Um modelo multicritério de apoio ao planeamento da localização de centros de tratamento de mercadorias

Com a globalização verificaram-se profundas mudanças ao nível político, social, económico, tecnológico, entre outras, originando uma evolução extraordinária da procura do sector dos transportes, com especial destaque para as mercadorias. O sector rodoviário tem sido o que mais tem crescido e consequentemente maiores problemas tem causado, nomeadamente o congestionamento, a sinistralidade, entre outros, com implicações económicas, sociais e ambientais. Uma das soluções passa por equilibrar o transporte de mercadorias entre os modos de transporte, com especial destaque para o crescimento do sector ferroviário, sendo que para tal é necessário investir em infra-estruturas de transporte e em nodos modais eficazes e eficientes, para promover a intermodalidade. A localização dos nodos modais é vital para o sucesso das operações logísticas, onde a economia do tempo e do custo de transporte são determinantes, assim como o enquadramento destas infra-estruturas no âmbito das políticas de ordenamento do território e de transportes e o respectivo impacte nos diversos domínios, a nível local e regional. A localização de centros de tratamento de mercadorias (CTM) é um exemplo de decisão de carácter estratégico, a concretizar num ambiente de crescente complexidade, onde se pretende estabelecer um equilíbrio entre múltiplos aspectos de avaliação. A complexidade inerente a este tipo de decisões advém das constantes evoluções das tecnologias, da estrutura dos mercados, das necessidades sociais e dos enquadramentos regulamentares, assim como da heterogeneidade de critérios de avaliação das acções potenciais que tem associados problemas de conflitualidade, de incomensurabilidade e de incerteza. Este é o retrato do caso de estudo, ao qual aplicamos uma metodologia sistémica de estruturação de situações problemáticas, denominada soft systems methodology, a partir da qual construímos um modelo multicritério de apoio ao planeamento da localização de CTMs. O modelo contempla a aplicação de uma metodologia de apoio multicritério à decisão, o ELECTRE TRI, numa problemática de afectação ordinal de potenciais alternativas de localização a categorias pré-definidas.

Mathematical modelling of supercritical CO2 extraction of volatile oils from aromatic plants

The modelling of the experimental data of the extraction of the volatile oil from six aromatic plants (coriander, fennel, savoury, winter savoury, cotton lavender and thyme) was performed using five mathematical models, based on differential mass balances. In all cases the extraction was internal diffusion controlled and the internal mass transfer coefficienty (k(s)) have been found to change with pressure, temperature and particle size. For fennel, savoury and cotton lavender, the external mass transfer and the equilibrium phase also influenced the second extraction period, since k(s) changed with the tested flow rates. In general, the axial dispersion coefficient could be neglected for the conditions studied, since Peclet numbers were high. On the other hand, the solute-matrix interaction had to be considered in order to ensure a satisfactory description of the experimental data.

A mathematical model for malaria transmission relating global warming and local socioeconomic conditions

OBJECTIVE: Sensitivity analysis was applied to a mathematical model describing malaria transmission relating global warming and local socioeconomic conditions. METHODS: A previous compartment model was proposed to describe the overall transmission of malaria. This model was built up on several parameters and the prevalence of malaria in a community was characterized by the values assigned to them. To assess the control efforts, the model parameters can vary on broad intervals. RESULTS: By performing the sensitivity analysis on equilibrium points, which represent the level of malaria infection in a community, the different possible scenarios are obtained when the parameters are changed. CONCLUSIONS: Depending on malaria risk, the efforts to control its transmission can be guided by a subset of parameters used in the mathematical model.

Analysis of glycosylation heterogeneity in antibody production by Pichia pastoris

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Biotecnologia

Mathematical model for HIV dynamics in HIV-specific helper cells

In this paper we study a delay mathematical model for the dynamics of HIV in HIV-specific CD4 + T helper cells. We modify the model presented by Roy and Wodarz in 2012, where the HIV dynamics is studied, considering a single CD4 + T cell population. Non-specific helper cells are included as alternative target cell population, to account for macrophages and dendritic cells. In this paper, we include two types of delay: (1) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and; (2) virus production period for new virions to be produced within and released from the infected cells. We compute the reproduction number of the model, R0, and the local stability of the disease free equilibrium and of the endemic equilibrium. We find that for values of R0<1, the model approaches asymptotically the disease free equilibrium. For values of R0>1, the model approximates asymptotically the endemic equilibrium. We observe numerically the phenomenon of backward bifurcation for values of R0⪅1. This statement will be proved in future work. We also vary the values of the latent period and the production period of infected cells and free virus. We conclude that increasing these values translates in a decrease of the reproduction number. Thus, a good strategy to control the HIV virus should focus on drugs to prolong the latent period and/or slow down the virus production. These results suggest that the model is mathematically and epidemiologically well-posed.

