View of /sankoff-paper/iterator.aux

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\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces   A parse tree for the grammar of Table\nobreakspace  {}1\hbox {}. Each internal node is labeled with a nonterminal ({\tt  Stem} or {\tt  Loop}); additionally, the subsequences $(X_{ij},Y_{kl})$ generated by each internal node are shown. The parse tree determines both the structure and alignment of the two sequences. The cut-points of the alignment are the sequence co-ordinates at which the alignment can be split, i.e. $\{ (0,0),\ (1,1),\ (2,2)\ \dots  \ (15,12),\ (16,13),\ (17,14) \}$. }}{28}}
\newlabel{fig:ParseTree}{{1}{28}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces   Parsing a pair of sequences $(X,Y)$ using the Inside algorithm involves iterating over subsequence-pairs $(X_{ij},Y_{kl})$ specified by four indices $(i,j,k,l)$. In the constrained Inside algorithm, these indices are only valid if the {\em  fold envelopes} (triangular grids) include the respective subsequences $(i,j)$ and $(k,l)$ (shown as black circles) and the {\em  alignment envelope} (rectangular grid) includes both cutpoints $(i,k)$ and $(j,l)$ (shown as short diagonal lines). The filled cells in the rectangular grid show the aligned nucleotides. Note that the co-ordinates $(i,j,k,l)$ lie on the grid-lines {\em  between} the nucleotides. }}{28}}
\newlabel{fig:ijkl}{{2}{28}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces   Bifurcation rules allow a subsequence-pair $(X_{ij},Y_{kl})$ to be composed from two adjoining subsequence-pairs $(X_{im},Y_{kn})$ and $(X_{nj},Y_{nl})$. For this to be permitted by the constraints, the $X$-fold envelope (upper triangular grid) must contain subsequences $(i,m)$, $(m,j)$ and $(i,j)$ (black dots), the $Y$-fold envelope (rightmost triangular grid) must contain subsequences $(k,n)$, $(n,l)$ and $(k,l)$ (black dots) and the alignment envelope (rectangular grid) must contain cutpoints $(i,k)$, $(m,n)$ and $(j,l)$ (short diagonal lines). The filled cells in the rectangular grid show the nucleotide homologies highlighted in the alignment. Note that all co-ordinates $(i,j,k,l,m,n)$ lie on the grid-lines between nucleotides. }}{28}}
\newlabel{fig:ijklmn}{{3}{28}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces   These fold envelopes (triangular grids) limit the maximum length of subsequences (black dots), while the alignment envelope (rectangular grid) limits the maximum deviation of cutpoints (short diagonal lines) from the main diagonal. }}{28}}
\newlabel{fig:Banding}{{4}{28}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces   These fold envelopes (triangular grids) and alignment envelope (rectangular grid) limit the subsequences (black dots) and cutpoints (short diagonal lines) to those consistent with a given alignment and consensus secondary structure (shown). The alignment path is also shown on the alignment envelope as a solid black line, broken by cutpoints. }}{28}}
\newlabel{fig:Alignment}{{5}{28}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces   Fold envelope size is highly correlated with $N$ in the $N$-best fold test, although the variance is large due to the diversity of alignments in the test. }}{28}}
\newlabel{fig:FoldEnvSize}{{6}{28}}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces   Alignment envelope size is highly correlated with $N$ in the $N$-best alignment test, although the variance is large due to the diversity of alignments in the test. }}{28}}
\newlabel{fig:AlignEnvSize}{{7}{28}}
\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces   Alignment sensitivity as a function of envelope size parameter $N$ for three different test regimes. }}{28}}
\newlabel{fig:AlignSens}{{8}{28}}
\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces   Alignment specificity as a function of envelope size parameter $N$ for three different test regimes. }}{28}}
\newlabel{fig:AlignSpec}{{9}{28}}
\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces   Fold sensitivity as a function of envelope size parameter $N$ for three different test regimes. }}{28}}
\newlabel{fig:FoldSens}{{10}{28}}
\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces   Fold specificity as a function of envelope size parameter $N$ for three different test regimes. }}{28}}
\newlabel{fig:FoldSpec}{{11}{28}}
\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces   Total running time of {\tt  stemloc}\ (including envelope generation phases) as a function of envelope size parameter $N$ for three different test regimes. }}{28}}
\newlabel{fig:Runtime}{{12}{28}}
\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces   Peak memory usage of {\tt  stemloc}\ (i.e. the size of the principal CYK matrix) as a function of envelope size parameter $N$ for three different test regimes. }}{29}}
\newlabel{fig:Memory}{{13}{29}}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces  {\bf  A stochastic context-free grammar for generating pairwise alignments of RNA structures.}}}{31}}
\newlabel{tab:StemLoopGrammar}{{1}{31}}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces   {\bf  The {\tt  stemloc}\ grammar, part 1 of 3: stem and loop structures.}}}{32}}
\newlabel{tab:StemlocStems}{{2}{32}}
\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces   {\bf  The {\tt  stemloc}\ grammar, part 2 of 3: bulges.}}}{33}}
\newlabel{tab:StemlocBulges}{{3}{33}}
\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces   {\bf  The {\tt  stemloc}\ grammar, part 3 of 3: emissions.}}}{34}}
\newlabel{tab:StemlocEmissions}{{4}{34}}
\@writefile{lot}{\contentsline {table}{\numberline {5}{\ignorespaces  {\bf  The subset of RFAM used to test the constrained SCFG algorithms.}}}{35}}
\newlabel{tab:TestSequences}{{5}{35}}