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  • 1. Accardi, Luigi
    et al.
    Khrennikov, Andrei
    Växjö universitet, Fakulteten för matematik/naturvetenskap/teknik, Matematiska och systemtekniska institutionen.
    Ohya, Masanori
    Quantum Markov Model for Data from Shafir-Tversky Experiments in Cognitive Psychology2009Inngår i: Open systems & information dynamics, ISSN 1230-1612, E-ISSN 1573-1324, Vol. 16, nr 4, s. 371-385Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We analyze, from the point of view of quantum probability, statistical data from two interesting experiments, done by Shafir and Tversky [1, 2] in the domain of cognitive psychology. These are gambling experiments of Prisoner Dilemma type. They have important consequences for economics, especially for the justification of the Savage "Sure Thing Principle" [3] (implying that agents of the market behave rationally). Data from these experiments were astonishing, both from the viewpoint of cognitive psychology and economics and probability theory. Players behaved irrationally. Moreover, all attempts to generate these data by using classical Markov model were unsuccessful. In this note we show (by inventing a simple statistical test — generalized detailed balance condition) that these data are non-Kolmogorovian. We also show that it is neither quantum (i.e., it cannot be described by Dirac-von Neumann model). We proceed towards a quantum Markov model for these data.

  • 2.
    Accardi, Luigi
    et al.
    Univ Rome Torvergata, Italy.
    Khrennikov, Andrei
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Ohya, Masanori
    Tokyo Univ Sci, Japan.
    Tanaka, Yoshiharu
    Tokyo Univ Sci, Japan.
    Yamato, Ichiro
    Tokyo Univ Sci, Japan.
    Application of Non-Kolmogorovian Probability and Quantum Adaptive Dynamics to Unconscious Inference in Visual Perception Process2016Inngår i: Open systems & information dynamics, ISSN 1230-1612, E-ISSN 1573-1324, Vol. 23, nr 2, artikkel-id 1650011Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Recently a novel quantum information formalism - quantum adaptive dynamics - was developed and applied to modelling of information processing by bio-systems including cognitive phenomena: from molecular biology (glucose-lactose metabolism for E.coli bacteria, epigenetic evolution) to cognition, psychology. From the foundational point of view quantum adaptive dynamics describes mutual adapting of the information states of two interacting systems (physical or biological) as well as adapting of co-observations performed by the systems. In this paper we apply this formalism to model unconscious inference: the process of transition from sensation to perception. The paper combines theory and experiment. Statistical data collected in an experimental study on recognition of a particular ambiguous figure, the Schroer stairs, support the viability of the quantum(-like) model of unconscious inference including modelling of biases generated by rotation-contexts. From the probabilistic point of view, we study (for concrete experimental data) the problem of contextuality of probability, its dependence on experimental contexts. Mathematically contextuality leads to non-Komogorovness: probability distributions generated by various rotation contexts cannot be treated in the Kolmogorovian framework. At the same time they can be embedded in a "big Kolmogorov space" as conditional probabilities. However, such a Kolmogorov space has too complex structure and the operational quantum formalism in the form of quantum adaptive dynamics simplifies the modelling essentially.

  • 3. Asano, Masanari
    et al.
    Ohya, Masanori
    Tanaka, Yoshiharu
    Khrennikov, Andrei
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Basieva, Irina
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    On application of Gorini-Kossakowski-Sudarshan-Lindblad equation in cognitive psychology.2011Inngår i: Open systems & information dynamics, ISSN 1230-1612, E-ISSN 1573-1324, Vol. 18, nr 1, s. 55-69Artikkel i tidsskrift (Fagfellevurdert)
  • 4.
    Khrennikov, Andrei
    Växjö universitet, Fakulteten för matematik/naturvetenskap/teknik, Matematiska och systemtekniska institutionen. Matematik.
    Algorithm for Quantum-like Representation:Transformation of Probabilistic Data into Vectors on Bloch's Sphere.2008Inngår i: Open systems & information dynamics, ISSN 1230-1612, E-ISSN 1573-1324, Vol. 15, nr 3, s. 223-230Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we present a simple algorithm for representation of statis-tical data of any origin by complex probability amplitudes. Numerical simulation withMathematica-6 is performed, cf. [1] and [2] on recent numerical simulation for quantumcorrelations. The Bloch's sphere is used for the visualization of results of numerical sim-ulation. On the one hand, creation of such a quantum-like (QL) representation and itsnumerical approval is an important step in clari¯cation of extremely complicated inter-relation between classical and quantum randomness. On the other hand, it opens newpossibilities for applying the mathematical formalism of QM in other domains of science.

