Student Number : 9708525G - PhD thesis - School of Mathematics - Faculty of Science / Sequences of numbers have important applications in the field of Computer Science. As a result they have become increasingly regarded in Mathematics, since analysis can be instrumental in investigating algorithms. Three concepts are discussed in this thesis, all of which are concerned with ‘words’ or ‘sequences’ of natural numbers where repeated letters are allowed: • The number of distinct values in a sequence with geometric distri- bution In Part I, a sample which is geometrically distributed is considered, with the objective of counting how many different letters occur at least once in the sample. It is concluded that the number of distinct letters grows like log n as n → ∞. This is then generalised to the question of how many letters occur at least b times in a word. • The position of the maximum (and/or minimum) in a sequence with geometric distribution Part II involves many variations on the central theme which addresses the question: “What is the probability that the maximum in a geometrically distributed sample occurs in the first d letters of a word of length n?” (assuming d ≤ n). Initially, d is considered fixed, but in later chapters d is allowed to grow with n. It is found that for 1 ≤ d = o(n), the results are the same as when d is fixed. • The average depth of a key in a binary search tree formed from a sequence with repeated entries Lastly, in Part III, random sequences are examined where repeated letters are allowed. First, the average left-going depth of the first one is found, and later the right-going path to the first r if the alphabet is {1, . . . , r} is examined. The final chapter uses a merge (or ‘shuffle’) operator to obtain the average depth of an arbitrary node, which can be expressed in terms of the left-going and right-going depths.

In South Africa, citizen participation is regarded as an integral part of all social, economic and political activity. There is always an attempt to either involve citizens/communities in different programmes or at least to pretend to have involved people. Community participation is a constitutional prerogative that the broader masses should meaningfully participate in issues affecting their lives. Thus overgrowing concern by development practitioners to utilize participatory methods has become notable in recent years and participation has become an established orthodoxy within the development discourse in South Africa. The practice of participation has become embodied in what is popularly known to be people-centered development in which it is favored that community needs take precedence over those of other stakeholders when designing and implementing development projects. This study explores community participation in income generating projects at the Tembisa / Kempton Park Development Center. Using a case study as a qualitative inquiry method, the researcher sought to establish the evidence of community participation and the extent to which participants in income generating projects were involved as the main role players. The research sample constituted of 15 participants; ten were beneficiaries of income generating projects, three were staff members at the Tembisa / Kempton Park Development Center and two participants where drawn from the main funders of the Tembisa / Kempton Park Development Center. The different categories of the participants drawn into the sample enabled the researcher to holistically capture how the development process unfolded. The findings of the research indicated that the development model used at Tembisa / Kempton Park Development Center is largely participatory. The model allowed community members to have more say and control in the initiation, design, implementation, monitoring and evaluation of the projects. However this model has challenges that are institutional, social and structural of nature and barriers which hinder effective and meaningful community participation. Government intervention was recommended to address some of the challenges to community participation on a macro level.

Eradicating poverty is one of the biggest challenges in South Africa. A Development Centre Model was developed by the Department of Social Development as a strategy to empower citizens of South Africa to become independent and self-reliant in an attempt to alleviate poverty. The Department fulfils the role of programme monitoring and evaluation of different programmes offered by the Development Centres. A Social Development Approach was used as a guide to the theoretical framework of the study. The primary aim of the study was to explore the perceptions about the effectiveness of monitoring and evaluation of incomegenerating projects rendered to the development centres by the Department of Social Development in the Gauteng North Region. A qualitative research strategy was followed and a multiple case study design was applied. Purposive sampling was used to initially select six beneficiaries, six centre managers, two service providers and two departmental officials involved in the development centres that are government-funded. However, the total number of the participants in the end came to thirteen; five beneficiaries; five centre managers; two evaluators and one departmental official. Data was collected via face-to-face interviews with participants and the interviews were tape recorded. To analyse data, thematic content analysis was applied. Some of the findings and the recommendations are, firstly, that the study contributes to the understanding of the effectiveness of programme monitoring and evaluation; secondly, that programme monitoring and evaluation is in fact effective; and thirdly, that beneficiaries should participate in monitoring and evaluation of their projects. Fourthly, the majority of the beneficiaries and the centre managers felt that the process has no impact on the actual programme or projects. These participants felt that there is no follow-up to solve problems that have been identified during this process of monitoring and evaluation. The participants recommended that the department do more visits thereby making sure that problems identified during monitoring and evaluation are immediately resolved through constant visits to the development centres.

