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Near kinematic thresholds S encodes nonperturbative information, while far from thresholds S can be computed with an expansion in operators.

We show that, similarly to the case of truss structures, these values can be computed with an equivalent deterministic approach and the stochastic model can be transformed into a nonlinear programming problem, reducing the complexity of this kind of problems.

For algorithms that rely heavily on electron repulsion integrals (ERIs), exploitation of SIMD processing requires extrinsic vectorization, i.e. the sorting of ERIs into sets with equivalent class that may be computed with an identical instruction stream.

The components can be computed with an extension of a recent approach called Group Factor Analysis.

The rank, however, can easily be computed with an O(1) operation while constructing the ancestor sets.

Then, the primary outcome will be computed with an analysis of covariance (ANCOVA), using the pre-scores as a covariate and the post-scores as the dependent variable.

The reflectance ratios of regions in the scene can be computed with a second scan of the image.

The local displacement can be computed with a particle image velocimetry algorithm (PIV).

The error rate is to be computed with a soft decision.

Thresholds T1 and T2 may be computed with a heuristic algorithm, as explained in Section 3.1.

Robust alternatives to the correlation coefficients in [6] can be computed with a weighting of gradients proportional to the inverse of (absleft( {tilde{e}_{i} } right)).