Wave functions for the methane molecule

If the potential field due to the nuclei in the methane molecule is expanded in terms of a set of spherical harmonics about the carbon nucleus, only the terms involving s, f, and higher harmonic functions differ from zero in the equilibrium configuration. Wave functions have been calculated for the equilibrium configuration, first including only the spherically symmetric s term in the potential, and secondly including both the s and the f terms. In the first calculation the complete Hartree-Fock S.C.F. wave functions were determined; in the second calculation a variation method was used to determine the best form of the wave function involving f harmonics. The resulting wave functions and electron density functions are presented and discussed

Analytical functions for the ground state potential surfaces of C3 (X 1 Σ g+) and HCN (X 1 Σ +)

Analytic functions have been obtained to represent the potential energy surfaces of C3 and HCN in their ground electronic states. These functions closely reproduce the available data on the energy, geometry, and force constants in all stable conformations, as well as data on the various dissociation products, and ab initio calculations of the energy at other conformations. The form of the resulting surfaces are portrayed in various ways and discussed briefly.

Potential energy functions for ground state surfaces of HCO and HNO

Analytical potential functions are reported for the ground state surfaces of HCO and HNO, the functions being derived from spectroscopic and ab initio data. Harmonized force fields have been deduced for the stable configurations of both molecules and vibration frequencies predicted for the metastable species COH and NOH.

A comparative evaluation of functions for partitioning nitrogen and amino acid intake between maintenance and growth in broilers

The results from three types of study with broilers, namely nitrogen (N) balance, bioassays and growth experiments, provided the data used herein. Sets of data on N balance and protein accretion (bioassay studies) were used to assess the ability of the monomolecular equation to describe the relationship between (i) N balance and amino acid (AA) intake and (ii) protein accretion and AA intake. The model estimated the levels of isoleucine, lysine, valine, threonine, methionine, total sulphur AAs and tryptophan resulting in zero balance to be 58, 59, 80, 96, 23, 85 and 32 mg/kg live weight (LW)/day, respectively. These estimates show good agreement with those obtained in previous studies. For the growth experiments, four models, specifically re-parameterized for analysing energy balance data, were evaluated for their ability to determine crude protein (CP) intake at maintenance and efficiency of utilization of CP intake for producing gain. They were: a straight line, two equations representing diminishing returns behaviour (monomolecular and rectangular hyperbola) and one equation describing smooth sigmoidal behaviour with a fixed point of inflexion (Gompertz). The estimates of CP requirement for maintenance and efficiency of utilization of CP intake for producing gain varied from 5.4 to 5.9 g/kg LW/day and 0.60 to 0.76, respectively, depending on the models.

An evaluation of different growth functions for describing the profile of live weight with time (age) in meat and egg strains of chicken

A total of 86 profiles from meat and egg strains of chickens (male and female) were used in this study. Different flexible growth functions were evaluated with regard to their ability to describe the relationship between live weight and age and were compared with the Gompertz and logistic equations, which have a fixed point of inflection. Six growth functions were used: Gompertz, logistic, Lopez, Richards, France, and von Bertalanffy. A comparative analysis was carried out based on model behavior and statistical performance. The results of this study confirmed the initial concern about the limitation of a fixed point of inflection, such as in the Gompertz equation. Therefore, consideration of flexible growth functions as an alternatives to the simpler equations (with a fixed point of inflection) for describing the relationship between live weight and age are recommended for the following reasons: they are easy to fit, they very often give a closer fit to data points because of their flexibility and therefore a smaller RSS value, than the simpler models, and they encompasses simpler models for the addition of an extra parameter, which is especially important when the behavior of a particular data set is not defined previously.

A comparative evaluation of functions for the analysis of growth in male broilers

Data from six studies with male broilers fed diets covering a wide range of energy and protein were used in the current two analyses. In the first analysis, five models, specifically re-parameterized for analysing energy balance data, were evaluated for their ability to determine metabolizable energy intake at maintenance and efficiency of utilization of metabolizable energy intake for producing gain. In addition to the straight line, two types of functional form were used. They were forms describing (i) diminishing returns behaviour (monomolecular and rectangular hyperbola) and (ii) sigmoidal behaviour with a fixed point of inflection (Gompertz and logistic). These models determined metabolizable energy requirement for maintenance to be in the range 437-573 kJ/kg of body weight/day depending on the model. The values determined for average net energy requirement for body weight gain varied from 7(.)9 to 11(.)2 kJ/g of body weight. These values show good agreement with previous studies. In the second analysis, three types of function were assessed as candidates for describing the relationship between body weight and cumulative metabolizable energy intake. The functions used were: (a) monomolecular (diminishing returns behaviour), (b) Gompertz (smooth sigmoidal behaviour with a fixed point of inflection) and (c) Lopez, France and Richards (diminishing returns and sigmoidal behaviour with a variable point of inflection). The results of this analysis demonstrated that equations capable of mimicking the law of diminishing returns describe accurately the relationship between body weight and cumulative metabolizable energy intake in broilers.

