Neste trabalho analisa-se o problema do transporte do feixe de elétrons em canhões de elétrons, estruturas periódicas de ímãs permanentes e em coletores de simples e múltiplos estágios. Essa análise é de relevância em projetos de dispositivos de micro-ondas de potência dos tipos amplicador klystron e válvula TWT. Determina-se a dinâmica das partículas a partir da solução da equação da trajetória que é derivada da força de Lorentz e da conservação de energia. A equação da trajetória obtida é diferencial de segunda ordem, não-linear e independentemente do tempo para o potencial generalizado. Utiliza-se o método de Runge-Kutta de 4a Ordem para integrar a equação da trajetória das partículas. Obtém-se o potencial escalar elétrico a partir da solução da equação de Poisson. Numericamente, obtêm-se os po- tenciais escalares elétricos e magnéticos, por meio do Método de Elementos Finitos (MEF). Ao longo do movimento de uma partícula, obtida a partir da solução da equação da trajetória, deposita-se carga elétrica. Utilizam-se macropartículas, uma vez que é praticamente impossível modelar cada partícula do problema, a partir do método Partícula na Célula (Particle in Cell - PIC). Neste caso, tem-se um problema acoplado para o potencial escalar elétrico e as trajetórias das macropartículas, uma vez que, as trajetórias das macropartículas dependem dos potenciais e estes, por sua vez, dependem das trajetórias. À convergência deste problema acoplado utiliza-se o Método das Aproximações Sucessivas (MAS). A plataforma desenvolvida, baseada nos métodos acima, compõe-se de duas ferramentas computacionais. A primeira, XMGUN, dedica-se ao projeto de: canhões de elétrons com grades e grades de sombreamento; e coletores de simples e múltiplos estágios considerando, ainda, a emissão de elétrons secundários. A segunda, XMAGUN, volta-se ao projeto de estruturas periódicas com ímãs permanentes. Afere-se o desempenho da ferramenta computacional XMGUN com o diodo plano de Pierce operando na condição em que a corrente é limitada pelas cargas espaciais. Por sua vez, verica-se o desempenho do XMAGUN por meio de simulações com estruturas do tipo PPM separadas pelo vácuo e na presença de pole pieces. Os resultados obtidos em todas as simulações convergiram satisfatoriamente para as soluções analíticas. Utilizando o XMGUN, projeta-se um canhão de elétrons com 30 kV de tensão de anodo e uma perveância de 1,37 Perv com capacidade de fornecer uma corrente elétrica de 7,1 A. Esse canhão tem uma malha com 2796 elementos e 5057 nós. As principais características geométricas do canhão de elétrons são: raio do catodo rc=14,6 mm; raio do disco do catodo rk =6,2 mm; e ângulo do eletrodo de focalização = 37. Neste caso, a velocidade transversal normalizada e o alcance do feixe zw observados são de 0,068 e 26,88 mm respectivamente. Obtém-se uma concordância superior a 93% em corrente e perveância com o EGUN. Utilizando, ainda, o XMGUN, são simulados coletores de simples e múltiplos estágios. O coletor de simples estágio apresenta 1612 nós e 2969 elementos, e o de 4 (quatro) estágios, 2496 nós e 4257 elementos. As tensões dos eletrodos do 1o, 2o, 3o e 4o estágio são de 9,45 kV, 8,65 kV, 6,45 kV e 3,45 kV respectivamente. Durante as simulações, devido à emissão de elétrons secundários, observa-se, para o coletor de simples estágio, macropartículas penetrando na região de deriva, fenômeno este indesejado, e não observado para o coletor de 4 (quatro) estágios. Considerando o XMAGUN, projeta-se um arranjo periódico com pole pieces e 5 (cinco) ímãs permanentes, capaz de fornecer um campo magnético, no centro da estrutura, de 0,42 T. Neste caso, a geometria do arranjo periódico obtida é: raio interno rm1 e externo rm2 do ímã permanente são iguais a 3,5 mm e 7,5 mm respectivamente; raio externo do pole piece r3 = 7,5 mm ; raio interno rf1 e externo rf2 da ponteira do pole piece são 1,6 mm e 3,05 mm respectivamente; espessura do ímã permanente T=2,95 mm; período magnético L =8,5 mm. A remanência do ímã permanente utilizada é de Br=0,85 T. A