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In the present paper it is demonstrated that the bound electronic states of multiple quantum wells structures may be calculated very efficiently by expanding their eigenstates in terms of the eigenfunctions of a particle in a box.
By formulating an adjoint version of the optimization problem, the gradient of this cost function with respect to the excitation may be calculated very efficiently, and a straight forward gradient ascent procedure follows.
Therefore, a more pragmatic approach was followed by first identifying the most likely plausible model based on known tracer kinetics, visual inspection of the fits, and AIC results, which can be calculated very efficiently.
The eigenvectors form a set of basis functions for the analysis of the structure as a whole, allowing the global dynamic stiffness matrix to be built easily and then the forced response to be calculated very efficiently.
First, compared to other similarity measures used for comparing compound structures, Euclidean distances can be calculated very efficiently.
For the profile kernel, the matrix can be calculated very efficiently with the suffix tree-based 'kernel trick' introduced by the groups of Christina Leslie and Bill Noble Leslieetet al., 2004).
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Because of the independence of different feature dimensions, { ν ̂ d ( s ) } d = 1 D can be calculated in parallel very efficiently.
Using a compact yet accurate basis of atom-centred non-orthogonal generalised Wannier functions that are optimised in situ to their unique local chemical environment, the transmission and related properties of very large systems can be calculated efficiently and accurately.
Can a hall's aural warmth be calculated from how efficiently bass notes rebound from the same surfaces?
The FBF coefficients can be calculated efficiently using the Levinson-Durbin recursion.
Both of the expectations can be calculated efficiently (see Supplementary Material).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com