Nicolay, S. (26 September 2024). *Functional spaces defined via Boyd functions* [Paper presentation]. Function Spaces, Differential Operators, and Nonlinear Analysis, Oberhof, Germany.

In this work, we present several generalized functional spaces, primarily the $T_p^u$ spaces, originally introduced in essence by Calderón and Zygmund through the lens of Boyd functions. We provide...

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Faulx, E., Fettweis, X., Mabille, G., & Nicolay, S. (April 2024). *Wavelet-Induced Mode Extraction procedure: Application to climatic data* [Poster presentation]. EGU General Assembly 2024, Vienne, Austria.

The Wavelet-Induced Mode Extraction procedure (WIME) was developed drawing inspiration from Empirical Mode Decomposition. The concept involves decomposing the signal into modes, each presenting a c...

Lamby, T., & Nicolay, S. (February 2024). Interpolation with a function parameter from the category point of view. *Journal of Functional Analysis, 286* (3), 110249. doi:10.1016/j.jfa.2023.110249

We generalize here the notion of interpolation space of given exponent by replacing this exponent with Boyd functions. In particular, this approach leads to the usual interpolation method with a fu...

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Molla, A., & Nicolay, S. (February 2024). A functional definition of polynomial for connected Lie groups. *Journal of Mathematical Analysis and Applications, 530* (1), 127679. doi:10.1016/j.jmaa.2023.127679

In this paper, we look at the local and global solutions of the Fréchet functional equation for connected Lie groups. In particular, we give a characterization of these solutions using the lower ce...

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Bennabi, S., & Nicolay, S. (2024). Aconstruction of the real numbers based on Weierstrass's approach. *Rocky Mountain Journal of Mathematics*.

In this paper, we put forth a construction of real numbers rooted in theWeierstraß approach. We depart from the original method by replacing the aliquot parts with rational numbers and employing ep...

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Kleyntssens, T., & Nicolay, S. (2023). Generalized Sν spaces. *Mathematische Nachrichten*. doi:10.1002/mana.202200133

In this work, we introduce a generalization of the Snu spaces underlying a multifractal formalism for non-concave spectra. We prove among other things that the essential topological properties of t...

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Molla, A., & Nicolay, S. (2023). The monomial functional equation for connected Lie groups. *Aequationes Mathematicae*. doi:10.1007/s00010-023-00969-8

In this work, we present the Cauchy functional equation in the context of connected Lie groups. We consider two generalizations of this equation with higher orders of the finite difference.

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Nicolay, S. (January 2023). Sur les démonstrations du théorème de Borel-Lebesgue. *Quadrature: Magazine de Mathématiques Pures et Appliquées, 127*, 35-39.

Nous considérons ici le théorème de Borel-Lebesgue sur le plan historique. En particulier, nous présentons les démonstrations essentiellements dues à Cousin et Lebesgue. Finalement, nous donnons un...

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Lamby, T., & Nicolay, S. (30 August 2022). Some remarks on the Boyd functions related to the admissible sequences. *Zeitschrift für Analysis und ihre Anwendungen, 41*, 211-227. doi:10.4171/zaa/1705

In this paper, we discuss the existing relations between the Boyd functions and the admissible sequences, with a particular interest to the Boyd indices. We introduce several results binding these ...

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Loosveldt, L., & Nicolay, S. (01 July 2022). Some Prevalent Sets in Multifractal Analysis: How Smooth is Almost Every Function in $T_p^\alpha (x)$. *Journal of Fourier Analysis and Applications, 28* (4). doi:10.1007/s00041-022-09951-5

We present prevalent results concerning generalized versions of the $T_p^\alpha$ spaces, initially introduced by Calderón and Zygmund. We notably show that the logarithmic correction appearing in t...

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Lamby, T., & Nicolay, S. (20 June 2022). *Generalized Interpolation: a Functorial Point of View* [Paper presentation]. WFCA22-VALLADOLID, Valladolid, Spain.

Many spaces, such as the Besov spaces, naturally arise through the (real)
interpolation theory. A classical generalization of these interpolation methods has been introduced in
the eighties. The id...

Nicolay, S. (08 June 2022). *Statistical results for the multifractal formalism based on the $S^\nu$ spaces* [Paper presentation]. Scale Invariance and Randomness, Villeneuve d'Ascq, France.

Computing the spectrum of singularities of a real-life signal by using the definition is impossible. One rather uses an indirect way to compute it: the multifractal formalism. The first multifracta...

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Kleyntssens, T., & Nicolay, S. (2022). From the Brownian motion to a multifractal process using the Lévy-Ciesielski construction. *Statistics and Probability Letters, 186C*, 109450. doi:10.1016/j.spl.2022.109450

We give a construction of a multifractal process with prescribed Hölder exponents starting from the Lévy–Ciesielski construction of a Brownian motion. We also show that this method preserves the la...

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Nicolay, S. (27 September 2021). *A refinement of the Snu-based multifractal formalism* [Paper presentation]. Journées annuelles du GDR AMA, Porquerolles, France.

In this work, we introduce a generalization of the Snu spaces underlying a multifractal formalism for non-concave spectra. We prove that the essential topological properties of the Snu spaces can b...

Loosveldt, L., & Nicolay, S. (09 August 2021). Generalized spaces of pointwise regularity: toward a general framework for the WLM. *Nonlinearity, 34*, 6561-6586. doi:10.1088/1361-6544/ac1724

In this work we generalize the spaces ${T}_{u}^{p}$ introduced by Calderón and Zygmund using pointwise conditions emanating from generalized Besov spaces. We give conditions binding the functions b...

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Molla, A., & Nicolay, S. (27 February 2021). The Fréchet Functional Equation for Lie Groups. *Mediterranean Journal of Mathematics, 18* (2). doi:10.1007/s00009-021-01701-z

We study a generalization of the Fréchet functional equation in the setting of Lie groups. We provide theorems that give a description of the solutions and their regularity. These properties are ap...

