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Khrennikov, A. & Yurova, E. (2018). Subcoordinate Representation of p-adic Functions and Generalization of Hensel Lemma. Izvestiya. Mathematics, 82(2).
Open this publication in new window or tab >>Subcoordinate Representation of p-adic Functions and Generalization of Hensel Lemma
2018 (English)In: Izvestiya. Mathematics, ISSN 1064-5632, E-ISSN 1468-4810, Vol. 82, no 2Article in journal (Refereed) In press
Place, publisher, year, edition, pages
Institute of Physics (IOP), 2018
National Category
Other Mathematics
Identifiers
urn:nbn:se:lnu:diva-61501 (URN)10.1070/IM8578 (DOI)
Available from: 2017-03-21 Created: 2017-03-21 Last updated: 2018-02-15
Haven, E. & Khrennikov, A. (2017). A brief introduction to quantum formalism. In: Emmanuel Haven, Andrei Khrennikov (Ed.), The Palgrave Handbook of Quantum Models in Social Science: Applications and Grand Challenges (pp. 1-17). Palgrave Macmillan.
Open this publication in new window or tab >>A brief introduction to quantum formalism
2017 (English)In: The Palgrave Handbook of Quantum Models in Social Science: Applications and Grand Challenges / [ed] Emmanuel Haven, Andrei Khrennikov, Palgrave Macmillan, 2017, p. 1-17Chapter in book (Other academic)
Abstract [en]

The authors present briefly the basic notions of the quantum formalism: pure and mixed states; quantum observables; quantum probability; Born’s rule, superposition, and ‘state collapse’; the projection postulate (von Neumann–Lüders postulate); Dirac’s ket and bra-vector notations; elements of quantum information theory and quantum logic; Schrödinger’s and von Neumann’s equations; unitary dynamics; and positive operator valued measures. They also define the basic mathematical notions related to the quantum formalism: Hilbert space; scalar product; norm; Hermitian operator (matrix); projector; and unitary operator and adjoint operator. This chapter may be useful for newcomers to the field, but for those readers who have preliminary knowledge about quantum mechanics (QM) they can proceed directly to advanced chapters.

Place, publisher, year, edition, pages
Palgrave Macmillan, 2017
National Category
Probability Theory and Statistics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-64655 (URN)10.1057/978-1-137-49276-0_1 (DOI)2-s2.0-85018946665 (Scopus ID)9781137492760 (ISBN)9781137492753 (ISBN)
Available from: 2017-06-02 Created: 2017-06-02 Last updated: 2017-06-27Bibliographically approved
Bagarello, F., Haven, E. & Khrennikov, A. (2017). A model of adaptive decision-making from representation of information environment by quantum fields. Philosophical Transactions. Series A: Mathematical, physical, and engineering science, 375(2106), Article ID 20170162.
Open this publication in new window or tab >>A model of adaptive decision-making from representation of information environment by quantum fields
2017 (English)In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 375, no 2106, article id 20170162Article in journal (Refereed) Published
Abstract [en]

We present the mathematical model of decisionmaking (DM) of agents acting in a complex and uncertain environment (combining huge variety of economical, financial, behavioural and geopolitical factors). To describe interaction of agents with it, we apply the formalism of quantum field theory (QTF). Quantum fields are a purely informational nature. The QFT model can be treated as a far relative of the expected utility theory, where the role of utility is played by adaptivity to an environment (bath). However, this sort of utility- adaptivity cannot be represented simply as a numerical function. The operator representation in Hilbert space is used and adaptivity is described as in quantum dynamics. We are especially interested in stabilization of solutions for sufficiently large time. The outputs of this stabilization process, probabilities for possible choices, are treated in the framework of classical DM. To connect classical and quantum DM, we appeal to Quantum Bayesianism. We demonstrate the quantumlike interference effect in DM, which is exhibited as a violation of the formula of total probability, and hence the classical Bayesian inference scheme. This article is part of the themed issue 'Second quantum revolution: foundational questions'.

