Simplex algorithms have been used to optimize for size, number and morphology of lysozyme and apoferritin crystals. This approach requires fewer experiments than the single-factor-at-a-time method or factorial designs and will be useful in conserving materials on the International Space Station. The simplex method has the possible advantage that it conserves on materials by reducing the number of experiments required to optimize a crystallization system. The process is iterative and exploratory and should allow optimum microgravity conditions to be determined which might very well be different from the optimum conditions on Earth. Because the simplex method uses simple mathematical operations to calculate the next set of crystallization conditions it will be easier for crystal growers to implement than factorial designs. Factorial experiments are based on varying all factors simultaneously at a limited number of factor levels. This results in a model that is used to determine the influence of each factor and their interactions. Factorial design experiments are especially useful at the beginning of an experimental study and as a screening tool to investigate a large number of factors. The simplex method is an optimization method which is model-independent and requires no fitting of models to data. Also, when applied to protein crystal growth the simplex method does not rely on an absolute quality score. Instead, with each iteration a comparison is made to the last experiment and the results are assigned as being "better or worse". In this study, commercially obtained apoferritin was purified from 65% monomeric apoferritin to 92% monomeric apoferritin by size exclusion chromatography. Simplex optimization found the best apoferritin crystals were obtained at 15 mg/ml apoferritin, 2.0% CdSO4, 25°C using the hanging drop vapor diffusion method of crystallization and at 24 mg/ml apoferritin, 1.5% CdSO4, 25°C using the containerless crystallization method. For lysozyme, the simplex method found the best crystals at 19 mg/ml lysozyme, 7.0% (w/v) NaCl, pH 4.0, 25°C using the hanging drop vapor diffusion method of crystallization. For both proteins, the optimum conditions were found with less than ten experiments using very little protein. Finally, we report that the factors to be considered in the successful application of this method to crystallization are the number of variables to be studied, the initial conditions, step size and analysis of crystal quality.

Two-level factorial experiments are widely used in experimental design because they are simple to construct and interpret while also being efficient. However, full factorial designs for many factors can quickly become inefficient, time consuming, or expensive and therefore fractional factorial designs are sometimes preferable since they provide information on effects of interest and can be performed in fewer experimental runs. The disadvantage of using these designs is that when using fewer experimental runs, information about effects of interest is sometimes lost. Although there are methods for selecting fractional designs so that the number of runs is minimized while the amount of information provided is maximized, sometimes the design must be augmented with a follow-up experiment to resolve ambiguities. Using a fractional factorial design augmented with an optimal follow-up design allows for many factors to be studied using only a small number of additional experimental runs, compared to the full factorial design, without a loss in the amount of information that can be gained about the effects of interest. This thesis looks at discovering regularities in the number of follow-up runs that are needed to estimate all aliased effects in the model of interest for 4-, 5-, 6-, and 7-factor resolution III and IV fractional factorial experiments. From this research it was determined that for all of the resolution IV designs, four or fewer (typically three) augmented runs would estimate all of the aliased effects in the model of interest. In comparison, all of the resolution III designs required seven or eight follow-up runs to estimate all of the aliased effects of interest. It was determined that D-optimal follow-up experiments were significantly better with respect to run size economy versus fold-over and semi-foldover designs for (i) resolution IV designs and (ii) designs with larger run sizes.

