In the 1980s and 1990s, Joyal and Street developed a graphical notation for various flavours of monoidal category using graphs drawn in the plane, commonly known as string diagrams. In particular, their work comprised a rigorous topological foundation of the notation. In 2007, Harmer, Hyland and Melliès gave a formal mathematical foundation for game semantics using a notions they called ⊸-schedules, ⊗-schedules and heaps. Schedules described interleavings of plays in games formed using ⊸ and ⊗, and heaps provided pointers used for backtracking. Their definitions were combinatorial in nature, but researchers often draw certain pictures when working in practice. In this thesis, we extend the framework of Joyal and Street to give a formal account of the graphical methods already informally employed by researchers in game semantics. We give a geometric formulation of ⊸-schedules and ⊗-schedules, and prove that the games they describe are isomorphic to those described in Harmer et al.’s terms, and also those given by a more general graphical representation of interleaving across games of multiple components. We further illustrate the value of the geometric methods by demonstrating that several proofs of key properties (such as that the composition of ⊸-schedules is associative) can be made straightforward, reflecting the geometry of the plane, and overstepping some of the cumbersome combinatorial detail of proofs in Harmer et al.’s terms. We further extend the framework of formal plane diagrams to account for the heaps and pointer structures used in the backtracking functors for O and P.

abstract: This research is aimed at studying the impact of building design parameters in terms of their importance and mutual interaction, and how these aspects vary across climates and HVAC system types. A methodology is proposed for such a study, by examining the feasibility and use of two different statistical methods to derive all realistic ‘near-optimum’ solutions which might be lost using a simple optimization technique. DOE prototype medium office building compliant with ASHRAE 90.1-2010 was selected for the analysis and four different HVAC systems in three US climates were simulated. The interaction between building design parameters related to envelope characteristics and geometry (total of seven variables) has been studied using two different statistical methods, namely the ‘Morris method’ and ‘Predictive Learning via Rule Ensembles’. Subsequently, a simple graphical tool based on sensitivity analysis has been developed and demonstrated to present the results from parametric simulations. This tool would be useful to better inform design decisions since it allows imposition of constraints on various parameters and visualize their interaction with other parameters. It was observed that the Radiant system performed best in all three climates, followed by displacement ventilation system. However, it should be noted that this study did not deal with performance optimization of HVAC systems while there have been several studies which concluded that a VAV system with better controls can perform better than some of the newer HVAC technologies. In terms of building design parameters, it was observed that ‘Ceiling Height’, ‘Window-Wall Ratio’ and ‘Window Properties’ showed highest importance as well as interaction as compared to other parameters considered in this study, for all HVAC systems and climates. Based on the results of this study, it is suggested to extend such analysis using statistical methods such as the ‘Morris method’, which require much fewer simulations to categorize parameters based on their importance and interaction strength. Usage of statistical methods like ‘Rule Ensembles’ or other simple visual tools to analyze simulation results for all combinations of parameters that show interaction would allow designers to make informed and superior design decisions while benefiting from large reduction in computational time. / Dissertation/Thesis / Masters Thesis Built Environment 2015

For both randomized clinical trials and prospective cohort studies, the Cox regression model is a powerful tool for evaluating the effect of a treatment or an explanatory variable on time-to-event outcome. This method assumes proportional hazards over time. Systematic approaches to efficiently evaluate non-proportionality and to model data in the presence of non-proportionality are investigated. Six graphical methods are assessed to verify the proportional hazards assumption based on characteristics of the survival function, cumulative hazard, or the feature of residuals. Their performances are empirically evaluated with simulations by checking their ability to be consistent and sensitive in detecting proportionality or non-proportionality. Two-sample data are generated in three scenarios of proportional hazards and five types of alternatives (that is, non-proportionality). The usefulness of these graphical assessment methods depends on the event rate and type of non-proportionality. Three numerical (statistical testing) methods are compared via simulation studies to investigate the proportional hazards assumption. In evaluating data for proportionality versus non-proportionality, the goal is to test a non-zero slope in a regression of the variable or its residuals on a specific function of time, or a Kolmogorov-type supremum test. Our simulation results show that statistical test performance is affected by the number of events, event rate, and degree of divergence of non-proportionality for a given hazards scenario. Determining which test will be used in practice depends on the specific situation under investigation. Both graphical and numerical approaches have benefits and costs, but they are complementary to each other. Several approaches to model and summarize non-proportionality data are presented, including non-parametric measurements and testing, semi-parametric models, and a parametric approach. Some illustrative examples using simulated data and real data are also presented. In summary, we present a systemic approach using both graphical and numerical methods to identify non-proportionality, and to provide numerous modeling strategies when proportionality is violated in time-to-event data.

