In the thesis "On Boundaries of Statistical Models" problems related to a description of probability distributions with zeros, lying in the boundary of a statistical model, are treated. The distributions considered are joint distributions of finite collections of finite discrete random variables. Owing to this restriction, statistical models are subsets of finite dimensional real vector spaces. The support set problem for exponential families, the main class of models considered in the thesis, is to characterize the possible supports of distributions in the boundaries of these statistical models. It is shown that this problem is equivalent to a characterization of the face lattice of a convex polytope, called the convex support. The main tool for treating questions related to the boundary are implicit representations. Exponential families are shown to be sets of solutions of binomial equations, connected to an underlying combinatorial structure, called oriented matroid. Under an additional assumption these equations are polynomial and one is placed in the setting of commutative algebra and algebraic geometry. In this case one recovers results from algebraic statistics. The combinatorial theory of exponential families using oriented matroids makes the established connection between an exponential family and its convex support completely natural: Both are derived from the same oriented matroid. The second part of the thesis deals with hierarchical models, which are a special class of exponential families constructed from simplicial complexes. The main technical tool for their treatment in this thesis are so called elementary circuits. After their introduction, they are used to derive properties of the implicit representations of hierarchical models. Each elementary circuit gives an equation holding on the hierarchical model, and these equations are shown to be the "simplest", in the sense that the smallest degree among the equations corresponding to elementary circuits gives a lower bound on the degree of all equations characterizing the model. Translating this result back to polyhedral geometry yields a neighborliness property of marginal polytopes, the convex supports of hierarchical models. Elementary circuits of small support are related to independence statements holding between the random variables whose joint distributions the hierarchical model describes. Models for which the complete set of circuits consists of elementary circuits are shown to be described by totally unimodular matrices. The thesis also contains an analysis of the case of binary random variables. In this special situation, marginal polytopes can be represented as the convex hulls of linear codes. Among the results here is a classification of full-dimensional linear code polytopes in terms of their subgroups. If represented by polynomial equations, exponential families are the varieties of binomial prime ideals. The third part of the thesis describes tools to treat models defined by not necessarily prime binomial ideals. It follows from Eisenbud and Sturmfels' results on binomial ideals that these models are unions of exponential families, and apart from solving the support set problem for each of these, one is faced with finding the decomposition. The thesis discusses algorithms for specialized treatment of binomial ideals, exploiting their combinatorial nature. The provided software package Binomials.m2 is shown to be able to compute very large primary decompositions, yielding a counterexample to a recent conjecture in algebraic statistics.

This thesis consists of a summary and five papers, dealing with self-normalized sums of independent, identically distributed random variables, and three-decision procedures for directional conclusions. In Paper I, we investigate a general set-up for Student's t-statistic. Finiteness of absolute moments is related to the corresponding degree of freedom, and relevant properties of the underlying distribution, assuming independent, identically distributed random variables. In Paper II, we investigate a certain kind of self-normalized sums. We show that the corresponding quadratic moments are greater than or equal to one, with equality if and only if the underlying distribution is symmetrically distributed around the origin. In Paper III, we study linear combinations of independent Rademacher random variables. A family of universal bounds on the corresponding tail probabilities is derived through the technique known as exponential tilting. Connections to self-normalized sums of symmetrically distributed random variables are given. In Paper IV, we consider a general formulation of three-decision procedures for directional conclusions. We introduce three kinds of optimality characterizations, and formulate corresponding sufficiency conditions. These conditions are applied to exponential families of distributions. In Paper V, we investigate the Benjamini-Hochberg procedure as a means of confirming a selection of statistical decisions on the basis of a corresponding set of generalized p-values. Assuming independence, we show that control is imposed on the expected average loss among confirmed decisions. Connections to directional conclusions are given.

