SL(2, C) Scheme Processing of Singularities in Quantum Computing and Genetics

Michel Planat; Marcelo Amaral; David Chester; Klee Irwin

doi:10.20944/preprints202301.0529.v2

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preprints.org > computer science and mathematics > geometry and topology > doi: 10.20944/preprints202301.0529.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

SL(2, C) Scheme Processing of Singularities in Quantum Computing and Genetics

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These authors contributed equally to this work

Version 1 : Received: 20 January 2023 / Approved: 30 January 2023 / Online: 30 January 2023 (01:21:36 CET)
Version 2 : Received: 12 February 2023 / Approved: 14 February 2023 / Online: 14 February 2023 (01:43:07 CET)

A peer-reviewed article of this Preprint also exists.

Planat, M.; Amaral, M.M.; Chester, D.; Irwin, K. $S L (2, C)$ Scheme Processing of Singularities in Quantum Computing and Genetics. Axioms 2023, 12, 233. Planat, M.; Amaral, M.M.; Chester, D.; Irwin, K. SL(2,C) Scheme Processing of Singularities in Quantum Computing and Genetics. Axioms 2023, 12, 233.

Planat, M.; Amaral, M.M.; Chester, D.; Irwin, K.

S L (2, C)

Scheme Processing of Singularities in Quantum Computing and Genetics. Axioms 2023, 12, 233. Planat, M.; Amaral, M.M.; Chester, D.; Irwin, K. SL(2,C) Scheme Processing of Singularities in Quantum Computing and Genetics. Axioms 2023, 12, 233.

Abstract

Revealing the time structure of physical or biological objects is usually performed thanks to the tools of signal processing like the fast Fourier transform, Ramanujan sum signal processing and many other techniques. For space-time topological objects in physics and biology, we propose a type of algebraic processing based on schemes in which the discrimination of singularities within objects is based on the space-time-spin group SL(2,C). Such topological objects possess an homotopy structure encoded in their fundamental group and the related SL(2,C) multivariate polynomial character variety contains a plethora of singularities somehow analogous to the frequency spectrum in time structures. Our approach is applied to an Akbulut cork in exotic R4, to an hyperbolic model of topological quantum computing based on algebraic surfaces and to microRNAs in genetics. Such diverse topics reveal the manifold of possibilities of using the concept of a scheme spectrum.

Keywords

Finitely generated group; SL(2,C) character variety; algebraic surfaces; schemes; exotic R4; topological quantum computing; microRNAs.

Subject

Computer Science and Mathematics, Geometry and Topology

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Received: 14 February 2023
Commenter: Michel Planat
Commenter's Conflict of Interests: Author

Comment: The changes are highlighted in the attached pdf.

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