For intermediate values of q, the distance between two spike trains is small if they have a similar number of spikes, occurring with similar intervals. Neurons which show post-tetanic potentiation and similar mechanisms might care about this distance. That is, each spike is labelled with its neuron of origin. A new kind of elementary step is introduced, in which the label for the neuron of origin is changed. See an application to real data.
Time is considered cyclic.
See an application to real data. This doesn't seem to matter much. Our dynamic programming algorithm cannot readily be applied to these extensions, but they are nevertheless interesting. On the theory and computation of evolutionary distances. SIAM J. Appl.