A fundamental problem of fault-tolerant distributed computing is for the reliable processes to reach a consensus. For a synchronous distributed system of n processes with up to t crash failures and f failures actually occur, we prove using a straightforward bivalency argument that the lower bound for reaching uniform consensus is (f + 2)-rounds in the case of 0 < f ≤ t −2, and a new lower bound for early-stopping consensus is min (t + 1, f + 2)-rounds where 0 ≤ f ≤ t. Both proofs are simpler and more intuitive than the traditional methods such as backward induction. Our main contribution is that we solve the open problem of proving that bivalency can be applied to show the (f + 2)-rounds lower bound for synchronous uniform consensus. / Singapore-MIT Alliance (SMA)

This thesis studies the non-linear (Barkas) effects on stopping of fast moving molecular ions through solids. We model the solid target by a rigid lattice of positive ion cores surrounded by a gas of electrons. To model the electron gas we use a hydrodynamic model with a Thomas-Fermi-von Weizsacker expression for the internal energy. The disturbance to the charge density and velocity profile of the gas due to the intruder is assumed small and a perturbation expansion is used. The gas is assumed to be initially at rest. A derivation for the first and second order stopping force on an projectile due to the induced charge density of the target is given. Structure factors are introduced to capture the physics relating to the structure of the projectile and to allow maximum flexibility and generalization. The second order stopping force is calculated using a novel ”holepunch” integration method and is compared to other available methods. Results are obtained for the case of a dicluster of protons which are colinear with their direction of motion as well as for a dicluster of protons which are randomly oriented incident on an aluminum target and compared to the single proton case.

This thesis studies the non-linear (Barkas) effects on stopping of fast moving molecular ions through solids. We model the solid target by a rigid lattice of positive ion cores surrounded by a gas of electrons. To model the electron gas we use a hydrodynamic model with a Thomas-Fermi-von Weizsacker expression for the internal energy. The disturbance to the charge density and velocity profile of the gas due to the intruder is assumed small and a perturbation expansion is used. The gas is assumed to be initially at rest. A derivation for the first and second order stopping force on an projectile due to the induced charge density of the target is given. Structure factors are introduced to capture the physics relating to the structure of the projectile and to allow maximum flexibility and generalization. The second order stopping force is calculated using a novel ”holepunch” integration method and is compared to other available methods. Results are obtained for the case of a dicluster of protons which are colinear with their direction of motion as well as for a dicluster of protons which are randomly oriented incident on an aluminum target and compared to the single proton case.

Thesis (M.S. in Physics)--United States Naval Postgraduate School, 1959. / "Physics and Mathematics" -t.p. Includes bibliographical references (p. 39).

In prophet problems, two players with different levels of information make decisions to optimize their return from an underlying optimal stopping problem. The player with more information is called the "prophet" while the player with less information is known as the "gambler." In this thesis, as in the majority of the literature on such problems, we assume that the prophet is omniscient, and the gambler does not know future outcomes when making his decisions. Certainly, the prophet will get a better return than the gambler. But how much better? The goal of a prophet problem is to find the least upper bound on the difference (or ratio) between the prophet's return, M, and the gambler's return, V. In this thesis, we present new prophet problems where we seek the least upper bound on M-V when there is a fixed cost per observations. Most prophet problems in the literature compare M and V when prophet and gambler buy (or sell) one asset. The new prophet problems presented in Chapters 3 and 4 treat a scenario where prophet and gambler optimize their return from selling two assets, when there is a fixed cost per observation. Sharp bounds for the problems on small time horizons are given; for the n-day problem, rough bounds and a description of the distributions for the random variables that maximize M-V are presented.