malha dessa estrutura periódica magnética apresenta pouco mais de 20.000 nós e 40.000 elementos. / In this paper we analyze the problem of transport of the electron beam in electron guns, periodic arrays of permanent magnets and collectors of simple and multiple stages. This analysis is of relevance in the design of power microwave devices such as klystron amplier and TWT valve. The dynamics of particles is determined from the solution of the equation of the trajectory that is derived from the Lorentz force and energy conservation law. The equation of the trajectory obtained is differential of second-order, non-linear and time independent for the generalized potential. It is used the Runge-Kutta 4th order method to integrate the equation of the trajectory of the particles. The electric scalar potential is obtained from the solution of the Poisson equation. Numerically, we obtain the electric and magnetic scalar potentials, using the Finite Element Method (FEM). Throughout the motion of a particle, obtained from the solution of the equation of the trajectory, electrical charge it is deposited. Macroparticles are used, since it is virtually impossible to model each particle of the problem, based on Particle in Cell scheme (Particle in Cell - PIC). In this case, there is a coupled problem for the electric scalar potential and the trajectories of the macroparticles, since these trajectories depend on the potential and the potential, in turn, depends on the trajectories. In order to abtain the convergence of this coupled problem, it used the Method of Successive Approximations (MSA). The platform developed, based on the above methods, consists of two computational tools. The rst, XMGUN, is dedicated to the project of: electron guns with grids and shadow-grids, and collectors of simple and multiple stages, where secondary electrons emission is considered. The second, XMAGUN, is used to the design of periodic permanent magnets structures. The XMGUN was benchmarked against the plan Pierce diode under space charge limited condiction. In turn, the XMAGUN was benchmarked against PPM like structures, separated by a vacuum and in the presence of pole pieces. The results, in all simulations, converged satisfactorily to the analytical solu- tions. Using XMGUN, it is designed an electron gun with 30 kV anode voltage, 1.37 Perv capable of supplying an electric current of 7.1 A. This gun has a mesh with 2796 elements and 5057 nodes. The main geometric characteristics of the electron gun are: cathode radius rc = 14.6 mm; cathode disc radius rk = 6.2 mm; and half cone angle = 37. In this case, the normalized transverse velocity and beam-waist distance from anode zw are 0.068 and 26.88 mm respectively. An agreement above 93% in current and perveance is found when compared with EGUN. XMGUN is also used to simulate single and multi stage collectors. The single-stage collector has 1612 nodes and 2969 elements, while the 4 (four) stages collector has 2496 nodes and 4257 we elements. The collector electrode voltages of the 1st, 2nd, 3rd and 4th stage are 9.45 kV 8.65 kV 3.45 kV 6.45 kV, respectively. During the simulations, due to yield of secondary electrons, for the single stage collector, it is observed macroparticles entering into the drift region, a phenomenon unwanted, and not observed for the 4 (four) stage collector. Whereas XMAGUN is projected at a periodic arrangement with pole pieces and 5 (ve) permanent magnets, capable of providing a magnetic eld in the center of the structure was 0.42 T. In this case, the geometry of the periodic arrangement is obtained: inner and outer radius of the permanent magnet rm1 = 3.5 mm and 7.5 mm respectively rm2 =; outer radius of the pole piece r3 = 7.5 mm, internal radius and external tip of the pole piece rf1=rf2 =1.6 mm and 3.05 mm respectively; permanent magnet thickness T = 2.95 mm magnetic period L = 8.5 mm. The remanence of the permanent magnet used is Br = 0.85 T. The net periodic structure of magnetic features little more than 20,000 nodes and 40,000 elements.

