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The primary distance measurement is the RMSD of atomic positions.
Similar statistical significance was obtained for all primary distance separations from 1 to 30 (p<1×10−307, separate K-S tests for each minimum primary distance).
Example molecular distance distributions (for the 10 and 30 primary distance minimums) are given in the supplemental data (Figure S2).
Using the known primary distance estimates, it is possible, by a simple subtraction, to derive an estimate of the distance between A and the secondary neighbours.
Residues within an α-helix exhibited a strong peak at 3 and 4 amino acids primary distance, coincident with the first turn of an alpha-helix (3.6 amino acids, first dashed line in Figure 4B).
For increasing minimum primary distance thresholds from 1 through 6, a moderate decrease in the difference between the median coevolving distances and the median for all sites was observed (Figure 4D, dashed line).
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This avoids computing the primary distances among all units using Floyd's algorithm, whose time complexity is O(n3).
The first step consists in generating a large number of alternative, mathematically equivalent partitions of the network using the distances among the units (primary distances, according to our nomenclature) and conventional (e. g. average linkage) hierarchical clustering.
The propensity to coevolve quickly died off for primary distances past 4 amino acids, probably because subsequent helix turns become further and further away from each other in the molecular structure.
This has an important consequence, given that, if we fix AC = 100, UVCluster-based iterative hierarchical clustering can be performed using the adjacency matrix of the network instead of the matrix of primary distances.
Secondary distances, obtained by weighting the 10000 alternative trees, have clear advantages over primary distances [ 15].
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