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page 184:
WAS: Here, a has become c = ATGC.
IS: Here, a has become c = ACGC.
Correction by
page 187:
WAS: $a \choose b$ corresponds to an indentity . . .
IS: $a \choose b$ corresponds to an identity . . .
Correction by Richard Lanthrop, 11 April 1996.
page 187:
WAS: (ii) f(n,n) ~ (1 + \sqrt{2})^{2n+1} n^{-1/2},
IS: (ii) f(n,n) ~ 2^{5/4} \pi^{-1/2} (1 + \sqrt{2})^{2n+1} n^{-1/2},
Correction by Joseph B. Slowinski, 17 Nov 1996.
page 187:
WAS: f(1000,1000) \approx (1 + \sqrt{2})^{2001} \sqrt{1000} = 10^{767.4}
IS: f(1000,1000) \approx 2^{-5/4} \pi^{-1/2} (1 + \sqrt{2})^{2001} 1000^{-1/2} = 7.03 \times 10^{763}
Correction by Joseph B. Slowinski, 17 Nov 1996.
page 191:
WAS: Proof. . . . Then the last loop of the algorithm states that. . .
IS: Proof. . . . Then the current loop of the algorithm states that. . .
Correction by Richard Lanthrop, 11 April 1996
page 191:
WAS: b = ATGGAA
IS: b = ATGGGAA
Correction by Richard Lanthrop, 11 April 1996
page 192:
WAS:
A T G G A
\ /\
T A G G C A
IS:
A T G G G A A
\ / \
T A G G C A
Correction by Andrea Iabrudi taraves,23/09/96
page 193:
WAS:
The optimal alignment has least cost of these three possibilities and (1) is proven.
Another statement of Equation (9.1) with . . .
IS:
The optimal alignment has least cost of these three possibilities and (9.2) is proven.
Another statement of Equation (9.2) with . . .
Correction by Andrea Iabrudi Taraves,23/09/96
page 194:
WAS: [in Algorithm 9.2]
D_{i,j} = 0 for i = 0, j=0,\ldots,m and j=1, i=0, 1, \ldots, n.
IS:
D_{i,0} = i\delta and D_{0,j} = j\delta
WAS:
$\mu = -1$
IS:
$\mu = 1$
Correction by Andrea iabrudi Tavares, 23/09/96
page 195:
WAS: Theorem 9.6 . . . Set E_{0,0} = F_{0,0} = D_{0,0} = 0, E_{i,0} = D_{i,0} = g(i), and F_{0,j} = D_{0,j} = g(j).
IS: Theorem 9.6 . . . Set E_{i,0} = \infty for all i, F_{0,j} = \infty for all j, D_{0,0} = 0, D_{i,0} = g(i) for all i > 0, and D_{0,j} = g(j) for all j > 0.
Correction by Jens Stoye, 28 June 1996
WAS:
$E_{i,j^*} = min...D_{i,j^*}$ for 0 <=j ^* < j
IS:
$E_{i,j^*} = min...D_{i,j^*-k}$ for 1 <= j^* <j
Correction by Andrea Iabrudi Tavares, 23/09/96
page 197:
WAS: F_{i,j} = \min\{D_{i-1,j} + \alpha_j, F_{i,j-1} + \beta_j\},
IS: F_{i,j} = \min\{D_{i-1,j} + \alpha_i, F_{i-1,j} + \beta_i\},
Correction by Andrea Iabrudi Tavares, 23/09/96
page 198:
WAS : To illustrate the similarity algorithm, we align the same sequences as above, E. coli threonine tRNA and E. coli valine tRNA. We use a single letter indel algorithm and choose the parameters s(a,a) = +1; s(a,b) = -1 if a is not equal to b; and \hat{\g} = 2.
IS : To illustrate the similarity algorithm, we align the same sequences as above, E. coli threonine tRNA and E. coli valine tRNA. We use a single letter indel algorithm and choose the parameters s(a,a) = +1; s(a,b) = -1 if a is not equal to b; and \hat{\delta} = 2.
