A research report submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, in partial fulfilment of the requirements for the degree of Master of Science in Mining Engineering. February, 2016 / Mineral Resource estimation provides an assessment of the quantity, quality, shape and grade distribution of a mineralised deposit. The resource estimation process involves; the assessment of data available, creation of geological and/or grade models for the deposit, statistical and geostatistical analyses of the data, as well as determination of the appropriate grade interpolation methods. In the grade estimation process, grades are interpolated/extrapolated into a two or three – dimensional resource block model of a deposit. The process uses a search volume ellipsoid, centred on each block, to select samples used for estimation. Traditionally, a global orientated search ellipsoid is used during the estimation process. An improvement in the estimation process can be achieved if the direction and continuity of mineralisation is acknowledged by aligning the search ellipsoid accordingly. The misalignment of the search ellipsoid by just a few degrees can impact the estimation results. Representing grade continuity in undulating and folded structures can be a challenge to correct grade estimation. One solution to this problem is to apply the method of Dynamic Anisotropy in the estimation process. This method allows for the anisotropy rotation angles defining the search ellipsoid and variogram model, to directly follow the trend of the mineralisation for each cell within a block model. This research report will describe the application of Dynamic Anisotropy to a slightly undulating area which lies on a gently folded limb of a syncline at Driefontein gold mine and where Ordinary Kriging is used as the method of estimation. In addition, the optimal Dynamic Anisotropy resolution that will provide an improvement in grade estimates will be determined. This will be achieved by executing the estimation process on various block model grid sizes. The geostatistical literature research carried out for this research report highlights the importance of Dynamic Anisotropy in resource estimation. Through the application and analysis on a real-life dataset, this research report will put theories and opinions about Dynamic Anisotropy to the test.

A thesis submitted in fulfillment of the requirements for the Degree of Doctor of Philosophy, School of Statistics and Actuarial Science, Faculty of Science University of Witwatersrand, Johannesburg. February 2017. / The work done in this thesis on finite planning horizon inspection models has demonstrated that with the advent of powerful computers these days it is possible to easily find an optimal inspection schedule when the lifetime distribution is known. For the case of system time to failure following a uniform distribution, a result for the maximum number of inspections for the finite planning models has been derived. If the time to failure follows an exponential distribution, it has been noted that periodically carrying out inspections may not result in maximization of expected profit. For the Weibull distributions family (of which the exponential distribution is a special case), evenly spreading the inspections over a given finite planning horizon may not lead to any serious prejudice in profit. The case of inspection models where inspections are of non-negligible duration has also been explored. The conditions necessary for inspections that are evenly spread over the entire planning horizon to be near-optimal when system time to failure either follows a uniform distribution or exponential distribution have been explored. Finite and infinite planning horizon models where inspections are imperfect have been researched on. Interesting observations on the impact of Type I and Type II errors in inspection have been made. These observations are listed on page 174. A clear and easy to implement road map on how to get an optimal inspection permutation in problems first discussed by Zuckerman (1989) and later reviewed by Qiu (1991) for both the undiscounted and discounted cases has been given. The only challenge envisaged when a system has a large number of components is that of computer memory requirements - which nowadays is fast being overcome. In particular, it has been clearly demonstrated that the impact of repair times and per unit of time repair costs on the optimal inspection permutation cannot be ignored. The ideas and procedures of determining optimal inspection permutations which have been developed in this thesis will no doubt lead to huge cost savings especially for systems where the cost of inspecting components is huge. / XL2018

A Dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, in fulfilment of the requirements for the Degree of Masters in Engineering by research only and to the Stochastic Mine Planning Laboratory, McGill University as part of the COSMO scholarship in Mine Planning under uncertainty Johannesburg, 2017 / This dissertation discusses the use of stochastic orebody modelling techniques for assessing geological uncertainty associated with gold mineralisation at Geita Gold Mine in Tanzania, and proposes a practical methodology that can be applied to similar studies. As part of the pre-feasibility stage studies for underground mining at Geita, stochastic simulations were required to assess the geological uncertainty associated with isolating (modelled) high grade lenses that occur within the known low grade mineralisation currently targeted for underground mining. Two different simulation techniques are applied in this research: Sequential Indicator Simulation to generate lithofacies realisations from which to assess ore category boundaries and shapes for use in quantifying volumetric uncertainty; and Direct Block Simulations to simulate gold grade realisations from which to assess grade uncertainty. This study identified potential upside and downside mine planning scenarios for volumes and total metal content from the ore category and grade simulations respectively. The findings of the results demonstrated that the high grade zones are much more broken up and discontinuous than the currently modelled high grade shape. The current business case uses a probabilistic high grade shape based on a single grade indicator and a probability choice of 50 percent as the threshold for high grade. The results of the study consider a simulation of possible outcomes based on the same threshold grade indicator and hence quantify the uncertainty or total geological risk. This geological risk may be introduced to mine designs, production schedules and NPV predictions The stochastic workflow developed can be applied to analogous deposit types to assess the risk related to geological uncertainty. The work includes a description of practical considerations to be accounted for when applying the techniques. / MT 2017

A dissertation submitted in fulfilment of the requirements for the Degree of Master of Science in Archaeology of the University of Witwatersrand in 2017. / Over the past decade a new method of statistical shape analysis, geometric morphometrics, has been applied to the study of artefact shapes. Later Stone Age (LSA) tanged stone arrowheads, hypothesized to act as stylistic markers among prehistoric southern African hunter-gatherer groups, have been analysed with geometric morphometrics and reveal spatially coherent variations in their shape. After being tested against several variables that may have had an effect on arrowhead shape, these stylistic spatial variations could very well indicate large scale linguistic or other kinds of boundaries between different elements of prehistoric San populations. Understanding them can shed light on the social and economic organization of southern African hunter-gatherers during the later Holocene. / LG2017

Orientador: Manoel Henrique Salgado / Banca: José de Souza Rodrigues / Banca: João Pedro Albino / Resumo: O propósito desta dissertação é analisar a implantação da ferramenta Controle Estatístico de Processo (CEP) para a gestão de operações de uma empresa do setor alimentício. Para tanto, realizou-se uma fundamentação que compreende: o Controle de Qualidade, a Variabilidade do Processo e o CEP. Esta fundamentação teórica apoiou o presente estudo de caso, consequentemente, foi possível descrever e discutir todas as etapas de aplicação da ferramenta no contexto de iplementação de um novo sistema de Gestão. Em adição, sugerir a proposta de um roteiro para auxílio na implantação da ferramenta CEP em processos de manufatura. Os resultados permitem constatar que as ferramentas que compõe um pacote corporativo podem não ser eficazes, quando esta não é analisada quanto à sua dimensão teórica de aplicabilidade no local a ser utilizado. Outro ponto constatado nos resultados é a necessidade de formalizar uma norma padrão de aplicabilidade de ferramentas de gestão, evitando a ocorrência de erros comuns de erros comuns, como, a não existência de um estudo para identificar não apenas a característica da qualidade, mas quais equipamentos ou pontos de operação devem ser monitorados pela ferramenta contida no Sistema de Gestão / Abstract: The purpose of this dissertation is to analize the implentation of the SPC (Statistical Process Control) for the management of operations in a food company. Furthermore, it was performer a theoretical review that includes: Quality Control, Process Variability and SPC. This theoretical review supported this case study, and it has possible to describe and discuss all the steps of deployment the tool in the new System of Management. In addition, to suggest a proposal of a guide to aid the implementation of the SPC in manufacturing processes. The results reveal that comprise a corporative guide may not be effective, when this is not analyzed in a techinical dimension of applicability on the local to be used. Moreover, the point observed in the results, all the System of Management need to formalize a standard applicatibility of management tools, avoiding common mistakes; for instance, non-existence of a study to identify which equipment or point of operatio must be monitored / Mestre

For years attribution research has been dominated by the ANOVA model of behavior which proposes that people construct their dispositional attributions of others by carefully comparing and weighing all situational information using mental computations similar to the processes used by researchers to analyze data. A preliminary experiment successfully determined that participants were able to distinguish differences in variability assessed across persons (high vs. low consensus) and across situations (high vs. low distinctiveness). Also, it was clear that the subjects could evaluate varying levels of situational constraint. A primary experiment administered to participants immediately following the preliminary study determined that participants grossly under-utilized those same variables when making dispositional attributions. Results gave evidence against the use of traditional ANOVA models and support for the use of the Behavior Averaging Principle of Attribution. / by Kori A. Hakala. / Thesis (M.A.)--Florida Atlantic University, 2008. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2008. Mode of access: World Wide Web.