Em regiões tropicais e subtropicais, a alta intensidade da radiação solar associada aos altos valores de temperatura e umidade proporcionam condições de desconforto dentro dos aviários comerciais, afetando a sanidade e produção dos lotes de frango. Nesse sentido, o presente trabalho propôs-se avaliar dados de conforto animal em aviários construídos em escala reduzida com diferentes tipos de telhas (cerâmica e fibrocimento) e forros (A e B). Modelos lineares mistos foram utilizados objetivando-se o estudo dos índices de conforto \"entalpia específica\" (h) e \"temperatura de globo e umidade\" (ITGU). A obtenção dos modelos envolveu a escolha de efeitos aleatórios, fixos e estruturas de covariância utilizando técnicas gráficas e analíticas. Para selecionar os modelos que melhor se ajustavaram aos dados, foram utilizados testes de razão de verossimilhanças, teste Wald-F e os critérios de informação AIC e BIC, em um método de seleção top-down. Para a variável entalpia específica, não houve diferença entre os tratamentos avaliados, sendo todos representados por uma parábola que apresentou ponto máximo em 50,68 kJ.kg ar seco-1 às 13h 51min. Para a variável ITGU, houve interação entre os fatores testados, sendo a combinação telha de cerâmica e forro B a de melhor desempenho, apresentando máximo em 74,08 às 14h 21min. As análises de diagnóstico confirmaram o bom ajuste dos modelos. Era esperado que os diferentes índices de conforto gerassem conclusões equivalentes, no entanto isso não foi observado. / In tropical and subtropical regions, the high intensity of solar radiation associated with high values of temperature and humidity provide discomfort inside the commercial poultry houses, which affects animal health and production batches. Therefore, this works\'s goal is to analyse data of performance of small-scale poultry houses built with different types of tiles (ceramic and cement) and liners (A and B) in animal comfort. Linear mixed models were used aiming to study two thermal comfort indexes: specific enthalpy (h) and black globe temperature and humidity (GTHI). Model building involved choosing fixed and random effects and covariance structures using graphical and analytical techniques. To select the best model fit, likelihood ratio tests were used, as well as Walf-F tests and the AIC and BIC criteria in a top-down selection method. For the specific enthalpy variable, there was no significant difference among the treatments and all were represented by a single curve which presented a peak at 50.68 kJ.kg of dry air-1 at 13h 51min. For the variable GTHI, there was a significant interaction effect between the factors and the combination of ceramic tile and liner B provided the best performance, with a maximum of 74.08 at 14h 21min. The diagnostic tests confirmed that the models were well fitted. It was expected that the different comfort indexes would generate equivalent conclusions, however this was not observed.

Introdução: O amaranto apresenta potencial funcional devido ao seu efeito hipocolesterolemizante e alto valor nutritivo. Sua aplicação na alimentação humana pode ser ampliada pela sua utilização como uma farinha instantânea obtida a partir da extrusão termoplástica e o seu consumo poderá ter impacto na saúde pública, prevenindo doenças cardiovasculares e melhorando o estado nutricional da população. Objetivo: Avaliar os efeitos da extrusão termoplástica nas características tecnológicas da farinha de amaranto. Métodos: O amaranto foi moído, preparado e extrusado em extrusora de rosca única de acordo com um planejamento fatorial fracionário. As variáveis independentes em estudo foram: tipo de farinha (integral e desengordurada), umidade (15 por cento e 25 por cento ), temperatura na terceira zona da extrusora (120°C e 180°C) e rotação da rosca (60 por cento e 90 por cento ). Resultados: Nas condições do experimento, a variável tipo de farinha apresentou efeitos superiores aos efeitos das variáveis consideradas clássicas da extrusão como temperatura, umidade e rotação da rosca. Obteve-se farinha extrusada com alta solubilidade em água, alto grau de gelatinização, baixa viscosidade e baixa tendência à retrogradação, apresentando potencial para aplicação como um produto instantâneo e não sendo sua qualidade nutricional afetada pela extrusão. O planejamento experimental realizado pode servir como um caminho para a otimização das respostas estudadas / Introduction. Amaranth presents great potential as a functional food due to its cholesterol-lowering effect and its high nutritive value. The use of amaranth can be increased through its use as an instant flour produced by the thermoplastic extrusion process. Amaranth consumption can benefit public health by preventing cardiovascular disease and by improving the nutritional status of the population. Objective. The aim of this work was to evaluate the effect of thermoplastic extrusion on the technological characteristics of amaranth flour. Methodology. Amaranth was milled, prepared and extruded in a single-screw laboratory extruder following a fractionated factorial design. The independent variables were: type of flour (whole and defatted), moisture (15 per cent and 25 per cent ), third zone barrel temperature (120°C and 180°C) and screw speed (60 per cent and 90 per cent ). Results. The variable type of flour presented a greater effect than classic extrusion variables such as temperature, moisture and screw speed. Extruded flour with high solubility in water, high degree of gelatinization, low viscosity and low retrogradation tendency was obtained by extrusion and could be used as an instant food product. The nutritive quality of the flour was not affected by extrusion. The factorial experiment conducted in this work can be employed as a way for optimization of the dependent variables studied

