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Information Theory and the Embedding Problem for Riemannian Manifolds

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Geometric Science of Information (GSI 2021)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12829))

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Abstract

This paper provides an introduction to an information theoretic formulation of the embedding problem for Riemannian manifolds developed by the author. The main new construct is a stochastic relaxation scheme for embedding problems and hard constraint systems. This scheme is introduced with examples and context.

Partial support for this work was provided by the National Science Foundation (DMS 1714187), the Simons Foundation (Award 561041), the Charles Simonyi Foundation and the School of Mathematics at the Institute for Advanced Study. The author is grateful to the anonymous referees of this paper for many valuable comments.

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Author information

Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Govind Menon

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  1. Govind Menon
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Correspondence to Govind Menon .

Editor information

Editors and Affiliations

  1. Sony Computer Science Laboratories Inc., Tokyo, Japan

    Frank Nielsen

  2. THALES Land & Air Systems, Meudon, France

    Frédéric Barbaresco

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Menon, G. (2021). Information Theory and the Embedding Problem for Riemannian Manifolds. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science(), vol 12829. Springer, Cham. https://doi.org/10.1007/978-3-030-80209-7_65

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  • DOI: https://doi.org/10.1007/978-3-030-80209-7_65

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-80208-0

  • Online ISBN: 978-3-030-80209-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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