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International audienceIn this paper, we present a detector of transient acoustic signals that combines two powerful detection tools: a local wavelet analysis and higher-order statistical properties of the signals. The use of both techniques makes detection possible in low signal-to-noise ratio conditions, when other means of detection are no longer su1cient. The proposed algorithm uses the adapted wavelet packet transform. It leads to a partition of the signal which is 'optimal' according to a criterion that tests the Gaussian nature of the frequency bands. To get a time dependent detection curve, we perform a de-noising procedure on the wavelet coe1cients: The Gaussian coe1cients are set to zero. We then apply a classical method of detection on the time reconstructed de-noised signal. We study the performance of the detector in terms of experimental ROC curves. We show that the detector performs better than decompositions using other classical splitting criteria. In the last part, we present an application of the algorithm on real 8ow recordings of nuclear plant pipings. The detector indicates the presence of a missing body in the piping at some instants not seen with a classical energy detector

Permutation Entropy (PE) and Multiscale Permutation Entropy (MPE) have been extensively used in the analysis of time series searching for regularities. Although PE has been explored and characterized, there is still a lack of theoretical background regarding MPE. Therefore, we expand the available MPE theory by developing an explicit expression for the estimator’s variance as a function of time scale and ordinal pattern distribution. We derived the MPE Cramér–Rao Lower Bound (CRLB) to test the efficiency of our theoretical result. We also tested our formulation against MPE variance measurements from simulated surrogate signals. We found the MPE variance symmetric around the point of equally probable patterns, showing clear maxima and minima. This implies that the MPE variance is directly linked to the MPE measurement itself, and there is a region where the variance is maximum. This effect arises directly from the pattern distribution, and it is unrelated to the time scale or the signal length. The MPE variance also increases linearly with time scale, except when the MPE measurement is close to its maximum, where the variance presents quadratic growth. The expression approaches the CRLB asymptotically, with fast convergence. The theoretical variance is close to the results from simulations, and appears consistently below the actual measurements. By knowing the MPE variance, it is possible to have a clear precision criterion for statistical comparison in real-life applications.

In this paper, a natural extension of the Lempel-Ziv complexity for several finitetime sequences, defined on finite size alphabets is proposed. Some results on the defined joint Lempel-Ziv complexity are given, as well as properties in connection with the Lempel-Ziv complexity of the individual sequences. Also, some links with Shannon entropies are exhibited and, by analogy, some derived quantities are proposed. Lastly, the potential use of the extended complexities for data analysis is illustrated on random boolean networks and on a proposed multidimensional extension of the minority game.

Dynamic Light Scattering (DLS) is a widely used technique for measuring the size distributions of nano- and micro-particles dispersed in a liquid. The principle is based on the analysis of the temporal fluctuations of light scattered by the particles at a given scattering angle. However, single-angle DLS measurements may lack resolution and robustness, particularly for multimodal and/or polydisperse samples. Multi-angle Dynamic Light Scattering (MDLS) provides more robust, reproducible and accurate Particle Size Distributions (PSDs) than single-angle DLS. In this paper, a novel inversion method based on Bayesian inference is proposed for the estimation of the number PSD from MDLS measurements. The efficiency and robustness of this method is demonstrated through simulated and real data.

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