The time-dependent Schrödinger equation (TDSE) models the quantum nature of molecular processes.  Numerical simulations based on the TDSE help in understanding and predicting the outcome of chemical reactions. This thesis is dedicated to the derivation and analysis of efficient and reliable simulation tools for the TDSE, with a particular focus on models for the interaction of molecules with time-dependent electromagnetic fields. Various time propagators are compared for this setting and an efficient fourth-order commutator-free Magnus-Lanczos propagator is derived. For the Lanczos method, several communication-reducing variants are studied for an implementation on clusters of multi-core processors. Global error estimation for the Magnus propagator is devised using a posteriori error estimation theory. In doing so, the self-adjointness of the linear Schrödinger equation is exploited to avoid solving an adjoint equation. Efficiency and effectiveness of the estimate are demonstrated for both bounded and unbounded states. The temporal approximation is combined with adaptive spectral elements in space. Lagrange elements based on Gauss-Lobatto nodes are employed to avoid nondiagonal mass matrices and ill-conditioning at high order. A matrix-free implementation for the evaluation of the spectral element operators is presented. The framework uses hybrid parallelism and enables significant computational speed-up as well as the solution of larger problems compared to traditional implementations relying on sparse matrices. As an alternative to grid-based methods, radial basis functions in a Galerkin setting are proposed and analyzed. It is found that considerably higher accuracy can be obtained with the same number of basis functions compared to the Fourier method. Another direction of research presented in this thesis is a new algorithm for quantum optimal control: The field is optimized in the frequency domain where the dimensionality of the optimization problem can drastically be reduced. In this way, it becomes feasible to use a quasi-Newton method to solve the problem. / eSSENCE

This paper considers the problem of model uncertainty associated with variable selection and specification of the spatial weight matrix in spatial growth regression models in general and growth regression models based on the matrix exponential spatial specification in particular. A natural solution, supported by formal probabilistic reasoning, is the use of Bayesian model averaging which assigns probabilities on the model space and deals with model uncertainty by mixing over models, using the posterior model probabilities as weights. This paper proposes to adopt Bayesian information criterion model weights since they have computational advantages over fully Bayesian model weights. The approach is illustrated for both identifying model covariates and unveiling spatial structures present in pan-European growth data. (authors' abstract) / Series: Department of Economics Working Paper Series

CAPES / Este trabalho apresenta uma proposta de metodologia do objeto matemático Função Exponencial, que possibilite o desenvolvimento de habilidades interpretativas e criativas de potencial significado para os alunos, a partir de uma sequência didática estruturada à luz da Teoria das Situações Didáticas de Guy Brousseau e, dos Registros de Representações Semiótica de Duval, proporcionando interações entre o aluno, o professor e o meio em um ambiente de aprendizagem cooperativo, onde os alunos se sintam livres para expressar as suas ideias e para sugerir as suas próprias abordagens. A metodologia proposta foi desenvolvida de acordo com o conhecimento a priori do aluno, valorizando as suas diferentes formas de registros, os quais são de extrema importância durante os processos de ensino e de aprendizagem. A proposta foi aplicada a alunos do primeiro ano do ensino médio do Colégio Estadual José de Anchieta Ensino Fundamental e Médio, localizado na Cidade de Dois Vizinhos – Paraná. Para o desenvolvimento da pesquisa utilizou-se a ferramenta metodológica Engenharia Didática de Artigue, uma metodologia originada especificamente para a pesquisa com situações didáticas. A princípio o objetivo proposto foi atingido, o qual consistia de trabalhar a parte conceitual, do significado da Função Exponencial, da relação de dependência e sua principal característica, ou seja, que a parte variável se encontra no expoente. E, sem imposição, mas a partir de situações didáticas apropriadas, segundo a teoria das situações didáticas, os alunos foram capazes de perceber essa característica, de resolverem problemas que envolviam a função exponencial e, além disso, de inventarem problemas (de acordo com o seu universo) modelados por este tipo de função. Acredita-se que a metodologia à luz da teoria das situações didáticas, análises dos registros dos alunos, observações sobre os erros e obstáculos e reflexões sobre aspectos do contrato didático são de fundamental importância para a prática docente e, determinantes durante o processo de ensino aprendizagem. / This essay presents a proposal on methodology over the mathematical object Exponential Function which enables the development of interpretative and creative skills with potential meaning to the students starting from a didactic sequence structured on the light of The Theory of Didactic Situations from Guy Brousseau and, from the Records of Semiotic Representation of Duval, providing interactions among the students, the teacher and the environment of cooperative learning where the students feel free to express their own ideas as well as to suggest their own approaches. The methodology presented has been developed according to the students first knowledge, valuing their different ways of registering, which have such an important role during the teaching and learning processes. The proposal has been applied to the students from the first year of high school of Colégio Estadual José de Anchieta Ensino Fundamental e Médio, located in a town called Dois Vizinhos –Paraná. In order to the development of the research the methodological tool Didactic Engineering Artigue which consists in a methodology developed only to the research with didactic situations. The main goal has been reached at first, which was to work on the conceptual part of the Exponential Function, the relation of dependence and its main characteristic so that the variable part is in the exponent. Moreover with no imposition but starting from suitable didactic situations, the students were able to realize that they could solve the problems which involve the exponential function and furthermore create new problems (according to their universe) modeled by this kind of function. Its believed that the methodology based on the theory of didactic situations, analysis of students registers, observation on mistakes and obstacles as well as reflections over the aspects of the didactic contract are of fundamental importance to the teaching practice and determinant during the teaching-learning process.

Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-02-17Bitstream added on 2014-06-13T18:30:54Z : No. of bitstreams: 1 barreiro_rc_me_sjrp.pdf: 585027 bytes, checksum: 039155145a6c7b9e6e1fc03a02180b55 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O objetivo deste trabalho ée estabelecer similaridades entre a análise complexa e os quatérnios. Nele é feito um estudo da regularidade de funções quaterniônicas e são estabelecidas as funções exponencial e logarítmica para os quatérnios sendo feito um estudo da hiperpe- riodicidade dessas funções. Outro resultado apresentado é a generalização quaterniônica da fórmula integral de Cauchy um dos principais teoremas da análise complexa. / The objective of this work is to establish similarities between the complex analysis and the quaternions. In it is made a study of the regularity of quaternionic functions and are established the exponential and logarithmic functions for the quaternions being made a study of the hiperperiodicity of these functions. Another presented result is the quater- nionic generalization of the Cauchy's integral formula one of the main theorems of the complex analysis.

Made available in DSpace on 2015-03-26T13:32:15Z (GMT). No. of bitstreams: 1 texto completo.pdf: 512216 bytes, checksum: fd4223913c0ad60bce75a563695255ec (MD5) Previous issue date: 2012-03-13 / In survival analysis, the response variable is the time of occurrence of an event of interest, denominated failure time. Another characteristic of the survival analysis is to incorporate to the study incomplete sample data, in which for a determined reason the occurrence of the event was not verified, being these data defined as censured. The objective of this paper was to compare the use of the parametric and non-parametric techniques to estimate the survival time of C. externa (Neuroptera: Chrysopidae), predator insect which feed on other insects as well as mite, under the effect of three commercial products nim-based: Neempro (10 g of azadirachtina L-1), Organic neem (3,3 g of Azadirachtina L-1) and Natuneem (1,5 g of azadirachtina L-1). With this objective the survival functions for the different concentrations of each product, through the non-parametric method of Kaplan-Meier were estimated and compared by the logrank test and by parametric techniques, using the Weibull and log-normal exponential tests. Besides that, a study in order to select the most parsimonious model was done, using for that the likelihood ratio test (LRT) as well as the Akaike information criterion (AIC). The estimates of the selected parametric model were used to determine the survival functions in the concentrations of the three products, with the purpose of comparing with the nonparametric estimator Kaplan-Meier. Once the best model was defined the median survival time of C. externa was calculated in the tested concentrations of the products. Taking into consideration the conditions described in this experiment, one can conclude that the concentrations of the nim-based products have influence in the survival of C. externa. The higher the concentration of the used products, the lower was the survival time and among the evaluated products, Neempro was the one which presented the least lethal to the natural predator. / Em análise de sobrevivência, a variável resposta é o tempo de ocorrência de um evento de interesse, denominado tempo de falha. Outra característica da análise de sobrevivência é incorporar ao estudo dados amostrais incompletos, que por algum motivo a ocorrência do evento não foi verificada, dados estes definidos como censurados. O objetivo deste trabalho foi comparar o uso das técnicas paramétricas e não-paramétricas para estimar o tempo de sobrevivência de C. externa (Neuroptera: Chrysopidae), inseto predador que se alimenta de outros insetos e ácaros, sob efeito de três produtos comerciais à base de nim: Neempro (10 g de azadirachtina L-1), Organic neem (3,3 g de Azadirachtina L-1) e Natuneem (1,5 g de azadiractina L-1). Com esse objetivo foram estimadas as funções de sobrevivência para as diferentes concentrações de cada produto, por meio do método não-paramétrico de Kaplan-Meier, e comparadas pelo teste logrank e por meio das técnicas paramétricas, utilizando os modelos exponencial, de Weibull e log-normal. Foi realizado ainda, um estudo com a finalidade de selecionar o modelo mais parcimonioso, utilizando para isto o teste da razão de verossimilhança (TRV) e o critério de informação de Akaike (AIC). As estimativas do modelo paramétrico selecionado foram usadas para determinar as funções de sobrevivência nas concentrações dos três produtos, com o objetivo de comparar com o estimador não-paramétrico de Kaplan-Meier. Definido o melhor modelo foi calculado o tempo mediano de sobrevivência do C. externa nas concentrações testadas dos produtos. Levando em consideração as condições descritas neste experimento, pode-se concluir que as concentrações dos produtos a base de nim possuem influencia na sobrevivência de C. externa. Quanto maior foi a concentração dos produtos utilizados, menor foi o tempo de sobrevivência e entre os produtos avaliados o Neempro foi o que apresentou ser o menos letal ao predador natural.