A função básica de um sistema de energia elétrica é fornecer aos seus clientes energia elétrica economicamente e tão confiável quanto possível. A importância da confiabilidade dos sistemas de energia elétrica é claramente notada quando as pessoas são confrontadas com a perda de energia elétrica, não importando se a perda provoca parada das linhas de produção ou mesmo impactos financeiros às empresas, o que pode consequentemente causar enorme impacto econômico além de situações que impactam o conforto da população. Dentro deste contexto esta tese apresenta uma metodologia para avaliação da confiabilidade de plantas de geração de energia elétrica que possibilita avaliar qualitativamente e quantitativamente a confiabilidade e disponibilidade dos principais componentes elétricos e mecânicos necessários à geração confiável de energia. A análise qualitativa foi realizada levando-se em consideração as características físicas das usinas hidroelétricas e as características construtivas das unidades geradoras para que fosse possibilitada a classificação das unidades geradoras em grupos estatisticamente significativos. A análise quantitativa foi fundamentada em métodos estatísticos de estimação e inferência e aspectos relacionados ao desempenho e disponibilidade de usinas hidroelétricas brasileiras tendo como referência os índices preconizados pelas agências regulatórias. As unidades geradoras foram modeladas através de métodos estatísticos e probabilísticos que permitem avaliar por meio de técnicas de confiabilidade a frequência e a duração das falhas além das probabilidades associadas a cada estado de falha. Os dados de falha foram obtidos por meio de bancos de dados consolidados por agentes geradores e órgãos federais responsáveis pela operação do sistema interligado nacional. Os dados representam a história operativa de grande parte das usinas hidrelétricas brasileiras operadas e despachadas de forma centralizada. A metodologia apresentada nesta tese preenche uma lacuna na existência de metodologias focadas em avaliação de confiabilidade de plantas de geração em fase de projeto, que possibilitariam a mitigação de riscos de falhas e perdas produtivas quando da operação comercial da planta de geração. / The basic function of a power system is to provide their customers electricity as economically and reliably as possible. The importance of the reliability of electric power systems is clearly noted when people are confronted with the loss of energy, no matter if the loss stops the production lines or even causes financial impacts on companies, which may consequently cause huge economic impact beyond situations that influence the comfort of the population. Within this context, this thesis presents a methodology for assessing the reliability of plants generating electricity that enables qualitatively and quantitatively evaluate the reliability and availability of key electrical and mechanical components needed to generate reliable power. Qualitative analysis was performed taking into account the physical characteristics of hydroelectric and constructive features of the generating units to which the classification was made to enable pool and cluster generating units in groups statistically significant. Quantitative analysis was based on statistical methods of estimation and inference and aspects related to performance and availability of Brazilian hydroelectric plants with reference to the indices recommended by regulatory agencies. The units were modeled using probabilistic and statistical methods for assessing, by means of reliability techniques, the frequency and duration of failures plus the probabilities associated with each state of failure. The failure data were obtained from consolidated databases by agents and federal agencies responsible for the operation of the national grid. The data represent the operational history of much of Brazil\'s hydroelectric facilities operated and dispatched centrally. The methodology presented in this thesis fills a gap in the existence of methodologies focused on reliability assessment of power plants in the design phase, which would allow the mitigation of risks of failures and production losses when the commercial operation of the generating plant.

