Theoretical: How many substrings / subsequences does a string of length n have? Give examples of typical alphabets.

Practical: Compute the reverse complement of a given string, compute the resulting protein, given the DNA or RNA sequence (genetic code supplied).

Theoretical: What is the difference between global and local alignment, when are they applied? Give the definition of the cell D(i,j) for global and of the cell L(i,j) for local alignment (as opposed to how they are computed). Give the recursion for the computation. Give the running times and space requirements of these algorithms. Why are these preferable to the exhaustive search algorithm? Recursive formula for number of alignments. Explain space-saving variant of N-W algorithm.

Practical: Compute the score of a given alignment, for given scoring function; compute sim(s,t) using the DP algorithm of Needleman-Wunsch; compute an optimal alignment/all optimal alignments using the DP-table. Connection between the table and alignments: write down the alignment represented by a path in the table and vice versa; find all optimal local alignments using the DP-algorithm of Smith-Waterman.

Theoretical: Which version would you choose for a given problem (e.g. for computing overlaps, deciding whether t is substring of s, ...). Running times of algorithms. Be able to explain the algorithms. Explain the recursion of the affine gap penalty algorithm, why do we need 3 matrices, what is the definition of the cells, where is the final result?

Practical: Apply the algorithms to concrete examples (small examples).

Topics: Definition of a metric. Edit distance (unit cost and general cost), Hamming distance, LCS-distance, q-gram distance.

Theoretical: What is a metric? Define unit cost edit distance. How do we have to choose the scoring function in order to have a parallel between edit distance and alignment? Explain and analyse the DP algorithm for edit distance. Define LCS distance and Hamming distance. Define the q-gram distance. How is it computed? Which of these is a metric? Prove it.

Practical: Compute the edit distance between two strings, using the DP-algorithm. Give the series of edit operations corresponding to an alignment and vice versa. Compute the Hamming distance and the LCS distance for two strings. Compute the q-gram distance between two strings. Give two distinct strings with q-gram distance 0.

Topics: Definition of MSA, projections (=induced alignments), SP-score. Theorem about optimal MSA and optimal projections.

Theoretical: What are induced alignments? What is the SP-score? Explain and analyse the DP algorithm. Is it feasible? Complexity status of MSA with SP-score.

Practical: Score a multiple alignment with the SP-score. Give the induced alignments of an MSA.

Topics: Star alignment (for similarity and for distance). Progressive alignment.

Theoretical: Which algorithms do you know? Are they heuristics or approximation algorithms, are they exact? What is the difference between a heuristic and a running time heuristic? And an approximation algorithm?

Practical: Apply the star alignment algorithm to a small example. Apply the progressive alignment algorithm to a small example (say which alignments we would do in what order, given a phylogenetic tree). Align two alignments (small example).

Topics: Motivation for different match and mismatch scores. PAM scoring matrices. Computation of PAM scoring matrices. BLOSUM matrices (sketched only).

Theoretical: Explain how the PAM scoring matrices are computed. Explain the biological motivation. What is the underlying idea? What data were used? What does the number k mean in PAMk? What is the difference between the probability matrix and the scoring matrix? What do the entries represent? Interpret their values. Why do we use a "log-odds" matrix? What are the main differences between PAM and BLOSUM matrices?

Practical: Use a given PAMk or BLOSUM-k matrix (supplied) to score an alignment.

Topics: BLAST.

Theoretical: What is a heuristic? Explain the underlying ideas of BLAST. What is the advantage over the DP-algorithms? What is the primary application? Why are heuristics used and not the DP-algorithms?

Practical: Given a small example (a query and some db sequences), explain how BLAST works on the example: list some high-scoring words, show where there is a hit, show how to extend it.

Practical: Construct a de Bruijn sequence over a given alphabet and given k. Given the alphabet and k, draw / complete the de Bruijn graph of order k.

Topics: De Bruijn graphs: definition (de Bruijn subgraphs). De Bruijn graph of a string or of a set of strings. Walks in de Bruijn graphs. Sequencing by Euler tours/paths in de Bruijn graphs.

Theoretical: What does an Euler tour / path in the de Bruijn graph of a string correspond to? How do we compute an Euler tour / path? Complexity of algorithm (Hierholzer's algorithm).

Practical: Given a set of reads, apply the algorithm for reconstructing the target sequence.

Theoretical: What is a phylogenetic tree? Kinds of phylogenetic trees. How many ways are there to root a tree? How many phylogenetic trees are there on a given set of taxa? What are the two types of input data?

Practical: Check if a given graph is a tree. Identify in a rooted tree leaves, root, and for a given node, its parent, siblings, children, ancestors, descendants. Check whether two drawings depict the same phylogenetic tree (very small examples). Root unrooted trees. Identify whether a phylogenetic tree is rooted/unrooted, binary/multifurcating, whether the branch lengths matter.

Theoretical: Explain the aim of distance based phylogenetic reconstruction. What is given (input), what are we looking for (output)? Explain the running time of UPGMA. Def. of ultrametric. What does "molecular clock" mean? Def. of additive metric. Explain the connection between rooted phylogenetic trees and ultrametrics, and unrooted phylogenetic trees and additive metrics. Define metric.

Practical: Check whether a given distance matrix is ultrametric. Apply the algorithm UPGMA to a distance matrix. Check whether a given distance matrix is additive. Apply the algorithm Neighbor Joining to a distance matrix.

Theoretical: What are convergence and reversal? Def. of compatibility (of a character with a tree). Def. of Perfect Phylogeny. Does it always exist? When can Gusfield's algorithm be applied? Is it efficient? Define parsimony (of a phylogenetic tree). What is the status of the Perfect Phylogeny Problem? What is the status of the Small Parsimony and Large Parsimony problems? Which of the LP algorithms is exact, which is a heuristic?

Practical: Check whether a phylogenetic tree is a PP for a character-state matrix M. Apply Gusfield's algorithm. Compute the parsimony score of a given labelled tree. Identify cases of reversal and convergence in a phylogenetic tree. Apply Fitch' algorithm to a tree. Apply one of the 3 algorithms for Large Parsimony to a small example.