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Loosveldt, L., & Nicolay, S. (October 2020). Generalized T_u^p spaces: On the trail of Calderón and Zygmund. *Dissertationes Mathematicae, 554*. doi:10.4064/dm798-4-2020

We generalize the T_u^p spaces introduced by Calderón and Zygmund and show that most of
the results obtained in their study of the pointwise estimates for solutions of elliptic partial
differential...

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Nicolay, S. (03 October 2019). *A time-filling talk about fractals* [Paper presentation]. Journées GdR analyse multifractale 2019, Vielsalm, Belgium.

We presents here two applications of the multifractal formalism for functions: the first one concerns DNA sequences and the second one temperature data.

Loosveldt, L., & Nicolay, S. (October 2019). Some equivalent definitions of Besov spaces of generalized smoothness. *Mathematische Nachrichten, 292* (10), 2262-2282. doi:10.1002/mana.201800111

In this paper, we present some alternative definitions of Besov spaces of general-ized smoothness, defined via Littlewood–Paley-type decomposition, involving weakderivatives, polynomials, convoluti...

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Allan, M., Deliège, A., Verheyden, S., Nicolay, S., Quinif, Y., & Fagel, N. (2019). Corrigendum to “Evidence for solar influence in a Holocene speleothem record (Père Nöel cave, SE Belgium)” (Quaternary Science Reviews (2018) 192 (249–262), (S0277379118302038) (10.1016/j.quascirev.2018.05.039)). *Quaternary Science Reviews*. doi:10.1016/j.quascirev.2019.02.024

When this paper was originally published, there was an error in Fig. 7g. Indeed the curve of percentage of hematite-stained grains measured on North Atlantic MC52-VM29-191 core, published by Bond e...

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Nicolay, S. (2019). Sur la notion de dimension. *Quadrature: Magazine de Mathématiques Pures et Appliquées, 111*, 31-36.

Nous proposons ici quelques considérations sur la notion de dimension, inspirées par la notion physique renvoyant au nombre de degrés de liberté. L’objectif est d’introduire de manière naturelle la...

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Loosveldt, L., & Nicolay, S. (07 November 2018). *Generalized regularity spaces : toward the detection of a logarithmic correction in multi fractal analysis* [Paper presentation]. FNRS Contact Group "Wavelets and applications", Bruxelles, Belgium.

The aim of the talk will first be to present the notion of Hölder pointwise spaces and some functions that are studied with this notion. Then, we will introduce generalization of these spaces and e...

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Molla, A., Nicolay, S., & Schneiders, J.-P. (October 2018). On some generalizations of the Fréchet functional equations. *Journal of Mathematical Analysis and Applications, 466* (2), 1400-1409. doi:10.1016/j.jmaa.2018.06.058

In this paper we study the Fréchet functional equation in the n-dimensional Euclidian space as well as in the context of distributions. We also generalizethe Cauchy functional equation for distribu...

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Loosveldt, L., & Nicolay, S. (19 September 2018). *Generalized Regularity spaces. Part I: A wavelet-based approach* [Paper presentation]. Journées GdR Analyse Multifractale 2018, Domaine de Chalès, France.

The aim of this talk is to convince the audience of the interest of the generalized regularity spaces in the field of the multifractal analysis.

Editorial reviewed

Loosveldt, L., & Nicolay, S. (19 September 2018). *Generalized regularity spaces. Part II: on the trail of Calderon and Zygmund* [Paper presentation]. Journées GdR Analyse Multifractale 2018, Domaine de Chalès, France.

We present a result about the regularity of the solution of an elliptic partial differentiable equation if we assume regularity condition for the coefficients of this equation.

Editorial reviewed

Allan, M., Deliège, A., Verheyden, S., Nicolay, S., & Fagel, N. (2018). Evidence for solar influence in a Holocene speleothem record (Père Noël cave, SE Belgium). *Quaternary Science Reviews*. doi:10.1016/j.quascirev.2018.05.039

We present a decadal-centennial scale Holocene climate record based on trace elements contents from a 65cm stalagmite from Belgian Père Noël cave. “Père Noël” (PN) stalagmite covers the last 12.7 k...

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Nicolay, S. (2018). *Analyse Mathématique : Fonctions définies sur une partie de la droite réelle*. Paris, France: Ellipses.

Ce livre s’adresse aux étudiants désireux d’obtenir des bases rigoureuses en analyse. L’auteur s’est donné pour objectif d’aborder la théorie des fonctions à une variable de manière complète et dét...

Kreit, D., & Nicolay, S. (May 2018). Generalized Pointwise Hoelder Spaces Defined via Admissible Sequences. *Journal of Function Spaces, 2018*, 11. doi:10.1155/2018/8276258

We introduce in this paper a generalization of the pointwise Hölder spaces. We give alternative definitions of these spaces, look at their relationship with the wavelets, and introduce a notion of ...

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Kleyntssens, T., Reynaerts, L., & Nicolay, S. (12 April 2018). *A study of histograms of wavelet coefficients of the Mars topography to determine its scaling properties* [Poster presentation]. European Geosciences Union General Assembly 2018.

Recently, the scaling properties of Mars topography have been analyzed through the Wavelet Leaders Method. The signals studied have often a few values radically different from the rest of the signa...

Deliège, A., & Nicolay, S. (April 2018). *Analysis and indication on long-term forecasting of the Oceanic Niño index with wavelet-induced components* [Poster presentation]. European Geosciences Union General Assembly 2018, Wien, Austria.

The present work provides an analysis and a long-term forecasting scheme of the Oceanic Niño Index (ONI) using the continuous wavelet transform. First, it appears that oscillatory components with ...

Reynaerts, L., Fettweis, X., & Nicolay, S. (April 2018). *Global warming and natural variability* [Poster presentation]. European Geosciences Union General Assembly 2018, Wien, Austria.

In this work, we show that the lull periods of the warming episodes observed in the surface temperatures (GISS,...) can be explained through the natural variability of the climate. To do so, we use...

Kleyntssens, T., Esser, C., & Nicolay, S. (2018). An algorithm for computing non-concave multifractal spectra using the Sν spaces. *Communications in Nonlinear Science and Numerical Simulation, 56*, 526-543. doi:10.1016/j.cnsns.2017.08.029

We present an implementation of a multifractal formalism based on the Sν spaces and show that it effectively gives the right Hölder spectrum in numerous cases. In particular, it allows to recover n...

