Crump-Mode-Jagers Branching Process: Modelling and Application for Human Population

2010 Mathematics Subject Classification: 60J85, 92D25.

Projecting mammographic screens

Objective-The purpose of mammographic screening is to reduce mortality from breast cancer. This study describes a method for projecting the number of screens to be performed by a mammographic screening programme, and applies this method in the context of New South Wales, Australia. Method-The total number of mammographic screens was projected as the sum of initial screens and re-screens, and is based on projections of the population, rates of new recruitment, rates of attrition within the programme, and the mix of screening intervals. The baseline scenario involved: 70% participation of women aged 50-69 years, 90% return rate for the second and subsequent re-screens, 5% annual screens (95% biennial screens), and a specified population projection. The results were assessed with respect to variations in these assumptions. Results-The projections were strongly influenced by: the rate of screening of the target age group; the proportion of women re-screened annually; and the rates of attrition within the programme. Although demographic change had a notable effect, there was little difference between different population projections. Standard assumptions about attrition within the programme suggest that the current target participation rates in NSW may not be achieved in the long term. Conclusions-A practical model for projecting mammographic screens for populations is described which is capable of forecasting the number of screens under different scenarios. Implications-Projections of mammographic screens provide important information for the planning and financing of equipment and personnel, and for testing the effects of variations in important operational parameters. Re-screening attrition is an important contributor to screening viability.

O envelhecimento da população e o seu impacto na habitação – Prospectiva até 2050

Dissertação apresentada como requisito parcial para obtenção do grau de Mestre em Estatística e Gestão de Informação

Orthogonal models, structure crossing, nesting and inference

We intend to study the algebraic structure of the simple orthogonal models to use them, through binary operations as building blocks in the construction of more complex orthogonal models. We start by presenting some matrix results considering Commutative Jordan Algebras of symmetric matrices, CJAs. Next, we use these results to study the algebraic structure of orthogonal models, obtained by crossing and nesting simpler ones. Then, we study the normal models with OBS, which can also be orthogonal models. We intend to study normal models with OBS (Orthogonal Block Structure), NOBS (Normal Orthogonal Block Structure), obtaining condition for having complete and suffcient statistics, having UMVUE, is unbiased estimators with minimal covariance matrices whatever the variance components. Lastly, see ([Pereira et al. (2014)]), we study the algebraic structure of orthogonal models, mixed models whose variance covariance matrices are all positive semi definite, linear combinations of known orthogonal pairwise orthogonal projection matrices, OPOPM, and whose least square estimators, LSE, of estimable vectors are best linear unbiased estimator, BLUE, whatever the variance components, so they are uniformly BLUE, UBLUE. From the results of the algebraic structure we will get explicit expressions for the LSE of these models.

Impact de la récolte sur la survie et la croissance de deux plantes médicinales cries, Sarracenia purpurea et Rhododendron groenlandicum, dans le Nord du Québec

Au cours des dernières décennies, la popularité des plantes médicinales s’est accrue auprès des civilisations occidentales de sorte que la quantité de plantes récoltées, la plupart provenant de populations sauvages, a grandement augmenté. Dans ce contexte, l’objectif principal de mon mémoire est d’évaluer l’impact de la récolte de deux plantes médicinales (Sarracenia purpurea et Rhododendron groenlandicum) utilisées par la Nation Crie du Nord du Québec. Pour y parvenir, des parcelles expérimentales, simulant différentes intensités de récolte (S. purpurea) et différentes méthodes de récolte (R. groenlandicum), ont été mises en place, puis des suivis annuels de la reprise ont été réalisés. Les résultats obtenus suggèrent que les techniques de récolte chez R. groenlandicum devraient exclure les nouvelles pousses, leur exploitation causant une forte mortalité. Par ailleurs, chez S. purpurea, la récolte de 20 % des individus semble peu dommageable, mais critique lorsque plus de 50 % des plants sont récoltés. Un modèle démographique pour S. purpurea a aussi été construit à partir des observations de terrain. Ce modèle a permis de réaliser des projections temporelles en variant les taux de récoltes ainsi que les intervalles entre les récoltes. Les résultats indiquent qu’une récolte de 20 % des individus est acceptable une fois tous les 20 ans. Pour une récolte plus régulière, 5 % tous les trois ans serait soutenable. Mon projet permettra d’assurer une exploitation soutenable de deux plantes médicinales ayant un grand potentiel pour le traitement du diabète de type II.

