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Antoniouk, A. V., Oleschko, K., Kochubei, A. N. & Khrennikov, A. (2018). A stochastic p-adic model of the capillary flow in porous random medium. Physica A: Statistical Mechanics and its Applications, 505, 763-777
Open this publication in new window or tab >>A stochastic p-adic model of the capillary flow in porous random medium
2018 (English)In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 505, p. 763-777Article in journal (Refereed) Published
Abstract [en]

We develop the p-adic model of propagation of fluids (e.g., oil or water) in capillary networks in a porous random medium. The hierarchic structure of a system of capillaries is mathematically modeled by endowing trees of capillaries with the structure of an ultra metric space. Considerations are restricted to the case of idealized networks represented by homogeneous p-trees with p branches leaving each vertex, where p > 1 is a prime number. Such trees are realized as the fields of p-adic numbers. We introduce and study an inhomogeneous Markov process describing the penetration of fluid into a porous random medium. (C) 2018 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
Elsevier, 2018
Keywords
P-adic numbers, P-adic theoretical physics, Porous random medium, Capillary network, Penetration of fluid, Inhomogeneous Markov process
National Category
Physical Sciences Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-76948 (URN)10.1016/j.physa.2018.03.049 (DOI)000437061000067 ()
Available from: 2018-07-19 Created: 2018-07-19 Last updated: 2018-07-19Bibliographically approved
Lozada Aguilar, M. A., Khrennikov, A. & Oleschko, K. (2018). From axiomatics of quantum probability to modelling geological uncertainty and management of intelligent hydrocarbon reservoirs with the theory of open quantum systems. Philosophical Transactions. Series A: Mathematical, physical, and engineering science, 376(2118), Article ID 20170225.
Open this publication in new window or tab >>From axiomatics of quantum probability to modelling geological uncertainty and management of intelligent hydrocarbon reservoirs with the theory of open quantum systems
2018 (English)In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 376, no 2118, article id 20170225Article in journal (Refereed) Published
Abstract [en]

As was recently shown by the authors, quantum probability theory can be used for the modelling of the process of decision-making (e.g. probabilistic risk analysis) for macroscopic geophysical structures such as hydrocarbon reservoirs. This approach can be considered as a geophysical realization of Hilbert's programme on axiomatization of statistical models in physics (the famous sixth Hilbert problem). In this conceptual paper, we continue development of this approach to decision-making under uncertainty which is generated by complexity, variability, heterogeneity, anisotropy, as well as the restrictions to accessibility of subsurface structures. The belief state of a geological expert about the potential of exploring a hydrocarbon reservoir is continuously updated by outputs of measurements, and selection of mathematical models and scales of numerical simulation. These outputs can be treated as signals Dfrom the information environment E. The dynamics of the belief state can be modelled with the aid of the theory of open quantum systems: a quantum state (representing uncertainty in beliefs) is dynamically modified through coupling with E; stabilization to a steady state determines a decision strategy. In this paper, the process of decision-making about hydrocarbon reservoirs (e.g. 'explore or not?'; 'open new well or not?'; 'contaminated by water or not?'; 'double or triple porosity medium?') is modelled by using the Gorini-Kossakowski- Sudarshan-Lindblad equation. In our model, this equation describes the evolution of experts' predictions about a geophysical structure. We proceed with the information approach to quantum theory and the subjective interpretation of quantum probabilities (due to quantum Bayesianism).

Keywords
decision-making and risk analysis, geology, Hilbert's sixth problem, quantum versus classical Bayesian inference, heterogeneity, open quantum systems
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-76464 (URN)10.1098/rsta.2017.0225 (DOI)000427878700004 ()29555799 (PubMedID)
Available from: 2018-07-10 Created: 2018-07-10 Last updated: 2018-07-10Bibliographically approved
Melkikh, A. V. & Khrennikov, A. (2018). Mechanisms of directed evolution of morphological structures and the problems of morphogenesis. Biosystems (Amsterdam. Print), 168, 26-44
Open this publication in new window or tab >>Mechanisms of directed evolution of morphological structures and the problems of morphogenesis
2018 (English)In: Biosystems (Amsterdam. Print), ISSN 0303-2647, E-ISSN 1872-8324, Vol. 168, p. 26-44Article, review/survey (Refereed) Published
Abstract [en]

Morphogenesis mechanisms are considered from the point of view of complexity. It has been shown that the presence of long-range interactions between biologically important molecules is a necessary condition for the formation and stable operation of morphological structures. A quantum model of morphogenesis based on non-Archimedean analysis and the presence of long-range interactions between biologically important molecules has been constructed. This model shows that the evolution of morphological structures essentially depends on the availability of a priori information on these structures. Critical steps in evolution related to the most important morphological and behavioral findings have been analyzed; the results have shown that the implementation of such steps can only be explained within the framework of a partially directed evolution. Thus, the previously proposed model for a partially directed evolution is established for modeling the evolution of morphological structures.

