Characterizations of the elements of generalized Hölder-Zygmund spaces by means of their representation

in Journal of Approximation Theory (2013), 172

We give three characterizations of the elements of generalized Hölder-Zygmund spaces. The first one, based on the Littlewood-Paley decomposition is already known, but the proof given here is much simpler ... [more ▼]

We give three characterizations of the elements of generalized Hölder-Zygmund spaces. The first one, based on the Littlewood-Paley decomposition is already known, but the proof given here is much simpler. The second one, based on the wavelet decompositions generalizes a result obtained by Jaffard and Meyer. The third one uses generalized interpolation spaces. These results naturally extend the ones holding for the classical Hölder-Zygmund spaces. The manuscript has been accepted for publication in Journal of Approximation Theory. [less ▲]

About Generic Properties of "Nowhere Analyticity"

Conference (2012, May 08)

A infinitely differentiable function f is is analytic at a point x if its Taylor series at this point converges to f on an open neighbourhood of x; if this is not the case, f has a singularity at x. A ... [more ▼]

A infinitely differentiable function f is is analytic at a point x if its Taylor series at this point converges to f on an open neighbourhood of x; if this is not the case, f has a singularity at x. A function with a singularity at each point of the interval is called nowhere analytic on the interval. In this talk, we show that the set of nowhere analytic functions is prevalent in the Frechet space C([0;1]). We get then a deeper result using Gevrey classes. [less ▲]

Several years El Niño forecast using a wavelet-based mode decomposition

Conference (2012, April 23)

Prevalence of ''nowhere analyticity''

in Studia Mathematica (2012), 210(3),

This note brings a complement to the study of genericity of functions which are nowhere analytic mainly in a measure-theoretic sense. We extend this study in Gevrey classes of functions.

A Wavelet Characterization for the Upper Global Hölder Index

in Journal of Fourier Analysis and Applications (2012), 18(4), 750-769

The upper Hölder index has been introduced to describe smoothness properties of a continuous function. It can be seen as the irregular counterpart of the usual Hölder index and has been used to ... [more ▼]

The upper Hölder index has been introduced to describe smoothness properties of a continuous function. It can be seen as the irregular counterpart of the usual Hölder index and has been used to investigate the behavior at the origin of the modulus of smoothness in many classical cases. In this paper, we prove a characterization of the upper Hölder index in terms of wavelet coefficients. This result is a first step in the estimation of this exponent using wavelet methods. [less ▲]

Estimation of the Sea Level Rise by 2100 Resulting from Changes in the Surface Mass Balance of the Greenland Ice Sheet

in Blanco, Juan; Kheradmand, Houshang (Eds.) Climate Change - Geophysical Foundations and Ecological Effects (2011)

We present here future projections of the Greenland climate performed by the regional climate model MAR coupled with a snow model and forced by two scenarios of greenhouse gas emissions from the global ... [more ▼]

We present here future projections of the Greenland climate performed by the regional climate model MAR coupled with a snow model and forced by two scenarios of greenhouse gas emissions from the global model CanESM2 of the next IPCC assessment report (AR5). Knowing that MAR forced by CanESM2 over the current climate (1970-1999) compares well with the reference MAR simulation performed by using the ERA-40 reanalysis as forcing, this gives us confidence in our future projections. For the RCP4.5 scenario (optimistic) and respectively RCP8.5 scenario (pessimistic), MAR projects a sea level rise in 2100 of 6.5 +/- 1.5 cm and respectively 14+/-2 cm as result of increasing surface melt of the Greenland ice sheet over 2000-2100. It is true that MAR projects a small increase of snowfall in the winter because the atmosphere will be warmer and therefore can contain more water vapor. But this is not sufficient to offset the acceleration of melt, notably for the scenario RCP8.5 which projects an increase of 10 °C in 2100 above the ice sheet. This work fits in the ICE2SEA project (http://www.ice2sea.eu) of the 7th Framework Program (FP7) which aims to improve the projections of the continental ice melting contribution to sea level rise. [less ▲]

A wavelet-based mode decomposition

in European Physical Journal B -- Condensed Matter (2011), 80

We propose a wavelet-based method for analyzing non-stationary data. The idea, inspired by the empirical mode decomposition, is to decompose a data set into a finite number of components, well separated in ... [more ▼]

We propose a wavelet-based method for analyzing non-stationary data. The idea, inspired by the empirical mode decomposition, is to decompose a data set into a finite number of components, well separated in the time-frequency plane, plus a residue, such that each component has a zero mean and is associated to one frequency only. When applied to climatic data, this method gives interesting results. [less ▲]

