Population, immigration and growth in a Romer endogenous growth model

Producción CientíficaEndogenous growth theory has not yet consistently incorporated population growth or immigration into its models. As a result, in the present day, there is no universally accepted endogenous growth model explaining the empirical observed relationships between growth, population and immigration. The present paper overcomes this inconvenience by designing a fully specified Romer endogenous growth model, completely micro-founded, that incorporates the existence of population growth and immigration and that allows the stylised facts of growth as well as the relationships between growth, population and immigration to be explained. In addition, the proposed model is susceptible to calibration and simulation, and, when applied to the US economy, provides a good fit to the data.Financial support from Spanish Office of Economy and Competitiveness and European FEDER Funds, Research Projects MTM2014-56022-C2-2-P and MTM2017-85476-C2-1-P, is gratefully acknowledged

The effects of time valuation in cancer optimal therapies: a study of chronic myeloid leukemia

Background The mathematical design of optimal therapies to fight cancer is an important research field in today’s Biomathematics and Biomedicine given its relevance to formulate patient-specific treatments. Until now, however, cancer optimal therapies have considered that malignancy exclusively depends on the drug concentration and the number of cancer cells, ignoring that the faster the cancer grows the worse the cancer is, and that early drug doses are more prejudicial. Here, we analyze how optimal therapies are affected when the time evolution of treated cancer is envisaged as an additional element determining malignancy, analyzing in detail the implications for imatinib-treated Chronic Myeloid Leukemia. Methods Taking as reference a mathematical model describing Chronic Myeloid Leukemia dynamics, we design an optimal therapy problem by modifying the usual malignancy objective function, unaware of any temporal dimension of cancer malignance. In particular, we introduce a time valuation factor capturing the increase of malignancy associated to the quick development of the disease and the persistent negative effects of initial drug doses. After assigning values to the parameters involved, we solve and simulate the model with and without the new time valuation factor, comparing the results for the drug doses and the evolution of the disease. Results Our computational simulations unequivocally show that the consideration of a time valuation factor capturing the higher malignancy associated with early growth of cancer and drug administration allows more efficient therapies to be designed. More specifically, when this time valuation factor is incorporated into the objective function, the optimal drug doses are lower, and do not involve medically relevant increases in the number of cancer cells or in the disease duration. Conclusions In the light of our simulations and as biomedical evidence strongly suggests, the existence of a time valuation factor affecting malignancy in treated cancer cannot be ignored when designing cancer optimal therapies. Indeed, the consideration of a time valuation factor modulating malignancy results in significant gains of efficiency in the optimal therapy with relevant implications from the biomedical perspective, specially when designing patient-specific treatments.This work was supported by projects MTM2014-56022-C2-2-P and MTM2017-85476-C2-1-P of the Spanish Office of Innovation and Competitiveness and European FEDER Funds, and by projects of the Castile and León Autonomous Government: VA041P17 (with European FEDER Funds), VA138G18 and VA148G18

A new equilibrated residual method improving accuracy and efficiency of flux-free error estimates

This paper presents a new methodology to compute guaranteed upper bounds for the energy norm of the error in the context of linear finite element approximations of the reaction–diffusion equation. The new approach revisits the ideas in Parés et al. (2009) [6, 4], with the goal of substantially reducing the computational cost of the flux-free method while retaining the good quality of the bounds. The new methodology provides also a technique to compute equilibrated boundary tractions improving the quality of standard equilibration strategies. The zeroth-order equilibration conditions are imposed using an alternative less restrictive form of the first-order equilibration conditions, along with a new efficient minimization criterion. This new equilibration strategy provides much more accurate upper bounds for the energy and requires only doubling the dimension of the local linear systems of equations to be solved.Postprint (author's final draft

Goal-oriented h-adaptivity for the Helmholtz equation: error estimates, local indicators and refinement strategies

The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-010-0557-2This paper introduces a new goal-oriented adaptive technique based on a simple and effective post-process of the finite element approximations. The goal-oriented character of the estimate is achieved by analyzing both the direct problem and an auxiliary problem, denoted as adjoint or dual problem, which is related to the quantity of interest. Thus, the error estimation technique proposed in this paper would fall into the category of recovery-type explicit residual a posteriori error estimates. The procedure is valid for general linear quantities of interest and it is also extended to non-linear ones. The numerical examples demonstrate the efficiency of the proposed approach and discuss: (1) different error representations, (2) assessment of the dispersion error, and (3) different remeshing criteria.Peer ReviewedPostprint (author's final draft

A note on the convergence of the secant method for simple and multiple roots

The secant method is one of the most popular methods for root finding. Standard text books in numerical analysis state that the secant method is super linear: the rate of convergence is set by the gold number. Never- theless, this property holds only for simple roots. If the multiplicity of the root is larger than one, the convergence of the secant method becomes linear. This communication includes a detailed analysis of the secant method when it is used to approximate multiple roots. Thus, a proof of the linear convergence is shown. Moreover, the values of the corresponding asymptotic convergence factors are determined and are found to be also related with the golden ratio.Peer ReviewedPostprint (author’s final draft