A regulação endócrina dos balanços de cálcio

RESUMO: As concentrações circulantes de cálcio são notavelmente constantes a despeito das variações diárias na absorção intestinal e na eliminação renal deste elemento. A regulação da calcémia é um sistema complexo que compreende vários factores controladores (a calcémia, a fosforémia, as concentrações circulantes de paratormona (PTH) e calcitriol além de muitos outros factores como hormonas esteróides em geral, outros iões como o magnésio e outros factores hormonais) e vários órgãos alvo (glândulas paratiroideias, osso, rim e intestino). As respostas dos órgãos alvo também são muito variadas. No caso mais simples, a cristalização de sais de cálcio corresponde a uma mudança de fase em que participam moléculas orgânicas que a iniciam, aceleram ou inibem. Em geral a combinação de um factor controlador com o respectivo receptor de membrana (para polipeptídeos ou iões) ou intracelular (hormonas esteróides) é apenas o primeiro passo de uma cadeia bioquímica que introduz uma enorme amplificação na resposta. A esta variedade de mecanismos de resposta correspondem grandes diferenças nos tempos de resposta que podem ser de minutos a semanas. É hoje possível “observar” (medir) com apreciável rigor nos líquidos biológicos (sangue, urina, fezes, etc.) os factores mais importantes do sistema de regulação da calcémia (cálcio, fósforo, paratormona e calcitriol) assim como administrar estes factores em experiências agudas. Esta possibilidade reflecte – se na literatura neste campo que tem vindo a crescer. O advento das técnicas da biologia molecular tem permitido a caracterização molecular de algumas das disfunções da homeostase do cálcio e é de esperar um diagnóstico fisiopatológico cada vez mais rigoroso dessas disfunções. Com o avanço dos conhecimentos nesta área que não cessa de aumentar temos cada vez maiores capacidades para fazer diagnósticos e é cada vez mais difícil interpretar com rigor os correspondentes quadros metabólicos. A análise ou síntese de sistemas complexos é a actividade mais nobre dos engenheiros que lhes permite desenhar pontes, diques, barcos, aviões ou automóveis. Com o aparecimento de computadores de médio ou grande porte foi – lhes possível utilizar descrições matemáticas não só para desenhar sistemas como ainda para interpretar eventuais falhas na sua operação. Essas descrições matemáticas consistem numa sequência de operações realizadas num computador segundo um “programa informático” que receberam a designação genérica de modelos, por analogia com as famosas leis (equações) da física que foram deduzidas a partir de um certo número de postulados e que permitem representar matematicamente processos físicos. As famosas leis de Newton são talvez os exemplos mais famosos de “modelos” de sistemas físicos. A introdução de modelos matemáticos em biologia e particularmente em medicina só se deu recentemente.MÉTODOS No trabalho que aqui se apresenta construiu - se um modelo simplificado da homeostase do cálcio destinado ao cálculo de variáveis observáveis (concentrações de cálcio, fósforo, PTH e calcitriol) de modo a poderem comparar-se valores calculados com valores observados. A escolha dos componentes do modelo foi determinada pela nossa experiência clínica e pela informação fisiopatológica e clínica publicada. Houve a preocupação de construir o modelo de forma modular de modo a ser possível a sua expansão sem grandes transformações na descrição matemática (e informática) já existente. Na sua fase actual o modelo não pode ser usado como instrumento de diagnóstico. É antes uma ferramenta destinada a esclarecer “em princípio” mecanismos fisiopatológicos. Usou – se o modelo para simular um certo número de observações publicadas e para exemplificar a sua eventual aplicação clínica na simulação de situações hipotéticas e na análise de possíveis mecanismos fisiopatológicos responsáveis por situações de hipo ou hipercalcémias. Simultaneamente fez – se uma análise dos dados acumulados relativos a doentes vistos no Serviço de Endocrinologia do Instituto Português de Oncologia de Francisco Gentil – Centro Regional Oncológico de Lisboa, S.A. CONCLUSÕES Numa população de 894 doentes com patologias variadas do Instituto Português de Oncologia de Lisboa os valores da calcémia tiveram uma distribuição normal unimodal com uma média de 9.56 mg/dl, e um erro padrão de 0.41 mg/dl. Estas observações sugerem que a calcémia está sujeita a regulação. A partir dos resultados publicados em que o metabolismo do cálcio foi perturbado por infusões de cálcio, calcitriol ou PTH, de estudos bioquímicos e fisiológicos sobre os mecanismos de acção de factores controladores da calcémia e do estudo do comportamento de órgãos alvo (paratiroideias, intestino, osso e rim) foi possível construir um modelo matemático de parâmetros concentrados do sistema de regulação da calcémia. As expressões analíticas usadas foram baseadas na cinética enzimática de modo a que os seus parâmetros tivessem um significado físico ou fisiológico simples. O modelo revelou apreciável robustez e flexibilidade. É estável quando não perturbado e transita entre estados estacionários quando perturbado. Na sua forma actual gera simulações que reproduzem satisfatoriamente um número apreciável de dados experimentais colhidos em doentes. Isto não significa que possa ser usado como instrumento de diagnóstico aplicável a doentes individuais. O desenho do modelo comporta a adição posterior de novas relações quando surgirem situações para as quais se revele insuficiente. A utilização exaustiva do modelo permitiu explicitar aspectos do metabolismo do cálcio que ou não estão contidas na sua formulação actual – o aparecimento de hipertrofia ou de adenomas das paratiroideias e as alterações na estrutura óssea , a participação de outros factores controladores – magnésio, ou estão insuficientemente descritas – alterações do metabolismo do fósforo nos hipoparatiroidismos. A análise dos dados relativos aos doentes do Serviço de Endocrinologia do IPO permitiu o início da caracterização dos tipos de patologia que representam e de possíveis mecanismos fisiopatológicos subjacentes. Estas observações são o ponto de partida para análises futuras. São exemplos das relações encontradas: a distribuição dos doentes por dois grandes grupos conforme a calcémia é determinada pelas concentrações circulantes de PTH ou estas são determinadas pela calcémia; a distribuição sazonal das concentrações de Vit. D25. no sangue; a correlação negativa entre estas e as concentrações de PTH no sangue. Também foi possível extrair a cinética do controlo da PTH sobre a síntese de calcitriol. O estudo dos níveis circulantes de PTH no pós-operatório imediato de doentes paratiroidectomizados permitiu determinar as suas taxas de degradação metabólica. O modelo permitiu simular as relações Ca/PTH no sangue, Ca/Fracção excretada da carga tubular, Ca/P no sangue para valores normais ou altos de Ca. Foram feitas simulações de situações fisiopatológicas (em “doentes virtuais”): infusões crónicas de cálcio, PTH e calcitriol; alterações no comportamento de receptores. Estas simulações correspondem a experiências que não podem ser realizadas em humanos. São exemplos da utilização do modelo na exploração de possíveis mecanismos fisiopatológicos através da observação de resultados quantitativos inacessíveis à intuição. O modelo foi útil em duas fases do trabalho: Primeiro, durante a sua síntese implicou uma escolha criticamente selectiva de informação, sua análise quantitativa e processamento, uma explicitação rigorosa (analítica) das relações funcionais entre os controladores e as variáveis e da sua integração numa estrutura global; Segundo, a simulação de situações experimentais ou clínicas (dados do Serviço de Endocrinologia do IPO) em doentes obrigou a explicitar raciocínios fisiopatológicos habitualmente formulados em bases puramente intuitivas. Esta prática revelou comportamentos óbvios após as simulações – acção reduzida das infusões PTH (simulação de hiperparatiroidismos primários) enquanto não há inibição total da respectiva secreção, necessidade de aumento da massa secretora da paratiroideia nas insuficiências renais avançadas, etc. A