Leaky Integrate and Fire neuron with $N$ input afferents spiking at $\{t_i\}$. Each afferent contributes to the membrane potential $w_ix_i$, $x_i = \sum_{\{t_i<t\}} u(t-t_i)$, where $u(t)=U_0(\exp(-t/\tau_m)-\exp(-t/\tau_s))$, $U_0$ is chosen so that peak of $u(t)$ is $1$.
$\tau_m$ is the membrane time constant [very interesting -- didn't expect this to appear directly here! Won't dendritic properties change time constants? Perhaps this is only for LIF], and $\tau_s$ is the synaptic time constant.
A spike is generated whenever $\mathbf{w}^T\mathbf{x} > U_t$.
They have an interesting way to include the spike reset in the membrane potential equation:
$U(t)=\mathbf{w}^T\mathbf{x}-U_t x_{reset}(t)$
$x_{reset}(t) = \sum_{\{t_i<t\}}\exp(-(t-t_i)/\tau_m)H(t-t_i)$
[I've put in the Heaviside function.]
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