Title: Methods for periodic and irregular time series Author: Mgr. Tomáš Hanzák Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Tomáš Cipra, DrSc. Abstract: The thesis primarily deals with modifications of exponential smoothing type methods for univariate time series with periodicity and/or certain types of irregularities. A modified Holt method for irregular times series robust to the problem of "time-close" observations is suggested. The general concept of seasonality modeling is introduced into Holt-Winters method including a linear interpolation of seasonal indices and usage of trigonometric functions as special cases (the both methods are applicable for irregular observations). The DLS estimation of linear trend with seasonal dummies is investigated and compared with the additive Holt-Winters method. An autocorrelated term is introduced as an additional component in the time series decomposition. The suggested methods are compared with the classical ones using real data examples and/or simulation studies. Keywords: Discounted Least Squares, Exponential smoothing, Holt-Winters method, Irregular observations, Time series periodicity

[pt] A presente dissertação tem como principal objetivo a conceituação e apresentação das metodologias básicas de previsão de demanda e, a partir de um estudo de caso, a seleção da metodologia mais adequada e sua respectiva implantação. No primeiro capítulo é apresentada, além da importância do referido tema, a empresa selecionada para aplicação dos conceitos levantados, com a descrição de seus principais processos internos. No segundo capítulo foram abordados os conceitos de previsão de demanda e uma revisão dos principais modelos existentes. No capítulo seguinte, o problema que deverá ser tratado com a metodologia proposta é apresentado. Neste momento a metodologia conceituada é aplicada, através da seleção do método de previsão mais adequado ao caso estudado e respectiva modelagem, buscando melhorias em relação aos métodos de previsão existentes na empresa. Neste processo de modelagem utilizou-se o software Forecast Pro, um dos mais conceituados aplicativos de previsão de demanda no mercado. Por fim, na conclusão, avalia-se o impacto das mudanças propostas nos resultados da empresa, principalmente o aumento da precisão da previsão da demanda e, conseqüentemente, redução dos custos de importação e dos índices de stockout. / [en] The main objective of this dissertation is the presentation of basic forecasting methods and their implementation in a case study in supply chain. The first chapter points out the importance of forecasting in this context and describes the company selected for the case study and some of its internal processes that will be under scrutiny in the case study presented in this dissertation. The second chapter discusses the concepts and models of forecasting and reviews some of the major techniques in the field. In chapter three, standard forecasting techniques are apllied to real data (ten time series) from the company and select the most appropriate model in each case. Model adjustment is performed through the Forecast Pro software, one of the best-known products in the market. Chapter four contains the conclusions and the evaluation of the impacts of the proposed methodology on the company s results, especially the increased accuracy of forecasting and, consequently, the reduction in the import costs and stock out index.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-11T14:07:58Z No. of bitstreams: 1 HUGO SARAIVA TAVARES - DISSERTAÇÃO PPGMAT 2016..pdf: 830543 bytes, checksum: d315a3d95e0d2b08d4251cbb487964b6 (MD5) / Made available in DSpace on 2018-08-11T14:07:58Z (GMT). No. of bitstreams: 1 HUGO SARAIVA TAVARES - DISSERTAÇÃO PPGMAT 2016..pdf: 830543 bytes, checksum: d315a3d95e0d2b08d4251cbb487964b6 (MD5) Previous issue date: 2016-06 / Capes / Para ler o resumo deste trabalho recomendamos o download do arquivo, uma vez que o mesmo possui fórmulas e caracteres matemáticos que não foram possíveis trascreve-los aqui. / To read the summary of this work we recommend downloading the file, since it has formulas and mathematical characters that were not possible to transcribe them here.