síntese e utilização do modelo não implicaram uma preparação matemática avançada e foram possíveis mercê da disponibilidade de “software” interactivo especificamente desenhado para a simulação de sistemas dinâmicos em que os programas se escrevem em inglês usando a simbologia simples da álgebra elementar. A função nobre de modelos desta natureza é semelhante à dos modelos usados pelos físicos desde o século XVII: permitir explicações de carácter geral funcionando como uma ferramenta intelectual para manipulação de conceitos e para a realização de “experiências pensadas” (“thought experiments”) respeitando certos princípios físicos (princípios de conservação) que estabelecem as fronteiras da realidade. -------ABSTRACT: Calcium blood levels are remarkably constant despite great variations in calcium daily intake, intestinal absorption and renal excretion. The regulation of the calcium concentration in the blood is achieved by a complex system that includes several controller factors (mainly the serum levels of calcium, phosphorus, parathyroid hormone (PTH) and calcitriol but also of steroid hormones, ions such as magnesium and other hormonal factors) and several target organs (parathyroid glands, bone, kidney and intestine). The functional response to the controlling factors obeys a variety of kinetics. The precipitation of calcium salts is a simple phase transition in which organic molecules may provide nucleation centres or inhibit the process. The combination of a controller factor with its receptor located in the cell membrane (for peptides or ions) or in the nucleus (for steroid hormones) is only the first step of a biochemical chain that introduces a huge amplification in the response. To this great variability of response we have to add the times of response that vary from minutes to weeks. It is possible to “observe” (measure) with great accuracy in biological fluids (blood, urine, faeces, etc.) the most important factors intervening in the calcium regulation (calcium, phosphorus, PTH and calcitriol). The response of the system to acute infusions of the controlling factors has also been studied. Using molecular biology techniques it has been possible to characterize some calcium homeostasis dysfunctions and better physiopathological diagnosis are expected. With the increasingly new knowledge in this area we have better capacity to diagnose but it is harder to explain correctly the underlying metabolic mechanisms. The analysis or synthesis of complex systems is the noble activity of engineers that enables them to draw bridges, dams, boats, airplanes or cars. With the availability of medium-large frame computers it was possible to use mathematical descriptions not only to draw systems but also to explain flaws in its operations. These mathematical descriptions are generally known as models by analogy with the laws (equations) of physics that allow the mathematical description of physical processes. In practice it is not possible to find general solutions for the mathematical descriptions of complex systems but (numeric) computations for specific situations can be obtained with digital computers. The introduction of mathematical models in biology and particularly in medicine is a recent event. METHODS In this thesis a simplified model of calcium homeostasis was built that enables the computation of observable variables (concentrations of calcium, phosphorus, PTH and calcitriol) and allows the comparison between the simulation values and observed values. The choice of the model’s components was made according to our clinical experience and to the published clinical and physiopathological data. The model has a modular design that allows future expansions with minor alterations in its structure. In its present form the model cannot be used for diagnosis. It is a tool designed to enlighten physiopathological processes. To exemplify its possible clinical application in the simulation of hypothetical situations and in the analysis of possible mechanisms responsible for hypo or hypercalcemias the model was used to simulate a certain number of published observations. An analysis of clinical and laboratory data from the Endocrinology Department of the Portuguese Cancer Institute (I.P.O.F.G.-C.R.O.L.,S.A.) is also presented. CONCLUSIONS In a population of 188 patients without an identifiable disease of the calcium metabolism at the Portuguese Cancer Institute the calcemia levels had a unimodal distribution with an average of 9.56 mg/dL and a S.E.M of 0.41 mg/dL. This observation confirms that serum calcium is regulated. Using published data; in which calcium metabolism was disrupted by calcium, PTH or calcitriol infusions; from biochemical and physiological studies of the action of controller factors on the calcemia; in which the response of target organs (parathyroid glands, intestine, bone, kidney) was studied it was possible to build a mathematical model of concentrated parameters of the calcium homeostasis. Analytical expressions used were based on enzymatic kinetics. The model is flexible and robust. It is stable when not disturbed and changes between steady states when disturbed. In its present form it provides simulations that reproduce closely a number of experimental clinical data. This does not mean that it can be used as a diagnostic tool for individual patients. The exhaustive utilisation of the model revealed the need of future expansions to include aspects of the calcium metabolism not included in its present form –hypertrophy or adenomas of the parathyroid glands, bone structure changes, participation of other controller factors such as magnesium – or insufficiently described – phosphate metabolism in hypoparathyroidism. The analysis of the data collected from the I.P.O.’s Endocrinology Department allowed the initial characterization of the different pathologies represented and of their possible physiopathological mechanisms. These observations are a starting point for future analysis. As examples of the relations found were: the distribution of patients in two groups according to the dependency of calcium by PTH levels or PTH levels by calcium concentration; the seasonal distribution of the serum concentrations of D25; its negative correlation with PTH concentration. It was also possible to extract the kinetics of the control of the synthesis of calcitriol by PTH. The analysis of immediate post-surgical levels of PTH in parathyroidectomized patients allowed the determination of its metabolic clearance. The model also allowed the simulation of the relations between Ca/PTH in blood, serum Ca/Fraction of tubular load excreted and Ca/P in blood for normal and high values of calcium. Simulations were made of pathological situations (in “virtual patients”): chronic infusions of calcium, PTH and calcitriol; changes in the characteristics of receptors. These simulations are not possible in real persons. They are an example of the use of this model in exploring possible mechanisms of disease through the observation of quantitative results not accessible to simple intuition. This model was useful in two phases: Firstly, its construction required a careful choice of data, its quantitative analysis and processing, an analytical description of the relations between controller factors and variables and their integration in a global structure. Secondly, the simulation of experimental or clinical (I.P.O.’s Endocrinology Department) data implied testing physiopathological explanations that previously were based on intuition. The construction and utilisation of the model didn’t demand an advanced mathematical preparation since user-friendly interactive software was used. This software was specifically designed for the simulation of dynamic systems. The programs are written in English using elementary algebra symbols. The essential function of this type of models is identical to that of those used by physicists since the XVII century which describe quantitatively natural processes and are an intellectual tool for the manipulation of concepts and the performance of “thought experiments” based in certain physical principles (conservation principles) that are the frontiers of reality.