Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Determining Levels of Biological Geometric Information at Polygonal Shape Patterns

Philipp von Bülow
,
Juan Lopez-Sauceda
* ORCID logo ,
Jose Gerardo Carrillo-Gonzalez
,
Carlos Ortega-Laurel
,
Gerardo Abel Laguna-Sánchez
ORCID logo ,
Jacobo Sandoval-Gutierrez
,
Francisco Perez-Martinez
,
Kalina Miranda-Perkins
Version 1 : Received: 7 April 2021 / Approved: 9 April 2021 / Online: 9 April 2021 (10:05:49 CEST)

How to cite: von Bülow, P.; Lopez-Sauceda, J.; Carrillo-Gonzalez, J.G.; Ortega-Laurel, C.; Laguna-Sánchez, G.A.; Sandoval-Gutierrez, J.; Perez-Martinez, F.; Miranda-Perkins, K. Determining Levels of Biological Geometric Information at Polygonal Shape Patterns. Preprints 2021, 2021040253. https://doi.org/10.20944/preprints202104.0253.v1 von Bülow, P.; Lopez-Sauceda, J.; Carrillo-Gonzalez, J.G.; Ortega-Laurel, C.; Laguna-Sánchez, G.A.; Sandoval-Gutierrez, J.; Perez-Martinez, F.; Miranda-Perkins, K. Determining Levels of Biological Geometric Information at Polygonal Shape Patterns. Preprints 2021, 2021040253. https://doi.org/10.20944/preprints202104.0253.v1

Abstract

Based on a measuring system to determine the statistical heterogeneity of individual polygons we propose a method to use polygonal shape patterns as a source of data in order to determine the Shannon entropy of biological organizations. In this research, the term entropy is a particular amount of data related with levels of spatial heterogeneity in a series of different geometrical meshes and sets of random polygons. We propose that this notion of entropy is important to measure levels of information in units of bits, measuring quantities of heterogeneity in geometrical systems. In fact, one important result is that binarization of heterogeneity frequencies yields a supported metric to determine geometrical information from complex configurations. Thirty-five geometric aggregates are tested; biological and non-biological, in order to obtain experimental results of their spatial heterogeneity which is verified with the Shannon entropy parameter defining low particular levels of geometrical information in biological samples. Geometrical aggregates (meshes) include a spectrum of organizations ranging from cell meshes to ecological patterns. Experimental results show that a particular range (0.08 and 0.27) of information is intrinsically associated with low rates of heterogeneity. We conclude it as an intrinsic feature of geometrical organizations in multi-scaling biological systems.

Keywords

Biocomplexity; Geometrical heterogeneity; Information theory

Subject

Computer Science and Mathematics, Algebra and Number Theory

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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