removed subsubsection
TeX Live 2016 doesn't work with section and content on the same line.
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@ -518,7 +518,8 @@
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\def\subsubsection{%
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\@startsection{subsubsection}{3}{\z@}
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{-11\p@ plus -1\p@}{-1em}
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%{-11\p@ plus -1\p@}{-1em}
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{-11\p@ plus -1\p@}{0.001em}
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{\reset@font\normalfont\normalsize\itshape}}
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\def\textcolon{\text{\rm :}}
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@ -885,7 +886,8 @@
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{\reset@font\raggedright\mathversion{bold}\fontseries{b}\fontsize{10}{12}\selectfont}}
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\def\subsubsection{%
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\@startsection{subsubsection}{3}{\z@}
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{-6\p@ plus -1\p@}{-1em}
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% {-6\p@ plus -1\p@}{-1em}
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{-6\p@ plus -1\p@}{0.001em}
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{\reset@font\normalfont\normalsize\itshape}}
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\footnotesize
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\par}
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@ -65,7 +65,7 @@ and the ability to produce detailed alignment.
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\subsection{Chaining}
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\subsubsection{Chaining}
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%\subsubsection{Chaining}
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An \emph{anchor} is a 3-tuple $(x,y,w)$, indicating interval $[x-w+1,x]$ on the
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reference matching interval $[y-w+1,y]$ on the query. Given a list of anchors
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sorted by the ending reference position $x$, let $f(i)$ be the maximal chaining
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@ -96,7 +96,7 @@ score after up to $h$ iterations. This approach reduces the average time to
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$O(h\cdot m)$. In practice, we can almost always find the optimal chain with
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$h=50$; even if the heuristic fails, the optimal chain is often close.
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\subsubsection{Backtracking}
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%\subsubsection{Backtracking}
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Let $P(i)$ be the index of the best predecessor of anchor $i$. It equals 0 if
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$f(i)=w_i$ or $\argmax_j\{f(j)+\eta(j,i)-\gamma(j,i)\}$ otherwise. For each
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anchor $i$ in the descending order of $f(i)$, we apply $P(\cdot)$ repeatedly to
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@ -104,7 +104,7 @@ find its predecessor and mark each visited $i$ as `used', until $P(i)=0$ or we
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reach an already `used' $i$. This way we find all chains with no anchors used
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in more than one chains.
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\subsubsection{Identifying primary chains}
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%\subsubsection{Identifying primary chains}
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In the absence of copy number changes, each query segment should not be mapped
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to two places in the reference. However, chains found at the previous step may
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have significant or complete overlaps due to repeats in the reference.
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@ -233,6 +233,7 @@ issues.
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\bibliography{minimap2}
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\pagebreak
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\appendix
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\begin{methods}
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\section*{Appendix}
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@ -317,7 +318,6 @@ y_{rt}&=&\max\{0,y_{r-1,t}+u_{r-1,t}-z_{rt}+q\}-q-e\\
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In this formulation, cells with the same row index $r$ are independent of each
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other. This allows us to fully vectorize the computation of all cells on the
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same anti-diagonal in one inner loop.
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On the condition that $q+e<\tilde{q}+\tilde{e}$ and $e>\tilde{e}$, the boundary
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condition of this equation in the diagonal-anti-diagonal coordinate is
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\[
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@ -336,6 +336,7 @@ r\cdot(e-\tilde{e})-(\tilde{q}-q)-\tilde{e} & (r=\lceil\frac{\tilde{q}-q}{e-\til
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-\tilde{e} & (r>\lceil\frac{\tilde{q}-q}{e-\tilde{e}}-1\rceil)
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\end{array}\right.
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\]
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\citet{Suzuki:2016} first derived a similar set of equations under affine gap
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cost but with different notations.
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\end{methods}
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