The Subcommittee has attempted to elucidate the nature of problems encountered in the definition and use of statistical descriptors as applied to crystallography and to propose procedural improvements. The report contains (a) a dictionary of statistical terms established for use by experimentalists; (b) a description of the statistical basis for refinement procedures; (c) sections dealing with defects in the physical model used for refinement, and with the choice and significance of weighting schemes; and (d) recommendations, some of which may be readily implemented, whilst others may require a long-term effort to bring them into general use.
The formal refinement methods of least-squares adjustment or difference-map analysis give atomic positions in protein structures with standard deviations which are large compared with the standard deviations of accepted molecular dimensions. This paper describes a method of adjusting the Cartesian coordinates to obtain a properly weighted fit to both the positions from the refinement and the molecular parameters. The equations which have to be solved have many unknowns but few coefficients, and an effective iterative method can be used. The results of applications of the method to insulin are summarized.
The structure of histidine hydrochloride monohydrate has been refined by three-dimensional least-squares methods. The amino acid part of the molecule is in the zwitter ion form; the imidazole ring is positively charged. The distances in the imidazole ring, combined with some previous results, are satisfactorily interpreted with the valence bond theory, and imply a carbon-nitrogen double-bond distance of 1.265 /~. All available hydrogen atoms form hydrogen bonds.
SUMMARYA series of numerical experiments on the Cray XMP/48 and on the Cray 2 investigate the robustness and economy of direct and unsymmetric conjugate gradient (CG) type methods for the solution of matrix systems arising from a 3D FEM discretization of fluid flow problems. Computations on a Boussinesq flow model problem with either ILU preconditioned or unpreconditioned unsymmetric CG methods are presented. Such experiments seem to indicate that the unpreconditioned BICG method is robust for moderately non-linear incompressible Navier-Stokes FEM discretizations and that the ILU preconditioned BICG method is very robust and more economic than an unsymmetric frontal solver when the generous memory of the Cray 2 is exploited to store both the matrix and its preconditioner. We cover some of the programming aspects of direct and iterative methods on a supercomputer and find that direct methods have advantages: the crucial CPU-consuming area of code is compact but overwhelming, and its percentage of total CPU usage is independent of the spectral properties of the matrix involved. An optimal implementation of the unsymmetric CG method is more difficult because its work is related to the spectral distribution of the matrix considered and because there is no single portion of the code that overwhelmingly dominates the CPU usuage.
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