Extended Data Fig. 1: Simulating the bifurcation of reference and query trajectories using change point kernels.

(Note: A change point kernel defines shifts and changes in covariance between discrete time points in a time series that describes a particular Gaussian process. In the context of a single-cell pseudotime trajectory, each discrete time point corresponds to a single cell. The change point kernel can be represented by a pairwise covariance matrix between those time points, visualized using heatmaps). a, Change point kernel heatmaps for each approximate bifurcation point (change point) \(\in\) [0.25,0.5,0.75]. b, The same change point kernels binarized based on the 0.01 covariance threshold (top), c, The average covariance plotted for each \(i\times i\) sub square matrix from \(i=0\) to \(i=\) change point, showing that the branching effect can approximately start before the specified change point. d, Expected bifurcation region is taken from the point where we begin to see > 0.01 covariance in the change point kernel, until the particular change point. e, Illustration of the main regions of match and mismatch expected in trajectory alignment under Divergence class (left) and Convergence class (right). A Divergence alignment is described by a start-match region followed by an end-mismatch region, whereas a Convergence alignment is described by a start-mismatch region followed by an end-match region. Illustrations in d-e were created using BioRender (https://biorender.com).