High-breakdown linear discriminant analysis

The classification rules of linear discriminant analysis are defined by the true mean vectors and the common covariance matrix of the populations from which the data come. Because these true parameters are generally unknown, they are commonly estimated by the sample mean vector and covariance matrix of the data in a training sample randomly drawn from each population. However, these sample statistics are notoriously susceptible to contamination by outliers, a problem compounded by the fact that the outliers may be invisible to conventional diagnostics. High-breakdown estimation is a procedure designed to remove this cause for concern by producing estimates that are immune to serious distortion by a minority of outliers, regardless of their severity. In this article we motivate and develop a high-breakdown criterion for linear discriminant analysis and give an algorithm for its implementation. The procedure is intended to supplement rather than replace the usual sample-moment methodology of discriminant analysis either by providing indications that the dataset is not seriously affected by outliers (supporting the usual analysis) or by identifying apparently aberrant points and giving resistant estimators that are not affected by them.

Race modeling: An effective cognitive strategy for the 100 m sprinter?

The purpose of this study was to investigate the effects of a specific cognitive race plan on 100 m sprint performance, Twelve elite sprinters (11 male and 1 female) performed 100 m time trials under normal (control) conditions and then under experimental conditions (use of race cues). In the experimental condition, participants were asked to think about specific thought content in each of three segments of the 100 m. A multiple baseline design was employed. A mean improvement of 0.26 s was found. Eleven of the 12 participants showed improvement using the specific cognitive race plan (p < .005). Participants also produced more consistent sprint performances when using the cues (p < .01). Subjective evaluations made by the participants unanimously supported the use of the race plan for optimizing sprint performance. Environmental conditions, effort, and practice effects were considered as possible influences on the results.

Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with an adaptive move generation procedure

The acceptance-probability-controlled simulated annealing with an adaptive move generation procedure, an optimization technique derived from the simulated annealing algorithm, is presented. The adaptive move generation procedure was compared against the random move generation procedure on seven multiminima test functions, as well as on the synthetic data, resembling the optical constants of a metal. In all cases the algorithm proved to have faster convergence and superior escaping from local minima. This algorithm was then applied to fit the model dielectric function to data for platinum and aluminum.

Applying linear time-varying constraints to econometric models: With an application to demand systems

When linear equality constraints are invariant through time they can be incorporated into estimation by restricted least squares. If, however, the constraints are time-varying, this standard methodology cannot be applied. In this paper we show how to incorporate linear time-varying constraints into the estimation of econometric models. The method involves the augmentation of the observation equation of a state-space model prior to estimation by the Kalman filter. Numerical optimisation routines are used for the estimation. A simple example drawn from demand analysis is used to illustrate the method and its application.

Simulated-annealing-based genetic algorithm for modeling the optical constants of solids

We propose a simulated-annealing-based genetic algorithm for solving model parameter estimation problems. The algorithm incorporates advantages of both genetic algorithms and simulated annealing. Tests on computer-generated synthetic data that closely resemble optical constants of a metal were performed to compare the efficiency of plain genetic algorithms against the simulated-annealing-based genetic algorithms. These tests assess the ability of the algorithms to and the global minimum and the accuracy of values obtained for model parameters. Finally, the algorithm with the best performance is used to fit the model dielectric function to data for platinum and aluminum. (C) 1997 Optical Society of America.

Modeling of subcutaneous absorption kinetics of infusion solutions in the elderly using technetium

Absorption kinetics of solutes given with the subcutaneous administration of fluids is ill-defined. The gamma emitter, technitium pertechnetate, enabled estimates of absorption rate to be estimated independently using two approaches. In the first approach, the counts remaining at the site were estimated by imaging above the subcutaneous administration site, whereas in the second approach, the plasma technetium concentration-time profiles were monitored up to 8 hr after technetium administration. Boluses of technetium pertechnetate were given both intravenously and subcutaneously on separate occasions with a multiple dosing regimen using three doses on each occasion. The disposition of technetium after iv administration was best described by biexponential kinetics with a V-ss of 0.30 +/- 0.11 L/kg and a clearance of 30.0 +/- 13.1 ml/min. The subcutaneous absorption kinetics was best described as a single exponential process with a half-life of 18.16 +/- 3.97 min by image analysis and a half-life of 11.58 +/- 2.48 min using plasma technetium time data. The bioavailability of technetium by the subcutaneous route was estimated to be 0.96 +/- 0.12. The absorption half-life showed no consistent change with the duration of the subcutaneous infusion. The amount remaining at the absorption site with time was similar when analyzed using image analysis, and plasma concentrations assuming multiexponential disposition kinetics and a first-order absorption process. Profiles of fraction remaining at the absorption sire generated by deconvolution analysis, image analysis, and assumption of a constant first-order absorption process were similar. Slowing of absorption from the subcutaneous administration site is apparent after the last bolus dose in three of the subjects and can De associated with the stopping of the infusion. In a fourth subject, the retention of technetium at the subcutaneous site is more consistent with accumulation of technetium near the absorption site as a result of systemic recirculation.

Anisotropy-based performance analysis of linear discrete time invariant control systems

The anisotropic norm of a linear discrete-time-invariant system measures system output sensitivity to stationary Gaussian input disturbances of bounded mean anisotropy. Mean anisotropy characterizes the degree of predictability (or colouredness) and spatial non-roundness of the noise. The anisotropic norm falls between the H-2 and H-infinity norms and accommodates their loss of performance when the probability structure of input disturbances is not exactly known. This paper develops a method for numerical computation of the anisotropic norm which involves linked Riccati and Lyapunov equations and an associated special type equation.