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Most multiple sequence alignment programs use heuristic methods rather than global optimization because identifying the optimal alignment between more than a few sequences of moderate length is prohibitively computationally expensive.
The graph representation of an MSA, that can itself be aligned directly by pairwise dynamic programming, guarantees that the optimal alignment between each pair of sequences will be considered.
In this paper, we apply a dynamic time warping (DTW) algorithm [ 21] to align the rows of matrices, which is a technique to find an optimal alignment between two given sequences.
Determining the optimal alignment between two protein structures, however, remains a hard problem.
In this work, DTW is used to obtain the optimal alignment between two sequences of points that minimizes the cumulative distance between them.
The first part is a pair-wise global alignment module that finds an optimal alignment between two sequences.
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H-GRAAL, which is a variation of GRAAL [ 15], uses the Hungarian algorithm to solve assignment problems and determine the optimal alignments between networks.
Depletion of VEGFR3 in HDLECs shifted the optimal alignment to between 10 to 20 dynesimilar similar to HUVECs.
I i, j, k) and D i, j, k) are the optimal alignment scores between the paths of the de Bruijn graph (ending at position i in contig k) and the prefix of the input reference sequence (ending at position j), ending with insertion and deletion in the alignment, respectively.
Let S i, j, k) be the optimal alignment score between all possible paths ending at position i of contig k in the input de Bruijn graph and the prefix of the input reference sequence ending at position j (i.e., t1 t2 ··· t j).
Time warping is done by finding the optimal alignment ϕ(k) between the corruption-free channel of the current segment Y i a and the corresponding channel of the match Ŷ i a (Equations 12 and 13).
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