Slow sand filtration is a proven and sustainable technology for drinking water treatment in small communities. The process, however, is sensitive to lower water temperatures that can lead to decreased biological treatment, and high raw water turbidity levels that can lead to premature clogging of the filter and frequent cleaning requirements, resulting in increased risk of pathogen breakthrough. Multistage filtration, consisting of roughing filtration followed by slow sand filtration, can overcome these treatment limitations and provide a robust treatment alternative for surface water sources of variable water quality in northern climates, which typically experience water temperatures ranging down to 2&deg;C. Prior to this study, however, multistage filtration had yet to be systematically challenged in colder climates, including testing of its performance under increased hydraulic loadings and elevated influent turbidity together with cold water conditions. The primary goal of this research was to demonstrate the reliability of multistage filtration for small communities in northern climates with reference to the Ontario Safe Drinking Water Act. In this research, testing was conducted on two different pilot multistage filtration systems and fed with water from the Grand River, a municipally and agriculturally impacted river in Southern Ontario. One system featured pre-ozonation and post-granular activated carbon (GAC) stages, and shallower bed depths in the roughing filter and slow sand filter. The other system featured deeper bed depths in the roughing filter and slow sand filter, two parallel roughing filters of different design for comparison, and a second stage of slow sand filtration for increased robustness. Removal of turbidity, total coliforms, and fecal coliforms under a range of influent turbidities (1 to >100 NTU), water temperatures (~2 to 20&deg;C), and hydraulic loading rates (0. 2 to 0. 8 m/h) were investigated. In addition, the slow sand filters in each pilot system were challenged with high concentrations (~10⁶ oocyst/L) of inactivated <i>Cryptosporidium parvum</i> oocysts. The performance of both pilot multistage filtration systems was highly dependent on the biological maturity of the system and its hydraulic loading rate. In a less mature system operating in cold water conditions (<5&deg;C), effluent turbidity was mostly below 0. 5 NTU during periods of stable influent turbidity (no runoff events) and a hydraulic loading of 0. 4 m/h, however, runoff events of high influent turbidity (>50 NTU), increased hydraulic loadings (0. 6 m/h), and filter cleaning occasionally resulted in effluent turbidity above 1 NTU. Furthermore, in a less mature system operating during runoff events of high turbidity, reducing the hydraulic loading rate to 0. 2 m/h was important for achieving effluent turbidity below 1 NTU. However, in a more mature system operating in warm water conditions (19-22&deg;C), effluent turbidity was consistently below 0. 3 NTU at a hydraulic loading rate of 0. 4 m/h, and below 0. 5 NTU at 0. 8 m/h, despite numerous events of high influent turbidity (>25 NTU). It remains to be seen whether this performance could be sustained in colder water temperatures with a fully mature filter. Removal of coliform bacteria was occasionally incomplete in a less mature multistage system, whereas, in a more mature system operating in warm water conditions (>9&deg;C), removal was complete in all measurements. Furthermore, the average removal of <i>Cryptosporidium</i> was greater than 2. 5 logs in both systems (with hydraulic loading rates ranging from 0. 4 to 0. 8 m/h) and improved with increased filter maturity. Each individual stage of the multistage system was an important treatment barrier in the overall process of turbidity and pathogen removal. The roughing filter was not only important for protecting the slow sand filter from solids loading and increasing its run length, but was also a significant contributor to coliform removal when the system was less mature. Removal of turbidity was significantly improved when the roughing filter was more mature, suggesting that biological treatment was an important treatment mechanism in the roughing filter. Although pre-ozonation was used mainly for the removal of organic carbon and colour, it achieved complete removal of coliform bacteria and was also suspected to be important for enhanced removal of turbidity. The second slow sand filter in series provided additional robustness to the process by reducing effluent turbidity to below 1 NTU during cold water runoff events of high turbidity and increased hydraulic loadings (0. 6 m/h), while achieving effluent below 0. 3 NTU during normal periods of operation. It also provided additional removals of coliforms under challenging operating conditions, and contributed an additional average removal of <i>Cryptosporidium</i> of 0. 8 logs, which resulted in cumulative removal of 3. 7 logs, approximately 1 log greater than all the other challenge tests. Collectively, the entire multistage system performed well with water temperatures ranging down to 2&deg;C, limited filter maturity, elevated raw water turbidities, and increased hydraulic loading rates. Its ability to meet the current Ontario turbidity regulations and greater than 2 log removal of <i>Cryptosporidium</i> over a range of operating conditions, with little or no process adjustment, is a testament to the robustness and minimal maintenance requirements of the process, which are desirable attributes for small water systems that are often located in rural areas. While this research demonstrated the performance of multistage filtration using pilot scale testing, it is important to note that full-scale plants tend to produce significantly better results than pilot facilities, due to long term biological maturation of the system. Overall, multistage filtration is a sustainable and cost-effective technology that, through this research, appears to be a safe, reliable, and robust treatment alternative for small and non-municipal water systems in North America and the developing world. Further, based on its performance with challenging influent water quality and cold water conditions, multistage filtration holds particular promise for small communities in northern climates that are required to meet safe drinking water regulations, but are dependent on surface water sources of variable water quality and temperatures.