Em regiões tropicais e subtropicais, a alta intensidade da radiação solar associada aos altos valores de temperatura e umidade proporcionam condições de desconforto dentro dos aviários comerciais, afetando a sanidade e produção dos lotes de frango. Nesse sentido, o presente trabalho propôs-se avaliar dados de conforto animal em aviários construídos em escala reduzida com diferentes tipos de telhas (cerâmica e fibrocimento) e forros (A e B). Modelos lineares mistos foram utilizados objetivando-se o estudo dos índices de conforto \"entalpia específica\" (h) e \"temperatura de globo e umidade\" (ITGU). A obtenção dos modelos envolveu a escolha de efeitos aleatórios, fixos e estruturas de covariância utilizando técnicas gráficas e analíticas. Para selecionar os modelos que melhor se ajustavaram aos dados, foram utilizados testes de razão de verossimilhanças, teste Wald-F e os critérios de informação AIC e BIC, em um método de seleção top-down. Para a variável entalpia específica, não houve diferença entre os tratamentos avaliados, sendo todos representados por uma parábola que apresentou ponto máximo em 50,68 kJ.kg ar seco-1 às 13h 51min. Para a variável ITGU, houve interação entre os fatores testados, sendo a combinação telha de cerâmica e forro B a de melhor desempenho, apresentando máximo em 74,08 às 14h 21min. As análises de diagnóstico confirmaram o bom ajuste dos modelos. Era esperado que os diferentes índices de conforto gerassem conclusões equivalentes, no entanto isso não foi observado. / In tropical and subtropical regions, the high intensity of solar radiation associated with high values of temperature and humidity provide discomfort inside the commercial poultry houses, which affects animal health and production batches. Therefore, this works\'s goal is to analyse data of performance of small-scale poultry houses built with different types of tiles (ceramic and cement) and liners (A and B) in animal comfort. Linear mixed models were used aiming to study two thermal comfort indexes: specific enthalpy (h) and black globe temperature and humidity (GTHI). Model building involved choosing fixed and random effects and covariance structures using graphical and analytical techniques. To select the best model fit, likelihood ratio tests were used, as well as Walf-F tests and the AIC and BIC criteria in a top-down selection method. For the specific enthalpy variable, there was no significant difference among the treatments and all were represented by a single curve which presented a peak at 50.68 kJ.kg of dry air-1 at 13h 51min. For the variable GTHI, there was a significant interaction effect between the factors and the combination of ceramic tile and liner B provided the best performance, with a maximum of 74.08 at 14h 21min. The diagnostic tests confirmed that the models were well fitted. It was expected that the different comfort indexes would generate equivalent conclusions, however this was not observed.

