Light and voltage noise in AI,Gal_,As-GaAs heterolasers are studied in a wide range of forward currents (i = to 4 A) and frequencies (f = 1 to lo7 Hz). The noise characteristics obtained are compared with those observed on GaAs laser diodes. Results of investigations carried out on samples of both types are similar. Components of l/f-type are found in the spectra of light noise as well as in the spectra of voltage noise. At currents below the threshold value, these components are correlated with each other and are due t o the fluctuations of the nonradiative component of the diode current. The reasons for the changes in the l/f-noise which take place a t the sample change-over to the laser action are discussed. As the change-over to the laser action occurs, the sharp increase of frequencyindependent high-frequency light and voltage noise predicted by the theory is found experimentally. These noises appear t o be fully correlated with each other, the phase shift between the fluctuations of light and of voltage on the diode contacts being equal t o 180". I n addition, the change of the noise characteristics taking place in the course of diode operation is disclosed and analysed. As a result a connection is established between the processes of the slow laser degradation and the peculiarities of the excess component of the diode current as well as of its low-frequency noise. 41"

Deconvolution is the process of estimating a system's input using measurements of a causally related output where the relationship between the input and output is known and linear. Regularization parameters are used to balance smoothness of the estimated input with accuracy of the measurement values. In this paper we present a maximum marginal likelihood method for estimating unknown regularization (and other) parameters used during deconvolution of dynamical systems. Our computational approach uses techniques that were developed for Kalman filters and smoothers. As an example application we consider estimating insulin secretion rate (ISR) following an intravenous glucose stimulus. This procedure is referred to in the medical literature as an intravenous glucose tolerance test (IVGTT). This estimation problem is difficult because ISR is a strongly non-stationary signal; it presents a fast peak in the first minutes of the experiment, followed by a smoother release. We use three regularization parameters to define a smooth model for ISR variance. This model takes into account the rapid variation of ISR during the beginning of an IVGTT and its slower variation as time progresses. Simulations are used to assess marginal likelihood estimation of these regularization parameters as well as of other parameters in the system. Simulations are also used to compare our model for ISR variance with other stochastic ISR models. In addition, we apply maximum marginal likelihood and our ISR variance model to real data that have previous ISR estimation results reported in the literature.

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