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Equation 5 · Part 4 · Comparing the Main Approaches to AI for Science and Medicine

Symbol hatx_i

RMSD=1N∑i=1N∥xi−x^i∥2\text{RMSD} = \sqrt{\frac{1}{N} \sum_{i=1}^{N} \lVert x_i - \hat{x}_i \rVert^2}
x^i\hat{x}_i

What this part means

the corresponding coordinate in the predicted structure after optimal superposition of the two.

Its job in the formula

hatxix_i is one of the signed contributions combined to compute the quantity on the left.

Where the article explains it

where xix_i is the coordinate of atom i in the experimentally solved structure, x^i\hat{x}_i is the corresponding coordinate in the predicted structure after optimal superposition of the two, and N is the number of atoms compared.

The passage around this formula

…actually measures is worth stating explicitly, because the number is often quoted without the definition it depends on: RMSD=1N∑i=1N∥xi−x^i∥2\text{RMSD} = \sqrt{\frac{1}{N} \sum_{i=1}^{N} \lVert x_i - \hat{x}_i \rVert^2}. where xix_i is the coordinate of atom i in the experimentally solved structure, x^i\hat{x}_i is the corresponding coordinate in the predicted structure after optimal superposition of the two, and N is the number of atoms compared. This is a statement about the average positional deviation of one predicted, static conformation from one experimentally solved, static conformation.…

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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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