This paper reports an analysis and comparison of the use of 51 different similarity coefficients for computing the similarities between binary fingerprints for both simulated and real chemical data sets. Five pairs and a triplet of coefficients were found to yield identical similarity values, leading to the elimination of seven of the coefficients. The remaining 44 coefficients were then compar...

We evaluate the virial coefficients Bk for k ≤ 10 for hard spheres in dimensions D = 2, · · · , 8. Virial coefficients with k even are found to be negative when D ≥ 5. This provides strong evidence that the leading singularity for the virial series lies away from the positive real axis when D ≥ 5. Further analysis provides evidence that negative virial coefficients will be seen for some k > 10 ...

k-Adic formulations (for groups of objects of size k) of a variety of 2adic similarity coefficients (for pairs of objects) for binary (presence/absence) data are presented. The formulations are not functions of 2-adic similarity coefficients. Instead, the main objective of the the paper is to present k-adic formulations that reflect certain basic characteristics of, and have a similar interpret...

This paper gives a qualitative description how Young tableaux can be used to perform a Clebsch-Gordan decomposition of tensor products in SU(3) and how this can be generalized to SU(N).

This essay describes the development of groups used for the specification of symmetries from ordinary and magnetic point groups to Fedorov and magnetic space groups, as well as other varieties of groups useful in the study of symmetric objects. In particular, we consider the problem of some incorrectness in Vol. A of the International Tables for Crystallography. Some results of tensor calculus ...

The present study compared different similarity and dissimilarity coefficients and their influence in maize inbred line clustering. Ninety maize S0:1 inbred lines were used and genotyped with 25 microsatellite markers (simple sequence repeat). The simple matching, Rogers and Tanimoto, Russel and Rao, Hamann, Jaccard, Sorensen-Dice, Ochiai, and Roger's modified distance coefficients were compare...