dynamo.vf.transition_rate¶
- dynamo.vf.transition_rate(X_input, F, D=0.1, lambda_=1)[source]¶
Calculate the rate to convert from one cell state to another cell state by taking the optimal path.
In the small noise limit (D -> 0) the Wentzell-Freidlin theory states that the transition rate from one basin to another one to a leading order is related to the minimum action corresponding zero energy path (Eeff = 0) connecting the starting fixed point and the saddle point x_{sd} by k pprox exp(−S0 (x_{sd})). To take into account that for finite noise, the actual optimal path bypasses the saddle point, in Eqn. 2 of the main text a transition rate is actually estimated by the action of the whole path connecting the two fixed points, giving that the portion of the path following the vector field contributes zero action. Here we have neglected some pre-exponential factor (see Eq. 5.24 of reference [15]), which is expected to be on the order of 1 [12]. (Reference: Epigenetic state network approach for describing cell phenotypic transitions. Ping Wang, Chaoming Song, Hang Zhang, Zhanghan Wu, Xiao-Jun Tian and Jianhua Xing)
- Parameters
X_input (numpy.ndarray) – The initial guess of the least action path. Default is a straight line connecting the starting and end path.
F (Function) – The reconstructed vector field function
D (float) – The diffusion constant. Note that this can be a space-dependent matrix.
lamada (float) – Regularization parameter
- Returns
- Return type
The transition to convert from one cell state to another.