I think the answer is necessarily "no," because the rhythm is a sign we observe of some functional system in the brain, not the functional system itself. Similar to how your heart rate is just a sign of the beating of your heart, only the latter of which is a real functional mechanism. Something is happening in the brain that generates these patterns and which also has to do with the cognitive faculties described in the paper; I don't think anyone has a very clear idea what that mechanism is, though.
I'm not sure if this answers your question, or is just pedantry. :)