Cargando…

A space for lattice representation and clustering

Algorithms for quantifying the differences between two lattices are used for Bravais lattice determination, database lookup for unit cells to select candidates for molecular replacement, and recently for clustering to group together images from serial crystallography. It is particularly desirable fo...

Descripción completa

Detalles Bibliográficos
Autores principales: Andrews, Lawrence C., Bernstein, Herbert J., Sauter, Nicholas K.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: International Union of Crystallography 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6492488/
https://www.ncbi.nlm.nih.gov/pubmed/31041913
http://dx.doi.org/10.1107/S2053273319002729
_version_ 1783415153972215808
author Andrews, Lawrence C.
Bernstein, Herbert J.
Sauter, Nicholas K.
author_facet Andrews, Lawrence C.
Bernstein, Herbert J.
Sauter, Nicholas K.
author_sort Andrews, Lawrence C.
collection PubMed
description Algorithms for quantifying the differences between two lattices are used for Bravais lattice determination, database lookup for unit cells to select candidates for molecular replacement, and recently for clustering to group together images from serial crystallography. It is particularly desirable for the differences between lattices to be computed as a perturbation-stable metric, i.e. as distances that satisfy the triangle inequality, so that standard tree-based nearest-neighbor algorithms can be used, and for which small changes in the lattices involved produce small changes in the distances computed. A perturbation-stable metric space related to the reduction algorithm of Selling and to the Bravais lattice determination methods of Delone is described. Two ways of representing the space, as six-dimensional real vectors or equivalently as three-dimensional complex vectors, are presented and applications of these metrics are discussed. (Note: in his later publications, Boris Delaunay used the Russian version of his surname, Delone.)
format Online
Article
Text
id pubmed-6492488
institution National Center for Biotechnology Information
language English
publishDate 2019
publisher International Union of Crystallography
record_format MEDLINE/PubMed
spelling pubmed-64924882019-05-03 A space for lattice representation and clustering Andrews, Lawrence C. Bernstein, Herbert J. Sauter, Nicholas K. Acta Crystallogr A Found Adv Research Papers Algorithms for quantifying the differences between two lattices are used for Bravais lattice determination, database lookup for unit cells to select candidates for molecular replacement, and recently for clustering to group together images from serial crystallography. It is particularly desirable for the differences between lattices to be computed as a perturbation-stable metric, i.e. as distances that satisfy the triangle inequality, so that standard tree-based nearest-neighbor algorithms can be used, and for which small changes in the lattices involved produce small changes in the distances computed. A perturbation-stable metric space related to the reduction algorithm of Selling and to the Bravais lattice determination methods of Delone is described. Two ways of representing the space, as six-dimensional real vectors or equivalently as three-dimensional complex vectors, are presented and applications of these metrics are discussed. (Note: in his later publications, Boris Delaunay used the Russian version of his surname, Delone.) International Union of Crystallography 2019-04-30 /pmc/articles/PMC6492488/ /pubmed/31041913 http://dx.doi.org/10.1107/S2053273319002729 Text en © Lawrence C. Andrews et al. 2019 http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.http://creativecommons.org/licenses/by/4.0/
spellingShingle Research Papers
Andrews, Lawrence C.
Bernstein, Herbert J.
Sauter, Nicholas K.
A space for lattice representation and clustering
title A space for lattice representation and clustering
title_full A space for lattice representation and clustering
title_fullStr A space for lattice representation and clustering
title_full_unstemmed A space for lattice representation and clustering
title_short A space for lattice representation and clustering
title_sort space for lattice representation and clustering
topic Research Papers
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6492488/
https://www.ncbi.nlm.nih.gov/pubmed/31041913
http://dx.doi.org/10.1107/S2053273319002729
work_keys_str_mv AT andrewslawrencec aspaceforlatticerepresentationandclustering
AT bernsteinherbertj aspaceforlatticerepresentationandclustering
AT sauternicholask aspaceforlatticerepresentationandclustering
AT andrewslawrencec spaceforlatticerepresentationandclustering
AT bernsteinherbertj spaceforlatticerepresentationandclustering
AT sauternicholask spaceforlatticerepresentationandclustering