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Deliège, A., & Nicolay, S. (11 September 2017). Extracting oscillating components from nonstationary time series: A wavelet-induced method. *Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 96*. doi:10.1103/PhysRevE.96.033307

This paper consists in the description and application of a method called wavelet-induced mode extraction (WIME) in the context of time-frequency analysis. WIME aims to extract the oscillating comp...

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Esser, C., Kleyntssens, T., & Nicolay, S. (September 2017). A multifractal formalism for non-concave and non-increasing spectra: the leaders profile method. *Applied and Computational Harmonic Analysis, 43* (2), 269-291. doi:10.1016/j.acha.2015.12.006

We present an implementation of a multifractal formalism based on the types of histogram of wavelet leaders. This method yields non-concave spectra and is not limited to their increasing part. We s...

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Allan, M., Deliège, A., Nicolay, S., verheyden, S., & Fagel, N. (2017). *Does Belgian Holocene speleothem record solar forcing and cold events?* ORBi-University of Liège. https://orbi.uliege.be/handle/2268/213231. doi:10.5194/cp-2017-91

We present a decadal-centennial scale Holocene climate record based on trace elements contents from a 65 cm stalagmite (Père Noël) from Belgian Père Noël cave. Père Noël (PN) stalagmite covers the ...

Allan, M., Deliège, A., Nicolay, S., verheyden, S., & Fagel, N. (12 May 2017). *Belgian speleothem records Holocene cold events?* [Poster presentation]. PAGES-OSM, Zaragoza, Spain.

Speleothem is now regarded as valuable archive of climatic conditions on the continents, offering a number of advantages relative to other continental climate proxy recorders such as lake sediments...

Deliège, A., & Nicolay, S. (February 2017). Analysis and indications on long-term forecasting of the Oceanic Niño Index with wavelet-induced components. *Pure and Applied Geophysics, 174* (4), 1815-1826. doi:10.1007/s00024-017-1491-4

The present paper provides an analysis and a long-term forecasting scheme of the Oceanic Niño Index (ONI) using the continuous wavelet transform. First, it appears that oscillatory components with ...

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Clausel, M., & Nicolay, S. (2017). A Weak Local Irregularity Property in Sν Spaces. *Mediterranean Journal of Mathematics, 14* (3), 102. doi:10.1007/s00009-017-0902-1

It has been shown that, from the prevalence point of view, elements of the Sν spaces are almost surely multifractal, while the Hölder exponent at almost every point is almost surely equal to the ma...

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Deliège, A.* , Kleyntssens, T.* , & Nicolay, S. (2017). Mars Topography Investigated Through the Wavelet Leaders Method: a Multidimensional Study of its Fractal Structure. *Planetary and Space Science, 136C*, 46-58. doi:10.1016/j.pss.2016.12.008

This work examines the scaling properties of Mars topography through a wavelet-based formalism. We conduct exhaustive one-dimensional (both longitudinal and latitudinal) and two-dimensional studies...

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Kleyntssens, T., & Nicolay, S. (19 September 2016). *Raffinement de l'estimation asymptotique de l'exposant de Hölder* [Paper presentation]. Journées du GDR Analyse Multifractale - Avignon 2016.

Dans cet exposé, nous proposons une nouvelle approche basée sur les ondelettes (via les espaces Snu) permettant d'étudier plus finement la régularité Höldérienne d'une fonction

Nicolay, S., & Simons, L. (June 2016). About the multifractal nature of Cantor's bijection: Bounds for the Hölder exponent at almost every irrational point. *Fractals, 24* (2), 1650014-1 - 1650014-9. doi:10.1142/S0218348X16500146

In this note, we investigate the regularity of Cantor’s one-to-one mapping between the irrational numbers of the unit interval and the irrational numbers of the unit square. In particular, we explo...

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Kleyntssens, T., Kreit, D., & Nicolay, S. (12 April 2016). *A Refined Method for Estimating the Global Hölder Exponent* [Paper presentation]. 13th International Conference on Information Technology : New Generations, Las Vegas, United States - Nevada.

We give a wavelet characterization of the generalized Hölder spaces and show how this result can be applied to detect logarithmic corrections appearing in Brownian processes.

Deliège, A., Kleyntssens, T., & Nicolay, S. (April 2016). *Poster EGU 2016: Mars Topography Investigated Through the Wavelet Leaders Method* [Poster presentation]. European Geosciences Union General Assembly 2016, Vienne, Austria.

This work examines the scaling properties of Mars topography through a wavelet-based formalism. We conduct exhaustive one-dimensional (both longitudinal and latitudinal) and two-dimensional studies...

Deliège, A., & Nicolay, S. (2016). A New Wavelet-Based Mode Decomposition for Oscillating Signals and Comparison with the Empirical Mode Decomposition. In *Information Technology: New Generations* (pp. 959-968). Switzerland: Springer. doi:10.1007/978-3-319-32467-8_83

We introduce a new method based on wavelets (EWMD) for decomposing a signal into quasi-periodic oscillating components with smooth time-varying amplitudes. This method is inspired by both the “clas...

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Deliège, A., & Nicolay, S. (April 2016). *[Beamer] A New Wavelet-Based Mode Decomposition for Oscillating Signals and Comparison with the Empirical Mode Decomposition* [Paper presentation]. 13th International Conference on Information Technology : New Generations, Las Vegas, United States - Nevada.

We introduce a new method based on wavelets (EWMD)
for decomposing a signal into quasi-periodic oscillating components with
smooth time-varying amplitudes. This method is inspired by both the
“clas...

Kleyntssens, T., Deliège, A., & Nicolay, S. (2016). The Fractal Nature of Mars Topography Analyzed via the Wavelet Leaders Method. In *Information Technology: New Generations*. Switzerland: Springer. doi:10.1007/978-3-319-32467-8_117

This paper studies the scaling properties of Mars topography based on Mars Orbiter Laser Altimeter (MOLA) data through the wavelet leaders method (WLM). This approach shows a scale break at 15 km. ...

