  Based on multiple simulation trajectories, which started from dispersively
selected initial conformations, the weighted ensemble dynamics method is
designed to robustly and systematically explore the hierarchical structure of
complex conformational space through the spectral analysis of the
variance-covariance matrix of trajectory-mapped vectors. Non-degenerate ground
state of the matrix directly predicts the ergodicity of simulation data. The
ground state could be adopted as statistical weights of trajectories to
correctly reconstruct the equilibrium properties, even though each trajectory
only explores part of the conformational space. Otherwise, the degree of
degeneracy simply gives the number of meta-stable states of the system under
the time scale of individual trajectory. Manipulation on the eigenvectors leads
to the classification of trajectories into non-transition ones within the
states and transition ones between them. The transition states may also be
predicted without a priori knowledge of the system. We demonstrate the
application of the general method both to the system with a one-dimensional
glassy potential and with the one of alanine dipeptide in explicit solvent.
