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Updated: Aug 26, 2026

Phase Diagram Characterization Using Magnetic Beads as Liquid Carriers
Published on: September 4, 2015
Statistical approach to the phase problem
Hongliang Xu1, Herbert A Hauptman
1Hauptman-Woodward Medical Research Institute and Department of Structural Biology, School of Medicine and Biomedical Sciences, State University of New York at Buffalo, 73 High Street, Buffalo, NY 14203, USA. xu@hwi.buffalo.edu
Abstract:
The minimal function and its minimal principle employed in the traditional Shake-and-Bake algorithm rely on the probabilistic estimates of the cosines of the structure invariants. In this paper, a novel statistical approach to the phase problem, which utilizes statistical properties of the structure invariants, is proposed. The statistical maximal function and its maximal principle are formulated, and the corresponding statistical Shake-and-Bake algorithm and its associated statistical parameter-shift procedure are proposed and tested. The test results show that the statistical approach to the phase problem is a simple, reliable, less computationally intensive and more efficient procedure for phase determination in X-ray crystallography.
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