By Ibragimov I. A., Solev V. N.
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Additional info for Some analytic problems arising in the theory of stationary random processes
Example text
5a). The Wilson plot has been extended toward incommensurate crystals, then involving additional parameters for the average modulation amplitudes [7]. Intensities of individual reflections are not expected to follow the linear dependence of Eq. 5a. Instead, one expects that they cover a wide range about the average value. This property is used for the definition of normalized structure factors, E(H), which are given by the corresponding structure factor divided by the square root of the average intensity according to (Eq.
The method of charge flipping starts with a set of random phases. In each cycle the density is replaced by its negative value for all pixels with a density less than some positive threshold δ. That is, negative densities become positive and small positive densities become negative. The threshold δ is chosen as a fraction of the value of the density in the local maxima of light atoms, but it should be above the noise level as followed from the inverse Fourier transform of the observed data. Charge flipping converges to a bistable state, where the density in the low-density regions alternates between positive and negative values in consecutive cycles.
Appl. , 27, 613–621. 13. Bricogne, G. , 276, 361–423. 14. Oszlanyi, G. and Suto, A. , Sect. A, 64, 123–134. 15. Palatinus, L. and Chapuis, G. (2007) J. Appl. , 40, 786–790. 16. , and Main, P. (2006) Phase improvement by iterative density modification, in International Tables for Crystallography, vol. G. Rossmann and E. Arnold), Kluwer Academic Publishers, Dordrecht, pp. 311–324. 17. Rupp, B. (2009) Biomolecular Crystallography: Principles, Practice, and Application to Structural Biology, Garland Science, London.
