[en] The sensitivity and dynamic range of a Shack-Hartmann wavefront sensor is enhanced when the spots produced by the lenslet array are allowed to shift more than one lenslet radius from their on-axis positions. However, this presents the problem of accurately and robustly associating the spots with their respective subapertures. This paper describes a method for sorting spots that takes advantage of the local spot position distortions to unwrap the spot pattern. The described algorithm is both simple and robust and also applicable to any lenslet array geometry that can be described as a two-dimensional lattice, including hexagonal arrays, which are shown here to be more efficient than square arrays

[en] We create a stochastic resolution of identity representation to the second-order Matsubara Green’s function (sRI-GF2) theory. Using a stochastic resolution of the Coulomb integrals, the second order Born self-energy in GF2 is decoupled and reduced to matrix products/ contractions, which reduces the computational cost from O(N⁵) to O(N³) (with N being the number of atomic orbitals). Currently, the method can be viewed as an extension to our previous work on stochastic resolution of identity second order Møller-Plesset perturbation theory [T. Y. Takeshita et al., J. Chem. Theory Comput. 13, 4605 (2017)] and offers an alternative to previous stochastic GF2 formulations [D. Neuhauser et al., J. Chem. Theory Comput. 13, 5396 (2017)]. We show that sRI-GF2 recovers the deterministic GF2 results for small systems, is computationally faster than deterministic GF2 for N > 80, and is a practical approach to describe weak correlations in systems with 10³ electrons and more.