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Bhattacharya method for path integration

Source: R/Bhattacharya_method.R
path_integral_B.Rd

A method to construct potential landscapes using path integration. See references for details.

Usage

path_integral_B(
  f,
  lims,
  n_path_int = 20,
  stepsize = 0.01,
  tol = 0.01,
  numTimeSteps = 1400,
  ...
)

Arguments

f

The vector field function. It should return c(<dx/dt>, <dy/dt>)

lims

The limits of the range for the estimation as c(<xl>, <xu>, <yl>, <yu>).

n_path_int

The number of equally spaced points in each axis, at which the path integrals is to be calculated.

stepsize

The time step used in each iteration.

tol

The tolerance to test convergence.

numTimeSteps

Number of time steps for integrating along each path (to ensure uniform arrays). Choose high-enough number for convergence with given stepsize.

...

Not in use.

Value

A list with the following elements:

  • numPaths Integer. Total Number of paths for defined grid spacing.

  • pot_path Matrix. Potential along the paths.

  • path_tag Vector. Tag for given paths.

  • attractors_pot Vector. Potential value of each identified attractor by the path integral approach.

  • x_path Vector. x-coord. along path.

  • y_path Vector. y-coord. along path.

References

Bhattacharya, S., Zhang, Q., & Andersen, M. E. (2011). A deterministic map of Waddington’s epigenetic landscape for cell fate specification. BMC Systems Biology, 5(1), 85. https://doi.org/10.1186/1752-0509-5-85. The functions in this file were translated from the Matlab code provided with the reference above, and its Python translation at https://dynamo-release.readthedocs.io/en/v0.95.2/_modules/dynamo/vectorfield/Bhattacharya.html