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  • 1. Accardi, L.
    et al.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Ohya, M.
    The problem of quantum-like representation in economy, cognitive science, and genetics2009In: Quantum Bio-Informatics II: from Quantum Information toBio-Informatics, Singapore: WSP , 2009, p. 1-8Chapter in book (Refereed)
  • 2. Accardi, Luigi
    et al.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Ohya, Masanori
    Quantum Markov Model for Data from Shafir-Tversky Experiments in Cognitive Psychology2009In: Open systems & information dynamics, ISSN 1230-1612, E-ISSN 1573-1324, Vol. 16, no 4, p. 371-385Article in journal (Refereed)
    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.

  • 3.
    Accardi, Luigi
    et al.
    Univ Rome Torvergata, Italy.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    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 Process2016In: Open systems & information dynamics, ISSN 1230-1612, E-ISSN 1573-1324, Vol. 23, no 2, article id 1650011Article in journal (Refereed)
    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.

  • 4.
    Adenier, Guillaume
    et al.
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Fair sampling and rotational invariance in EPR experiments2007In: The Nature of Light: What Are Photons?, 2007Conference paper (Other academic)
    Abstract [en]

    We have previously shown that the use of the fair sampling assumption in EPR experiments could be questioned on the basis of experimental data. We continue our analysis of the data from the optical EPR experimental performed by Weihs et al. in Innsbruck 1997-1998, and we discuss whether a non-rotationally invariant source can account for the experimental results.

  • 5.
    Adenier, Guillaume
    et al.
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Fair Sampling vs No-Signalling Principle in EPR experiments2007In: Beyond the Quantum, World Scientific Publishing, Singapore , 2007, p. 181-187Conference paper (Other (popular science, discussion, etc.))
    Abstract [en]

    We present some recent results of a new statistical analysis of the optical EPR experiment performed by Weihs et al in Innsbruck 1997-1998. Under the commonly used assumption of fair sampling, we show that the coincidence counts exhibit a small and anomalous non-signalling component, which seems impossible to explain by using the conventional quantum mechanics, and we discuss some possible interpretations of this phenomenon.

  • 6.
    Adenier, Guillaume
    et al.
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Khrennikov, AndreiVäxjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Foundations of probability and Physics - 42007Conference proceedings (editor) (Refereed)
  • 7.
    Adenier, Guillaume
    et al.
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering. Mathematics.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering. Mathematics.
    Is the fair sampling assumption supported by EPR experiments?2007In: Journal of Physics B: At. Mol. Opt. Phys., ISSN 0953-4075, Vol. 40, no 1, p. 131-141Article in journal (Refereed)
    Abstract [en]

    We analyse optical EPR experimental data performed by Weihs et al in Innsbruck 1997–1998. We show that for some linear combinations of the raw coincidence rates, the experimental results display some anomalous behaviour that a more general source state (like non-maximally entangled state) cannot straightforwardly account for. We attempt to explain these anomalies by taking account of the relative efficiencies of the four channels. For this purpose, we use the fair sampling assumption, and assume explicitly that the detection efficiencies for the pairs of entangled photons can be written as a product of the two corresponding detection efficiencies for the single photons. We show that this explicit use of fair sampling cannot be maintained to be a reasonable assumption as it leads to an apparent violation of the no-signalling principle.

  • 8.
    Adenier, Guillaume
    et al.
    INRiM, Italy.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Test of the no-signaling principle in the Hensen loophole-free CHSH experiment2017In: Fortschritte der Physik, ISSN 0015-8208, E-ISSN 1521-3978, Vol. 65, no 9, article id 1600096Article in journal (Refereed)
    Abstract [en]

    We analyze the data from the loophole-free CHSH experiment performed by Hensen et al., and show that it is actually not exempt of an important loophole. By increasing the size of the sample of event-ready detections, one can exhibit in the experimental data a violation of the no-signaling principle with a statistical significance at least similar to that of the reported violation of the CHSH inequality, if not stronger. The data from the loophole-free CHSH experiment performed by Hensen et al. are analysed, It is shown that it is actually not exempt of an important loophole. By increasing the size of the sample of event-ready detections, one can exhibit in the experimental data a violation of the no-signaling principle with a statistical significance at least similar to that of the reported violation of the CHSH inequality, if not stronger.