Brisure de symétrie par la réduction des groupes de Lie simples à leurs sous-groupes de Lie réductifs maximaux

Dans ce travail, nous exploitons des propriétés déjà connues pour les systèmes de poids des représentations afin de les définir pour les orbites des groupes de Weyl des algèbres de Lie simples, traitées individuellement, et nous étendons certaines de ces propriétés aux orbites des groupes de Coxeter non cristallographiques. D'abord, nous considérons les points d'une orbite d'un groupe de Coxeter fini G comme les sommets d'un polytope (G-polytope) centré à l'origine d'un espace euclidien réel à n dimensions. Nous introduisons les produits et les puissances symétrisées de G-polytopes et nous en décrivons la décomposition en des sommes de G-polytopes. Plusieurs invariants des G-polytopes sont présentés. Ensuite, les orbites des groupes de Weyl des algèbres de Lie simples de tous types sont réduites en l'union d'orbites des groupes de Weyl des sous-algèbres réductives maximales de l'algèbre. Nous listons les matrices qui transforment les points des orbites de l'algèbre en des points des orbites des sous-algèbres pour tous les cas n<=8 ainsi que pour plusieurs séries infinies des paires d'algèbre-sous-algèbre. De nombreux exemples de règles de branchement sont présentés. Finalement, nous fournissons une nouvelle description, uniforme et complète, des centralisateurs des sous-groupes réguliers maximaux des groupes de Lie simples de tous types et de tous rangs. Nous présentons des formules explicites pour l'action de tels centralisateurs sur les représentations irréductibles des algèbres de Lie simples et montrons qu'elles peuvent être utilisées dans le calcul des règles de branchement impliquant ces sous-algèbres.

Fitness of hybrids between rapeseed (Brassica napus) and wild Brassica rapa in natural habitats

Fitness of hybrids between genetically modified (GM) crops and wild relatives influences the likelihood of ecological harm. We measured fitness components in spontaneous (non-GM) rapeseed x Brassica rapa hybrids in natural populations. The F-1 hybrids yielded 46.9% seed output of B. rapa, were 16.9% as effective as males on B. rapa and exhibited increased self-pollination. Assuming 100% GM rapeseed cultivation, we conservatively predict < 7000 second-generation transgenic hybrids annually in the United Kingdom (i.e. similar to 20% of F-1 hybrids). Conversely, whilst reduced hybrid fitness improves feasibility of bio-containment, stage projection matrices suggests broad scope for some transgenes to offset this effect by enhancing fitness.

