We note that this result appears in contradiction with the well-known theorem of Mermin and Wagner [41] in statistical mechanics. The theorem states that no long-range order (synchrony) exists in one- or two-dimensional isotropic Heisenberg models (X-Y models). The fact that our system (equation 2) is not an equilibrium statistical mechanical system and it is not isotropic (see figures 2 and 3) makes it not subject to the theorem. On the other hand, sinusoidal oscillators, such as the one defined in equation 1, tend to be isotropic and are probably subject to the theorem. This might account for the qualitative difference between non-sinusoidal and sinusoidal oscillators. I am indebted to Drs. J. Cheyes and C. Jayaprakash who assured me this observation.

The cross correlation between two time functions and is .

Early reports appeared in Wang [65,66]. The journal version was submitted in September 1993, accepted in March 1994, and is awaiting publication [68].

Horizontal connections are probably myelinated, but it is not quite clear how fast they conduct neural signals (Charles Gilbert, personal communication 1992).

... [55,63]
It may be argued that coherent oscillations in the visual cortex span up to 7 mm, and thus may be consistent with all-to-all connectivity of the horizontal connections. But a closer look reveals that a diameter of 6-8 mm of the horizontal connections can only support all-to-all connectivity of a 3-4 mm range.