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Khrennikov, A. & Asano, M. (2020). A Quantum-Like Model of Information Processing in the Brain. Applied Sciences, 10(2), 1-14, Article ID 707.
Open this publication in new window or tab >>A Quantum-Like Model of Information Processing in the Brain
2020 (English)In: Applied Sciences, E-ISSN 2076-3417, Vol. 10, no 2, p. 1-14, article id 707Article in journal (Refereed) Published
Abstract [en]

We present the quantum-like model of information processing by the brain's neural networks. The model does not refer to genuine quantum processes in the brain. In this model, uncertainty generated by the action potential of a neuron is represented as quantum-like superposition of the basic mental states corresponding to a neural code. Neuron's state space is described as complex Hilbert space (quantum information representation). The brain's psychological functions perform self-measurements by extracting concrete answers to questions (solutions of problems) from quantum information states. This extraction is modeled in the framework of open quantum systems theory. In this way, it is possible to proceed without appealing to the state's collapse. Dynamics of the state of psychological function F is described by the quantum master equation. Its stationary states represent classical statistical mixtures of possible outputs of F (decisions). This model can be used for justification of quantum-like modeling cognition and decision-making. The latter is supported by plenty of statistical data collected in cognitive psychology.

Place, publisher, year, edition, pages
MDPI, 2020
Keywords
brain, information processing, quantum-like model, action potential, uncertainty, quantum information state, neural code, neuron firing, frequency, open quantum systems, quantum master equation, differentiation
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-94821 (URN)10.3390/app10020707 (DOI)000522540400283 ()
Available from: 2020-05-18 Created: 2020-05-18 Last updated: 2020-05-18Bibliographically approved
Iurato, G. & Khrennikov, A. (2020). A Reader's Comment on: "Hysteresis Model of Unconscious-Conscious Interconnection: Exploring Dynamics on m-Adic Trees". P-Adic Numbers, Ultrametric Analysis, and Applications, 12(1), 68-71
Open this publication in new window or tab >>A Reader's Comment on: "Hysteresis Model of Unconscious-Conscious Interconnection: Exploring Dynamics on m-Adic Trees"
2020 (English)In: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 12, no 1, p. 68-71Article in journal, Editorial material (Other academic) Published
Abstract [en]

This comment is aimed to point out that the recent work due to H. Kim, J-Y. Moon, G. A. Mashour and U. Lee ([22]), in which the clinical and experiential assessment of a brain network model suggests that asymmetry of synchronization suppression is the key mechanism of hysteresis observed during loss and recovery of consciousness in general anesthesia, has indirectly provided empirical confirmation of the theoretical model outlined in [8] (Iurato and Khrennikov, 2015), based on a possible implementation of an hysteretic pattern into a formal model of unconscious-conscious interconnection worked out on the basis of representations of mental entities by p-adic numbers. One of the main assumptions done by the authors of [22], is that (physical) hysteresis (of their brain network model took into account) observed during anesthetic state transitions shares the same underlying mechanism as that observed in non-biological networks. This makes licit to put into comparative relations [8] and [22].

Place, publisher, year, edition, pages
Pleiades Publishing Inc, 2020
Keywords
hysteresis model, unconscious-conscious, m-adic tree
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-93692 (URN)10.1134/S2070046620010070 (DOI)000519374300007 ()
Available from: 2020-04-23 Created: 2020-04-23 Last updated: 2020-04-23Bibliographically approved
Ozawa, M. & Khrennikov, A. (2020). Application of Theory of Quantum Instruments to Psychology: Combination of Question Order Effect with Response Replicability Effect. Entropy, 22(1), 1-14, Article ID 37.
Open this publication in new window or tab >>Application of Theory of Quantum Instruments to Psychology: Combination of Question Order Effect with Response Replicability Effect
2020 (English)In: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 22, no 1, p. 1-14, article id 37Article in journal (Refereed) Published
Abstract [en]

Recently, quantum formalism started to be actively used outside of quantum physics: in psychology, decision-making, economics, finances, and social science. Human psychological behavior is characterized by a few basic effects; one of them is the question order effect (QOE). This effect was successfully modeled (Busemeyer-Wang) by representing questions A and B by Hermitian observables and mental-state transformations (back action of answering) by orthogonal projectors. However, then it was demonstrated that such representation cannot be combined with another psychological effect, known as the response replicability effect (RRE). Later, this no-go result was generalized to representation of questions and state transformations by quantum instruments of the atomic type. In light of these results, the possibility of using quantum formalism in psychology was questioned. In this paper, we show that, nevertheless, the combination of the QOE and RRE can be modeled within quantum formalism, in the framework of theory of non-atomic quantum instruments.

