Table 2.

Summary of model dynamics after Nordlie et al. (2009)

Neuron models
Name	HVCRA, HVCI and auditory neurons (precise)
Type	Leaky integrate-and-fire, α-current input
Subthreshold dynamics	\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\begin{array}{rll} \tau_m \dot{V}(t) &=& -V(t) + R I(t) \,\text{if} \; t > t^*+\tau_{\text{ref}} \\ V(t) &=& V_{0} \qquad\qquad\qquad \text{else} \\[6pt]I(t) &=& I_0 +\hat{i}\frac{e}{\tau_{\alpha}}\sum_{k}(t-\tilde{t}_k)e^{-\frac{(t-\tilde{t}_k)}{\tau_\alpha}}H(t-\tilde{t}_k), {\rm where} H(x) {\text{ is the Heaviside step function}}\end{array}$\end{document}
Spiking	If V(t − ) < V th ∧ V(t + ) ≥ V th    1. calculate retrospective threshold crossing with bisectioning method (Hanuschkin et al. 2010d)    2. set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$t^{*}=t+\Delta_{\mathrm{offset}}$\end{document}    3. emit spike with time stamp t *

Neuron models
Name	HVCRA, HVCI and auditory neurons (grid constrained)
Type	Leaky integrate-and-fire, α-current input
Subthreshold dynamics	\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\begin{array}{rll} \tau_m \dot{V}(t) &=& -V(t) + R I(t) \,\text{if} \; t > t^*+\tau_{\text{ref}} \\ V(t) &=& V_{0} \qquad\qquad\qquad \text{else} \\[6pt]I(t) &=& I_0 +\hat{i}\frac{e}{\tau_{\alpha}}\sum_{k}(t-\tilde{t}_k)e^{-\frac{(t-\tilde{t}_k)}{\tau_\alpha}}H(t-\tilde{t}_k), {\rm where} H(x) {\text{ is the Heaviside step function}}\end{array}$\end{document}
Spiking	If V(t − ) < V th ∧ V(t + ) ≥ V th emit spike with time stamp t +

Synapse Model
Name	STDP synapse
Type	Simple STDP with additive update rule for potentiation and depression. Exponential decay of weights.
Spike pairing scheme	All-to-all (for nomenclature see Morrison et al. 2008)
Pair-based update rule	Δw  +  =\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lambda e^{-\Delta t/\tau_{+}}$\end{document} if Δt > 0 Δw  −  = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$-\lambda e^{-\left|\Delta t\right|/\tau_{-}}$\end{document} else Δt: temporal difference between post- and presynaptic spikes
Weight dependence	Fixed upper W max and lower W min bounds. Exponential decay: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w(t)=w_{0}e^{-t/\tau_{\mathrm{decay}}}$\end{document}.

Inputs
Type	Target	Description
Poisson generator	SFCj	Independent for all targets, rate ν x, weight J x
Poisson generator	IN	Independent for all targets, rate ν IN,ext, weight J IN,ext
Poisson generator	j Au	Independent for all targets, rate ν AN, weight J E,AN
Measurements		Spike activity of all neurons, synaptic weights if plasticity is present