dynamo.vf.path_integral(VecFnc, x_lim, y_lim, xyGridSpacing, dt=0.01, tol=0.01, numTimeSteps=1400)[source]

A deterministic map of Waddington’s epigenetic landscape for cell fate specification Sudin Bhattacharya, Qiang Zhang and Melvin E. Andersen

  • VecFnc (Callable) – The function of vector field that takes in x, y and returns the velocity at that point.

  • x_lim (ndarray) – Lower or upper limit of x-axis.

  • y_lim (ndarray) – Lower or upper limit of y-axis

  • xyGridSpacing (Union[int, float]) – Grid spacing for “starting points” for each “path” on the potential surface

  • dt (float) – Time step for the path integral.

  • tol (float) – Tolerance to test for convergence.

  • numTimeSteps (int) – A high-enough number for convergence with given dt.


numAttractors: Number of attractors identified by the path integral approach. attractors_num_X_Y: Attractor number and the corresponding x, y coordinates. sepx_old_new_pathNum: The IDs of the two attractors for each separaxis per row. numPaths_att: Number of paths per attractor numPaths: Total Number of paths for defined grid spacing. numTimeSteps: A high-enough number for convergence with given dt. pot_path: Potential along the path. (dimension: numPaths x numTimeSteps) path_tag: Tag for given path (to denote basin of attraction). (dimension: numPaths x 1) attractors_pot: Potential value of each identified attractors by the path integral approach. x_path: x-coord along path. y_path: y-coord along path.

Return type:

A tuple containing