Keyword
decision-making, ladder and number operators, game theory
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-68548 (URN)10.1098/rsta.2017.0162 (DOI)000412179900015 ()
Available from: 2017-11-01 Created: 2017-11-01 Last updated: 2017-11-01Bibliographically approved
Asano, M., Basieva, I., Khrennikov, A. & Yamato, I. (2017). A model of differentiation in quantum bioinformatics. Progress in Biophysics and Molecular Biology, 130, 88-98.
Open this publication in new window or tab >>A model of differentiation in quantum bioinformatics
2017 (English)In: Progress in Biophysics and Molecular Biology, ISSN 0079-6107, E-ISSN 1873-1732, Vol. 130, p. 88-98Article, review/survey (Refereed) Published
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.

Place, publisher, year, edition, pages
Elsevier, 2017
Keyword
Differentiation, Quantum-like approach, Decoherence process
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-70576 (URN)10.1016/j.pbiomolbio.2017.05.013 (DOI)000423002900010 ()28579516 (PubMedID)
Available from: 2018-02-07 Created: 2018-02-07 Last updated: 2018-02-07Bibliographically approved
Asano, M., Basieva, I., Khrennikov, A., Ohya, M. & Tanaka, Y. (2017). A quantum-like model of selection behavior. Journal of mathematical psychology (Print), 78, 2-12.
Open this publication in new window or tab >>A quantum-like model of selection behavior
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2017 (English)In: Journal of mathematical psychology (Print), ISSN 0022-2496, E-ISSN 1096-0880, Vol. 78, p. 2-12Article in journal (Refereed) Published
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.

Keyword
Prospect theory, Ellsberg paradox, Machina paradox, WTA and WTP, Quantum-like approach
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-66896 (URN)10.1016/j.jmp.2016.07.006 (DOI)000403636800002 ()
Available from: 2017-07-12 Created: 2017-07-12 Last updated: 2017-07-12Bibliographically approved
Khrennikov, A. (2017). After Bell. Paper presented at Conference on Frontiers of Quantum and Mesoscopic Thermodynamics (FQMT), JUL 27-AUG 01, 2015, Prague, CZECH REPUBLIC. Fortschritte der Physik, 65(6-8), Article ID 1600044.
Open this publication in new window or tab >>After Bell
2017 (English)In: Fortschritte der Physik, ISSN 0015-8208, E-ISSN 1521-3978, Vol. 65, no 6-8, article id 1600044Article in journal (Refereed) Published
Abstract [en]

We analyze foundational consequences of recently reported loophole free tests of violation of Bell's inequality. We consider two interpretations of these remarkable experiments. The conventional one is Einstein was wrong and Bohr was right, there is spooky action at a distance, quantum realism is incompatible with locality. However, in line with discussions in literature during last decade, we show that it is still possible to treat quantum mechanics without appealing to nonlocality or denying realism. We hope that this note will call the attention of experts in quantum foundations and convince them that the case is not closed, so that they should come with their own comments on the status of the final Bell test.

Place, publisher, year, edition, pages
Wiley-VCH Verlagsgesellschaft, 2017
Keyword
Bell inequality, loophole free test, interpretations
National Category
Physical Sciences Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-66898 (URN)10.1002/prop.201600044 (DOI)000403351700014 ()
Conference
Conference on Frontiers of Quantum and Mesoscopic Thermodynamics (FQMT), JUL 27-AUG 01, 2015, Prague, CZECH REPUBLIC
Available from: 2017-07-12 Created: 2017-07-12 Last updated: 2017-07-12Bibliographically approved
Khrennikov, A. & Stacey, B. C. (2017). Aims and Scope of the Special Issue, "Quantum Foundations: Informational Perspective". Foundations of physics, 47(8), 1003-1008.
Open this publication in new window or tab >>Aims and Scope of the Special Issue, "Quantum Foundations: Informational Perspective"
2017 (English)In: Foundations of physics, ISSN 0015-9018, E-ISSN 1572-9516, Vol. 47, no 8, p. 1003-1008Article in journal, Editorial material (Other academic) Published
Place, publisher, year, edition, pages
Springer, 2017
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-67395 (URN)10.1007/s10701-017-0106-3 (DOI)000405964600001 ()
Available from: 2017-08-24 Created: 2017-08-24 Last updated: 2017-08-24Bibliographically approved
Oleschko, K. & Khrennikov, A. (2017). Applications of p-adics to geophysics: Linear and quasilinear diffusion of water-in-oil and oil-in-water emulsions. Theoretical and mathematical physics, 190(1), 154-163.
Open this publication in new window or tab >>Applications of p-adics to geophysics: Linear and quasilinear diffusion of water-in-oil and oil-in-water emulsions
2017 (English)In: Theoretical and mathematical physics, ISSN 0040-5779, E-ISSN 1573-9333, Vol. 190, no 1, p. 154-163Article in journal (Refereed) Published
Abstract [en]

