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- Aerts, D. and Czachor, M. (2006). Abstract DNA-type systems.
Nonlinearity,19, pp. 575-589. Archive reference and link: http://uk.arxiv.org/abs/q-bio/0411031. doi: 10.1088/0951-7715/19/3/003. download pdf.

Abstract:An abstract DNA-type system is defined by a set of nonlinear kinetic equations with polynomial nonlinearities that admit soliton solutions associated with helical geometry. The set of equations allows for two different Lax representations: A von Neumann form and a Darboux-covariant Lax pair. We explain why non-Kolmogorovian probability models occurring in soliton kinetics are naturally associated with chemical reactions. The most general known characterization of soliton kinetic equations is given and a class of explicit soliton solutions is discussed. Switching between open and closed states is a generic behaviour of the helices. The effect does not crucially depend on the order of nonlinearity (i.e. types of reactions), a fact that may explain why simplified models possess properties occuring in realistic systems. We explain also why fluctuations based on Darboux transformations will not destroy the dynamics but only switch between a finite number of helical structures.- Aerts, D., Czachor, M. and D'Hooghe, B. (2006). Towards a quantum evolutionary scheme: violating Bell's inequalities in language. In N. Gontier, J. P. Van Bendegem and D. Aerts (Eds.),
Evolutionary Epistemology, Language and Culture - A non adaptationist systems theoretical approach. [Theory and Decision Library Series A: Philosophy and Methodology of the Social Sciences. Series editor: Julian Nida-Ruemelin]. Dordrecht: Springer. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0407150. download pdf.

Abstract:We show the presence of genuine quantum structures in human language. The neo-Darwinian evolutionary scheme is founded on a probability structure that satisfies the Kolmogorovian axioms, and as a consequence cannot incorporate quantum-like evolutionary change. In earlier research we revealed quantum structures in processes taking place in conceptual space. We argue that the presence of quantum structures in language and the earlier detected quantum structures in conceptual change make the neo-Darwinian evolutionary scheme strictly too limited for Evolutionary Epistemology. We sketch how we believe that evolution in a more general way should be implemented in epistemology and conceptual change, but also in biology, and how this view would lead to another relation between both biology and epistemology.- Aerts, D., Czachor, M., Gabora, L. and Polk, P. (2006). Soliton kinetic equations with non-Kolmogorovian structure: A new tool for biological modeling?,
AIP Conference Proceedings,810, pp. 19-33. download pdf.

Abstract:Non-commutative diagrams, where X goes to Y goes to Z is allowed and X goes Z goes to 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 'brainÐheart' system. The model involves non-Kolmogorovian probability calculus and soliton kinetic equations integrable by Darboux transformations.- Aerts, D., Czachor, M. and Pawlowski, M. (2006). Entangled-state cryptographic protocol that remains secure even if nonlocal hidden variables exist and can be measured with arbitrary precision,
Physical Review A,73, 034303. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0501003. doi: 10.1103/PhysRevA.73.034303. download pdf.

Abstract:Standard quantum cryptographic protocols are not secure if one assumes that nonlocal hidden variables exist and can be measured with arbitrary precision. The security can be restored if one of the communicating parties randomly switches between two standard protocols.- Aerts, D., Czachor, M. and Pawlowski, M. (2006). Entangled-state cryptographic protocol that remains secure even if nonlocal hidden variables exist and can be measured with arbitrary precision,
Erratum - Physical Review A,73, 059901(E).- Aerts, D. and Pulmannova, S. (2006). Representation of state property systems.
Journal of Mathematical Physics,47, 072105. doi: 10.1063/1.2217807. download pdf.

Abstract:A state property system is the mathematical structure which models an arbitrary physical system by means of its set of states, its set of properties, and a relation of 'actuality of a certain property for a certain state'. We work out a new axiomatization for standard quantum mechanics, starting with the basic notion of state property system, and making use of a generalization of the standard quantum mechanical notion of 'superposition' for state property systems.- Broekaert, J., Aerts, D. and D'Hooghe, B. (2006). The generalised Liar Paradox: A quantum model and interpretation.
Foundations of Science,11, pp. 399-418. Archive reference and link: http://uk.arxiv.org/abs/quant-ph/0404066. doi: 10.1007/s10699-004-6248-8. download pdf.

Abstract:The formalism of abstracted quantum mechanics is applied in a model of the generalized Liar Paradox. Here, the Liar Paradox, a consistently testable configuration of logical truth properties, is considered a dynamic conceptual entity in the cognitive sphere. Basically, the intrinsic contextuality of the truth-value of the Liar Paradox is appropriately covered by the abstracted quantum mechanical approach. The formal details of the model are explicited here for the generalized case. We prove the possibility of constructing a quantum model of the m-sentence generalizations of the Liar Paradox. This includes (i) the truth-falsehood state of the m-Liar Paradox can be represented by an embedded 2m-dimensional quantum vector in a 2m to the power m dimensional complex Hilbert space, with cognitive interactions corresponding to projections, (ii) the construction of a continuous 'time' dynamics is possible: typical truth and falsehood value oscillations are described by Schrodinger evolution, (iii) Kirchoff and von Neumann axioms are satisfied by introduction of 'truth-value by inference' projectors, (iv) time invariance of unmeasured state.- Gontier, N., Van Bendegem, J. P. and Aerts, D. (Eds.), (2006).
Evolutionary Epistemology, Language and Culture - A non adaptationist systems theoretical approach. [Theory and Decision Library Series A: Philosophy and Methodology of the Social Sciences. Series editor: Julian Nida-Ruemelin]. Dordrecht: Springer.

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1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000,