Theory of localized synfire chain
  Neuron is a noisy information processing unit and conventional view is that information in the cortex is carried on the rate of neurons spike emission. More recent studies on the activity propagation through the homogeneous network have demonstrated that signals can be transmitted with millisecond fidelity; this model is called the Synfire chain and suggests the possibility of the spatio-temporal coding. However, the more biologically realistic, structured feedforward network generates spatially distributed inputs. It results in the difference of spike timing. This poses a question on how the spatial structure of a network effect the stability of spatio-temporal spike patterns, and the speed of a spike packet propagation. By formulating the Fokker-Planck equation for the feedforwardly coupled network with Mexican-Hat type connectivity, we show the stability of localized spike packet and existence of Multi-stable phase where both uniform and localized spike packets are stable depending on the initial input structure. The Multi-stable phase enables us to show that a spike pattern, or the information of its own, determines the propagation speed. 
Kosuke Hamaguchi, Masato Okada and Kazuyuki Aihara