Transitional dynamics of an endogenous growth model with an erosion effect

The convergence features of an Endogenous Growth model with Physical capital, Human Capital and R&D have been studied. We add an erosion effect (supported by empirical evidence) to this model, and fully characterize its convergence properties. The dynamics is described by a fourth-order system of differential equations. We show that the model converges along a one-dimensional stable manifold and that its equilibrium is saddle-path stable. We also argue that one of the implications of considering this “erosion effect” is the increase in the adherence of the model to data.

In-house ELISA method to analyze anti-Trypanosoma cruzi IgG reactivity for differential diagnosis and evaluation of Chagas disease morbidity

INTRODUCTION: The goal was to develop an in-house serological method with high specificity and sensitivity for diagnosis and monitoring of Chagas disease morbidity. METHODS: With this purpose, the reactivities of anti-T. cruzi IgG and subclasses were tested in successive serum dilutions of patients from Berilo municipality, Jequitinhonha Valley, Minas Gerais, Brazil. The performance of the in-house ELISA was also evaluated in samples from other relevant infectious diseases, including HIV, hepatitis C (HCV), syphilis (SYP), visceral leishmaniasis (VL), and American tegumentary leishmaniasis (ATL), and noninfected controls (NI). Further analysis was performed to evaluate the applicability of this in-house methodology for monitoring Chagas disease morbidity into three groups of patients: indeterminate (IND), cardiac (CARD), and digestive/mixed (DIG/Mix), based on their clinical status. RESULTS: The analysis of total IgG reactivity at serum dilution 1:40 was an excellent approach to Chagas disease diagnosis (100% sensitivity and specificity). The analysis of IgG subclasses showed cross-reactivity, mainly with NI, VL, and ATL, at all selected serum dilutions. Based on the data analysis, the IND group displayed higher IgG3 levels and the DIG/Mix group presented higher levels of total IgG as compared with the IND and CARD groups. CONCLUSIONS: These findings demonstrated that methodology presents promising applicability in the analysis of anti-T. cruzi IgG reactivity for the differential diagnosis and evaluation of Chagas disease morbidity.

Evolution of reputation in networks: A mean field game approach

This work models the competitive behaviour of individuals who maximize their own utility managing their network of connections with other individuals. Utility is taken as a synonym of reputation in this model. Each agent has to decide between two variables: the quality of connections and the number of connections. Hence, the reputation of an individual is a function of the number and the quality of connections within the network. On the other hand, individuals incur in a cost when they improve their network of contacts. The initial value of the quality and number of connections of each individual is distributed according to an initial (given) distribution. The competition occurs over continuous time and among a continuum of agents. A mean field game approach is adopted to solve the model, leading to an optimal trajectory for the number and quality of connections for each individual.

High performance electromechanical actuators based on ionic liquid/poly(vinylidene fluoride)

Due to the increasing need of low voltage actuators, independent from electrochemical processes, electroactive actuators based on poly(vinylidene fluoride) composites with 10, 25 and 40 % of 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, [C2mim] [NTf2], ionic liquid are prepared by solvent casting and melting. We show that the charge structure of [C2mim] [NTf2] induces the complete piezoelectric -phase crystallization of the PVDF within the composite and decreases its crystallinity fraction significantly. [C2mim] [NTf2] also works as a plasticizer of PVDF, reducing the elastic modulus down to 12 % of the initial value. Moreover, the composites show significant displacement and bending under applied voltages of 2, 5 and 10 Vpp. The displacement and bending of the composite membranes are also evaluated as a function of [C2mim] [NTf2] content and sample thickness. Increasing amounts of ionic liquid result in larger deformations independently of the applied voltage.

Da modelação matemática à simulação computacional: a experimentação matemática no ensino

Tese de Doutoramento em Ciências (área de especialização em Matemática).

Da modelação matemática à simulação computacional: a experimentação matemática no ensino

Tese de Doutoramento em Ciências (área de especialização em Matemática).

Desenvolvimento de modelos numéricos e análise experimental de subestruturas soldadas de transformadores de potência, sujeitas a forças de curto-circuito em regime transitório

Dissertação de mestrado integrado em Engenharia Mecânica

Mortar-Techniken zur Behandlung von Grenzschichtproblemen

Elliptic differential equations, finite element method, mortar element method, streamline diffusion FEM, upwind method, numerical method, error estimate, interpolation operator, grid generation, adaptive refinement

Desensitization of thermal hyperemia in the skin is reproducible.

OBJECTIVE: Local heating increases skin blood flow SkBF (thermal hyperemia). In a previous study, we reported that a first local thermal stimulus could attenuate the hyperemic response to a second one applied later on the same skin spot, a phenomenon that we termed desensitization. However, other studies found no evidence for desensitization in similar conditions. The aim of the present work was to test whether it was related to differences in instrumentation. METHODS: Twenty-eight healthy young males were studied. Two pairs of heating chambers, one custom-made (our study) and one commercial (other groups), were affixed to forearm skin. SkBF was measured with single-point laser-Doppler flowmetry (LDF) (780nm) in one pair, and laser-Doppler imaging (LDI) (633nm) in the other. A temperature step from 34 to 41°C, was applied for 30minutes and repeated after two hours. RESULTS: During the second thermal challenge, the plateau SkBF was lower than during the first thermal and was observed with each of the four combinations of SkBF measurement techniques and heating equipment (p<0.05 for all conditions, range -9% to -16% of the initial value). CONCLUSION: Desensitization of thermal hyperemia is not specific to peculiar operating conditions.