When applying statistical methods for analyzing data, with normality as an assumption there are different procedures of determining if a sample is drawn from a normally distributed population. Because normality is such a central assumption, the reliability of the procedures is of most importance. Much research focus on how good formal tests of normality are, while the performance of statisticians when using graphical methods are far less examined. Therefore, the aim of the study was to empirically examine how good students in statistics are at assessing if samples are drawn from normally distributed populations through graphical methods, done by a web survey. The results of the study indicate that the students distinctly get better at accurately determining normality in data drawn from a normally distributed population when the sample size increases. Further, the students are very good at accurately rejecting normality of data when the sample is drawn from a symmetrical non-normal population and fairly good when the sample is drawn from an asymmetrical distribution. In comparison to some common formal tests of normality, the students' performance is superior at accurately rejecting normality for small sample sizes and inferior for large, when drawn from a non-normal population.

A análise de dados de sobrevivência tem sido tradicionalmente baseada no modelo de regressão de Cox (COX, 1972). No entanto, a suposição de taxas de falha proporcionais assumida para esse modelo pode não ser atendida em diversas situações práticas. Essa restrição do modelo de Cox tem gerado interesse em abordagens alternativas, dentre elas os modelos dinâmicos que permitem efeito das covariáveis variando no tempo. Neste trabalho, foram revisados os principais modelos de sobrevivência dinâmicos com estrutura aditiva e multiplicativa nos contextos não paramétrico e semiparamétrico. Métodos gráficos baseados em resíduos foram apresentados com a finalidade de avaliar a qualidade de ajuste desses modelos. Uma versão tempo-dependente da área sob a curva ROC, denotada por AUC(t), foi proposta com a finalidade de avaliar e comparar a qualidade de predição entre modelos de sobrevivência com estruturas aditiva e multiplicativa. O desempenho da AUC(t) foi avaliado por meio de um estudo de simulação. Dados de três estudos descritos na literatura foram também analisados para ilustrar ou complementar os cenários que foram considerados no estudo de simulação. De modo geral, os resultados obtidos indicaram que os métodos gráficos apresentados para avaliar a adequação dos modelos em conjunto com a AUC(t) se constituem em um conjunto de ferramentas estatísticas úteis para o próposito de avaliar modelos de sobrevivência dinâmicos nos contextos não paramétrico e semiparamétrico. Além disso, a aplicação desse conjunto de ferramentas em alguns conjuntos de dados evidenciou que se, por um lado, os modelos dinâmicos são atrativos por permitirem covariáveis tempo-dependentes, por outro lado podem não ser apropriados para todos os conjuntos de dados, tendo em vista que estimação pode apresentar restrições para alguns deles. / Analysis of survival data has been traditionally based on the Cox regression model (COX, 1972). However, the proportionality of the hazards required by this model may not be attended for many practical situations. This restriction of the Cox model has generated interest in alternative approaches, among them dynamic models that allow covariates with time-varying effect. In this work, the main dynamic survival models with additive and multiplicative structures were revised under the nonparametric and semiparametric settings. Graphical methods based on residuals were presented in order to evaluate the goodness-of-fit of these models. A time-dependent version of the area under the ROC curve, denoted by AUC(t), was proposed to evaluate and compare the predictive accuracy of additive and multiplicative survival models. The performance of the AUC(t) was evaluated by means of a simulation study. Data from three studies described in the literature were also analyzed to illustrate or complement the scenarios that were considered in the simulation study. Overall, the results indicate that the graphical methods presented to assess the goodness-of-fit of the models together with the AUC(t) provide a useful set of statistics tools for the purpose of evaluating dynamic survival models in the nonparametric and semiparametric settings. Moreover, applying this set of tools in some data sets showed that on the one hand dynamic models are attractive because they allow time-dependent covariates, but on the other hand they may not be appropriate for all data sets since estimation may present restrictions for some of them.

With the abundance of written information available online, it is useful to be able to automatically synthesize and extract meaningful information from text corpora. We present a unique method for visualizing relationships between documents in a text corpus. By using Latent Dirichlet Allocation to extract topics from the corpus, we create a graph whose nodes represent individual documents and whose edge weights indicate the distance between topic distributions in documents. These edge lengths are then scaled using multidimensional scaling techniques, such that more similar documents are clustered together. Applying this method to several datasets, we demonstrate that these graphs are useful in visually representing high-dimensional document clustering in topic-space.