------------------RESUMÉE: Les concentrations circulantes de calcium sont constantes même pendant des variations de l’absorption intestinale et de l’élimination rénale de cet élément. La régulation de la calcémie est un système complexe qui comprend plusieurs éléments contrôleurs (la calcémie, la phosphorémie, les concentrations circulantes de l’hormone parathyroïdienne (PTH) e du calcitriol et d’autres comme les hormones stéroïdes ou des ions comme le magnésium) et plusieurs organes (glandes parathyroïdiennes, l’os, le rein et l’intestin). Les réponses de ces organes sont variées. Dans le cas plus simple, la cristallisation des sels de calcium correspond à un changement de phase dans lequel y participent des molécules organiques que la débutent, l’accélèrent ou l’inhibent. Généralement la combinaison d’un élément contrôleur avec leur récepteur de membrane (pour les peptides ou les ions) ou intracellulaire (pour les hormones stéroïdes) n’est que le premier pas d’une chaîne biochimique qu’introduit une grande amplification de la réponse. A cette variété de réponses correspondent des grandes différences des temps de réponses qu’y vont des minuits a semaines. Il est possible « observer » (mesurer) dans les fluides biologiques (sang, urine, fèces, etc.) les éléments plus importants du système de régulation de la calcémie (calcium, phosphate, PTH et le calcitriol) et les administrer en expérimentes aigus. Cette possibilité est visible dans la littérature publiée dans ce domaine qui est en croissance permanente. L’avenir des techniques de biologie moléculaire a permis caractériser des nombreuses dysfonctions de la régulation de la calcémie et on attend un diagnostique physiopathologique de ces dysfonctions chaque fois plus rigoureuses. Les connaissances dans ce domaine s’agrandissent et on a de plus de capacités pour faire des diagnostiques et il est chaque fois plus difficile les interpréter. L’analyse ou synthèse de systèmes complexes est l’activité plus noble des ingénieurs qui les permit dessiner des ponts, bateaux, avions ou automobiles. Avec des ordinateurs de médium ou grand port il les est possible utiliser descriptions mathématiques pour dessiner les systèmes et interpréter des éventuelles fautes d’opération. Ces descriptions mathématiques sont une séquence d’opérations réalisées dans un ordinateur selon « un programme informatique » qui ont reçu la désignation générique de modèles, pour analogie avec les équations de la physique qui ont été déduits d’un nombre de postulées et qu’ont permit représenter des processus physiques en équations mathématiques. Les fameuses équations de Newton sont peut-être les exemples plus connus des systèmes physiques. L’introduction des modèles mathématiques en biologie et en particulier en médecine est un évènement récent. Dans ce travaille, on a construit un modèle simplifié de l’homéostasie du calcium pour calculer les variables observables (concentrations de calcium, phosphate, PTH et calcitriol) pour les comparer. Les choix des components a été déterminés par notre expérience clinique et par l’information physiopathologique et clinique publiée. Le modèle a été construit de façon modulaire ce que permit leur postérieur expansion sans des grandes altérations dans la description mathématique et informatique déjà existante. Dans cette forme le modèle ne peut être utilisé comme un instrument de diagnostique. Il est un outil pour éclairer la physiopathologie. Le modèle a été utilisé pour simuler un certain nombre d’observations publiées et pour exemplifier leur possible utilisation clinique dans la simulation des hypothèses et de la physiopathologie des situations d’hypo ou hypercalcémie. On a fait une analyse des éléments des procès cliniques des malades observées dans le Service d’Endocrinologie de l’IPOFG-CROL, SA. Dans une population de 894 malades avec des différentes pathologies les valeurs de calcémie on une distribution uni modale avec une Médie de 9.56 mg/dL et une erreur standard de 0.41 mg/dL. Ces observations suggèrent que la calcémie soit sujette de régulation. En utilisant des résultats de travaux publiés dans lesquels le métabolisme du calcium a été changé par des infusions de calcium, calcitriol ou PTH, des études biochimiques et physiologiques sur des mécanismes d’action des éléments contrôleurs de la calcémie et de l’étude du comportement des organes cible (parathyroïdes, intestin, rein, os), il a été possible de construire un modèle mathématique de paramètres concentrés du système de régulation de la calcémie. Les expressions analytiques utilisées ont été basées sur la cinétique enzymatique de façon à que les paramètres aient eu une signification physique ou biologique. Le modèle est stable quand il n’est pas perturbé et transit entre états stationnaires quand il est sujet a des perturbations. A ce moment il fait des simulations qui reproduisent de façon satisfaisant un nombre d’observations expérimentales. La construction du modèle permit l’addiction de nouvelles relations dans les cas ou il est insuffisant. L’utilisation exhaustive du modèle a permit expliciter des aspects du métabolisme du calcium qui y ne sont pas compris – l’hyperplasie ou la formation des adénomes des parathyroïdes, les altérations de la structure des os, la participation d’outres éléments régulateurs (magnésium), ou sont insuffisamment décrites – les altérations du métabolisme des phosphates dans l’hypoparathyroidism. L’analyse de l’information des malades du Service d’Endocrinologie a permit caractériser les pathologies représentées et leurs possibles mécanismes physiopathologiques. Ces observations sont le point de départ pour les analyses futures. Sont des exemples des relations trouvées: la distribution des malades par deux groupes: ceux dans lequel la calcémie est déterminée par la PTH ou ceux dans lesquels la PTH est déterminée par la calcémie; la distribution sazonale de la concentration de la vitamine D; la corrélation négative entre la vitamine D et la PTH. On a eu la possibilité de déduire la cinétique de control de la PTH sur la synthèse du calcitriol. L’étude des niveaux circulants de PTH sur des sujets parathyroidectomisées a permit déduire leur taux de dégradation métabolique. Le modèle a permit simuler les relations Ca/PTH dans le sang, Ca/fraction éliminée par le rein, Ca/P dans le sang pour des valeurs normales ou hautes de calcium. On a fait des simulations de situations physiopathologiques (dans “malades virtuelles”): Infusions chroniques de calcium, PTH ou calcitriol; altérations des récepteurs. Ces simulations ne peuvent pas être réalisées dans les humains. Sont des exemples d’utilisation du modèle dans l’exploration des possibles mécanismes de la physiopathologie en observant des résultats quantitatifs inaccessibles à l’intuition. Le modèle a été utile pendant deux étapes des travaux: La première, dans sa construction on a choisi l’information disponible, son analyse quantitative, l’explicitation rigoureuse (analytique) des relations fonctionnelles entre les contrôleurs et les variables et sa intégration dans une structure globale. La deuxième, la simulation de situations expérimentales ou cliniques (du Service d’Endocrinologie) a obligé d’expliciter des raisonnements physiopathologiques généralement formulés utilisant l’intuition. Cette pratique a montré des comportements – action réduite des infusions de PTH (jusqu’à l’inhibition totale de leur respective sécrétion), nécessité d’augmenter la masse sécréteuse de la parathyroïde dans les insuffisants rénales, etc. La synthèse et utilisation du modèle n’ont pas besoin d’une formation avancée en mathématique et sont possibles grâce à un programme interactif qui a été conçu pour la simulation des systèmes dynamiques dans lesquels le programme se construit en anglais en utilisant la symbolique élémentaire de l’algèbre. La fonction noble de ces modèles est semblable à celles des physiques du XVII siècle: Permettre établir explications générales en fonctionnant comme un outil intellectuel pour manipuler des concepts et pour la réalisation d’expérimentes pensées en respectant certains principes de la physique (principe de la conservation) qu’établissent les frontières de la réalité.

