Nonuniform Fourier transforms for rigid-body and multidimensional rotational correlations. The task of evaluating correlations is central to computational structural biology. The rigid-body correlation problem seeks the rigid-body transformation (R,t), R∈SO(3), t∈ℝ 3 , that maximizes the correlation between a pair of input scalar-valued functions representing molecular structures. Exhaustive solutions to the rigid-body correlation problem take advantage of the fast Fourier transform to achieve a speedup with respect to either the sought translation or rotation. We present PF corr , a new exhaustive solution, based on the nonequispaced SO(3) Fourier transform, to the rigid-body correlation problem; unlike previous solutions, ours achieves a combination of translational and rotational speedups without requiring equispaced grids. PF corr can be straightforwardly applied to a variety of problems in protein structure prediction and refinement that involve correlations under rigid-body motions of the protein. Additionally, we show how it applies, along with an appropriate flexibility model, to analogues of the above problems in which the flexibility of the protein is relevant.
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- Bajaj, Chandrajit; Bauer, Benedikt; Bettadapura, Radhakrishna; Vollrath, Antje: Nonuniform Fourier transforms for rigid-body and multidimensional rotational correlations (2013)