...MacLennan

This paper will appear in Self-Organization, Computational Maps and Motor Control, ed. by Pietro G. Morasso and Vittorio Sanguineti, Elsevier-North Holland, in press.

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...networks.

Specifically, they are Hilbert-Schmidt operators, to which the following remarks apply.

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...r.

Correlation can be defined relative to other kinds of transformation besides displacement, and to other measures of similarity besides the inner product; see MacLennan (1994) for details.

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...function

The Dirac delta is a ``generalized function'' that has the value zero everywhere except at the origin, where it has the value infinity.

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...approach.

See Section 6 for a discussion of some representations and MacLennan (1994) for example adaptive algorithms.

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...b.

For a typical case shown in Georgopoulos (1995, Fig. 32.1) and normalized vectors, it appears 280#280 impulses/sec. and 281#281 impulses/sec.

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...saccade.

This process may take place in the superior colliculus, frontal eye field or posterior parietal cortex (Droulez & Berthoz 1991b).

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...content,

Gabor's notion of information is not the same as Shannon's; they are complementary rather than mutually exclusive. See MacLennan (1991) and citations therein for a discussion.

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...Principle).

The precise constant, 391#391 in this case, depends on the quantification of the uncertainty of measurement (MacLennan 1991).

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...cells.

For technical reasons (see MacLennan 1991), these MN complex coefficients comprise only 2MN-M, as opposed to 2MN, independent real coefficients.

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...phase.

There is an additional complication in that the Gaussian envelopes extend outside the nominal 415#415 (= standard deviation) widths of the elementary function. This could be solved by two or three banks of generators activated in rotation; however a better solution lies in the Gabor transform, discussed below.

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...generation).

For a clear, insightful introduction to least action principles, it is difficult to do better than Feynman et al. (1963-5, ch. II.19).

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...computations.

For example, least action principles are fundamental to Pribram's (1991) holonomic brain theory (see especially Apps. A, B).

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...amplitude.

For this cancelation to occur, the impulses must be shaped so that their average amplitude is zero. Also, the neurons must sample sufficiently many paths coming into their region to ensure that cancelation is possible; in effect, the neural net must represent the search space at sufficiently high resolution.

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