Toxoplasma gondii (T. gondii) is an intracellular protozoan parasite. The parasite can infect all warm-blooded vertebrates. Up to 30% of the world's human population carry a Toxoplasma infection. However, the transmission dynamics of T. gondii has not been well understood, although a lot of mathematical models have been built. In this thesis, we adopt a complex life cycle model developed by Turner et al. and extend their work to include diffusion of hosts. Most of researches focus on the deterministic models. However, some scientists have reported that deterministic models sometimes are inaccurate or even inapplicable to describe reaction-diffusion systems, such as gene expression. In this case stochastic models might have qualitatively different properties than its deterministic limit. Consequently, the transmission pathways of T. gondii and potential control mechanisms are investigated by both deterministic and stochastic model by us. A stochastic algorithm due to Gillespie, based on the chemical master equation, is introduced. A compartment-based model and a Smoluchowski equation model are described to simulate the diffusion of hosts. The parameter analyses are conducted based on the reproduction number. The analyses based on the deterministic model are verified by stochastic simulation near the thresholds of the parameters. / Master of Science

The chemical master equation, formulated on the Markov assumption of underlying chemical kinetics, offers an accurate stochastic description of general chemical reaction systems on the mesoscopic scale. The chemical master equation is especially useful when formulating mathematical models of gene regulatory networks and protein-protein interaction networks, where the numbers of molecules of most species are around tens or hundreds. However, solving the master equation directly suffers from the so called "curse of dimensionality" issue. This thesis first tries to study the numerical properties of the master equation using existing numerical methods and parallel machines. Next, approximation algorithms, namely the adaptive aggregation method and the radial basis function collocation method, are proposed as new paths to resolve the "curse of dimensionality". Several numerical results are presented to illustrate the promises and potential problems of these new algorithms. Comparisons with other numerical methods like Monte Carlo methods are also included. Development and analysis of the linear Shepard algorithm and its variants, all of which could be used for high dimensional scattered data interpolation problems, are also included here, as a candidate to help solve the master equation by building surrogate models in high dimensions. / Ph. D.

<p>For agricultural soils to be perpetually productive, farmers must maintain and improve the physical, chemical, and biological properties of the soil. The loss of soil to erosion is a major challenge to soil health, contributing to farmland loss and declines in productivity. This is a long-term problem for agriculture because there is a limited amount of topsoil available. Another costly loss happens when<em> residual nitrogen is lost to leaching or carried away in runoff. This is a particular problem in the fall and winter months when fields lie fallow, and there are no plants to take up excess nitrogen. Losing nitrogen is a problem for both the nutrient content of the soil as well as a serious concern in terms of water contamination.</em><em> </em>Cover crops provide a way to at least partially address each of these and many other agronomic and soil health issues. Although there has been a steady increase in cover crop use, adoption has been relatively slow. This is likely due to a lack of economic information and understanding of the associated risk. To address this problem, field level data was gathered from farmers across central and northeastern Indiana. The data included information on cash crop yield, cover crops grown, fertilizer use, among many other variables. The sample was trimmed based on the estimated propensity to cover crop, in order to reduce selection bias. Using this data, the effect of cover crops on the mean and variation of the subsequent cash crop yield was estimated using regression analysis. This information was combined in a stochastic analysis of a farm enterprise budget. The effects of cover crops on farm finance and risk were evaluated. These final analyses provide agricultural producers with more information to make informed decisions regarding the adoption of cover crops. The information may also provide insight to policy makers, who may wish to understand more completely the private economics of cover crops. The results indicated that cover crops have the ability to provide economic benefits when grown prior to corn in our study region. These include increased yield, reduced need for nitrogen fertilizer, and increased temporal yield stability. These benefits translate into higher revenue from the sale of the grain, lower input costs, and lower risk and uncertainty. However, the results for soybeans showed cover crops had a negative, albeit statistically insignificant, effect on desirable measures. This led to lower projected revenue, higher projected costs, and increased expected risk. Even so, the average corn-soybean contribution margin with cover crops was nearly equal to the baseline scenario. Furthermore, the analysis of risk showed that the corn-soybean two-year average would be preferred by farmers with moderate to high risk aversion. The difference between the effect of cover crops in corn and soybeans may be due to differences in the crop’s inherent nitrogen needs and the difficulty of cover crop establishment after corn in the region.<br></p>

