Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

Habitat predictive modelling of demersal fish species in the Azores

Dissertação de Mestrado, Estudos Integrados dos Oceanos, 25 de Março de 2013, Universidade dos Açores.

Economic, environmental and mixed objective functions in non-linear process optimization using simulated annealing and tabu search

Screening of topologies developed by hierarchical heuristic procedures can be carried out by comparing their optimal performance. In this work we will be exploiting mono-objective process optimization using two algorithms, simulated annealing and tabu search, and four different objective functions: two of the net present value type, one of them including environmental costs and two of the global potential impact type. The hydrodealkylation of toluene to produce benzene was used as case study, considering five topologies with different complexities mainly obtained by including or not liquid recycling and heat integration. The performance of the algorithms together with the objective functions was observed, analyzed and discussed from various perspectives: average deviation of results for each algorithm, capacity for producing high purity product, screening of topologies, objective functions robustness in screening of topologies, trade-offs between economic and environmental type objective functions and variability of optimum solutions.

Pseudo-fractional ARMA modelling using a double Levinson recursion

IET Control Theory & Applications, Vol. 1, Nº 1

Project, modelling and simulation of air stripping columns for the treatment of groundwater contaminated with volatile organic compounds

Volatile organic compounds are a common source of groundwater contamination that can be easily removed by air stripping in columns with random packing and using a counter-current flow between the phases. This work proposes a new methodology for the column design for any particular type of packing and contaminant avoiding the necessity of a pre-defined diameter used in the classical approach. It also renders unnecessary the employment of the graphical Eckert generalized correlation for pressure drop estimates. The hydraulic features are previously chosen as a project criterion and only afterwards the mass transfer phenomena are incorporated, in opposition to conventional approach. The design procedure was translated into a convenient algorithm using C++ as programming language. A column was built in order to test the models used either in the design or in the simulation of the column performance. The experiments were fulfilled using a solution of chloroform in distilled water. Another model was built to simulate the operational performance of the column, both in steady state and in transient conditions. It consists in a system of two partial non linear differential equations (distributed parameters). Nevertheless, when flows are steady, the system became linear, although there is not an evident solution in analytical terms. In steady state the resulting system of ODE can be solved, allowing for the calculation of the concentration profile in both phases inside the column. In transient state the system of PDE was numerically solved by finite differences, after a previous linearization.

New insights into pseudo-fractional ARMA modelling

Proceedings of the International Conference on Computational Cybernetics, Vienna University of Technology, August 30 - September 1, 2004

Prognostic modelling of breast cancer patients: a benchmark of predictive models with external validation

Dissertação apresentada para obtenção do Grau de Doutor em Engenharia Electrotécnica e de Computadores – Sistemas Digitais e Percepcionais pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

Modelling HIV/AIDS length of stay in Portugal

Tese apresentada como requisito parcial para obtenção do grau de Doutor em Estatística e Gestão de Informação pelo Instituto Superior de Estatística e Gestão de Informação da Universidade Nova de Lisboa

Modelling and Forecasting Mortality Patterns

Thesis submitted in partial fulfillment of the requirements for the Degree of Doctor of Statistics and Information Management

