Interpretation of kernels. II. same-signed 1st- and 2nd-degree (main-diagonal) kernels of the human pupillary system

Abstract The human pupillary system exhibits a dynamic asymmetry between responses to on and off stimuli. From pupil random-light-stimulus experimental data and by frequency-domain analysis, we obtained the 1st- and 2nd-degree kernels of the human pupillary system. The pupil kernel model produces responses to on and off pulse and step stimuli that are similar to pupil experimental responses. Extrapolation from a power-series representation of the pupil kernels, using only slope and curvature values to replace the major effects of the 1st- and 2nd-degree kernels respectively, indicates that both 1st and 2nd-degree main-diagonal kernels should have the same (negative) sign in order to give the kernel model dynamic asymmetry of response. Indeed, the experimentally derived pupil 1st- and 2nd-degree kernels were found to have the same sign. This result provides insight into the relationship between signs of derived kernels and the response nonlinearities of a physiological system.

[1]  D. Brillinger.  The identification of polynomial systems by means of higher order spectra , 1970 .

[2]  T. Gasser,et al.  Statistical methods for investigating phase relations in stationary stochastic processes , 1971 .

[3]  L. Stark,et al.  Pupil response to light and electrical stimulation: static and dynamic characteristics. , 1969, Brain research.

[4]  K. Naka,et al.  White-Noise Analysis of a Neuron Chain: An Application of the Wiener Theory , 1972, Science.

[5]  P. Eykhoff.  System Identification Parameter and State Estimation , 1974 .

[6]  Lawrence Stark,et al.  Interpretation of kernels. III. positive off-diagonal Kernels as correlates of the dynamic process of pupillary escape☆ , 1979 .

[7]  Leo J. Tick,et al.  The Estimation of “Transfer Functions” of Quadratic Systems , 1961 .

[8]  Y. W. Lee,et al.  Measurement of the Wiener Kernels of a Non-linear System by Cross-correlation† , 1965 .

[9]  P LEVATIN,et al.  Pupillary escape in disease of the retina or optic nerve. , 1959, Archives of ophthalmology.

[10]  L. Stark,et al.  Wiener G-function analysis as an approach to non-linear characteristics of human pupil light reflex. , 1968, Brain research.

[11]  J Semmlow,et al.  Pupil movements to light and accommodative stimulation: a comparative study. , 1973, Vision research.

[12]  N. Wiener,et al.  Nonlinear Problems in Random Theory , 1964 .

[13]  S Usui,et al.  Sensory and motor mechanisms interact to control amplitude of pupil noise , 1978, Vision Research.

[14]  Lawrence Stark,et al.  Stability, Oscillations, and Noise in the Human Pupil Servomechanism , 1959, Proceedings of the IRE.

[15]  Jacob Katzenelson,et al.  The Design of Nonlinear Filters and Control Systems. Part I , 1962, Inf. Control..

[16]  Lawrence Stark,et al.  Kernel method for nonlinear analysis: identification of a biological control system , 1975 .

[17]  Lawrence Stark,et al.  A Physiological Basis of Pupillary Dynamics , 1974 .

[18]  Vito Volterra,et al.  Theory of Functionals and of Integral and Integro-Differential Equations , 2005 .

[19]  L. Stark,et al.  The kernel identification method (1910–1977)— review of theory, calculation, application, and interpretation , 1977 .

[20]  John H. Milsum,et al.  Biological Control Systems Analysis , 1966 .

[21]  M. Fréchet.  Sur les fonctionnelles continues , 1910 .

[22]  Isaac N. Gibra.  Probability and Statistical Inference for Scientists and Engineers , 1973 .