# What are "unspecified" differentials in a differential characteristic?

I've been studying many papers on differential cryptanalysis and I see that in the published differential characteristics, such as in the appendices of [1], [2] and [3], some differences are left "unspecified" (usually denoted by ** or -).

Why are these differences left unspecified? Since the differentials pass through an S-box, shouldn't their probability be counted? Additionally, how to determine which differentials can be left unspecified and which cannot? Specifically, I'm asking in the context of boomerang attacks

For a more concrete example, section 3.2 from this paper [1] lists a toy example of computing the probability of a differential characteristic for SKINNY:

Example 1. Figure 3 shows a toy example of boomerang characteristic with two differential characteristics on 3 rounds of SKINNY-64(the upper characteristic is above the lower characteristic). We suppose that we are not adding differences in the key (SK model), so we omit the key from the figure as it will not modify the differences. Lime (for the upper characteristic) and pink (for the lower characteristic) colored cells are non zero differences,and grey cells are unspecified differences. All the differences are given in hexadecimal. We denote the input and output differences by ∆ex= [0,d,d,0,0,0,0,0,0,5,0,0,0,0,0,0] and ∇ex= [0,0,2,0,0,2,0,0,0,0,0,0,0,0,0,0] respectively.

In R1 of the upper characteristic, the cell in position 1 (starting from top left, from left to right) with value "2" passes through the SB layer to the "unspecified" gray cell, thus its probability is not counted. It's not clear to me why these cells in particular do not have their probabilities counted in the total prob. of the distinguisher, and why some cells are seemingly more important than others.