nnmt.lif.exp._transfer_function_shift

nnmt.lif.exp._transfer_function_shift(mu, sigma, tau_m, tau_s, tau_r, V_th_rel, V_0_rel, omegas, synaptic_filter=True)[source]

Calcs value of transfer func for one population at given frequency omega.

Calculates transfer function based on \tilde{n} in Schuecker et al. [2015]. The expression is to first order in \sqrt{\tau_\mathrm{s} / \tau_\mathrm{m}} equivalent to nnmt.lif.exp._transfer_function_taylor().

The difference to the equation in Schuecker et al. [2015] is that the linear response of the system is considered with respect to a perturbation of the input to the current I, leading to an additional synaptic low pass filter 1/(1+i omega tau_s). Compare with the second equation of Eq. 18 and the text below Eq. 29.

Assumptions and approximations:

  • Diffusion approximation
  • Linear response theory
  • Fast synapses: \sqrt{\tau_\mathrm{s} / \tau_\mathrm{m}} \ll 1
  • Low frequencies: \omega\sqrt{\tau_\mathrm{m} \tau_\mathrm{s}} \ll 1
Parameters:
mu[float | np.array]

Mean neuron activity of one population in V.

sigma[float | np.array]

Standard deviation of neuron activity of one population in V.

tau_m[float | np.array]

Membrane time constant of post-synatic neuron in s.

tau_sfloat

Pre-synaptic time constant in s.

tau_r[float | np.array]

Refractory time in s.

V_th_rel[float | np.array]

Relative threshold potential in V.

V_0_rel[float | np.array]

Relative reset potential in V.

omegas[float | np.array]

Input angular frequency to population in Hz.

synaptic_filterbool

Whether an additional synaptic low pass filter is to be used or not. Default is True.
Returns:
[float | np.array]

Transfer function in Hz/V.