Esta tese aborda diversos temas em evolução molecular, usando extensivamente o formalismo de funções geratrizes para obter resultados analíticos sempre que possível. Em primeiro lugar, apresenta-se a solução exata para o comportamento dinâmico de uma população infinita de seqüências infinitamente longas (não há mutações reversas) evoluindo sob a ação de mutações deletérias em um relevo adaptativo multiplicativo ou truncado. Além disso, foi estudado o comportamento de uma população submetida a sucessivas diluições de intensidades arbitrárias, como ocorre em alguns protocolos de evolução experimental. Foram obtidas expressões matemáticas que, em princípio, podem ser úteis na caracterização de populações reais de microorganismos. Demonstrou-se também que um processo estocástico de ramificação multidimensional generalizado é uma excelente ferramenta para analisar numericamente os efeitos da degeneração mutacional (especificamente, de um fenômeno denominado catraca de Muller) em populações sob variadas condições de crescimento exponencial. Finalmente, simulações foram extensivamente utilizadas para analisar a história evolutiva de populações finitas e averiguar a possibilidade de certas grandezas, como certas medidas da topologia de árvores genealógicas, serem empregadas na elaboração de testes estatísticos capazes de detectar as marcas deixadas pela seleção natural. / This thesis discusses some topics of molecular evolution, extensively using generating function methods to find analytical results whenever possible. In first place, it gives the exact solution for the dynamics of an infinite population of infinitely long sequences (no back mutations) evolving under the action of deleterious mutations on either multiplicative or truncated fitness landscapes. In addition, the behavior of a population subject to successive dilutions of arbitrary intensity, just like some experimental evolution protocols, is found. The mathematical expressions, in principle, may prove useful in characterizing real populations of microor¬ganisms. It was also demonstrated that a generalized multidimensional branching process is a nice tool in numerically studying mutational degeneration effects (specifically a pheno¬menon called Muller\'s ratchet) in populations under a wide variety of exponential growth settings. Finally, the evolutionary history of finite populations was studied by simulations to probe the viability of certain statistic, like some topological measures in genealogical trees, being incorporated in statistical tests to detect the fingerprints of natural selection.

Os efeitos multidisciplinares presentes em projetos de engenharia, sobretudo naqueles de infra-estrutura, têm alargado as fronteiras de pesquisas para avaliá-los não só do ponto de vista convencional técnico econômico, mas também sob a ótica ambiental e social. Por outro lado, o investidor que tradicionalmente buscava oportunidades apenas considerando o desempenho econômico e financeiro, atualmente é levado a analisar os empreendimentos também no âmbito social e ambiental. Fundamentado em várias informações disponíveis em bases de dados constituídas por diversas instituições, o modelo desenvolvido nesta pesquisa é uma solução para avaliar o mérito de um empreendimento de geração distribuída de origem térmica, considerando os aspectos econômico, social e ambiental, por meio de indicadores que quantificam, objetivamente, aspectos econômicos como taxa de retorno de capital e margem liquida, bem como fatores sociais como o impacto na educação, na saúde, na renda e no emprego e ainda, verifica o atendimento das restrições ambientais. A solução apresentada, sem prejuízo da avaliação dos aspectos pragmáticos relativos à viabilidade econômica e respeito à regulamentação ambiental, traz uma forma simples e clara de atribuir um grau de mérito agregado às alternativas de implementação de geração distribuída, considerando a intensidade da responsabilidade social subjetiva do investidor. A análise de cenários e de sensibilidade diante da variação de parâmetros diversos que o modelo oferece, permite aferir o grau de robustez e de importância da precisão de variáveis específicas. Embora não esgote o tema, o modelo apresentado contribui para estimular diferentes formas de avaliar e priorizar multidisciplinarmente a implementação um empreendimento de geração distribuída, podendo inclusive, se prestar como indicador de financiamentos privilegiados ou outros incentivos do gênero. / The multidiscipline effects in engineering projects, mainly in those of infrastructure, have extended the borders of research to not only evaluate them of the conventional point of view, economic and technical, but also environmental and social. On the other hand, the investor who traditionally searched alternatives only considering the economic and financial performance currently is taken to analyze also the social and environmental aspects. Based on some information available in several institutions databases, the model developed in this research is a solution to evaluate the merit of an enterprise of distributed generation of thermal origin, considering the economic, social and environmental aspects, using merit indexes that quantify, directly, economic aspects as capital return tax and operating income eliminates, as well as social factors like the impact in the education, health, income and employment rates and still, it verifies the attendance of the environmental restrictions. The solution presented, without damage the evaluation of the pragmatic aspects related to economic viability and respect to the ambient regulation, brings a simple and clear form to attribute a merit degree of aggregate to the alternatives to embed distributed generation, considering the intensity of the subjective social responsibility of the investor. The analysis of sceneries and sensitivity ahead of the diverse parameter variation that the model offers, allows investigating the robustness degree and accuracy importance of specific variable. Although it does not deplete the subject, the presented model is an important contribution to stimulate a form to evaluate and to prioritize the multidiscipline implementation to a distributed generation enterprise, also being able, to be used as financial index or other incentives of the sort.