O aumento do uso de água para consumos diversos tem gerado o crescimento de pesquisas relacionadas aos recursos hídricos subterrâneos. A quantificação de sua recarga é requisito indispensável para o manejo desses recursos. O objetivo dessa pesquisa é analisar a influência dos eventos de precipitação e de características do solo na variação do nível dágua em área de recarga do Aquífero Guarani, utilizando a bacia-piloto do Ribeirão da Onça como local de estudo. A variação do nível d\'água foi monitorada em 12 poços no período de setembro de 2004 a agosto de 2008. A estação climatológica do CRHEA-USP forneceu as alturas diárias de precipitação, no período de outubro de 2004 a setembro de 2008. Para alcançar os objetivos propostos foram utilizados três métodos estatísticos: técnicas de agrupamento, análise de séries temporais e análises de correlação. Há um padrão de sazonalidade das chuvas na região e, a variação do nível d\'água nos poços monitorados acompanha esse padrão, com exceção dos poços localizados em culturas de eucalipto. As técnicas de agrupamento sugerem a formação de cinco grupos de poços. A correlação entre as variações mensais do nível d\'água em poços de mesma cultura gerou altos coeficientes. Esse resultado, juntamente com os agrupamentos, mostra que há uma maior influência da cultura de solo na variação do nível d\'água, enfatizando a necessidade de estudos mais aprofundados a respeito das características do solo, uma vez que a porosidade também se mostrou como importante característica. Os coeficientes de correlação entre variação do nível d\'água no aqüífero e precipitação para intervalos de tempo diários e mensais foram muito baixos, mostrando a existência de um período de defasagem entre os eventos. Verificou-se a existência de uma defasagem de 10 a 20 dias entre precipitação e elevação do nível d\'água. A ocorrência de curtos períodos de elevação é resultado de precipitações acumuladas ocorrentes no mesmo intervalo de tempo. / The increasing of water use to different consumes have generated the growing of researches related about groundwater resources. The recharge\'s quantification is a indispensible requirement to management of these resources. The main objective of this research is to analyze the influence of precipitation and soil characteristics on the water level fluctuations on the recharge area of the Guarani aquifer system, using the Ribeirão da Onça pilot-basin to study area. The water level fluctuation was monitoring in 12 wells, during the period of September 2004 until August 2008. The climatology station of CRHEA-USP provides the data about dairy precipitation, to the period of October 2004 to September 2008. In order to reach the proposal objectives were used three statistical methods: clustering techniques, time series analysis and correlation analysis. There is a seasonal pattern of the rains in the region, and the water level fluctuations have the same behavior, with except of wells located in areas where eucalypt are cultivated. The clustering techniques surgeries the formation of five wells groups. The correlation between months variations water level of the wells generated high coefficients. This result, analyzed with the clustering, shows that there are an more importance of soil culture on the water level fluctuation, empathizing the necessity of more specific studies about the soil characteristics, once a time that the porosity was also showed like a important characteristic. The coefficients of correlation between water level dairy fluctuation on the aquifer and dairy precipitation were very small (r < 0.5), which shows the existence of a lag period between the events. It was verified that this lag varies from 10 to 20 days. The occurrences of shorts periods of elevation of the water level is result of accumulated precipitations currents on the same period.