  • 5.
    Khrennikov, Andrei
    Linnéuniversitetet, Fakulteten för teknik (FTK), Institutionen för matematik (MA).
    Bell Could Become the Copernicus of Probability2016Inngår i: Open systems & information dynamics, ISSN 1230-1612, E-ISSN 1573-1324, Vol. 23, nr 2, artikkel-id 1650008Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Our aim is to emphasize the role of mathematical models in physics, especially models of geometry and probability. We briefly compare developments of geometry and probability by pointing to similarities and differences: from Euclid to Lobachevsky and from Kolmogorov to Bell. In probability, Bell could play the same role as Lobachevsky in geometry. In fact, violation of Bell's inequality can be treated as implying the impossibility to apply the classical probability model of Kolmogorov (1933) to quantum phenomena. Thus the quantum probabilistic model (based on Born's rule) can be considered as the concrete example of the non-Kolmogorovian model of probability, similarly to the Lobachevskian model - the first example of the non-Euclidean model of geometry. This is the "probability model" interpretation of the violation of Bell's inequality. We also criticize the standard interpretation - an attempt to add to rigorous mathematical probability models additional elements such as (non)locality and (un)realism. Finally, we compare embeddings of non-Euclidean geometries into the Euclidean space with embeddings of the non-Kolmogorovian probabilities (in particular, quantum probability) into the Kolmogorov probability space. As an example, we consider the CHSH-test. © 2016 World Scientific Publishing Company.

  • 6.
    Khrennikov, Andrei
    Linnéuniversitetet, Fakultetsnämnden för naturvetenskap och teknik, Institutionen för datavetenskap, fysik och matematik, DFM.
    Born's Rule from Measurements of Classical Random Signals under the Assumption of Ergodicity at the Subquantum Time Scale2012Inngår i: Open systems & information dynamics, ISSN 1230-1612, E-ISSN 1573-1324, Vol. 19, nr 3, s. Article ID: 1250019-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The very old problem of the statistical content of quantum mechanics is studied in a novel framework. We show that quantum mechanics (QM) can be considered as a measurement model of prequantum classical statistical field theory (PCSFT): a pure field theory reproducing quantum correlations. We present a measurement scheme for classical signals which reproduces the basic rule of QM, the Born's rule. This is the scheme of threshold type detection. Calibration of detectors plays a crucial role. The size of the detection threshold is determined by the mean energy of a prequantum signal. QM is interpreted as theory of measurements of classical random signals with threshold type detectors which are calibrated in a proper way. The essence of this paper is the creation of a rigorous mathematical model of threshold detection of classical (ergodic) stochastic processes.

  • 7.
    Khrennikov, Andrei
    et al.
    Växjö universitet, Fakulteten för matematik/naturvetenskap/teknik, Matematiska och systemtekniska institutionen.
    Kozyrev, S.V
    Contextual quantization and the principle of complementarity of Probabilities2005Inngår i: Open systems & information dynamics, ISSN 1230-1612, E-ISSN 1573-1324, Vol. 12, nr 3, s. 303-318Artikkel i tidsskrift (Fagfellevurdert)
  • 8.
    Khrennikov, Andrei
    et al.
    Växjö universitet, Fakulteten för matematik/naturvetenskap/teknik, Matematiska och systemtekniska institutionen.
    Smolyanov, Oleg
    Truman, A
    Kolmogorov probability spaces describing Accardi models for quantum correlations2005Inngår i: Open systems & information dynamics, ISSN 1230-1612, E-ISSN 1573-1324, Vol. 12, nr 4, s. 371-384Artikkel i tidsskrift (Fagfellevurdert)
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