Ubiquitous computing results in access to vast amounts of data, which is changing the way humans interact with each other, with computers, and with their environments. Information is literally at our fingertips with touchscreen technology, but it is not valuable until it is understood. As a result, selecting which information to use in a decision process is a challenge in the current information environment (Lu & Yuan, 2011). The purpose of this dissertation was to investigate how individual decision makers, in different decision contexts, determine when to stop collecting information given the availability of virtually unlimited information. Decision makers must make an ultimate decision, but also must make a decision that he or she has enough information to make the final decision (Browne, Pitts, & Wetherbe, 2007). In determining how much information to collect, researchers found that people engage in ‘satisficing' in order to make decisions, particularly when there is more information than it is possible to manage (Simon, 1957). A more recent elucidation of information use relies on the idea of stopping rules, identifying five common stopping rules information seekers use: mental list, representational stability, difference threshold, magnitude threshold, and single criterion (Browne et al., 2007). Prior research indicates a lack of understanding in the areas of information use (Prabha, Connaway, Olszewski, & Jenkins, 2007) and information overload (Eppler & Mengis, 2004) in Information Systems literature. Moreover, research indicates a lack of clarity in what information should be used in different decision contexts (Kowalczyk & Buxmann, 2014). The increase in the availability of information further complicates and necessitates research in this area. This dissertation seeks to fill these gaps in the literature by determining how information use changes across decision contexts and the relationships between stopping rules. Two unique methodologies were used to test the hypotheses in the conceptual model, which both contribute to research on information stopping rules. One tracks the participant during an online search, the second asks follow-up survey questions on a Likert scale. One of four search tasks (professional or personal context and a big data analytics understanding or restaurant location search) was randomly assigned to each participant. Results show different stopping rules are more useful for different decision contexts. Specifically, professional tasks are more likely to use stopping rules with an a priori decision on how much information to collect, while personal tasks encourage users to determine how much information to collect during the search process. The analysis also shows that different stopping rules have different emphases on quality and quantity of information. Specifically, representational stability requires both a high quality and quantity of information, while other stopping rules indicate a preference for one of the two. Finally, information quality and quantity ultimately have a positive relationship with decision confidence, satisfaction, and efficiency. The findings of this research are useful to practitioners and academics tackling issues with the availability of more information. As systems are designed for information search, understanding information stopping rules become increasingly important.

Estudos recentes utilizaram filtração com absorvedores de W para representar o efeito da rugosidade do ânodo. Para verificar a validade desta metodologia, neste trabalho, foram avaliados espectros de energia na faixa utilizada em radiologia diagnóstica convencional (40, 80 e 150 kV), gerados por tubos de raios X com ânodos rugosos por meio de simulações baseadas no Método de Monte Carlo. Para isto, foi desenvolvido um programa computacional com a ferramenta GEANT4, a qual simula a interação da radiação com a matéria. Neste programa, foram abordados: a modelagem geométrica do sistema, os processos físicos envolvidos e a aplicação de uma técnica de redução de variância baseada no fracionamento (splitting) de bremsstrahlung. Para a modelagem geométrica, as superfícies rugosas dos ânodos foram geradas a partir de um modelo estocástico de crescimento baseado na equação de Edwards-Wilkinson. Os ânodos foram modelados com um ângulo fixo de 16º e de material constituído de 95% de tungstênio e 5% de rênio. As superfícies dos ânodos foram geradas com rugosidades de 0,0; 0,5; 1,0; 2,0; 3,0; 4,0; 5,0 e 6,0 ?m. Também foi realizada a caracterização do feixe de radiação X pelos parâmetros da energia média e da camada semi-redutora (CSR). Estes parâmetros foram calculados numericamente a partir dos espectros de raios X gerados por simulação de Monte Carlo. Os valores das energias médias sofreram aumentos da ordem de 20 a 30% e as CSR\'s entre 11 a 25% aproximadamente, com o aumento das rugosidades, dependendo da energia máxima do espectro. A comparação entre os espectros produzidos com ânodo rugoso e os espectros gerados com a adição de filtração de W no feixe primário de radiação X mostraram que ambos alteram a forma da distribuição espectral, porém de modos distintos. Ou seja, o efeito da rugosidade é diferente do efeito da filtração. / Recent studies employed the filtration with tungsten absorbers to represent the effect of the anode roughness. To verify the validity of this method, in this work, the Monte Carlo method was used to simulate the spectra of X rays employed in conventional radiodiagnostics (40, 80 and 150 kV), generated by anode roughness. To perform this task, a computational program was developed with the GEANT4 toolkit, which simulates the interaction of radiation with matter. In this program, the geometric modeling of the system, the relevant physical processes and the application of a variance reduction technique based on bremsstrahlung splitting were implemented. In the geometric modeling, the rough surfaces of the anodes were generated from a stochastic model of roughness growth based on the Edwards-Wilkinson equation. The anodes were modeled with a fixed angle of 16º and material consisting of 95% tungsten and 5% of rhenium. The anode surfaces were generated with roughness of 0.0, 0.5, 1.0, 2.0, 3.0, 4.0, 5.0 and 6.0 ?m. The X ray spectra were characterized by the half-value layers (HVL) and mean energies. These parameters were calculated numerically from X ray spectra generated by the Monte Carlo simulation. The increase in the mean energy values was of the order of 20 to 30% and in the HVLs between 11 and 25% approximately growing with the roughness, depending on maximum energy of the spectrum. Comparison between spectra from anodes with roughness and spectra generated by adding tungsten filtration on primary X ray beam showed that both change the shape of the spectral distribution, but in different ways. In other words, the roughness effect and the filtration effect are not equivalent.

