Instructions:

ANSWER ANY THREE PROBLEMS OF YOUR CHOICE

For each problem, you should submit, through Blackboard, your program in a file named 'problemX.YOURNAME.R' or 'problemX.YOURNAME.py', where 'X' is the number of the problem and YOURNAME is your name. For example, my program for problem 5 would be named 'problem5.Huseyin_Kocak.py'. If a problem asks for more than one program, put a character 'a', 'b', etc. after the problem number (for example, 'problem4a.Huseyin_Kocak.py').

You are allowed to use our websites only: computingforscientists.org, rforbiologists.org, and pythonforbiologists.org. You are NOT allowed to use any collaboration software, including but not limited to email, chat, social networking websites, etc. We will be monitoring the network in the lab, filtering packets for such communication and storing all information for future verification and reference. Any attempt to transfer information and cheat in any way will result at least in a grade of '0' for this exam and possibly further disciplinary action.

Problems:

Problem 1 (33 points)

• Logistic model in R: The picture below contains XiVersusTime views of the discrete logistic model. Examine this picture carefully and write an R code to recreate this picture as faithfully as you can. Submit your R code. Make sure that you iterate the logistic difference equation in your R code. Do not import numbers from Phaser. You can, of course, check your numbers using Phaser.

  

   

• Problem 2 (43 points)

  Heating of a probe: A student held a temperature probe between her two fingers and recorded the following temperatures every 2 seconds:
  Time     Temp
      00     32.77
      02     33.16
      04     33.35
      06     33.57
      08     33.67
      10     33.75
      12     33.85
      14     33.94
      16     33.98
      18     34.03
      20     34.04
  

  • Plot the numerical approximation of the derivative from the data vs. the temperature. Notice that this graph looks almost linear.
  • Now compute and plot the least squares fit line to this graph.
  • What is the differential equation (y' = a + by) and the initial condition governing this experiment? You can write your answer as a comment at the end of your code.

• Problem 3 (33 points)

  Answer the question Regular Expressions Exercises VII, problem 3 on the pythonforbiologists.org Web site. Your code should read in the file MT233521.1 and print out if the sequence in it is alive or not. DO NOT worry about the protein sequence.

• Problem 4 (34 points)

  Ebola polymerase protein sequence:
  Download the FASTA file (accession number AGL73456) containing the ebola virus polymerase protein sequence. You can use the "Send" widget on the upper-right corner of the page to download fasta file. Write a python code that does the following:

  • Reads in the protein sequence in fasta format,
  • Extracts the first 800 amino acids.
  • Asks the user to enter an amino acid (single capital letter, say, A).
  • Prints out the number of occurences of the entered amino acid.