A comparative evaluation of functions for describing the relationship between live-weight gain and metabolizable energy intake in turkeys

The suitability of models specifically re-parameterized for analyzing energy balance data relating metabolizable energy intake to growth rate has recently been investigated in male broilers. In this study, the more adequate of those models was applied to growing turkeys to provide estimates of their energy needs for maintenance and growth. Three functional forms were used. They were: two equations representing diminishing returns behaviour (monomolecular and rectangular hyperbola); and one equation describing smooth sigmoidal behaviour with a fixed point of inflexion (Gompertz). The models estimated the metabolizable energy requirement for maintenance in turkeys to be 359-415 kJ/kg of live-weight/day. The predicted values of average net energy requirement for producing 1 g of gain in live-weight, between 1 and 4 times maintenance, varied from 8.7 to 10.9 kJ. These results and those previously reported for broilers are a basis for accepting the general validity of these models.

The use of early lactation milk protein content to predict subsequent fertility performance and likelihood of culling, in commercial dairy cows

A dataset of 1,846,990 completed lactation record,; was created Using milk recording data from 8,967 commercial dairy farms in the United Kingdom over a five year period. Herd-specific lactation curves describing levels of milk, Cat and protein by lactation number and month of calving were generated for each farm. The actual yield of milk and protein proportion at the first milk recording of individual cow lactations were compared with the levels taken from the lactation curves. Logistic regression analysis showed that cows production milk with a lower percentage of protein than average had a significantly lower probability of being in-calf at 100 days post calving and it significantly higher probability of being culled at the end of lactation. The culling rates derived from the studied database demonstrate the current high wastage rate of commercial dairy cows. Well of this wastage is due to involuntary culling as a result of reproductive failure.

Meta-analysis: a unifying meta-likelihood approach framing unobserved heterogeneity, study covariates, publication bias, and study quality

OBJECTIVES: This contribution provides a unifying concept for meta-analysis integrating the handling of unobserved heterogeneity, study covariates, publication bias and study quality. It is important to consider these issues simultaneously to avoid the occurrence of artifacts, and a method for doing so is suggested here. METHODS: The approach is based upon the meta-likelihood in combination with a general linear nonparametric mixed model, which lays the ground for all inferential conclusions suggested here. RESULTS: The concept is illustrated at hand of a meta-analysis investigating the relationship of hormone replacement therapy and breast cancer. The phenomenon of interest has been investigated in many studies for a considerable time and different results were reported. In 1992 a meta-analysis by Sillero-Arenas et al. concluded a small, but significant overall effect of 1.06 on the relative risk scale. Using the meta-likelihood approach it is demonstrated here that this meta-analysis is due to considerable unobserved heterogeneity. Furthermore, it is shown that new methods are available to model this heterogeneity successfully. It is argued further to include available study covariates to explain this heterogeneity in the meta-analysis at hand. CONCLUSIONS: The topic of HRT and breast cancer has again very recently become an issue of public debate, when results of a large trial investigating the health effects of hormone replacement therapy were published indicating an increased risk for breast cancer (risk ratio of 1.26). Using an adequate regression model in the previously published meta-analysis an adjusted estimate of effect of 1.14 can be given which is considerably higher than the one published in the meta-analysis of Sillero-Arenas et al. In summary, it is hoped that the method suggested here contributes further to a good meta-analytic practice in public health and clinical disciplines.

A likelihood ratio appropach to family-based association studies with covariates

We introduce a procedure for association based analysis of nuclear families that allows for dichotomous and more general measurements of phenotype and inclusion of covariate information. Standard generalized linear models are used to relate phenotype and its predictors. Our test procedure, based on the likelihood ratio, unifies the estimation of all parameters through the likelihood itself and yields maximum likelihood estimates of the genetic relative risk and interaction parameters. Our method has advantages in modelling the covariate and gene-covariate interaction terms over recently proposed conditional score tests that include covariate information via a two-stage modelling approach. We apply our method in a study of human systemic lupus erythematosus and the C-reactive protein that includes sex as a covariate.