Aplicação de um modelo de programação linear inteira mista (PLIM) na expansão da rede de distribuição de energia elétrica em Angola

Em Angola, apenas cerca de 30% da população tem acesso à energia elétrica, nível que decresce para valores inferiores a 10% em zonas rurais mais remotas. Este problema é agravado pelo facto de, na maioria dos casos, as infraestruturas existentes se encontrarem danificadas ou não acompanharem o desenvolvimento da região. Em particular na capital angolana, Luanda que, sendo a menor província de Angola, é a que regista atualmente a maior densidade populacional. Com uma população de cerca de 5 milhões de habitantes, não só há frequentemente problemas relacionados com a falha do fornecimento de energia elétrica como há ainda uma percentagem considerável de municípios onde a rede elétrica ainda nem sequer chegou. O governo de Angola, no seu esforço de crescimento e aproveitamento das suas enormes potencialidades, definiu o setor energético como um dos fatores críticos para o desenvolvimento sustentável do país, tendo assumido que este é um dos eixos prioritários até 2016. Existem objetivos claros quanto à reabilitação e expansão das infraestruturas do setor elétrico, aumentando a capacidade instalada do país e criando uma rede nacional adequada, com o intuito não só de melhorar a qualidade e fiabilidade da rede já existente como de a aumentar. Este trabalho de dissertação consistiu no levantamento de dados reais relativamente à rede de distribuição de energia elétrica de Luanda, na análise e planeamento do que é mais premente fazer relativamente à sua expansão, na escolha dos locais onde é viável localizar novas subestações, na modelação adequada do problema real e na proposta de uma solução ótima para a expansão da rede existente. Depois de analisados diferentes modelos matemáticos aplicados ao problema de expansão de redes de distribuição de energia elétrica encontrados na literatura, optou-se por um modelo de programação linear inteira mista (PLIM) que se mostrou adequado. Desenvolvido o modelo do problema, o mesmo foi resolvido por recurso a software de otimização Analytic Solver e CPLEX. Como forma de validação dos resultados obtidos, foi implementada a solução de rede no simulador PowerWorld 8.0 OPF, software este que permite a simulação da operação do sistema de trânsito de potências.

Distribuição de Contaminantes Orgânicos em Solos Calcários – Influência dos minerais de Argila

O solo é um recurso multifuncional e vital para a humanidade, apresentando funções ecológicas, técnico-industriais, socioeconómicas e culturais, estabelecendo um vasto capital natural insubstituível. Face à sua taxa de degradação potencialmente rápida que, devido ao crescente desenvolvimento económico e incremento da população mundial, tem vindo a aumentar nas últimas décadas, o solo é, atualmente, um recurso finito e limitado. Devido a esta problemática, o presente documento visa abordar a progressiva preocupação sobre as questões geoambientais e toda a investigação que as envolvem, avaliando o modo como os contaminantes se dispersam pelo solo nas diferentes fases do mesmo (fases sólida, líquida e gasosa). A parte experimental centrou-se na análise da adsorção do benzeno, a partir da determinação das isotérmicas de adsorção. Para tal, foram previamente preparados reatores com calcário, sendo alguns deles previamente contaminados com um biocombustível, biodiesel, a uma concentração constante. Este processo foi monitorizado com base na evolução temporal da concentração na fase gasosa, através da cromatografia gasosa. De entre os objetivos, procurou-se analisar a distribuição dos contaminantes pelas fases constituintes do solo, ajustar os dados experimentais obtidos os modelos matemáticos de Langmuir, Freundlich e Polinomial, e verificar e discutir as soluções mais adequadas.

