If you have the 2H perks "Berserker" and "Vandal," do they apply if you're using 1H or polearm?

[Targyr Darksun]

There's perks in the 2H line that specifically say for "Two Handed Weapons." But there's a few perks, like Berserker, and Vandal that don't specifically say that. Berserker just says, "speed bonus modifier while player is on foot," and Vandal says, "damage to objects increased by 40%."

Does anyone know for sure whether these perks affect you when you're using 1H or polearm? It doesn't specifically say it's only for 2H.