Fig. 3. Rotational frequencies are conserved between different reaches.

a Eigenvalues of a single condition’s dynamics (left), and probability density of eigenvalues for all conditions (right). Data shown from M1-N. b Eigenvalue distance between conditions was calculated by averaging over the distances between corresponding eigenvalues in complex space. c Histograms of eigenvalue distance observed between condition (black) and distribution expected from estimation noise (gray). d We used a matrix factorization to identify temporal basis functions shared across conditions, along with the condition-specific loading matrix. e Each condition’s loading matrix specifies the rotational plane, phase, and magnitude, or “parameters” of a rotation. f Each condition’s loading matrix specifies the dimension and magnitude of firing rate offsets, or the “state space location”. g Temporal basis functions identified for M1-J. h Rotations recovered from motor cortex activity by projecting onto loading matrix. Solid line, mean projection across conditions; translucent lines, projections of single conditions. i Warping reaches (gray) induced a negative correlation between model fit and extremity of reach duration not observed in the original data (blue).