Computational Biology - Lecture 4

Today's class will continue with combinatory geometry covering the following topics:

• Polytope algebra.
• Tropical algebra as one-dimensional polytope algebra.
• Newton polytopes.

Now we will be able to solve the parametric pairwise-alignment problem:

• Polytope propagation of marginal probabilities.
• For the resulting polytope, construct the normal fan; in  particular, the normal cones of the vertices.
• These normal cones correspond one-to-one with the optimal pairwise alignments.