A national coastal erosion susceptibility model for Scotland

The upland nature of the Scottish landscape means that much of the social and economic activity has a coastal bias. The importance of the coast is further highlighted by the wide range of ecosystem services that coastal habitats provide. It follows that the threat posed by coastal erosion and flooding has the potential to have a substantial effect on the socioeconomic activity of the whole country. Currently, the knowledge base of coastal erosion is poor and this serves to hinder the current and future management of the coast. To address this knowledge gap, two interrelated models have been developed and are presented here: the Underlying Physical Susceptibility Model (UPSM) and the Coastal Erosion Susceptibility Model (CESM). The UPSM is generated within a GIS at a 50 m2 raster of national coverage, using data relating to ground elevation, rockhead elevation, wave exposure and proximity to the open coast. The CESM moderates the outputs of the UPSM to include the effects of sediment supply and coastal defence data. When validated against locations in Scotland that are currently experiencing coastal erosion, the CESM successfully identifies these areas as having high susceptibility. This allows the UPSM and CESM to be used as tools to identify assets inherently exposed to coastal erosion, areas where coastal erosion may exacerbate coastal flooding, and areas are inherently resilient to erosion, thus allow more efficient and effective management of the Scottish coast

Pa\u27s Old Girl : Was My First And Best Girl

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Index theory for locally compact noncommutative geometries

Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, we prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and we illustrate this point with two examples in the text. In order to understand what is new in our approach in the commutative setting we prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds our index formula appears to be completely new. As we prove our local index formula in the framework of semifinite noncommutative geometry we are also able to prove, for manifolds of bounded geometry, a version of Atiyah's L^2-index Theorem for covering spaces. We also explain how to interpret the McKean-Singer formula in the nonunital case. In order to prove the local index formula, we develop an integration theory compatible with a refinement of the existing pseudodifferential calculus for spectral triples. We also clarify some aspects of index theory for nonunital algebras.Comment: 133 pages. to appear in Memoirs of the American Mathematical Society. Published version will have different pagination, and an inde

Outlier detection in network revenue management

This paper presents an automated approach for providing ranked lists of outliers in observed demand to support analysts in network revenue management. Such network revenue management, e.g. for railway itineraries, needs accurate demand forecasts. However, demand outliers across or in parts of a network complicate accurate demand forecasting, and the network structure makes such demand outliers hard to detect. We propose a two-step approach combining clustering with functional outlier detection to identify outlying demand from network bookings observed on the leg level. The first step clusters legs to appropriately partition and pool booking patterns. The second step identifies outliers within each cluster and uses a novel aggregation method across legs to create a ranked alert list of affected instances. Our method outperforms analyses that consider leg data without regard for network implications and offers a computationally efficient alternative to storing and analysing all data on the itinerary level, especially in highly-connected networks where most customers book multi-leg products. A simulation study demonstrates the robustness of the approach and quantifies the potential revenue benefits from adjusting demand forecasts for offer optimisation. Finally, we illustrate the applicability based on empirical data obtained from Deutsche Bahn