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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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@ -68,7 +68,7 @@ and the ability to produce detailed alignment.
%\subsubsection{Chaining} %\subsubsection{Chaining}
An \emph{anchor} is a 3-tuple $(x,y,w)$, indicating interval $[x-w+1,x]$ on the 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 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 score up to the $i$-th anchor in the list. $f(i)$ can be calculated with
dynamic programming (DP): dynamic programming (DP):
\begin{equation}\label{eq:chain} \begin{equation}\label{eq:chain}
@ -186,7 +186,7 @@ GraphMap~\citep{Sovic:2016aa},
minialign~\citep{Suzuki:2016} and minialign~\citep{Suzuki:2016} and
NGMLR~\citep{Sedlazeck169557}. We excluded rHAT~\citep{Liu:2016ab}, NGMLR~\citep{Sedlazeck169557}. We excluded rHAT~\citep{Liu:2016ab},
LAMSA~\citep{Liu:2017aa} and Kart~\citep{Lin:2017aa} because they either 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 power to distinguish unique and repetitive hits, and achieves overall
higher mapping accuracy (Fig.~\ref{fig:eval}a). It is still the most accurate 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 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 In addition to reference-based read mapping, minimap2 inherits minimap's
ability to search against huge multi-species databases and to find read 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 overlaps. On a few test data sets, minimap2 appears to yield slightly better
miniasm assembly. Minimap2 can also align long assemblies or closely related miniasm assembly. Minimap2 can also align closely related genomes, though it
genomes, though more thorough evaluations are needed. Genome alignment is an would benefit from more thorough evaluations. Genome alignment is an intricate
intricate topic. topic.
\section*{Acknowledgements} \section*{Acknowledgements}
We owe a debt of gratitude to Hajime Suzuki for releasing his masterpiece and 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} \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{array}\right.
\end{equation*} \end{equation*}
In this formulation, cells with the same row index $r$ are independent of each In this formulation, cells with the same diagonal index $r$ are independent of
other. This allows us to fully vectorize the computation of all cells on the each other. This allows us to fully vectorize the computation of all cells on
same anti-diagonal in one inner loop. the same anti-diagonal in one inner loop.
On the condition that $q+e<\tilde{q}+\tilde{e}$ and $e>\tilde{e}$, the boundary 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 condition of this equation in the diagonal-anti-diagonal coordinate is