Correction by Steven Salzberg, 10/5/95
page 199:
WAS: Theorem 9.10 Let \hat{g} = \alpha + \beta(k-1) for constants \alpha and \beta. Set E_{0,0} = F_{0,0} = S_{0,0} = 0, E_{i,0} = S_{i,0} = -\hat{g}(i), and F_{0,j} = S_{0,j} = -\hat{g}(j).
IS: Theorem 9.10 Let \hat{g} = \alpha + \beta(k-1) for constants \alpha and \beta. Set E_{i,0} = -\infty for all i, F_{0,j} = -\infty for all j, S_{0,0} = 0, S_{i,0} = -\hat{g}(i) for all i > 0, and S_{0,j} = -\hat{g}(j) for all j > 0.
Correction by Jens Stoye, 28 June 1996
page 201:
WAS: \sum_{k=1}^m \sum_{k=l}^m n(l-k) = O(nm^3).
IS: \sum_{k=1}^m \sum_{l=k}^m n(l-k) = O(nm^3).
WAS: Corollary 9.3
T(a,b) = max{T(n,j),j : 1 \le j \le m}.
IS: Corollary 9.3
T_{a,b} = max{T_{n,j} : 1 \le j \le m}.
Corrections by Richard Lathrop, 11 April 1996
page 203:
WAS: Theorem 9.13 . . . \max_{1 \le l \le j} \{H_{i,j-l} - g(k)\}\}.
IS: Theorem 9.13 . . . \max_{1 \le l \le j} \{H_{i,j-l} - g(l)\}\}.
Correction by Jim Holloway, 28 May 1996
page 208: (Tandem Repeats, range of j)
WAS: R_{i,j} = best score of an alignment that ends at a_i and b_j.
IS: R_{i,j} = best score of an alignment that ends at a_i and b_{j+1}.
page 208: (Tandem Repeats, range of j)
REPLACE ALL: 1 \le j \le k
WITH: 0 \le j \le k-1
page 208: (Tandem Repeats, range of j)
REPLACE ALL: R_{i,k} and R_{i,k}^*
WITH: R_{i,k-1} and R_{i,k-1}^*, respectively.
page 208: (Tandem Repeats; substitute b_{j+1} for b_j)
WAS:
R_{i,j}^* = max\{0,
R_{i,j-1} - \delta,
R_{i-1,j} - \delta,
R_{i-1,j-1} + s(a_i, b_j)\},
IS: (substitute b_{j+1} for b_j)
R_{i,j}^* = max\{0,
R_{i,j-1} - \delta,
R_{i-1,j} - \delta,
R_{i-1,j-1} + s(a_i, b_{j+1})\},
page 209: Algorithm 9.6 (wrap)
WAS:
1. R_{0,j} = 0 for 0 \le j \le k
R_{i,0} = 0 for 0 \le i \le n
2. for i = 1 to n
for j = 1 to k
R_{i,j} = \max\{0,
R_{i,j-1} - \delta,
R_{i-1,j-1} + s(a_i, b_j),
R_{i-1,j} - \delta\}
R_{i,0} = R_{i,k}
for j = 1 to k
R_{i,j} = \max\{0,
R_{i,j-1} - \delta,
R_{i-1,j-1} + s(a_i, b_j),
R_{i-1,j} - \delta\}
3. R(a,b) = max\{R_{i,j} : 1 \le i \le n, 1 \le j \le k\}.
IS: (substitute b_{j+1} for b_j and so loop to j=k-1; change wraparound step)
1. R_{0,j} = 0 for 0 \le j \le k-1
R_{i,0} = 0 for 0 \le i \le n
2. for i = 1 to n
for j = 1 to k-1
R_{i,j} = \max\{0,
R_{i,j-1} - \delta,
R_{i-1,j-1} + s(a_i, b_{j+1}),
R_{i-1,j} - \delta\}
R_{i,0} = \max\{0,
R_{i,k-1} - \delta,
R_{i-1,k-1} + s(a_i, b_1),
R_{i-1,0} - \delta\}
for j = 1 to k-1
R_{i,j} = \max\{0,
R_{i,j-1} - \delta,
R_{i-1,j-1} + s(a_i, b_{j+1}),
R_{i-1,j} - \delta\}
3. R(a,b) = max\{R_{i,j} : 1 \le i \le n, 0 \le j \le k-1\}.
Corrections by Paul Hardy, 2 April 1996
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