Practical identification of functional expansions of nonlinear systems submitted to non-Gaussian inputs.

Time-domain identification of nonlinear systems represented by functional expansions is considered. A general framework is defined for the analysis of three identification methods: the widely used cross-correlation method, Korenberg's method, and a suboptimal least-squares method based on a stochastic approximation algorithm. First, the major characteristics of the underlying estimation problem are pointed out. Then, the identification methods are interpreted as approximations to an optimal estimator, which helps gain insight into their internal functioning and to the investigation of their connections and differences. Examination of results previously published and of the simulations reported in this article indicate that stochastic approximation is an interesting alternative to other existing methods. Identification of a biological system stimulated by a non-Gaussian input confirms the practicality of this approach.

Light and target distance interact to control pupil size.

Light and target distance stimuli were presented to normal human subjects, and their pupillary responses were measured. A homeomorphic computer model of the pupillary control system is presented in which the form of interaction of controller signals due to light and target distance was investigated. The error remaining when model parameters were optimized to fit experimental pupil size (area or diameter) was smaller for the linear interaction hypothesis than for either power law or logical law interaction. A generalized second-order nonlinear model with six parameters (vs. 3 for each of the other models) yielded somewhat lower residual error. With the use of a modified Akaike information criterion, the value (in an information theoretic sense) of the improved fit afforded by the three additional parameters in the generalized nonlinear model was shown to be small, and thus the generalized second-order nonlinear model was rejected in favor of the simpler and more parsimonious linear model.

Systems model for pupil size effect. II. Feedback model.

The human pupillary control system has been the subject of interest to biologists and engineers as an example of a sensorimotor reflex which can be embedded in a control system paradigm. We present a nonlinear feedback model whose compact structure allows us to hypothesize possible physiological mechanisms which generate the proper behavior of the pupil system. The important pupil responses, including pupil size effect, asymmetry, and response the high-frequency stimuli, are defined. This model was simulated on a digital computer and comparisons to the paradigm experimental responses were performed, demonstrating a fit to each of the observed conditions. Improvements on previous models are discussed.

A systems model for the pupil size effect. I. Transient data.

The human pupillary control system is a paradigm for linearized biological control systems. It also exhibits a series of interesting nonlinear behaviors, particularly asymmetry, "pupillary escape," and "pupillary capture." We present a nonlinear model in which a signal dependent upon pupil size is fed back internally to cause a change in system parameters related to gains and rates of light adaptation. The model was simulated on a digital computer, a variety of experimental data was well matched, and improvements over previous pupil models demonstrated. A candidate physiological mechanism for adaptive components of the model might have the form of an inverse "Henneman coded" neuronal pool.