Hierarchy and information in feedforward networks

SFI WORKING PAPER: 2010-12-036 SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peer-reviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for papers by our external faculty, papers must be based on work done at SFI, inspired by an invited visit to or collaboration at SFI, or funded by an SFI grant. ©NOTICE: This working paper is included by permission of the contributing author(s) as a means to ensure timely distribution of the scholarly and technical work on a non-commercial basis. Copyright and all rights therein are maintained by the author(s). It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may be reposted only with the explicit permission of the copyright holder. www.santafe.edu

[1]  C. H. Coombs,et al.  Mathematical psychology : an elementary introduction , 1970 .

[2]  R. Ulanowicz,et al.  Information theoretical analysis of the aggregation and hierarchical structure of ecological networks , 1985 .

[3]  J. Gross,et al.  Graph Theory and Its Applications , 1998 .

[4]  John D. Nystuen,et al.  Human Geography: Spatial Design in World Society , 1986 .

[5]  Patrick Suppes,et al.  Axiomatic set theory , 1969 .

[6]  An-Ping Zeng,et al.  Hierarchical structure and modules in the Escherichia coli transcriptional regulatory network revealed by a new top-down approach , 2004, BMC Bioinformatics.

[7]  W. Miller.  The Hierarchical Structure of Ecosystems: Connections to Evolution , 2007, Evolution: Education and Outreach.

[8]  G. Toulouse,et al.  Ultrametricity for physicists , 1986 .

[9]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[10]  R. Solé,et al.  Self-organization versus hierarchy in open-source social networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Joaqu'in Goni,et al.  Topological reversibility and causality in feed-forward networks , 2010, 1007.1829.

[12]  Sergei Maslov,et al.  Hierarchy measures in complex networks. , 2003, Physical review letters.

[13]  B. Corominas-Murtra,et al.  On the basic computational structure of gene regulatory networks. , 2009, Molecular bioSystems.

[14]  A. Barabasi,et al.  Hierarchical Organization of Modularity in Metabolic Networks , 2002, Science.

[15]  E. Bullmore,et al.  Hierarchical Organization of Human Cortical Networks in Health and Schizophrenia , 2008, The Journal of Neuroscience.

[16]  M. Cosentino Lagomarsino,et al.  Hierarchy and feedback in the evolution of the Escherichia coli transcription network , 2007, Proceedings of the National Academy of Sciences.

[17]  L. Goddard.  Information Theory , 1962, Nature.

[18]  M. Newman,et al.  Hierarchical structure and the prediction of missing links in networks , 2008, Nature.

[19]  A. Wilson,et al.  Hierarchical structures. , 1969, Science.

[20]  C. Kuratowski.  Sur la notion de l'ordre dans la Théorie des Ensembles , 1921 .

[21]  Alessandro Vespignani,et al.  Large-scale topological and dynamical properties of the Internet. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Tad Hogg,et al.  Complexity and adaptation , 1986 .

[23]  N. Eldredge.  Unfinished Synthesis: Biological Hierarchies and Modern Evolutionary Thought , 1985 .

[24]  Aleksandr Yakovlevich Khinchin,et al.  Mathematical foundations of information theory , 1959 .

[25]  Edward T. Bullmore,et al.  Neuroinformatics Original Research Article , 2022 .

[26]  Joaquín Goñi,et al.  Exploring the randomness of Directed Acyclic Networks , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Ernesto Estrada,et al.  Information mobility in complex networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Roger Guimerà,et al.  Extracting the hierarchical organization of complex systems , 2007, Proceedings of the National Academy of Sciences.

[29]  M. Gerstein,et al.  Genomic analysis of the hierarchical structure of regulatory networks , 2006, Proceedings of the National Academy of Sciences.

[30]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[31]  Howard Hunt Pattee,et al.  Hierarchy Theory: The Challenge of Complex Systems , 1973 .

[32]  HERBERT A. SIMON,et al.  The Architecture of Complexity , 1991 .

[33]  John F. Kolars.  Human geography : spatial design in world society / by John F. Kolars and John D. Nystuen , 1974 .

[34]  D. McShea.  The hierarchical structure of organisms: a scale and documentation of a trend in the maximum , 2001, Paleobiology.