Empirical evidences of a common multifractal signature in economic, biological and physical systems

Pont, Oriol; Turiel, Antonio; Pérez-Vicente, Conrad J.

doi:10.1016/j.physa.2009.01.041

Cited by 30 publications

(40 citation statements)

References 53 publications

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“…This method provides more stable and accurate results for discretised signals even at maximum resolution [30,34,38]. This approach provides the basic bricks of the so-called Microcanonical Multiscale Formalism (MMF) [22,37], which gives access to unveil key physical descriptors for turbulence and turbulent-like systems [10,21,23,24,35,37,39,40]. This way, estimating the singularity exponents of a signal also provides information about the physical process behind it.…”

Section: Introductionmentioning

confidence: 99%

Singularity analysis of digital signals through the evaluation of their unpredictable point manifold

Pont

Turiel

Yahia

2013

International Journal of Computer Mathematics

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The local singularity exponents of a signal are directly related to the distribution of information in it. This fact implies that accurate evaluation of such exponents opens the door to signal reconstruction and characterisation of the dynamical parameters of the process originating the signal. Many practical implications arise in a context of digital signal processing, since the information on singularity exponents is usable for compact encoding, reconstruction and inference. Since singularity exponents are conceptually associated to differential calculus, its evaluation in a digital context is not straightforward and it requires the calculation of the Unpredictable Point Manifold of the signal. In this paper, we present an algorithm for estimating the values of singularity exponents at every point of a digital signal of any dimension. We show that the key ingredient for robust and accurate reconstructibility performance lies on the definition of multiscale measures in the sense that they encode the degree of singularity and the local predictability at the same time.

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Section: Introductionmentioning

confidence: 99%

Singularity analysis of digital signals through the evaluation of their unpredictable point manifold

Pont

Turiel

Yahia

2013

International Journal of Computer Mathematics

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“…Recently, Pont et al (2009) searched for a common multifractal signature in six different systems. According to them, these six systems had the same shape of the singularity spectra exponents, f (α), after using the reduced singularity spectrum.…”

Section: Introductionmentioning

confidence: 99%

“…According to them, these six systems had the same shape of the singularity spectra exponents, f (α), after using the reduced singularity spectrum. The objective of this work is to discover the possible differences of the f (α) from two Brazilian sites (equatorial region and low latitude), without using the approach of Pont et al (2009) to obtain the common multifractal signatures from the two sites. Our approach is based on four data sets, and at least one relevant aspect is addressed in this paper, which is the comparative study for two Brazilian sites based on the multifractal characteristic at different time scales.…”

Section: Introductionmentioning

confidence: 99%

Multifractal analysis of vertical total electron content (VTEC) at equatorial region and low latitude, during low solar activity

et al. 2013

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Abstract. This paper analyses the multifractal aspects of the GPS data (measured during a period of low solar activity) obtained from two Brazilian stations: Belém (01.3 • S, 48.3 • W) and São José dos Campos (SJC) (23.2 • S, 45.9 • W). The results show that the respective geographic sites show important scaling differences as well as similarities when their multifractal signatures for vertical total electron content (VTEC) are compared. The f (α) spectra have a narrow shape for great scales, which indicates the predominance of deterministic phenomena, such as solar rotation (27 days) over intermittent phenomena. Furthermore, the f (α) spectra for both sites have a strong multifractality degree at small scales. This strong multifractality degree observed at small scales (1 to 12 h) at both sites is because the ionosphere over Brazil is a non-equilibrium system. The differences found were that Belém presented a stronger multifractality at small scales (1 h to 12 h) compared with SJC, particularly in 2006. The reason for this behaviour may be associated with the location of Belém, near the geomagnetic equator, where at this location the actions of X-rays, ultraviolet, and another wavelength from the Sun are more direct, strong, and constant throughout the whole year. Although the SJC site is near ionospheric equatorial anomaly (IEA) peaks, this interpretation could explain the higher values found for the intermittent parameter µ for Belém compared with SJC. Belém also showed the presence of one or two flattening regions for f (α) spectra at the same scales mentioned before. These differences and similarities also were interpreted in terms of the IEA content, where this phenomenon is an important source of intermittence due the presence of the VTEC peaks at ±20 • geomagnetic latitudes.

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“…The properties of physical cascading variables reflect the transfer of energy, or more generally information, taking place from larger scales to smaller ones. Recent developments in microcanonical framework for the computation of singularity exponents and the derivation of singularity spectra have lead to a sensible improvement in the numerical techniques for the determination of multiscale characteristics of real signals [1,2]. Experimental analysis on different real world signals, ranging from stock market time series to atmospheric perturbated optical path shows that these systems are not only found to be multiscale, but their singularity spectra are also coincident.…”

Section: Introductionmentioning

confidence: 99%

Inferring Information Across Scales in Acquired Complex Signals

Maji

Pont

Yahia

et al. 2013

Proceedings of the European Conference on Complex Systems 2012

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Abstract. Transmission of information across the scales of a complex signal has some interesting potential, notably in the derivation of subpixel information, cross-scale inference and data fusion. It follows the structure of complex signals themselves, when they are considered as acquisitions of complex systems. In this work we contemplate the problem of cross-scale information inference through the determination of appropriate multiscale decomposition. Our goal is to derive a generic methodology that can be applied to propagate information across the scales in a wide variety of complex signals. Consequently, we first focus on the determination of appropriate multiscale characteristics, and we show that singularity exponents computed in microcanonical formulations are much better candidates for the characterization of transitions in complex signals : they outperform the classical «linear filtering» approach of the state-of-the-art edge detectors (for the case of 2D signals). This is a fundamental topic as edges are usually considered as important multiscale features in an image. The comparison is done within the formalism of reconstructible systems. Critical exponents, naturally associated to phase transitions and used in complex systems methods in the framework of criticality are key notions in Statistical Physics that can lead to the complete determination of the geometrical cascade properties in complex signals. We study optimal multiresolution analysis associated to critical exponents through the concept of «optimal wavelet». We demonstrate the usefulness of multiresolution analysis associated to critical exponents in two decisive examples : the reconstruction of perturbated optical phase in Adaptive Optics (AO) and the generation of high resolution ocean dynamics from low resolution altimetry data.

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Empirical evidences of a common multifractal signature in economic, biological and physical systems

Cited by 30 publications

References 53 publications

Singularity analysis of digital signals through the evaluation of their unpredictable point manifold

Singularity analysis of digital signals through the evaluation of their unpredictable point manifold

Multifractal analysis of vertical total electron content (VTEC) at equatorial region and low latitude, during low solar activity

Inferring Information Across Scales in Acquired Complex Signals

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