O desempenho operacional e econômico de empreendimentos de mineração é de suma importância para a sustentação dos níveis de produção demandados, sendo imprescindível um nível de governança capaz de prever e gerenciar eficazmente as incertezas e riscos inerentes ao processo de lavra, sejam eles geológicos, operacionais ou financeiros. O recente desenvolvimento de tecnologias e do conceito de \"mina do futuro\" ou \"mina autônoma\" indica a possibilidade de captura de dados através de sensores variados e do uso destes dados para geração de simulações estocásticas, para otimização tanto do ativo físico quanto do aproveitamento do recurso ou ativo mineral, minimizando riscos e custos. O planejamento estocástico de lavra vem nos últimos anos apresentando potenciais ferramentas para esse nível de gerenciamento de riscos na mineração, contudo sua resposta em diversos tipos de depósito é ainda pouco conhecida e carece de esforços de pesquisa e desenvolvimento. A presente pesquisa tem o objetivo de descrever essas abordagens probabilísticas de planejamento comparando com as tradicionais (determinísticas), definir procedimentos de aplicação desses conceitos na indústria, integrados em um sistema de gestão, quantificar seus impactos no desempenho de uma operação mineira e gerar informações para a comunidade acadêmica e técnica da indústria mineral preocupados com o futuro da mineração, quanto à aplicabilidade efetiva de técnicas como planejamento estocástico de lavra e simulação de lavra, englobando incertezas relativas ao ativo mineral e ativo físico da operação mineira. Para tanto, foi realizada inicialmente uma extensa pesquisa bibliográfica em relação ao tema proposto, destacando os pontos de maior relevância, permitindo então o desenvolvimento de uma metodologia de gestão que auxilie, de forma eficaz, o processo de tomada de decisões referentes à otimização de ativos em minas a céu aberto. Visando-se atingir tais objetivos, serão realizados testes piloto em uma mina na Província Mineral de Carajás-PA. A Mina do Sossego, em operação desde 2004, é a primeira mina de cobre da VALE, está entre as maiores minas brasileiras e será o foco do estudo da presente pesquisa. / Both operational and economic performance of mining projects are critical for sustaining the demanded production levels, being indispensable a level of governance able to predict and effectively manage the uncertainties and risks inherent to mining process such as geological, operational or financial risks. Recent developments of technologies and concepts of \"mine of the future\" or \"Autonomous mine\" indicates a possibility of on-line data acquisition by a number of sensors and the use of such data to generate stochastic simulations for optimization of equipments assets and mineral resource, minimizing risks and costs. Stochastic mining planning recently have been presenting potential tools for this level of risk management in mining, but the response of such approach in various types of deposit is still poorly understood and requires research and development efforts. This research aims to describe these probabilistic mine planning approaches comparing to traditional approaches (deterministic), to define procedures for implementation of these concepts in the industry in an integrated management system, to quantify their performance impacts of a mining operation and to generate information for the academic community and mineral industry technical staff concerned about the future of mining, as the applicability of planning techniques such as stochastic mining planning and discrete event simulation, covering uncertainties related to mineral assets and physical assets (equipments) of the mining operation. Thus, initially will be performed an extensive literature review regarding the proposed theme, highlighting the points of major relevance, thus allowing the development of a management methodology that effectively assists the decision making process regarding asset optimization in open pit mines. Aiming to achieve these goals, pilot tests will be performed at an operating mine in the Carajás Mineral Province-PA. The Sossego Mine, in operation since 2004, is the first VALE copper mine, is among the largest Brazilian mines and will be the focus of the case study of this research.