  • 9.
    Adenier, Guillaume
    et al.
    Tokyo University of Science, Japan.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Watabanabe, Noboru
    Tokyo University of Science, Japan.
    A Fair sampling test for Ekert protocol2011In: Quantum Bio-inforamtics IV: From Quantum Information to BioInformatics / [ed] Luigi Accardi, Wolfgang Freudenberg, Masanori Ohya, World Scientific, 2011, p. 403-412Chapter in book (Refereed)
  • 10.
    Adenier, Guillaume
    et al.
    Oslo University.
    Ohya, Masanori
    Tokyo University of Science.
    Watanabe, Noboru
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Double Blinding-Attack on Entanglement-Based Quantum Key Distribution Protocols2012In: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1424, no 1, p. 9-16Article in journal (Refereed)
    Abstract [en]

    We propose a double blinding-attack on entangled-based quantum key distribution protocols. The principle of the attack is the same as in existing blinding attack except that instead of blinding the detectors on one side only, Eve is blinding the detectors of both Alice and Bob. In the BBM92 protocol, the attack allows Eve to get a full knowledge of the key and remain undetected even if Alice and Bob are using 100% efficient detectors. The attack can be easily extended to Ekert protocol, with an efficiency as high as 85.3%.

  • 11.
    Adenier, Guillaume
    et al.
    University of Oslo, Norway.
    Watanabe, Noboru
    Tokyo University of Science, Japan.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Multiple-photon absorption attack on entanglement-based quantum key distribution protocols2013In: Quantum Bio-Informatics V: Proceedings of the Quantum Bio-Informatics 2011 : Tokyo University of Science, Japan, 7 – 12 March 2011 / [ed] Luigi Accardi, Wolfgang Freudenberg, Masanori Ohya, Singapore: World Scientific, 2013, vol. 30, p. 171-180Conference paper (Refereed)
    Abstract [en]

    We propose a multiple-photon absorption attack on Quantum Key Distribution protocols. In this attack, the eavesdropper (Eve) is in control of the source and sends pulses correlated in polarization (but not entangled) containing several photons at frequencies for which only multiple-photon absorptions are possible in Alice's and Bob's detectors. Whenever the number of photons from one pulse are dispatched in insufficient number to trigger a multiple-photon absorption in either channel, the pulse remains undetected. We show that this simple feature is enough to reproduce the type of statistics on the detected pulses that are considered as indicating a secure quantum key distribution in entangled-based protocols, even though the source is controlled by Eve, and we discuss possible countermeasures.

  • 12. Albeverio, S.
    et al.
    Cianci, R.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Operator calculus for p-adic valued symbols and quantization2009In: Rendicoti Del Seminario Matematico, ISSN 0373-1243, Vol. 67, no 2, p. 137-150Article in journal (Refereed)
    Abstract [en]

    The aim of this short review is to attract the attention of the pseudo-differentialcommunity to possibilities in the development of operator calculus for symbols (dependingon p-adic conjugate variables) taking values in fields of p-adic numbers. Essentials of thiscalculus were presented in works of the authors of this paper in order to perform p-adic valuedquantization. Unfortunately, this calculus still has not attracted a great deal of attentionfrom pure mathematicians, although it opens new and interesting domains for the theory ofpseudo-differential operators.

  • 13. Albeverio, S
    et al.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Shelkovich, M
    Nonlinear singular problems of $p$-adic analysis: associative algebras of $p$-adic distributions2005In: Izvestiya. Mathematics, ISSN 1064-5632, E-ISSN 1468-4810, Vol. 69, no 2, p. 221-263Article in journal (Refereed)
  • 14. Albeverio, S
    et al.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Shelkovich, V
    Theory of p-adic distributions: linear and nonlinear models2010Book (Refereed)
  • 15. Albeverio, S
    et al.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Shelkovich, V.M.
    p-adic Colombeau-Egorov type theory of generalized functions2005In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 278, no 1-2, p. 3-16Article in journal (Refereed)
  • 16. Albeverio, Sergio
    et al.
    Cianci, Roberto
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    p-Adic valued quantization2009In: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 1, no 2, p. 91-104Article, review/survey (Refereed)
    Abstract [en]

    This review covers an important domain of p-adic mathematical physics — quantum mechanics with p-adic valued wave functions. We start with basic mathematical constructions of this quantum model: Hilbert spaces over quadratic extensions of the field of p-adic numbers ℚ p , operators — symmetric, unitary, isometric, one-parameter groups of unitary isometric operators, the p-adic version of Schrödinger’s quantization, representation of canonical commutation relations in Heisenberg andWeyl forms, spectral properties of the operator of p-adic coordinate.We also present postulates of p-adic valued quantization. Here observables as well as probabilities take values in ℚ p . A physical interpretation of p-adic quantities is provided through approximation by rational numbers.