Slow sand filtration is a proven and sustainable technology for drinking water treatment in small communities. The process, however, is sensitive to lower water temperatures that can lead to decreased biological treatment, and high raw water turbidity levels that can lead to premature clogging of the filter and frequent cleaning requirements, resulting in increased risk of pathogen breakthrough. Multistage filtration, consisting of roughing filtration followed by slow sand filtration, can overcome these treatment limitations and provide a robust treatment alternative for surface water sources of variable water quality in northern climates, which typically experience water temperatures ranging down to 2&deg;C. Prior to this study, however, multistage filtration had yet to be systematically challenged in colder climates, including testing of its performance under increased hydraulic loadings and elevated influent turbidity together with cold water conditions. The primary goal of this research was to demonstrate the reliability of multistage filtration for small communities in northern climates with reference to the Ontario Safe Drinking Water Act. In this research, testing was conducted on two different pilot multistage filtration systems and fed with water from the Grand River, a municipally and agriculturally impacted river in Southern Ontario. One system featured pre-ozonation and post-granular activated carbon (GAC) stages, and shallower bed depths in the roughing filter and slow sand filter. The other system featured deeper bed depths in the roughing filter and slow sand filter, two parallel roughing filters of different design for comparison, and a second stage of slow sand filtration for increased robustness. Removal of turbidity, total coliforms, and fecal coliforms under a range of influent turbidities (1 to >100 NTU), water temperatures (~2 to 20&deg;C), and hydraulic loading rates (0. 2 to 0. 8 m/h) were investigated. In addition, the slow sand filters in each pilot system were challenged with high concentrations (~10⁶ oocyst/L) of inactivated <i>Cryptosporidium parvum</i> oocysts. The performance of both pilot multistage filtration systems was highly dependent on the biological maturity of the system and its hydraulic loading rate. In a less mature system operating in cold water conditions (<5&deg;C), effluent turbidity was mostly below 0. 5 NTU during periods of stable influent turbidity (no runoff events) and a hydraulic loading of 0. 4 m/h, however, runoff events of high influent turbidity (>50 NTU), increased hydraulic loadings (0. 6 m/h), and filter cleaning occasionally resulted in effluent turbidity above 1 NTU. Furthermore, in a less mature system operating during runoff events of high turbidity, reducing the hydraulic loading rate to 0. 2 m/h was important for achieving effluent turbidity below 1 NTU. However, in a more mature system operating in warm water conditions (19-22&deg;C), effluent turbidity was consistently below 0. 3 NTU at a hydraulic loading rate of 0. 4 m/h, and below 0. 5 NTU at 0. 8 m/h, despite numerous events of high influent turbidity (>25 NTU). It remains to be seen whether this performance could be sustained in colder water temperatures with a fully mature filter. Removal of coliform bacteria was occasionally incomplete in a less mature multistage system, whereas, in a more mature system operating in warm water conditions (>9&deg;C), removal was complete in all measurements. Furthermore, the average removal of <i>Cryptosporidium</i> was greater than 2. 5 logs in both systems (with hydraulic loading rates ranging from 0. 4 to 0. 8 m/h) and improved with increased filter maturity. Each individual stage of the multistage system was an important treatment barrier in the overall process of turbidity and pathogen removal. The roughing filter was not only important for protecting the slow sand filter from solids loading and increasing its run length, but was also a significant contributor to coliform removal when the system was less mature. Removal of turbidity was significantly improved when the roughing filter was more mature, suggesting that biological treatment was an important treatment mechanism in the roughing filter. Although pre-ozonation was used mainly for the removal of organic carbon and colour, it achieved complete removal of coliform bacteria and was also suspected to be important for enhanced removal of turbidity. The second slow sand filter in series provided additional robustness to the process by reducing effluent turbidity to below 1 NTU during cold water runoff events of high turbidity and increased hydraulic loadings (0. 6 m/h), while achieving effluent below 0. 3 NTU during normal periods of operation. It also provided additional removals of coliforms under challenging operating conditions, and contributed an additional average removal of <i>Cryptosporidium</i> of 0. 8 logs, which resulted in cumulative removal of 3. 7 logs, approximately 1 log greater than all the other challenge tests. Collectively, the entire multistage system performed well with water temperatures ranging down to 2&deg;C, limited filter maturity, elevated raw water turbidities, and increased hydraulic loading rates. Its ability to meet the current Ontario turbidity regulations and greater than 2 log removal of <i>Cryptosporidium</i> over a range of operating conditions, with little or no process adjustment, is a testament to the robustness and minimal maintenance requirements of the process, which are desirable attributes for small water systems that are often located in rural areas. While this research demonstrated the performance of multistage filtration using pilot scale testing, it is important to note that full-scale plants tend to produce significantly better results than pilot facilities, due to long term biological maturation of the system. Overall, multistage filtration is a sustainable and cost-effective technology that, through this research, appears to be a safe, reliable, and robust treatment alternative for small and non-municipal water systems in North America and the developing world. Further, based on its performance with challenging influent water quality and cold water conditions, multistage filtration holds particular promise for small communities in northern climates that are required to meet safe drinking water regulations, but are dependent on surface water sources of variable water quality and temperatures.

