We consider a neural network that evolves in discrete time. At each timestep $t$ a neuron $i$ either fires ($f_i(t)=1$) with probability $\sigma_i(t)$, or does not fire ($f_i(t)=0$) with probability $1 - \sigma_i(t)$. The neurons are connected through plastic synapses with efficacies $w_{ij}(t)$, where $i$ is the index of the postsynaptic neuron. The efficacies $w_{ij}$ can be either positive or negative (corresponding to excitatory and inhibitory synapses, respectively). " For each articulation there were 4 corresponding input neurons. The activation of 2 of them was proportional to the angle between the orientation of the articulation and the leftmost possible orientation; the activation of the other 2 corresponded to the angle between the orientation of the articulation and the rightmost possible orientation. " < if both of the 2 is angle between two orientations, then why 2 are needed?> "The activations were normalized between 0 and 1. The input neurons fired Poisson spike trains, with a firing rate proportional to the activation, between 0 and 50 Hz."

[motor-neron] - [effector] "The spikes of motor neurons were converted to effector activations by integrating them with a leaky accumulator of time constant $\tau_e =2 s$. This is equivalent to performing a weighted estimate of the firing rate using an exponential kernel with the same time constant. The motor activations $a$ evolved according to \begin{displaymath} a(t)= a(t -\delta)\exp (-\delta t/\tau_e) + (1 - \exp (-1/\nu_e \tau_e)) f(t) \end{displaymath} where f(t) indicates whether the motor neuron has fired. The factor that weighed the contribution f(t) of the spikes insured that the activation was normalized to 1 when the neuron fired regularly with frequency $\tau_e =25 Hz$." The activations of 2 motor neurons were averaged to yield the activation of one effector. There were two antagonist effectors per articulation; if their activations were $a_{+}$ and $a_{-}$, the articulation was set to a relative angle $(a_{+} - a_{-}\theta_{max}$. "The network was thus composed of 80 input neurons and 80 motor neurons. The network also had 200 hidden neurons ... The network was simulated with a time step $\delta t =1 ms$. Since effector activations were initially set to 0 and bending of an articulation required an imbalance in the activities of the antagonist effectors, the initial position of the worm was vertical."