William D. O'Neill

Curve fitting by a sum of Gaussians

Gaussians are useful in multiscale representation of video data. An algorithm is presented which approximates a sequence of uniformly spaced single-valued data by a sum of Gaussians with a prescribed accuracy. The scale-space image [6] of the data is used to estimate the number of Gaussians and their initial parameters. The Marquardt algorithm (J. SIAM 11(2), 1963, 431-441) is then used to optimize the parameters.

Surface fitting to scattered data by a sum of Gaussians

Abstract We study the computational behavior and the interpolation accuracy of functions defined by a sum of Gaussians (SOG) in surface fitting. We compare the interpolation accuracies of SOG and multiquadrics (MQ) in data interpolation, and describe an algorithm for approximation of scattered data by SOG with minimal least-squares error. We also characterize the computational behaviors of SOG and MQ in data interpolation as functions of their parameters σ and r, respectively.

Dynamic visco-elastic properties of the lens

Abstract Displacement responses of lenses extracted from cats and dogs are studied experimentally for the case of sudden release of mechanical force applied on the lens anterior. The existence of three time constants is clarified through a computer-aided linear simulation, where the lens is regarded as a series connection of three pairs of springs and dashpots. Nonlinear simulation is also made and the viscous coefficient of the lens is represented as a function of displacement.

Application of Time-Series Modeling to Human Operator Dynamics

Time-series analysis is applied to model human operator dynamics in pursuit and compensatory tracking modes. The normalized residual criterion is used as a one-step analytical tool to encompass the processes of identification, estimation, and diagnostic checking. A parameter constraining technique is introduced to develop more reliable models of human operator dynamics. The human operator is adequately modeled by a second-order dynamic system both in pursuit and compensatory tracking modes. In comparing the data sampling rates, 100 ms between samples is adequate and is shown to provide better results than a 200 ms sampling. The residual power spectrum and eigenvalue analysis show that the human operator is not a generator of periodic characteristics.

Neurological pupillary noise in narcolepsy

SUMMARY Pupillometry has a long but inconclusive history as a means of measuring human alertness. Spontaneous pupillary oscillations in narcoleptics and the sleep deprived are a recognized but quantitatively elusive indication of alertness. Stimulation of the pupillary light reflex (PLR) has provided contradictory or confusing indications of alertness levels. Results from 10 diagnosed narcoleptics and 10 control subjects in which the PLR system was stimulated and a reliable (90%) discriminator derived for classifying narcoleptics and controls was reported. Random pupillary oscillations, which is called pupillary noise to distinguish these oscillations from spontaneous ones, were estimated from continuous pupil diameter recordings using a recursive least squares method applied to a subject–specific PLR system model. Pupillary noise sum of squares indicate that narcoleptics have significantly (P < 0.005) less PLR noise than controls. This difference was attributed to supranuclear inhibition of randomly active Edinger‐Westphal neurons long hypothesized to be the source of random papillary oscillations. This inhibition also has been suggested as a cause of PLR sensitivity to nocturnal sleep quality so it may be that these findings apply to the sleep deprived and not just specifically to narcoleptics.

A Minimum Variance, Time Optimal, Control System Model of Human Lens Accommodation

Experimental data relating ciliary nerve stimulation and lens motion are used to identify the open-loop plant dynamics of the lens accommodation system via a parameter identication variation of the Kalman filter equations. Using the resultant minimum variance plant model, experimental closed-loop responses of the human accommodative system are predicted by synthesizing the system closed-loop controller. The resultant control signals are shown to minimize the time required to change the refractive state of the eye. The plant dynamic model and the closed-loop model are further verified by comparing their frequency responses to experimental data. The optimal performance of the lens system is compared to analogous performance of another ocular control system, and a possible general theory of optimal control is discussed.

Adaptive Linear Predictive Coding of Time-Varying Images Using Multidimensional Recursive Least Squares Ladder Filters

This paper presents several adaptive linear predictive coding techniques based upon extension of recursive ladder filters to two and three dimensions (2-D/3-D). A 2-D quarter-plane autoregressive ladder filter is developed using a least square criterion in an exact recursive fashion. The 2-D recursive ladder filter is extended to a 3-D case which can adaptively track the variation of both spatial and temporal changes of moving images. Using the 2-D/3-D ladder filters and a previous frame predictor, two types of adaptive predictor-control schemes are proposed in which the prediction error at each pel can be obtained at or close to a minimum level. We also investigate several modifications of the basic encoding methods. Performance of the 2D/3-D ladder filters, their adaptive control schemes, and variations in coding methods are evaluated by computer simulations on two real sequences and compared to the results of motion compensation and frame differential coders. As a validity test of the ladder filters developed, the error signals for the different predictors are compared and the visual quality of output images is verified.

Estimation and Verification of a Stochastic Neuron Model

The treatment of a neuron as an information processor is complicated by the nonlinear, time-varying, and distributed parameter attributes of the classical Hodgkin-Huxley neuron model. In this paper, we fit data from experiments on spontaneously firing snail neurons to a much simpler integrate and fire model featuring random process descriptions of the input current density, threshold, and reset potentials. The method of generalized least squares is used to show that the integrate and fire model explains 99.6 percent of the variation in the data used to describe the population behavior of neurons on the visceral ganglion of the Helix Aspersa snail. Experimental histograms suggest that most of the random variation in the interspike interval is caused by the randomness in the input current density and comparatively little by the random fluctuations in threshold and reset potentials, although the latter are still significant from an information processing viewpoint. Residuals from the regression are used to estimate the range of the input current density random process. The residuals also show that slight, but significant, autocorrelation exists in the input current densities. This suggests that information in addition to the mean input current density is being transmitted in the interspike interval code.

An application of Shannon's coding theorem to information transmission in economic markets

Abstract By considering an established aggregate economic model and several of its variants as information channels, we show that Shannons coding theorem allows one to precisely define the sense in which information is transmitted by an economic market. Unique to economic markets is the structural existence of a noiseless feedback path from the channel output, the market clearing price, to the channel input, market trader bids and offers which simultaneously account for source information and market clearing prices. Known results in information theory are used to show that economic equilibrium occurs when market agents can predict the market input information from price observations with arbitrarily small error probability. The agent signaling rates achieve channel capacity in this instance. The paper concludes by showing that the natural extension of the multiple agent market is the multiple access information channel since multiple users of a single channel are analogous to multiple agents using a single commodity market.

Functional dependence of optical parameters on circumferential forces in the cat lens

Abstract It has been suggested that the accommodative mechanism acting in the cat eye may involve a function of translation of the lens on the optic axis as well as a shape change. The effect of changes in lens shape was investigated in the isolated cat lens as a function of circumferential forces. It is shown that, relative to observed amplitudes of accommodation in the cat eye, there is a small dioptric power change in the lens as a result of shape change. This offers support for the theory that the major accommodative mechanism in the cat eye is that of translation of the lens on the optic axis.