This thesis includes three self-contained projects: In the first project Bidding strategies and their impact on the auctioneer's revenue in combinatorial auctions, focusing on combinatorial auctions, we propose a simple and efficient model for evaluating the value of any bundle given limited information, design bidding strategies that efficiently select desirable bundles, and evaluate the performance of different bundling strategies under various market settings. In the second project Retailer shelf-space management with promotion effects, promotional investment effects are integrated with retail store assortment decisions and shelf space allocation. An optimization model for the category shelf-space allocation incorporating promotion effects is presented. Based on the proposed model, a category shelf space allocation framework with trade allowances is presented where a multi-player Retailer Stackelberg game is introduced to model the interactions between retailer and manufacturers. In the third project Supply-chain oriented robust parameter design, we introduce the game theoretical method, commonly used in supply-chain analysis to solve potential conflicts between manufacturers at various stages. These manufacturing chain partners collaboratively decide parameter design settings of the controllable factors to make the product less sensitive to process variations.

Esta tese apresenta uma sistemática para seleção de variáveis de processo e determinação da condição ótima de operação em processos contínuos multivariados e em múltiplos estágios. O método proposto é composto por seis etapas. Um pré-tratamento nos dados é realizado após a identificação das variáveis de processo e do estabelecimento dos estágios de produção, onde são descartadas observações com valores espúrios e dados remanescentes são padronizados. Em seguida, cada estágio é modelado através de uma regressão Partial Least Squares (PLS) que associa a variável dependente daquele estágio às variáveis independentes de todos os estágios anteriores. A posterior seleção de variáveis independentes apoia-se nos coeficientes da regressão PLS; a cada interação, a variável com menor coeficiente de regressão é removida e um novo modelo PLS é gerado. O erro de predição é então avaliado e uma nova eliminação é promovida até que o número de variáveis remanescentes seja igual ao número de variáveis latentes (condição limite para geração de novos modelos PLS). O conjunto com menor erro determina as variáveis de processo mais relevantes para cada modelo. O conjunto de modelos PLS constituído pelas variáveis selecionadas é então integrado a uma programação quadrática para definição das condições de operação que minimizem o desvio entre os valores preditos e nominais das variáveis de resposta. A sistemática proposta foi validada através de dois exemplos numéricos. O primeiro utilizou dados de uma empresa do setor avícola, enquanto que o segundo apoiou-se em dados simulados. / This dissertation proposes a novel approach for process variable selection and determination of the optimal operating condition in multiple stages, multivariate continuous processes. The proposed framework relies on six steps. First, a pre-treatment of the data is carried out followed by the definition of production stages and removal of outliers. Next, each stage is modeled by a Partial Least Squares regression (PLS) which associates the dependent variable of each stage to all independent variables from previous stages. Independent variables are then iteratively selected based on PLS regression coefficients as follows: the variable with the lowest regression coefficient is removed and a new PLS model is generated. The prediction error is then evaluated and a new elimination is promoted until the number of remaining variables is equal to the number of latent variables (boundary condition for the generation of new PLS models). The subset of independent variables yielding the lowest predictive in each PLS model error is chosen. The set of PLS models consisting of the selected variables is then integrated to a quadratic programming aimed at defining the optimal operating conditions that minimize the deviation between the predicted and nominal values of response variables. The proposed approach was validated through two numerical examples. The first was applied to data from a poultry company, while the second used simulated data.

