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