In a very general setting, we discuss possibilities of applying p-adics to geophysics using a p-adic diffusion representation of the master equations for the dynamics of a fluid in capillaries in porous media and formulate several mathematical problems motivated by such applications. We stress that p-adic wavelets are a powerful tool for obtaining analytic solutions of diffusion equations. Because p-adic diffusion is a special case of fractional diffusion, which is closely related to the fractal structure of the configuration space, p-adic geophysics can be regarded as a new approach to fractal modeling of geophysical processes.

Place, publisher, year, edition, pages
Pleiades Publishing, 2017
Keyword
master equation, geophysics, water-in-oil and oil-in-water emulsions, p-adic number, p-adic diffusion, quasilinear p-adic diffusion
National Category
Geophysics Other Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-61500 (URN)10.1134/S0040577917010135 (DOI)000394442700013 ()
Available from: 2017-03-21 Created: 2017-03-21 Last updated: 2017-05-22Bibliographically approved
Khrennikov, A. & Yurova, E. (2017). Automaton model of protein: Dynamics of conformational and functional states. Progress in Biophysics and Molecular Biology, 130(A), 2-14.
Open this publication in new window or tab >>Automaton model of protein: Dynamics of conformational and functional states
2017 (English)In: Progress in Biophysics and Molecular Biology, ISSN 0079-6107, E-ISSN 1873-1732, Vol. 130, no A, p. 2-14Article in journal (Refereed) Published
Abstract [en]

In this conceptual paper we propose to explore the analogy between ontic/epistemic description of quantum phenomena and interrelation between dynamics of conformational and functional states of proteins. Another new idea is to apply theory of automata to model the latter dynamics. In our model protein's behavior is modeled with the aid of two dynamical systems, ontic and epistemic, which describe evolution of conformational and functional states of proteins, respectively. The epistemic automaton is constructed from the ontic automaton on the basis of functional (observational) equivalence relation on the space of ontic states. This reminds a few approaches to emergent quantum mechanics in which a quantum (epistemic) state is treated as representing a class of prequantum (ontic) states. This approach does not match to the standard protein structure-function paradigm. However, it is perfect for modeling of behavior of intrinsically disordered proteins. Mathematically space of protein's ontic states (conformational states) is modeled with the aid of p-adic numbers or more general ultrametric spaces encoding the internal hierarchical structure of proteins. Connection with theory of p-adic dynamical systems is briefly discussed.

Place, publisher, year, edition, pages
Elsevier, 2017
Keyword
Automaton-model; Conformational and functional states; Proteins; Quantum-like model; Structure-function paradigm
National Category
Biophysics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-61120 (URN)10.1016/j.pbiomolbio.2017.02.003 (DOI)000423002900002 ()28214530 (PubMedID)
Projects
Modeling of Complex Hierarchic systemsEU-project Quantum Information Access and Retrieval Theory (QUARTZ), Grant No. 721321
Funder
EU, European Research Council, 721321
Available from: 2017-03-07 Created: 2017-03-07 Last updated: 2018-02-07Bibliographically approved
Khrennikov, A. (2017). Bohr against Bell: complementarity versus nonlocality. Open Physics, 15(1), 734-738.
Open this publication in new window or tab >>Bohr against Bell: complementarity versus nonlocality
2017 (English)In: Open Physics, E-ISSN 2391-5471, Vol. 15, no 1, p. 734-738Article in journal (Refereed) Published
Abstract [en]

In this note we compare the views of Bohr (known as the Copenhagen interpretation of quantum mechanics) with the views of Bell: complementarity versus nonlocality.

Place, publisher, year, edition, pages
De Gruyter Open, 2017
Keyword
Violation of Bell's inequality, nonlocality, the principle of complementarity, Kolmogorov model, quantum technologies
National Category
Mathematics Physical Sciences
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-69782 (URN)10.1515/phys-2017-0086 (DOI)000417931400021 ()
Available from: 2018-01-12 Created: 2018-01-12 Last updated: 2018-01-12Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-9857-0938

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