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minor wording improvement

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Heng Li 2017-08-03 21:28:01 -04:00
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tex/minimap2.tex
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@ -68,7 +68,7 @@ and the ability to produce detailed alignment.
%\subsubsection{Chaining}
An \emph{anchor} is a 3-tuple $(x,y,w)$, indicating interval $[x-w+1,x]$ on the
reference matching interval $[y-w+1,y]$ on the query. Given a list of anchors
sorted by the ending reference position $x$, let $f(i)$ be the maximal chaining
sorted by ending reference position $x$, let $f(i)$ be the maximal chaining
score up to the $i$-th anchor in the list. $f(i)$ can be calculated with
dynamic programming (DP):
\begin{equation}\label{eq:chain}
@ -186,7 +186,7 @@ GraphMap~\citep{Sovic:2016aa},
minialign~\citep{Suzuki:2016} and
NGMLR~\citep{Sedlazeck169557}. We excluded rHAT~\citep{Liu:2016ab},
LAMSA~\citep{Liu:2017aa} and Kart~\citep{Lin:2017aa} because they either
crashed or produced malformatted output. In this evaluation, Minimap2 has a
crashed or produced malformatted output. In this evaluation, Minimap2 has
higher power to distinguish unique and repetitive hits, and achieves overall
higher mapping accuracy (Fig.~\ref{fig:eval}a). It is still the most accurate
even if we skip DP-based alignment (data not shown), suggesting chaining alone
@ -219,9 +219,9 @@ banding~\citep{Suzuki130633} or incremental banding.
In addition to reference-based read mapping, minimap2 inherits minimap's
ability to search against huge multi-species databases and to find read
overlaps. On a few test data sets, minimap2 appears to yield slightly better
miniasm assembly. Minimap2 can also align long assemblies or closely related
genomes, though more thorough evaluations are needed. Genome alignment is an
intricate topic.
miniasm assembly. Minimap2 can also align closely related genomes, though it
would benefit from more thorough evaluations. Genome alignment is an intricate
topic.
\section*{Acknowledgements}
We owe a debt of gratitude to Hajime Suzuki for releasing his masterpiece and
@ -315,9 +315,9 @@ y_{rt}&=&\max\{0,y_{r-1,t}+u_{r-1,t}-z_{rt}+q\}-q-e\\
\tilde{y}_{rt}&=&\max\{0,\tilde{y}_{r-1,t}+u_{r-1,t}-z_{rt}+\tilde{q}\}-\tilde{q}-\tilde{e}
\end{array}\right.
\end{equation*}
In this formulation, cells with the same row index $r$ are independent of each
other. This allows us to fully vectorize the computation of all cells on the
same anti-diagonal in one inner loop.
In this formulation, cells with the same diagonal index $r$ are independent of
each other. This allows us to fully vectorize the computation of all cells on
the same anti-diagonal in one inner loop.
On the condition that $q+e<\tilde{q}+\tilde{e}$ and $e>\tilde{e}$, the boundary
condition of this equation in the diagonal-anti-diagonal coordinate is