Wavelets and multifractal formalism for singular signals: Application to turbulence data

Muzy, Jean–François; Bacry, Emmanuel; Arnéodo, A.

doi:10.1103/physrevlett.67.3515

Cited by 731 publications

(619 citation statements)

References 12 publications

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“…See also [21,22,23], and [24] for a recent review. Onsager's prediction of near-singularities in turbulent velocity fields with Hölder index ≤ 1/3 has been confirmed by analysis of high-Reynolds number data from experiments and numerical simulations [25,26,27].…”

Section: H Alfvén (1942)mentioning

confidence: 68%

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The breakdown of Alfvén’s theorem in ideal plasma flows: Necessary conditions and physical conjectures

Eyink

Aluie

2006

Physica D: Nonlinear Phenomena

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This paper presents both rigorous results and physical theory on the breakdown of magnetic flux conservation for ideal plasmas, by nonlinear effects. Our analysis is based upon an effective equation for magnetohydrodynamic (MHD) modes at length-scales > ℓ, with smaller scales eliminated, as in renormalization-group methodology. We prove that flux-conservation can be violated for an arbitrarily small length-scale ℓ, and in the absence of any non-ideality, but only if singular current sheets and vortex sheets both exist and intersect in sets of large enough dimension. This result gives analytical support to and rigorous constraints on theories of fast turbulent reconnection. Mathematically, our theorem is analogous to

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Section: H Alfvén (1942)mentioning

confidence: 68%

“…The discontinuities in the tangential components u t , b t are related by (25), (26), which follow from (22), (23). Here v n denotes the velocity of the surface D normal to itself.…”

Section: Physical Breakdown Of Alfvén's Theorem?mentioning

confidence: 99%

The breakdown of Alfvén’s theorem in ideal plasma flows: Necessary conditions and physical conjectures

Eyink

Aluie

2006

Physica D: Nonlinear Phenomena

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“…By considering analyzing wavelets that make the microscope blind to low frequency trends, one can reveal and quantify the scale invariance properties of DNA walks [102,115,121]. In a previous work, by applying the so-called wavelet transform modulus maxima (WTMM) method [119,120,122] to the analysis of various genomic sequences mainly selected in the human genome, we have found that the fluctuations in the patchy landscapes of both coding and noncoding DNA walks are homogeneous with Gaussian statistics [102,115]. The main consequence of this result is the justification of using a single exponent, namely the Hurst or roughness exponent H , to characterize the underlying fractal organization of DNA sequences.…”

Section: Introductionmentioning

confidence: 99%

Wavelet Analysis of DNA Bending Profiles reveals Structural Constraints on the Evolution of Genomic Sequences

Audit

Vaillant

Arnéodo

et al. 2004

Journal of Biological Physics

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Abstract. Analyses of genomic DNA sequences have shown in previous works that base pairs are correlated at large distances with scale-invariant statistical properties. We show in the present study that these correlations between nucleotides (letters) result in fact from long-range correlations (LRC) between sequence-dependent DNA structural elements (words) involved in the packaging of DNA in chromatin. Using the wavelet transform technique, we perform a comparative analysis of the DNA text and of the corresponding bending profiles generated with curvature tables based on nucleosome positioning data. This exploration through the optics of the so-called 'wavelet transform microscope' reveals a characteristic scale of 100 − 200 bp that separates two regimes of different LRC. We focus here on the existence of LRC in the small-scale regime ( 200 bp). Analysis of genomes in the three kingdoms reveals that this regime is specifically associated to the presence of nucleosomes. Indeed, small scale LRC are observed in eukaryotic genomes and to a less extent in archaeal genomes, in contrast with their absence in eubacterial genomes. Similarly, this regime is observed in eukaryotic but not in bacterial viral DNA genomes. There is one exception for genomes of Poxviruses, the only animal DNA viruses that do not replicate in the cell nucleus and do not present small scale LRC. Furthermore, no small scale LRC are detected in the genomes of all examined RNA viruses, with one exception in the case of retroviruses. Altogether, these results strongly suggest that small-scale LRC are a signature of the nucleosomal structure. Finally, we discuss possible interpretations of these small-scale LRC in terms of the mechanisms that govern the positioning, the stability and the dynamics of the nucleosomes along the DNA chain. This paper is maily devoted to a pedagogical presentation of the theoretical concepts and physical methods which are well suited to perform a statistical analysis of genomic sequences. We review the results obtained with the so-called waveletbased multifractal analysis when investigating the DNA sequences of various organisms in the three kingdoms. Some of these results have been announced in B. Audit et al. [1,2].

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“…The concept of multifractality was developed in order to describe the scaling properties of singular measures and functions which exhibit the presence of various distinct scaling exponents in their different parts [19,20]. Soon the related formalism was successfully applied to characterize empirical data in many distant fields like turbulence [21,22], earth science [23], genetics [24,25,26], physiology [27,28,29] and, as already mentioned, in finance. The problem of detecting multifractality in real data is delicate, however.…”

Section: Introductionmentioning

confidence: 99%

Multifractality in the stock market: price increments versus waiting times

̧cimka

Kwapień

Dróżdż

2005

Physica A: Statistical Mechanics and its Applications

144

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By applying the multifractal detrended fluctuation analysis to the high-frequency tick-by-tick data from Deutsche Börse both in the price and in the time domains, we investigate multifractal properties of the time series of logarithmic price increments and inter-trade intervals of time. We show that both quantities reveal multiscaling and that this result holds across different stocks. The origin of the multifractal character of the corresponding dynamics is, among others, the long-range correlations in price increments and in inter-trade time intervals as well as the non-Gaussian distributions of the fluctuations. Since the transaction-to-transaction price increments do not strongly depend on or are almost independent of the inter-trade waiting times, both can be sources of the observed multifractal behaviour of the fixed-delay returns and volatility. The results presented also allow one to evaluate the applicability of the Multifractal Model of Asset Returns in the case of tick-by-tick data.

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Wavelets and multifractal formalism for singular signals: Application to turbulence data

Cited by 731 publications

References 12 publications

The breakdown of Alfvén’s theorem in ideal plasma flows: Necessary conditions and physical conjectures

The breakdown of Alfvén’s theorem in ideal plasma flows: Necessary conditions and physical conjectures

Wavelet Analysis of DNA Bending Profiles reveals Structural Constraints on the Evolution of Genomic Sequences

Multifractality in the stock market: price increments versus waiting times

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