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page 257:
WAS:
...and s(a,b) = 0 if a is not equal to b, s(a,a)= s(b,b) = 1, and indel penalty function (\delta)=0.
IS :
...and s(a,b) = 0 if a is not equal to b, s(a,a)= s(b,b) = 1, and indel penalty function g(k)=0.
Correction by Warren J. Ewens, 10/4/95.
page 259:
WAS:
...As usual, our alignment is scored by s(a,b) and g(k) which is subadditive (g(k+l) <= g(k)+g(l)).
IS :
...As usual, our alignment is scored by s(a,b) and indel function g(k) which is subadditive (g(k+l) <= g(k)+g(l)).
Correction by Warren J. Ewens, 10/4/95.
page 261:
WAS :
Theorem 11.6 Assume A=A_1 ... A_n and B=B_1 ... B_n have iid letters A_i and B_i. Define S_n=S(A,B) to be the global alignment score. Then, if c^*=max{0,min{s^* + 2g(1), s^* - s_*}} and p=P(A_1=B_1),
Var (S_n) <= n(1-p)c*.
IS :
Theorem 11.6 Assume A=A_1 ... A_n and B=B_1 ... B_n have iid letters A_i and B_i. Define S_n=S(A,B) to be the global alignment score. Then, if c^*=max{s^* + 2g(1), s^* - s_*} and p=P(A_1=B_1),
Var (S_n) <= n(1-p)(c^*)^2.
Correction by Warren J. Ewens, 10/4/95.
WAS :
Observe also that r and H are related:H^{'}(a,p)=...
IS :
Observe also that r and H are related; H^{'}(/alpha,p)=...
Correction by George, 30/07/96
WAS :
Theorem 11.13 ... p = P(X_1 = Y_1) in (0,1).
IS :
Theorem 11.13 ... p = P(A_1 = B_1) in (0,1).
Correction by Warren J. Ewens, 10/4/95.
page 270: [in Theorem 11.14]
WAS: Let H^*_n(k) be . . .
IS: Let H^*_n(l) be . . .
Correction by Sabine Mercier, 10 April 1997.
page 270: [in Theorem 11.14]
WAS: it follows that $\lim_n M^*_n(l) . . .
IS: it follows that $\lim_n H^*_n(l) . . .
Correction by Sabine Mercier, 10 April 1997.
page 272:
WAS: Theorem 11.17 . . . Let p > 0 be the largest real root of
IS: Theorem 11.17 . . . Let p be the unique positive root not equal to 1 of
Correction by Warren Evans, 1 November 1995.
page 272:
WAS: M_n ~ log(n^2) . . .
IS: H_n ~ . . .
Correction by Sabine Mercier, 10 April 1997.
page 276:
WAS :
Remarkably, the mean
E(Y_n) =log(m)/\lambda+E(V)/\lambda=log(m)/\lambda+\gamma/\lambda
where \gamma=0.5722... is the Euler-Macheroni constant. On the other hand,
Var(max_{1 <= i <= m}W_i) = Var(V)/\lambda^2
=(\pi^2/6)/\lambda^2
is independent of m. This is very different from the Central Limit Theorem where \sum_{i=1}^m W_i has mean mE(W) and variance mVar(W).
IS :
Remarkably, the mean
E(Y_n) =log(n)/\lambda+E(V)/\lambda=log(n)/\lambda+\gamma/\lambda
where \gamma=0.5722... is the Euler-Macheroni constant. On the other hand,
Var(max_{1 <= i <= n}W_i) = Var(V)/\lambda^2
=(\pi^2/6)/\lambda^2
is independent of n. This is very different from the Central Limit Theorem where \sum_{i=1}^n W_i has mean nE(W) and variance nVar(W).
Correction by Warren J. Ewens, 10/4/95.
page 280:
WAS:
Already, two analyses of long headruns have been given. R_n= length of the longest headrun was shown to satisfy...
IS :
Already, two analyses of long headruns have been given in sections 11.2.1 and 11.3. R_n= length of the longest headrun was shown to satisfy...
Correction by Warren J. Ewens, 10/4/95.
page 281:
WAS:
For our fixed alignment or coin tossing problem, D_i=I(A_i = B_i),or P(D_i=1) = 1 - P(D_i = 0) = p.
IS:
For our fixed alignment or coin tossing problem, D_i=I(A_i = B_i),and P(D_i=1) = 1 - P(D_i = 0) = p.
page 288:
WAS:
For ease of exposition, the disscussion...
IS :
For ease of exposition, the discussion...
Correction by Warren J. Ewens, 10/4/95.
page 292: [in the Proof of Theorem 11.25]
WAS: X_{v,i} is a function of D_{v-s} \cdots D_{v-1}
IS: X_{v,i} is a function of Y_{v-s} \cdots Y_{v-1}
Correction by Sabine Mercier, 10 April 1997.
page 292: [in the Proof of Theorem 11.25]
WAS: for dependence, $i = i, 2, \ldots, k-1.$
IS: for dependence, $i = 1, 2, \ldots, k-1.$
Correction by Sabine Mercier, 10 April 1997.
page 296:
WAS:
Proof. The proof is in two parts... The upper bound is ... ommitted.
IS :
Proof. The proof is in two parts... The upper bound is ... omitted.
Correction by Warren J. Ewens, 10/4/95.
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