Equacions diferencials i models

En tot cas, jo voldria que aquesta conferència fos això que he dit: una breu lliçó sobre la importància de les equacions diferencials. Parlaré d'elles des de el punt de vista del models, és a dir, dels fenòmens que modelitzeu. I intentaré explicar que malgrat el seu origen antic, totes elles segueixen presentant avui en dia problemes nous i interessants, tant des de el punt de vista teòric com pràctic.

Application of theoretical models to financial innovation

The present paper is aimed at providing a general strategic overview of the existing theoretical models that have applications in the field of financial innovation. Whereas most financialdevelopments have relied upon traditional economic tools, a new stream of research is defining a novel paradigm in which mathematical models from diverse scientific disciplines are being applied to conceptualize and explain economic and financial behavior. Indeed, terms such as ‘econophysics’ or ‘quantum finance’ have recently appeared to embrace efforts in this direction. As a first contact with such research, the project will present a brief description of some of the main theoretical models that have applications in finance and economics, and will try to present, if possible, potential new applications to particular areas in financial analysis, or new applicable models. As a result, emphasiswill be put on the implications of this research for the financial sector and its future dynamics.

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

Background: Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results: Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions: Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

Identifying the preferred subset of enzymatic profiles in nonlinear kinetic metabolic models via multiobjective global optimization and pareto filters

Optimization models in metabolic engineering and systems biology focus typically on optimizing a unique criterion, usually the synthesis rate of a metabolite of interest or the rate of growth. Connectivity and non-linear regulatory effects, however, make it necessary to consider multiple objectives in order to identify useful strategies that balance out different metabolic issues. This is a fundamental aspect, as optimization of maximum yield in a given condition may involve unrealistic values in other key processes. Due to the difficulties associated with detailed non-linear models, analysis using stoichiometric descriptions and linear optimization methods have become rather popular in systems biology. However, despite being useful, these approaches fail in capturing the intrinsic nonlinear nature of the underlying metabolic systems and the regulatory signals involved. Targeting more complex biological systems requires the application of global optimization methods to non-linear representations. In this work we address the multi-objective global optimization of metabolic networks that are described by a special class of models based on the power-law formalism: the generalized mass action (GMA) representation. Our goal is to develop global optimization methods capable of efficiently dealing with several biological criteria simultaneously. In order to overcome the numerical difficulties of dealing with multiple criteria in the optimization, we propose a heuristic approach based on the epsilon constraint method that reduces the computational burden of generating a set of Pareto optimal alternatives, each achieving a unique combination of objectives values. To facilitate the post-optimal analysis of these solutions and narrow down their number prior to being tested in the laboratory, we explore the use of Pareto filters that identify the preferred subset of enzymatic profiles. We demonstrate the usefulness of our approach by means of a case study that optimizes the ethanol production in the fermentation of Saccharomyces cerevisiae.

L’educador/a social com a tècnic/a d'orientació i inserció laboral, en el marc de la formació reglada. Proposta de creació d’un servei d’orientació i inserció laboral.

Anàlisi al voltant del rol de l’educador/a social com a tècnic/a d’orientació i inserció laboral en el col·lectiu de joves, i reflexió sobre com aquest pot desenvolupar aquesta ocupació en el marc de l’educació formal, en concret, en la formació professional. Aquest anàlisi i reflexió es complementa amb una proposta d’acció socioeducativa que es centra en el disseny d’un servei d’orientació i inserció laboral per a joves estudiants, ubicat en un centre de formació professional.

A measure of stability as a criterion for the verification and analysis of simulation models

The aim of this study is to define a new statistic, PVL, based on the relative distance between the likelihood associated with the simulation replications and the likelihood of the conceptual model. Our results coming from several simulation experiments of a clinical trial show that the PVL statistic range can be a good measure of stability to establish when a computational model verifies the underlying conceptual model. PVL improves also the analysis of simulation replications because only one statistic is associated with all the simulation replications. As well it presents several verification scenarios, obtained by altering the simulation model, that show the usefulness of PVL. Further simulation experiments suggest that a 0 to 20 % range may define adequate limits for the verification problem, if considered from the viewpoint of an equivalence test.