Peer reviewed

Nicolay, S., & Kreit, D. (2016). A Refined Method for Estimating the Global Hölder Exponent. In S. Latifi (Ed.), *Information Technology: New Generations* (1st ed, pp. 949-958). Switzerland: Springer. doi:10.1007/978-3-319-32467-8_82

In this paper, we recall basic results we have obtained about generalized Hölder spaces and present a wavelet characterization that holds under more general hypothesis than previously stated. This ...

Peer reviewed

Kleyntssens, T., & Nicolay, S. (23 March 2016). *Wavelet-based Methods to Study the Regularity of a Signal: from Theory to Practice* [Paper presentation]. BeNeLuxMC 2016 : KWG prize for PhD student.

In this talk, I use the notion of wavelet to design multifractal formalisms. I present the theoritical results obtained on the generalized Snu spaces and I show the utility of these generalization....

Kreit, D., & Nicolay, S. (2016). *Some characterizations about Generalized Hölder-Zygmund Spaces Λ_{σ,N}^{α}(R^d)*. (Version en attente de soumission 02/2016). ORBi-University of Liège. https://orbi.uliege.be/handle/2268/196532.

Generalized Hölder-Zygmund spaces $\Lambda_{\sigma, N}^{\alpha}(\R^{d})$ were recently introduced and are based on a generalization of Besov spaces. Under some conditions, generalized Hölder-Zygmun...

Bastin, F., Nicolay, S., & Simons, L. (2016). About the Uniform Hölder Continuity of Generalized Riemann Function. *Mediterranean Journal of Mathematics, 13* (1), 101-117. doi:10.1007/s00009-014-0501-3

In this paper, we study the uniform H\"{o}lder continuity of the generalized Riemann function~$R_{\alpha,\beta}$ (with $\alpha>1$ and $\beta>0$) defined by
\[
R_{\alpha,\beta}(x)=\sum_{n=1}^{+\inft...

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Deliège, A., & Nicolay, S. (2016). Köppen–Geiger Climate Classification for Europe Recaptured via the Hölder Regularity of Air Temperature Data. *Pure and Applied Geophysics, 173*, 2885-2898. doi:10.1007/s00024-016-1339-3

In this paper, we make use of the monoHölder nature of surface air temperature data to recapture the Köppen–Geiger climate classification in Europe. Using data from the European climate Assessment ...

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Kleyntssens, T., Deliège, A., & Nicolay, S. (2016). *The Fractal Nature of Mars Topography Analyzed via the Wavelet Leaders Method* [Poster presentation]. 13th International Conference on Information Technology : New Generations.

This work studies the scaling properties of Mars topography based on Mars Orbiter Laser Altimeter (MOLA) data through the wavelet leaders method (WLM). This approach shows a scale break at 15 km. A...

Nicolay, S. (2016). Une construction des nombres hyperréels. *Quadrature: Magazine de Mathématiques Pures et Appliquées, 102*, 20-23.

Nous proposons ici une brève construction classique des nombres hyperréels à partir des nombres réels. Dans un soucis de pédagogie, nous omettons les détails les plus techniques. La présentation es...

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Kreit, D., & Nicolay, S. (24 September 2015). *On generalized Hölder spaces* [Paper presentation]. Fractals and Related Fields, Porquerolles, France.

We introduce generalized pointwise Hölder spaces as the point wise version of generalized uniform Hölder spaces. These last ones can be seen as a special case of generalized Besov spaces.

Kleyntssens, T., Nicolay, S., Vandomme, E., & Rigo, M. (23 September 2015). *Use of the wavelet theory as a tool to investigate the l-abelian complexity of a sequence* [Poster presentation]. Fractals and Related Fields III, Porquerolles, France.

The concept of k-automatic sequences is at the intersection of number theory and formal language theory. It has been generalized by the notion of k-regularity that allows to study sequences with va...

Deliège, A., & Nicolay, S. (08 September 2015). *A wavelet-based mode decomposition compared to the EMD* [Poster presentation]. GRETSI 2015, Lyon, France.

We introduce a new method based on wavelets for decomposing a signal into quasi-periodic oscillating components with smooth time-varying amplitudes.
This method is inspired by both the "classic" wa...

Kleyntssens, T., & Nicolay, S. (08 September 2015). *The leaders profile method: detection of distinct processes in a signal* [Poster presentation]. Gretsi 2015.

The leaders profile method is a multifractal formalism that allows to compute non-concave and non-increasing spectra. Our implementation can detect the presence of distinct processes in a signal. W...

Peer reviewed

Kleyntssens, T., & Nicolay, S. (16 June 2015). *A generalization of the Snu spaces: getting rid of dyadic scales* [Paper presentation]. Workshop on Functional Analysis Valencia 2015 on the occasion of the 60th birthday of José Bonet.

The Snu spaces have been introduced by S. Jaffard to develop a new multifractal formalism that allows to improve the study of irregular functions. This type of formalism is connected to Besov space...

Deliège, A., Nicolay, S., & Fettweis, X. (June 2015). *A forecasting method using a wavelet-based mode decomposition and application to the ENSO index* [Paper presentation]. 35th International Symposium on Forecasting, Riverside, California, United States.

This work consists of a presentation and applications of a forecasting methodology based on a mode decomposition performed through a continuous wavelet transform. The idea is comparable to the Four...

Simons, L., & Nicolay, S. (25 May 2015). *About the Regularity of Cantor's Bijection* [Paper presentation]. Automatic Sequences 2015, Liège, Belgium.

In 1878, Cantor proved that there exists a one-to-one correspondence between the points of the unit line segment [0,1] and the points of the unit square [0,1]². Since this application is defined vi...

Deliège, A., Nicolay, S., & Fettweis, X. (13 April 2015). *EGU2015 - ENSO forecast using a wavelet-based mode decomposition* [Paper presentation]. European Geosciences Union General Assembly 2015, Vienne, Austria.

