dynamo.vf.path_integral

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

Parameters
  • VecFnc

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

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

  • xyGridSpacing (float) – Grid spacing for “starting points” for each “path” on the pot. surface

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

  • tol (float (default: 1.0e-2)) – Tolerance to test for convergence.

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

Returns

  • numAttractors (int) – Number of attractors identified by the path integral approach.

  • attractors_num_X_Y (numpy.ndarray) – Attractor number and the corresponding x, y coordinates.

  • sepx_old_new_pathNum (numpy.ndarray) – The IDs of the two attractors for each separaxis per row.

  • numPaths_att numpy.ndarray – Number of paths per attractor

  • numPaths (int) – Total Number of paths for defined grid spacing.

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

  • pot_path (numpy.ndarray (dimension: numPaths x numTimeSteps)) – Potential along the path.

  • path_tag (numpy.ndarray (dimension: numPaths x 1)) – Tag for given path (to denote basin of attraction).

  • attractors_pot (numpy.ndarray) – Potential value of each identified attractors by the path integral approach.

  • x_path (numpy.ndarray) – x-coord. along path.

  • y_path (numpy.ndarray) – y-coord. along path.