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Can you tell us more what you mean by "activity"? It does not necessarily mean that something goes to the top of the heap if there's a new comment...although that might be something to consider. Or not.
The rank is determined by the sum of a couple of decaying exponential equations, each that are affected by a few variables. Obviously, shares play a big role, but comments are also a key variable. They aren't terribly complex equations. I don't think much good could come of sharing them, however, aside from satisfying curiosity. We don't change it very often, and not by much when we do.
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