Magister Artium (Development Studies) - MA (DVS) / Formal microfinance institutions have been an important tool in the fight against poverty in developing countries, but their reach for rural people and urban slum poor are limited. Following this, Village Savings and Loan Associations (VSLAs) are established as an alternative, informal mechanism for saving and borrowing that do not require external capital or ongoing financial or administrative support from a founding organization or government bodies. Thus, this study aimed to assess the effects of women participation in VSLA on poverty reduction with a case study in Hawassa city, Ethiopia. Using a mixed qualitative and quantitative research methodology, the study tried to focus on examining the effects of VSLAs contribution to economic and social wellbeing of households, and decision makings, and women participation in community activities. The study used 254 samples (127 VSLA participants, and 127 non-participants) and collected data using questionnaire and focus group discussion. The study used propensity score matching (PSM) to estimate the impact of women participation in VSLA on average monthly household income, and the result indicated the average effect of women participation in VSLA on average monthly household income of participant women is positive and significant at 5% significant level, ranging from 169.63 Birr/month (nearest neighbor matching) to 141.55 Birr/month (Kernel matching), on average. Besides, comparison between participants and non-participants using hypothesis testing shows that women participation in VSLA has a significant positive association with improvements in household diet, health, children's education, and women’s involvement in household decisions. However, although hypothesized, no significant association is found in relation to women participation in community activities. Findings from the focus group discussions are also consistent with the results from the PSM and hypothesis testing. Following the findings, the study recommends government and nongovernmental organizations to provide regular, timely and need based capacity building trainings for VSLA participants; Link VSLA participants with formal microfinance institutions; conduct regular monitoring and follow ups by either the city or sub-cities Women Children Affairs Department/offices or concerned government body; different concerned stakeholders in the city including government, nongovernmental organizations, microfinance institutions and others need to work in coordinated manner to solve the recurrent challenges of VSLA participants in Hawassa city; and finally government and/or nongovernmental organizations need to take best practices and lessons from existing VSLAs and expand the VSLA initiative to address more impoverished women in the city.

