  Many problems in materials science and biology involve particles interacting
with strong, short-ranged bonds, that can break and form on experimental
timescales. Treating such bonds as constraints can significantly speed up
sampling their equilibrium distribution, and there are several methods to
sample probability distributions subject to fixed constraints. We introduce a
Monte Carlo method to handle the case when constraints can break and form. More
generally, the method samples a probability distribution on a stratification: a
collection of manifolds of different dimensions, where the lower-dimensional
manifolds lie on the boundaries of the higher-dimensional manifolds. We show
several applications of the method in polymer physics, self-assembly of
colloids, and volume calculation in high dimensions.