The aim of this work is to introduce a new method for forecasting major El Niño/ La Niña events with the use of a wavelet-based mode decomposition. These major events are related to sea surface tem...

Deliège, A., Nicolay, S., & Fettweis, X. (December 2014). *ENSO forecast using a wavelet-based mode decomposition* [Poster presentation]. 577 WE-Heraeus-Seminar on Health, Energy & Extreme Events in a Changing Climate, Bad Honnef, Germany.

We introduce a new method for forecasting major El Niño/ La Niña events based on a wavelet mode decomposition. This methodology allows us to approximate the ENSO time series with a superposition of...

Kleyntssens, T., & Nicolay, S. (23 September 2014). *De l’importance des échelles dyadiques dans les espaces Snu* [Paper presentation]. Journées du GDR Analyse Multifractale.

Le but de l’analyse multifractale est de fournir une méthode permettant d’approximer le spectre de singularités d’une fonction. En 1985, Frisch et Parisi ont proposé un premier formalisme. D'autres...

Simons, L., Bastin, F., & Nicolay, S. (22 September 2014). *Fonction de Riemann généralisée* [Paper presentation]. Journées du GDR Analyse Multifractale, Nouan-le-Fuzelier, France.

Dans cet exposé, nous étudions la régularité de la fonction de Riemann généralisée~$R_{\alpha,\beta}$ (avec $\alpha>1$ et $\beta>0$) définie par
\[
R_{\alpha,\beta}(x)=\sum_{n=1}^{+\infty}\frac{\si...

Deliège, A., & Nicolay, S. (20 August 2014). *A multifractal analysis of air temperature signals based on the wavelet leaders method* [Paper presentation]. Seventh Solar Information Processing Workshop, La Roche en Ardenne, Belgium.

We present the wavelet leaders method (introduced by S. Jaffard) as a tool to study the Hölder regularity of signals, which is closely related to some functional spaces. We use the associated multi...

Deliège, A., & Nicolay, S. (25 June 2014). *A wavelet leaders-based climate classification of European surface air temperature signals* [Paper presentation]. International work-conference on time series analysis, Grenade, Spain.

We present the wavelet leaders method as a tool to study the pointwise regularity of signals, which is closely related to some functional spaces. We use the associated multifractal formalism to sho...

Deliège, A., & Nicolay, S. (2014). A wavelet leaders-based climate classification of European surface air temperature signals. In G. Ruiz Garcia & I. Rojas Ruiz (Eds.), *Proceedings of the International work-conference on Time Series: Volume 1, Granada 25-27 June 2014* (pp. 40-51). Grenade, Spain: Copicentro Granada S.L.

We explain the wavelet leaders method, a tool to study the pointwise regularity of signals, which is closely related to some functional spaces. We use the associated multifractal formalism to show ...

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Deliège, A., & Nicolay, S. (19 June 2014). *A wavelet-based analysis of surface air temperature regularity* [Paper presentation]. Séminaire interne entre doctorants, Liège, Belgium.

The aim of the talk is to present the "wavelet transform microscope" and the wavelet leaders method to show that surface air temperature signals of weather stations selected in Europe are monofract...

Deliège, A., & Nicolay, S. (06 June 2014). *A wavelet-based analysis of surface air temperature variability* [Paper presentation]. MeteoClim 2014, Antwerp's Ecohuis, Belgium.

We study the Hölder regularity of surface air temperature signals using the wavelet leaders method (WLM). This method has been successfully applied in several domains such as DNA analysis, fully de...

Deliège, A., & Nicolay, S. (22 May 2014). *Multifractal analysis of air temperature signals using the wavelet leaders method* [Paper presentation]. Groupe de contact FNRS "Wavelets and Applications", Bruxelles (ULB), Belgium.

We use the discrete "wavelet transform microscope" to show that the surface air temperature signals of weather stations selected in Europe are monofractal. This study reveals that the information o...

Esser, C., Kleyntssens, T., Bastin, F., & Nicolay, S. (22 May 2014). *Detection of non concave and non increasing multifractal spectra using wavelet leaders (Part I)* [Paper presentation]. FNRS Contact Group “Wavelets and Applications”.

Multifractal analysis is concerned with the study of very irregular signals. For such functions, the pointwise regularity may change widely from a point to another. Therefore, it is more interestin...

Kleyntssens, T., Esser, C., & Nicolay, S. (22 May 2014). *Detection of non concave and non increasing multifractal spectra using wavelet leaders (Part II)* [Paper presentation]. FNRS Contact Group “Wavelets and Applications”.

This talk follows "Detection of non concave and non increasing multifractal spectra using wavelet leaders (Part I)" given by Céline Esser. A multifractal formalism is a numerically computable formu...

Deliège, A., & Nicolay, S. (25 March 2014). *A multifractal-based climate analysis* [Paper presentation]. Fractal Geometry and Stochastics V, Tabarz, Germany.

This work consists of a multifractal analysis of surface air temperature in Western and Eastern Europe. The wavelet leaders method enables us to exhibit the monofractal nature of these signals. The...

Esser, C., Kleyntssens, T., Nicolay, S., & Bastin, F. (25 March 2014). *A new multifractal formalism based on wavelet leaders : detection of non concave and non increasing spectra (Part I)* [Paper presentation]. Fractal Geometry and Stochastics V, Tabarz, Germany.

Multifractal analysis is concerned with the study of very irregular signals. For such functions, the pointwise regularity may change widely from a point to another. Therefore, it is more interestin...

Kleyntssens, T., Esser, C., & Nicolay, S. (25 March 2014). *A new multifractal formalism based on wavelet leaders: detection of non concave and non increasing spectra (Part II)* [Paper presentation]. Fractal Geometry and Stochastics V.

This talk follows "A new multifractal formalism based on wavelet leaders: detection of non concave and non increasing spectra (Part I)" given by Céline Esser. For real-life signals, it is impossibl...

Simons, L., & Nicolay, S. (25 March 2014). *About the Multifractal Nature of Cantor's Bijection* [Paper presentation]. Fractal Geometry and Stochastics V, Tabarz, Germany.