Sheaves, local homeomorphisms and local sets as Hilbert locale modules

We give a thorough account of the various equivalent notions for \sheaf" on a locale, namely the separated and complete presheaves, the local home- omorphisms, and the local sets, and to provide a new approach based on quantale modules whereby we see that sheaves can be identi¯ed with certain Hilbert modules in the sense of Paseka. This formulation provides us with an interesting category that has immediate meaningful relations to those of sheaves, local homeomorphisms and local sets. The concept of B-set (local set over the locale B) present in [3] is seen as a simetric idempotent matrix with entries on B, and a map of B-sets as de¯ned in [8] is shown to be also a matrix satisfying some conditions. This gives us useful tools that permit the algebraic manipulation of B-sets. The main result is to show that the existing notions of \sheaf" on a locale B are also equivalent to a new concept what we call a Hilbert module with an Hilbert base. These modules are the projective modules since they are the image of a free module by a idempotent automorphism On the ¯rst chapter, we recall some well known results about partially ordered sets and lattices. On chapter two we introduce the category of Sup-lattices, and the cate- gory of locales, Loc. We describe the adjunction between this category and the category Top of topological spaces whose restriction to spacial locales give us a duality between this category and the category of sober spaces. We ¯nish this chapter with the de¯nitions of module over a quantale and Hilbert Module. Chapter three concerns with various equivalent notions namely: sheaves of sets, local homeomorphisms and local sets (projection matrices with entries on a locale). We ¯nish giving a direct algebraic proof that each local set is isomorphic to a complete local set, whose rows correspond to the singletons. On chapter four we de¯ne B-locale, study open maps and local homeo- morphims. The main new result is on the ¯fth chapter where we de¯ne the Hilbert modules and Hilbert modules with an Hilbert and show this latter concept is equivalent to the previous notions of sheaf over a locale.

Plano diretor setorial do sistema de esgotamento sanitário: alternativas de concepção para a área de maior adensamento populacional do município de Belém - PA

São propostas concepções para subsidiar o planejamento da ampliação da coleta, tratamento e destino final de esgoto no município de Belém, mais especificamente na área de maior densidade populacional, que apresenta 1.143.946 habitantes e baixo índice de atendimento com Sistema de Esgotamento Sanitário (SES). Para isso, são necessárias ações voltadas à expansão dessa infra-estrutura, o que deve ocorrer de forma sustentável, eficiente, integrada e planejada. No trabalho são analisados estudos e projetos anteriormente realizados na área em questão, diagnosticado o SES existente, elaborada a projeção populacional no período de 2005-2025 e calculada a demanda de esgoto nos próximos 20 anos, para, então, serem formuladas as alternativas de concepção. As 6 (seis) alternativas de concepção são fundamentadas na descentralização progressiva do SES, apresentando variações no número de Estações de Tratamento de Esgoto - ETEs e nas características de coleta e transposição de esgoto sanitário entre as bacias de esgotamento e de localização das ETEs. A melhor alternativa foi a de número 3 (três), que apresenta tratamento de esgoto o mais próximo do local de geração. O trabalho pretende contribuir na tomada de decisão para ampliação do SES no Município de Belém.

Urban water demand model: the case study of Emilia Romagna (Italy)

Water is the driving force in nature. We use water for washing cars, doing laundry, cooking, taking a shower, but also to generate energy and electricity. Therefore water is a necessary product in our daily lives (USGS. Howard Perlman, 2013). The model that we created is based on the urban water demand computer model from the Pacific Institute (California). With this model we will forecast the future urban water use of Emilia Romagna up to the year of 2030. We will analyze the urban water demand in Emilia Romagna that includes the 9 provinces: Bologna, Ferrara, Forli-Cesena, Modena, Parma, Piacenza, Ravenna, Reggio Emilia and Rimini. The term urban water refers to the water used in cities and suburbs and in homes in the rural areas. This will include the residential, commercial, institutional and the industrial use. In this research, we will cover the water saving technologies that can help to save water for daily use. We will project what influence these technologies have to the urban water demand, and what it can mean for future urban water demands. The ongoing climate change can reduce the snowpack, and extreme floods or droughts in Italy. The changing climate and development patterns are expected to have a significant impact on water demand in the future. We will do this by conducting different scenario analyses, by combining different population projections, climate influence and water saving technologies. In addition, we will also conduct a sensitivity analyses. The several analyses will show us how future urban water demand is likely respond to changes in water conservation technologies, population, climate, water price and consumption. I hope the research can contribute to the insight of the reader’s thoughts and opinion.

