1. Sequence alignment (Wikipedia applet)
• Inputs:
  • Explicit- Two sequences {a₁, a₂, ...., a_m} and {b₁, b₂, ...., b_n} (e.g. query and database)
  • Implicit- A scoring procedure, e.g. pairwise scores  s(a_i,b_j) and gap costs
• Alignment algorithm: global, local, gapped, gapless (dynamic programming, applet)
• Output:  matching (sub)sequences with an overall score  S . (example)
• Significance: What is the probability of getting a score S by chance?
2. Statistics of gapless local alignments:
• Random walks of scores as a function of matching length
• Extreme Value Distributions, the Gumbel distribution,
• Tails of distribution in a gapless alignment
• The Karlin-Dembo formula
3. Gapped alignments and Statistical Physics
• Transfer Matrix method for Directed Paths in Random Media
• Dynamic Programming method for Sequence Alignment (Example)

(Lecture Notes)

• Tutorial by Ralf Bundschuh on Sequence Alignment (and associated paper)
• Wikipedia applet for Needleman-Wunsch alignment