  • 17. Albeverio, Sergio
    et al.
    Gundlach, Mathias
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Lindahl, Karl-Olof
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    On the Markovian Behavior of p-Adic Random Dynamical Systems2001In: Russ. J. Math. Phys., Vol. 8, no 2, p. 135-152Article in journal (Refereed)
  • 18. Albeverioa, S.
    et al.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Shelkovichg,, V.M.
    The Cauchy problems for evolutionary pseudo-differential equations over p-adic field and the wavelet theory2011In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 375, no 1, p. 82-98Article in journal (Refereed)
  • 19. Allahverdyan, A
    et al.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Nieuwenhuizen, Th. M
    Brownian entanglement2005In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 72, p. 032102-Article in journal (Refereed)
  • 20. Anashin,, V
    et al.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Yurova, Ekaterina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Using van der Put basis to determine if a 2-adic function is measure-preserving or ergodic w.r.t. Haar measure2011In: Advances in Non-Archimedean Analysis: 11th International Conference p-adic Funcional Analysis, July 5-9, 2010, Université Blaise Pascal, Clemont-Ferrand, France / [ed] Jesus Araujo-Gomez, Bertin Diarra and Alain Escassut, American Mathematical Society (AMS), 2011, Vol. 551, p. 33-38Chapter in book (Refereed)
  • 21.
    Anashin, V. S.
    et al.
    Moscow State University, Russia.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Yurova, Ekaterina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Characterization of ergodicity of p-adic dynamical systems by using the van der Put basis.2011In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 83, no 3, p. 306-308Article in journal (Refereed)
  • 22.
    Anashin, V. S.
    et al.
    Moscow State Univeristy.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Yurova, Ekaterina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Ergodicity of dynamical systems on 2-adic spheres2012In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 86, no 3, p. 843-845Article in journal (Refereed)
  • 23.
    Anashin, Vladimir
    et al.
    Russian State University.
    Khrennikov, Andrei
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    Applied algebraic dynamics2009Book (Refereed)
  • 24.
    Anashin, Vladimir
    et al.
    Moscow MV Lomonosov State Univ, Fac Computat Math & Cybernet, Moscow 119991, Russia.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Yurova, Ekaterina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ergodicity criteria for non-expanding transformations of 2-adic spheres2014In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 34, no 2, p. 367-377Article in journal (Refereed)
    Abstract [en]

    In the paper, we obtain necessary and sufficient conditions for ergodicity (with respect to the normalized Haar measure) of discrete dynamical systems < f; S2-r (a)> on 2-adic spheres S2-r (a) of radius 2(-r), r >= 1, centered at some point a from the ultrametric space of 2-adic integers Z(2). The map f: Z(2) -> Z(2) is assumed to be non-expanding and measure-preserving; that is, f satisfies a Lipschitz condition with a constant 1 with respect to the 2-adic metric, and f preserves a natural probability measure on Z(2), the Haar measure mu(2) on Z(2) which is normalized so that mu(2)(Z(2)) = 1.

  • 25.
    Anashin, Vladimir
    et al.
    Lomonosov Moscow State University.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Yurova, Ekaterina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    T-functions revisited: new criteria for bijectivity/transitivity2014In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 71, no 3, p. 383-407Article in journal (Refereed)
    Abstract [en]

    The paper presents new criteria for bijectivity/transitivity of T-functions and a fast knapsack-like algorithm of evaluation of a T-function. Our approach is based on non-Archimedean ergodic theory: Both the criteria and algorithm use van der Put series to represent 1-Lipschitz p-adic functions and to study measure-preservation/ergodicity of these.

  • 26.
    Aref’eva, I. Ya.
    et al.
    Russian Academy of Sciences, Russia.
    Djordjevic, G. S.
    Niš, Serbia.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Kozyrev, S. V.
    Russian Academy of Sciences, Russia.
    Rakic, Z.
    University of Belgrade, Serbia.
    Volovich, I. V.
    Russian Academy of Sciences, Russia.
    p-Adic mathematical physics and B. Dragovich research2017In: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 9, no 1, p. 82-85Article in journal (Refereed)
    Abstract [en]

    We present a brief review of some parts of p-adic mathematical physics related to the scientific work of Branko Dragovich on the occasion of his 70th birthday.

