In this article they are talking about multiply aligned sequences. But, I can't find a formal definition of that. Is it simply the fact that the sequence was multiplexed?
Multiple sequence, intuitively would just be a collection of sequences.
Multi-mapped sequences are those reads that can equally map well in multiple locations in a reference. You can think of repeat regions which can allow this (especially if the reads are much shorter than the actual repeats).
Multiplexing is adding index sequences to fragments from a sample (one per sample), so multiple samples can be pooled and sequenced as a part of single pool. Useful when sequencing capacity exceeds desired coverage per sample.
Multiple sequence alignments are simply alignments where regions of identity are arranged in such as way that identical (or conserved) bases align in a columnar fashion (gaps can be introduced as needed). These are generally used for determining relatedness of sequences or for generating a consensus from a fragment of DNA being sequenced over and over starting at different locations, which yields overlapping sequences.
Multiple sequence alignments
Cool! But what about multiply aligned sequences?
Based on the publication you linked that would be a sequence aligned to an existing multiple-sequence alignment (where differences would be expressed as regular expressions). I will need to look at the paper more closely to be sure.
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