. 2014 Oct 30;8:136. doi: 10.3389/fncom.2014.00136

Table 1.

Model and simulation description.

A	MODEL SUMMARY
Populations	Three: excitatory (E), inhibitory (I), external input (E_ext)
Connectivity	Random convergent connectivity with probability ϵ
Neuron model	Leaky integrate-and-fire (LIF), fixed voltage threshold, exact integration scheme (Rotter and Diesmann, 1999) (update every 0.1 ms)
Synapse model	α-shaped post-synaptic current (PSC)
Input	Independent Poisson spike trains
B	POPULATIONS
Name	Elements	Size
E,I	LIF neuron	N_E, N_I = γN_E
E_ext	Poisson generator	N_ext = N_E + N_I
C	CONNECTIVITY
Source	Target	Pattern
{E,I}	E ∪ I	Random convergent C_E = ϵN_E → 1, C_I = ϵN_I → 1
E_ext	E ∪ I	Non-overlapping 1→ 1
D	NEURON AND SYNAPSE MODEL
Name	Leaky integrate-and-fire neuron with α-shaped PSCs
Subthreshold dynamics	$\begin{array}{l} τ_{m} {\dot{V}}_{i} (t) = - V_{i} (t) + R_{m} (I_{syn, i} (t - d) + I_{ext, i} (t)) if t > t^{*} + τ_{ref} \\ V_{i} (t) = V_{res} else \end{array}$
Spiking	If V(t −) < V_thr ∧ V(t +) ≥ V_thr
	1. Set spike time t^* = t
	2. Emit spike with time-stamp t_k = t^*
Postsynaptic currents	$\begin{array}{l} I_{syn, i} (t) = \sum_{j, k} {PSC}_{i j} (t - t_{j, k}) Network input current of neuron i \\ I_{ext, i} (t) = \sum_{k} {PSC}_{ext, i} (t - t_{k}) External input current of neuron i \\ {PSC}_{i j} (t) = A (J_{i j}) \frac{t}{τ_{syn}} e^{1 - t / τ_{syn}} H (t), J_{i j} \in {- g J, 0, J} \\ {PSC}_{ext, i} (t) = A (J) \frac{t}{τ_{syn}} e^{1 - t / τ_{syn}} H (t) \end{array}$
E	INPUT
Type	Description
Poisson generators	Spike times t_k in I_ext(t) are Poisson point processes of rate ν_ext