- ...oscillations
- 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.
- ...trial
- The cross correlation between two time functions
and is .
- ...1993
- Early reports appeared in Wang
[65,66]. The journal
version was submitted in September 1993, accepted in March 1994, and
is awaiting publication
[68].
- ...impulses
- 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.