Inside Cover, Volume 33, Issue 25


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Debye summation arises in computation of small and wide-angle scattering of X-rays or neutrons by molecules in solution and in powder diffraction. Its direct evaluation has quadratic cost, resulting in a computational bottleneck where such evaluation is iteratively used to predict scattering data from a structure model under refinement. On page 1981, Nail A. Gumerov, Konstantin Berlin, David Fushman, and Ramani Duraiswami present a computationally efficient summation algorithm with linear cost that avoids large global expansions, instead using a hierarchical algorithm to quickly aggregate small local expansions into a globally valid expansion, while ensuring that a user-prescribed error bound is satisfied. This significantly improves both computational complexity and accuracy over existing methods.