Utilizando um método de integração da área de espectros de energia, medidos a partir da combinação de técnicas de espalhamento em alvos espessos e transmissão, obtivemos a curva de perda de energia de partículas sobre absorvedores de Al, em torno do pico de Bragg, com incerteza entre 2% e 3%. Para tanto, foram realizadas duas medidas do espectro de energia de partículas , espalhadas por alvos espessos, sendo a primeira medida sem absorvedor e a segunda com o absorvedor de Al em frente ao detetor. Através da análise de porções das áreas sob os dois espectros, obtivemos uma curva, praticamente contínua, de perda de energia em função da energia das partículas. Implementamos também uma nova metodologia para a obtenção da curva de poder de freamento, diferente da tradicionalmente utilizada no método de transmissão. Inicialmente, parametrizamos uma curva de poder de freamento, obtida na literatura, utilizando uma expressão conveniente, com 6 parâmetros, que fornece o poder de freamento, em função da energia. Posteriormente, foi realizado um ajuste da curva de perda de energia, através da comparação dos valores teóricos e experimentais, e variando-se os parâmetros calculados anteriormente, através do método de mínimos quadrados, até se obter o melhor ajuste para a curva de perda de energia experimental. Deste modo, são obtidos novos parâmetros, que fornecem agora a curva de poder de freamento experimental. Os resultados obtidos foram comparados com outros resultados experimentais e também com algumas das parametrizações semi-empíricas mais comumente utilizadas. / We present in this work experimental energy loss curves for alpha particles in Al foils around the Bragg peak energy. Our method is based on an integration of the energy spectrum, combining elastic scattering in thick targets with transmission method, providing an almost continuous energy loss curve with $2-3\\%$ precision. To achieve this precision we perform two independent measurements of energy spectra. The first one consist of a traditional elastic scattering measurement in thick foil and the second one consists of adding the absorver foil in front of the detector. The energy spectrum from the second measurement shows a shift to lower energies when compared to the one obtained in the first measurement. Through the analysis of the partial areas under the spectra the energy loss curve can be obtained. We also developed a new method to obtain the corresponding experimental stopping power curve, through a global analysis of the energy loss measurements. First, the stopping power of alpha particles in Al, obtained from the literature is parametrized with a convenient six parameters expression. Then we fit the experimental energy loss curve, with the energy loss derived from the stopping power fit using a chi^2 fitting method. From this fitting procedure we obtain a new set of parameters and the experimental stopping power curve is determined. Our results are compared with other experimental data and semi-empirical parametrization found in the literature.

Utilizando um método de integração da área de espectros de energia, medidos a partir da combinação de técnicas de espalhamento em alvos espessos e transmissão, obtivemos a curva de perda de energia de partículas sobre absorvedores de Al, em torno do pico de Bragg, com incerteza entre 2% e 3%. Para tanto, foram realizadas duas medidas do espectro de energia de partículas , espalhadas por alvos espessos, sendo a primeira medida sem absorvedor e a segunda com o absorvedor de Al em frente ao detetor. Através da análise de porções das áreas sob os dois espectros, obtivemos uma curva, praticamente contínua, de perda de energia em função da energia das partículas. Implementamos também uma nova metodologia para a obtenção da curva de poder de freamento, diferente da tradicionalmente utilizada no método de transmissão. Inicialmente, parametrizamos uma curva de poder de freamento, obtida na literatura, utilizando uma expressão conveniente, com 6 parâmetros, que fornece o poder de freamento, em função da energia. Posteriormente, foi realizado um ajuste da curva de perda de energia, através da comparação dos valores teóricos e experimentais, e variando-se os parâmetros calculados anteriormente, através do método de mínimos quadrados, até se obter o melhor ajuste para a curva de perda de energia experimental. Deste modo, são obtidos novos parâmetros, que fornecem agora a curva de poder de freamento experimental. Os resultados obtidos foram comparados com outros resultados experimentais e também com algumas das parametrizações semi-empíricas mais comumente utilizadas. / We present in this work experimental energy loss curves for alpha particles in Al foils around the Bragg peak energy. Our method is based on an integration of the energy spectrum, combining elastic scattering in thick targets with transmission method, providing an almost continuous energy loss curve with $2-3\\%$ precision. To achieve this precision we perform two independent measurements of energy spectra. The first one consist of a traditional elastic scattering measurement in thick foil and the second one consists of adding the absorver foil in front of the detector. The energy spectrum from the second measurement shows a shift to lower energies when compared to the one obtained in the first measurement. Through the analysis of the partial areas under the spectra the energy loss curve can be obtained. We also developed a new method to obtain the corresponding experimental stopping power curve, through a global analysis of the energy loss measurements. First, the stopping power of alpha particles in Al, obtained from the literature is parametrized with a convenient six parameters expression. Then we fit the experimental energy loss curve, with the energy loss derived from the stopping power fit using a chi^2 fitting method. From this fitting procedure we obtain a new set of parameters and the experimental stopping power curve is determined. Our results are compared with other experimental data and semi-empirical parametrization found in the literature.