Selection bias and the cross-validation of regression models for prediction

Strategies are compared for the development of a linear regression model with stochastic (multivariate normal) regressor variables and the subsequent assessment of its predictive ability. Bias and mean squared error of four estimators of predictive performance are evaluated in simulated samples of 32 population correlation matrices. Models including all of the available predictors are compared with those obtained using selected subsets. The subset selection procedures investigated include two stopping rules, C$\sb{\rm p}$ and S$\sb{\rm p}$, each combined with an 'all possible subsets' or 'forward selection' of variables. The estimators of performance utilized include parametric (MSEP$\sb{\rm m}$) and non-parametric (PRESS) assessments in the entire sample, and two data splitting estimates restricted to a random or balanced (Snee's DUPLEX) 'validation' half sample. The simulations were performed as a designed experiment, with population correlation matrices representing a broad range of data structures.^ The techniques examined for subset selection do not generally result in improved predictions relative to the full model. Approaches using 'forward selection' result in slightly smaller prediction errors and less biased estimators of predictive accuracy than 'all possible subsets' approaches but no differences are detected between the performances of C$\sb{\rm p}$ and S$\sb{\rm p}$. In every case, prediction errors of models obtained by subset selection in either of the half splits exceed those obtained using all predictors and the entire sample.^ Only the random split estimator is conditionally (on $\\beta$) unbiased, however MSEP$\sb{\rm m}$ is unbiased on average and PRESS is nearly so in unselected (fixed form) models. When subset selection techniques are used, MSEP$\sb{\rm m}$ and PRESS always underestimate prediction errors, by as much as 27 percent (on average) in small samples. Despite their bias, the mean squared errors (MSE) of these estimators are at least 30 percent less than that of the unbiased random split estimator. The DUPLEX split estimator suffers from large MSE as well as bias, and seems of little value within the context of stochastic regressor variables.^ To maximize predictive accuracy while retaining a reliable estimate of that accuracy, it is recommended that the entire sample be used for model development, and a leave-one-out statistic (e.g. PRESS) be used for assessment. ^

Use of an Inverse Method for Time Series to Estimate the Dynamics of and Management Strategies for the Box Jellyfish Carybdea marsupialis

Frequently, population ecology of marine organisms uses a descriptive approach in which their sizes and densities are plotted over time. This approach has limited usefulness for design strategies in management or modelling different scenarios. Population projection matrix models are among the most widely used tools in ecology. Unfortunately, for the majority of pelagic marine organisms, it is difficult to mark individuals and follow them over time to determine their vital rates and built a population projection matrix model. Nevertheless, it is possible to get time-series data to calculate size structure and densities of each size, in order to determine the matrix parameters. This approach is known as a “demographic inverse problem” and it is based on quadratic programming methods, but it has rarely been used on aquatic organisms. We used unpublished field data of a population of cubomedusae Carybdea marsupialis to construct a population projection matrix model and compare two different management strategies to lower population to values before year 2008 when there was no significant interaction with bathers. Those strategies were by direct removal of medusae and by reducing prey. Our results showed that removal of jellyfish from all size classes was more effective than removing only juveniles or adults. When reducing prey, the highest efficiency to lower the C. marsupialis population occurred when prey depletion affected prey of all medusae sizes. Our model fit well with the field data and may serve to design an efficient management strategy or build hypothetical scenarios such as removal of individuals or reducing prey. TThis This sdfsdshis method is applicable to other marine or terrestrial species, for which density and population structure over time are available.

Numerical methods for solar tomography in the STEREO era

In this thesis, we propose several advances in the numerical and computational algorithms that are used to determine tomographic estimates of physical parameters in the solar corona. We focus on methods for both global dynamic estimation of the coronal electron density and estimation of local transient phenomena, such as coronal mass ejections, from empirical observations acquired by instruments onboard the STEREO spacecraft. We present a first look at tomographic reconstructions of the solar corona from multiple points-of-view, which motivates the developments in this thesis. In particular, we propose a method for linear equality constrained state estimation that leads toward more physical global dynamic solar tomography estimates. We also present a formulation of the local static estimation problem, i.e., the tomographic estimation of local events and structures like coronal mass ejections, that couples the tomographic imaging problem to a phase field based level set method. This formulation will render feasible the 3D tomography of coronal mass ejections from limited observations. Finally, we develop a scalable algorithm for ray tracing dense meshes, which allows efficient computation of many of the tomographic projection matrices needed for the applications in this thesis.

