Browsing by Subject "ENTROPY"

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  • Annila, Arto; Salthe, Stanley (2010)
  • Silva, Jorge M.; Pinho, Eduardo; Matos, Sergio; Pratas, Diogo (2020)
    Sources that generate symbolic sequences with algorithmic nature may differ in statistical complexity because they create structures that follow algorithmic schemes, rather than generating symbols from a probabilistic function assuming independence. In the case of Turing machines, this means that machines with the same algorithmic complexity can create tapes with different statistical complexity. In this paper, we use a compression-based approach to measure global and local statistical complexity of specific Turing machine tapes with the same number of states and alphabet. Both measures are estimated using the best-order Markov model. For the global measure, we use the Normalized Compression (NC), while, for the local measures, we define and use normal and dynamic complexity profiles to quantify and localize lower and higher regions of statistical complexity. We assessed the validity of our methodology on synthetic and real genomic data showing that it is tolerant to increasing rates of editions and block permutations. Regarding the analysis of the tapes, we localize patterns of higher statistical complexity in two regions, for a different number of machine states. We show that these patterns are generated by a decrease of the tape's amplitude, given the setting of small rule cycles. Additionally, we performed a comparison with a measure that uses both algorithmic and statistical approaches (BDM) for analysis of the tapes. Naturally, BDM is efficient given the algorithmic nature of the tapes. However, for a higher number of states, BDM is progressively approximated by our methodology. Finally, we provide a simple algorithm to increase the statistical complexity of a Turing machine tape while retaining the same algorithmic complexity. We supply a publicly available implementation of the algorithm in C++ language under the GPLv3 license. All results can be reproduced in full with scripts provided at the repository.
  • Gobat, R.; Daddi, E.; Coogan, R. T.; Le Brun, A. M. C.; Bournaud, F.; Melin, J. -B.; Riechers, D. A.; Sargent, M.; Valentino, F.; Hwang, H. S.; Finoguenov, A.; Strazzullo, V. (2019)
    We present Atacama Large Millimetre Array and Atacama Compact Array observations of the Sunyaev-Zel'dovich effect in the z = 2 galaxy cluster Cl J1449+0856, an X-ray-detected progenitor of typical massive clusters in the present day Universe. While in a cleaned but otherwise untouched 92 GHz map of this cluster little to no negative signal is visible, careful subtraction of known sub-millimetre emitters in the uv plane reveals a decrement at 5 sigma significance. The total signal is -190 +/- 36 mu Jy, with a peak offset by 5 ''-9 '' (similar to 50 kpc) from both the X-ray centroid and the still-forming brightest cluster galaxy. A comparison of the recovered uv-amplitude profile of the decrement with different pressure models allows us to derive total mass constraints consistent with the similar to 6 x 10(13) M-circle dot estimated from X-ray data. Moreover, we find no strong evidence for a deviation of the pressure profile with respect to local galaxy clusters, although a slight tension at small-to-intermediate spatial scales suggests a flattened central profile, opposite to that seen in a cool core and possibly an AGN-related effect. This analysis of the lowest mass single SZ detection so far illustrates the importance of interferometers when observing the SZ effect in high-redshift clusters, the cores of which cannot be considered quiescent, such that careful subtraction of galaxy emission is necessary.