On Bergman completeness of non-hyperconvex domains

We study the problem of the boundary behaviour of the Bergman kernel and the Bergman completeness in some classes of bounded pseudoconvex domains, which contain also non-hyperconvex domains. Among the classes for which we prove the Bergman completeness and the convergence of the Bergman kernel to infinity while tending to the boundary are all bounded pseudoconvex balanced domains, all bounded Hartogs domains with balanced fibers over regular domains and some bounded Laurent-Hartogs domains.Comment: 13 page

Estimating the Uncertainty in Population Projections by Resampling Methods

This paper proposes a new approach to introducing quantitatively measured uncertainty into population projections. It is to a lesser degree based on past time-series than other approaches, since it uses random walk models for migration, mortality and fertility, for which upper and lower bounds are defined. No parametric distribution is fitted to the observations, but the random walk is resampled from the past data. By putting bounds on the level that fertility can reach in the future, further substantive information is introduced that transcends the information derived from the observed time series. By sampling 10.000 path of the random walks in fertility, mortality and migration, the distributions of population size and structure up to 2050 for Austria, Mauritius and USA are estimated

Configurations of Series-Parallel Networks with Maximum Reliability

The optimal design problem for networks with 3-state components is the following: select from a given class of networks with n components, each of which can he operative or experience an open-mode or a shorted-mode failure state, the network with maximum reliability. We present an algorithm for solving this problem in the case of 2-stage series-parallel networks, i.e., networks consisting of a number of series configurations linked in parallel or vice versa. For practically relevant network sizes (up to 100 components), the algorithm is fast

Known source detection predictions for higher order correlators

The problem addressed in this paper is whether higher order correlation detectors can perform better in white noise than the cross correlation detector for the detection of a known transient source signal, if additional receiver information is included in the higher order correlations. While the cross correlation is the optimal linear detector for white noise, additional receiver information in the higher order correlations makes them nonlinear. In this paper, formulas that predict the performance of higher order correlation detectors of energy signals are derived for a known source signal. Given the first through fourth order signal moments and the noise variance, the formulas predict the SNR for which the detectors achieve a probability of detection of 0.5 for any level of false alarm, when noise at each receiver is independent and identically distributed. Results show that the performance of the cross correlation, bicorrelation, and tricorrelation detectors are proportional to the second, fourth, and sixth roots of the sampling interval, respectively, but do not depend on the observation time. Also, the SNR gains of the higher order correlation detectors relative to the cross correlation detector improve with decreasing probability of false alarm. The source signal may be repeated in higher order correlations, and gain formulas are derived for these cases as well. Computer simulations with several test signals are compared to the performance predictions of the formulas. The breakdown of the assumptions for signals with too few sample points is discussed, as are limitations on the design of signals for improved higher order gain. Results indicate that in white noise it is difficult for the higher order correlation detectors in a straightforward application to achieve better performance than the cross correlation. © 1998 Acoustical Society of America

Known source detection predictions for higher order correlators

The problem addressed in this paper is whether higher order correlation detectors can perform better in white noise than the cross correlation detector for the detection of a known transient source signal, if additional receiver information is included in the higher order correlations. While the cross correlation is the optimal linear detector for white noise, additional receiver information in the higher order correlations makes them nonlinear. In this paper, formulas that predict the performance of higher order correlation detectors of energy signals are derived for a known source signal. Given the first through fourth order signal moments and the noise variance, the formulas predict the SNR for which the detectors achieve a probability of detection of 0.5 for any level of false alarm, when noise at each receiver is independent and identically distributed. Results show that the performance of the cross correlation, bicorrelation, and tricorrelation detectors are proportional to the second, fourth, and sixth roots of the sampling interval, respectively, but do not depend on the observation time. Also, the SNR gains of the higher order correlation detectors relative to the cross correlation detector improve with decreasing probability of false alarm. The source signal may be repeated in higher order correlations, and gain formulas are derived for these cases as well. Computer simulations with several test signals are compared to the performance predictions of the formulas. The breakdown of the assumptions for signals with too few sample points is discussed, as are limitations on the design of signals for improved higher order gain. Results indicate that in white noise it is difficult for the higher order correlation detectors in a straightforward application to achieve better performance than the cross correlation. © 1998 Acoustical Society of America

Prediction of signal‐to‐noise ratio gain for passive higher‐order correlation detection of energy transients

In general, higher‐order correlation detectors perform well in passive detection for signals of high third‐ and fourth‐order moments. Previous studies by the authors have shown that the normalized third‐ and fourth‐order signal moments are reliable indicators of higher‐order correlation detector performance [Pflug et al. (1992b)]. For a deterministic energy transient of known moments through fourth order, it is possible to predict theoretically the amount of gain over an ordinary cross‐correlation detector for a bicorrelation or tricorrelation detector applied in a noise environment of known variance. In this paper, formulas that predict detector performance for passive detection at the minimum detectable level are derived. The noise is assumed to be stationary and zero mean with Gaussian correlation central ordinate probability density functions. To test the formulas, SNR detection and gain curves are generated using hypothesis testing and Monte Carlo simulations on a set of test signals. The test signals are created by varying the time width of a pulse‐like signal in a sampling window of fixed time duration, resulting in a set of test signals with varying signal moments. Good agreement is found between the simulated and theoretical results. The effects of observation time (length of detection window) and sampling interval on detector performance are also discussed and illustrated with computer simulations. The prediction formulas indicate that decreasing the observation time or the sampling interval (assuming the signal is sufficiently sampled and the detection window contains the entire signal) improves detection performance. However, the rate of improvement is different for the three detectors. The SNR required to achieve the minimum detectable level of detection performance at a given probability of false alarm (Pfa) decreases with the fourth root of the observation time and sampling interval for the cross‐correlation detector, the sixth root for the bicorrelation detector, and the eighth root for the tricorrelation detector. Relative detector performance also varies with Pfa. The probability of detection (Pd) for higher‐order detectors degrades less rapidly with decreasing Pfa than the Pd for ordinary correlations. Thus higher‐order correlators can be especially appropriate when a very low Pfa is required

CVaR minimization by the SRA algorithm

Using the risk measure CV aR in �nancial analysis has become more and more popular recently. In this paper we apply CV aR for portfolio optimization. The problem is formulated as a two-stage stochastic programming model, and the SRA algorithm, a recently developed heuristic algorithm, is applied for minimizing CV aR