O método aqui desenvolvido, bem como as aplicações feitas ao estudo de sistemas clássicos da dinâmica não-linear, tiveram por objetivo construir uma ferramenta adequada à descrição das características globais de fenômenos complexos da dinâmica não-linear. Uma característica típica da descrição probabilística do comportamento dinâmico de um sistema é sua expressão em termos da evolução temporal da função densidade de probabilidade dos estados, que é governada por uma equação diferencial linear, em contraste com a descrição temporal convencional, utilizada em dinâmica não-linear. Enquanto esta última, comumente dita determinística, exibe fenômenos tais como instabilidades, bifurcações, sensibilidade a condições iniciais etc, a descrição probabilística se manifesta, quando o sistema dinâmico detém propriedades de ergodicidade, em uma evolução não-reversível da função densidade de probabilidade em direção a um estado final invariante, mais especificamente tendendo ao equilíbrio global de um sistema linear. Este trabalho visa a aplicação da teoria probabilística da evolução de densidades de probabilidade em um problema de capotamento de veículos. Para isso, a teoria é descrita por meio de seus fundamentos e aplicada primeiramente em modelos clássicos da dinâmica não-linear, que, por serem bem estudados, podem comprovar a validade, bem como a extensão dessa forma de análise. / The method developed in this work, as well as its application in classical non-linear dynamics systems, had the main purpose of building a suitable tool in describing global complex phenomena of non-linear dynamics. A typical feature of the probabilistic approach of dynamics systems behavior is the ability to express it as a temporal probability density function evolution in terms of a linear evolution equation, which is ruled by a linear differential equation, as opposed to the regular temporal description used in non-linear dynamics. While the aforementioned description, also called deterministic, may face a variety of phenomena such as instabilities, bifurcation, high sensibility to initial conditions etc, in the probabilistic approach, as long as the dynamic system enjoys some ergodic properties, the probability density function will be driven irreversibly to a final invariant state, towards a global equilibrium of a linear system. This work consists in the application of probabilistic theory of density evolution in the problem of vehicle rollover subject to a certain maneuver. In order to accomplish that, all theory described is firstly applied to classical problems of nonlinear dynamics, since they have many established results, and as such, can validate and extend this sort of analysis for any dynamic system.