Income and mental health

RESUMO: A enorme carga e o sofrimento provocado pelas doenças mentais no mundo tornam imperioso conhecer melhor os seus determinantes. Combater as desigualdades em saude tornou-‐se uma prioridadade de saúde publica, mas e necessário estabelecer as suas vias causais para ser possível implementar intervenções e politicas efetivas. A literatura cientifica tem sugerido a importância dos determinantes sociais na etiologia e evolucao das principais doenças mentais e do suicidio, com especial enfase no papel da desvantagem social. Ainda assim, o papel dos factores psicossociais na saúde mental, e especificamente o papel do rendimento e da sua distribuição não tem sido investigado no meu pais, Portugal. No meu projecto de investigação proponho‐me a estudar se em Portugal existe uma associação entre as doenças mentais e o rendimento absoluto e relativo. Pretendo usar os dados do primeiro inquérito epidemiológico sobre saude mental realizado em Portugal,um inquérito nacional transversal no domicilio que foi conduzido em 2009, integrado no WHO World Mental Health Survey Consortium. Nesta tese de mestrado apresento os resultados da minha revisão da literatura Sobre a relação entre oestatuto socio-economico e a saúde mental e esboço uma proposta de pesquisa para continuar a investigar estetema. A evidencia que apresento mostra que a exposição aum vasto leque de riscos psicossociais, como o baixo rendimento, a educação limitada e o estatuto ocupacionalbaixo,aumenta a probabilidade de desenvolver problemas de saúde mental.. As diferencas em saúde seguem um gradiente social, com piores resultados de saúde a medida que a posição na hierarquia social diminui. Tambem sumarizo a literatura sobre o papel do contexto na produção de desigualdades em saúde para alem das características individuais. Tem especial interesse o potencial efeito na saúde do rendimento relativo e a importância da distribuição dos rendimentos como determinante de saude. Finalmente, delineio os possíveis mecanismos através dos quais o estatuto socio-economico contribui para as disparidades em saúde.-------------------ABSTRACT: The enormous burden and suffering from mental disorders worldwide makes it imperative to better understand its determinants. Tackling nhealth inequalities has become a public health priority, but it is necessary to establish their causalpathways in order to implement effective interventions and policies. Scientific literature has suggested the importance of social determinants in the aetiology and course of major mental disorders and suicide, with special emphasis on the role of social disadvantage. Nevertheless, the role of psychosocial factors on mental health, and specifically the role of income and its distribution, has not been researched in my home country, Portugal. In my research project I propose to study whether in Portugal there is an association between mental disorders and absolute and relative income. I intend to use data from the first Portuguese Mental Health Survey, a national cross-sectional household survey that was conducted in 2009, integrated in the WHO World Mental Health Survey Consortium. In this masters thesis I present the results of my literature review on the relation between Socioeconomic status and mental health and outline a research proposal to further nvestigate this topic. The body of evidence that I present shows that exposure to a wide range of psychosocial risks, such as low income, limited education, and low occupational status, increases the likelihood of mental health problems. Differences in health follow a social gradient, with worsening health as the position in the social ladder decreases. I also summarize the literature on the role of context in producing health inequalities beyond individual characteristics. Of special interest is the potential health effect of relative income and the importance of income distribution as a health determinant. Finally, I outline the various possible mechanisms for health disparities associated with socioeconomic status.

Progressivity in the Portuguese personal income tax system

This Work Project analyzes the evolution of the Portuguese personal income tax system’s progressivity over the period of 2005 through 2013. It presents the first computation of cardinal progressivity measures using administrative tax data for Portugal. We compute several progressivity indices and find that progressivity has had very modest variations from 2005 to 2012, whilst from 2012 to 2013 there has been a relatively stronger decrease, excluding the impact of the income tax surcharge of the years 2012 and 2013. When this latter is included, progressivity of 2012 and 2013 decreases considerably. Analyzing the effective average tax rates of the top income percentiles in the income scale, we find that these rates have increased over the period 2010–2013, suggesting that an analysis of effective tax rates is insufficient to assess progressivity in the whole tax scheme.

Bases para o estudo da genética de populações dos Hymenoptera em geral e dos Apinae sociais em particular

