<p>A key problem in the origin of life is to understand how an autocatalytic, self-replicating biopolymer system may have originated from a non-living chemical system. This thesis presents mathematical and computational models that address this issue. We consider a reaction system in which monomers (nucleotides) and polymers (RNAs) can be formed by chemical reactions at a slow spontaneous rate, and can also be formed at a high rate by catalysis, if polymer catalysts (ribozymes) are present. The system has two steady states: a ‘dead’ state with a low concentration of ribozymes and a ‘living’ state with a high concentration of ribozymes. Using stochastic simulations, we show that if a small number of ribozymes is formed spontaneously, this can drive the system from the dead to the living state. In the well mixed limit, this transition occurs most easily in volumes of intermediate size. In a spatially-extended two-dimensional system with finite diffusion rate, there is an optimal diffusion rate at which the transition to life is very much faster than in the well-mixed case. We therefore argue that the origin of life is a spatially localized stochastic transition. Once life has arisen in one place by a rare stochastic event, the living state spreads deterministically through the rest of the system. We show that similar autocatalytic states can be controlled by nucleotide synthases as well as by polymerase ribozymes, and that the same mechanism can also work with recombinases, if the recombination reaction is not perfectly reversible. Chirality is introduced into the polymerization model by considering simultaneous synthesis and polymerization of left- and right-handed monomers. We show that there is a racemic non-living state and two chiral living states. In this model, the origin of life and the origin of homochirality may occur simultaneously due to the same stochastic transition.</p> / Doctor of Philosophy (PhD)

Water distribution systems are critical infrastructure systems enabling the social and economic welfare of a community. While normal failures are expected and repaired quickly, low-probability and high consequence disruptive events have potential to cause severe damage to the infrastructure and significantly reduce their performance or even stop their function altogether. Resilient infrastructure is a necessary component towards achieving resilient and sustainable communities. Resilience concepts allow improved decision making in relation with risk assessment and management in water utilities. However, in order to operationalize infrastructure resilience concepts, it is fundamental to develop practical resilience assessment methods such as the methodology and tool proposed in this research, named Effective Resilience Assessment Methodology for Utilities (ERASMUS). ERASMUS utilizes a stochastic simulation model to evaluate the probability of resilient response from a water distribution system in case of disruption. This methodology utilizes a parametric concept of resilience, in which a resilient infrastructure system is defined in terms of a set of performance parameters compared with their socially acceptable values under a variety of disruptive events. The methodology is applied to two actual water distribution networks in the East and West coasts of the US. / Ph. D.

Stochastic effects in cellular systems are usually modeled and simulated with Gillespie's stochastic simulation algorithm (SSA), which follows the same theoretical derivation as the chemical master equation (CME), but the low efficiency of SSA limits its application to large chemical networks. To improve efficiency of stochastic simulations, Haseltine and Rawlings proposed a hybrid of ODE and SSA algorithm, which combines ordinary differential equations (ODEs) for traditional deterministic models and SSA for stochastic models. In this dissertation, accuracy analysis, efficient implementation strategies, and application of of Haseltine and Rawlings's hybrid method (HR) to a budding yeast cell cycle model are discussed. Accuracy of the hybrid method HR is studied based on a linear chain reaction system, motivated from the modeling practice used for the budding yeast cell cycle control mechanism. Mathematical analysis and numerical results both show that the hybrid method HR is accurate if either numbers of molecules of reactants in fast reactions are above certain thresholds, or rate constants of fast reactions are much larger than rate constants of slow reactions. Our analysis also shows that the hybrid method HR allows for a much greater region in system parameter space than those for the slow scale SSA (ssSSA) and the stochastic quasi steady state assumption (SQSSA) method. Implementation of the hybrid method HR requires a stiff ODE solver for numerical integration and an efficient event-handling strategy for slow reaction firings. In this dissertation, an event-handling strategy is developed based on inverse interpolation. Performances of five wildly used stiff ODE solvers are measured in three numerical experiments. Furthermore, inspired by the strategy of the hybrid method HR, a hybrid of ODE and SSA stochastic models for the budding yeast cell cycle is developed, based on a deterministic model in the literature. Simulation results of this hybrid model match very well with biological experimental data, and this model is the first to do so with these recently available experimental data. This study demonstrates that the hybrid method HR has great potential for stochastic modeling and simulation of large biochemical networks. / Ph. D.