The 1958–2009 Greenland ice sheet surface melt and the mid-tropospheric atmospheric circulation

in Climate Dynamics (2011), 36(1 (2011)), 139-159

In order to assess the impact of the mid-tropospheric circulation over the Greenland ice sheet (GrIS) on surface melt, as simulated by the regional climate model MAR, an automatic Circulation type ... [more ▼]

In order to assess the impact of the mid-tropospheric circulation over the Greenland ice sheet (GrIS) on surface melt, as simulated by the regional climate model MAR, an automatic Circulation type classification (CTC) based on 500 hPa geopotential height from reanalyses is developed. General circulation correlates significantly with the surface melt anomalies for the summers in the period 1958–2009. The record surface melt events observed during the summers of 2007–2009 are linked to the exceptional persistence of atmospheric circulations favouring warm air advection. The CTC emphasizes that summer 500 hPa circulation patterns have changed since the beginning of the 2000s; this process is partly responsible for the recent warming observed over the GrIS. [less ▲]

Wavelet-based method to disentangle transcription-and replication-associated strand asymmetries in mammalian genomes

in Applied & Computational Harmonic Analysis (2010), 28

During genome evolution, the two strands of the DNA double helix are not subjected to the same mutation patterns. This mutation bias is considered as a by-product of replicative and transcriptional ... [more ▼]

During genome evolution, the two strands of the DNA double helix are not subjected to the same mutation patterns. This mutation bias is considered as a by-product of replicative and transcriptional activities. In this paper, we develop a wavelet-based methodology to analyze the DNA strand asymmetry profiles with the specific goal to extract the contributions associated with replication and transcription respectively. In a first step, we use an adapted N-shaped analyzing wavelet to perform a multi-scale pattern recognition analysis of the sum of the TA and GC skews along human chromosomes. This method provides an 1 Mbp characteristic objective segmentation of the human genome in skew domains of size, bordered by two putative replication origins recognized as large amplitude upward jumps in the noisy skew profile. In a second step, we use a least-square fitting procedure to disentangle, in these skew domains, the small-scale (the mean human gene size 30 kbp) square-like transcription component from the global N-shaped component induced by replication. When applying this procedure to the 22 human autosomes, we delineate 678 replication domains of mean length L = 1.2 ± 0.6 Mbp spanning 33.8% of the human genome and we predict 1062 replication origins. When investigating the distribution of transcription-associated skew inside the replication N-domains, we reveal some dependence upon the distance to the putative replication origins located at N- domain extremities, the closer the genes to the origin, the larger their transcription bias as the signature of a higher transcriptional activity in the germ-line. As a comparative analysis, we further apply our wavelet-based methodology to skew profiles along the mouse chromosomes. The striking similarity of the results in human and mouse indicates that the remarkable gene organization observed inside the human replication N-domains is likely to be a general feature of mammalian genomes. [less ▲]

Multi-Months Cycles Observed in Climatic Data

in Simard, Suzanne (Ed.) Climate Change and Variability (2010)

Climatic variations happen at all time scales and since the origins of these variations are usually of very complex nature, climatic signals are indeed chaotic data. The identification of the cycles ... [more ▼]

Climatic variations happen at all time scales and since the origins of these variations are usually of very complex nature, climatic signals are indeed chaotic data. The identification of the cycles induced by the natural climatic variability is therefore a knotty problem, yet the knowing of these cycles is crucial to better understand and explain the climate (with interests for weather forecasting and climate change projections). Due to the non-stationary nature of the climatic time series, the simplest Fourier-based methods are inefficient for such applications (see e.g. Titchmarsh (1948)). This maybe explains why so few systematic spectral studies have been performed on the numerous datasets allowing to describe some aspects of the climate variability (e.g. climatic indices, temperature data). However, some recent studies (e.g. Matyasovszky (2009); Paluš & Novotná (2006)) show the existence of multi-year cycles in some specific climatic data. This shows that the emergence of new tools issued from signal analysis allows to extract sharper information from time series. Here, we use a wavelet-based methodology to detect cycles in air-surface temperatures obtained from worldwide weather stations, NCEP/NCAR reanalysis data, climatic indices and some paleoclimatic data. This technique reveals the existence of universal rhythms associated with the periods of 30 and 43 months. However, these cycles do not affect the temperature of the globe uniformly. The regions under the influence of the AO/NAO indices are influenced by a 30 months period cycle, while the areas related to the ENSO index are affected by a 43 months period cycle; as expected, the corresponding indices display the same cycle. We next show that the observed periods are statistically relevant. Finally, we consider some mechanisms that could induce such cycles. This chapter is based on the results obtained in Mabille & Nicolay (2009); Nicolay et al. (2009; 2010). [less ▲]