Place, publisher, year, edition, pages
Elsevier, 2018
Keywords
Morphogenesis topology, Complexity, Partially-directed evolution, Non-Archimedean analysis, Quantum models of interaction, Active information, Bohmian-like dynamics
National Category
Biological Sciences Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-76952 (URN)10.1016/j.biosystems.2018.04.004 (DOI)000436913300003 ()29758243 (PubMedID)
Available from: 2018-07-19 Created: 2018-07-19 Last updated: 2018-07-19Bibliographically approved
Bagarello, F., Basieva, I. & Khrennikov, A. (2018). Quantum field inspired model of decision making: Asymptotic stabilization of belief state via interaction with surrounding mental environment. Journal of mathematical psychology (Print), 82, 159-168
Open this publication in new window or tab >>Quantum field inspired model of decision making: Asymptotic stabilization of belief state via interaction with surrounding mental environment
2018 (English)In: Journal of mathematical psychology (Print), ISSN 0022-2496, E-ISSN 1096-0880, Vol. 82, p. 159-168Article in journal (Refereed) Published
Abstract [en]

This paper is devoted to a justification of quantum-like models of the process of decision making based on the theory of open quantum systems, i.e. decision making is considered as decoherence. This process is modeled as interaction of a decision maker, Alice, with a mental (information) environment R, surrounding her. Such an interaction generates "dissipation of uncertainty" from Alice's belief-state rho(t) into R, and asymptotic stabilization of rho(t) to a steady belief-state. The latter is treated as the decision state. Mathematically the problem under study is about finding constraints on 72, guaranteeing such stabilization. We found a partial solution of this problem (in the form of sufficient conditions). We present the corresponding decision making analysis for one class of mental environments, the so-called "almost homogeneous environments", with the illustrative examples: (a) behavior of electorate interacting with the mass-media "reservoir"; (b) consumers' persuasion. We also comment on other classes of mental environments. (C) 2017 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
Academic Press, 2018
Keywords
Decision making, Quantum-like model, Mental (information) environment, Open quantum systems, Dissipation of uncertainty, Voters' behavior, Consumers' persuasion
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-72692 (URN)10.1016/j.jmp.2017.10.002 (DOI)000428361300013 ()
Available from: 2018-04-13 Created: 2018-04-13 Last updated: 2018-04-13Bibliographically approved
Bagarello, F., Basieva, I., Pothos, E. M. & Khrennikov, A. (2018). Quantum like modeling of decision making: Quantifying uncertainty with the aid of Heisenberg-Robertson inequality. Journal of mathematical psychology (Print), 84, 49-56
Open this publication in new window or tab >>Quantum like modeling of decision making: Quantifying uncertainty with the aid of Heisenberg-Robertson inequality
2018 (English)In: Journal of mathematical psychology (Print), ISSN 0022-2496, E-ISSN 1096-0880, Vol. 84, p. 49-56Article in journal (Refereed) Published
Abstract [en]

This paper contributes to quantum-like modeling of decision making (DM) under uncertainty through application of Heisenberg's uncertainty principle (in the form of the Robertson inequality). In this paper we apply this instrument to quantify uncertainty in DM performed by quantum-like agents. As an example, we apply the Heisenberg uncertainty principle to the determination of mutual interrelation of uncertainties for "incompatible questions" used to be asked in political opinion pools. We also consider the problem of representation of decision problems, e.g., in the form of questions, by Hermitian operators, commuting and noncommuting, corresponding to compatible and incompatible questions respectively. Our construction unifies the two different situations (compatible versus incompatible mental observables), by means of a single Hilbert space and of a deformation parameter which can be tuned to describe these opposite cases. One of the main foundational consequences of this paper for cognitive psychology is formalization of the mutual uncertainty about incompatible questions with the aid of Heisenberg's uncertainty principle implying the mental state dependence of (in)compatibility of questions. (C) 2018 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
Elsevier, 2018
Keywords
Compatible and incompatible questions, Decision making, Heisenberg uncertainty principle, Mental state, Order effect
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-76883 (URN)10.1016/j.jmp.2018.03.004 (DOI)000435529400004 ()
Available from: 2018-07-17 Created: 2018-07-17 Last updated: 2018-07-17Bibliographically approved
Khrennikov, A. (2018). Social laser model: from color revolutions to Brexit and election of Donald Trump. Paper presented at Congress of the World-Organisation-of-Systems-and-Cybernetics (WOSC), 2017, Univ Rome, Fac Econ Sapienza, Dept Management, Rome, ITALY. Kybernetes, 47(2), 273-288
Open this publication in new window or tab >>Social laser model: from color revolutions to Brexit and election of Donald Trump
2018 (English)In: Kybernetes, ISSN 0368-492X, E-ISSN 1758-7883, Vol. 47, no 2, p. 273-288Article in journal (Refereed) Published
Abstract [en]

