Symmetry and Algorithmic Complexity of Polyominoes and Polyhedral Graphs

Handle URI:
http://hdl.handle.net/10754/627341
Title:
Symmetry and Algorithmic Complexity of Polyominoes and Polyhedral Graphs
Authors:
Zenil, Hector; Kiani, Narsis A.; Tegner, Jesper ( 0000-0002-9568-5588 )
Abstract:
We introduce a definition of algorithmic symmetry able to capture essential aspects of geometric symmetry. 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 enumeration 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 properties of polyominoes, polytopes, regular and quasi-regular polyhedra as well as polyhedral networks, thereby demonstrating its profiling capabilities.
KAUST Department:
Biological and Environmental Sciences and Engineering (BESE) Division; Bioscience Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
arXiv
Issue Date:
24-Feb-2018
ARXIV:
arXiv:1803.02186
Type:
Preprint
Additional Links:
http://arxiv.org/abs/1803.02186v1; http://arxiv.org/pdf/1803.02186v1
Appears in Collections:
Other/General Submission; Bioscience Program; Biological and Environmental Sciences and Engineering (BESE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorZenil, Hectoren
dc.contributor.authorKiani, Narsis A.en
dc.contributor.authorTegner, Jesperen
dc.date.accessioned2018-03-15T11:35:54Z-
dc.date.available2018-03-15T11:35:54Z-
dc.date.issued2018-02-24en
dc.identifier.urihttp://hdl.handle.net/10754/627341-
dc.description.abstractWe introduce a definition of algorithmic symmetry able to capture essential aspects of geometric symmetry. 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 enumeration 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 properties of polyominoes, polytopes, regular and quasi-regular polyhedra as well as polyhedral networks, thereby demonstrating its profiling capabilities.en
dc.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1803.02186v1en
dc.relation.urlhttp://arxiv.org/pdf/1803.02186v1en
dc.rightsArchived with thanks to arXiven
dc.titleSymmetry and Algorithmic Complexity of Polyominoes and Polyhedral Graphsen
dc.typePreprinten
dc.contributor.departmentBiological and Environmental Sciences and Engineering (BESE) Divisionen
dc.contributor.departmentBioscience Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.eprint.versionPre-printen
dc.contributor.institutionAlgorithmic Nature Group, LABORES for the Natural and Digital Sciences, Paris, Franceen
dc.contributor.institutionScience for Life Laboratory, SciLifeLab, Stockholm, Swedenen
dc.contributor.institutionUnit of Computational Medicine, Department of Medicine, Karolinska Institute, Stockholm, Swedenen
dc.contributor.institutionAlgorithmic Dynamics Lab, Centre for Molecular Medicine, Karolinska Institute, Stockholm, Swedenen
dc.identifier.arxividarXiv:1803.02186en
kaust.authorTegner, Jesperen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.