A new model developed for the entire bathtub-shaped hazard rate curve has been evaluated as to its usefulness as a method of reliability estimation. The model is of the form: F(t) = 1 - exp - (ϴ1tL + ϴ2t + ϴ3tM) where "L" and "M" were assumed known. The estimate of reliability obtained from the new model was compared with the traditional restricted sample estimate for four different time intervals and was found to have less bias and variance for all time points. The was a monte carlo study and the data generated showed that the new model has much potential as a method for estimating reliability. (51 pages)

<p> The Kolmogorov-Smirnov tests of homogeneity or goodness-of-fit and the binomial group tests for eliminating defectives are of different nature. But they are both popular in applications. The former are widely used in nonparametric comparison, while the later are usually adopted in the group screening problems. When the experimenter has k populations, k-sample statistics should be considered for the testing of homogeneity or goodness-of-fit. On the other hand, when there are k experimenters available for performing group testing on a given population, a k-sample group testing procedure should be used.</p> <p> In this thesis, the distribution functions of k-sample analogues of the Kolmogorov-Smirnov statistics have been found under certain conditions and a k-sample group testing procedure has been defined. This procedure has also been shown to be optimal in the sense that it requires a minimum expected number of k-sample group tests for finding a single defective from a binomial population.</p> <p> Our methods are mainly combinatorial: matrix enumeration, tree counting and construction algorithms are explored as a foundation of our study.</p> / Thesis / Doctor of Philosophy (PhD)

Que ce soit à des fins spéculatives ou pour financer des conflits armés, une grande opacité entoure les filières des concentrés de matières premières minérales dont la demande ne cesse d'augmenter. Compte-tenu de l'éloignement entre les sites primaires d'extraction et les sites de production de produits finis, il est difficile d'identifier l'origine de ces produits. Dans un souci de traçabilité des concentrés, l'établissement d'une carte d'identité du minerai permettrait le contrôle des échanges dans l'industrie minérale. Le problème peut être posé en termes d'inversion: remonter au minerai d'origine en étudiant le produit vendu. Deux stades doivent être distingués: 1) la caractérisation du minerai brut et 2) la « perte de mémoire » des caractéristiques du tout-venant au cours du traitement minéralurgique. Les paramètres retenus sont la composition minéralogique, l'identification de microfaciès caractéristiques des minéraux cibles, la pseudo-succession paragénétique, le contenu et la distribution en éléments mineurs de minéraux cibles. Les minéraux cibles retenus sont la pyrite pour son ubiquité, la sphalérite car elle est susceptible d'incorporer une grande variété d'éléments mineurs, éventuellement valorisants ainsi que la chalcopyrite car elle est souvent liée aux deux autres minéraux. La comparaison de la composition chimique des phases minérales est effectuée en calculant la distance de Kolmogorov-Smirnov et de Colin-White. Des tests ont été réalisés sur les gîtes de type amas sulfuré volcanogène. Ils ont montré que les caractéristiques retenues permettaient de distinguer les pyrites, les sphalérites et les chalcopyrites de deux gisements de la province Sud-Ibérique (IPB), de sept gisements de la province d’Oural et du fumeur noir actuel de Rainbow. Les cartes d’identité obtenues permettent de discriminer les différents sites (IPB, Oural et Rainbow) et les gisements d’une même province. Les paramètres minéralogiques et microtexturaux ont également été suivis au cours du traitement minéralurgique de la mine de Neves Corvo. Pour une chaîne de traitement donnée, le paramètre « perte de mémoire » est une estimation de l'erreur commise lors de l'inversion, mais aussi une façon de caractériser une succession d'opérations minéralurgiques. / The demand in mineral resources is increasing rapidly, but there is a lack of transparency in the trade of concentrated raw mineral materials because of speculation and involvement in the financing of armed conflicts. Because of the distance between the primary extraction and the final production sites it is difficult to check the origin of such products. An identity card is required for minerals which would permit trading in the mineral industry to be verified and ensure traceability of concentrates. This problem may be considered as an inversion process: studying the products sold to identify the original ore. Two steps may be distinguished: 1) the characterization of the raw ore and 2) the “memory loss” of the crude ore characteristics during its mineral processing. The discriminant parameters are mineralogical composition, identification of textural microfacies of the target minerals, pseudo-paragenetic sequence, and the contents and distribution of minor elements of target minerals. The selected target minerals are pyrite, for its ubiquity, sphalerite for its ability to host numerous discriminant and potentially valuable minor elements in its lattice and chalcopyrite for its proximity with the two others minerals. The Kolmogorov-Smirnov distance and the Colin-White test are used to compare the chemical composition of the three target minerals. The application to Volcanic Massive Sulfide ore deposit showed that the selected characteristics permit to distinguish pyrite, sphalerite and chalcopyrite between two ore deposits in the Iberian Pyrite Belt province, seven ore deposits from the Urals province and a currently active Rainbow blacksmoker. From the established identity cards ore deposits from different provinces may be discriminated. Identity cards can also distinguish different deposits in the same province. Evolution of mineralogical and microtextural parameters was studied during the mineral processing of the Neves Corvo mine. For a given processing chain, the “memory loss” parameter is an estimate of the errors introduced in the inversion from concentrate to the original ore and can be used to characterize a given processing flow.

