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University of Delaware Computer and Information Sciences CISC 467/667 Final Exam December 14, 2004
1. This is a closed-book exam. 2. Check that you have all pages. There are four problems for a total of 100 points 3. Write your name on every page in the space provided 4. If you need more space, use the back of the same page. But do not feel obligated to fill up all the space that is provided. 5. Give clear, concise answers to each question do not tell me everything that you know about the topic just answer the question that is asked.
Problem 1 2 3 4 Total
Grade
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Problem 1 (35 points) Analysis for Primary Sequences
a. [6 points] When using Needleman Welch algorithm with linear gap penalty for pairwise alignment of sequences X[1..n] and Y[1..m], the optimal alignment trajectory passes position (i, j) in the DP table. Will the 2nd leg of that trajectory automatically give an optimal alignment for subsequences X[i..n] and Y[j..m]? why?
b.
[8 points] Write down the recurrence equation used for Smith-Waterman algorithm.
c.
[6 points] Describe the major steps of the progressive approach to multiple sequence alignment.
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d.
[15 points] Let M be a hidden Markov model consisting of N states, ej(x) be the emission frequency for residue x at state j, ajk be the transition probability from state j to state k, and x[1..L] be an observed sequence. What does the Viterbi algorithm calculate? Define the value to be filled in the cells of the DP table, write down the recursive equation used for filling out the DP table.
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Problem 2 (25 points) Support Vector Machines
a. [12 points] Describe the prime form Rosenblatts algorithm either in plain English or in pseudo
code.
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b. [5 points] Given a training dataset of size n that is linearly separable with a margin of size , what
is the upper bound of the number of iterations before Rosenblatts algorithm converges?
c. [8 points] short answers
i. If K(x, y) is a kernel function, then K(x, y) must be equal to K(y, x). Is this statement true or false?
ii.
If K(x, y) is a kernel function, then K(x, x) must be equal to and less than zero. Is this statement true or false?
iii.
Which of the following are the support vectors? - Training examples that have been misclassified during the training - Training examples that have never been misclassified during the training
iv.
Based on Novikoff Theorem, Rosenblatts algorithm is guaranteed to find the separating hyperplane with maximum margin with respect to the training dataset provided the dataset is linearly separable. True or false?
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Problem 3 (20 points) Structural Prediction
a. [12 points] Nussinov algorithm for RNA secondary structure. v. down Write the recurrence equation used Nussinov algorithm
vi.
What is the time complexity for this algorithm?
vii.
Give the values for X, Y and Z in the following DP table and mark the tracceback arrows for the three corresponding cells.
A A G A A U C U G G C C C 0 0
G 0 0 0
A 0 0 0 0
A 0 0 0 0 0
U 1 1 1 1 0 0
C 2 2 1 1 0 0 0
U X 2 2 1 0 0 0 0
G
G
C
C
C
Y 1 1 0 0 0 1 1 0 0 0 0 2 1 1 1 0 0 Z 2 1 0 0 0 2 1 0 0 0
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viii.
[session 667 only] For the following RNA sequences, which one sequence is less likely homologous to other sequences?
Seq1 Seq2 Seq3 Seq4
= = = =
AAAGGGCCCUUU ACACACGUGUGU ACACACCACUGU UGUGUGCACACA
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b.
[8 points] Protein structures i. Describe the Anfinsen Hypothesis.
ii.
In HP models simulating the hydrophobic force, the energy contribution from a pair of topologically neighboring hydrophobic residues (represented as shaded circles) is -1, and energy contribution from all other neighboring arrangements is 0. For a sequence of 7 residues HHPHHPH, the following two conformations A and B are given. List the topological neighboring pairs, and calculate the total energy for each conformation. Which conformation is better?
1 7 1
7
2
3
6
5
6
5
A
4
2
3
B
4
iii.
In order to apply the Genetic Algorithm for optimization, the lattice conformations are first encoded. Here is an encoding scheme: 01 for going up, 10 for going down, 00 for going right, and 11 for going left. For example, in this encoding scheme, conformation A will be expressed as 10 00 10 11 11 01. Encode conformation B.
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[session 667 only] If conformation B and a conformation 01...