  • 27.
    Asano, M
    et al.
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, M
    Tokyo University of Science.
    Tanaka, Y
    Tokyo University of Science.
    Quantum-Like Representation of Non-Bayesian Inference2013In: Quantum Bio-Informatics V - Proceedings of the Quantum Bio-Informatics 2011: Tokyo University of Science, Japan, 7 – 12 March 2011 / [ed] Luigi Accardi, Wolfgang Freudenberg, Masanori Ohya, World Scientific, 2013, p. 57-67Conference paper (Refereed)
    Abstract [en]

    This research is related to the problem of “irrational decision making or inference” that have been discussed in cognitive psychology. There are some experimental studies, and these statistical data cannot be described by classical probability theory. The process of decision making generating these data cannot be reduced to the classical Bayesian inference. For this problem, a number of quantum-like coginitive models of decision making was proposed. Our previous work represented in a natural way the classical Bayesian inference in the frame work of quantum mechanics. By using this representation, in this paper, we try to discuss the non-Bayesian (irrational) inference that is biased by effects like the quantum interference. Further, we describe “psychological factor” disturbing “rationality” as an “environment” correlating with the “main system” of usual Bayesian inference.

  • 28.
    Asano, M
    et al.
    Tokyo University of Science.
    Ohya, M
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    General Formalism of Decision Making Based on Theory of Open Quantum Systems2013In: Quantum Bio-Informatics V - Proceedings of the Quantum Bio-Informatics 2011: Tokyo University of Science, Japan, 7 – 12 March 2011 / [ed] Luigi Accardi, Wolfgang Freudenberg, and Masanori Ohya, World Scientific, 2013, p. 49-56Conference paper (Refereed)
    Abstract [en]

    We present the general formalism of decision making which is based on the theory of open quantum systems. A person (decision maker), say Alice, is considered as a quantum-like system, i.e., a system which information processing follows the laws of quantum information theory. To make decision, Alice interacts with a huge mental bath. Depending on context of decision making this bath can include her social environment, mass media (TV, newspapers, INTERNET), and memory. Dynamics of an ensemble of such Alices is described by Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. We speculate that in the processes of evolution biosystems (especially human beings) designed such “mental Hamiltonians” and GKSL-operators that any solution of the corresponding GKSL-equation stabilizes to a diagonal density operator (In the basis of decision making.) This limiting density operator describes population in which all superpositions of possible decisions has already been resolved. In principle, this approach can be used for the prediction of the distribution of possible decisions in human populations.

  • 29. Asano, M
    et al.
    Ohya, M
    Tanaka, Y
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Quantum uncertainty and decision-making in game theory2011In: Quantum Bioinformatics-4 / [ed] Luigi Accardi , Wolfgang Freudenberg,, Masanori Ohya, World Scientific, 2011, p. 51-60Chapter in book (Refereed)
  • 30. Asano, M
    et al.
    Ohya, M
    Tanaka, Y
    Yamato, I
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Quantum-like paradigm from molecular biology to cognitive psychology.2011In: Quantum Interaction, Springer, 2011, p. 182-191Chapter in book (Refereed)
  • 31.
    Asano, Masanari
    et al.
    Tokuyama Coll, Japan.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tokyo Univ Sci, Japan.
    Tanaka, Yoshiharu
    Tokyo Univ Sci, Japan.
    A quantum-like model of selection behavior2017In: Journal of mathematical psychology (Print), ISSN 0022-2496, E-ISSN 1096-0880, Vol. 78, p. 2-12Article in journal (Refereed)
    Abstract [en]

    In this paper, we introduce a new model of selection behavior under risk that describes an essential cognitive process for comparing values of objects and making a selection decision. This model is constructed by the quantum-like approach that employs the state representation specific to quantum theory, which has the mathematical framework beyond the classical probability theory. We show that our quantum approach can clearly explain the famous examples of anomalies for the expected utility theory, the Ellsberg paradox, the Machina paradox and the disparity between WTA and WTP. Further, we point out that our model mathematically specifies the characteristics of the probability weighting function and the value function, which are basic concepts in the prospect theory. (C) 2016 Elsevier Inc. All rights reserved.