In this talk, we present the Cantor's bijection between the irrational numbers of the unit interval [0,1] and the irrational numbers of the unit square [0,1]². We explore the regularity and the fra...

de Marchin, T., Ghysels, B., Nicolay, S., & Franck, F. (January 2014). Analysis of PSII antenna size heterogeneity of Chlamydomonas reinhardtii during state transitions. *Biochimica et Biophysica Acta. Bioenergetics, 1837* (1), 121-130. doi:10.1016/j.bbabio.2013.07.009

PSII antenna size heterogeneity has been intensively studied in the past. Based on DCMU fluorescence rise kinetics, multiple types of photosystems with different properties were described. However,...

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Nicolay, S., & Kreit, D. (31 October 2013). *Generalized Pointwise Hölder Spaces* [Paper presentation]. Nord Pas de Calais/Belgium congress of mathematics, Valenciennes, Belgium.

In [8,7], the properties of generalized uniform Hölder spaces have been investigated. The idea underlying the definition is to replace the exponent α of the usual spaces Λ^α(R^d) (see e.g. [6]) wit...

Kleyntssens, T., & Nicolay, S. (29 October 2013). *Snu Spaces, from Theory to Practice* [Poster presentation]. 1st Nord Pas de Calais/Belgium conference.

Computing the spectrum of singularities of a real-life signal by using the definition is impossible. One rather uses an indirect way to compute it: the multifractal formalism. The first multifracta...

Kreit, D., & Nicolay, S. (29 October 2013). *On generalized Hölder-Zygmund spaces* [Poster presentation]. Nord Pas de Calais/Belgium Congress of mathematics, Valenciennes, France.

The Hölder spaces provide a natural way for measuring the smoothness of a function. These spaces appear in different areas such as approximation theory and multifractal analysis. The purpose of thi...

Kleyntssens, T., & Nicolay, S. (24 September 2013). *Mise en oeuvre du formalisme multifractal sur les espaces Snu* [Paper presentation]. Colloque GDR Multifractales 2013.

When considering very irregular functions, it does not make sense to try to characterize the pointwise irregularity because it can change from one point to another. It is more interesting to comput...

Kleyntssens, T., & Nicolay, S. (09 September 2013). *Implementation of the Multifractal Formalism on Snu Spaces* [Paper presentation]. Fourth PhD-Day : Royal Academy, September 9th, 2013.

A multifractal formalism is a formula, numerically computable, which approximate the spectrum of singularities of a function. The first multifractal formalism (Frisch and Parisi, 1985) has the main...

de Marchin, T., Ghysels, B., Nicolay, S., & Franck, F. (18 June 2013). *Analysis of PSII antenna size heterogeneity of Chlamydomonas reinhardtii during state transitions - Colloque annuel de la Société Française de Photosynthèse* [Paper presentation]. Colloque annuel de la Société Française de Photosynthèse.

PSII antenna size heterogeneity has been extensively studied in the past. Based on in vivo DCMU fluorescence rise kinetics, at least two types of photosystems were described. They differ by their a...

Simons, L., Bastin, F., & Nicolay, S. (31 May 2013). *An adaptation of $S^{\nu}$ spaces* [Paper presentation]. Mini-cours, Analyse fonctionnelle et harmonique et théorie des opérateurs, Lens, France.

The $S^\nu$ spaces have been introduced in 2004 by S. Jaffard in the context of multifractal analysis. In comparison with Besov spaces (the classical functional setting to study signals), these spa...

Simons, L., & Nicolay, S. (28 January 2013). *Régularité de la fonction de Cantor* [Paper presentation]. Séminaires compréhensibles, Liège, Belgium.

La fonction de Cantor, bijection entre $[0,1]$ et $[0,1]^2$, est définie via les fractions continues. Par conséquent, il est assez difficile d'avoir une quelconque intuition sur son comportement. L...

Kreit, D., & Nicolay, S. (2013). Characterizations of the elements of generalized Hölder-Zygmund spaces by means of their representation. *Journal of Approximation Theory, 172*, 23-36. doi:10.1016/j.jat.2013.04.003

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 s...

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Bastin, F., Nicolay, S., & Esser, C. (08 May 2012). *About Generic Properties of "Nowhere Analyticity"* [Paper presentation]. Functional Analysis: Applications to Complex Analysis and Partial Differential Equations, Poznan (Bedlewo), Poland.

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...

Simons, L., & Nicolay, S. (07 May 2012). *About the Regularity of Cantor's Bijection* [Paper presentation]. Functional Analysis : Applications to Complex Analysis and Partial Differential Equations, Bedlewo (Poznan), Poland.

Multifractal analysis has been introduced in the context of turbulence. Some tools have
been developed to study the solutions of some PDEs. In this talk, we will examine
the regularity of Cantor's ...

Bastin, F., Esser, C., & Nicolay, S. (2012). Prevalence of ''nowhere analyticity''. *Studia Mathematica, 210* (3). doi:10.4064/sm210-3-4

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.

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Clausel, M., & Nicolay, S. (2012). A Wavelet Characterization for the Upper Global Hölder Index. *Journal of Fourier Analysis and Applications, 18* (4), 750-769. doi:10.1007/s00041-012-9220-y

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 inv...

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Kreit, D., & Nicolay, S. (2012). Some characterizations of generalized Hölder spaces. *Mathematische Nachrichten, 285* (17-18), 2157-2172. doi:10.1002/mana.201100291

In this paper, we show that the main properties of the usual Hölder spaces can be transposed in the setting of the Hölder spaces defined via admissible sequences. We give several alternative defini...

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Mabille, G., Fettweis, X., Erpicum, M., & Nicolay, S. (2012). Étude fréquentielle de données via la transformée en ondelette : application aux cycles climatiques. *Bulletin de la Société Géographique de Liège, 58*, 5-15.

Understanding the climate requires a complex study of time series connected to weather parameters. The climatologist frequently applies signal processing tools and often uses the harmonic analysis ...

