Optimisation of the global model $\mathfrak{S}$

The global model is defined as

$$\mathfrak{S}= \mathfrak{D}\cup \left( \bigcup_{i=1}^l \mathfrak{F}_i \right),$$ (15.6)

where i is the residue index and l is the total number of residues used in the analysis. This is the most complex of the four categories as both diffusion tensor parameters and model-free parameters of all selected residues are optimised simultaneously. The dimensionality of the model $\mathfrak{S}$ is much greater than the other categories and is equal to

$$\mathfrak{S}= \dim \mathfrak{D}+ \sum_{i=1}^l k_i \leqslant 6 + 5l,$$ (15.7)

where k_i is the number of model-free parameters for the residue i and is equal to dim$\mathfrak{F}_i$, the number six corresponds to the maximum dimensionality of $\mathfrak{D}$, and the number five corresponds to the maximum dimensionality of $\mathfrak{F}_i$.