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- Nyqvist, Robert
(författare)
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Algebraic Dynamical Systems, Analytical Results and Numerical Simulations
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we study discrete dynamical system, given by a polynomial, over both finite extension of the fields of p-adic numbers and over finite fields. Especially in the p-adic case, we study fixed points of dynamical systems, and which elements that are attracted to them. We show with different examples how complex these dynamics are.For certain polynomial dynamical systems over finite fields we prove that the normalized average of the numbers of linear factors modulo prime numbers exists. We also show how to calculate the average, by using Chebotarev's Density Theorem. The non-normalized version of the average of the number of linear factors of linearized polynomials modulo prime numbers, tends to infinity, so in that case we find an asymptotic formula instead.We have also used a computer to study different behaviors, such as iterations of polynomials over the p-adic fields and the asymptotic relation mention above. In the last chapter we present the computer programs used in different part of the thesis.
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| 2. |
- Khrennikov, Andrei
(författare)
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Bell Could Become the Copernicus of Probability
- 2016
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Ingår i: Open systems & information dynamics. - 1230-1612 .- 1573-1324. ; 23:2
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Tidskriftsartikel (refereegranskat)abstract
- Our aim is to emphasize the role of mathematical models in physics, especially models of geometry and probability. We briefly compare developments of geometry and probability by pointing to similarities and differences: from Euclid to Lobachevsky and from Kolmogorov to Bell. In probability, Bell could play the same role as Lobachevsky in geometry. In fact, violation of Bell's inequality can be treated as implying the impossibility to apply the classical probability model of Kolmogorov (1933) to quantum phenomena. Thus the quantum probabilistic model (based on Born's rule) can be considered as the concrete example of the non-Kolmogorovian model of probability, similarly to the Lobachevskian model - the first example of the non-Euclidean model of geometry. This is the "probability model" interpretation of the violation of Bell's inequality. We also criticize the standard interpretation - an attempt to add to rigorous mathematical probability models additional elements such as (non)locality and (un)realism. Finally, we compare embeddings of non-Euclidean geometries into the Euclidean space with embeddings of the non-Kolmogorovian probabilities (in particular, quantum probability) into the Kolmogorov probability space. As an example, we consider the CHSH-test. © 2016 World Scientific Publishing Company.
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| 4. |
- Asano, Masanari, et al.
(författare)
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Quantum-Like Model for Decision Making Process inTwo Players Game : A Non-Kolmogorovian Model
- 2011
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Ingår i: Foundations of physics. - : Springer Science and Business Media LLC. - 0015-9018 .- 1572-9516. ; 41:3, s. 538-548
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Tidskriftsartikel (refereegranskat)abstract
- In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov (Information Dynamics in Cognitive, Psychological and Anomalous Phenomena. Fundamental Theories of Physics, Kluwer Academic, Norwell, 2004; Fuzzy Sets Syst. 155:4-17, 2005; Biosystems 84:225-241, 2006; Found. Phys. 35(10):1655-1693, 2005; in QP-PQ Quantum Probability and White Noise Analysis, vol. XXIV, pp. 105-117, 2009), it was pointed out that statistics collected in such the experiments have "quantum-like" properties, which can not be explained in classical probability theory. In this paper, we design a simple quantum-like model describing a decision-making process in a two-players game and try to explain a mechanism of the irrational behavior of players. Finally we discuss a mathematical frame of non-Kolmogorovian system in terms of liftings (Accardi and Ohya, in Appl. Math. Optim. 39:33-59, 1999).
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| 7. |
- Basieva, Irina, 1974-, et al.
(författare)
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Testing Boundaries of Applicability of Quantum Probabilistic Formalism to Modeling of Cognition : Metaphors of Two and Three Slit Experiments
- 2017
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Ingår i: QUANTUM INTERACTION, QI 2016. - Cham : Springer. - 9783319522883 - 9783319522890 ; , s. 49-56
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Konferensbidrag (refereegranskat)abstract
- Analogy between the two slit experiment in quantum mechanics (QM) and the disjunction effect in psychology led to fruitful applications of the mathematical formalism of quantum probability to cognitive psychology. These quantum-like studies demonstrated that quantum probability (QP) matches better with the experimental statistical data than classical probability (CP). Similar conclusion can be derived from comparing QP and CP models for a variety of other cognitive-psychological effects, e.g., the order effect. However, one may wonder whether QP covers completely cognitive-psychological phenomena or cognition exhibits even more exotic probabilistic features and we have to use probabilistic models with even higher degree of nonclassicality than quantum probability. It is surprising that already a cognitive analog of the triple slit experiment in QM can be used to check this problem.
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| 9. |
- Dragovich, Branko, et al.
(författare)
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Ultrametrics in the genetic code and the genome
- 2017
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Ingår i: Applied Mathematics and Computation. - : Elsevier. - 0096-3003 .- 1873-5649. ; 309, s. 350-358
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Tidskriftsartikel (refereegranskat)abstract
- Ultrametric approach to the genetic code and the genome is considered and developed. p-Adic degeneracy of the genetic code is pointed out. Ultrametric tree of the codon space is presented. It is shown that codons and amino acids can be treated as p-adic ultrametric networks. Ultrametric modification of the Hamming distance is defined and noted how it can be useful. Ultrametric approach with p-adic distance is an attractive and promising trend towards investigation of bioinformation. © 2017 Elsevier Inc.
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| 10. |
- Dzhafarov, Ehtibar, et al.
(författare)
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Foreword
- 2017
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Ingår i: Journal of mathematical psychology (Print). - USA : Elsevier BV. - 0022-2496 .- 1096-0880. ; 78, s. 1-1
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Tidskriftsartikel (refereegranskat)
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