This paper presents a new verification procedure for articulated arm coordinate measuring machines (AACMMs) together with a capacitive sensor-based indexed metrology platform (IMP) based on the generation of virtual reference distances. The novelty of this procedure lays on the possibility of creating virtual points, virtual gauges and virtual distances through the indexed metrology platform's ...

The Wiener index of a graph G is defined as the sum of all distances between distinct vertices of G. In this paper an algorithm for constructing distance matrix of a zig-zag polyhex nanotube is introduced. As a consequence, the Wiener index of this nanotube is computed.

A new approach to goodness-of-fit for Pareto distributions is introduced. Based on Euclidean distances between sample elements, the family of statistics and tests is indexed by an exponent in (0,2) on Euclidean distance. The corresponding tests are statistically consistent and have excellent performance when applied to heavy-tailed distributions. The exponent can be tailored to the particular P...

In comparing clusterings, several different distances and indices are in use. We prove that the Misclassification Error distance, the Hamming distance (equivalent to the unadjusted Rand index), and the dχ2 distance between partitions are equivalent in the neighborhood of 0. In other words, if two partitions are very similar, then one distance defines upper and lower bounds on the other and vice...