Sinusoidal arrays paper on Neuroprose (corrections/amplification)

[David Redish]

In referrence to:

   Neural Representation of Space Using Sinusoidal Arrays

   David S. Touretzky     A. David Redish     Hank S. Wan


Some people have had trouble uncompressing the file.
The problem should be fixed now.

Some people have also noted that the name I gave for the extra figure
was incorrect.  The correct filenames are 

   touretzky.sinusoidal-arrays.ps.Z
   touretzky.extra-fig.ps.Z

Sorry for the inconvenience

Dave Redish

[I'm also including a more detailed version of the abstract.  -- DST]


	EXTENDED ABSTRACT:

Any vector in polar coordinates v=(r,phi) can be represented as a
sine wave f(t) = r cos (omega t + phi), where r is amplitude, phi
is phase, and omega is (constant) frequency.  This is commonly known as
a phasor.  The advantage of phasor representation is that translation
and rotation of a vector are both trivial operations.  Translation is
achieved by addition of sine waves, and rotation can be obtained by phase
shifting or temporal delay.  O'Keefe (1991) has suggested that rats
might use phasors to encode angle and distance to landmarks.  In his
proposal, hippocampal theta provides the reference signal for determining
phase.

This temporal approach to encoding a sine wave has some drawbacks.  The
7-12 Hz theta rhythm may be too slow to support real-time spatial
reasoning tasks requiring rapid manipulation of phasors.  Furthermore,
maintaining even a modest angular resolution of 10 degrees relative to a
roughly 10 Hz reference signal requires a temporal resolution of 3 msec.
Although some specialized sensory systems are known to make much finer
discriminations (e.g., acoustic imaging in bats and dolphins, or auditory
localization in barn owls), we are reluctant to require this degree of
temporal precision at the higher cognitive level associated with spatial
reasoning.  Instead, we suggest that phasor operations are more plausibly
realized by re-coding the temporal dimension of the sine wave spatially,
using populations of spiking neurons.  We propose an architecture called
the sinusoidal array for manipulating vectors in phasor form, and
report the results of computer simulations.

There is some experimental evidence that sinusoidal array representations
may exist in rat parietal cortex and in rhesus motor or parietal cortex.
We propose an experiment to test this hypothesis in rats.