A função básica de um sistema de energia elétrica é fornecer aos seus clientes energia elétrica economicamente e tão confiável quanto possível. A importância da confiabilidade dos sistemas de energia elétrica é claramente notada quando as pessoas são confrontadas com a perda de energia elétrica, não importando se a perda provoca parada das linhas de produção ou mesmo impactos financeiros às empresas, o que pode consequentemente causar enorme impacto econômico além de situações que impactam o conforto da população. Dentro deste contexto esta tese apresenta uma metodologia para avaliação da confiabilidade de plantas de geração de energia elétrica que possibilita avaliar qualitativamente e quantitativamente a confiabilidade e disponibilidade dos principais componentes elétricos e mecânicos necessários à geração confiável de energia. A análise qualitativa foi realizada levando-se em consideração as características físicas das usinas hidroelétricas e as características construtivas das unidades geradoras para que fosse possibilitada a classificação das unidades geradoras em grupos estatisticamente significativos. A análise quantitativa foi fundamentada em métodos estatísticos de estimação e inferência e aspectos relacionados ao desempenho e disponibilidade de usinas hidroelétricas brasileiras tendo como referência os índices preconizados pelas agências regulatórias. As unidades geradoras foram modeladas através de métodos estatísticos e probabilísticos que permitem avaliar por meio de técnicas de confiabilidade a frequência e a duração das falhas além das probabilidades associadas a cada estado de falha. Os dados de falha foram obtidos por meio de bancos de dados consolidados por agentes geradores e órgãos federais responsáveis pela operação do sistema interligado nacional. Os dados representam a história operativa de grande parte das usinas hidrelétricas brasileiras operadas e despachadas de forma centralizada. A metodologia apresentada nesta tese preenche uma lacuna na existência de metodologias focadas em avaliação de confiabilidade de plantas de geração em fase de projeto, que possibilitariam a mitigação de riscos de falhas e perdas produtivas quando da operação comercial da planta de geração. / The basic function of a power system is to provide their customers electricity as economically and reliably as possible. The importance of the reliability of electric power systems is clearly noted when people are confronted with the loss of energy, no matter if the loss stops the production lines or even causes financial impacts on companies, which may consequently cause huge economic impact beyond situations that influence the comfort of the population. Within this context, this thesis presents a methodology for assessing the reliability of plants generating electricity that enables qualitatively and quantitatively evaluate the reliability and availability of key electrical and mechanical components needed to generate reliable power. Qualitative analysis was performed taking into account the physical characteristics of hydroelectric and constructive features of the generating units to which the classification was made to enable pool and cluster generating units in groups statistically significant. Quantitative analysis was based on statistical methods of estimation and inference and aspects related to performance and availability of Brazilian hydroelectric plants with reference to the indices recommended by regulatory agencies. The units were modeled using probabilistic and statistical methods for assessing, by means of reliability techniques, the frequency and duration of failures plus the probabilities associated with each state of failure. The failure data were obtained from consolidated databases by agents and federal agencies responsible for the operation of the national grid. The data represent the operational history of much of Brazil\'s hydroelectric facilities operated and dispatched centrally. The methodology presented in this thesis fills a gap in the existence of methodologies focused on reliability assessment of power plants in the design phase, which would allow the mitigation of risks of failures and production losses when the commercial operation of the generating plant.

Having a meaningful system for expressing common needs and thoughts is important for overall quality of life for students with intellectual disability and limited expressive language. The current study was conducted to evaluate whether one communication system, Proloquo2Go ($249.99) or SwiftKey Symbols (FREE), is more effective in the acquisition of targeted expressive phrases in one student with intellectual disability who exhibited expressive communication difficulties. The student was provided with instruction in both systems using task analytic instruction and system of least prompting and encouraged to use each system at different times in a single case, alternating treatment design. Results indicated that Proloquo2Go led to faster acquisition of targeted phrases, although gains were shown with both devices. Although, given the cost difference, teachers and parents may want to consider free options, like SwiftKeys, given the student made gains with this device. Future research is needed to provide generalizability of these results.

An isohedral tiling is a tiling of congruent polygons that are also transitive, which is to say the configuration of degrees of vertices around each face is identical. Regular tessellations, or tilings of congruent regular polygons, are a special case of isohedral tilings. Viewing these tilings as graphs in planes, both Euclidean and non-Euclidean, it is possible to pose various problems of enumeration on the respective graphs. In this paper, we investigate some near-regular isohedral tilings of triangles and quadrilaterals in the hyperbolic plane. For these tilings we enumerate vertices as classified by number of edges in the shortest path to a given origin, by combinatorially deriving their respective generating functions.