A análise de dados de sobrevivência tem sido tradicionalmente baseada no modelo de regressão de Cox (COX, 1972). No entanto, a suposição de taxas de falha proporcionais assumida para esse modelo pode não ser atendida em diversas situações práticas. Essa restrição do modelo de Cox tem gerado interesse em abordagens alternativas, dentre elas os modelos dinâmicos que permitem efeito das covariáveis variando no tempo. Neste trabalho, foram revisados os principais modelos de sobrevivência dinâmicos com estrutura aditiva e multiplicativa nos contextos não paramétrico e semiparamétrico. Métodos gráficos baseados em resíduos foram apresentados com a finalidade de avaliar a qualidade de ajuste desses modelos. Uma versão tempo-dependente da área sob a curva ROC, denotada por AUC(t), foi proposta com a finalidade de avaliar e comparar a qualidade de predição entre modelos de sobrevivência com estruturas aditiva e multiplicativa. O desempenho da AUC(t) foi avaliado por meio de um estudo de simulação. Dados de três estudos descritos na literatura foram também analisados para ilustrar ou complementar os cenários que foram considerados no estudo de simulação. De modo geral, os resultados obtidos indicaram que os métodos gráficos apresentados para avaliar a adequação dos modelos em conjunto com a AUC(t) se constituem em um conjunto de ferramentas estatísticas úteis para o próposito de avaliar modelos de sobrevivência dinâmicos nos contextos não paramétrico e semiparamétrico. Além disso, a aplicação desse conjunto de ferramentas em alguns conjuntos de dados evidenciou que se, por um lado, os modelos dinâmicos são atrativos por permitirem covariáveis tempo-dependentes, por outro lado podem não ser apropriados para todos os conjuntos de dados, tendo em vista que estimação pode apresentar restrições para alguns deles. / Analysis of survival data has been traditionally based on the Cox regression model (COX, 1972). However, the proportionality of the hazards required by this model may not be attended for many practical situations. This restriction of the Cox model has generated interest in alternative approaches, among them dynamic models that allow covariates with time-varying effect. In this work, the main dynamic survival models with additive and multiplicative structures were revised under the nonparametric and semiparametric settings. Graphical methods based on residuals were presented in order to evaluate the goodness-of-fit of these models. A time-dependent version of the area under the ROC curve, denoted by AUC(t), was proposed to evaluate and compare the predictive accuracy of additive and multiplicative survival models. The performance of the AUC(t) was evaluated by means of a simulation study. Data from three studies described in the literature were also analyzed to illustrate or complement the scenarios that were considered in the simulation study. Overall, the results indicate that the graphical methods presented to assess the goodness-of-fit of the models together with the AUC(t) provide a useful set of statistics tools for the purpose of evaluating dynamic survival models in the nonparametric and semiparametric settings. Moreover, applying this set of tools in some data sets showed that on the one hand dynamic models are attractive because they allow time-dependent covariates, but on the other hand they may not be appropriate for all data sets since estimation may present restrictions for some of them.

Selected methods of mortality analysis focused on adults and the oldest age-groups Abstract Questions about human life span, longevity and mortality in general are natural to almost everyone. This Doctoral Thesis deals with one central question - whether some limit of human life span or of its improvements exists. It is rather a methodological work, therefore its aim is to introduce not only relevant theories but above all the methods usable in the mortality analysis focused on adults or the oldest-old. At the beginning the most important theories and opinions of scientist dealing with mortality are introduced. In the first half of the analytical part mainly the traditional and basic approaches are included. The theme of life tables is opened by an analysis of its construction in the Czech Republic, together with its possible modifications. As a result the independent macro code for the SAS software is attached in the electronic Appendix. This macro enables to calculate the unknown parameters of selected mortality laws by the method of weighted non-linear least squares and to produce the smoothed and extrapolated values of mortality rates. Using the individual life durations, life tables according to education attainment were constructed (also attached in the electronic Appendix). In the second half of the...

The master's thesis deals with the fundamental and technical analysis of stock Philip Morris ČR. The aim of the thesis is a specification of investment recommendation. The fundamental analysis specifies an intrinsic value of the stock Philip Morris ČR, compares it with a real stock price and recommends sale or purchase of this stock. Technical analysis uses graphical methods and technical indicators to determine an appropriate time to sale or purchase this stock.

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