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dc.contributor.authorZenil, Hector
dc.contributor.authorKiani, Narsis
dc.contributor.authorTegner, Jesper
dc.date.accessioned2019-03-11T07:14:54Z
dc.date.available2019-03-11T07:14:54Z
dc.date.issued2018-07-18
dc.identifier.citationZenil H, Kiani N, Tegnér J (2018) Symmetry and Correspondence of Algorithmic Complexity over Geometric, Spatial and Topological Representations. Entropy 20: 534. Available: http://dx.doi.org/10.3390/e20070534.
dc.identifier.issn1099-4300
dc.identifier.doi10.3390/e20070534
dc.identifier.urihttp://hdl.handle.net/10754/631529
dc.description.abstractWe introduce a definition of algorithmic symmetry in the context of geometric and spatial complexity able to capture mathematical aspects of different objects using as a case study polyominoes and polyhedral graphs. We review, study and apply a method for approximating the algorithmic complexity (also known as Kolmogorov-Chaitin complexity) of graphs and networks based on the concept of Algorithmic Probability (AP). AP is a concept (and method) capable of recursively enumerate all properties of computable (causal) nature beyond statistical regularities. We explore the connections of algorithmic complexity-both theoretical and numerical-with geometric properties mainly symmetry and topology from an (algorithmic) information-theoretic perspective. We show that approximations to algorithmic complexity by lossless compression and an Algorithmic Probability-based method can characterize spatial, geometric, symmetric and topological properties of mathematical objects and graphs.
dc.description.sponsorshipThis research was funded by Swedish Research Council (Vetenskapsrådet) grant number [2015-05299].
dc.publisherMDPI AG
dc.relation.urlhttps://www.mdpi.com/1099-4300/20/7/534
dc.rightsThis 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 (CC BY 4.0).
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectAlgorithmic coding theorem
dc.subjectAlgorithmic probability
dc.subjectInformation content
dc.subjectKolmogorov-Chaitin complexity
dc.subjectMolecular complexity
dc.subjectPolyhedral networks
dc.subjectPolyominoes
dc.subjectPolytopes
dc.subjectRecursive transformation
dc.subjectShannon entropy
dc.subjectSymmetry breaking
dc.subjectTuring machines
dc.titleSymmetry and Correspondence of Algorithmic Complexity over Geometric, Spatial and Topological Representations
dc.typeArticle
dc.contributor.departmentBiological and Environmental Sciences and Engineering (BESE) Division
dc.contributor.departmentBioscience Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalEntropy
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionAlgorithmic Nature Group, Laboratoire de Recherche Scientifique (LABORES) for the Natural and Digital Sciences, Paris, 75005, , France
dc.contributor.institutionScience for Life Laboratory (SciLifeLab), Stockholm, 171 77, , Sweden
dc.contributor.institutionUnit of Computational Medicine, Department of Medicine, Karolinska Institute, Stockholm, 171 77, , Sweden
dc.contributor.institutionAlgorithmic Dynamics Lab, Centre for Molecular Medicine, Karolinska Institute, Stockholm, 171 77, , Sweden
kaust.personTegner, Jesper
refterms.dateFOA2019-03-12T12:14:16Z


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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 (CC BY 4.0).
Except where otherwise noted, this item's license is described as 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 (CC BY 4.0).