Place, publisher, year, edition, pages
MDPI, 2020
Keywords
quantum-like models, psychology, decision making, social science, quantum instruments, order effect, response replicability effect, non-atomic quantum instruments
National Category
Mathematics Psychology
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-93690 (URN)10.3390/e22010037 (DOI)000516825400069 ()
Available from: 2020-04-23 Created: 2020-04-23 Last updated: 2020-04-23Bibliographically approved
Iurato, G. & Khrennikov, A. (2020). Entropy, externality and human evolution. Biosystems (Amsterdam. Print), 191, 1-8, Article ID 104130.
Open this publication in new window or tab >>Entropy, externality and human evolution
2020 (English)In: Biosystems (Amsterdam. Print), ISSN 0303-2647, E-ISSN 1872-8324, Vol. 191, p. 1-8, article id 104130Article in journal (Refereed) Published
Abstract [en]

Considering biosphere as a closed thermodynamical system, inside it, biological organisms may be considered as open thermodynamical systems exchanging energy and matter with ecosystem. Making appeal to non-equilibrium thermodynamics, anthropology, biology, sociology and cliodynamics, we discuss, from an interdisciplinary stance, some main moments of human evolution from either the phylogenetic and the ontogenetic standpoint, highlighting the crucial bifurcation which saw the rising of the modern societies with respect to primitive ones.

Place, publisher, year, edition, pages
Elsevier, 2020
Keywords
Entropy, Biology, Time, Externality, Anthropology, Sociology, Knowledge, Human evolution, Society, Neuroendocrinology
National Category
Evolutionary Biology Sociology
Research subject
Ecology, Evolutionary Biology; Social Sciences, Sociology
Identifiers
urn:nbn:se:lnu:diva-94790 (URN)10.1016/j.biosystems.2020.104130 (DOI)000527332300007 ()32173336 (PubMedID)
Available from: 2020-05-18 Created: 2020-05-18 Last updated: 2020-05-18Bibliographically approved
Antoniouk, A. V., Khrennikov, A. & Kochubei, A. N. (2020). Multidimensional nonlinear pseudo-differential evolution equation with p-adic spatial variables. Journal of Pseudo-Differential Operators and Applications, 11(1), 311-343
Open this publication in new window or tab >>Multidimensional nonlinear pseudo-differential evolution equation with p-adic spatial variables
2020 (English)In: Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, E-ISSN 1662-999X, Vol. 11, no 1, p. 311-343Article in journal (Refereed) Published
Abstract [en]

We study the Cauchy problem for p-adic non-linear evolutionary pseudo-differential equations for complex-valued functions of a real positive time variable and p-adic spatial variables. Among the equations under consideration there is the p-adic analog of the porous medium equation (or more generally, the nonlinear filtration equation) which arise in numerous application in mathematical physics and mathematical biology. Our approach is based on the construction of a linear Markov semigroup on a p-adic ball and the proof of m-accretivity of the appropriate nonlinear operator. The latter result is equivalent to the existence and uniqueness of a mild solution of the Cauchy problem of a nonlinear equation of the porous medium type.

Place, publisher, year, edition, pages
Springer, 2020
Keywords
p-adic numbers, Porous medium equation, Markov process, m-accretive operator
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-94041 (URN)10.1007/s11868-019-00320-3 (DOI)000522490100013 ()
Available from: 2020-04-28 Created: 2020-04-28 Last updated: 2020-04-28Bibliographically approved
Khrennikov, A. (2020). Two Faced Janus of Quantum Nonlocality. Entropy, 22(3), 1-17, Article ID 303.
Open this publication in new window or tab >>Two Faced Janus of Quantum Nonlocality
2020 (English)In: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 22, no 3, p. 1-17, article id 303Article in journal (Refereed) Published
Abstract [en]

