deletions | additions       diff --git a/M&M - analytical.tex b/M&M - analytical.tex  index 5a1959f..6593b40 100644  --- a/M&M - analytical.tex  +++ b/M&M - analytical.tex 
...
By writing the surviving fraction as $S_\text{GNP} = \exp(-\alpha_\text{GNP}D-\beta_\text{GNP}D^2)$, then performing a Taylor expansion of both left and right sides of Equation \ref{eq_sapprox} and retaining only the linear and quadratic terms in the dose, the following relations are obtained  \begin{align}  \label{analytical} %\label{analytical}  \alpha_\text{GNP} &= \bar{N}^0_\text{ion} \bar{N}_\text{GNP} \\  \beta_\text{GNP} &= 0  \end{align} 
...
Since the quadratic terms is zero, it is possible to obtain the net survival by just multiplying the fractions due to the bare gamma radiation with those due to the GNP ionizations, $S = S_\gamma \times S_\text{GNP}$ (additive approximation), whose LQ parameters in presence of GNPs are expressed as  \begin{align}  \label{analytical2} %\label{analytical2}  \alpha &= \alpha_\gamma + \bar{N}^0_\text{ion} \bar{N}_\text{GNP} \\  \beta &= \beta_\gamma  \end{align}