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Topological Evolution and Inverse Problems

In: Optimization and Inverse Problems in Electromagnetism

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  • Aleš Gottvald

    (Academy of Sciences of the CR, Institute of Scientific Instruments)

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.

Suggested Citation

  • Aleš Gottvald, 2003. "Topological Evolution and Inverse Problems," Springer Books, in: Marek Rudnicki & Sławomir Wiak (ed.), Optimization and Inverse Problems in Electromagnetism, pages 181-192, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-2494-4_18
    DOI: 10.1007/978-94-017-2494-4_18
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