This paper deals with problems on population genetics in Hymenoptera and particularly in social Apidae. 1) The studies on populations of Hymenoptera were made according to the two basic types of reproduction: endogamy and panmixia. The populations of social Apinae have a mixed method of reproduction with higher percentage of panmixia and a lower of endogamy. This is shown by the following a) males can enter any hive in swarming time; b) males of Meliponini are expelled from hives which does not need them, and thus, are forced to look for some other place; c) Meliponini males were seen powdering themselves with pollen, thus becoming more acceptable in any other hive. The panmixia is not complete owing to the fact that the density of the breeding population as very low, even in the more frequent species as low as about 2 females and 160 males per reproductive area. We adopted as selection values (or survival indices) the expressions according to Brieger (1948,1950) which may be summarised as follows; a population: p2AA + ²pq Aa + q2aa became after selection: x p2AA + 2pq Aa + z q²aa. For alge-braics facilities Brieger divided the three selective values by y giving thus: x/y p2 AA + y/y 2 pq Aa + z/y q²aa. He called x/y of RA and z/y of Ra, that are survival or selective index, calculated in relation to the heterozygote. In our case all index were calculated in relation to the heterozygote, including the ones for haploid males; thus we have: RA surveval index of genotype AA Ra surveval index of genotype aa R'A surveval index of genotype A R'a surveval index of genotype a 1 surveval index of genotype Aa The index R'A ande R'a were equalized to RA and Ra, respectively, for facilities in the conclusions. 2) Panmitic populations of Hymenoptera, barring mutations, migrations and selection, should follow the Hardy-Weinberg law, thus all gens will be present in the population in the inicial frequency (see Graphifc 1). 3) Heterotic genes: If mutation for heterotic gene ( 1 > RA > Ra) occurs, an equilibrium will be reached in a population when: P = R A + Ra - 2R²a _____________ (9) 2(R A + Ra - R²A - R²a q = R A + Ra - 2R²A _____________ (10) 2(R A + Ra - R²A - R²a A heterotic gene in an hymenopteran population may be maintained without the aid of new mutation only if the survival index of the most viable mutant (RA) does not exced the limiting value given by the formula: R A = 1 + √1+Ra _________ 4 If RA has a value higher thah the one permitted by the formula, then only the more viable gene will remain present in the population (see Graphic 10). The only direct proof for heterotic genes in Hymenoptera was given by Mackensen and Roberts, who obtained offspring from Apis mellefera L. queens fertilized by their own sons. Such inbreeding resulted in a rapid loss of vigor the colony; inbred lines intercrossed gave a high hybrid vigor. Other fats correlated with the "heterosis" problem are; a) In a colony M. quadrifasciata Lep., which suffered severely from heat, the percentage of deths omong males was greater .than among females; b) Casteel and Phillips had shown that in their samples (Apis melifera L). the males had 7 times more abnormalities tian the workers (see Quadros IV to VIII); c) just after emerging the males have great variation, but the older ones show a variation equal to that of workers; d) The tongue lenght of males of Apis mellifera L., of Bombus rubicundus Smith (Quadro X), of Melipona marginata Lep. (Quadro XI), and of Melipona quadrifasciata Lep. Quadro IX, show greater variationthan that of workers of the respective species. If such variation were only caused by subviables genes a rapid increasse of homozigoty for the most viable alleles should be expected; then, these .wild populations, supposed to be in equilibrium, could .not show such variability among males. Thus we conclude that heterotic genes have a grat importance in these cases. 4) By means of mathematical models, we came to the conclusion tht isolating genes (Ra ^ Ra > 1), even in the case of mutations with more adaptability, have only the opor-tunity of survival when the population number is very low (thus the frequency of the gene in the breeding population will be large just after its appearence). A pair of such alleles can only remain present in a population when in border regions of two races or subspecies. For more details see Graphics 5 to 8. 5) Sex-limited genes affecting only females, are of great importance toHymenoptera, being subject to the same limits and formulas as diploid panmitic populations (see formulas 12 and 13). The following examples of these genes were given: a) caste-determining genes in the genus Melipona; b) genes permiting an easy response of females to differences in feeding in almost all social Hymenoptera; c) two genes, found in wild populations, one in Trigona (Plebéia) mosquito F. SMITH (quadro XII) and other in Melipona marginata marginata LEP. (Quadro XIII, colonies 76 and 56) showing sex-limited effects. Sex-limited genes affecting only males do not contribute to the plasticity or genie reserve in hymenopteran populations (see formula 14). 6) The factor time (life span) in Hymenoptera has a particular importance for heterotic genes. Supposing one year to be the time unit and a pair of heterotic genes with respective survival indice equal to RA = 0, 90 and Ra = 0,70 to be present; then if the life time of a population is either one or two years, only the more viable gene will remain present (see formula 11). If the species has a life time of three years, then both alleles will be maintained. Thus we conclude that in specis with long lif-time, the heterotic genes have more importance, and should be found more easily. 7) The colonies of social Hymenoptera behave as units in competition, thus in the studies of populations one must determine the survival index, of these units which may be subdivided in indice for egg-laying, for adaptive value of the queen, for working capacity of workers, etc. 8) A study of endogamic hymenopteran populations, reproduced by sister x brother mating (fig. 2), lead us to the following conclusions: a) without selection, a population, heterozygous for one pair of alleles, will consist after some generations (theoretically after an infinite number of generation) of females AA fecundated with males A and females aa fecundated with males a (see Quadro I). b) Even in endogamic population there is the theoretical possibility of the presence of heterotic genes, at equilibrium without the aid of new mutations (see Graphics 11 and 12), but the following! conditions must be satisfied: I - surveval index of both homozygotes (RA e Ra) should be below 0,75 (see Graphic 13); II - The most viable allele must riot exced the less viable one by more than is permited by the following formula (Pimentel Gomes 1950) (see Gra-fic 14) : 4 R5A + 8 Ra R4A - 4 Ra R³A (Ra - 1) R²A - - R²a (4 R²a + 4 Ra - 1) R A + 2 R³a < o Considering these two conditions, the existance of heterotic genes in endogamic populations of Hymenoptera \>ecames very improbable though not - impossible. 9) Genie mutation offects more hymenopteran than diploid populations. Thus we have for lethal genes in diploid populations: u = q2, and in Hymenoptera: u = s, being u the mutation ratio and s the frequency of the mutant in the male population. 10) Three factors, important to competition among species of Meliponini were analysed: flying capacity of workers, food gathering capacity of workers, egg-laying of the queen. In this connection we refer to the variability of the tongue lenght observed in colonies from several localites, to the method of transporting the pollen in the stomach, from some pots (Melliponi-ni storage alveolus) to others (e. g. in cases of pillage), and to the observation that the species with the most populous hives are almost always the most frequent ones also. 11) Several defensive ways used for Meliponini to avoid predation are cited, but special references are made upon the camouflage of both hive (fig. 5) and hive entrance (fig. 4) and on the mimetism (see list in page ). Also under the same heading we described the method of Lestrimelitta for pillage. 12) As mechanisms important for promoting genetic plasticity of hymenopteran species we cited: a) cytological variations and b) genie reserve. As to the former, duplications and numerical variations of chromosomes were studied. Diprion simile ATC was cited as example for polyploidy. Apis mellife-ra L. (n •= 16) also sugests polyploid origen since: a) The genus Melipona, which belongs to a" related tribe, presents in all species so far studied n = 9 chromosomes and b) there occurs formation of dyads in the firt spermatocyte division. It is su-gested that the origin of the sex-chromosome of Apis mellifera It. may be related to the possible origin of diplo-tetraploidy in this species. With regards to the genie reserve, several possible types of mutants were discussed. They were classified according to their survival indices; the heterotic and neutral mutants must be considered as more important for the genie reserve. 13) The mean radius from a mother to a daghter colony was estimated as 100 meters. Since the Meliponini hives swarm only once a year we may take 100 meters a year as the average dispersion of female Meliponini in ocordance to data obtained from Trigona (tetragonisca) jaty F. SMITH and Melipona marginata LEP., while other species may give different values. For males the flying distance was roughly estimated to be 10 times that for females. A review of the bibliography on Meliponini swarm was made (pg. 43 to 47) and new facts added. The population desity (breeding population) corresponds in may species of Meliponini to one male and one female per 10.000 square meters. Apparently the males are more frequent than the females, because there are sometimes many thousands, of males in a swarm; but for the genie frequency the individuals which have descendants are the ones computed. In the case of Apini and Meliponini, only one queen per hive and the males represented by. the spermatozoos in its spermateca are computed. In Meliponini only one male mate with the queen, while queens of Apis mellijera L. are fecundated by an average of about 1, 5 males. (Roberts, 1944). From the date cited, one clearly sees that, on the whole, populations of wild social bees (Meliponini) are so small that the Sewall Wright effect may become of great importance. In fact applying the Wright's formula: f = ( 1/aN♂ + 1/aN♀) (1 - 1/aN♂ + 1/aN♀) which measures the fixation and loss of genes per generation, we see that the fixation or loss of genes is of about 7% in the more frequent species, and rarer species about 11%. The variation in size, tergite color, background color, etc, of Melipona marginata Lep. is atributed to this genetic drift. A detail, important to the survival of Meliponini species, is the Constance of their breeding population. This Constance is due to the social organization, i. e., to the care given to the reproductive individuals (the queen with its sperm pack), to the way of swarming, to the food storage intended to control variations of feeding supply, etc. 14) Some species of the Meliponini are adapted to various ecological conditions and inhabit large geographical areas (e. g. T. (Tetragonisca jaty F. SMITH), and Trigona (Nanno-trigona testaceicornis LEP.) while others are limited to narrow regions with special ecological conditions (e. g. M. fuscata me-lanoventer SCHWARZ). Other species still, within the same geographical region, profit different ecological conditions, as do M. marginata LEP. and M. quadrifasciata LEP. The geographical distribution of Melipona quadrifasciata LEP. is different according to the subspecies: a) subsp anthidio-des LEP. (represented in Fig. 7 by black squares) inhabits a region fron the North of the S. Paulo State to Northeastern Brazil, ,b) subspecies quadrifasciata LEP., (marked in Fig. 7 with black triangles) accurs from the South of S. Paulo State to the middle of the State of Rio Grande do Sul (South Brazil). In the margined region between these two areas of distribution, hi-brid colonies were found (Fig. 7, white circles); they are shown with more details in fig. 8, while the zone of hybridization is roughly indicated in fig. 9 (gray zone). The subspecies quadrifasciata LEP., has 4 complete yellow bands on the abdominal tergites while anthidioides LEP. has interrupted ones. This character is determined by one or two genes and gives different adaptative properties to the subspecies. Figs. 10 shows certains meteorological isoclines which have aproximately the same configuration as the limits of the hybrid zone, suggesting different climatic adaptabilities for both genotypes. The exis-tance of a border zone between the areas of both subspecies, where were found a high frequency of hybrids, is explained as follows: being each subspecies adapted to a special climatic zone, we may suppose a poor adaptation of either one in the border region, which is also a region of intermediate climatic conditions. Thus, the hybrids, having a combination of the parent qualities, will be best adapted to the transition zone. Thus, the hybrids will become heterotic and an equilibrium will be reached with all genotypes present in the population in the border region.