Purpose - This paper aims to present the basic assumptions for creation of social lasers and attract attention of other researchers (both from physics and socio-political science) to the problem of modeling of Stimulated Amplification of Social Actions (SASA). Design/methodology/approach - The model of SASA and its analysis are based on the mathematical formalism of quantum thermodynamics and field theory (applied outside of physics). Findings - The presented quantum-like model provides the consistent operational model of such complex socio-political phenomenon as SASA. Research limitations/implications - The model of SASA is heavily based on the use of the notion of social energy. This notion has not yet been formalized. Practical implications - Evidence of SASA ("functioning of social lasers") is rapidly accumulating, from color revolutions to such democratically structured protest actions as Brexit and the recent election of Donald Trump as the President of the USA. The corresponding socio-political studies are characterized by diversity of opinions and conclusions. The presented social laser model can be used to clarify these complex sociopolitical events and even predict their possibility. Social implications - SASA is the powerful source of social instability. Understanding its informational structure and origin may help to stabilize the modern society. Originality/value - Application of the quantum-like model of laser technology in social and political sciences is really a novel and promising approach.

Place, publisher, year, edition, pages
Emerald Group Publishing Limited, 2018
Keywords
Bose-Einstein and Fermi-Dirac statistics, Information field, Quantum field theory, Quantum thermodynamics, Social energy, Stimulated amplification of social actions
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-71226 (URN)10.1108/K-03-2017-0101 (DOI)000424477400004 ()
Conference
Congress of the World-Organisation-of-Systems-and-Cybernetics (WOSC), 2017, Univ Rome, Fac Econ Sapienza, Dept Management, Rome, ITALY
Available from: 2018-03-02 Created: 2018-03-02 Last updated: 2018-03-02Bibliographically approved
Asano, M., Basieva, I., Pothos, E. M. & Khrennikov, A. (2018). State Entropy and Differentiation Phenomenon. Entropy, 20(6), Article ID 394.
Open this publication in new window or tab >>State Entropy and Differentiation Phenomenon
2018 (English)In: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 20, no 6, article id 394Article in journal (Refereed) Published
Abstract [en]

In the formalism of quantum theory, a state of a system is represented by a density operator. Mathematically, a density operator can be decomposed into a weighted sum of (projection) operators representing an ensemble of pure states (a state distribution), but such decomposition is not unique. Various pure states distributions are mathematically described by the same density operator. These distributions are categorized into classical ones obtained from the Schatten decomposition and other, non-classical, ones. In this paper, we define the quantity called the state entropy. It can be considered as a generalization of the von Neumann entropy evaluating the diversity of states constituting a distribution. Further, we apply the state entropy to the analysis of non-classical states created at the intermediate stages in the process of quantum measurement. To do this, we employ the model of differentiation, where a system experiences step by step state transitions under the influence of environmental factors. This approach can be used for modeling various natural and mental phenomena: cell's differentiation, evolution of biological populations, and decision making.

Place, publisher, year, edition, pages
MDPI, 2018
Keywords
density operator, state entropy, von Neumann entropy, quantum measurement, differentiation
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-77406 (URN)10.3390/e20060394 (DOI)000436275400003 ()
Available from: 2018-08-29 Created: 2018-08-29 Last updated: 2018-08-29Bibliographically approved
Yurova, E. & Khrennikov, A. (2018). Subcoordinate Representation of p-adic Functions and Generalization of Hensel's Lemma. Izvestiya. Mathematics, 82(3), 632-645
Open this publication in new window or tab >>Subcoordinate Representation of p-adic Functions and Generalization of Hensel's Lemma
2018 (English)In: Izvestiya. Mathematics, ISSN 1064-5632, E-ISSN 1468-4810, Vol. 82, no 3, p. 632-645Article in journal (Refereed) Published
Abstract [en]

In this paper we describe a new representation of p-adic functions, the so-called subcoordinate representation. The main feature of the subcoordinaterepresentation of a p-adic function is that the values of the function f are given in the canonical form of the representation of p-adic numbers. The function f itself is determined by a tuple of p-valued functions from the set {0, 1,..., p-1} into itself and by the order in which these functions are used to determine the values of f. We also give formulae that enable one to pass from the subcoordinate representation of a 1-Lipschitz function to its van der Put series representation. The effective use of the subcoordinate representation of p-adic functions is illustrated by a study of the feasibility of generalizing Hensel's lemma.