Le point de départ de cette thèse est la conjecture de Bieberbach : sa démonstration par De Branges utilise deux ingrédients, à savoir la théorie de Loewner des domaines plans croissants et une inégalité de Milin qui concerne les coefficients logarithmiques. Nous commençons par étudier les coefficients logarithmiques du whole-plane SLE en utilisant une méthode combinatoire, assistée par ordinateur. Nous retrouvons les résultats en utilisant une équation aux dérivées partielles analogue à celle obtenue par Beliaev et Smirnov. Nous généralisons ces résultats en définissant le spectre généralisé du whole-plane SLE, que nous calculons par la même méthode, à savoir en dérivant, par le calcul d’Itô, une EDP parabolique satisfaite par les quantités que nous moyennons. Cette famille à deux paramètres d’EDP admet une riche structure algébrique que nous étudions en détail. La dernière partie de la thèse concerne l’opérateur de Grunsky et ses généralisations. Plus expérimentale, nous y mettons à jour, grâce à un logiciel de calcul formel, une structure assez complexe dont nous avons commencé l’exploration. / The starting point of this thesis is Bieberbach’s conjecture: its proof, given by De Branges, uses two ingredients, namely Loewner’s theory of increasing plane domains and an inequality from Milin about the logarithmic coefficients. We start with a study of the logarithmic coefficients of the whole-plane SLE by using a combinatorial method, assisted by computer. We find the results by using a partial differential equation similar to that obtained by Beliaev and Smirnov. We generalize these results by defining the generalized spectrum of the whole-plane SLE, that we calculate by the same method, namely by deriving, thanks to Itô calculus, a parabolic PDE satisfied by the quantities of which we take the average. This two-parameter family of PDEs admits a rich algebraic structure that we study in detail. The last part of this thesis is about the Grunsky operator and its generalizations. In this part that is more experimental we update, thanks to a computer algebra system, a rather complex structure of which we began the exploration.

