. En el Capítulo 2 se proponen dos modelos diferentes, los cuales describen respectivamente el comportamiento de biorreactores mezclados y no mezclados.