Not that all the computation are scaled by the genome size and not at the read number as in [Hu et al.](https://doi.org/10.1093/nar/gkv670), this is also why we add a scaling factor (default to $10^3$).
This scaling the $\text{ratio}IP\left(t\right)$ is multiplied by this scaling factor.
The $\text{ratio}IP\left(t\right)$ is multiplied by this scaling factor.
With this method, we retain the interesting properties of [Hu et al.](https://doi.org/10.1093/nar/gkv670) normalization on the average read density between samples (i.e., we can compare two different samples in a quantitative way) and we account for the local bias of read density observed in the WCE samples (differential chromatin accessibility, repetition, low mappability region, etc.).
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@@ -112,6 +112,6 @@ With this method, we retain the interesting properties of [Hu et al.](https://do
To compute the coverage density $X_y(t)$ with $X \in \left[IP, WCE\right]$ and $y \in \left[c, x\right]$ we count the number of read $r(t)$ overlapping with position $t$.
For properly paired reads (with a mate read on the same chromosome and with a starting position ending after the end of the read) we also count a density of 1 between the end of the first reads and the start of his mate read $g(t)$. $X_y(t) = r(t) + g(t)$.
Some fragment can be artificially long, therefore, we compute a robust mean $\mu$ of the gap size, between two reads of a pair, by removing the 0.1 upper and lower value of fragment length. Fragment that has a size higher than $\phi^{-1}(0.95, /mu, 1.0)$ are set to end at the $\phi^{-1}(0.95, /mu, 1.0)$ value, with $\phi()$ the Normal CDF function.
Some fragment can be artificially long, therefore, we compute a robust mean $\mu$ of the gap size, between two reads of a pair, by removing the 0.1 upper and lower value of fragment length. Fragment that has a size higher than $\phi^{-1}(0.95, \mu, 1.0)$ are set to end at the $\phi^{-1}(0.95, \mu, 1.0)$ value, with $\phi()$ the Normal CDF function.
Some fragment can be shorter than the read length in this case we don't count the overlapping reads region as a coverage of 2 fragment but as a coverage of 1 fragment.
