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dc.contributor.authorZenil, Hector
dc.contributor.authorKiani, Narsis A.
dc.contributor.authorTegner, Jesper
dc.date.accessioned2017-08-23T11:54:06Z
dc.date.available2017-08-23T11:54:06Z
dc.date.issued2017-07-07
dc.identifier.citationZenil H, Kiani NA, Tegnér J (2017) Low-algorithmic-complexity entropy-deceiving graphs. Physical Review E 96. Available: http://dx.doi.org/10.1103/PhysRevE.96.012308.
dc.identifier.issn2470-0045
dc.identifier.issn2470-0053
dc.identifier.doi10.1103/PhysRevE.96.012308
dc.identifier.urihttp://hdl.handle.net/10754/625386
dc.description.abstractIn estimating the complexity of objects, in particular, of graphs, it is common practice to rely on graphand information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these measures are not independent of the way in which an object, such as a graph, can be described or observed. From observations that can reconstruct the same graph and are therefore essentially translations of the same description, we see that when applying a computable measure such as the Shannon entropy, not only is it necessary to preselect a feature of interest where there is one, and to make an arbitrary selection where there is not, but also more general properties, such as the causal likelihood of a graph as a measure (opposed to randomness), can be largely misrepresented by computable measures such as the entropy and entropy rate. We introduce recursive and nonrecursive (uncomputable) graphs and graph constructions based on these integer sequences, whose different lossless descriptions have disparate entropy values, thereby enabling the study and exploration of a measure's range of applications and demonstrating the weaknesses of computable measures of complexity.
dc.description.sponsorshipN.A.K. was supported by aVinnovaVINNMERfellowship, Stratneuro. H. Z. was supported by the Swedish Research Council (VR).
dc.publisherAmerican Physical Society (APS)
dc.relation.urlhttps://journals.aps.org/pre/abstract/10.1103/PhysRevE.96.012308
dc.rightsArchived with thanks to Physical Review E. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.titleLow-algorithmic-complexity entropy-deceiving graphs
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.journalPhysical Review E
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionAlgorithmic Nature Group, LABoRES, Paris, 75006, , France
dc.contributor.institutionDepartment of Computer Science, University of Oxford, Oxford, OX1 3QD, , United Kingdom
dc.contributor.institutionInformation Dynamics Lab, Unit of Computational Medicine, Department of Medicine Solna, Center for Molecular Medicine, SciLifeLab, Karolinska Institute, Stockholm, 171 76, , Sweden
dc.identifier.arxividarXiv:1608.05972
kaust.personTegner, Jesper
refterms.dateFOA2018-06-13T18:43:42Z


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Archived with thanks to Physical Review E. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Except where otherwise noted, this item's license is described as Archived with thanks to Physical Review E. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.