Suchergebnisse

Let D be an invertible matrix and L1 (x) denote the well‐known 1‐norm of x∈Rn. In this note we analyse the kth moment of the ratio L1 (D−1z) and its asymptotics in special cases, where z is uniformly distributed over the unit hypersphere. Conceptually, L1 (D−1z) can be seen as the (weighted) length, measured along fixed orientations, of a path connecting any two points relative to their straight line distance.

AbstractA hazard is often spatially local in a network system, but its impact can spread out through network topology and become global. To qualitatively and quantitatively assess the impact of spatially local hazards on network systems, this article develops a new spatial vulnerability model by taking into account hazard location, area covered by hazard, and impact of hazard (including direct impact and indirect impact), and proposes an absolute spatial vulnerability index (ASVI) and a relative spatial vulnerability index (RSVI). The relationship between the new model and some relevant traditional network properties is also analyzed. A case study on the spatial vulnerability of the Chinese civil aviation network system is conducted to demonstrate the effectiveness of the model, and another case study on the Beijing subway network system to verify its relationship with traditional network properties.