Objetivo. Desenvolvimento de uma estrutura para aplicação de simulação numérica estocástica no estudo de espalhamento de doenças em metapopulações de maneira que esta incorpore a topologia dinâmica de contatos entre as subpopulações, verificando as peculiaridades do modelo e aplicando este modelo às redes de movimentação de animais de Pernambuco para estudar o papel das feiras de animais. Método. Foi utilizado o paradigma de modelos híbridos para tratar do espalhamento de doenças nas metapopulações que, das nossas aplicações, resultou na união de duas estratégias de modelagem: Modelos Baseados no Indivíduo e o Algorítimo de Simulação Estocástica. Aplicamos os modelos híbridos em redes de movimentação de animais reais e fictícias para destacar as diferenças dos modelos híbridos com diferentes abordagens de migração (pendular e definitiva) e comparamos estes modelos com modelos clássicos de equações diferenciais. Ainda, através do pacote hybridModels, estudamos o papel das feiras de animais em cenários de epidemia de febre aftosa na rede de movimentação de animais de Pernambuco, introduzindo a doença numa feira de animais contida numa amostra da base de Guia de Trânsito Animal e calculamos a cadeia de infecção dos estabelecimentos. Resultados. Constatamos que no estudo de epidemias com o uso de modelo híbrido, a migração pendular, na média, subestima o número de animais infectados no cenário de comercialização de animais (migração defi nitiva), além de traduzir uma dinâmica de espalhamento enganosa, ignorando cenários mais complexo oferecido pela migração definitiva. Criamos o pacote hybridModels que generaliza os modelos híbridos com migração definitiva e com ele aplicamos um modelo híbrido SIR na rede de Pernambuco e verificamos que as feiras de animais de Pernambuco são potentes disseminadores de doenças transmissíveis. Conclusão. Apesar de custo computacional maior no estudo de espalhamento de doenças, a migração definitiva é o mais adequado tipo de conexão entre as subpopulações de animais de produção. Ainda, de acordo com as nossas analises, as feiras de animais estão entre os mais importantes nós na rede de movimentação de Pernambuco e devem ter lugar de destaque nas estratégias de controle e vigilância epidemiológica / Objective. Development of framework applied to stochastic numerical simulation for the study of disease spreading in metapopulations, in a way that it incorporates the dynamic topology of contacts between subpopulations, checking the framework peculiarities and applying it to the animal movement network of Pernambuco to study the role of animal markets. Method. We used hybrid models paradigm to treat disease spread in metapopulations. From our applications it has resulted in the union of two modeling strategies: Individual-based model and the Algorithm for Stochastic Simulation. We applied hybrid models in real and fictitious networks to highlight the differences between different animal movement approaches (commuting and migration) and we compared these models with classic models of differential equations. Furthermore, through the hybridModels package, we studied the role of animal markets in epidemic scenarios of Foot and Mouth Disease (FMD) in animal movement networks of Pernambuco, introducing the disease in an animal market of a sample from the Animal Transit Record of Pernambuco&rsquo;s database and calculating the contact infection chain of premises. Results. We noted that in the study of epidemics using a hybrid model, commuting can underestimates the number of infected animals in the animal trade scenario (migration), and resulting in a misleading spreading dynamic by ignoring a more complex scenario that occurs with migration. We created the hybridModels package that generalizes the hybrid models with migration, applied a SIR hybrid model to the animal movement network of Pernambuco and verified that animal markets are important disease spreaders. Conclusion. Despite its higher computational cost in the study of epidemics in animal movement networks, migration is the most suitable type of connection between subpopulations. Furthermore, animal markets of Pernambuco are among the most important nodes for disease transmission and should be considered in strategies of surveillance and disease control

Neste trabalho é apresentado um método probabilístico para avaliação do desempenho de redes de distribuição considerando incertezas na demanda das cargas e na potência gerada por sistemas distribuídos intermitentes. Os consumidores são divididos em agrupamentos por classe e faixa de consumo e a modelagem da demanda horária dos consumidores de cada agrupamento é realizada por uma lei de distribuição acumulada de probabilidade (CDF) adequada. A geração distribuída é contemplada pela consideração de fonte solar fotovoltaica. O procedimento de simulação do Método de Monte Carlo é empregado e a técnica da Joint Normal Transform é utilizada na geração de números aleatórios correlacionados, empregados na amostragem da demanda dos consumidores e da energia produzida pelos sistemas de geração distribuídos. O método proposto foi aplicado ao conhecido sistema de 13 barras do IEEE e os resultados dos indicadores de perdas na operação bem como indicadores de violação de tensão crítica e precária obtidos com o modelo probabilístico são comparados aos obtidos com o modelo determinístico convencional. É demonstrado que nem sempre a média é uma descrição suficiente para o comportamento dos componentes de redes de distribuição e que é mais adequado utilizar uma representação com intervalos de confiança para as grandezas de interesse. / This work presents a probabilistic method for performance evaluation of distribution networks considering uncertainties in load demand and power generated by intermittent distributed systems. Consumers are divided into clusters by class and consumption range, so the modeling for the hourly demand of the consumers on each cluster is performed by a suitable cumulative probability distribution (CDF). Distributed generation is considered by means of solar photovoltaic sources. The Monte Carlo Simulation (MCS) Method is employed and the Joint Normal Transform technique is applied for correlated random numbers generation, used to sample consumer demand and the energy generated by distributed generation systems. The proposed method was applied in the well-known IEEE 13 node test feeder and the results of the operation losses as well as voltage violation indices obtained by the probabilistic model are compared to those obtained with the conventional deterministic model. It is shown that the mean is not always a sufficient description for the behavior of distribution network components and that it is more appropriate to use confidence intervals for the quantities of interest.