Caracteritació de models funcionals d'àmfores romanes mitjançant Finite Element Analysis

Projecte de recerca elaborat a partir d’una estada al Laboratory of Archaeometry del National Centre of Scientific Research “Demokritos” d’Atenes, Grècia, entre juny i setembre 2006. Aquest estudi s’emmarca dins d’un context més ampli d’estudi del canvi tecnològic que es documenta en la producció d’àmfores de tipologia romana durant els segles I aC i I dC en els territoris costaners de Catalunya. Una part d’aquest estudi contempla el càlcul de les propietats mecàniques d’aquestes àmfores i la seva avaluació en funció de la tipologia amforal, a partir de l’Anàlisi d’Elements Finits (AEF). L’AEF és una aproximació numèrica que té el seu origen en les ciències d’enginyeria i que ha estat emprada per estimar el comportament mecànic d’un model en termes, per exemple, de deformació i estrès. Així, un objecte, o millor dit el seu model, es dividit en sub-dominis anomenats elements finits, als quals se’ls atribueixen les propietats mecàniques del material en estudi. Aquests elements finits estan connectats formant una xarxa amb constriccions que pot ser definida. En el cas d’aplicar una força determinada a un model, el comportament de l’objecte pot ser estimat mitjançant el conjunt d’equacions lineals que defineixen el rendiment dels elements finits, proporcionant una bona aproximació per a la descripció de la deformació estructural. Així, aquesta simulació per ordinador suposa una important eina per entendre la funcionalitat de ceràmiques arqueològiques. Aquest procediment representa un model quantitatiu per predir el trencament de l’objecte ceràmic quan aquest és sotmès a diferents condicions de pressió. Aquest model ha estat aplicat a diferents tipologies amforals. Els resultats preliminars mostren diferències significatives entre la tipologia pre-romana i les tipologies romanes, així com entre els mateixos dissenys amforals romans, d’importants implicacions arqueològiques.

Characterizations of Lojasiewicz inequalities and applications

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative characterizations of this type of inequalities for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In a metric context, we show that a generalized form of the Lojasiewicz inequality (hereby called the Kurdyka- Lojasiewicz inequality) relates to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by -∂f are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka- Lojasiewicz inequality is satisfied. Further characterizations in terms of talweg lines -a concept linked to the location of the less steepest points at the level sets of f- and integrability conditions are given. In the convex case these results are significantly reinforced, allowing in particular to establish the asymptotic equivalence of discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex C2 function in R2 is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka- Lojasiewicz inequality.

Stability of Growth Models with Generalised Lag Structures

This paper considers the lag structures of dynamic models in economics, arguing that the standard approach is too simple to capture the complexity of actual lag structures arising, for example, from production and investment decisions. It is argued that recent (1990s) developments in the the theory of functional differential equations provide a means to analyse models with generalised lag structures. The stability and asymptotic stability of two growth models with generalised lag structures are analysed. The paper concludes with some speculative discussion of time-varying parameters.

Computing Markov-Perfect Optimal Policies in Business-Cycle Models

Time-inconsistency is an essential feature of many policy problems (Kydland and Prescott, 1977). This paper presents and compares three methods for computing Markov-perfect optimal policies in stochastic nonlinear business cycle models. The methods considered include value function iteration, generalized Euler-equations, and parameterized shadow prices. In the context of a business cycle model in which a scal authority chooses government spending and income taxation optimally, while lacking the ability to commit, we show that the solutions obtained using value function iteration and generalized Euler equations are somewhat more accurate than that obtained using parameterized shadow prices. Among these three methods, we show that value function iteration can be applied easily, even to environments that include a risk-sensitive scal authority and/or inequality constraints on government spending. We show that the risk-sensitive scal authority lowers government spending and income-taxation, reducing the disincentive households face to accumulate wealth.

Structured and unstructured continuous models for Wolbachia infections

We introduce and investigate a series of models for an infection of a diplodiploid host species by the bacterial endosymbiont Wolbachia. The continuous models are characterized by partial vertical transmission, cytoplasmic incompatibility and fitness costs associated with the infection. A particular aspect of interest is competitions between mutually incompatible strains. We further introduce an age-structured model that takes into account different fertility and mortality rates at different stages of the life cycle of the individuals. With only a few parameters, the ordinary differential equation models exhibit already interesting dynamics and can be used to predict criteria under which a strain of bacteria is able to invade a population. Interestingly, but not surprisingly, the age-structured model shows significant differences concerning the existence and stability of equilibrium solutions compared to the unstructured model.

Rigid flat webs on the projective plane

This paper studies global webs on the projective plane with vanishing curvature. The study is based on an interplay of local and global arguments. The main local ingredient is a criterium for the regularity of the curvature at the neighborhood of a generic point of the discriminant. The main global ingredient, the Legendre transform, is an avatar of classical projective duality in the realm of differential equations. We show that the Legendre transform of what we call reduced convex foliations are webs with zero curvature, and we exhibit a countable infinity family of convex foliations which give rise to a family of webs with zero curvature not admitting non-trivial deformations with zero curvature.