As described by Benzer (1959), for n mutants, the probability that a randomly chosen, symmetric, binary matrix can be arranged in dictionary order is n!/2n(n- 1)/2. Consider the following statements about the above expression and mark the INCORRECT one:
a) The number 2 raised by the expression n(n- 1)/2 relates to the matrix data alphabet (zeros and ones).
b) The number 2 raised by the expression n(n- 1)/2 relates to the matrix dimensions (columns and rows).
c) n! is the number of rearrangements that any given set of data may be subjected in one specific dimension (columns or rows).
d) n! is the number of possible row arrangements in satisfactory patterns.
e) None of the above.
Original idea by: Raphael Cristofaro
sexta-feira, 29 de maio de 2015
quinta-feira, 21 de maio de 2015
Week 12 - Unichromosomal genomes: block interchange
Select the alternative with the minimum number of block interchange operations that are needed to sort optimally the following genome:
+1 +8 +4 +7 +5 +2 +9 +6 +3 +10
a. 2.
b. 3.
c. 4.
d. 5.
e. None of the above.
+1 +8 +4 +7 +5 +2 +9 +6 +3 +10
a. 2.
b. 3.
c. 4.
d. 5.
e. None of the above.
sexta-feira, 15 de maio de 2015
Week 11 - Unichromossomal genomes, reversal
Given the permutation (0 2 4 3 5 1 6 8 7 9), consider the following statements according to the definitions by Bergeron (2005) on the Hannenhalli-Pevzner Theory.
I - This permutation contains only a simple hurdle, which is 2 4 3 5.
II - The whole permutation is a framed interval which also counts as a hurdle.
III - If the hurdle 2 4 3 5 is cutted, the permutation can be reduced in (0 2 1 3 5 4 6), which still has more than one hurdle.
Select the alternative with all the CORRECT statements and no others:
a. I.
b. II.
c. III.
d. II and III.
e. None of the above.
Original idea by: Raphael Cristofaro
I - This permutation contains only a simple hurdle, which is 2 4 3 5.
II - The whole permutation is a framed interval which also counts as a hurdle.
III - If the hurdle 2 4 3 5 is cutted, the permutation can be reduced in (0 2 1 3 5 4 6), which still has more than one hurdle.
Select the alternative with all the CORRECT statements and no others:
a. I.
b. II.
c. III.
d. II and III.
e. None of the above.
Original idea by: Raphael Cristofaro
quinta-feira, 7 de maio de 2015
Week 10 - Algebraic distance, definition
Given the graph α and its inverse, choose the CORRECT statement.
a. β = (2,4,5) is a cycle that divides both α and α-1.
b. β = (4,2,1) is a cycle that divides α but not α-1.
c. β = (1,3,5) is a cycle that divides α but not α-1.
d. β = α-1 is a cycle that divides α.
e. None of the above.
References: Kiltinen, John O. Oval Track And Other Permutation Puzzles: And Just Enough Group Theory To Solve Them. Washington, D.C.: Published and distributed by the Mathematical Association of America Press, 2003.
Original idea by: Raphael Cristofaro
Image 1 - Cycle arrow notation from a) α and b) α-1 (extracted from Kiltinen, 2003).
a. β = (2,4,5) is a cycle that divides both α and α-1.
b. β = (4,2,1) is a cycle that divides α but not α-1.
c. β = (1,3,5) is a cycle that divides α but not α-1.
d. β = α-1 is a cycle that divides α.
e. None of the above.
References: Kiltinen, John O. Oval Track And Other Permutation Puzzles: And Just Enough Group Theory To Solve Them. Washington, D.C.: Published and distributed by the Mathematical Association of America Press, 2003.
Original idea by: Raphael Cristofaro
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