Métodos estatísticos aplicados à modelação de dados oncológicos

RESUMO: A estrutura demográfica portuguesa é marcada por baixas taxas de natalidade e mortalidade, onde a população idosa representa uma fatia cada vez mais representativa, fruto de uma maior longevidade. A incidência do cancro, na sua generalidade, é maior precisamente nessa classe etária. A par de outras doenças igualmente lesivas (e.g. cardiovasculares, degenerativas) cuja incidência aumenta com a idade, o cancro merece relevo. Estudos epidemiológicos apresentam o cancro como líder mundial na mortalidade. Em países desenvolvidos, o seu peso representa 25% do número total de óbitos, percentagem essa que mais que duplica noutros países. A obesidade, a baixa ingestão de frutas e vegetais, o sedentarismo, o consumo de tabaco e a ingestão de álcool, configuram-se como cinco dos fatores de risco presentes em 30% das mortes diagnosticadas por cancro. A nível mundial e, em particular no Sul de Portugal, os cancros do estômago, recto e cólon apresentam elevadas taxas de incidência e de mortalidade. Do ponto de vista estritamente económico, o cancro é a doença que mais recursos consome enquanto que do ponto de vista físico e psicológico é uma doença que não limita o seu raio de ação ao doente. O cancro é, portanto, uma doença sempre atual e cada vez mais presente, pois reflete os hábitos e o ambiente de uma sociedade, não obstante as características intrínsecas a cada indivíduo. A adoção de metodologia estatística aplicada à modelação de dados oncológicos é, sobretudo, valiosa e pertinente quando a informação é oriunda de Registos de Cancro de Base Populacional (RCBP). A pertinência é justificada pelo fato destes registos permitirem aferir numa população específica, o risco desta sofrer e/ou vir a sofrer de uma dada neoplasia. O peso que as neoplasias do estômago, cólon e recto assumem foi um dos elementos que motivou o presente estudo que tem por objetivo analisar tendências, projeções, sobrevivências relativas e a distribuição espacial destas neoplasias. Foram considerados neste estudo todos os casos diagnosticados no período 1998-2006, pelo RCBP da região sul de Portugal (ROR-Sul). O estudo descritivo inicial das taxas de incidência e da tendência em cada uma das referidas neoplasias teve como base uma única variável temporal - o ano de diagnóstico - também designada por período. Todavia, uma metodologia que contemple apenas uma única variável temporal é limitativa. No cancro, para além do período, a idade à data do diagnóstico e a coorte de nascimento, são variáveis temporais que poderão prestar um contributo adicional na caracterização das taxas de incidência. A relevância assumida por estas variáveis temporais justificou a sua inclusão numaclasse de modelos designada por modelos Idade-Período-Coorte (Age-Period-Cohort models - APC), utilizada na modelação das taxas de incidência para as neoplasias em estudo. Os referidos modelos permitem ultrapassar o problema de relações não lineares e/ou de mudanças súbitas na tendência linear das taxas. Nos modelos APC foram consideradas a abordagem clássica e a abordagem com recurso a funções suavizadoras. A modelação das taxas foi estratificada por sexo. Foram ainda estudados os respectivos submodelos (apenas com uma ou duas variáveis temporais). Conhecido o comportamento das taxas de incidência, uma questão subsequente prende-se com a sua projeção em períodos futuros. Porém, o efeito de mudanças estruturais na população, ao qual Portugal não é alheio, altera substancialmente o número esperado de casos futuros com cancro. Estimativas da incidência de cancro a nível mundial obtidas a partir de projeções demográficas apontam para um aumento de 25% dos casos de cancro nas próximas duas décadas. Embora a projeção da incidência esteja associada a alguma incerteza, as projeções auxiliam no planeamento de políticas de saúde para a afetação de recursos e permitem a avaliação de cenários e de intervenções que tenham como objetivo a redução do impacto do cancro. O desconhecimento de projeções da taxa de incidência destas neoplasias na área abrangida pelo ROR-Sul, levou à utilização de modelos de projeção que diferem entre si quanto à sua estrutura, linearidade (ou não) dos seus coeficientes e comportamento das taxas na série histórica de dados (e.g. crescente, decrescente ou estável). Os referidos modelos pautaram-se por duas abordagens: (i)modelos lineares no que concerne ao tempo e (ii) extrapolação de efeitos temporais identificados pelos modelos APC para períodos futuros. Foi feita a projeção das taxas de incidência para os anos de 2007 a 2010 tendo em conta o género, idade e neoplasia. É ainda apresentada uma estimativa do impacto económico destas neoplasias no período de projeção. Uma questão pertinente e habitual no contexto clínico e a que o presente estudo pretende dar resposta, reside em saber qual a contribuição da neoplasia em si para a sobrevivência do doente. Nesse sentido, a mortalidade por causa específica é habitualmente utilizada para estimar a mortalidade atribuível apenas ao cancro em estudo. Porém, existem muitas situações em que a causa de morte é desconhecida e, mesmo que esta informação esteja disponível através dos certificados de óbito, não é fácil distinguir os casos em que a principal causa de morte é devida ao cancro. A sobrevivência relativa surge como uma medida objetiva que não necessita do conhecimento da causa específica da morte para o seu cálculo e dar-nos-á uma estimativa da probabilidade de sobrevivência caso o cancro em análise, num cenário hipotético, seja a única causa de morte. Desconhecida a principal causa de morte nos casos diagnosticados com cancro no registo ROR-Sul, foi determinada a sobrevivência relativa para cada uma das neoplasias em estudo, para um período de follow-up de 5 anos, tendo em conta o sexo, a idade e cada uma das regiões que constituem o registo. Foi adotada uma análise por período e as abordagens convencional e por modelos. No epílogo deste estudo, é analisada a influência da variabilidade espaço-temporal nas taxas de incidência. O longo período de latência das doenças oncológicas, a dificuldade em identificar mudanças súbitas no comportamento das taxas, populações com dimensão e riscos reduzidos, são alguns dos elementos que dificultam a análise da variação temporal das taxas. Nalguns casos, estas variações podem ser reflexo de flutuações aleatórias. O efeito da componente temporal aferida pelos modelos APC dá-nos um retrato incompleto da incidência do cancro. A etiologia desta doença, quando conhecida, está associada com alguma frequência a fatores de risco tais como condições socioeconómicas, hábitos alimentares e estilo de vida, atividade profissional, localização geográfica e componente genética. O “contributo”, dos fatores de risco é, por vezes, determinante e não deve ser ignorado. Surge, assim, a necessidade em complementar o estudo temporal das taxas com uma abordagem de cariz espacial. Assim, procurar-se-á aferir se as variações nas taxas de incidência observadas entre os concelhos inseridos na área do registo ROR-Sul poderiam ser explicadas quer pela variabilidade temporal e geográfica quer por fatores socioeconómicos ou, ainda, pelos desiguais estilos de vida. Foram utilizados os Modelos Bayesianos Hierárquicos Espaço-Temporais com o objetivo de identificar tendências espaço-temporais nas taxas de incidência bem como quantificar alguns fatores de risco ajustados à influência simultânea da região e do tempo. Os resultados obtidos pela implementação de todas estas metodologias considera-se ser uma mais valia para o conhecimento destas neoplasias em Portugal.