Mathematical model of visual perception.

A mathematical model of visual perception is presented with the intention of throwing some light on the problem of perceptual invariance. Two types of differential manifolds (receptive and effector) are associated with the repertoire which is the fundamental concept in the model. The elements of the repertoire carry weights which control the input-output relation in the repertoire and which can be modified by a learning process. It is shown that, under reasonable conditions, these repertoires possess good stability properties and can adjust to the various environments to which they may be subjected. In particular cases, it is shown that the stochastic learning process can be considered as deterministic to a first approximation.

A new model of the acoustic reflex.

A system-type model of the acoustic reflex in man is proposed with the intention of sheding light on certain of its nonlinear behaviors. This model is the first to incorporate into the multipath structure of the reflex arc the adaptation and recovery processes. Parameter distribution in the parallel pathways is based on the current knowledge on the stapedius muscle and on motoneuron pool organization. A piecewise linear system is used in modeling adaptation at onset and recovery at offset. The model is calibrated at 2000 Hz, a frequency for which all the important parameters are available. Two nonlinear behaviors of the adaptation rate are explained: the frequency and intensity dependence, related respectively to the frequency dependence of the feedback gain and to the sigmoidal shape of the closed-loop stimulus-response curve. Underlying physiological mechanisms are discussed, along with other plausible nonlinear models, and extensions of the model to other stimuli are suggested.