Computer Science homework help. Homework 1 – due 17.03.2020
Instructions: Please return your homework by e-mail as a single PDF document by the due date with
“EE550” in the subject line. Sharing of ideas and discussions is encouraged, but sharing of results and/or text
is not. Show the details of your work including the intermediary results if applicable.
Question (100 points)
For this question, generate a random transition rate matrix ? to model the rates of nucleic acid substitutions
in such a way that the off-diagonal entries vary between 0 and 1 and the diagonal entries are set so that each
row sums to 0.
a) (50 points) Calculate the transition probability matrix ?(?) corresponding to the transition rate matrix ?
above and plot the corresponding transition probabilities between each nucleotide pair in a 4 × 4 table for
? ∈ [0,5].
(Hint: You need to figure out how to calculate matrix exponentials.)
b) (50 points) Given the transition probability matrix ?(?) above, calculate the functional relationship
between the sequence distance ? and the evolutionary distance ? between two nucleotide sequences. Show
the calculated relationship as a graph of ? versus �