From: W. Trevor King Date: Thu, 13 Aug 2009 18:03:17 +0000 (-0400) Subject: The (P_N = NP_1) bug that triggered 0.7 -> 0.8 isn't so bad. X-Git-Tag: v0.9~2 X-Git-Url: http://git.tremily.us/?a=commitdiff_plain;h=7596a627169c637952720adb14158655d47c99ff;p=sawsim.git The (P_N = NP_1) bug that triggered 0.7 -> 0.8 isn't so bad. Added notes to that effect. Still, it's better for having thought it out more clearly ;). --- diff --git a/src/sawsim.nw b/src/sawsim.nw index 96a786b..850e7a9 100644 --- a/src/sawsim.nw +++ b/src/sawsim.nw @@ -153,11 +153,10 @@ Version 0.7 added tension model inverses, which seems to reduce computation time by about a factor of 2. I was expecting more, but I'll take what I can get. -Version 0.8 fixed a \emph{major} bug in unfolding probability for +Version 0.8 fixed a minor bug in unfolding probability for multi-domain groups. The probability of at least one domain unfolding -had been calculated as $P_N=NP_1$, rather than $P_N=1-(1-P_1)^N$. I -dunno how that slipped by before. Now there are multi-domain tests in -testing to check for this sort of mistake. +had been calculated as $P_N=NP_1$, rather than $P_N=1-(1-P_1)^N$. +However, for small $P$ the two are equivalent. <>= #define VERSION "0.8" @@ -564,6 +563,10 @@ so the probability that \emph{at least one} domain unfolds is $$ p(n>0) = 1-(1-P)^N. $$ +Note that for small $P$, +$$ + p(n>0) = 1-(1-NP+\mathcal{O}(P^2)) = NP - \mathcal{O}(P^2) \approx NP. +$$ We take some time to discuss the meaning of $p(n>1)$ (i.e. multi-unfolding timesteps) in Section \ref{sec.timescales}.