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Dynamical System and Information Geometry - A Complementary Approach to Complex Systems -

Abstract : Recently emerging complex systems sciences tackle the systems where complex in- teractions between components lead to the manifestation of emergent property linking different levels of organization. This thesis aims to reveal the mechanism of emergent property in complex systems, both in concrete modeling as well as comparative analysis between different systems. We tackle various sub jects in complex systems science with newly proposed unified theoretical framework, based on the dialectic between dynam- ical system theory and information geometry. The thesis has therefore two levels of ob jectives: 1) Modeling and understanding of concrete complex systems with the use of constructive and interaction-analytical methodologies, and 2) comparison between different complex systems to characterize universal structure of emergence. The thesis consists of 7 Parts, in which Part 2 to 6 correspond to the first ob jective, and the Part 7 to the second one: In Part 1, we review the historical context of complex systems science and propose a dialectical strategy between the constructive and interaction-analytical methodology, based on the dynamical system theory and information geometry, respectively. In Part 2, we treat a candidate model of brain cortex dynamics known as “chaotic itinerancy”, and incorporate the effect of autonomous learning seeking for the creativity of intelligence as emergent property of neural system. The interpretation of emergence in terms of the internal measurement theory is extended to derive the concept of “chaotic itinerancy as catalyst of learning”. In Part 3, the dynamics of chaotic neural network is applied to emergent collective behavior of robots, so that to realize optimal intermittent search of sporadic informa- tion. The effectiveness of the collective infotaxis is analyzed on a simulator basis. In Part 4, we define novel complexity measures from information geometrical point of view and apply to the analysis of social network data. The established complexity measures play a key role in comparative analysis between different systems in Part 7. In Part 5, we apply the dialectical strategy between dynamical system and infor- mation geometry toward the understanding of morphogenesis during zebrafish embryo- genesis. Theoretical propositions are tested with tentative experimental data from two european pro jects, Embryomics and BioEMERGENCES. In Part 6, complex systems related to linguistics are investigated. We discovered novel invariants and geometrical relation between japanese vowels, as a system-level emergent property. Ecological modeling approach to multilingual environment is also proposed along the dialectical strategy between linguistic theory and mathematical modeling. In Part 7, we review the obtained results in previous Parts with comparative per- spective, seeking for a characterization of universal structure of emergence in terms of the organization of interactions that does not explicitly depend on the property of components. Comparison between Part 2 and 4, as well as 5 and 6, derived candi- date qualitative dynamics of emergence and its detection strategy as the dynamics and constraint between functors and meta-functors. Further possibility of the proposed strategy is discussed.
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Contributor : Masatoshi Funabashi <>
Submitted on : Tuesday, January 18, 2011 - 9:00:12 AM
Last modification on : Friday, October 23, 2020 - 4:37:16 PM


  • HAL Id : pastel-00556873, version 1



Masatoshi Funabashi. Dynamical System and Information Geometry - A Complementary Approach to Complex Systems -. General Physics [physics.gen-ph]. Ecole Polytechnique X, 2010. English. ⟨pastel-00556873⟩



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