This paper is a new step towards understanding why "quantum nonlocality" is a misleading concept. Metaphorically speaking, "quantum nonlocality" is Janus faced. One face is an apparent nonlocality of the Luders projection and another face is Bell nonlocality (a wrong conclusion that the violation of Bell type inequalities implies the existence of mysterious instantaneous influences between distant physical systems). According to the Luders projection postulate, a quantum measurement performed on one of the two distant entangled physical systems modifies their compound quantum state instantaneously. Therefore, if the quantum state is considered to be an attribute of the individual physical system and if one assumes that experimental outcomes are produced in a perfectly random way, one quickly arrives at the contradiction. It is a primary source of speculations about a spooky action at a distance. Bell nonlocality as defined above was explained and rejected by several authors; thus, we concentrate in this paper on the apparent nonlocality of the Luders projection. As already pointed out by Einstein, the quantum paradoxes disappear if one adopts the purely statistical interpretation of quantum mechanics (QM). In the statistical interpretation of QM, if probabilities are considered to be objective properties of random experiments we show that the Luders projection corresponds to the passage from joint probabilities describing all set of data to some marginal conditional probabilities describing some particular subsets of data. If one adopts a subjective interpretation of probabilities, such as Qbism, then the Luders projection corresponds to standard Bayesian updating of the probabilities. The latter represents degrees of beliefs of local agents about outcomes of individual measurements which are placed or which will be placed at distant locations. In both approaches, probability-transformation does not happen in the physical space, but only in the information space. Thus, all speculations about spooky interactions or spooky predictions at a distance are simply misleading. Coming back to Bell nonlocality, we recall that in a recent paper we demonstrated, using exclusively the quantum formalism, that CHSH inequalities may be violated for some quantum states only because of the incompatibility of quantum observables and Bohr's complementarity. Finally, we explain that our criticism of quantum nonlocality is in the spirit of Hertz-Boltzmann methodology of scientific theories.

Place, publisher, year, edition, pages
MDPI, 2020
Keywords
quantum nonlocality, Bell nonlocality, Einstein-Luders nonlocality, projection postulate, state-transformation, probability conditioning, individual vs, statistical interpretations, quantum vs, classical superpositions, ontic-epistemic, spooky action vs, prediction at a distance
National Category
Physical Sciences Mathematics
Research subject
Natural Science, Physics; Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-94801 (URN)10.3390/e22030303 (DOI)000526524300050 ()
Available from: 2020-05-18 Created: 2020-05-18 Last updated: 2020-05-18Bibliographically approved
Atmanspacher, H., Basieva, I., Busemeyer, J. R., Khrennikov, A., Pothos, E. M., Shiffrin, R. M. & Wang, Z. (2020). What are the appropriate axioms of rationality for reasoning under uncertainty with resource-constrained systems?. Behavioral and Brain Sciences, 43, Article ID e2.
Open this publication in new window or tab >>What are the appropriate axioms of rationality for reasoning under uncertainty with resource-constrained systems?
Show others...
2020 (English)In: Behavioral and Brain Sciences, ISSN 0140-525X, E-ISSN 1469-1825, Vol. 43, article id e2Article in journal, Editorial material (Other academic) Published
Abstract [en]

When constrained by limited resources, how do we choose axioms of rationality? The target article relies on Bayesian reasoning that encounter serious tractability problems. We propose another axiomatic foundation: quantum probability theory, which provides for less complex and more comprehensive descriptions. More generally, defining rationality in terms of axiomatic systems misses a key issue: rationality must be defined by humans facing vague information.

Place, publisher, year, edition, pages
Cambridge University Press, 2020
National Category
Mathematics Psychology
Research subject
Mathematics, Applied Mathematics; Social Sciences, Psychology
Identifiers
urn:nbn:se:lnu:diva-94090 (URN)10.1017/S0140525X19001535 (DOI)000525619100002 ()32159476 (PubMedID)
Available from: 2020-05-05 Created: 2020-05-05 Last updated: 2020-05-05Bibliographically approved
Khrennikov, A. (2019). Basics of Quantum Theory for Quantum-Like Modeling Information Retrieval. In: Diederik Aerts, Andrei Khrennikov, Massimo Melucci, Bourama Toni (Ed.), Quantum-Like Models for Information Retrieval and Decision-Making: (pp. 51-82). Springer
Open this publication in new window or tab >>Basics of Quantum Theory for Quantum-Like Modeling Information Retrieval
2019 (English)In: Quantum-Like Models for Information Retrieval and Decision-Making / [ed] Diederik Aerts, Andrei Khrennikov, Massimo Melucci, Bourama Toni, Springer, 2019, p. 51-82Chapter in book (Refereed)
Abstract [en]

This chapter contains a brief introduction to the mathematical formalism and axiomatics of quantum mechanics (QM). Recently quantum mathematics and methodology started to be widely used for modeling decision making for humans and AI-systems, including quantum-like modeling information retrieval. Experts in such areas do not go deeply into the details of quantum theory. Moreover, typically such consumers of quantum theory do not use all its components. Quantum measurement theory is the most useful for application, including information retrieval. The main issue is the quantum treatment of incompatible observables represented mathematically by noncommuting Hermitian operators. At the level of statistical data incompatibility is represented as interference of probabilities, in the form of modification of the formula of total probability by adding the interference term.

