Initial data truncation for multivariate output of discrete-event simulations using the Kalman filter

Data truncation is a commonly accepted method of dealing with initialization bias in discrete-event simulation. An algorithm for determining the appropriate initial-data truncation point for multivariate output is proposed. The technique entails averaging across independent replications and estimating a steady-state output model in a state-space framework. A Bayesian technique called Multiple Model Adaptive Estimation (MMAE) is applied to compute a time varying estimate of the output's steady-state mean vector. This MMAE implementation features the use, in paralle, of a bank of Kalman filters. Each filter is constructed under a different assumption concerning the output's steady-state mean vector. One of the filters assumes that the steady-state mean vector is accurately reflected by an estimate, called the assumed steady-state mean vector, taken from the last half of the simulation data. As the filters process the output through the effective transient, this particular filter becomes more likely (in a Bayesian sense) to be the best filter to represent the data and the MMAE mean estimator is influenced increasingly towards the assumed steady-state mean vector. The estimated truncation point is selected when a norm of the MMAE mean vector estimate is within a small tolerance of the assumed steady-state mean vector. A Monte Carlo analysis using data from simulations of open and closed queueing models is used to evaluate the technique. The evaluation criteria include the ability to construct accurate and reliable confidence regions for the mean response vector based on the truncated sequences.     

Observation of the early stages of growth and the formation of growth spirals in epitaxial YBa2Cu3O7-δ thin films by AFM

Ultrathin epitaxial films of YBa₂Cu₃O_7– on SrTiO₃ prepared by Direct Current (DC) sputtering and pulsed laser deposition were imaged by Atomic Force Microscopy (AFM) to follow the different stages of growth of the thin films. Series of films with thicknesses between 1.2 nm and 12 nm (1–10 monolayers of YBa₂Cu₃O_7–) were prepared under identical conditions, optimized with respect to electrical and structural properties, to obtain information on the mechanisms responsible for the formation of growth spirals which are commonly observed in films having a thickness of several 10 nm or more. It could be shown that few layers are formed by a layered growth mode where material is attached laterally to 2D islands which are only one c-axis unit cell in height. In a later stage of growth when about 8–10 layers have been formed, the growth process changes to a mode which is mediated by growth spirals. This could be directly monitored in the AFM images where different defect structures like vertically sheared growth fronts and dendrite-like terraces of stacked islands as well as the resulting growth spirals could be identified.