Sentence examples for bottleneck distance from inspiring English sources
One of the most commonly employed distance functions is the bottleneck distance (W_{infty}[L_{infty}]).
The first stability theorem for PH, proven in [151], asserts that, under favorable conditions, step (2) in the pipeline in Figure 6 is 1-Lipschitz with respect to suitable distance functions on filtered complexes and the bottleneck distance for barcodes (see Section 5.4).
We describe the distance between P i and P j as the bottleneck distance: (1) D (P i, P j ) = max k D (P i k, P j k ).
This article introduces a proper redefinition of the concept of bottleneck Steiner distance for the prize-collecting Steiner problem.
It has been noticed that, despite the corridor is characterized by single-track segments (bottlenecks) with distances between consecutive stations (e.g. Albacina, Genga and Serra S. Quirico) of around 7.5 km and low permissible speeds (max 95 km/h), the total number of trains indicated in the integrated database ETISPLUS/UNECE is related to the whole corridor.
We also discuss the computation of the bottleneck and Wasserstein distances.
Until recently, the library Dionysus [64] was the only library to implement computation of the bottleneck and Wasserstein distances (for (mathrm{d}=L_{infty})); the library hera [138] implements a new algorithm [139] for the computation of the bottleneck and Wasserstein distances that significantly outperforms the implementation in Dionysus.
Also, each node keeps "close bottlenecks", which is a set of bottleneck nodes of which distance from the nodes ≤ 2. Each node in the starting node set forms an initial cluster.
The variability in the distance of bottlenecks from the start point was rather large, i.e., up to 8 Å (53%).
The results showed that the geometrical properties and physicochemical properties of the found channels typically varied by less than 20% except for the distance of bottlenecks from the starting point.
Also, the number of bottlenecks over a given distance may differ.
