Topological Evolution and Inverse Problems

Aleš Gottvald
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Aleš Gottvald: Academy of Sciences of the CR, Institute of Scientific Instruments

A chapter in Optimization and Inverse Problems in Electromagnetism, 2003, pp 181-192 from Springer

Abstract: Abstract Topology is manifest in Inverse Problems, Electromagnetic Theory and many other fields. Cartan’s exterior calculus of differential forms, Lie groups and Exponential Family are central tools for investigating phenomena where some topological changes take place. A fundamental law of topological evolution is equivalent to the First Law of Statistical Thermodynamics, involving a topological interpretation of heat. We link Bayes’ Theorem with Triality, D4-group, and Octonions. We propose that the inner symmetries of Probability Theory itself correspond to an exceptional A-D-E sequence of Lie groups, with vital implications for fundamental physical laws.

Keywords: Topological evolution; inverse problems; Cartan’s exterior calculus; Lie groups; exponential family; triality; A-D-E sequence (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-2494-4_18

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DOI: 10.1007/978-94-017-2494-4_18

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