Place, publisher, year, edition, pages
Springer, 2019
Series
STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, ISSN 2520-193X, E-ISSN 2520-1948
National Category
Other Mathematics
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-93480 (URN)10.1007/978-3-030-25913-6_4 (DOI)978-3-030-25912-9 (ISBN)978-3-030-25913-6 (ISBN)
Available from: 2020-04-16 Created: 2020-04-16 Last updated: 2020-04-17Bibliographically approved
Baladron, C. & Khrennikov, A. (2019). Bell inequality violation in the framework of a Darwinian approach to quantum mechanics. The European Physical Journal Special Topics, 227(15-16), 2119-2132
Open this publication in new window or tab >>Bell inequality violation in the framework of a Darwinian approach to quantum mechanics
2019 (English)In: The European Physical Journal Special Topics, ISSN 1951-6355, E-ISSN 1951-6401, Vol. 227, no 15-16, p. 2119-2132Article, review/survey (Refereed) Published
Abstract [en]

A fundamental particle in physical space subject to conservation of momentum and energy, and characterized by its average mass and its position is methodologically supplemented with an information processor - a classical Turing machine - and a randomizer both defined on an information space localized on every particle. In this way the particle can be considered a generalized Darwinian system on which natural selection could act steering the evolution on the information space of the algorithms that govern the behaviour of the particles, giving rise plausibly to emergent quantum behaviour from initial randomness. This theory is applied to an EPR-Bohm experiment for electrons in order to analyse Bell inequality violation. A model for the entanglement of two particles has been considered. The model includes shared randomness - each particle stores its own randomizer and that of its partner - and the mutual transfer of their algorithms - sharing programs - that contain their respective anticipation modules. This fact enables every particle to anticipate not only the possible future configurations of its surrounding systems, but also those of the surrounding systems of its entangled partner. Thus, while preserving locality and realism, this theory implies outcome dependence - through shared randomness - and parameter dependence - through shared anticipation - for entangled states and, as a consequence, the violation of the Bell inequality in an EPR-Bohm experiment.

Place, publisher, year, edition, pages
Springer, 2019
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-81846 (URN)10.1140/epjst/e2019-800061-1 (DOI)000462523100023 ()2-s2.0-85062772552 (Scopus ID)
Available from: 2019-04-12 Created: 2019-04-12 Last updated: 2019-08-29Bibliographically approved
Khrennikov, A. & Alodjants, A. (2019). Classical (Local and Contextual) Probability Model for Bohm-Bell Type Experiments: No-Signaling as Independence of Random Variables. Entropy, 21(2), 1-20, Article ID 157.
Open this publication in new window or tab >>Classical (Local and Contextual) Probability Model for Bohm-Bell Type Experiments: No-Signaling as Independence of Random Variables
2019 (English)In: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 21, no 2, p. 1-20, article id 157Article, review/survey (Refereed) Published
Abstract [en]

We start with a review on classical probability representations of quantum states and observables. We show that the correlations of the observables involved in the Bohm-Bell type experiments can be expressed as correlations of classical random variables. The main part of the paper is devoted to the conditional probability model with conditioning on the selection of the pairs of experimental settings. From the viewpoint of quantum foundations, this is a local contextual hidden-variables model. Following the recent works of Dzhafarov and collaborators, we apply our conditional probability approach to characterize (no-)signaling. Consideration of the Bohm-Bell experimental scheme in the presence of signaling is important for applications outside quantum mechanics, e.g., in psychology and social science. The main message of this paper (rooted to Ballentine) is that quantum probabilities and more generally probabilities related to the Bohm-Bell type experiments (not only in physics, but also in psychology, sociology, game theory, economics, and finances) can be classically represented as conditional probabilities.

Place, publisher, year, edition, pages
MDPI, 2019
Keywords
quantum versus classical probability, Bohm-Bell type experiments in physics and psychology, localty, contextual hidden-variables models, (no-)signaling, random generators, selection of experimental settings, conditional probability
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-81409 (URN)10.3390/e21020157 (DOI)000460742200058 ()2-s2.0-85061988569 (Scopus ID)
Available from: 2019-03-29 Created: 2019-03-29 Last updated: 2019-08-29Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-9857-0938

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