Linear least squares estimation of the first order moving average parameter

We propose an iterative procedure to minimize the sum of squares function which avoids the nonlinear nature of estimating the first order moving average parameter and provides a closed form of the estimator. The asymptotic properties of the method are discussed and the consistency of the linear least squares estimator is proved for the invertible case. We perform various Monte Carlo experiments in order to compare the sample properties of the linear least squares estimator with its nonlinear counterpart for the conditional and unconditional cases. Some examples are also discussed

Linear least squares estimation of the first order moving average parameter

We propose an iterative procedure to minimize the sum of squares function which avoids the nonlinear nature of estimating the first order moving average parameter and provides a closed form of the estimator. The asymptotic properties of the method are discussed and the consistency of the linear least squares estimator is proved for the invertible case. We perform various Monte Carlo experiments in order to compare the sample properties of the linear least squares estimator with its nonlinear counterpart for the conditional and unconditional cases. Some examples are also discussed

Estudi sobre equalització electrònica per a sistemes de comunicació per fibra òptica

Estudi realitzat a partir d’una estada a Bell Labs (Lucent Technologies), New Jersey (Estats Units), entre el 15 de setembre de 2005 i el 15 de gener de 2006. Els sistemes de transmissió per fibra òptica fonamenten les principals xarxes de comunicacions. A mesura que la demanda d’ample de banda per usuari creixi, seran necessaris nous sistemes que siguin capaços de cobrir les necessitats a curt i llarg termini. La tecnologia dels sistemes òptics limita fortament la complexitat dels sistemes de transmissió / recepció en comparació, per exemple, als sistemes d’ones de ràdio. La tendència és la de dissenyar sistemes avançats amb detecció directa i mirar d’aplicar tècniques bàsiques de processat del senyal. Una d’aquestes tècniques és l’equalització electrònica, és a dir, fer ús de les tècniques de processament del senyal per tal de compensar la distorsió introduïda pel canal, deguda per una o diverses degradacions típiques: dispersió cromàtica, efectes no lineals, dispersió del mode de polarització (PMD) ... Dins d’un entorn comercial d’empresa, s’ha avaluat el funcionament dels sistemes d’equalització FFE-DFE aixi com MLSE en presència de dispersió cromàtica i/o dispersió del mode de polarització (PMD) en transmissions NRZ/RZ.

Interfaz web para mostrar los genes según las relaciones que mantienen sus expresiones

La investigació entre les relacions dels nivells d’expressió dels gens aporta molta informació sobre els processos biològics i patològics. Mitjançant la tècnica de les microarrays es possibilita la investigació de les relacions d’expressió de milers de gens a la vegada. La finalitat d’aquest projecte es fent ús de l’aplicatiu web PCOPGene-Net, permetre la identificació dels gens per les relacions d’expressió no lineals que tenen amb la resta de gens i permetre també la identificació de les relacions d’expressió no lineals entre els gens d’una microarray.

Europa als ulls dels Annales (1093-1933)

During this first third of this century, the continent of Europe witnessed far-reaching territorial transformations in the nineteenth century model. To some extent, the setting wich had inspired the epistemological structure of the French regional school was being replaced by one in which -at least to externa1 appearances- the relationship between the physical environment and human activities was much less evident. The adaptation of the theoretical and methodological context to the new Europe seems to take the form of a non-lineal evolution, for in the latter years of the period examined, evolutionary tendencies indicate a return to the more classical model. In this way, the growing interest which the publication had shown in Atlantic Europe and topics of a more economic nature, was truncated. The traditional settings --especially the Mediterranean- came to the fore again and interest in rural societies was renewed. Likewise, the monographic studies which had demonstrated distinct functional objectives in the midtwenties, recovered elements of ecological explanation, and the search for the relationship between environment and society

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.

Extracción de parámetros de un resonador FBAR por optimización

L’objectiu d’aquest projecte que consisteix a elaborar un algoritme d’optimització que permeti, mitjançant un ajust de dades per mínims quadrats, la extracció dels paràmetres del circuit equivalent que composen el model teòric d’un ressonador FBAR, a partir de les mesures dels paràmetres S. Per a dur a terme aquest treball, es desenvolupa en primer lloc tota la teoria necessària de ressonadors FBAR. Començant pel funcionament i l’estructura, i mostrant especial interès en el modelat d’aquests ressonadors mitjançant els models de Mason, Butterworth Van-Dyke i BVD Modificat. En segon terme, s’estudia la teoria sobre optimització i programació No-Lineal. Un cop s’ha exposat la teoria, es procedeix a la descripció de l’algoritme implementat. Aquest algoritme utilitza una estratègia de múltiples passos que agilitzen l'extracció dels paràmetres del ressonador.

A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex conguration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases.

Non-constant discounting in finite horizon: The free terminal time case

This paper derives the HJB (Hamilton-Jacobi-Bellman) equation for sophisticated agents in a finite horizon dynamic optimization problem with non-constant discounting in a continuous setting, by using a dynamic programming approach. A simple example is used in order to illustrate the applicability of this HJB equation, by suggesting a method for constructing the subgame perfect equilibrium solution to the problem.Conditions for the observational equivalence with an associated problem with constantdiscounting are analyzed. Special attention is paid to the case of free terminal time. Strotz¿s model (an eating cake problem of a nonrenewable resource with non-constant discounting) is revisited.

Non-constant discounting in finite horizon: The free terminal time case

This paper derives the HJB (Hamilton-Jacobi-Bellman) equation for sophisticated agents in a finite horizon dynamic optimization problem with non-constant discounting in a continuous setting, by using a dynamic programming approach. A simple example is used in order to illustrate the applicability of this HJB equation, by suggesting a method for constructing the subgame perfect equilibrium solution to the problem.Conditions for the observational equivalence with an associated problem with constantdiscounting are analyzed. Special attention is paid to the case of free terminal time. Strotz¿s model (an eating cake problem of a nonrenewable resource with non-constant discounting) is revisited.

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.