Numerous challenges arise in modeling and simulation as biochemical networks are discovered with increasing complexities and unknown mechanisms. With the improvement in experimental techniques, biologists are able to quantify genes and proteins and their dynamics in a single cell, which calls for quantitative stochastic models for gene and protein networks at cellular levels that match well with the data and account for cellular noise. This dissertation studies a stochastic spatiotemporal model of the Caulobacter crescentus cell cycle. A two-dimensional model based on a Turing mechanism is investigated to illustrate the bipolar localization of the protein PopZ. However, stochastic simulations are often impeded by expensive computational cost for large and complex biochemical networks. The hybrid stochastic simulation algorithm is a combination of differential equations for traditional deterministic models and Gillespie's algorithm (SSA) for stochastic models. The hybrid method can significantly improve the efficiency of stochastic simulations for biochemical networks with multiscale features, which contain both species populations and reaction rates with widely varying magnitude. The populations of some reactant species might be driven negative if they are involved in both deterministic and stochastic systems. This dissertation investigates the negativity problem of the hybrid method, proposes several remedies, and tests them with several models including a realistic biological system. As a key factor that affects the quality of biological models, parameter estimation in stochastic models is challenging because the amount of empirical data must be large enough to obtain statistically valid parameter estimates. To optimize system parameters, a quasi-Newton algorithm for stochastic optimization (QNSTOP) was studied and applied to a stochastic budding yeast cell cycle model by matching multivariate probability distributions between simulated results and empirical data. Furthermore, to reduce model complexity, this dissertation simplifies the fundamental cooperative binding mechanism by a stochastic Hill equation model with optimized system parameters. Considering that many parameter vectors generate similar system dynamics and results, this dissertation proposes a general α-β-γ rule to return an acceptable parameter region of the stochastic Hill equation based on QNSTOP. Different objective functions are explored targeting different features of the empirical data. / Doctor of Philosophy / Modeling and simulation of biochemical networks faces numerous challenges as biochemical networks are discovered with increased complexity and unknown mechanisms. With improvement in experimental techniques, biologists are able to quantify genes and proteins and their dynamics in a single cell, which calls for quantitative stochastic models, or numerical models based on probability distributions, for gene and protein networks at cellular levels that match well with the data and account for randomness. This dissertation studies a stochastic model in space and time of a bacterium’s life cycle— Caulobacter. A two-dimensional model based on a natural pattern mechanism is investigated to illustrate the changes in space and time of a key protein population. However, stochastic simulations are often complicated by the expensive computational cost for large and sophisticated biochemical networks. The hybrid stochastic simulation algorithm is a combination of traditional deterministic models, or analytical models with a single output for a given input, and stochastic models. The hybrid method can significantly improve the efficiency of stochastic simulations for biochemical networks that contain both species populations and reaction rates with widely varying magnitude. The populations of some species may become negative in the simulation under some circumstances. This dissertation investigates negative population estimates from the hybrid method, proposes several remedies, and tests them with several cases including a realistic biological system. As a key factor that affects the quality of biological models, parameter estimation in stochastic models is challenging because the amount of observed data must be large enough to obtain valid results. To optimize system parameters, the quasi-Newton algorithm for stochastic optimization (QNSTOP) was studied and applied to a stochastic (budding) yeast life cycle model by matching different distributions between simulated results and observed data. Furthermore, to reduce model complexity, this dissertation simplifies the fundamental molecular binding mechanism by the stochastic Hill equation model with optimized system parameters. Considering that many parameter vectors generate similar system dynamics and results, this dissertation proposes a general α-β-γ rule to return an acceptable parameter region of the stochastic Hill equation based on QNSTOP. Different optimization strategies are explored targeting different features of the observed data.

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.