60,792 research outputs found

    Energy Levels of "Hydrogen Atom" in Discrete Time Dynamics

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    We analyze dynamical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. In particular we study the problem of discrete energy levels of hydrogen atom. We are able to reconstruct potential which in discrete time formalism leads to energy levels of unperturbed hydrogen atom. We also consider linear energy levels of quantum harmonic oscillator and show how they are produced in the discrete time formalism. More generally, we show that in discrete time formalism finite motion in central potential leads to discrete energy spectrum, the property which is common for quantum mechanical theory. Thus deterministic (but discrete time!) dynamics is compatible with discrete energy levels.Comment: accepted for publication in Open Systems & Information Dynamic

    A tool for model-checking Markov chains

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    Markov chains are widely used in the context of the performance and reliability modeling of various systems. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both discrete [34, 10] and continuous time settings [7, 12]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen-Twente Markov Chain Checker EƎMC2, where properties are expressed in appropriate extensions of CTL. We illustrate the general benefits of this approach and discuss the structure of the tool. Furthermore, we report on successful applications of the tool to some examples, highlighting lessons learned during the development and application of EƎMC2

    Viewpoint Development of Stochastic Hybrid Systems

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    Nowadays, due to the explosive spreading of networked and highly distributed systems, mastering system complexity becomes a critical issue. Two development and verification paradigms have become more popular: viewpoints and randomisation. The viewpoints offer large freedom and introduce concurrency and compositionality in the development process. Randomisation is now a traditional method for reducing complexity (comparing with deterministic models) and it offers finer analytical analysis tools (quantification over non-determinism, multi-valued logics, etc). In this paper, we propose a combination of these two paradigms introducing a viewpoint methodology for systems with stochastic behaviours

    What is Computational Intelligence and where is it going?

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    What is Computational Intelligence (CI) and what are its relations with Artificial Intelligence (AI)? A brief survey of the scope of CI journals and books with ``computational intelligence'' in their title shows that at present it is an umbrella for three core technologies (neural, fuzzy and evolutionary), their applications, and selected fashionable pattern recognition methods. At present CI has no comprehensive foundations and is more a bag of tricks than a solid branch of science. The change of focus from methods to challenging problems is advocated, with CI defined as a part of computer and engineering sciences devoted to solution of non-algoritmizable problems. In this view AI is a part of CI focused on problems related to higher cognitive functions, while the rest of the CI community works on problems related to perception and control, or lower cognitive functions. Grand challenges on both sides of this spectrum are addressed
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