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Fettweis, X., Belleflamme, A., Erpicum, M., Franco, B., & Nicolay, S. (2011). Estimation of the Sea Level Rise by 2100 Resulting from Changes in the Surface Mass Balance of the Greenland Ice Sheet. In J. Blanco & H. Kheradmand (Eds.), *Climate Change - Geophysical Foundations and Ecological Effects* (pp. 503-520). Croatia: Intech.

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 gl...

Kreit, D., & Nicolay, S. (June 2011). *On generalized Hölder spaces* [Poster presentation]. Meeting on self-similarity and related fields, Le Touquet-Paris-Plage, France.

The Hölder spaces provide a natural way for measuring the smoothness of a function. These spaces appear in different areas such as approximation theory and multifractal analysis and lead to natural...

Nicolay, S. (09 March 2011). A wavelet-based mode decomposition. *European Physical Journal B -- Condensed Matter, 80*, 223-232. doi:10.1140/epjb/e2011-10756-3

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 separ...

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Clausel, M., & Nicolay, S. (2011). Wavelets Techniques for Pointwise Anti-Hölderian Irregularity. *Constructive Approximation, 33*, 41-75. doi:10.1007/s00365-010-9120-9

In this paper, we introduce a notion of weak pointwise Hölder regularity,
starting from the definition of the pointwise anti-Hölder irregularity. Using this concept,
a weak spectrum of singularitie...

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Fettweis, X., Mabille, G., Erpicum, M., Nicolay, S., & Van den Broeke, M. (2011). The 1958–2009 Greenland ice sheet surface melt and the mid-tropospheric atmospheric circulation. *Climate Dynamics, 36* (1 (2011)), 139-159. doi:10.1007/s00382-010-0772-8

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 ...

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Franco, B., Fettweis, X., Erpicum, M., & Nicolay, S. (2011). Present and future climates of the Greenland ice sheet according to the IPCC AR4 models. *Climate Dynamics, 36*. doi:10.1007/s00382-010-0779-1

The atmosphere–ocean general circulation models (AOGCMs) used for the IPCC 4th Assessment Report (IPCC AR4) are evaluated for the Greenland ice sheet (GrIS) current climate modelling. The most suit...

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Baker, A., Nicolay, S., Zaghloul, L., D'Aubenton-Carafa, Y., Thermes, C., Audit, B., & Arneodo, A. (2010). Wavelet-based method to disentangle transcription-and replication-associated strand asymmetries in mammalian genomes. *Applied and Computational Harmonic Analysis, 28*, 150-170. doi:10.1016/j.acha.2009.10.003

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...

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Clausel, M., & Nicolay, S. (2010). Some prevalent results about strongly monoHölder functions. *Nonlinearity, 23*, 2101-2116. doi:10.1088/0951-7715/23/9/004

We study the typical behaviour of strongly monoHölder functions from the prevalence point of view. To this end we first prove wavelet-based criteria for strongly monoHölder functions. We then use t...

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Jaffard, S., & Nicolay, S. (2010). Space-Filling Functions and Davenport Series. In J. Barral & S. Seuret (Eds.), *Recent Developments in Fractals and Related Fields* (pp. 19-34). Boston, United States: Birkhäuser. doi:10.1007/978-0-8176-4888-6_2

In this paper, we study the pointwise Hölder regularity of some spacefilling functions. In particular, we give some general results concerning the pointwise regularity of the Davenport series.

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Nicolay, S., Mabille, G., Fettweis, X., & Erpicum, M. (2010). A statistical validation for the cycles found in air temperature data using a Morlet wavelet-based method. *Nonlinear Processes in Geophysics, 17*, 269-272. doi:10.5194/npg-17-269-2010

Recently, new cycles, associated with periods of 30 and 43 months, respectively, have been observed by the authors in surface air temperature time series, using a wavelet-based methodology. Althoug...

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Nicolay, S., Mabille, G., Fettweis, X., & Erpicum, M. (2010). Multi-Months Cycles Observed in Climatic Data. In S. Simard (Ed.), *Climate Change and Variability* (pp. 27-44). Sciyo.

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 cycle...

Franco, B., Fettweis, X., Erpicum, M., & Nicolay, S. (April 2009). *Greenland ice sheet projections from IPCC AR4 global models* [Poster presentation]. European Geosciences Union General Assembly 2009, Vienna, Austria.

The atmosphere-ocean general circulation models (AOGCMs) used for the IPCC 4th Assessment Report (IPCC AR4) are evaluated for the Greenland ice sheet (GrIS) current climate modelling. The most effi...

Mabille, G., Fettweis, X., Erpicum, M., & Nicolay, S. (April 2009). *Confidence Levels for the Cycles Found in Air Temperature Data* [Poster presentation]. European Geosciences Union General Assembly, Vienne, Austria.

Recently, new cycles have been observed in air temperature data and proxy series using a wavelet-based methodology. Although many evidences attest the validity of this method applied to climatic da...

Nicolay, S., Mabille, G., Fettweis, X., & Erpicum, M. (April 2009). *Cycles in the Temperature Data Are Induced by the Sun* [Poster presentation]. European Geosciences Union General Assembly, Vienne, Austria.

The presence of two cycles of period of 30 and 42 months approximatively has been observed in temperature records and climatic indices. Moreover, it has been shown that these cycles are statistical...

Nicolay, S., Mabille, G., Fettweis, X., & Erpicum, M. (13 January 2009). *New cycles found in air temperature data and proxy series using the Morlet wavelet method* [Paper presentation]. FNRS Contact Group "Wavelets and applications", Bruxelles, Belgium.

We use the wavelet transform to detect cycles in air temperature data and proxy series

Arneodo, A., Audit, B., Brodie of Brodie, E. B., Nicolay, S., Touchon, M., D'Aubenton-Carafa, Y., Huvet, M., & Thermes, C. (2009). Fractals and wavelets: What can we learn on transcription and replication from wavelet-based multifractal analysis of DNA sequences? In R. A. Meyers (Ed.), *Encyclopedia of Complexity and Systems Science* (pp. 3893-3924). Springer.

