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IEEE Transactions on Systems Man and Cybernetics Part C (Applications and Reviews)

Applying Wave Probabilistic Functions for Dynamic System Modeling

Miroslav Svítek

Published Mar 29, 2011• 18 citations
Publisher

Abstract

The goal of this paper is to provide an introduction to the application of wave probabilistic functions in the area of dynamic system models. This paper presents dynamic features of wave probabilistic models that are basic principles of quantum cybernetics. These features are mathematically described, and the illustrative examples demonstrate possible applications of the theory.

DOI
10.1109/tsmcc.2010.2093127

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The goal of this paper is to provide an introduction to the application of wave probabilistic functions in the area of dynamic system models. This paper presents dynamic features of wave probabilistic models that are basic principles of quantum cybernetics. These features are mathematically described, and the illustrative examples demonstrate possible applications of the theory.
This paper presents the theory of wave probabilistic models, which in turn represents the basic principles of quantum cybernetics. The features of the theory presented here are mathematically formulated, and selected illustrative examples demonstrate possible applications of the theory. The proposed methodology represents an original approach that emerges from defined assumptions like single-valuedness, the resonance principle, etc. From these simple assumptions, a set of principles of quantum cybernetics can be derived, e.g., quantization, spin, and entanglement.
The paper presents the theory of wave probabilistic models together with their features that represent basic principles of quantum informatics. These features are mathematically described and the illustrative examples are shown to demonstrate the possible applications of the presented theory. The proposed methodology represents the original approach which comes from defined mathematical assumptions like single-valuedness, resonance principle, etc. From these simple assumptions a lot of principle of quantum informatics can be derived like quantization principle, spin, entanglement, etc.
The paper presents the theory of wave probabilistic models together with their important features like inclusion-exclusion rule, product rule and entanglement. These features are athematically described and the illustrative example is shown to demonstrate the possible applications of the theory. The presented theory can be also applied for modeling of quasi-non-ergodic probabilistic systems. First of all we show the new methodology on binary non-ergodic time series. The theory is extended into M-dimensional non-ergodic n-valued systems with linear ergodicity evolution that are called quasi-on-ergodic probabilistic systems.
What about a process theory? How does quantum theory explain changes in confidence across time or how does quantum theory predict the time that it takes to make a decision? So far we have only made use of the structural part of quantum theory introduced in Chapter 2. This chapter introduces some of the basic principles for quantum dynamics. It is useful to compare quantum dynamics with Markov dynamics (Howard, 1971). Markov theory is a general mathematical framework for describing probabilistic-dynamic systems, which is commonly used in all areas of cognitive and decision sciences. For example, it is the mathematical basis that underlies random walk/diffusion models of decision making (Busemeyer & Diederich, 2009), or stochastic models of information processing (Townsend & Ashby, 1983), or multinomial processing tree models of memory retrieval (Batchelder & Reiffer, 1999), or the even more general field of stochastic processes (Bhattacharya & Waymire, 1990). Quantum theory provides an alternative general mathematical framework for describing probabilistic-dynamic systems (Gudder, 1979). However, quantum theory is similar in many ways to Markov theory, and so if you already know Markov theory, then it will be easy to learn about quantum dynamics too. This chapter introduces the Kolmogorov forward equation used to describe time evolution in Markov models, as well as the quantum analogue – the Schrödinger equation – which describes time evolution in quantum models. This chapter examines the similarities and differences between these two types of evolution, and why they are both useful for cognitive and decision modelling.