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The partial distance τ1 is calculated (line 9 in Algorithm 3).
For the node under checking, the partial distance resulted by the current path is compared with the radius.
If the partial distance is smaller than the radius, the search moves on to the children nodes on the next level.
As one of the first works, Hathaway and Bezdek [9] developed four different strategies handling incomplete data in fuzzy clustering: the whole data strategy (WDS), the partial distance strategy (PDS), the optimal completion strategy (OCS), the nearest prototype strategy (NPS) similar to OCS except for using the nearest prototypes.
The search is terminated in two cases: (a) if this partial distance is greater than the current minimum branch distance (τ1>p1) and (b) if the overall distance is beyond the current radius of the sphere decoder in the tree search phase ((τ1+d2+d3+d4+d)>radius).
A partial distance field update strategy is provided for simplex meshes therein.
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The sequence in which the sibling nodes are visited is determined according to the their partial distances in an ascending order.
A peculiar addition was a pedal-operated windscreen washer, while other more ordinary changes included a second odometer, also known as a 'trip meter', for measuring partial distances.
This algorithm employs a table of size l × l (where l = m a x S 1, | S 2 | ) to compute partial distances (see e.g., [ 34]).
Partial Procrustes distance, the square root of the summed squared Euclidean distances between homologous landmarks between each specimen and the sample average shape [65], was calculated of all of the specimens.
Finally, we obtained 22,231 models by merging the overlapping models into the same loci, linking the neighboring partial models (distance ≤ 30 bp, and in the same loci) together and linking neighboring loci (distance ≤ 10 bp) together.
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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