PubMed · 5582965
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H K Moed. 1967. Constancy and contrast. 3B.. https://doi.org/10.1016/0001-6918(67)90031-5
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There are relationships among the phases and magnitudes of the structure factors that have not been extensively studied regarding their potential for enhancing procedures for structure determination. These relationships arise from a special way of writing the determinantal inequalities that form the necessary and sufficient conditions for a Fourier series to be non-negative. This particular form also lends itself readily to the development of probability measures by the use of the central limit theorem. Higher-order determinants are of interest. The relationships among the phases and magnitudes of the structure factors are algebraic relationships and the focus is on those which retain their reliability, even though the magnitudes of the structure factors contain experimental errors. The future utility of the algebraic relationships depends upon the development of suitable algorithms for solving them to obtain values for the unknown phases. One approach concerns a method for extending the range of least-squares calculations by modifying the defining equations without changing the global minima and by further altering the nature of the minimization function from time to time during the course of the least-squares calculation, while still preserving the global minima. The objective is to smooth the minimization function and alter the remaining false minima from time to time so that the minimization function is not trapped in a false minimum. Some calculations have been made that indicate the nature of the algebraic relationships among the phases and magnitudes and how the results of the calculations are benefited by having large values for the structure-factor magnitudes in the determinants.(ABSTRACT TRUNCATED AT 250 WORDS)
An analysis of possible tight packing of hydrophobic groups simultaneously at the both surfaces of beta-hyperboloid-8 was conducted. This analysis shows that the disposition of amino acid side chains at the real beta-structure's surface is unique. If we sign the mean distance between adjacent beta-strands as "a," and the mean distance along beta-strand between C alpha atoms, whose side chains are directed to one side of the beta-sheet, as "b," the ratio b/a = square root of 2 very precisely. This ratio ensures the most efficient packing of side hydrophobic groups at the outer surface of beta-hyperboloid-8, forming, at the same time, the second by efficiency packing at its inner surface.
Monte Carlo analysis is increasingly employed as a means of quantifying uncertainties in risk assessment. However, the output of any Monte Carlo analysis is extremely sensitive to the input distributions used. In this paper we present a simple set of guidelines for the selection of input distributions. The guidelines involve allocating variables with unknown distributions to appropriate distributional "classes," based on the range of possible values that could be obtained for the data and known characteristics about the behavior of the variable. If the class of distribution is not identifiable, then variables can be related to a specific distribution using goodness-of-fit techniques. If these identification schemes fail, bootstrapping techniques may be used to generate a sampled distribution from the available data. Finally, "default" distributions may be employed using analogous data if site-specific data are unavailable.