El seguro de caución directa

El presente trabajo aborda una cuestión relativa al seguro de caución sobre el que la doctrina o guarda silencio o parece encallar. Se trata de la referencia que hace la Ley de Ordenación y Supervisión de los Seguros Privados a la “caución indirecta”, a la que, sin embargo, no alude la Ley de Contrato de Seguro. Su significado y trascendencia práctica han venido permaneciendo ocultos. Este estudio pone al descubierto cómo al amparo de aquella figura es posible canalizar determinadas operaciones internacionales de seguro, que se sustentan sobre un complejo entramado contractual. Pero la caución indirecta también permite suministrar cobijo normativo a una posible estrategia cooperativa entre los dos rivales tradicionales del mercado de las garantías: los bancos y las aseguradoras de caución. Algunas de las cuestiones que parecían pacíficas en la tradicional visión del art. 68 LCS se reavivan y adquieren nueva luz al hilo del análisis de la caución indirecta.Este trabajo se enmarca en el Proyecto de Investigación DER 2011-25237 (Derecho Mercantil y análisis del Derecho VI), dirigido por el Prof. C. Paz-Ares, y financiado por el Ministerio de Educación y Cultura

Curso de economía multimedia

Este curso de economía multimedia es fruto de un largo proceso de su autor como profesor universitario y como profesor preocupado por el proceso de enseñaza aprendizaje, concretamente en el campo de la economía. El curso se ha planteado como soporte a la enseñanza presencial o, incluso, como elemento básico para la enseñanza no presencial. En estos momentos (hasta donde está desarrollado) es un curso accesible vía Internet (www.upc.es) en el que se exponen los fundamentos del análisis económico en pantallas muy claras y simples: una parte para el texto, con un tipo de letra grande y fácilmente comprensible y otra para la imagen con figuras interactivas, que permiten al estudiante observar las diversas situaciones posibles. En el texto, todos aquellos conceptos importantes y que requieren alguna aclaración complementaria están vinculados de forma hipertextual a unas ventanas flotantes que se abren a petición del estudiante. A su vez, el curso va acompañado de diferentes pruebas de autoevaluación: test, ejercicios, etc. con las correspondientes soluciones. También incorpora otros elementos necesarios para un buen proceso de enseñanza aprendizaje: léxico, webs relacionadas con la materia, forum de alumnos, contacto con el profesor, etc

Semi-explicit residual goal-oriented estimate for linear mechanics

El objetivo de este trabajo es definir un método semiexplícito para estimar el error en cantidades de interés derivado de la resolución por elementos finitos de un problema de elasticidad lineal. En este proceso, se identifican dos etapas: una estimación implícita del error del problema adjunto y otra, explícita, asociada al problema directo (primal). La parte implícita de la estimación requiere dos fases, cada una de las cuales consiste en hacer proyecciones sobre espacios de funciones burbuja. Estas proyecciones sobre espacios burbuja comportan operaciones locales y, por tanto, son de bajo coste. Las dos fases se encargan de estimar el error interior en los elementos y la contribución de las aristas (asociada a los saltos de tensiones normales). El carácter implícito de esta parte de la estimación se aplica a la resolución de los problemas locales en espacios de dimensión pequeña. Se analiza también la posibilidad de escoger espacios de funciones burbuja locales de una sola dimensión (fijando la forma de la burbuja y determinando únicamente el coeficiente escalar que la multiplica), lo cual, en la práctica, convierte esta fase en explícita. La parte explícita de la estimación inyecta en el residuo débil primal la aproximación del error adjunto estimada en la primera fase. Esta estrategia es similar a la empleada en el método DWR, pero utilizando una formulación débil del residuo e inyectando un error dual en vez de utilizar una solución posprocesada. La metodología propuesta se valida con su aplicación a un ejemplo numérico.We aim at defining a semi-explicit approach to estimate the error in quantities of interest associated with the Finite Element solution of a linear elasticity problem. The advocated procedure is split in two parts, an implicit error estimate for the adjoint problem and an explicit estimate assessing the error in the direct (primal) problem. The implicit part of the estimate (on the adjoint problem) embraces two phases, each consisting in projecting the error on “bubble” functional spaces. The projections are low-cost operations due to their local nature. The two phases account the error in the interior of the elements and the contribution of the elementary edges (associated with the tractions jump). The implicit character of this part is provided by the solution of the local problems in low-dimensional functional spaces. We also analyze the particular case of selecting one-dimensional functional spaces (setting the shape of the bubble and computing a scalar coefficient), which, in practice, make this part of the process explicit. The explicit part of the estimate consists in injecting in the weak primal residual the approximation of the adjoint error obtained in the first phase. This approach is similar to the DWR method but using a weak formulation of the residual and injecting an implicitly estimated adjoint error rather than a post-processed solution. The proposed methodology is validated in a numerical examplePeer ReviewedPostprint (published version

Strict error bounds in linear solid mechanics using a subdomain-based flux-free approach

In this paper, we derive, in the framework of the ux-free method, strict bounds for the energy norm of the error associated to a finite element computation. In that framework, and when using linear elements, the problems posed on the subdomains are solvable only when modified by the introduction of a projection operator in the residual. We introduce a new such operator, and show that, in the context of a dual formulation, it further allows to construct statically admissible fields over each subdomain. When combined, these local stress fields provide the desired strict bound

Hierarchical x-fem applied to n-phase flow

In this work we proposed an extencion of the level set technique to track any number of free surfaces. This extension is based in a hierarchical ordering of several level set functions. To complete the X–FEM approach, the enrichment via partition of the unity method is also extended. The ridge function, base of the enriched interpolation, is restated to include several level sets and the hierarchy between them