The paper is dedicated to the modeling and the simulation of random processes and fields. Using the concept and the theory of weakly correlated functions a consistent representation of sufficiently smooth random processes will be derived. Special applications will be given with respect to the simulation of road surfaces in vehicle dynamics and to the confirmation of theoretical results with respect to the zeros of random polynomials.

Biochemical reactions make up most of the activity in a cell. There is inherent stochasticity in the kinetic behavior of biochemical reactions which in turn governs the fate of various cellular processes. In this work, the precision of a method for dimensionality reduction for stochastic modeling of biochemical reactions is evaluated. Further, a method of stochastic simulation of reaction kinetics is implemented in case of a specific biochemical network involved in maintenance of long-term potentiation (LTP), the basic substrate for learning and memory formation. The dimensionality reduction method diverges significantly from a full stochastic model in prediction the variance of the fluctuations. The application of the stochastic simulation method to LTP modeling was used to find qualitative dependence of stochastic fluctuations on reaction volume and model parameters. / text

Darbe trumpai apžvelgtos figūrų pakavimo ištakos, aprašyti keli figūrų pakavimui naudojami stochastinio modeliavimo algoritmai. Išnagrinėtas perturbacijos metodas, sukurtos dvi šiuo metodu vienetiniame kvadrate vienodus apskritimus pakuojan��ios programos, detaliai aprašyti jų algoritmai. Eksperimentiškai ištirtos programų galimybės: kiekviena programa po 30 kartų buvo pakuojami n apskritimų, kur 3 ≤ n ≤ 15 ir n = 25, 50, 75, 100. Buvo fiksuojami ir apibendrinami pakavimų rezultatai. Pastarieji lyginti tarpusavy ir kartu su Violetos Sabonienės magistriniame darbe ,,Biliardinio modeliavimo algoritmai ieškant talpiausio geometrinių figūrų pakavimo“ biliardiniu metodu atliktais pakavimo rezultatais. Prieduose pateikti programų tekstai ir skaičiavimų lentelės. / In this work are examined the sources of figure packing, described the stochastic simulation algorithms of finding the densest packing of geometric figures. Here is analysed the method of perturbation and made two programmes of equal circle packing in unit square and their algorithms are being described in detail. The possibilities of programmes were analysed experimentally: using each programme 30 times. In each experiment were packed n circles, were 3 ≤ n ≤ 15 end n = 25, 50, 75, 100. The results of packing were fixed and summarized. The latter rezults were compared between themselves and also with the results of Violeta Sabonienė master of science work “The billiarding simulation algorithms of finding the densest packing of geometric figures“. The text and the calculation charts of the program are giver in the appendices.

Fluctuations, or "noise", can play a key role in determining the behaviour of living systems. The molecular-level fluctuations that occur in genetic networks are of particular importance. Here, noisy gene expression can result in genetically identical cells displaying significant variation in phenotype, even in identical environments. This variation can act as a basis for natural selection and provide a fitness benefit to cell populations under stress. This thesis focuses on the development of new conceptual knowledge about how gene expression noise and gene network topology influence drug resistance, as well as new simulation techniques to better understand cell population dynamics. Network topology may at first seem disconnected from expression noise, but genes in a network regulate each other through their expression products. The topology of a genetic network can thus amplify or attenuate noisy inputs from the environment and influence the expression characteristics of genes serving as outputs to the network. The main body of the thesis consists of five chapters: 1. A published review article on the physical basis of cellular individuality. 2. A published article presenting a novel method for simulating the dynamics of cell populations. 3. A chapter on modeling and simulating replicative aging and competition using an object-oriented framework. 4. A published research article establishing that noise in gene expression can facilitate adaptation and drug resistance independent of mutation. 5. An article submitted for publication demonstrating that gene network topology can affect the development of drug resistance. These chapters are preceded by a comprehensive introduction that covers essential concepts and theories relevant to the work presented.