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Equation 5 · Part 13 · Comparing the Main Approaches to AI for Science and Medicine

Ending index or upper bound: N

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}
NN

What this part means

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

Its job in the formula

N occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

The passage around this formula

…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. It is not, by construction, a statement about how the molecule moves, how quickly it interconverts between…

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Learn the underlying idea

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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Sources cited in the surrounding passage

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