Methods of information theory and algorithmic complexity for network biology

Seminars in Cell & Developmental Biology
Hector ZenilJesper Tegnér

Abstract

We survey and introduce concepts and tools located at the intersection of information theory and network biology. We show that Shannon's information entropy, compressibility and algorithmic complexity quantify different local and global aspects of synthetic and biological data. We show examples such as the emergence of giant components in Erdös-Rényi random graphs, and the recovery of topological properties from numerical kinetic properties simulating gene expression data. We provide exact theoretical calculations, numerical approximations and error estimations of entropy, algorithmic probability and Kolmogorov complexity for different types of graphs, characterizing their variant and invariant properties. We introduce formal definitions of complexity for both labeled and unlabeled graphs and prove that the Kolmogorov complexity of a labeled graph is a good approximation of its unlabeled Kolmogorov complexity and thus a robust definition of graph complexity.

References

Apr 23, 2002·Nature Genetics·Shai S Shen-OrrUri Alon
Oct 26, 2002·Science·Tong Ihn LeeRichard A Young
Oct 10, 2003·Bioinformatics·Pedro MendesKeying Ye
Feb 28, 2004·Science·Duncan T OdomRichard A Young
Mar 6, 2004·Science·Ron MiloUri Alon
Sep 13, 2005·Cell·Laurie A BoyerRichard A Young
May 19, 2007·Nature Reviews. Genetics·Uri Alon

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Citations

Mar 19, 2016·Seminars in Cell & Developmental Biology·Ali Masoudi-Nejad, Hector Zenil
Oct 5, 2016·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Jesper TegnérDavid Gomez-Cabrero
Jan 20, 2018·Physical Review. E·Hector ZenilJesper Tegnér
Sep 5, 2019··Martin NehézPeter Bartalos

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