Figure 1.

An illustration of the Stratified RE-SWHAM algorithm. This drawing shows two λ-states with “grey” or “cyan” color. Each λ-state has two macrostates A and B. The grey λ-state is locally equilibrated while the simulations at the cyan λ-state are approximately equilibrated among the macrostates. The white gap between macrostates at the grey λ-state represents an uncrossable barrier for the “move” procedure during the Stratified RE-SWHAM analysis. Beforehand, we construct each λ-state a database which contains all the observations obtained from that λ-state, and each observation is tagged by the macrostate which it belongs to. As shown in the picture, the observations are separated into two subgroups A and B. Then Stratified RE-SWHAM is run in cycles, which consists of a “move” procedure and an “exchange” procedure. In the move procedure, Stratified RE-SWHAM chooses an observation to associate with the replica at each λ-state. At the cyan λ-state, the next observation is chosen from the whole database of that λ-state with equal probability. However, at the grey λ-state, the next observation is chosen from the subgroup which the previous observation belongs to with equal probability. In the exchange procedure, if the exchange attempt is accepted, in addition to the swap of the replicas, the observations associated with the replicas are also swapped to the database of the other λ-state. At the end of each cycle, the observation associated with each replica is recorded as the output of Stratified RE-SWHAM.