nnmt.lif.exp._derivative_of_firing_rates_wrt_mean_input¶

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

Derivative of the stationary firing rates with respect to the mean input.

See Appendix B in Schuecker et al. [2014].

Assumptions and approximations:

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

Parameters:

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

Returns:

float: Zero frequency limit of colored noise transfer function in Hz/V.