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Soliton Kinetic Equations with Non-Kolmogorovian Structure : A New Tool for Biological Modeling? Aerts, Diederik; Czachor, Marek; Gabora, Liane; Polk, Philippe

Abstract

Non-commutative diagrams, where X → Y → Z is allowed and X → Z → Y is not, may equally well apply to Malusian experiments with photons traversing polarizers, and to sequences of elementary chemical reactions. This is why non-commutative probabilistic, logical, and dynamical structures necessarily occur in chemical or biological dynamics. We discuss several explicit examples of such systems and propose an exactly solvable nonlinear toy model of a “brain–heart” system. The model involves non-Kolmogorovian probability calculus and soliton kinetic equations integrable by Darboux transformations.

Item Metadata

Title
Soliton Kinetic Equations with Non-Kolmogorovian Structure : A New Tool for Biological Modeling?
Creator
Aerts, Diederik; Czachor, Marek; Gabora, Liane; Polk, Philippe
Publisher
Springer Verlag
Date Issued
2006
Description
Non-commutative diagrams, where X → Y → Z is allowed and X → Z → Y is not, may equally well apply to Malusian experiments with photons traversing polarizers, and to sequences of elementary chemical reactions. This is why non-commutative probabilistic, logical, and dynamical structures necessarily occur in chemical or biological dynamics. We discuss several explicit examples of such systems and propose an exactly solvable nonlinear toy model of a “brain–heart” system. The model involves non-Kolmogorovian probability calculus and soliton kinetic equations integrable by Darboux transformations.
Subject
solitons; Darboux transformations; kinetic equations; non-Kolmogorovian probability; von Neumann equation
Genre
Article
Type
Text
Language
eng
Date Available
2018-01-19
Provider
Vancouver : University of British Columbia Library
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
DOI
10.14288/1.0363097
URI
http://hdl.handle.net/2429/64418
Affiliation
Arts and Sciences, Irving K. Barber School of (Okanagan); Non UBC; Psychology, Department of (Okanagan)
Citation
Aerts, D., Czachor, M., Gabora L., & Polk, P. (2006). Soliton kinetic equations with non-Kolmogorovian structure: A new tool for biological modeling. Quantum Theory: Reconsideration of Foundations 3, American Institute of Physics Publications, 810, 19–33.
Publisher DOI
10.1063/1.2158708
Peer Review Status
Reviewed
Scholarly Level
Faculty
Rights URI
http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository
DSpace

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Attribution-NonCommercial-NoDerivatives 4.0 International