------------ABSTRACT: mortality rates, with the elderly being an increasingly representative sector of the population, mainly due to greater longevity. The incidence of cancer, in general, is greater precisely in that age group. Alongside with other equally damaging diseases (e.g. cardiovascular,degenerative), whose incidence rates increases with age, cancer is of special note. In epidemiological studies, cancer is the global leader in mortality. In developed countries its weight represents 25% of the total number of deaths, with this percentage being doubled in other countries. Obesity, a reduce consumption of fruit and vegetables, physical inactivity, smoking and alcohol consumption, are the five risk factors present in 30% of deaths due to cancer. Globally, and in particular in the South of Portugal, the stomach, rectum and colon cancer have high incidence and mortality rates. From a strictly economic perspective, cancer is the disease that consumes more resources, while from a physical and psychological point of view, it is a disease that is not limited to the patient. Cancer is therefore na up to date disease and one of increased importance, since it reflects the habits and the environment of a society, regardless the intrinsic characteristics of each individual. The adoption of statistical methodology applied to cancer data modelling is especially valuable and relevant when the information comes from population-based cancer registries (PBCR). In such cases, these registries allow for the assessment of the risk and the suffering associated to a given neoplasm in a specific population. The weight that stomach, colon and rectum cancers assume in Portugal was one of the motivations of the present study, that focus on analyzing trends, projections, relative survival and spatial distribution of these neoplasms. The data considered in this study, are all cases diagnosed between 1998 and 2006, by the PBCR of Portugal, ROR-Sul.Only year of diagnosis, also called period, was the only time variable considered in the initial descriptive analysis of the incidence rates and trends for each of the three neoplasms considered. However, a methodology that only considers one single time variable will probably fall short on the conclusions that could be drawn from the data under study. In cancer, apart from the variable period, the age at diagnosis and the birth cohort are also temporal variables and may provide an additional contribution to the characterization of the incidence. The relevance assumed by these temporal variables justified its inclusion in a class of models called Age-Period-Cohort models (APC). This class of models was used for the analysis of the incidence rates of the three cancers under study. APC models allow to model nonlinearity and/or sudden changes in linear relationships of rate trends. Two approaches of APC models were considered: the classical and the one using smoothing functions. The models were stratified by gender and, when justified, further studies explored other sub-models where only one or two temporal variables were considered. After the analysis of the incidence rates, a subsequent goal is related to their projections in future periods. Although the effect of structural changes in the population, of which Portugal is not oblivious, may substantially change the expected number of future cancer cases, the results of these projections could help planning health policies with the proper allocation of resources, allowing for the evaluation of scenarios and interventions that aim to reduce the impact of cancer in a population. Worth noting that cancer incidence worldwide obtained from demographic projections point out to an increase of 25% of cancer cases in the next two decades. The lack of projections of incidence rates of the three cancers under study in the area covered by ROR-Sul, led us to use a variety of forecasting models that differ in the nature and structure. For example, linearity or nonlinearity in their coefficients and the trend of the incidence rates in historical data series (e.g. increasing, decreasing or stable).The models followed two approaches: (i) linear models regarding time and (ii) extrapolation of temporal effects identified by the APC models for future periods. The study provide incidence rates projections and the numbers of newly diagnosed cases for the year, 2007 to 2010, taking into account gender, age and the type of cancer. In addition, an estimate of the economic impact of these neoplasms is presented for the projection period considered. This research also try to address a relevant and common clinical question in these type of studies, regarding the contribution of the type of cancer to the patient survival. In such studies, the primary cause of death is commonly used to estimate the mortality specifically due to the cancer. However, there are many situations in which the cause of death is unknown, or, even if this information is available through the death certificates, it is not easy to distinguish the cases where the primary cause of death is the cancer. With this in mind, the relative survival is an alternative measure that does not need the knowledge of the specific cause of death to be calculated. This estimate will represent the survival probability in the hypothetical scenario of a certain cancer be the only cause of death. For the patients with unknown cause of death that were diagnosed with cancer in the ROR-Sul, the relative survival was calculated for each of the cancers under study, for a follow-up period of 5 years, considering gender, age and each one of the regions that are part the registry. A period analysis was undertaken, considering both the conventional and the model approaches. In final part of this study, we analyzed the influence of space-time variability in the incidence rates. The long latency period of oncologic diseases, the difficulty in identifying subtle changes in the rates behavior, populations of reduced size and low risk are some of the elements that can be a challenge in the analysis of temporal variations in rates, that, in some cases, can reflect simple random fluctuations. The effect of the temporal component measured by the APC models gives an incomplete picture of the cancer incidence. The etiology of this disease, when known, is frequently associated to risk factors such as socioeconomic conditions, eating habits and lifestyle, occupation, geographic location and genetic component. The "contribution"of such risk factors is sometimes decisive in the evolution of the disease and should not be ignored. Therefore, there was the need to consider an additional approach in this study, one of spatial nature, addressing the fact that changes in incidence rates observed in the ROR-Sul area, could be explained either by temporal and geographical variability or by unequal socio-economic or lifestyle factors. Thus, Bayesian hierarchical space-time models were used with the purpose of identifying space-time trends in incidence rates together with the the analysis of the effect of the risk factors considered in the study. The results obtained and the implementation of all these methodologies are considered to be an added value to the knowledge of these neoplasms in Portugal.

