The position value as a centrality measure in social networks

The position value, introduced by Meessen (1988), is a solution concept for cooperative games in which the value assigned to a player depends on the value of the connections or links he has with other players. This concept has been studied by Borm et al. (1992) and characterised by Slikker (2005). In this paper, we analyse the position value from the point of view of the typical properties of a measure of centrality in a social network. We extend the analysis already developed in Gomez et al. (2003) for the Myerson centrality measure, where the symmetric effect on the centralities of the end nodes of an added or removed edge is a fundamental part of its characterisation. However, the Position centrality measure, unlike the Myerson centrality measure, responds in a more versatile way to such addition or elimination. After studying the aforementioned properties, we will focus on the analysis and characterisation of the Position attachment centrality given by the position value when the underlying game is the attachment game. Some comparisons are made with the attachment centrality introduced by Skibski et al. (2019).Depto. de Estadística e Investigación OperativaFac. de Ciencias MatemáticasInstituto de Matemática Interdisciplinar (IMI)FALSEMinisterio de Ciencia e Innovaciónunpu

On the Design of Functionally Integrated Aero-engine Structures: Modeling and Evaluation Methods for Architecture and Complexity

The drive for airplanes with radically reduced fuel consumption and emissions motivates engine manufacturers to explore innovative engine designs. The novelty of such engines results in changed operating conditions, such as newly introduced constraints, increased loads or rearranged interfaces. To be competitive, component developers and manufacturers must understand and predict the consequences of such changes on their sub-systems. Presently, such assessments are based on detailed geometrical models (CAD or finite element) and consume significant amounts of time. The preparation of such models is resource intensive unless parametrization is employed. Even with parametrization, alternative geometrical layouts for designs are difficult to achieve. In contrast to geometrical model-based estimations, a component architecture representation and evaluation scheme can quickly identify the functional implications for a system-level change and likely consequences on the component. The schemes can, in turn, point to the type and location of needed evaluations with detailed geometry. This will benefit the development of new engine designs and facilitate improvements upon existing designs. The availability of architecture representation schemes for functionally integrated (all functions being satisfied by one monolithic structure) aero-engine structural components is limited. The research in this thesis focuses on supporting the design of aero-engine structural components by representing their architecture as well as by developing means for the quantitative evaluation and comparison of different component designs. The research has been conducted in collaboration with GKN Aerospace Sweden AB, and the components are aero-engine structures developed and manufactured at GKN. Architectural information is generated and described based on concepts from set theory, graph theory and enhanced function–means trees. In addition, the complexities of the components are evaluated using a new complexity metric. Specifically, the developed modeling and evaluation methods facilitate the following activities: \ub7\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0 identification and representation of function–means information for the component\ub7\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0 representation and evaluation of component architecture\ub7\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0 product complexity evaluation\ub7\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0 early selection of load path architecture\ub7\ua0\ua0\ua0\ua0\ua0\ua0\ua0\ua0 impact assessment for the component’s functioning in the systemBy means of the methods developed in this thesis, the design rationale for a component is made explicit, and the storing, communicating and retrieving of information about the component in the future is enabled. Through their application to real-life engine structures, the usability of the methods in identifying early load carrying configurations and selecting a manufacturing segmenting option is demonstrated. Together, the methods provide development engineers the ability to compare alternative architectures. Further research could focus on exploring the system (engine) effects of changes in component architecture and improvements to the complexity metric by incorporating manufacturing information