Esta tese apresenta uma sistemática para seleção de variáveis de processo e determinação da condição ótima de operação em processos contínuos multivariados e em múltiplos estágios. O método proposto é composto por seis etapas. Um pré-tratamento nos dados é realizado após a identificação das variáveis de processo e do estabelecimento dos estágios de produção, onde são descartadas observações com valores espúrios e dados remanescentes são padronizados. Em seguida, cada estágio é modelado através de uma regressão Partial Least Squares (PLS) que associa a variável dependente daquele estágio às variáveis independentes de todos os estágios anteriores. A posterior seleção de variáveis independentes apoia-se nos coeficientes da regressão PLS; a cada interação, a variável com menor coeficiente de regressão é removida e um novo modelo PLS é gerado. O erro de predição é então avaliado e uma nova eliminação é promovida até que o número de variáveis remanescentes seja igual ao número de variáveis latentes (condição limite para geração de novos modelos PLS). O conjunto com menor erro determina as variáveis de processo mais relevantes para cada modelo. O conjunto de modelos PLS constituído pelas variáveis selecionadas é então integrado a uma programação quadrática para definição das condições de operação que minimizem o desvio entre os valores preditos e nominais das variáveis de resposta. A sistemática proposta foi validada através de dois exemplos numéricos. O primeiro utilizou dados de uma empresa do setor avícola, enquanto que o segundo apoiou-se em dados simulados. / This dissertation proposes a novel approach for process variable selection and determination of the optimal operating condition in multiple stages, multivariate continuous processes. The proposed framework relies on six steps. First, a pre-treatment of the data is carried out followed by the definition of production stages and removal of outliers. Next, each stage is modeled by a Partial Least Squares regression (PLS) which associates the dependent variable of each stage to all independent variables from previous stages. Independent variables are then iteratively selected based on PLS regression coefficients as follows: the variable with the lowest regression coefficient is removed and a new PLS model is generated. The prediction error is then evaluated and a new elimination is promoted until the number of remaining variables is equal to the number of latent variables (boundary condition for the generation of new PLS models). The subset of independent variables yielding the lowest predictive in each PLS model error is chosen. The set of PLS models consisting of the selected variables is then integrated to a quadratic programming aimed at defining the optimal operating conditions that minimize the deviation between the predicted and nominal values of response variables. The proposed approach was validated through two numerical examples. The first was applied to data from a poultry company, while the second used simulated data.

Esta tese apresenta uma sistemática para seleção de variáveis de processo e determinação da condição ótima de operação em processos contínuos multivariados e em múltiplos estágios. O método proposto é composto por seis etapas. Um pré-tratamento nos dados é realizado após a identificação das variáveis de processo e do estabelecimento dos estágios de produção, onde são descartadas observações com valores espúrios e dados remanescentes são padronizados. Em seguida, cada estágio é modelado através de uma regressão Partial Least Squares (PLS) que associa a variável dependente daquele estágio às variáveis independentes de todos os estágios anteriores. A posterior seleção de variáveis independentes apoia-se nos coeficientes da regressão PLS; a cada interação, a variável com menor coeficiente de regressão é removida e um novo modelo PLS é gerado. O erro de predição é então avaliado e uma nova eliminação é promovida até que o número de variáveis remanescentes seja igual ao número de variáveis latentes (condição limite para geração de novos modelos PLS). O conjunto com menor erro determina as variáveis de processo mais relevantes para cada modelo. O conjunto de modelos PLS constituído pelas variáveis selecionadas é então integrado a uma programação quadrática para definição das condições de operação que minimizem o desvio entre os valores preditos e nominais das variáveis de resposta. A sistemática proposta foi validada através de dois exemplos numéricos. O primeiro utilizou dados de uma empresa do setor avícola, enquanto que o segundo apoiou-se em dados simulados. / This dissertation proposes a novel approach for process variable selection and determination of the optimal operating condition in multiple stages, multivariate continuous processes. The proposed framework relies on six steps. First, a pre-treatment of the data is carried out followed by the definition of production stages and removal of outliers. Next, each stage is modeled by a Partial Least Squares regression (PLS) which associates the dependent variable of each stage to all independent variables from previous stages. Independent variables are then iteratively selected based on PLS regression coefficients as follows: the variable with the lowest regression coefficient is removed and a new PLS model is generated. The prediction error is then evaluated and a new elimination is promoted until the number of remaining variables is equal to the number of latent variables (boundary condition for the generation of new PLS models). The subset of independent variables yielding the lowest predictive in each PLS model error is chosen. The set of PLS models consisting of the selected variables is then integrated to a quadratic programming aimed at defining the optimal operating conditions that minimize the deviation between the predicted and nominal values of response variables. The proposed approach was validated through two numerical examples. The first was applied to data from a poultry company, while the second used simulated data.

