Survivability of Deterministic Dynamical Systems

The notion of a part of phase space containing desired (or allowed) states of a dynamical system is important in a wide range of complex systems research. It has been called the safe operating space, the viability kernel or the sunny region. In this paper we define the notion of survivability: Given a random initial condition, what is the likelihood that the transient behaviour of a deterministic system does not leave a region of desirable states. We demonstrate the utility of this novel stability measure by considering models from climate science, neuronal networks and power grids. We also show that a semi-analytic lower bound for the survivability of linear systems allows a numerically very efficient survivability analysis in realistic models of power grids. Our numerical and semi-analytic work underlines that the type of stability measured by survivability is not captured by common asymptotic stability measures.Comment: 21 pages, 6 figure

Survivability : A Unifiying Concept for the Transient Resilience of Deterministic Dynamical Systems

16 pagesNon peer reviewedPreprin

The impact of model detail on power grid resilience measures

Peer reviewedPreprin

Generation of specific antibodies against the rap1A, rap1B and rap2 small GTP-binding proteins. Analysis of rap and ras proteins in membranes from mammalian cells

Specific antibodies against rap1A and rap1B small GTP-binding proteins were generated by immunization of rabbits with peptides derived from the C-terminus of the processed proteins. Immunoblot analysis of membranes from several mammalian cell lines and human thrombocytes with affinity-purified antibodies against rap1A or rap1B demonstrated the presence of multiple immunoreactive proteins in the 22-23 kDa range, although at strongly varying levels. Whereas both proteins were present in substantial amounts in membranes from myelocytic HL-60, K-562 and HEL cells, they were hardly detectable in membranes from lymphoma U-937 and S49.1 cyc- cells. Membranes from human thrombocytes and 3T3-Swiss Albino fibroblasts showed strong rap1B immunoreactivity, whereas rap1A protein was present in much lower amounts. In the cytosol of HL-60 cells, only small amounts of rap1A and rap1B proteins were detected, unless the cells were treated with lovastatin, an inhibitor of hydroxymethylglutaryl-coenzyme A reductase, suggesting that both proteins are isoprenylated. By comparison with recombinant proteins, the ratio of rap1A/ras proteins in membranes from HL-60 cells was estimated to be about 4:1. An antiserum directed against the C-terminus of rap2 reacted strongly with recombinant rap2, but not with membranes from tested mammalian cells. In conclusion, rap1A and rap1B proteins are distributed differentially among membranes from various mammalian cell types and are isoprenylated in HL-60 cells

Sound field synthesis for line source array applications in large-scale sound reinforcement

The thesis deals with optimized large-scale sound reinforcement using line source arrays. This is treated as a sound field synthesis problem. The synthesis of a virtual source via the line source array allows for audience adapted wavefront shaping. For practical array designs and setups this is affected by the deployed loudspeakers and their arrangement, its electronic control and spatial aliasing occurrence. The influence of these parameters is discussed with array signal processing revisiting the Wavefront Sculpture Technology and proposing Wave Field Synthesis as a suitable control method.Die Arbeit beschäftigt sich mit optimaler Beschallung großer Auditorien mit Line Source Arrays. Das Problem wird mit Schallfeldsynthese beschrieben. Die Synthese einer virtuellen Quelle mit einem Line Source Array ermöglicht eine für das Auditorium angepasste Wellenfront. In der Praxis wird dies beeinflusst von den verwendeten Lautsprechern, ihrer Anordnung, ihrer Ansteuerung und räumlichem Aliasing. Der Einfluss der Parameter wird mit Array-Signalverarbeitung diskutiert, wofür Wavefront Sculpture Technology aufgegriffen und Wellenfeldsynthese als Ansteuerungsmethode vorgeschlagen wird