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We derive a quantitative measure of the contributions of individual edges in the graph to the accuracy of the approximation, relative to the chosen measurement functional.
The deficiency of the approximation relative to the full process is given by taking the limit of the mean squared error (MSE) of Y ˜ − Y (equivalent to the stationary variance of Y ˜ − Y ), which, as shown in the proof of Lemma 1, is an expression of the sum over all neglected reactions.
It is shown that each entry takes the form Sij(E;ℏ)="Sij 0)(E;ℏ)(1+ℏσij(E;ℏ)) where S 0)ij(E;ℏ) is the WKB approximation relative to the modified potentialV x)+ℏ24⟨x⟩−2 and the correction terms σij satisfy |∂kEσij(E;ℏ)|⩽CkE−k for all k⩾0 and uniformly in (E,ℏ)∈ 0,E0)×(0,ℏ0) where E0,ℏ0 are small constants.
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These curated figures, modest approximations relative to national projections, illustrate some of the costs associated with public higher education in the United States.
Moreover the chosen PBLSTL probability values are approximations relative to their expected level (e.g. high, medium or low).
aLocal polynomial approximation-relative intersection of confidence intervals (for more detail see [97]).
Because the rate of malformation is relatively low, odds ratios and associated 95% confidence intervals were used as approximation for relative risk to measure the strength of the association and stability of the estimates.
That is in part because known cases can be compared with selected controls (as opposed to waiting for cases to emerge, which is required by other observational study designs) and in part because of the rare disease assumption, in which OR mathematically becomes an increasingly better approximation of relative risk as disease incidence declines.
As we have not integrated congestion control in our simulative and analytical approximation, the relative channel loads larger than 25% are overestimated.
The mean volumetric water contents explained up to 88% of active IRT values, which were a good approximation for relative differences in the spatial and temporal distribution of moisture contents.
Importantly, while free energy predictions are usually made on large collections of equilibrated structures sampled during molecular dynamics in water, we have found that a single minimized structure is a reasonable approximation if relative free energies of binding are to be calculated.
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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