Inferences about the coefficient of correlation in the standard bivariate normal distribution

The study of the association between two random variables that have a joint normal distribution is of interest in applied statistics; for example, in statistical genetics. This article, targeted to applied statisticians, addresses inferences about the coefficient of correlation (ρ) in the bivariate normal and standard bivariate normal distributions using likelihood, frequentist, and Baycsian perspectives. Some results are surprising. For instance, the maximum likelihood estimator and the posterior distribution of ρ in the standard bivariate normal distribution do not follow directly from results for a general bivariate normal distribution. An example employing bootstrap and rejection sampling procedures is used to illustrate some of the peculiarities.

Behavior of the PMD coefficient of optical links under influence of mechanical and thermal effects

This papers presents results on the variation of the PMD coefficient of optical links under influence of mechanical tests, such as tensile strength, bending and compression, and also during the application of a thermal cycle. Results revealed that the link coefficient is more influenced by the application of a tension load and also suffers significant variation under strong temperature changes. Copyrigth © SBMO.

The overall coefficient of the two-loop superstring amplitude using pure spinors

Using the results recently obtained for computing integrals over (non-minimal) pure spinor superspace, we compute the coefficient of the massless two-loop four-point amplitude from first principles. Contrasting with the mathematical difficulties in the RNS formalism where unknown normalizations of chiral determinant formulæ force the two-loop coefficient to be determined only indirectly through factorization, the computation in the pure spinor formalism can be smoothly carried out. © SISSA 2010.

A simple and environmentally friendly reflectometric method for the rapid quantitative analysis of captopril in pharmaceutical formulations

This paper describes a simple, environmentally friendly and rapid quantitative spot test procedure for the determination of captopril (CPT) in bulk drug and in pharmaceutical formulations by using diffuse reflectance spectroscopy. The proposed method is based on the reflectance measurements of the orange compound (λ max 490 nm) produced by the spot test reaction between CPT and p-chloranil (CL). Under optimal conditions, calibration curves were obtained for CPT by plotting the optical density of the reflectance signal (A R) vs. the log of the mol L -1 concentration, from 6.91×10 -3 to 1.17×10 -1, with a good coefficient of determination (R 2 = 0.9992). The common excipients used as additives in pharmaceuticals do not interfere in the proposed method. The method was applied to determine CPT in commercial pharmaceutical formulations. The results obtained by the proposed method are compared favorably with those obtained by an official procedure at 95% confidence level. The method validation results showed that the sensitivity and selectivity of the methods were adequated for drug monitoring in industrial quality control laboratories. © 2011 Moment Publication.

Positioning and number of nutritional levels in dose-response trials to estimate the optimal-level and the adjustment of the models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Improvement of water transport and carotenoid retention during drying of papaya by applying ultrasonic osmotic pretreatment

The effect of ultrasound and osmotic dehydration pretreatments on papaya drying kinetics was investigated. The ultrasound pretreatment was carried out in an ultrasonic bath at 30 A degrees C. The osmotic pretreatment in sucrose solution was carried out in an incubator at 34 A degrees C and agitation of 80 rpm for 210 min. The drying process was conducted in a fixed bed dryer at 70 A degrees C. Experimental data were fitted successfully using the Page model for dried fresh and pretreated fruits, with coefficient of determination greater than 0.9992 and average relative error lower that 14.4 %. The diffusional model was used to describe the moisture transfer, and the effective water diffusivity was identified in the order of 10(-9) m(2) s(-1). It was found that drying rates of osmosed fruits were the lowest due to the presence of infused solutes, while the ultrasound pretreatment contributed to faster drying rates. Evaluation of the dried fruit was performed by means of total carotenoids retention. Ultrasound treatments in distilled water prior to air-drying gave rise to dried papayas with retention of carotenoids in the range 30.4-39.8 % and the ultrasonic-assisted osmotic dehydration of papayas showed carotenoids retention values up to 64.9 %, whereas the dried fruit without pretreatment showed carotenoids retention lower than 24 %.

Productivity, stability and adaptability in open pollination progenies of Eucalyptus urophylla ST Blake

Prediction of genetic gains within breeding programs is not always compatible with those observed in practice. One reason for this inconsistency is the lack of knowledge of genotype-environment interaction (GxE). The aim of this study was to estimate genetic variation, evaluate the GxE, investigate the genetic correlation between pairs of environments and for the set, and to study the productivity, stability and adaptability at 2 years of age for diameter at breast height (DBH) in five progenies trials of Eucalyptus urophylla, used in a randomized complete block design, with the number of progenies ranging from 138 to 167, four to eight blocks and five to six plants per plot. Estimates of variance components and genetic parameters were obtained using the REML/BLUP method. For analysis of productivity, stability and adaptability, the HMRPGV method was used. The highest DBH growth was observed in Anhembi (10.52 cm) and Uberaba (10.20 cm). Estimates considered high were obtained for the coefficient of individual additive genetic variation (>13.3%) and average heritability among progenies (>0.40), indicating the possibility of obtaining genetic gains by selection among progenies. The coefficient of determination of the GxE was 1.7%, a fact that led to a high value of genotypic correlation between the performance of the progenies and environments (78.1%), indicating that the interaction is simple. The first six progenies showed a coincidence of 100% in the order of stability (HMGV), adaptability (RPGV) and productivity (HMRPGV), being 13% higher than the overall mean of five experiments (9.21 cm). When ordering the progenies, the selection of the 20 best in growth led to an increase in gain ranging of from 10.4 to 70%. Anhembi is the ideal place to have a breeding population which will be good in the other places as well.