Nanocomposites: the contribution of multiscale modelling to improve the dispersion levels

Tese de Doutoramento em Ciência e Engenharia de Polímeros e Compósitos

Joint modelling of longitudinal and survival data on breast cancer

Tese de Doutoramento em Ciências (Especialidade em Matemática)

Multilevel Modelling with Spatial Effects

In multilevel modelling, interest in modeling the nested structure of hierarchical data has been accompanied by increasing attention to different forms of spatial interactions across different levels of the hierarchy. Neglecting such interactions is likely to create problems of inference, which typically assumes independence. In this paper we review approaches to multilevel modelling with spatial effects, and attempt to connect the two literatures, discussing the advantages and limitations of various approaches.

Modelling the distribution of bats in relation to landscape structure in a temperate mountain environment

1. Landscape modification is often considered the principal cause of population decline in many bat species. Thus, schemes for bat conservation rely heavily on knowledge about species-landscape relationships. So far, however, few studies have quantified the possible influence of landscape structure on large-scale spatial patterns in bat communities. 2. This study presents quantitative models that use landscape structure to predict (i) spatial patterns in overall community composition and (ii) individual species' distributions through canonical correspondence analysis and generalized linear models, respectively. A geographical information system (GIS) was then used to draw up maps of (i) overall community patterns and (ii) distribution of potential species' habitats. These models relied on field data from the Swiss Jura mountains. 3. Fight descriptors of landscape structure accounted for 30% of the variation in bat community composition. For some species, more than 60% of the variance in distribution could be explained by landscape structure. Elevation, forest or woodland cover, lakes and suburbs, were the most frequent predictors. 4. This study shows that community composition in bats is related to landscape structure through species-specific relationships to resources. Due to their nocturnal activities and the difficulties of remote identification, a comprehensive bat census is rarely possible, and we suggest that predictive modelling of the type described here provides an indispensable conservation tool.

Linear Aggregation In The Social Accounting Matrix Framework

In economic literature, information deficiencies and computational complexities have traditionally been solved through the aggregation of agents and institutions. In inputoutput modelling, researchers have been interested in the aggregation problem since the beginning of 1950s. Extending the conventional input-output aggregation approach to the social accounting matrix (SAM) models may help to identify the effects caused by the information problems and data deficiencies that usually appear in the SAM framework. This paper develops the theory of aggregation and applies it to the social accounting matrix model of multipliers. First, we define the concept of linear aggregation in a SAM database context. Second, we define the aggregated partitioned matrices of multipliers which are characteristic of the SAM approach. Third, we extend the analysis to other related concepts, such as aggregation bias and consistency in aggregation. Finally, we provide an illustrative example that shows the effects of aggregating a social accounting matrix model.