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We give general mathematical results concerning oscillating singularities and we study examples of functions composed only of oscillating singularities. These functions are deened by explicit coeecients on an orthonormal wavelet basis. We compute their HH older regularity and oscillation at every point and we deduce their spectrum of oscillating(More)
The duplication of mammalian genomes is under the control of a spatiotemporal program that orchestrates the positioning and the timing of firing of replication origins. The molecular mechanisms coordinating the activation of about [Formula: see text] predicted origins remain poorly understood, partly due to the intrinsic rarity of replication bubbles,(More)
  • J.-F Muzy, D Sornette, J Delour, A Arneodo
  • 2001
We extend and test empirically the multifractal model of asset returns based on a multi-plicative cascade of volatilities from large to small time scales. Inspired by an analogy between price dynamics and hydrodynamic turbulence [Ghashghaie et al., 1996; Arneodo et al., 1998a], it models the time scale dependence of the probability distribution of returns(More)
[1] We reexamine the scaling structure of temporal rainfall using wavelet-based methodologies which, as we demonstrate, offer important advantages compared to the more traditional multifractal approaches such as box counting and structure function techniques. In particular, we explore two methods based on the Continuous Wavelet Transform (CWT) and the(More)
BACKGROUND The Intergenic Breakage Model, which is the current model of structural genome evolution, considers that evolutionary rearrangement breakages happen with a uniform propensity along the genome but are selected against in genes, their regulatory regions and in-between. However, a growing body of evidence shows that there exists regions along(More)
We explore the large-scale behavior of nucleotide compositional strand asymmetries along human chromosomes. As we observe for 7 of 9 origins of replication experimentally identified so far, the (TA+GC) skew displays rather sharp upward jumps, with a linear decreasing profile in between two successive jumps. We present a model of replication with well(More)
Advances in genomic studies have led to significant progress in understanding the epigenetically controlled interplay between chromatin structure and nuclear functions. Epigenetic modifications were shown to play a key role in transcription regulation and genome activity during development and differentiation or in response to the environment.(More)
We generalize the wavelet transform modulus maxima (WTMM) method to multifractal analysis of 3D random fields. This method is calibrated on synthetic 3D monofractal fractional Brownian fields and on 3D multifractal singular cascade measures as well as their random function counterpart obtained by fractional integration. Then we apply the 3D WTMM method to(More)
Singular behavior of functions are generally characterized by their HH older exponent. However, we show that this exponent poorly characterizes oscillating singularities. We thus introduce a second exponent that that accounts for the oscillations of a singular behavior and we give a characterization of this exponent using the wavelet transform. We then(More)