#### Z-score

The Z-score is calculated over 2000 random protein decoys and measures how much a Domain or Protein Unit deviates from the random mean value of foldability-likeliness in terms of standard deviation. For example, a Z-score of -3 means that the Domain or Protein Unit deviates from the random mean value by 3 standard deviations, which means that the structure is far from being random and therefore has an increased probability of being an autonomous structural unit.

#### AUL - Autonomous Units Likelihood

AUL is a percentage based on the Chebyshev's Theorem which estimates the minimum proportion of observed protein structures that fall within a specified number of standard deviations from the mean.

We calculate the percentage according to the following conditions: $$ \begin{cases} 0 & |k| \lt 1 \\ (1 - {1 \over k^2})\times100 & |k| \ge 1 \end{cases}$$ where k equals the number of standard deviations: Z-score.

For example, an AUL of 81% (Z-score of -2.3) means that at least 81% of the observed structures fall inside 2.3 standard deviations.