Soit f une instance du whole-plane $\SLE_\kappa$ : on sait que pour certaines valeurs de κ, p les moments dérivés $\mathbb{E}(\vert f'(z) \vert^p)$ peuvent être écrits sous une forme fermée, étude qui a permis de mettre au jour une nouvelle phase du spectre des moyennes intégrales. Le but de cette thèse est une étude des moments généralisés $\frac{\vert f'(z) \vert^p}{\vert f(z) \vert^q}$ : cette étude permet de confirmer la structure algébrique riche du whole-plane SLE. On montre que les formes fermées des moments mixtes $\mathbb{E}\big(\frac{\vert f'(z) \vert^p}{\vert f(z) \vert^q}\big)$ apparaissent sur une famille dénombrable de paraboles du plan (p, q), en étendant les équations de Beliaev-Smirnov à ce cas. Nous introduisons également le spectre généralisé β(p, q; κ), correspondant au comportement asymptotiques des moyennes intégrales mixtes. Le spectre généralisé moyen du whole-plane SLE prend quatre formes possibles, séparés par cinq séparatrices dans $\R^2$. Nous proposons également une approche semblable pour la dérivée Schwarziene S(f)(z) de l’application de SLE. Les calculs sur les équations de Beliaev-Smirnov d’une certaine générale forme de moment mène à une formulation explicite de $\mathbb{E}(S(f)(z))$ . Nous étudions finalement la variance asymptotique de McMullen et démontrons une relation entre la croissance infinitésimale du spectre de la moyenne intégrale et la variance asymptotique pour SLE₂. / Let f an instance of the whole-plane $\SLE_\kappa$ conformal map from the unit disk D to the slit plane: We know that for certain values of κ, p the derivative moments $\mathbb{E}(\vert f'(z) \vert^p)$ can be written in a closed form, study that has updated a new phase of the integral means spectrum. The goal of this thesis is a study on generalized moments $\frac{\vert f'(z) \vert^p}{\vert f(z) \vert^q}$ : ΒββThis study permit confirm the rich algebraic structure of the whole-plane version of SLE. It will be showed that closed forms of the mixed moments E mixtes $\mathbb{E}\big(\frac{\vert f'(z) \vert^p}{\vert f(z) \vert^q}\big)$ can be obtained on a countable family of parabolas in the moment plane (p, q), by extending the so-called Beliaev–Smirnov equation to this case. We also introduce the generalized integral means spectrum, β(p, q; κ), corresponding to the singular behavior of the mixed moments. The average generalized spectrum of whole-plane SLE takes four possible forms, separated by five phase transition lines in $\R^2$. We also propose a similar approach for the Schwarzian derivative S(f)(z) of SLE maps. Computations on the Beliaev–Smirnov equation of a certain general form of moment lead to an explicit formula of $\mathbb{E}(S(f)(z))$ . We finally study the McMullen asymptotic variance and prove a relation between the infinitesimal growth of the integral mean spectrum and the asymptotic variance in an expectation sense for SLE₂.

Orientador: Marcos Cesar Ferreira / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Geociências / Made available in DSpace on 2018-08-25T23:24:24Z (GMT). No. of bitstreams: 1 Messias_CassianoGustavo_M.pdf: 23638977 bytes, checksum: e704bfa68254415de27c9956b5cdab14 (MD5) Previous issue date: 2014 / Resumo: As paisagens rurais vêm sendo transformadas continuamente pela ocupação humana, principalmente em razão de adaptações técnicas requeridas para o desenvolvimento da agricultura. De maneira geral, estas alterações antrópicas estão diretamente ligadas à utilização dos recursos naturais como insumos da produção agrícola. Os recursos mais impactados por este modo de produção são a vegetação e o solo. Dentre as formas de avaliação do grau de comprometimento da paisagem em razão da exploração agrícola do território é o mapeamento da fragilidade ambiental. Esta pesquisa teve como principal objetivo avaliar os graus de fragilidade ambiental de diferentes áreas do Parque Nacional da Serra da Canastra, situado no sudoeste de Minas Gerais. Criado em 1972, o parque tem como meta principal preservar ecossistemas naturais ainda existentes no bioma do cerrado brasileiro. A metodologia de mapeamento da fragilidade ambiental utilizada neste trabalho baseia-se em cinco variáveis geográficas: índice de vegetação, probabilidade de ocorrência de chuvas intensas, declividades, densidade de estradas e densidade de lineamentos estruturais. Estas variáveis foram processadas em sistemas de informação geográfica, por meio de técnicas de análise espacial, utilizadas para a transformação destas, mapeadas segundo a lógica booleana, em variáveis probabilísticas fuzzy. Os mapas fuzzy foram combinados por meio de algoritmo baseado em soma ponderada, gerando-se um mapa de fragilidade ambiental do Parque Nacional. Este mapa final foi comparado a mapas de processos erosivos e de movimento de massa, checados em campo, com o objetivo de se atribuir pesos às variáveis ambientais por meio do teste de Kolmogorov-Smirnov. A metodologia se mostrou eficiente para a identificação e mapeamento de áreas com maior grau de fragilidade no parque, considerando-se a evidência dos processos erosivos e dos movimentos de massa / Abstract: Rural landscapes have been continually transformed by human occupation, mainly due to technical adjustments required for the development of agriculture. In general, these anthropogenic changes are directly linked to the use of natural resources as inputs into agricultural production. The resources most impacted by this mode of production are the vegetation and soil. Among the manners of assessing the degree of landscape vulnerability is the environmental fragility mapping. This research aimed to assess the degree of environmental vulnerability of different areas located within the Serra da Canastra National Park, located in southwestern Minas Gerais. Created in 1972, the park has as main goal to preserve remaining natural ecosystems of the Brazilian Cerrado biome. The methodology for environmental fragility mapping, used in this work, is based on five geographic variables: vegetation index, probability of intense rainfall, slope terrain, roads and structural lineaments densities. These variables, mapped according to the Boolean logic, were processed in a geographic information system through spatial analysis techniques and transformed in fuzzy probabilistic variables. The fuzzy maps were combined by means of algorithm based on a weighted sum, generating the environmental fragility map of the National Park. The estimative of weights values of the five environmental variables was carried out comparing erosion-mass movement maps and the fragility map, using the D-value of Kolmogorov-Smirnov test. Considering the evidence of erosion and mass movements, we concluded that the methodology is efficient for the identification and mapping of areas with the high degree of fragility in the park / Mestrado / Análise Ambiental e Dinâmica Territorial / Mestre em Geografia

