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The patterns associated to best performances are individuated and it is shown that they correspond to non-trivial alignment to wind direction.
For screening, this creates a non-trivial alignment problem [ 11, 12].
By definition of the Rooted-HSA- r T u v, S u ′ v ′ score, it corresponds to the score of the best non-trivial alignment between T u v and S u ′ v ′, minus the root alignment cost term a l i g n v, v′).
It is shown that non-trivial alignments with respect to the wind direction arise and important performance deviations occur among the most frequent configurations.
Denote by Rooted-HSA - r T u v, S u ′ v ′ the minimum w- r cost of a non-trivial rooted alignment between T u v and S u ′ v ′.
When u and u′ are leaves, the only non-trivial rooted alignment between T u v and S u ′ v ′ contains both pairs (v, v′) and (u, u′), and therefore we get that Rooted-HSA - r T u v, S u ′ v ′ = align (u, u ′ ).
We may cover the set of all possible non-trivial rooted alignments between T u v and S u ′ v ′ by three sets: (a) alignments in which u is unmatched, (b) alignments in which u′ is unmatched, and (c) alignments in which both u and u′ are matched (note that there might be an intersection between groups (a) and (b)).
This is obviously the case in our simple example but far from trivial for an alignment of two complex POGs.
Call a rooted alignment non-trivial if it aligns at least one additional pair of nodes besides the roots.
The alignment was trivial because all sequences were of the same length and with perfect biunivocal correspondence to the 3D structure.
All sequences are from protein-coding genes and thus alignment was trivial.
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