Sponsor
The publication of this article in an open access journal was funded by the Portland State University Library’s Open Access Fund.
Published In
Symmetry
Document Type
Article
Publication Date
4-2018
Subjects
Mathematical symmetry, Symmetry -- Physics, Akaike Information Criterion, Information theory, Crystallography
Abstract
Geometric Akaike Information Criteria (G-AICs) for generalized noise-level dependent crystallographic symmetry classifications of two-dimensional (2D) images that are more or less periodic in either two or one dimensions as well as Akaike weights for multi-model inferences and predictions are reviewed. Such novel classifications do not refer to a single crystallographic symmetry class exclusively in a qualitative and definitive way. Instead, they are quantitative, spread over a range of crystallographic symmetry classes, and provide opportunities for inferences from all classes (within the range) simultaneously. The novel classifications are based on information theory and depend only on information that has been extracted from the images themselves by means of maximal likelihood approaches so that these classifications are objective. This is in stark contrast to the common practice whereby arbitrarily set thresholds or null hypothesis tests are employed to force crystallographic symmetry classifications into apparently definitive/exclusive states, while the geometric feature extraction results on which they depend are never definitive in the presence of generalized noise, i.e., in all real-world applications. Thus, there is unnecessary subjectivity in the currently practiced ways of making crystallographic symmetry classifications, which can be overcome by the approach outlined in this review.
DOI
10.3390/sym10050133
Persistent Identifier
http://archives.pdx.edu/ds/psu/25085
Citation Details
Moeck, P. (2018). Towards generalized noise-level dependent crystallographic symmetry classifications of more or less periodic crystal patterns. arXiv preprint arXiv:1801.01202.
Description
© 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).