SIAM-AMS Proceedings
Volume 13
1981

WALTER J. FREEMAN

Introduction. The olfactory system in mammals poses an interesting problem
in stimulus equivalence. On the one hand the input to the system is provided by
an immense number of receptors ( Le Gros Clark [ 1957 ]), roughly 10⁸, embedded
in an intricately folded membrane exposed to the air in the nasal passages. The
number of types of receptor specificity for odor quality has been estimated
( Amoore [ 1971 ]) to lie between 10 and 10², suggesting that there may be 10⁶ or
more receptors that are sensitive to any one odor. On the other hand the
remarkable sensitivity of this system indicates that excitation of a small number
of receptors, say 10¹ to 10², suffices for detection by a trained animal of the
presence of an odor. The detection is consistent over multiple presentations, as
shown by the performance of a tracking dog. Considering the turbulence of air
flow through the nose, it is unlikely that an odorous substance falls on the same
small subset of receptors on any two or more sniffs. In order to explain the
perceptual invariance that is implied by the animal behavior, a neural mecha-
nism must be postulated that gives a fixed output for all samples of an odor
given to varying subsets of receptors among the set that is responsive to that
odor.

A mechanism that can do this is based on the postulate that an animal forms
a template of connections among those neurons in the olfactory bulb that are
activated by a given odor during a training or familiarization experience. This
postulate stems from observations on the spatial patterns of electrical waves
generated by the olfactory bulb in cats and rabbits that were trained to identify
particular odors.

© 1981 American Mathematical Society

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