An analytical connection between temporal and spatio-temporal growth rates in linear stability analysis

We derive an exact formula for the complex frequency in spatio-temporal stability analysis that is valid for arbitrary complex wave numbers. The usefulness of the formula lies in the fact that it depends only on purely temporal quantities, which are easily calculated. We apply the formula to two model dispersion relations: the linearized complex Ginzburg--Landau equation, and a model of wake instability. In the first case, a quadratic truncation of the exact formula applies; in the second, the same quadratic truncation yields an estimate of the parameter values at which the transition to absolute instability occurs; the error in the estimate decreases upon increasing the order of the truncation. We outline ways in which the formula can be used to characterize stability results obtained from purely numerical calculations, and point to a further application in global stability analyses.Comment: 36 pages, 16 figures; Article has been tweaked and reduced in size but essential features remain the same; Supplementary material (16 pages) is also include

Reliability analysis of dynamic systems by translating temporal fault trees into Bayesian networks

Classical combinatorial fault trees can be used to assess combinations of failures but are unable to capture sequences of faults, which are important in complex dynamic systems. A number of proposed techniques extend fault tree analysis for dynamic systems. One of such technique, Pandora, introduces temporal gates to capture the sequencing of events and allows qualitative analysis of temporal fault trees. Pandora can be easily integrated in model-based design and analysis techniques. It is, therefore, useful to explore the possible avenues for quantitative analysis of Pandora temporal fault trees, and we identify Bayesian Networks as a possible framework for such analysis. We describe how Pandora fault trees can be translated to Bayesian Networks for dynamic dependability analysis and demonstrate the process on a simplified fuel system model. The conversion facilitates predictive reliability analysis of Pandora fault trees, but also opens the way for post-hoc diagnostic analysis of failures

Spatio-Temporal Analysis of Unemployment Rate in Poland

The aim of this paper is to present results of spatio-temporal analysis of unemployment rate in Poland, with the usage of advanced spatial econometric methods. The analysis was done on data collected for ‘powiat’ level between 2006 and 2010. GlS and ESDA tools were applied for visualization of the spatiotemporal data and identification of spatial interactions between polish counties on labor market. Multi-equation spatial econometric models were used to describe unemployment rate in relation to selected social-economic variables.Celem opracowania jest przestrzenno-czasowa analiza poziomu stopy bezrobocia w Polsce, z wykorzystaniem zaawansowanych metod ekonometrii przestrzennej. Badanie przeprowadzono na danych statystycznych zebranych na poziomie powiatu, w latach 2006-2010. Narzędzia GIS i ESDA zostały wykorzystane w celu wizualizacji zmiennych oraz identyfikacji interakcji przestrzennych zachodzących pomiędzy badanymi jednostkami terytorialnymi na rynku pracy. Wielorównaniowe modele o równaniach pozornie niezależnych zastosowano do opisu wpływu wybranych zmiennych makroekonomicznych na kształtowanie się poziomu stopy bezrobocia w Polsce w badanym okresie