Estudos recentes utilizaram filtração com absorvedores de W para representar o efeito da rugosidade do ânodo. Para verificar a validade desta metodologia, neste trabalho, foram avaliados espectros de energia na faixa utilizada em radiologia diagnóstica convencional (40, 80 e 150 kV), gerados por tubos de raios X com ânodos rugosos por meio de simulações baseadas no Método de Monte Carlo. Para isto, foi desenvolvido um programa computacional com a ferramenta GEANT4, a qual simula a interação da radiação com a matéria. Neste programa, foram abordados: a modelagem geométrica do sistema, os processos físicos envolvidos e a aplicação de uma técnica de redução de variância baseada no fracionamento (splitting) de bremsstrahlung. Para a modelagem geométrica, as superfícies rugosas dos ânodos foram geradas a partir de um modelo estocástico de crescimento baseado na equação de Edwards-Wilkinson. Os ânodos foram modelados com um ângulo fixo de 16º e de material constituído de 95% de tungstênio e 5% de rênio. As superfícies dos ânodos foram geradas com rugosidades de 0,0; 0,5; 1,0; 2,0; 3,0; 4,0; 5,0 e 6,0 ?m. Também foi realizada a caracterização do feixe de radiação X pelos parâmetros da energia média e da camada semi-redutora (CSR). Estes parâmetros foram calculados numericamente a partir dos espectros de raios X gerados por simulação de Monte Carlo. Os valores das energias médias sofreram aumentos da ordem de 20 a 30% e as CSR\'s entre 11 a 25% aproximadamente, com o aumento das rugosidades, dependendo da energia máxima do espectro. A comparação entre os espectros produzidos com ânodo rugoso e os espectros gerados com a adição de filtração de W no feixe primário de radiação X mostraram que ambos alteram a forma da distribuição espectral, porém de modos distintos. Ou seja, o efeito da rugosidade é diferente do efeito da filtração. / Recent studies employed the filtration with tungsten absorbers to represent the effect of the anode roughness. To verify the validity of this method, in this work, the Monte Carlo method was used to simulate the spectra of X rays employed in conventional radiodiagnostics (40, 80 and 150 kV), generated by anode roughness. To perform this task, a computational program was developed with the GEANT4 toolkit, which simulates the interaction of radiation with matter. In this program, the geometric modeling of the system, the relevant physical processes and the application of a variance reduction technique based on bremsstrahlung splitting were implemented. In the geometric modeling, the rough surfaces of the anodes were generated from a stochastic model of roughness growth based on the Edwards-Wilkinson equation. The anodes were modeled with a fixed angle of 16º and material consisting of 95% tungsten and 5% of rhenium. The anode surfaces were generated with roughness of 0.0, 0.5, 1.0, 2.0, 3.0, 4.0, 5.0 and 6.0 ?m. The X ray spectra were characterized by the half-value layers (HVL) and mean energies. These parameters were calculated numerically from X ray spectra generated by the Monte Carlo simulation. The increase in the mean energy values was of the order of 20 to 30% and in the HVLs between 11 and 25% approximately growing with the roughness, depending on maximum energy of the spectrum. Comparison between spectra from anodes with roughness and spectra generated by adding tungsten filtration on primary X ray beam showed that both change the shape of the spectral distribution, but in different ways. In other words, the roughness effect and the filtration effect are not equivalent.