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The micro strains induced broadening in powders due to crystal imperfection and distortion was calculated using Eq. (2) [38] 38].
The strain-induced broadening in powders due to crystal imperfection and distortion was calculated using the formula, ε = β h k l 4 tan θ (11).
Strain-induced broadening due to crystal imperfection and distortion was calculated using the formula, ε = β h k l tan θ. (5).
The strain induced in powders due to crystal imperfection and distortion was calculated using the formula: ε = β hkl 4 tan θ.
The lattice distortion was calculated using the formula defined by Stokes and Wilson as ε = β/(4 tan θ), where β is the full width at half maximum of diffracted peaks and θ is the Bragg angle of the [h k l] reflection [25].
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In this case, distortion was introduced by adding Gaussian noise to the true DAG's adjacency matrix A T to obtain the prior matrix B. The distortion rate was calculated using d = Fro (A T – B /Fro(A T), where Fro A) represents the Frobenius norm of the matrix A (da Piedade et al., 2009).
Figure 4 shows a second related graph that compares the energy expenditure versus distortion (ED), where the energy per pixel was calculated using the numbers described in the previous section.
Any image distortion between the pre-treatment and post-treatment radio-graphic exposures was calculated using the crown length registrations.
Distortion of the inferred tree was assessed with the cophenetic correlation coefficient (CCCr) which was calculated using the Mantel test [ 30].
Statistical significance was calculated using R software.
Split support was calculated using SumTrees.
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