8,362 research outputs found

    On the Discontinuity of the Shannon Information Measures

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    Discontinuities in the Maximum-Entropy Inference

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    We revisit the maximum-entropy inference of the state of a finite-level quantum system under linear constraints. The constraints are specified by the expected values of a set of fixed observables. We point out the existence of discontinuities in this inference method. This is a pure quantum phenomenon since the maximum-entropy inference is continuous for mutually commuting observables. The question arises why some sets of observables are distinguished by a discontinuity in an inference method which is still discussed as a universal inference method. In this paper we make an example of a discontinuity and we explain a characterization of the discontinuities in terms of the openness of the (restricted) linear map that assigns expected values to states.Comment: 8 pages, 3 figures, 32nd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Garching, Germany, 15-20 July 201

    Recurrence and algorithmic information

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    In this paper we initiate a somewhat detailed investigation of the relationships between quantitative recurrence indicators and algorithmic complexity of orbits in weakly chaotic dynamical systems. We mainly focus on examples.Comment: 26 pages, no figure

    Function reconstruction as a classical moment problem: A maximum entropy approach

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    We present a systematic study of the reconstruction of a non-negative function via maximum entropy approach utilizing the information contained in a finite number of moments of the function. For testing the efficacy of the approach, we reconstruct a set of functions using an iterative entropy optimization scheme, and study the convergence profile as the number of moments is increased. We consider a wide variety of functions that include a distribution with a sharp discontinuity, a rapidly oscillatory function, a distribution with singularities, and finally a distribution with several spikes and fine structure. The last example is important in the context of the determination of the natural density of the logistic map. The convergence of the method is studied by comparing the moments of the approximated functions with the exact ones. Furthermore, by varying the number of moments and iterations, we examine to what extent the features of the functions, such as the divergence behavior at singular points within the interval, is reproduced. The proximity of the reconstructed maximum entropy solution to the exact solution is examined via Kullback-Leibler divergence and variation measures for different number of moments.Comment: 20 pages, 17 figure
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