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Soliton Kinetic Equations with Non-Kolmogorovian Structure: A New Tool for Biological Modeling?
 

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

Centrum Leo Apostel (CLEA) and Foundations of the Exact Sciences (FUND)
Vrije Universiteit Brussel, 1050 Brussels, Belgium

Katedra Fizyki Teoretycznej i Metod Matematycznych, Politechnika GdaŽnska, 80-952 GdaŽnsk, Poland

Department of Psychology, University of British Columbia, Canada

Department of Biology, Vrije Universiteit Brussel, 1050 Brussels, Belgium
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 "brain­heart"
system. The model involves non-Kolmogorovian probability calculus and soliton kinetic equations integrable by Darboux

  

Source: Aerts, Diederik - Leo Apostel Centre, Vrije Universiteit Brussel

 

Collections: Multidisciplinary Databases and Resources; Physics