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Used math tag for large latex blocks.
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gunjanbaid authored Jul 27, 2017
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12 changes: 6 additions & 6 deletions docs/source/70_algorithms.md
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Expand Up @@ -141,9 +141,9 @@ estimate the observed base quality using the below equation. This represents a
Bayesian model of the mismatch probability with Binomial likelihood and a
Beta(1, 1) prior.

`$
```math
\mathbf{E}(P_{err}|{cov}) = \frac{\text{\#errors}(cov) + 1}{\text{\#observations}(cov) + 2}
$`
```

After these probabilities are estimated, we go back across the input read
dataset and reconstruct the quality scores of the read by using the covariate
Expand Down Expand Up @@ -176,13 +176,13 @@ maximal convex hulls across the set of regions. For a set `$R$` of regions, we
define a maximal convex hull as the largest region `$\hat{r}$` that satisfies the
following properties:

`$
```math
\begin{align}
\hat{r} &= \cup_{r_i \in \hat{R}} r_i \\
\hat{r} \cap r_i &\ne \emptyset, \forall r_i \in \hat{R} \\
\hat{R} &\subset R
\end{align}
$`
```

In our problem, we seek to find all of the maximal convex hulls, given a set of
regions. For genomics, the convexity constraint described by equation
Expand Down Expand Up @@ -275,14 +275,14 @@ consensus sequence. Given a consensus sequence `$c$`, a reference sequence `$R$`
and a set of reads `$\mathbf{r}$`, we calculate this score using the equation
below.

`$
```math
\begin{align}
q_{i, j} &= \sum_{k = 0}^{l_{r_i}} Q_k I[r_I(k) = c(j + k)] \forall r_i \in \mathbf{R}, j \in \{0, \dots, l_c - l_{r_i}\} \\
q_{i, R} &= \sum_{k = 0}^{l_{r_i}} Q_k I[r_I(k) = c(j + k)] \forall r_i \in \mathbf{R}, j = \text{pos}(r_i | R) \\
q_i &= \min(q_{i, R}, \min_{j \in \{0, \dots, l_c - l_{r_i}\}} q_{i, j}) \\
q_c &= \sum_{r_i \in \mathbf{r}} q_i
\end{align}
$`
```

In the above equation, `$s(i)$` denotes the base at position `$i$` of sequence `$s$`,
and `$l_s$` denotes the length of sequence `$s$`. We pick the consensus sequence
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