Evaluation of measurement errors of temperature and relative humidity from HOBO data logger under different conditions of exposure to solar radiation

This study aimed to assess measurements of temperature and relative humidity obtained with HOBO a data logger, under various conditions of exposure to solar radiation, comparing them with those obtained through the use of a temperature/relative humidity probe and a copper-constantan thermocouple psychrometer, which are considered the standards for obtaining such measurements. Data were collected over a 6-day period (from 25 March to 1 April, 2010), during which the equipment was monitored continuously and simultaneously. We employed the following combinations of equipment and conditions: a HOBO data logger in full sunlight; a HOBO data logger shielded within a white plastic cup with windows for air circulation; a HOBO data logger shielded within a gill-type shelter (multi-plate prototype plastic); a copper-constantan thermocouple psychrometer exposed to natural ventilation and protected from sunlight; and a temperature/relative humidity probe under a commercial, multi-plate radiation shield. Comparisons between the measurements obtained with the various devices were made on the basis of statistical indicators: linear regression, with coefficient of determination; index of agreement; maximum absolute error; and mean absolute error. The prototype multi-plate shelter (gill-type) used in order to protect the HOBO data logger was found to provide the best protection against the effects of solar radiation on measurements of temperature and relative humidity. The precision and accuracy of a device that measures temperature and relative humidity depend on an efficient shelter that minimizes the interference caused by solar radiation, thereby avoiding erroneous analysis of the data obtained.

Estimativa da área foliar do antúrio com o uso de funções de regressão

O presente trabalho teve como objetivo determinar quais variáveis dimensionais da folha são mais adequadas para utilização na estimativa da área foliar do antúrio (Anthurium andraeanum), cv. Apalai, por meio de equação de regressão linear, e comparar o desempenho de diferentes funções de regressão obtidas com o uso de aprendizado de máquina (AM). A variável que melhor estimou a área foliar foi o produto das dimensões lineares (comprimento e largura), CxL, sendo a equação proposta Af = 0.9672 *C x L, com coeficiente de determinação (R²) de 0,99. Verificou-se, também, com o uso de AM, que as funções lineares são mais adequadas para a estimação da área foliar dessa espécie vegetal.

Modeling upper eyelid kinematics during spontaneous and reflex blinks

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Desenvolvimento e validação de modelo de previsão para mancha preta dos citros em função de variáveis meteorológicas

A mancha preta dos citros é uma doença causada pelo fungo Guignardia citricarpa que produz lesões em frutos em variedades de laranja doce comerciais, causando a queda precoce dos frutos, diminuindo a produtividade e levando a sua depreciação para o mercado de fruta fresca. O objetivo do trabalho foi desenvolver e validar um modelo de favorabilidade climática da mancha preta dos citros relacionado a ocorrência dos sintomas da doença no Estado de São Paulo. Desenvolveu-se um sistema empírico com base em um banco de dados da ocorrência da doença e das condições climáticas, em campo, nos municípios de Barretos/SP e Gavião Peixoto/SP, durante as Safras 2007/2008 e 2008/2009. A variedade de laranjeira doce utilizada nos experimentos foi a 'Valência' enxertada sobre limoeiro 'Cravo', com 10 anos de idade. Para a incidência da mancha preta foi avaliada a porcentagem de frutos com sintomas na planta e para a severidade, a porcentagem de casca lesionada por fruto. Na análise de regressão as variáveis climáticas e os dados de intensidade de doença de Barretos foram selecionados no procedimento 'stepwise'. As melhores equações de regressão foram selecionadas pelo coeficiente de determinação (R²) e pela significância da regressão no teste F (P < 0,05 e P < 0,01) que resultou na equação Y= -502,43 + 9,61 X10 + 4,78 X30 + 0,54 X46 - 7,9 X50 em que Y=Índice de Favorabilidade, X10 é a temperatura média, X30 é a umidade relativa média, X46 é o molhamento foliar e X50 é a temperatura média durante o molhamento foliar, determinados com dados de intervalos de sete dias. Procedeu-se a validação no campo no município de Gavião Peixoto durante a Safra 2008/2009, realizando a correlação entre a incidência e severidade observadas no experimento e os dados previstos que foram os determinados pela equação, sendo que a correlação mostrou-se positiva para a incidência da doença com um R²=0,87.