La Figura del pedagog/a dins l’àmbit de l’orientació professional

El treball pretén conèixer l’orientació professional d’una manera àmplia per tal d’analitzar quines són les competències professionals necessàries i fonamentals per tal d’exercir d’orientador/a professional. Es realitza una anàlisi sobre el perfil professional del pedagog/a que exerceix com orientador/a, alhora que realitza una reflexió partint de les competències professionals, que permet analitzar la figura del pedagog/a dins l’àmbit de l’orientació professional

Magnetização remanescente: um parâmetro crucial para a interpretação e modelamento de anomalias magnéticas em território brasileiro

A questão da magnetização remanescente na interpretação de anomalias magnéticas é frequentemente negligenciada, principalmente em função da dificuldade em se lidar com a mesma. Na maioria dos casos, tanto nos trabalhos acadêmicos quanto nos modelos que circulam nos meios profissionais da exploração mineral e de petróleo, assume-se que a magnetização remanescente é desprezível e utiliza-se apenas a induzida. O presente artigo mostra que o uso desse parâmetro é particularmente importante no tocante às anomalias magnéticas brasileiras, e procura fornecer subsídios para o uso desta informação. Discute-se o uso de duas técnicas consagradas, a Redução ao Pólo e o Sinal Analítico, em anomalias brasileiras com e sem magnetização remanescente. Mostramos a aplicação da técnica de determinação da magnetização total, permitindo que os modelos sejam construídos a partir da resultante da soma das magnetizações induzida e remanescente, e posteriormente apresentamos uma metodologia de uso da informação remanescente na datação das rochas fonte.

Aplicación del DEA en el análisis de beneficios en un sistema integrado verticalmente hacia adelante

En el presente trabajo se diseñan tres modelos DEA a partir de un sistema de producción cuyos componentes están colocados en un arreglo en serie que se integran verticalmente hacia adelante. El primer modelo busca optimizar los beneficios del sistema agregado, así como la mejora de los mismos en cada uno de los subsistemas. En el segundo de los modelos, además del objetivo anterior, se incluyen restricciones de transferencia de los recursos específicos asociados a cada subsistema, y en el tercer modelo se estima el intervalo de variación para los precios de transferencia de los inputs intermedios entre ambos subsistemas. Los modelos han sido programados y simulados en el software GAMS a partir de datos generados por una función de producción Cobb-Douglas para los inputs intermedios y los outputs finales.

La Solvencia financiera del asegurador de vida y su relación con el coste de capital

Esta investigación relaciona el margen de solvencia que normativamente deben acreditar los aseguradores de vida con los recursos propios que cualquier empresa debe poseer para poder ejercer su actividad. Analizaremos la incidencia que la remuneración de esos recursos tiene en la propia actividad de comercialización de los seguros demostrando su relación inversa con el tipo de interés garantizado en los contratos. Analizaremos asimismo la incidencia que los eventuales cambios en los tipos de interés pueden tener en la remuneración que puede ofrecerse a esos recursos y propondremos una ecuación que incorpore todos estos aspectos, comprobando que las relaciones que actualmente ofrece la disciplina académica son casos particulares de la ecuación general, casos que demostraremos que incorporan unas hipótesis implícitas bastante restrictivas.

Single period Markowitz portfolio selection, performance gauging and duality: a variation on Luenberger's shortage function

Markowitz portfolio theory (1952) has induced research into the efficiency of portfolio management. This paper studies existing nonparametric efficiency measurement approaches for single period portfolio selection from a theoretical perspective and generalises currently used efficiency measures into the full mean-variance space. Therefore, we introduce the efficiency improvement possibility function (a variation on the shortage function), study its axiomatic properties in the context of Markowitz efficient frontier, and establish a link to the indirect mean-variance utility function. This framework allows distinguishing between portfolio efficiency and allocative efficiency. Furthermore, it permits retrieving information about the revealed risk aversion of investors. The efficiency improvement possibility function thus provides a more general framework for gauging the efficiency of portfolio management using nonparametric frontier envelopment methods based on quadratic optimisation.

The Cost of ownership in the governance of interfirm collaborations

This paper investigates the selection of governance forms in interfirm collaborations taking into account the predictions from transaction costs and property rights theories. Transaction costs arguments are often used to justify the introduction of hierarchical controls in collaborations, but the ownership dimension of going from “contracts” to “hierarchies” has been ignored in the past and with it the so called “costs of ownership”. The theoretical results, tested with a sample of collaborations in which participate Spanish firms, indicate that the cost of ownership may offset the benefits of hierarchical controls and therefore limit their diffusion. Evidence is also reported of possible complementarities between reputation effects and forms of ownership that go together with hierarchical controls (i.e. joint ventures), in contrast with the generally assumed substitutability between the two.

A Rembrandt is a Rembrandt

As paintings are assets, we propose to model a painting's price dynamics as a diffusion process, i.e., as the financial literature models share prices, but correcting by size. We show that the influence of size on the artwork price diminishes as the paintings gets older because 1) prices incorporate progressively more noise and 2) for high quality artists, the relative importance of size on price decreases as the artist consolidates and authorship gains importance as explanatory variable. Our theoretical results are consistent with data from a sample of 19th- and 20th-century Catalan painters of similar quality. These findings suggest that an artist's quality and antiquity should be taken into account in order to obtain more efficient estimates of parameters in hedonic art market models.