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Three-Layer Precision, Three-Layer Recall, and Three-Layer F1 Score

This section needs fixing, it seems there are some problems with the math command. See here for a working version.

Three-layer precision ($P_{3}$), three-layer recall ($R_{3}$), and three-layer $F_{1}$ score ($F_{3}$) are defined as follows:

$F_{3}(\Pi ,\Xi )={\frac {2P_{3}(\Pi ,\Xi )R_{3}(\Pi ,\Xi )}{P_{3}(\Pi ,\Xi )+R_{3}(\Pi ,\Xi )}},$

where

Failed to parse (syntax error): {\displaystyle P_3(\Pi, \Xi) &=& \frac{1}{n_\mathcal{Q}} \sum_{j = 1}^{n_\mathcal{Q}} }