A simple and non-destructive model for individual leaf area estimation in citrus

Introduction. Leaf area is often related to plant growth, development, physiology and yield. Many non-destructive models have been proposed for leaf area estimation of several plant genotypes, demonstrating that leaf length, leaf width and leaf area are closely correlated. Thus, the objective of our study was to develop a reliable model for leaf area estimation from linear measurements of leaf dimensions for citrus genotypes. Materials and methods. Leaves of citrus genotypes were harvested, and their dimensions (length, width and area) were measured. Values of leaf area were regressed against length, width, the square of length, the square of width and the product (length x width). The most accurate equations, either linear or second-order polynomial, were regressed again with a new data set; then the most reliable equation was defined. Results and discussion. The first analysis showed that the variables length, width and the square of length gave better results in second-order polynomial equations, while the linear equations were more suitable and accurate when the width and the product (length x width) were used. When these equations were regressed with the new data set, the coefficient of determination (R(2)) and the agreement index 'd' were higher for the one that used the variable product (length x width), while the Mean Absolute Percentage Error was lower. Conclusion. The product of the simple leaf dimensions (length x width) can provide a reliable and simple non-destructive model for leaf area estimation across citrus genotypes.

Comparação de alguns modelos matemáticos para ajuste à curva de lactação média de um rebanho da raça Caracu

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Comparação de alguns modelos matemáticos para o ajuste às curvas de lactação individuais de vacas da raça Caracu

Foram ajustadas 7239 curvas de lactação de vacas Caracu, controladas semanalmente entre os anos de 1978 a 1988, pertencentes à Fazenda Chiqueirão, Poços de Caldas, MG. As funções utilizadas foram a linear hiperbólica (FLH), a quadrática logarítmica (FQL), a gama incompleta (FGI) e a polinomial inversa (FPI). Os parâmetros foram estimados por meio de regressões não lineares, usando-se processos iterativos. A verificação da qualidade do ajuste baseou-se no coeficiente de determinação ajustado (R²A), no teste de Durbin-Watson (DW) e nas médias e desvios-padrão estimados para os parâmetros e funções dos parâmetros dos modelos. Para a curva média, os R²A foram superiores a 0,90 para todas as funções. Bons ajustes, baseados nos R²A>0,80 foram obtidos, respectivamente, por 25,2%, 39,1%, 31,1% e 28,4% das lactações ajustadas pelas funções FLH, FQL, FGI e FPI. de acordo com o teste de DW, bons ajustes foram proporcionados para 29,4% das lactações ajustadas pela FLH, 54,9% pela FQL, 34,9% pela FGI e 29,6% pela FPI. Para ambos os critérios, a FQL foi superior às demais funções, indicando grande variação nas formas das curvas de lactação geradas pelos ajustes individuais. Curvas atípicas foram estimadas pelas funções, com picos ocorrendo antes do parto e algumas vezes após o término da lactação. Todas as funções apresentaram problemas quando ajustaram dados individuais.

Equações de predição da composição química corporal a partir do corte da 9-10-11ª costelas de bovinos castrados Nelore

Objetivou-se obter equações de regressão linear simples para estimativa da composição química corporal de novilhos Nelore a partir da composição química do corte da 9-10-11ª costelas. Foram utilizados 27 bovinos em confinamento, com 21 a 31 meses de idade e 338,0 a 503,6 kg de peso corporal. do total, foram abatidos seis animais (referência) ao início do experimento para estimativa da composição química corporal. A composição química em água, proteína, EE e cinzas foi determinada no corte da 9-10-11ª costelas e nos tecidos corporais. As equações de regressão para estimativa do peso de corpo vazio (PCVZ) a partir dos pesos de jejum (PV) e carcaça quente (PCQ) foram PCVZ = 0,8726 PV - 2,7399 e PCVZ = 1,5350 PCQ + 13,598 (R² = 0,98). O ganho de 1 kg de PCVZ correspondeu a aproximadamente 1,15 kg de PV. A porcentagem de água no corpo vazio (CVz) esteve altamente correlacionada às porcentagens de água (R² = 0,98) e EE (R² = 0,91) no corte das costelas. A equação mais indicada foi a desenvolvida a partir da porcentagem de água no corte das costelas (Sx, y = 0,46). Verificou-se alta correlação entre a porcentagem de EE no CVz e a porcentagem de EE (R² = 0,95) no corte das costelas, portanto, a equação %EE CVz = 0,9662%EE costelas + 1,5294 pode ser utilizada para estimativa da composição do CVz em EE. O mesmo ocorreu para a porcentagem de cinzas, sendo recomendada a equação %MM CVz = 0,5915%MM costelas + 0,7619 (R² = 0,88). A composição química percentual em água, EE e minerais no corte das 9-10-11ª costelas permitiu estimar com acuidade a composição do corpo vazio.