Many bipartite and unipartite real-world networks display a nested structure. Examples pervade different disciplines: biological ecosystems (e.g. mutualistic networks), economic networks (e.g. manufactures and contractors networks) to financial networks (e.g. bank lending networks), etc. A nested network has a topology such that a vertex’s neighbourhood contains the neighbourhood of vertices of lower degree; thus –upon vertex reordering– the adjacency matrix is step-wise. Despite its strict mathematical definition and the interest triggered by their common occurrence, it is not easy to measure the extent of nested graphs unequivocally. Among others, there exist three methods for detection and quantification of nestedness that are widely used: BINMATNEST, NODF, and fitness-complexity metric (FCM). However, these methods fail in assessing the existence of nestedness for graphs of low (NODF) and high (NODF, BINMATNEST) network density. Another common shortcoming of these approaches is the underlying assumption that all vertices belong to a nested component. However, many real-world networks have solely a sub-component (i.e. a subset of its vertices) that is nested. Thus, unveiling which vertices pertain to the nested component is an important research question, unaddressed by the methods available so far. In this contribution, we study in detail the algorithm Nestedness detection based on Local Neighbourhood (NESTLON). This algorithm resorts solely on local information and detects nestedness on a broad range of nested graphs independently of their nature and density. Further, we introduce a benchmark model that allows us to tune the degree of nestedness in a controlled manner and study the performance of different algorithms. Our results show that NESTLON outperforms both BINMATNEST and NODF.
The high potential of Friction Stir Welding (FSW) is already widely used in industrial applications. In combination with a suitable machine concept, this technology is appropriate for small components and can be extended to applications on structures of several meters in length. Using a 3D-capable system that is stiff enough to handle the high process forces, machining and friction stir welding of complex geometries can be carried out directly in one set-up. In order to ensure reproducible, high quality welds, appropriate control strategies are needed. Furthermore the use of various tool types such as standard or bobbin tools can extend the range of weldable geometries tremendously. The aforementioned aspects have been part of process development work for FSW at Fraunhofer IWS Dresden in the last few years. Within the current paper interesting findings are discussed in detail. This includes the realization of a fully 3D-capable FSW machine based on a so-called Pentapod concept. This parallel-kinematic system is suitable for large and complex three-dimensional structures up to 7 meters in length. The FSW research is focused on the welding of aircraft structures and mixed-material joints; examples of research projects and their results are given. Selected welding examples of wrought and cast aluminum, high strength alloys and copper will be presented as well as experiences, which have been made in terms of process development and process control.
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