Sequence alignment is a fundamental task in molecular biology. The primary objective of biological sequence alignment is to find positions in the sequences that are homologous. Homologous means that the symbols at those positions have been derived from the same position in a some anchestral sequence.
Today, the first lecture introduced three ways to represent squence alignments: two-row representations with inserted blanks, edit strings over the alphabet with H, D, and I, and paths in alignnment graphs. After this, scorings schemes were considered consisting of 33 parameters. Then the algebraic-statistical analogue was pictured that amounts to the pair hidden Markov model. Finally, the tropical algebra was defined and the mapping between the tropical algebra and the natural semiring of the non-negative real numbers, given by assigning x to -log x.
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