# Technological Uncertainty

The propagation of technological (modeling) uncertainties in SAUNA is based upon the equivalence of a change in the total cross section $$\sigma\_{t,i}$$ and concentration $$C\_i$$ of the corresponding nuclide $$i\in mat$$. That is, the sensitivities of a functional $$R$$ to the parameters are the same: $$S(R,\sigma\_{t,i})=S(R,C\_{i})$$. In the same manner, the sensitivity to the density of material $$\rho\_{mat}$$ is the sum of the changes:

$$
S(R,\rho\_{mat}) = \sum\_{i\in mat}S(R,\sigma\_{t,i})
$$

This can be expanded onto other parameters such as atomic fraction $$a\_i$$ and weight fraction $$w\_i$$.  However, these parameters are required to be renormalized to ensure the sums of the corresponding values are equal to unity. The renormalization is conducted in a Perfetti-like approach:

$$
S'(R,a\_i)=S(R,\sigma\_{t,i})-\frac{a\_i}{1-a\_i}\sum\_{j\neq i}S(R,\sigma\_{t,j})
$$

$$
S'(R,w\_i)=\frac{S(R,\sigma\_{t,i})}{1-w\_i}-\frac{w\_i}{1-w\_i}\sum\_{j\neq i}\frac{S(R,\sigma\_{t,j})}{1-w\_j}
$$

This approach does not pose any approximations beyond first-order perturbation theory since it does not assume perturbing the other technological parameters such as temperature and geometry that require special techniques to address.