Introdução: O amaranto apresenta potencial funcional devido ao seu efeito hipocolesterolemizante e alto valor nutritivo. Sua aplicação na alimentação humana pode ser ampliada pela sua utilização como uma farinha instantânea obtida a partir da extrusão termoplástica e o seu consumo poderá ter impacto na saúde pública, prevenindo doenças cardiovasculares e melhorando o estado nutricional da população. Objetivo: Avaliar os efeitos da extrusão termoplástica nas características tecnológicas da farinha de amaranto. Métodos: O amaranto foi moído, preparado e extrusado em extrusora de rosca única de acordo com um planejamento fatorial fracionário. As variáveis independentes em estudo foram: tipo de farinha (integral e desengordurada), umidade (15 por cento e 25 por cento ), temperatura na terceira zona da extrusora (120°C e 180°C) e rotação da rosca (60 por cento e 90 por cento ). Resultados: Nas condições do experimento, a variável tipo de farinha apresentou efeitos superiores aos efeitos das variáveis consideradas clássicas da extrusão como temperatura, umidade e rotação da rosca. Obteve-se farinha extrusada com alta solubilidade em água, alto grau de gelatinização, baixa viscosidade e baixa tendência à retrogradação, apresentando potencial para aplicação como um produto instantâneo e não sendo sua qualidade nutricional afetada pela extrusão. O planejamento experimental realizado pode servir como um caminho para a otimização das respostas estudadas / Introduction. Amaranth presents great potential as a functional food due to its cholesterol-lowering effect and its high nutritive value. The use of amaranth can be increased through its use as an instant flour produced by the thermoplastic extrusion process. Amaranth consumption can benefit public health by preventing cardiovascular disease and by improving the nutritional status of the population. Objective. The aim of this work was to evaluate the effect of thermoplastic extrusion on the technological characteristics of amaranth flour. Methodology. Amaranth was milled, prepared and extruded in a single-screw laboratory extruder following a fractionated factorial design. The independent variables were: type of flour (whole and defatted), moisture (15 per cent and 25 per cent ), third zone barrel temperature (120°C and 180°C) and screw speed (60 per cent and 90 per cent ). Results. The variable type of flour presented a greater effect than classic extrusion variables such as temperature, moisture and screw speed. Extruded flour with high solubility in water, high degree of gelatinization, low viscosity and low retrogradation tendency was obtained by extrusion and could be used as an instant food product. The nutritive quality of the flour was not affected by extrusion. The factorial experiment conducted in this work can be employed as a way for optimization of the dependent variables studied

A k × n array with entries from a q-letter alphabet is called a t-covering array if each t × n submatrix contains amongst its columns each one of the gt different words of length t that can be produced by the q letters. In the present article we use a probabilistic approach based on an appropriate Markov chain embedding technique, to study a t-covering problem where, instead of looking at all possible t ×n submatrices, we consider only submatrices of dimension t ×n with its rows being consecutive rows of the original k × n array. Moreover, an exact formula is established for the probability distribution function of the random variable, which enumerates the number of deficient submatrices (i.e., submatrices with at least one missing word, amongst their columns), in the case of a k × n binary matrix (q = 2) obtained by realizing kn Bernoulli variables.

In studies where the response variable is measured on a ratio scale, a ratio of means or medians provides a standardized measure of effect size that is an alternative to the popular standardized mean difference. Confidence intervals for ratios of population means and medians in independent-samples designs and paired-samples designs are proposed as supplements to the independent-samples t test and paired-samples t test. The performance of the proposed confidence intervals are evaluated in a simulation study. The proposed confidence interval methods are extended to the case of a 2 × m factorial design that includes propensity score stratification and meta-analysis as special cases. R functions that implement the recommended confidence intervals are provided in the Supplemental Material file, available in the online version of this article, and are illustrated with several examples.

Fractional factorial designs are a popular choice in designing experiments for studying the effects of multiple factors simultaneously. The first step in planning an experiment is the selection of an appropriate fractional factorial design. An appro- priate design is one that has the statistical properties of interest of the experimenter and has a small number of runs. This requires that a catalog of candidate designs be available (or be possible to generate) for searching for the "good" design. In the attempt to generate the catalog of candidate designs, the problem of design isomor- phism must be addressed. Two designs are isomorphic to each other if one can be obtained from the other by some relabeling of factor labels, level labels of each factor and reordering of runs. Clearly, two isomorphic designs are statistically equivalent. Design catalogs should therefore contain only designs unique up to isomorphism. There are two computational challenges in generating such catalogs. Firstly, testing two designs for isomorphism is computationally hard due to the large number of possible relabelings, and, secondly, the number of designs increases very rapidly with the number of factors and run-size, making it impractical to compare all designs for isomorphism. In this dissertation we present a new approach for tackling both these challenging problems. We propose graph models for representing designs and use this relationship to develop efficient algorithms. We provide a new efficient iso- morphism check by modeling the fractional factorial design isomorphism problem as graph isomorphism problem. For generating the design catalogs efficiently we extend a result in graph isomorphism literature to improve the existing sequential design catalog generation algorithm. The potential of the proposed methods is reflected in the results. For 2-level regular fractional factorial designs, we could generate complete design catalogs of run sizes up to 4096 runs, while the largest designs generated in literature are 512 run designs. Moreover, compared to the next best algorithms, the computation times for our algorithm are 98% lesser in most cases. Further, the generic nature of the algorithms makes them widely applicable to a large class of designs. We give details of graph models and prove the results for two classes of designs, namely, 2-level regular fractional factorial designs and 2-level regular fractional factorial split-plot designs, and provide discussions for extensions, with graph models, for more general classes of designs.

