Solutions to Math 3E03 Homework 5
2.96. We shall show the rst isomorphism U (I9 ) I6 . Note that the group U (I9 ) =
=
cfw_[1], [2], [4], [5], [7], [8] has order 6. Also one sees that [2]2 = [4], [2]3 = [8] and [2]6 = [1].
Thus [2] has order 6 and since U
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CHAPTER 11. COMPUTATIONAL PROTEOMICS
246
A
7
11 \
A
15
D
18
21
24
30
0
38
0
o o
43
-o
o o
A
11 13
19
22
0
0
0
25
31 33
38
Figure 11.8: Aligning spectra. The shared peaks count reveals only D(0) = 3 matching peaks
on the main diagonal, while spectral al
11.11. SOME OTHER PROBLEMS AND APPROACHES
249
11.11.2 Large-scale protein analysis
Complex protein mixtures can be separated by highly-resolving two-dimensional
gel-electrophoresis. After separation, the identity of each "spot" (peptide) in 2D gel is unkn
Bibliography
[1]
A.V. Aho and M.J. Corasick. Efficient string matching: an aid to bibliographic search. Communication of ACM, 18:333-340, 1975.
[2]
D.J. Aldous and P. Diaconis. Hammersley's interacting particle process and
longest increasing subsequences.
247
11.10. ALIGNING PEPTIDES AGAINST SPECTRA
7
11
15
18
21
24
30
38
43
11 13
19
22
25
31 33
38
Figure 11.9: Modification of a dynamic programming graph leads to a fast spectral alignment
algorithm.
To combine N-terminal and C-terminal series together, we
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Solutions to Math 3E03 Homework 4
2.18. (Reexivity) Let x X. Since one clearly has f (x) = f (x), x x.
(Symmetry) Let x1 , x2 X and x y. Then f (x) = f (y) which is the same as saying
f (y) = f (x). Hence y x.
(Transitivity) Let x1 , x2 , x3 X with x y an
Solutions to Math 3E03 Homework 6
2.116. Since D8 and Q are the only nonabelian groups, they are non-isomorphic to
the remaining three. From problem 2.87, D8 and Q are non-isomorphic to each other. It
remains to check that I8 , I4 I2 and I2 I2 I2 are mutu
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Solutions to Math 3E03 Homework 3
2.40. Let a denotes the order of y t . By the question, we have 1 = y m = (y t )d . It
follows from Lemma 2.53 (or Proposition 2.54) that a|d. On the other hand, we also have
1 = (y t )a = y at . This, again using Lemma 2
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234
CHAPTER 11. COMPUTATIONAL PROTEOMICS
Peptide ladder
3 types of fragment ions correspond to shifts cfw_0,1,3
* - \
3
Spectrum after shifts
Reverse shifts cfw_0, -1, -3
Reverse shifts do not reconstruct the peptide ladder
but create a ladder of peaks i