Neste trabalho estudamos deposição de partículas em redes unidimensionais, com uma abordagem estatística a partir de modelos como absorção sequencial aleatória (RSA) e cooperativa (CSA). O objetivo é a simulação de formação de monocamadas oligoméricas automontadas em substratos, que se justifica devido aos recentes avanços, por um lado, na área experimental, na formação de SAMs (self-assembled monolayers) e produção de nanoestruturas e, por um lado, na área teórica, no desenvolvimento de diversos modelos estocásticos para processos de adsorção sequencial. Introduzimos o modelo clássico de adsorção sequencial aleatória, a nomenclatura utilizada, e estudamos algumas de suas características. Analisamos a fração da rede que permanece vazia após ser atingida a saturação, para oligômeros formados por um número K de unidades. Em seguida, estudamos a cinética de um processo RSA, primeiro para o caso de monômeros, depois para dímeros, e então para oligômeros maiores. A estrutura da camada para o caso de dímeros é examinada a partir da distribuição de tamanhos de grãos (número de K-meros adjacentes), e da função de correlação. Os dados obtidos nas nossas simulações de Monte Carlo são comparados com resultados de modelos estocásticos existentes na literatura. A partir desse ponto, estudamos variações do processo de RSA simples. Adicionamos outro oligômero ao fluxo, chegando à adsorção sequencial de misturas. Estudamos a maneira como a fração de cada um dos oligômeros no fluxo de moléculas influi tanto na dinâmica do preenchimento da camada, como na taxa de saturação da rede. Em seguida analisamos a influência do oligômero adicional na estrutura da monocamada automontada obtida. Como antes, sempre que possível os dados obtidos são comparados com resultados da literatura. Introduzimos processos de relaxamento, chegando a adsorção-difusão, adsorção-evaporação e adsorção-difusão-evaporação, em todos os casos compilando modelos estocásticos disponíveis na literatura e, onde possível, comparando as previsões desses modelos com resultados de nossas simulações numéricas. Assim como no caso RSA simples, ao estudar esses processos derivados de RSA, analisamos tanto a cinética dos processos (incluindo o estado final do sistema), quanto as estruturas formadas (através da função de correlação e do tamanho de domínios), destacando as mudanças causadas quando se introduz processos de relaxamento durante a formação de uma SAM. Por fim, estudamos processos cooperativos, em que o destino dos oligômeros sendo depositados depende da vizinhança em que se encontram. Como é usual em modelos estatísticos de deposição sequencial, as interações são representadas por mudanças nas taxas de ocorrência de algum dos eventos, neste caso a difusão. Apresentamos dados inéditos, relativos ao modelo cooperativo de adsorção-difusão que simulamos numericamente, com o objetivo de demonstrar a influência que uma interação atrativa entre oligômeros pode ter na estrutura da monocamada depositada sobre o substrato. O objetivo é mostrar como a estrutura de um SAM pode fornecer indícios sobre as interações existentes entre oligômeros. / In this work we study particle deposition in one-dimensional lattices, through a statistical approach, using models such as random sequential adsorption (RSA) and cooperative sequential adsorption (CSA). The goal is to simulate the formation of oligomeric self-assembled monolayers (SAMs) on substrates, which are relevant right now important firstly because of recent advances in the experimental area, with manufacturing of nanostructures using SAMs, and secondly because of progresses in the theoretical field, with development of stochastic models of sequential adsorption process. We introduce the classical model of random sequential adsorption, the associated nomenclature, and some of its characteristics. We analyze the portion of the lattice that remains empty after reaching saturation, for oligomers formed with K units. Subsequently we study the kinetics of a RSA process, initially for the case of monomers, then for dimmers, and lastly for larger species. The structure of the monolayer is analysed in terms of grain or domain size (probability distribution p(n) for n contiguous ologomers), and correlation function, for dimmers. Data obtained in our Monte Carlo simulations are compared with existing results in literature. From this point on, we study variations of the simple RSA process. We add another oligomer to the flux, obtained RSA of mixtures. We examine how the flux of each of the oligomers affects the filling of the monolayer: not only the final coverage saturation, but the kinetics of the process. We further analyze the influence of the additional oligomer in the structure of the monolayer obtained. Also here we compare our results with models from the literature. We add relaxation to the adsorption processes, achieving adsorption-diffusion (RSAD), adsorption-desorption, and adsorption-diffusion-desorption, always compiling stochastic models available in the literature, and comparing our results where analytical models are available. As done previously with RSA, when studying these more complex processes, we analyze the kinetics (including the final coverage) as much as th resulting structure (correlation function and domain size distribution), highlighting changes caused by these relaxation processes. In the final chapter we study cooperative process, in which the destiny of oligomers being adsorbed depends on their neighborhood. As usual in statistical models of sequential adsorption, the interactions are represented by changes of rates of some event (in this case, diffusion). We present new data, concerning the cooperative adsorption-diffusion model we simulated, aiming to demonstrate the influence an attractive interaction between oligomers may have in the structure of the monolayer formed on the substrate. The objective is illustrate how a SAM structure may give clues about the existence of interactions between oligomers.

Epidemiologists rely on human interaction networks for determining states and dynamics of disease propagations in populations. However, such networks are empirical snapshots of the past. It will greatly benefit if human interaction networks are statistically predicted and dynamically created while an epidemic is in progress. We develop an application framework for the generation of human interaction networks and running epidemiological processes utilizing research on human mobility patterns and agent-based modeling. The interaction networks are dynamically constructed by incorporating different types of Random Walks and human rules of engagements. We explore the characteristics of the created network and compare them with the known theoretical and empirical graphs. The dependencies of epidemic dynamics and their outcomes on patterns and parameters of human motion and motives are encountered and presented through this research. This work specifically describes how the types and parameters of random walks define properties of generated graphs. We show that some configurations of the system of agents in random walk can produce network topologies with properties similar to small-world networks. Our goal is to find sets of mobility patterns that lead to empirical-like networks. The possibility of phase transitions in the graphs due to changes in the parameterization of agent walks is the focus of this research as this knowledge can lead to the possibility of disruptions to disease diffusions in populations. This research shall facilitate work of public health researchers to predict the magnitude of an epidemic and estimate resources required for mitigation.