nnmt.lif.exp._pairwise_effective_connectivity¶

nnmt.lif.exp._pairwise_effective_connectivity(nu, mu, sigma, J, V_0_rel, V_th_rel, tau_m, tau_s)[source]¶

Calcs the pairwise effective connectivity matrix in linear response theory.

Basically, this is the matrix version of _derivative_of_firing_rates_wrt_input_rate().

See Eq. A.3 in Appendix A of Helias et al. [2013].

Assumptions and approximations:

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

Parameters:

nunp.array: Firing rates of populations in Hz.
munp.array: Mean neuron activity in V.
sigmanp.array: Standard deviation of neuron activity in V.
Jnp.array: Pairwise connectivity matrix 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_sfloat: Pre-synaptic time constant in s.

Returns:

[float | np.array]: Pairwise effective connectivity matrix.