I'm a much bigger fan of the idea of "control" over the population rather than the concept of "hearts and minds", which as everyone notes is very fuzzy. Basically, I think Kalyvas is mostly right.

Control can come about through many different factors and context matters above all. In some places a substantial police presence may be enough, in others a combined mil/police or mil/only presence has to occur. But an effective and continuous presence among the population must be gained and maintained by the counterinsurgent force - whether this presence is a co-opted force of former insurgents, a warlord, an elected council with its own locally recruited militia, a secret police force, whatever. Using Kilcullen's term, "repetitive raiding" is not enough against an insurgency of any strength.