  • 32.
    Asano, Masanari
    et al.
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Ohya, Masanori
    Tokyo University of Science.
    Tanaka, Yoshiharu
    Tokyo University of Science.
    Quantum-like dynamics of decision-making2012In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 391, no 5, p. 2083-2099Article in journal (Refereed)
    Abstract [en]

    In cognitive psychology, some experiments for games were reported, and they demonstrated that real players did not use the "rational strategy" provided by classical game theory and based on the notion of the Nasch equilibrium. This psychological phenomenon was called the disjunction effect. Recently, we proposed a model of decision making which can explain this effect ("irrationality" of players) Asano et al. (2010, 2011) [23,24]. Our model is based on the mathematical formalism of quantum mechanics, because psychological fluctuations inducing the irrationality are formally represented as quantum fluctuations Asano et al. (2011)[55]. In this paper, we reconsider the process of quantum-like decision-making more closely and redefine it as a well-defined quantum dynamics by using the concept of lifting channel, which is an important concept in quantum information theory. We also present numerical simulation for this quantum-like mental dynamics. It is non-Markovian by its nature. Stabilization to the steady state solution (determining subjective probabilities for decision making) is based on the collective effect of mental fluctuations collected in the working memory of a decision maker. (C) 2011 Elsevier B.V. All rights reserved.

  • 33.
    Asano, Masanari
    et al.
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Ohya, Masanori
    Tokyo University of Science.
    Tanaka, Yoshiharu
    Tokyo University of Science.
    Quantum-like Dynamics of Decision-making in Prisoner's Dilemma Game2012In: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1424, p. 453-457Article in journal (Refereed)
    Abstract [en]

    In cognitive psychology, some experiments of games were reported [1, 2, 3, 4], and these demonstrated that real players did not use the "rational strategy" provided by classical game theory. To discuss probabilities of such "irrational choice", recently, we proposed a decision-making model which is based on the formalism of quantum mechanics [5, 6, 7, 8]. In this paper, we briefly explain the above model and calculate the probability of irrational choice in several prisoner's dilemma (PD) games.

  • 34.
    Asano, Masanari
    et al.
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tokyo University of Science.
    Tanaka, Yoshiharu
    Tokyo University of Science.
    Yamato, I.
    Tokyo University of Science.
    Lamarckian Evolution of Epigenome from Open Quantum Systems and Entanglement2014In: Quantum Interaction: 7th International Conference, QI 2013, Leicester, UK, July 25-27, 2013. Selected Papers / [ed] Harald Atmanspacher, Emmanuel Haven, Kirsty Kitto, Derek Raine, Springer, 2014, p. 324-334Conference paper (Refereed)
    Abstract [en]

    We develop a quantum-like (QL) model of cellular evolution based on the theory of open quantum systems and entanglement between epigenetic markers in a cell. This approach is applied to modeling of epigenetic evolution of cellular populations. We point out that recently experimental genetics discovered numerous phenomena of cellular evolution adaptive to the pressure of the environment. In such phenomena epigenetic changes are fixed in one generation and, hence, the Darwinian natural selection model cannot be applied. A number of prominent genetists stress the Lamarckian character of epigenetic evolution. In quantum physics the dynamics of the state of a system (e.g. electron) contacting with an environment (bath) is described by the theory of open quantum systems. Therefore it is natural to apply this theory to model adaptive changes in the epigenome. Since evolution of the Lamarckian type is very rapid – changes in the epigenome have to be inherited in one generation – we have to find a proper mathematical description of such a speed up. In our model this is the entanglement of different epigenetic markers.

  • 35.
    Asano, Masanari
    et al.
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tokyo University of Science.
    Tanaka, Yoshiharu
    Tokyo University of Science.
    Yamato, Ichiro
    Tokyo University of Science.
    A model of epigenetic evolution based on theory of open quantum systems2013In: Systems and Synthetic Biology, ISSN 1872-5325, Vol. 7, no 4, p. 161-173Article in journal (Refereed)
    Abstract [en]

    We present a very general model of epigenetic evolution unifying (neo-)Darwinian and (neo-)Lamarckian viewpoints. The evolution is represented in the form of adaptive dynamics given by the quantum(-like) master equation. This equation describes development of the information state of epigenome under the pressure of an environment. We use the formalism of quantum mechanics in the purely operational framework. (Hence, our model has no direct relation to quantum physical processes inside a cell.) Thus our model is about probabilities for observations which can be done on epigenomes and it does not provide a detailed description of cellular processes. Usage of the operational approach provides a possibility to describe by one model all known types of cellular epigenetic inheritance.

