Fig. 2: Evaluation of MuTrans in dynamical system simulation datasets.

a MuTrans distinguishes the stable and transition cells simulated using a stochastic saddle-bifurcation model. (Blue lines) The simulated trajectories of model. (Black Lines) Bifurcation plot of the underlying dynamical system. (Red Lines) The trajectory points corresponding to the transition cells that are switching between two states as the input to MuTrans (N=2,000). (Purple Lines) The transition cell score (TCS) values for transition cells calculated by MuTrans. The stable cells have TCS of value 0 or 1, while the TCS of transition cells decrease from 1 to 0 during transition. b, c The simulation dataset of over-damped Langevin dynamics in two-dimensional, triple potential-well system. b Simulated trajectories (red lines) and potential field (values indicated by color bars) in two-dimensional phase space. c Time series of the simulated trajectories, where the abrupt changes of values indicate state-transitions among attractor basins. d, e MuTrans reveals the transitions in triple-well system solely from sampled, snap-shot datasets (N = 2,001). d The method detects three attractor basins and coarse-grained transition probability matrix among them. Cells are colored by attractors. e The transition cells near saddle points have larger MuTrans transition entropy than the cells near fixed points. The calculated membership functions quantify the relative cell positions in each attractor. Entropy and membership values are indicated by color bars.