Trata-se de uma investigação sobre a influência de alguns fatores no comportamento mecânico de misturas asfálticas densas quanto à estabilidade e à flexibilidade. Foram testados três tipos de ligantes, asfalto convencional, modificado com 4,5% de SBS e modificado com 20% de borracha reciclada de pneu; duas distribuições granulométricas do agregado, centros das faixas B e C do DNER (1997); quatro teores de ligante, escolhidos com base nos valores de volumes de vazios e espessuras de película almejados; três condições de envelhecimento a longo prazo, mistura não envelhecida, envelhecida em estufa ventilada a 85ºC por 5 dias e envelhecida por exposição ao tempo por 4 meses; e duas condições de envelhecimento a curto prazo, mistura não envelhecida e envelhecida em estufa ventilada a 135ºC por 4 horas. A técnica de planejamento e análise de experimentos fatoriais fracionários assimétricos foi utilizada para a consideração simultânea dos fatores citados. O comportamento mecânico das misturas foi avaliado através dos ensaios de resistência à tração, módulo de resiliência e fluência por compressão uniaxial estática e dinâmica. A análise de variância dos resultados permitiu a identificação dos fatores com influência significativa nas respostas dos ensaios. O modo como cada fator interferiu nas propriedades apresentadas pelas misturas foi estabelecido através da construção de modelos estatísticos de comportamento. Os resultados mostraram que a adição de modificadores ao asfalto melhora a resistência das misturas à fadiga e à deformação permanente. Os processos de envelhecimento aumentaram os módulos de resiliência das misturas mas diminuíram sua capacidade de recuperação elástica, o que significa queda de resistência à fadiga. Por outro lado, a resistência a deformações permanentes das misturas, inclusive daquelas compostas por asfaltos modificados, aumentou com o envelhecimento. / This work deals with the influence of some factors in the mechanical behavior of asphalt mixtures stability and flexibility. Three types of binders were tested, conventional one, modified with 4,5% of SBS and modified with 20% of recycled tire rubber. Two aggregate gradations were tested, center of B and C gradations of DNER (1997). Four binder contents were chosen based on the air voids and film thickness. Three types of long-term aging were tested, not aged, aged in a forced-draft oven for 5 days at 85ºC and aged through weather exposition for the period of 4 months. Two types of short-term aging were tested; not aged and aged in a forced-draft oven for 4 hours at 135ºC. The technique of design and analysis of asymmetric fractional factorial experiments was used for the simultaneous analysis of the factors. The mechanical behavior of the mixtures was evaluated based on indirect tensile strength test, resilient modulus test and static and dynamic creep tests. The results of the analysis of variance allowed the identification of factors with significant influence in the answers. The influence of the factors in the mixtures properties was established through statistical models of behavior. The results showed that modified binders improves the mixtures resistance in relation to fatigue and to permanent deformation. The aging processes increased the resilient modulus of the mixtures, but also decreased its capacity of elastic return, resulting in a lost of fatigue resistance. On the other hand, the permanent deformation resistance of the aging mixtures increased, including the mixtures with modified binders cases.