  • 36. Asano, Masanari
    et al.
    Basieva, Irina
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tanaka, Yoshiharu
    Yamato, Ichiro
    Quantum Information Biology2016In: Contextuality from Quantum Physics to Psychology / [ed] Ehtibar Dzhafarov, Scott Jordan, Ru Zhang, Victor Cervantes, World Scientific, 2016, p. 399-413Chapter in book (Refereed)
  • 37.
    Asano, Masanari
    et al.
    Tokuyama Coll Technol, Japan.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tokyo Univ Sci, Japan.
    Tanaka, Yoshiharu
    Tokyo Univ Sci, Japan.
    Yamato, Ichiro
    Tokyo Univ Sci, Japan.
    Quantum Information Biology: From Information Interpretation of Quantum Mechanics to Applications in Molecular Biology and Cognitive Psychology2015In: Foundations of physics, ISSN 0015-9018, E-ISSN 1572-9516, Vol. 45, no 10, p. 1362-1378Article in journal (Refereed)
    Abstract [en]

    We discuss foundational issues of quantum information biology (QIB)-one of the most successful applications of the quantum formalism outside of physics. QIB provides a multi-scale model of information processing in bio-systems: from proteins and cells to cognitive and social systems. This theory has to be sharply distinguished from "traditional quantum biophysics". The latter is about quantum bio-physical processes, e.g., in cells or brains. QIB models the dynamics of information states of bio-systems. We argue that the information interpretation of quantum mechanics (its various forms were elaborated by Zeilinger and Brukner, Fuchs and Mermin, and D' Ariano) is the most natural interpretation of QIB. Biologically QIB is based on two principles: (a) adaptivity; (b) openness (bio-systems are fundamentally open). These principles are mathematically represented in the framework of a novel formalism- quantum adaptive dynamics which, in particular, contains the standard theory of open quantum systems.

  • 38.
    Asano, Masanari
    et al.
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Ohya, Masanori
    Tokyo University of Science.
    Tanaka, Yoshiharu
    Tokyo University of Science.
    Yamato, Ichiro
    Tokyo University of Science.
    Quantum-like model of diauxie in Escherichia coli: operational description of precultivation effect2012In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 314, p. 130-137Article in journal (Refereed)
    Abstract [en]

    In this paper we apply the quantum-like (QL) approach to microbiology to present an operational description of the complex process of diauxie in Escherichia coil. We take as guaranteed that dynamics in cells is adaptive, i.e., it depends crucially on the microbiological context. This very general assumption is sufficient to appeal to quantum and more general QL probabilistic models. The next step is to find the operational representation - by operators in complex Hilbert space (as in quantum physics). To determine QL operators, we used the statistical data from Inada et al. (1996). To improve the QL-representation, we needed better experimental data. Corresponding experiments were recently done by two of the authors and in this paper we use these new data. In these data we found that biochemical context of precultivation of populations of E. coli plays a crucial role in E. coli preferences with respect to sugars. Hence, the form of the QL operator representing lactose operon activation also depends crucially on precultivation. One of our results is decomposition of the lactose operon activation operator to extract the factor determined by precultivation. The QL operational approach developed in this paper can be used not only for description of the process of diauxie in E. coli, but also other processes of gene expression. However, new experimental statistical data are demanded. (C) 2012 Elsevier Ltd. All rights reserved.

  • 39.
    Asano, Masanari
    et al.
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Ohya, Masanori
    Tokyo University of Science.
    Tanaka, Yoshiharu
    Tokyo University of Science.
    Yamato, Ichiro
    Tokyo University of Science.
    Quantum-like model of glucose effect on Escherichia coli growth2012In: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1424, p. 507-512Article in journal (Refereed)
    Abstract [en]

    Recently, we proposed a new method to compute probabilities which do not satisfy basic law in classical probability theory. In this note, we analyze glucose effect in Escherichia coli's growth with the method, and we show an invariant quantity which Escherichia coli has.