Projection Par La Microsimulation de La Population Active Cap-Vert (2000-2025)

À l‟aide des microdonnées du recensement de 2000 et des données administratives sur l‟éducation et en s‟appuyant sur : 1) les scénarios concernant l‟évolution démographique, d‟éducation et d‟activité économique et 2) un modèle de microsimulation, on a projeté pour la période 2000 à 2025, certaines caractéristiques et comportements démographiques et socio-économiques de la population du Cap-Vert, notamment ceux liés à l‟évolution du statut d‟activité. Selon le scénario le plus plausible, à l‟horizon 2025, le pays se trouvera à l‟étape avancée de la seconde phase de sa transition démographique. Sa population continuerait de croître en raison de sa structure par âge relativement jeune. Bien que le solde migratoire tende à être nul et que la mortalité tende à se stabiliser (près de 5 à 7 décès pour 1 000 habitants par an), cette croissance sera à un rythme moins rapide (d‟environ 1,8 % par an) que celui de la décennie 1990-2000, et ce, malgré le déclin de la fécondité. De 2000 à 2025, le pays pourrait connaître également une augmentation des personnes âgées de 15 à 24 ans, variant de 26 % à 29 % selon les scénarios envisagés, soit ceux et celles qui entreront sur le marché du travail au cours de la période. Le nombre de ces jeunes n‟ayant pas obtenu un diplôme d‟études secondaire, en 2025, pourrait augmenter, selon les scénarios envisagés, variant de 30 % à 44 % de plus qu‟en 2000. Le nombre de personnes de ce groupe d‟âge ayant obtenu un diplôme d‟études secondaires ou plus, le pays pourrait voir leur nombre à décupler de 11 fois à 13 fois à la à l‟horizon 2025.

Future development of gastrointestinal cancer incidence and mortality rates in Switzerland: a tumour registry- and population-based projection up to 2030.

QUESTIONS UNDER STUDY: Since tumour burden consumes substantial healthcare resources, precise cancer incidence estimations are pivotal to define future needs of national healthcare. This study aimed to estimate incidence and mortality rates of oesophageal, gastric, pancreatic, hepatic and colorectal cancers up to 2030 in Switzerland. METHODS: Swiss Statistics provides national incidences and mortality rates of various cancers, and models of future developments of the Swiss population. Cancer incidences and mortality rates from 1985 to 2009 were analysed to estimate trends and to predict incidence and mortality rates up to 2029. Linear regressions and Joinpoint analyses were performed to estimate the future trends of incidences and mortality rates. RESULTS: Crude incidences of oesophageal, pancreas, liver and colorectal cancers have steadily increased since 1985, and will continue to increase. Gastric cancer incidence and mortality rates reveal an ongoing decrease. Pancreatic and liver cancer crude mortality rates will keep increasing, whereas colorectal cancer mortality on the contrary will fall. Mortality from oesophageal cancer will plateau or minimally increase. If we consider European population-standardised incidence rates, oesophageal, pancreatic and colorectal cancer incidences are steady. Gastric cancers are diminishing and liver cancers will follow an increasing trend. Standardised mortality rates show a diminution for all but liver cancer. CONCLUSIONS: The oncological burden of gastrointestinal cancer will significantly increase in Switzerland during the next two decades. The crude mortality rates globally show an ongoing increase except for gastric and colorectal cancers. Enlarged healthcare resources to take care of these complex patient groups properly will be needed.