The present work has objective to define wich is the distribution of probability that analysis of nutritional contents are adjusted, selecting a function that better explain its behavior and to estimate the limits values of nutrients contents for it classification on several vegetables tissues. It were used 176 datas et colected from 15,534 nutritional analysis of three forest species, Acacia mearnsii, Eucalyptus sp. and Pinus sp., determinated for 1999 to 2004 period, in Forest Ecological Laboratory, in UFSM. The analysis were separated by subgroups in macro and micronutrients, vegetables components (leaves, bark, wood, root), species and year of determination. The database determination trough it statistical describe with mean, standart-deveation, number of observations, maximum and dataset adjusts a Normal distribution, it was aplicated the Lilliofors Test. Where the dataset didn´t adjust the Normal, it was tested the functions Log-normal, Beta, Gamma and Weibull through Kolmogorov-Smirnov Test, with 5%. It was possible determinated that 70% of all dataset valued adjusts one of functions, being the Normal presented of 33.5% of settlings, the Log-normal 27.3%, the Gamma 3.4%, the Weibull 5.7% and the Beta function didn´t presented no one settling. Of all amount dataset valued, 30.1% didn´t adjust any one functions. The studied functions, exception Beta, can explain the results from chemical analysis of vegetables tissues and establis hed the control limits of nutrient contents in each species. / O presente trabalho teve como objetivo definir qual é a distribuição de probabilidade que os resultados de análises nutricionais se ajustam, selecionando uma função que melhor explica o comportamento dos teores e estimar os valores limites dos macro e micronutrientes para sua classificação nos diversos tecidos vegetais. Foram utilizados 176 conjuntos de dados coletados em 15.534 análises nutricionais de três espécies florestais, Acacia mearnsii, Eucalyptus sp. e Pinus sp., realizadas durante o período de 1999 a 2004 e determinadas no Laboratório de Ecologia florestal, da UFSM. As análises foram separadas em subgrupos por macro e micronutrientes, componente vegetal (folhas, galhos, casca, madeira, raiz, etc.), espécie e ano de determinação. O banco de dados passou pela determinação das estatísticas descritivas média, desvio padrão, número de observações, valores máximo e mínimo. Para verificar se os dados seguiam a distribuição Normal, foi aplicado o teste de Lilliofors. Nos casos onde o teste não foi normal, foram testadas as funções Log-normal, Beta, Gamma e Weibull, via teste de Kolmogorov-Smirnov, com alfa 5%. Foi possível determinar que 70% do total avaliado seguiam alguma das funções, sendo que a Normal apresentou 33,5% de ajustes, a Log-normal 27,3%, a Gamma 3,4%, a Weibull 5,7% e a função Beta não apresentou nenhum ajuste. Do total de conjunto de dados avaliados, 30,1% não se aderiu a nenhuma das funções. As funções estudadas, com exceção da Beta, podem explicar a distribuição dos resultados das análises químicas de tecidos vegetais e estabelecer limites de controle dos teores de elementos químicos em cada espécie.

