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Formatting update for github parsing of math expression in README.md
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davids60 committed Apr 2, 2025
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Expand Up @@ -158,7 +158,7 @@ Lastly, for all false positive calculations, primer sets being compared must all
## Scoring

Once all primer sets have had primer set performance features calculated, an overall score is calculated by ordering primer sets and weighting a primer sets individual score according to its placement in the resulting order amongst all primer sets. This is achieve using the following formulation:
$
S_k = \omega_{\bar{I}} \cdot \left( 1 - \frac{max \left( \bar{I} \right) - \bar{I}_k}{Range \left( \bar(I) \right)} \right) + \sum _x \omega _x \cdot \left( 1 - \frac{\text{min}(x) - x_k}{\text{Range}(x))} \right) + \sum _{i=0} ^n \left( i \cdot \alpha \cdot \left( 1 - \frac{\phi \left( \Omega \right)_i}{\text{max}(\phi (\Omega))_i} \right) \right)
$

$S_k = \omega_{\bar{I}} \cdot \left( 1 - \frac{max \left( \bar{I} \right) - \bar{I}_k}{Range \left( \bar(I) \right)} \right) + \sum _x \omega _x \cdot \left( 1 - \frac{\text{min}(x) - x_k}{\text{Range}(x))} \right) + \sum _{i=0} ^n \left( i \cdot \alpha \cdot \left( 1 - \frac{\phi \left( \Omega \right)_i}{\text{max}(\phi (\Omega))_i} \right) \right)$

where $k$ is a given primer set, $x$ indicates a given feature, $\omega_x$ is the weight allocated to feature $x$, $x_k$ is the feature value for primer set $k$, $\alpha$ is the false positive weighting factor, $n$ is the number of replicates, $\Omega_i$ is the reaction penalty for reaction $i$, and $\phi$ is the set of reaction penalities for each *false positive* reaction for a specific primer set ordered from smallest to largest such that an element $\Omega \in \phi$ if a given primer set has at least $i$ false positives, and $\text{max}(\phi (\Omega))_i $ is the maximum value of the $i$th reaction penalty of each primer set containing at least $i$ false positives.

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