  • 40.
    Asano, Masanari
    et al.
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tokyo University of Science.
    Yamato, Ichiro
    Tokyo University of Science.
    Non-Kolmogorovian approach to the context-dependent systems breaking the classical probability law.2013In: Foundations of physics, ISSN 0015-9018, E-ISSN 1572-9516, Vol. 43, no 7, p. 895-911Article in journal (Refereed)
    Abstract [en]

    There exist several phenomena breaking the classical probability laws. The systems related to such phenomena are context-dependent, so that they are adaptive to other systems. In this paper, we present a new mathematical formalism to compute the joint probability distribution for two event-systems by using concepts of the adaptive dynamics and quantum information theory, e.g., quantum channels and liftings. In physics the basic example of the context-dependent phenomena is the famous double-slit experiment. Recently similar examples have been found in biological and psychological sciences. Our approach is an extension of traditional quantum probability theory, and it is general enough to describe aforementioned contextual phenomena outside of quantum physics.

  • 41.
    Asano, Masanari
    et al.
    Tokyo University of Science .
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Ohyna, Masanori
    Tokyo University of Science.
    Tanaka, Yoshiharu
    Tokyo University of Science.
    Yamato, Ichiro
    Tokyo University of Science.
    Towards Modeling of Epigenetic Evolution with the Aid of Theory of Open Quantum Systems2012In: Quantum Theory: Reconsideration of Fundations 6 / [ed] Khrennikov, A; Atmanspacher, H; Migdall, A; Polyakov, S, American Institute of Physics (AIP), 2012, volume 1508, p. 75-78Conference paper (Refereed)
    Abstract [en]

    We apply theory of open quantum systems to modeling of epigenetic evolution. This is an attempt to unify Darwinian and Lamarckian viewpoints on evolution on the basis of a quantum-like model. The state of uncertainty of cell's epigenome is resolved to a stable and inherited epigenetic configuration. This process of evolution and stabilization is described by the quantum master equation (the Gorini-Kossakowski-Sudarshan-Lindblad equation). The initial state of epigenome starting interaction with a new environment is represented as a pure quantum state. It evolves to a steady state solution of the quantum master equation given by a diagonal density matrix. The latter represents the state resulting from a series of epimutations induced by the environment. We use the information interpretation of the wave function which was elaborated by C. Fuchs and A. Zeilinger.

  • 42.
    Asano, Masanari
    et al.
    Natl Inst Technol, Japan.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics. Natl Res Univ Informat Technol Mech & Opt ITMO, Russia.
    Yamato, Ichiro
    Tokyo Univ Sci, Japan.
    A model of differentiation in quantum bioinformatics2017In: Progress in Biophysics and Molecular Biology, ISSN 0079-6107, E-ISSN 1873-1732, Vol. 130, p. 88-98Article, review/survey (Refereed)
    Abstract [en]

    Differentiation is a universal process found in various phenomena of nature. As seen in the example of cell differentiation, the creation diversity on individual's character is caused by environmental interactions. In this paper, we try to explain its mechanism, which has been discussed mainly in Biology, by using the formalism of quantum physics. Our approach known as quantum bioinformatics shows that the temporal change of statistical state called decoherence fits to describe non-local phenomena like differentiation. (C) 2017 Elsevier Ltd. All rights reserved.

  • 43.
    Asano, Masanari
    et al.
    Tokuyama College of Technology Gakuendai, Japan.
    Hashimoto, Takahisa
    Tokuyama College of Technology Gakuendai, Japan.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tokuyama College of Technology Gakuendai, Japan.
    Tanaka, Yoshiharu
    Tokuyama College of Technology Gakuendai, Japan.
    Adaptive Dynamics and Optical Illusion on Schröder’s Stair2014In: Quantum Interaction: 7th International Conference, QI 2013, Leicester, UK, July 25-27, 2013. Selected Papers / [ed] Harald Atmanspacher, Emmanuel Haven, Kirsty Kitto, Derek Raine, Springer, 2014, p. 191-200Conference paper (Refereed)
    Abstract [en]

    Recently, various examples of non-Kolmogorovness in contextual dependent phenomena have been reported. In this study, we introduce non-Kolmogorovness in the measurement of depth inversion for the figure of Schröder’s stair. Also we propose a model of the depth inversion, based on a non-Kolmogorovian probability theory which is called adaptive dynamics.