The doctoral thesis deals with spectrum sensing in cognitive radio networks (CRN). A number of international organizations are currently actively engaged in standardization of CRN and it points out to the fact that this technology will be widely used in the near future. One of the key features of this technology is a dynamic access to the spectrum, which can be affected by many different harmful factors occurring in the communication chain. The thesis investigates the influence of selected factors on the spectrum sensing process. Another contribution of the work is the optimization of the Kolmogorov - Smirnov statistical test that can be applied for the primary user signal detection. The work also incorporates the analysis of the influence of the harmful effects caused by the commonly used transmitters and receivers on various spectrum sensing methods. The investigations are verified by the results of the simulations and also by the measurements with experimental platforms based on the software-defined radio (SDR).

This project studies the signal detection and identification problem in high-dimensional noisy data and the possibility of using it on microbiome data. An extensive simulation study was performed on generated data using as well as a microbiome dataset collected on patients with Parkinson's disease, using Donoho and Jin's Higher criticism, Jager and Wellner's phi-divergence-based goodness-of-fit-test and Stepanova and Pavlenko's CsCsHM statistic . We present some novel approaches based on established theory that perform better than existing methods and show that it is possible to use the signal identification framework to detect differentially abundant features in microbiome data. Although the novel approaches produce good results, they lack substantial mathematical foundations and should be avoided if theoretical rigour is needed. We also conclude that while we have found that it is possible to use signal identification methods to find abundant features in microbiome data, further refinement is necessary before it can be properly used in research. / Detta projekt studerar signaldetekterings- och identifieringsproblemet i högdimensionell brusig data och möjligheten att använda det på mikrobiomdata från människor. En omfattande simuleringsstudie utfördes på genererad data samt ett mikrobiomdataset som samlats in på patienter med Parkinsons sjukdom, med hjälp av ett antal goodness-of-fit-metoder: Donoho och Jins Higher criticis , Jager och Wellners phi-divergenser och Stepanova och Pavelenkos CsCsHM. Vi presenterar några nya tillvägagångssätt baserade på vedertagen teori som visar sig fungera bättre än befintliga metoder och visar att det är möjligt att använda signalidentifiering för att upptäcka olika funktioner i mikrobiomdata. Även om de nya metoderna ger goda resultat saknar de betydande matematiska grunder och bör undvikas om teoretisk formalism är nödvändigt. Vi drar också slutsatsen att medan vi har funnit att det är möjligt att använda signalidentifieringsmetoder för att hitta information i mikrobiomdata, är ytterligare experiment nödvändiga innan de kan användas på ett korrekt sätt i forskning.

We consider the problem of testing whether r (>=2) samples are drawn from the same continuous distribution F(x). The test statistic we will study in some detail is defined as the maximum of the circular differences of the empirical distribution functions, a generalization of the classical 2-sample Kolmogorov-Smirnov test to r (>=2) independent samples. For the case of equal sample sizes we derive the exact null distribution by counting lattice paths confined to stay in the scaled alcove $\mathcal{A}_r$ of the affine Weyl group $A_{r-1}$. This is done using a generalization of the classical reflection principle. By a standard diffusion scaling we derive also the asymptotic distribution of the test statistic in terms of a multivariate Dirichlet series. When the sample sizes are not equal the reflection principle no longer works, but we are able to establish a weak convergence result even in this case showing that by a proper rescaling a test statistic based on a linear transformation of the circular differences of the empirical distribution functions has the same asymptotic distribution as the test statistic in the case of equal sample sizes. / Series: Research Report Series / Department of Statistics and Mathematics