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# ThirdHourlyExam-answers - Third Hourly Exam ITI 111 Spring...

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Third Hourly Exam ITI 111 Spring 2011. I affirm that I have neither given nor received help while taking this exam: Signature ____________________________ Please print your name too: _____________________________________ ITI 111 Spring 2011 Practice final Exam There are 4 web pages in a small internet. Call them A,B,C,D Each has a representation using a basis of terms: Page People love Hate war 2 || P A 1 3 4 0 26 B 3 2 0 1 14 C 1 0 4 2 21 D 4 0 0 4 32 Q 0 0 1 1 2 A user has entered the query Q: “nations hate war”. 1. In the space provided in the table above, write the vector for Q in the same basis. 2. Rank the 4 web pages (p=A,B,C,D) using the inner product <Q|p>. Let’s call this ranking system R1 . Answer: Rank 1: C (6) Rank 2: A (4 and shorter than D) [Note: I also accepted C, D, A, B due to the tie.] Rank 3: D (4) Rank 4: B (1) 3. Now rank them using the cosine of the angle between the page and the query. Let’s call this ranking system R2 . C (acos(6 / (sqrt(21) * sqrt(2))) = 22.2076543 degrees) A (acos(4 / (sqrt(26) * sqrt(2))) = 56.3099325 degrees) D (acos(4 / (sqrt(32) * sqrt(2))) = 60 degrees) B (acos(1 / (sqrt(14) * sqrt(2))) = 79.1066054 degrees) 4. Now compute the modified Kendall’s Tau similarity between these two different ways of ranking, and . Total number of pairs TP = 4 2    = 6 Pairs out of order OO = 0 Tau = 1 OO TP = 1

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Third Hourly Exam ITI 111 Spring 2011. I affirm that I have neither given nor received help while taking this exam: Signature ____________________________ Please print your name too: _____________________________________ A B C D 5. These pages are linked in a tiny internet 5: Write the adjacency matrix of this digraph A= 0 1 0 1 1 0 1 0 1 1 0 2 1 0 0 0    6. Write the message matrix T MA M = 0 1 1 1 1 0 1 0 0 1 0 0 1 0 2 0
Third Hourly Exam ITI 111 Spring 2011. I affirm that I have neither given nor received help while taking this exam: Signature ____________________________ Please print your name too: _____________________________________ 7. Write the Flow matrix F F= 0 1/ 2 1/ 4 1 1/ 2 0 1/ 4 0 0 0 0 0 1/ 2 0    8. Let the limiting distribution of authority be represented as the vector a b x c d    Write out the 4 simultaneous equations that represent the matrix equation Fx x b/2 + c/4 + d = a a/2 + c/4 = b b/2 = c a/2 + c/2 = d 9.

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ThirdHourlyExam-answers - Third Hourly Exam ITI 111 Spring...

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