Evaluations of the beta probability integral by bayes and price

Summary The contribution of Bayes to statistical inference has been much discussed, whereas his evaluations of the beta probability integral have received little attention, and Price's improvements of these results have never been analysed in detail. It is the purpose of the present paper to redress this state of affairs and to show that the Bayes-Price approximation to the two-sided beta probability integral is considerably better than the normal approximation, which became popular under the influence of Laplace, although it had been stated by Price.The Bayes-Price results are obtained by approximating the skew beta density by a symmetric beta density times a factor tending to unity for n , the two functions having the same maximum and the same points of inflection. Since the symmetric beta density converges to the normal density, all the results of Laplace based on the normal distribution can be obtained as simple limits of the results of Bayes and Price. This fact was not observed either by Laplace or by Todhunter.     

Exogenous fibronectin modifies the aggregation of collagen-stimulated human platelets

Summary Fibronectins (FN) are adhesive glycoproteins whose role in platelet aggregation is unclear. Addition of 3, 6 and 12 g/ml of human plasma FN in vitro to isolated human platelets, which had been freed from plasma FN by gel filtration and subsequently stimulated with collagen, inhibited the last stage of platelet aggregation. With 3 and 6g/ml of FN a shortening of the lag-time was also observed. These data showed that FN may play a role in platelet-collagen interaction as well as in platelet-platelet interaction.     

Proton-induced dismutation of superoxide in aprotic media by bile pigments

Summary Cyclic voltammetry of molecular oxygen in aprotic media (dimethylformamide) and in the presence of bilirubin and other bile pigments shows that superoxide anion ( ) undergoes proton-induced dismutation. Lactam hydrogens of bile pigments are sufficiently acid to induce disproportionation to O₂ and H₂O₂. Because of its characteristic lipophilic behavior, a biological role for natural bilirubin similar to that of other non-enzymatic lipophilic scavengers of is suggested.     

Evidence from carbon isotope measurements for diverse origins of sedimentary hydrocarbons

The organic matter found in sedimentary rocks must derive from many sources; not only from ancient primary producers but also from consumers and secondary producers. In all of these organisms, isotope effects can affect the abundance and distribution of 13C in metabolites. Here, by using an improved form of a previously described technique in which the effluent of a gas chromatograph is continuously analysed isotopically, we report evidence of the diverse origins of sedimentary organic matter. The record of 13C abundances in sedimentary carbonate and total organic carbon can be interpreted in terms of variations in the global carbon cycle. Our results demonstrate, however, that isotope variations within sedimentary organic mixtures substantially exceed those observed between samples of total organic carbon. Resolution of isotope variations at the molecular level offers a new and convenient means of refining views both of localized palaeoenvironments and of control mechanisms within the global carbon cycle.     

Amino-acid synthesis in carbonaceous meteorites by aqueous alteration of polycyclic aromatic hydrocarbons

It has been suggested that amino acids and other organic compounds found in carbonaceous meteorites formed by aqueous alteration in the meteorite parent bodies. Observations of carbonaceous material in interstellar grains and interplanetary dust particles indicate that condensed organic compounds may have been present in meteorite parent bodies at the time of aqueous alteration. One group of compounds thought to be representative of this carbonaceous material is the polycyclic aromatic hydrocarbons (PAHs). Recently it was proposed that PAHs condense on SiC grains in the molecular envelopes of carbon-rich red-giant stars, which would allow for their subsequent incorporation into meteorite parent bodies during accretion. This incorporation mechanism is supported by the identification of SiC grains in carbonaceous chondrites. The possibility therefore exists that PAHs, and/or other condensed organic compounds, represent the starting material for aqueous alteration which leads to the formation of amino acids and other water-soluble organic compounds. Here we present calculations of the distribution of aqueous organic compounds in metastable equilibrium with representative PAHs as functions of the fugacities of O2, CO2 and NH3. The results reported here for pyrene and fluoranthene, two PAHs with different structures but the same stoichiometry, differ greatly but indicate that the formation of amino and carboxylic acids is energetically favourable at probable parent-body alteration conditions. The actual reaction mechanisms involved could be revealed by consideration of isotope data for PAHs, amino acids, other organic compounds and carbonates in carbonaceous chondrites.     

Innovators and contrapreneurs: Crucial alliances that connect and separate organizational change processes

This paper focuses on the coupling among alliances, relationships, management, and activities, when major strategic changes are carried out in an old organization. The paper also points out hownew alliances andchanged relationships seem to be developing in a Norwegian company. As a conclusion, we point out six elements which, according to our research, have to be present to minimize the implementation of reversible processes in organizations where organizational change processes have been implemented so that continued change can go on in the company.     

Error rates in quadratic discrimination with constraints on the covariance matrices

In multivariate discrimination of several normal populations, the optimal classification procedure is based on quadratic discriminant functions. We compare expected error rates of the quadratic classification procedure if the covariance matrices are estimated under the following four models: (i) arbitrary covariance matrices, (ii) common principal components, (iii) proportional covariance matrices, and (iv) identical covariance matrices. Using Monte Carlo simulation to estimate expected error rates, we study the performance of the four discrimination procedures for five different parameter setups corresponding to standard situations that have been used in the literature. The procedures are examined for sample sizes ranging from 10 to 60, and for two to four groups. Our results quantify the extent to which a parsimonious method reduces error rates, and demonstrate that choosing a simple method of discrimination is often beneficial even if the underlying model assumptions are wrong.The authors wish to thank the editor and three referees for their helpful comments on the first draft of this article. M. J. Schmid supported by grants no. 2.724-0.85 and 2.038-0.86 of the Swiss National Science Foundation.