Harmony is a process by which a feature spreads throughout a word or some other domain. The segment that initiates harmony is referred to as the trigger, and those that undergo harmony are its targets. Some segments seemingly do not participate in harmony; these are called neutral segments, and they are of two types. Transparent segments are those that do not undergo harmony but do not stop it ...

Proof. Consider p-bond percolation on an an infinite dregular tree T rooted at ρ and write CT (ρ) for the component containing ρ. Write CG(v) for the component of v in Gp. It is clear that we can couple such that |CG(v)| ≤ |CT (ρ)|. Recall the exploration process on T : At time t = 0 only ρ = v1 is active, other vertices neutral. At time t ≥ 0 if the number of active vertices Mt > 0, then set t...

Using a variety of different definitions of “neutrality,” this study presents significant evidence against the neutrality to market risk of hedge funds in a range of style categories. I generalize standard definitions of “market neutrality,” and propose five different neutrality concepts. I suggest statistical tests for each neutrality concept, and apply these tests to a database of monthly ret...