Confusing notation of the factor-to-variable message in the belief propagation algorithm for trees

[nbro]

The following equation is quite confusing

Specifically, you use x_{\mathcal N(s)} as input to f_s, but the summation is over x_{\mathcal N(s)\setminus i}, whose meaning is not very clear. I think you should clarify this point a little more. Here, $x$ is a random variable, so what could x_{\mathcal N(s)} mean?

[jiamings]

I think the \mathcal{N} should be N, which is defined above as all the neighbors of a node.
Will update this later.