Inequality in CO2 emissions across countries and its relationship with income inequality: a distributive approach

This paper analyses the inequality in CO2 emissions across countries (and groups of countries) and the relationship of this inequality with income inequality across countries for the period (1971-1999). The research employs the tools that are usually applied in income distribution analysis. The methodology used here gives qualitative and quantitative information on some of the features of the inequalities across countries that are considered most relevant for the design and discussion of policies aimed at mitigating climate change. The paper studies the relationship between CO2 emissions and GDP and shows that income inequality across countries has been followed by an important inequality in the distribution of emissions. This inequality has diminished mildly, although the inequality in emissions across countries ordered in the increasing value of income (inequality between rich and poor countries) has diminished less than the “simple” inequality in emissions. Lastly, the paper shows that the inequality in CO2 emissions is mostly explained by the inequality between groups with different per capita income level. The importance of the inequality within groups of similar per capita income is much lower and has diminished during the period, especially in the low-middle income group.

Equity and CO2 emissions distribution in climate change integrated assessment

Emissions distribution is a focus variable for the design of future international agreements to tackle global warming. This paper specifically analyses the future path of emissions distribution and its determinants in different scenarios. Whereas our analysis is driven by tools which are typically applied in the income distribution literature and which have recently been applied to the analysis of CO2 emissions distribution, a new methodological approach is that our study is driven by simulations run with a popular regionalised optimal growth climate change model over the 1995-2105 period. We find that the architecture of environmental policies, the implementation of flexible mechanisms and income concentration are key determinants of emissions distribution over time. In particular we find a robust positive relationship between measures of inequalities.

The Optimal Distribution of the Tax Burden over the Business Cycle

This paper analyses optimal income taxes over the business cycle under a balanced-budget restriction, for low, middle and high income households. A model incorporating capital-skill complementarity in production and differential access to capital and labour markets is developed to capture the cyclical characteristics of the US economy, as well as the empirical observations on wage (skill premium) and wealth inequality. We .nd that the tax rate for high income agents is optimally the least volatile and the tax rate for low income agents the least countercyclical. In contrast, the path of optimal taxes for the middle income group is found to be very volatile and counter-cyclical. We further find that the optimal response to output-enhancing capital equipment technology and spending cuts is to increase the progressivity of income taxes. Finally, in response to positive TFP shocks, taxation becomes more progressive after about two years.

Income stratification and the measurement of interdistributional inequality between multiple groups

This paper proposes a new class of stratification indices that measure interdistributional inequality between multiple groups. The class is based on a conceptualisation of stratification as a process that results in a hierarchical ordering of groups and therefore seeks to capture not only the extent to which groups form well-defined strata in the income distribution but also the scale of the resultant differences in income standards between them, where these two factors play the same role as identification and alienation respectively in the measurement of polarisation. The properties of the class as a whole are investigated as well as those of selected members of it: zeroth and first power indices may be interpreted as measuring the overall incidence and depth of stratification respectively, while higher power indices members are directly sensitive to the severity of stratification between groups. An illustrative application provides an empirical analysis of global income stratification by regions in 1993.