- Sequence alignment (Wikipedia applet)
- Inputs:
*Explicit*- Two sequences {a_{1}, a_{2}, ...., a_{m}} and {b_{1}, b_{2}, ...., 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? - 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
- Gapped alignments and Statistical Physics
- Transfer Matrix method for Directed Paths in Random Media
- Dynamic Programming method for Sequence Alignment (Example)

- Tutorial by Ralf Bundschuh on Sequence Alignment (and associated paper)
- Wikipedia applet for Needleman-Wunsch alignment
- Wikipedia page on the Tracy-Widom distribution.
- Article by Majumdar & Nechaev on Matching problems and Alignments

8.592 lec8- last update 2/29/16 by M. Kardar