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We represent an alignment A as a1, a2, …, a L where L is the alignment length and are the alignment state at position i.
One of the most common ways to represent an alignment is using the familiar row and column matrix format of sequence alignments using the single letter abbreviations for residues (Fig. 1).
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Figure 1 shows two such candidate trees, one representing an alignment of two short amino acid sequences and one representing a secondary structure of an RNA molecule.
Profile HMMs are probabilistic models representing an alignment of multiple amino acid sequences that are very effective at identifying related sequences [ 52].
Figure 1 shows an example of these steps, where (a) represents the input sequences, (b) represents an alignment of step (i), (c) shows the dendrogram obtained from step (ii), and (d) shows a pair-wise group-alignment in step (iii).
The first data set represents an alignment of 2522 nt positions consisting of a near complete SSU rRNA gene in combination with a segment of the LSU rRNA gene (SSU/LSU data set; Additional file 5: Figure S2).
The comparison of the two genomes is illustrated in fig. 1, which represents an alignment of the entire nucleotide sequences of the two phages, showing an identity of ≥95% over 94% of their genomes.
Wassinger et al. [ 17] noted that their test condition might not represent an exact alignment with the normal motion of subjects, which, in turn, could affect their results.
The idea of using graphs to represent a sequence alignment is old (Kruskal and Sankoff, 1983) and has been revisited regularly (Hein, 1989; Lee et al., 2002; Paten et al., 2008).
The new accounting rules highlight the efforts of the German regulator to introduce a set of accounting standards that represent an alternative to and alignment with IFRS without changing the main goals of German financial statements.
When aligning a pair of sequences, the problem can be represented by an alignment matrix.
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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