  • 44.
    Asano, Masanari
    et al.
    Tokuyama Coll Technol, Japan.
    Hashimoto, Takahisa
    Tokyo Univ Sci, Japan.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tokyo Univ Sci, Japan.
    Tanaka, Yoshiharu
    Tokyo Univ Sci, Japan.
    Violation of contextual generalization of the Leggett-Garg inequality for recognition of ambiguous figures2014In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. T163, article id 014006Article in journal (Refereed)
    Abstract [en]

    We interpret the Leggett-Garg (LG) inequality as a kind of contextual probabilistic inequality in which one combines data collected in experiments performed for three different contexts. In the original version of the inequality, these contexts have a temporal nature and they are represented by three pairs of instances of time, (t(1), t(2)), (t(2), t(3)), (t(3), t(4)), where t(1) < t(2) < t(3). We generalize LG conditions of macroscopic realism and noninvasive measurability in a general contextual framework. Our formulation is performed in purely probabilistic terms: the existence of the context-independent joint probability distribution P and the possibility of reconstructing the experimentally found marginal (two-dimensional) probability distributions from P. We derive an analog of the LG inequality, 'contextual LG inequality', and use it as a test of 'quantum-likeness' of statistical data collected in a series of experiments on the recognition of ambiguous figures. In our experimental study, the figure under recognition is the Schroder stair, which is shown with rotations for different angles. Contexts are encoded by dynamics of rotations: clockwise, anticlockwise and random. Our data demonstrated violation of the contextual LG inequality for some combinations of the aforementioned contexts. Since in quantum theory and experiments with quantum physical systems, this inequality is violated, e.g. in the form of the original LG-inequality, our result can be interpreted as a sign that the quantum-like models can provide a more adequate description of the data generated in the process of recognition of ambiguous figures.

  • 45. Asano, Masanari
    et al.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tanaka, Yoshiharu
    Yamato, Ichiro
    Quantum adaptivity in biology: From genetics to cognition2015Book (Refereed)
  • 46.
    Asano, Masanari
    et al.
    Tokuyama College of Technology, Japan.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tokyo University of Science, Japan.
    Tanaka, Yoshiharu
    Tokyo University of Science, Japan.
    Yamato, Ichiro
    Tokyo University of Science, Japan.
    Three-body system metaphor for the two-slit experiment and Escherichia coli lactose-glucose metabolism2016In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 374, no 2068, article id 20150243Article in journal (Refereed)
    Abstract [en]

    We compare the contextual probabilistic structures of the seminal two-slit experiment (quantum interference experiment), the system of three interacting bodies and Escherichia coli lactose-glucose metabolism. We show that they have the same non-Kolmogorov probabilistic structure resulting from multi-contextuality. There are plenty of statistical data with non-Kolmogorov features; in particular, the probabilistic behaviour of neither quantum nor biological systems can be described classically. Biological systems (even cells and proteins) are macroscopic systems and one may try to present a more detailed model of interactions in such systems that lead to quantum-like probabilistic behaviour. The system of interactions between three bodies is one of the simplest metaphoric examples for such interactions. By proceeding further in this way (by playing with n-body systems) we shall be able to find metaphoric mechanical models for complex bio-interactions, e.g. signalling between cells, leading to non-Kolmogorov probabilistic data.

  • 47. Asano, Masanari
    et al.
    Masanori, Ohya
    Tanaka, Yoshiharu
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Quantum-like model of brain's functioning: Decision making from decoherence2011In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 281, no 1, p. 56-64Article in journal (Refereed)
  • 48. Asano, Masanari
    et al.
    Ohya, Masanori
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Quantum-Like Model for Decision Making Process inTwo Players Game: A Non-Kolmogorovian Model2011In: Foundations of physics, ISSN 0015-9018, E-ISSN 1572-9516, Vol. 41, no 3, p. 538-548Article in journal (Refereed)
  • 49. Asano, Masanari
    et al.
    Ohya, Masanori
    Tanaka, Yoshiharu
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    On application of Gorini-Kossakowski-Sudarshan-Lindblad equation in cognitive psychology.2011In: Open systems & information dynamics, ISSN 1230-1612, E-ISSN 1573-1324, Vol. 18, no 1, p. 55-69Article in journal (Refereed)
  • 50. Asano, Masanori
    et al.
    Ohya, Masanori
    Tanaka, Yoshiharu
    Yamato, Ichiro
    Basieva, Irina
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    A Mathematical Treatment of Joint and Conditional Probability2013In: Quantum Bio-Informatics V - Proceedings of the Quantum Bio-Informatics 2011: Tokyo University of Science, Japan, 7 – 12 March 2011 / [ed] Accardi Luigi et al., World Scientific, 2013, p. 69-84Conference paper (Refereed)
1234567 1 - 50 of 407
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