Collective Excitation

11.1 Introduction Spiking neurons are highly non-linear oscillators. As such they display collective behavior that may have important calculational manifestations. Synchronization between the ring of diierent neurons is the rst topic to which we devote our attention. This behavior can be brought about in our integrate-and-re model through excita-tory synaptic couplings without delays, or inhibitory couplings with delays. Once the mechanism of synchronization is established, this phenomenon can be used for deening data clustering. The clusters correspond to neurons that re synchronously, with diierent clusters ring at diierent times. This behavior can also be described as temporal segmentation, separating data through phase lags between excitations of diierent aggregates. This separation is characteristically limited to a small number of segments, a limitation that is inherent to the behavior of coupled non-linear oscillators.