Hongliang Xu, Ph.D.
Medical Research Institute
700 Ellicott Street
Buffalo, NY 14203-1102
Mathematical and computational crystallography
My research interests lie in the area of mathematical biology, especially the development of novel mathematical models and optimal procedures for determining three-dimensional crystal structures from X-ray and neutron diffraction data. The so-called “phase problem” in crystallography is the problem of determining the phase angles of the diffracted rays. The phase information, which is lost in the diffraction experiment, is in fact recoverable from the measurable intensities alone. The methods devised to solve the phase problem are known as direct methods.
Mathematical Models for Crystallographic Phase Problem
In the minimal principle method, the crystallographic phase problem is formulated as a problem of constrained global optimization. Traditionally, a probabilistic model is used to derive the so-called cosine minimal function that plays a pivotal role for determining three-dimensional structures. We have recently established a novel statistical model and corresponding statistical minimal function based on the empirical distributions of the structure invariants. This statistical function serves as the foundation of an optimization procedure called statistical Shake-and-Bake. Favorable applications of this procedure have shown the overall improvement over the existing procedures.
Optimal Procedures for Crystallographic Computing
Crystallographic computing is one of the areas that would benefit greatly from mathematical optimization. In collaboration with Prof. Nikolaos Sahinidis (Univ. of Illinois), we are currently investigating novel procedures that combine the necessary complementary backgrounds from mathematical optimization and macromolecular crystallography. Specifically, we are developing mathematical optimization algorithms to solve the crystallographic phase problem in a reliable and efficient way. This work promises to lay the foundations of a new generation of crystallographic computing systems that will reveal structures important in the understanding of life, material science, and drug design.
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