Equation 5 · Part 3 · Comparing the Main Approaches to AI for Science and Medicine

Symbol x_i

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

x_i

What this part means

the coordinate of atom i in the experimentally solved structure, $\hat{x}_i$ is the corresponding coordinate in the predicted structure after optimal superposition of the two.

Its job in the formula

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

Full expressionSymbol x_iArticle meaning

Where the article explains it

where $x_i$ is the coordinate of atom i in the experimentally solved structure, $\hat{x}_i$ 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

…the next-best method [ 9 ] . What that root-mean-square-deviation figure actually measures is worth stating explicitly, because the number is often quoted without the definition it depends on: $\text{RMSD} = \sqrt{\frac{1}{N} \sum_{i=1}^{N} \lVert x_i - \hat{x}_i \rVert^2}$ . where $x_i$ is the coordinate of atom i in the experimentally solved structure, $\hat{x}_i$ 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,…

Read this part in the article →

Learn the underlying idea

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

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the surrounding passage

[9] Highly Accurate Protein Structure Prediction with AlphaFold ↗

These citations provide research context; check each source for the exact claim it supports.