nnmt.lif.exp._firing_rate_shift¶

nnmt.lif.exp._firing_rate_shift(mu, sigma, V_0_rel, V_th_rel, tau_m, tau_r, tau_s)[source]¶

Calculates stationary mean firing rates including synaptic filtering.

Based on the equation after Eq. 4.33 in Fourcaud and Brunel [2002], using shift of the integration boundaries in the white noise Siegert formula.

Assumptions and approximations:

Diffusion approximation
Fast synapses: $\sqrt{\tau_\mathrm{s} / \tau_\mathrm{m}} \ll 1$

Parameters:

mu[float | np.array]: Mean neuron activity in V.
sigma[float | np.array]: Standard deviation of neuron activity in V.
V_0_rel[float | np.array]: Relative reset potential in V.
V_th_rel[float | np.array]: Relative threshold potential in V.
tau_m[float | 1d array]: Membrane time constant of post-synatic neuron in s.
tau_r[float | 1d array]: Refractory time in s.
tau_sfloat: Pre-synaptic time constant in s.

Returns:

[float | np.array]: Stationary firing rate in Hz.