Place, publisher, year, edition, pages
Russian Academy of Sciences, 2018
Keywords
p-adic numbers; Lipschitz functions; coordinate representation; van der Put series
National Category
Other Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-61501 (URN)10.1070/IM8578 (DOI)000437922000010 ()
Available from: 2017-03-21 Created: 2017-03-21 Last updated: 2018-07-27Bibliographically approved
Khrennikov, A. (2018). Towards Better Understanding QBism. Foundations of Science, 23(1), 181-195
Open this publication in new window or tab >>Towards Better Understanding QBism
2018 (English)In: Foundations of Science, ISSN 1233-1821, E-ISSN 1572-8471, Vol. 23, no 1, p. 181-195Article in journal (Refereed) Published
Abstract [en]

Recently I posted a paper entitled "External observer reflections on QBism". As any external observer, I was not able to reflect all features of QBism properly. The comments I received from one of QBism's creators, C. A. Fuchs, were very valuable to me in better understanding the views of QBists. Some of QBism's features are very delicate and extracting them from articles of QBists is not a simple task. Therefore, I hope that the second portion of my reflections on QBism (or, strictly speaking, my reflections on Fuchs reflections on my earlier reflections) might be interesting and useful for other experts in quantum foundations and quantum information theory (especially, taking into account my previous aggressively anti-QBism position). In the present paper I correct some of my earlier posted critical comments on QBism. At the same time, other critical comments gained new validation through my recent deeper understanding of QBists views on a number of problems.

Place, publisher, year, edition, pages
Springer, 2018
Keywords
Quantum Bayesianism, Växjö interpretation, Formula of total probability, Interference of probability, Classical Bayesian physics, Universal agent
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-72025 (URN)10.1007/s10699-017-9524-0 (DOI)000426932100013 ()
Available from: 2018-03-29 Created: 2018-03-29 Last updated: 2018-03-29Bibliographically approved
Khrennikov, A. & Basieva, I. (2018). Towards Experiments to Test Violation of the Original Bell Inequality. Entropy, 20(4), Article ID 280.
Open this publication in new window or tab >>Towards Experiments to Test Violation of the Original Bell Inequality
2018 (English)In: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 20, no 4, article id 280Article in journal (Refereed) Published
Abstract [en]

The aim of this paper is to attract the attention of experimenters to the original Bell (OB) inequality that was shadowed by the common consideration of the Clauser-Horne-Shimony-Holt (CHSH) inequality. There are two reasons to test the OB inequality and not the CHSH inequality. First of all, the OB inequality is a straightforward consequence to the Einstein-Podolsky-Rosen (EPR) argumentation. In addition, only this inequality is directly related to the EPR-Bohr debate. The second distinguishing feature of the OB inequality was emphasized by Itamar Pitowsky. He pointed out that the OB inequality provides a higher degree of violations of classicality than the CHSH inequality. For the CHSH inequality, the fraction of the quantum (Tsirelson) bound Q(CHSH) = 2 root 2 to the classical bound C-CHSH = 2, i.e., F-CHSH = Q(CHSH)/C-CHSH= root 2 is less than the fraction of the quantum bound for the OB inequality Q(OB) = 3/2 to the classical bound C-OB = 1, i.e., F-OB = Q(OB)/C-OB = 3/2. Thus, by violating the OB inequality, it is possible to approach a higher degree of deviation from classicality. The main problem is that the OB inequality is derived under the assumption of perfect (anti-) correlations. However, the last few years have been characterized by the amazing development of quantum technologies. Nowadays, there exist sources producing, with very high probability, the pairs of photons in the singlet state. Moreover, the efficiency of photon detectors was improved tremendously. In any event, one can start by proceeding with the fair sampling assumption. Another possibility is to use the scheme of the Hensen et al. experiment for entangled electrons. Here, the detection efficiency is very high.

Place, publisher, year, edition, pages
MDPI, 2018
Keywords
original Bell inequality, preparation of singlet states, possible experimental test
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-76896 (URN)10.3390/e20040280 (DOI)000435181600069 ()
Available from: 2018-07-17 Created: 2018-07-17 Last updated: 2018-07-17Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-9857-0938

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