time_b?

[KPEKEP]

Hello!
First of all thank you for such an interesting work!
I have a couple questions:

1. Could you please elaborate how did you come from this formulae
   

to having extra term time_b? Where does it come from and what is it's meaning?

CfC/torch_cfc.py

Line 139 in 3ebaa03

t_b = self.time_b(x)

2. From my understanding, in minimal case of Cfc model, x0 is assumed to be zero:
   https://github.com/fullerf/LightningCfC/blob/6dc15040c5a003ae837bcbf24ddda45dd99f8cff/src/LightningCfC/torch_cfc.py#L129
   It it always the case though? And is it safe assumption to make?

Thanks, looking forward to your response.

[KPEKEP]

I wonder, if time_b is approximation of w_tau, then why it is not multiplied by time when calculating sigma?