Distance measures play an important role in shape classification and data analysis problems. Topological distances based on Reeb graphs and persistence diagrams have been employed to obtain effective algorithms in shape matching and scalar data analysis. In the current paper, we propose an improved distance measure between two multi-fields by computing a multi-dimensional Reeb graph (MDRG) each of which captures the topology of a multi-field through a hierarchy of Reeb graphs in different dimensions. A hierarchy of persistence diagrams is then constructed by computing a persistence diagram corresponding to each Reeb graph of the MDRG. Based on this representation, we propose a novel distance measure between two MDRGs by extending the bottleneck distance between two Reeb graphs. We show that the proposed measure satisfies the pseudo-metric and stability properties. We examine the effectiveness of the proposed multi-field topology-based measure on two different applications: (1) shape classification and (2) detection of topological features in a time-varying multi-field data. In the shape classification problem, the performance of the proposed measure is compared with the well-known topology-based measures in shape matching. In the second application, we consider a time-varying volumetric multi-field data from the field of computational chemistry where the goal is to detect the site of stable bond formation between Pt and CO molecules. We demonstrate the ability of the proposed distance in classifying each of the sites as occurring before and after the bond stabilization.

The Swedish Transport Agency Transportstyrelsen has given Scania approval to expand the route and range of its autonomous vehicle testing on the nation's roads. In February 2021, Scania was given permission to begin operating three autonomous trucks on a stretch of the E4 highway between the company's main production site in Södertälje and Nyköping, which lies 70 kilometres to the south. The success of that trial has now led to an expansion of the distance and parameters of the tests. The autonomous trucks will be able to drive on all types of roads – local and national – between Södertälje and the southern city of Jönköping, which is nearly 300 kilometres and three-and-a-half hours away. It's a development which has delighted Scania, which has been exploring this technology for the best part of the last decade, including in mining and delivery applications.