In this work the concept of multistage neural networks is going to be presented. The possibility of using this type of structure for pattern recognition would be discussed and examined with chosen problem from eld area. The results of experiment would be confront with other possible methods used for the problem.

A well-known fact about positional election procedures is that its ranking of m alternatives can change when some of the alternatives are removed from consideration—given a positional procedure on each of 2, 3, …, m alternatives and a collective preference order for each distinct subset of the m alternatives. Saari has established that with few exceptions, we can find a voter profile for which the collective preference order for each subset under the according positional procedure is the one given. However, Saari's results do not quantify the likelihood of finding such voter profiles. For small numbers of alternatives, William Gehrlein developed a statistical model to explore the probabilities that particular collective preference orders on subsets of alternatives can occur for large electorates. One goal of this research is to determine whether changes in the collective preference order as alternatives are removed can be considered to be the norm or an outlier for positional procedures. This dissertation extends the research headed by Gehrlein in two directions. One, I generalize his statistical model to explore probabilities for iterated election procedures. Gehrlein's model previously produced results only for three alternatives and in limited cases for four alternatives. I have extended this model to produce results for up to five alternatives, including analysis of instant-runoff voting and runoff elections. Two, Gehrlein's model required specific conditions on the probability distribution of individual voter preferences across the population. I relax this assumption so that for any probability distribution of individual voter preferences across the population, I can explore the probability that a collective preference order is inconsistent with the outcomes when alternatives are removed. These results provide a foundation for discussing the impact of removing alternatives on elections across all large electorates. I also apply these results to two recent United States elections wherein a third-party candidate received a significant share of the votes: the 1992 U.S. Presidential election and the 1998 Minnesota Gubernatorial election. Overall, my research will suggest that as the number of alternatives increases, the likelihood of finding changes in the collective preference order as alternatives are removed will approach one.

The selection of a best-subset regression model from a candidate family is a common problem that arises in many analyses. In best-subset model selection, we consider all possible subsets of regressor variables; thus, numerous candidate models may need to be fit and compared. One of the main challenges of best-subset selection arises from the size of the candidate model family: specifically, the probability of selecting an inappropriate model generally increases as the size of the family increases. For this reason, it is usually difficult to select an optimal model when best-subset selection is attempted based on a moderate to large number of regressor variables. Model selection criteria are often constructed to estimate discrepancy measures used to assess the disparity between each fitted candidate model and the generating model. The Akaike information criterion (AIC) and the corrected AIC (AICc) are designed to estimate the expected Kullback-Leibler (K-L) discrepancy. For best-subset selection, both AIC and AICc are negatively biased, and the use of either criterion will lead to overfitted models. To correct for this bias, we introduce a criterion AICi, which has a penalty term evaluated from Monte Carlo simulation. A multistage model selection procedure AICaps, which utilizes AICi, is proposed for best-subset selection. In the framework of linear regression models, the Gauss discrepancy is another frequently applied measure of proximity between a fitted candidate model and the generating model. Mallows' conceptual predictive statistic (Cp) and the modified Cp (MCp) are designed to estimate the expected Gauss discrepancy. For best-subset selection, Cp and MCp exhibit negative estimation bias. To correct for this bias, we propose a criterion CPSi that again employs a penalty term evaluated from Monte Carlo simulation. We further devise a multistage procedure, CPSaps, which selectively utilizes CPSi. In this thesis, we consider best-subset selection in two different modeling frameworks: linear models and generalized linear models. Extensive simulation studies are compiled to compare the selection behavior of our methods and other traditional model selection criteria. We also apply our methods to a model selection problem in a study of bipolar disorder.