Jaffard, S., & Nicolay, S. (2009). Pointwise smoothness of space-filling functions. *Applied and Computational Harmonic Analysis, 26* (2), 181-199. doi:10.1016/j.acha.2008.04.002

We study irregularity properties of generic Peano functions: we apply these results to the determination of the pointwise smoothness of a Peano function introduced by Lebesgue and of some related f...

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Mabille, G., & Nicolay, S. (2009). Multy-year cycles observed in air temperature data and proxy series. *European Physical Journal. Special Topics, 174*, 135-145. doi:10.1140/epjst/e2009-01096-4

First, palaeoclimatic time series are analyzed under the lens of the continuous wavelet transform. Two cycles, of period 30 and 43 months respectively, are detected in millennial temperature recons...

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Nicolay, S., Mabille, G., Fettweis, X., & Erpicum, M. (2009). 30 and 43 months period cycles found in air temperature time series using the Morlet wavelet. *Climate Dynamics, 33*, 1117-1129. doi:10.1007/s00382-008-0484-5

A wavelet-based methodology is applied to relevant climatic indices and air temperature records and
allow to detect the existence of unexpected cycles. The scale spectrum shows the presence of two ...

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Nicolay, S., Mabille, G., Fettweis, X., & Erpicum, M. (01 October 2008). *New cycles found in air temperature data and proxy series* [Paper presentation]. 1st International Workshop on Data Analysis and Modelling in Earth Sciences, Potsdam, Germany.

We apply the wavelet transform tool to detect unsuspected cycles in several climatic time series

Nicolay, S., Mabille, G., Fettweis, X., & Erpicum, M. (17 April 2008). *Solar activity in connection with a 2.5 years periode cycle in air temperature time series using the Morlet wavelet method* [Paper presentation]. European Geosciences Union General Assembly 2008, Vienna, Austria.

The Morlet wavelet is applied to air temperature time series obtained from several
weather stations and reveals the existence of a period cycle of 20-30 months since
1950, with an estimated amplitu...

Argoul, F., Arneodo, A., Audit, B., Berguiga, L., Fontaine, É., Juanico, B., Moskalenko, C., Moukhtar, J., Nicolay, S., Saint-Jean, P., Sanejouand, Y.-H., & Zhang, S. (2008). Le patrimoine génétique : une histoire de fil a coudre ? In J.-P. Gex (Ed.), *Voir l'invisible*. OmniScience.

Quand 101 chercheurs du monde de la science se mettent en tête de voir l'invisible... Ne doit-on croire que ce que l’on voit ? Et doit-on croire en la science ? Mais que voit la science ? Que voit-...

Nicolay, S., & Rigo, M. (20 April 2007). About frequencies of letters in generalized automatic sequences. *Theoretical Computer Science, 374* (1-3), 25-40. doi:10.1016/j.tcs.2006.11.013

We present some asymptotic results about the frequency of a letter appearing in a generalized unidimensional automatic sequence. Next, we study multidimensional generalized automatic sequences and ...

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Nicolay, S., Brodie, E. B., Touchon, M., Audit, B., d'Aubenton-Carafa, Y., Thermes, C., & Arneodo, A. (March 2007). Bifractality of human DNA strand-asymmetry profiles results from transcription. *Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 75* (3), 032902. doi:10.1103/PhysRevE.75.032902

We use the wavelet transform modulus maxima method to investigate the multifractal properties of strand-asymmetry DNA walk profiles in the human genome. This study reveals the bifractal nature of t...

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Audit, B., Nicolay, S., Huvet, M., Touchon, M., d'Aubenton-Carafa, Y., Thermes, C., & Arneodo, A. L. (2007). DNA replication timing data corroborate in silico human replication origin predictions. *Physical Review Letters, 99*, 248102. doi:10.1103/PhysRevLett.99.248102

We develop a wavelet-based multiscale pattern recognition methodology to disentangle the replication-
from the transcription-associated compositional strand asymmetries observed in the human genome...

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Huvet, M., Nicolay, S., Touchon, M., Audit, B., d'Aubenton-Carafa, Y., Arneodo, A., & Thermes, C. (2007). Human gene organization driven by the coordination of replication and transcription. *Genome Research, 17* (9), 1278-1285. doi:10.1101/gr.6533407

In this work, we investigated a large-scale organization of the human genes with respect to putative replication origins. We developed an appropriate multiscale method to analyze the nucleotide com...

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Arneodo, A., d'Aubenton-Carafa, Y., Audit, B., Brodie of Brodie, E. B., Nicolay, S., St Jean, P., Thermes, C., Touchon, M., & Vaillant, C. (2006). Large-scale Analysis of the human genome: from DNA sequence analysis to the modeling of replication in higher eukaryotes. In *Proceeding of the 14th EUSIPCO* (pp. 1-6). IEEE Xplore.

We explore large-scale nucleotide compositional fluctuations along
the human genome through the optics of the wavelet transform mi-
croscope. Analysis of the TA and GC skews reveals the existence
o...

Arneodo, d'Aubenton-Carafa, Y., Audit, B., Brodie of Brodie, E. B., Nicolay, S., St Jean, P., Thermes, C., Touchon, M., & Vaillant, C. (2006). DNA in chromatin: from genome-wide sequence analysis to the modelling of replication in mammals. *Advances in Chemical Physics, 135*, 203-252.

Understanding how chromatin is spatially and dynamically organized in the nucleus
of eukaryotic cells and how this affects genome functions is one of the main challenges of
cell biology. In that co...

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Nicolay, S. (2006). *Analyse de Séquences ADN par la Transformée en ondelettes : extraction d'informations structurelles, dynamiques et fonctionnelles* [Doctoral thesis, ULiège - Université de Liège]. ORBi-University of Liège. https://orbi.uliege.be/handle/2268/73056

Les recents programmes de sequençage du génome humain, et plus généralement des génomes des eucaryotes supérieurs, ont révélé que seule une faible proportion de l’ADN code pour la synthèse de proté...

Brodie of Brodie, E. B., Nicolay, S., Touchon, M., Audit, B., d'Aubenton-Carafa, Y., Thermes, C., & Arneodo, A. (2005). From DNA sequence analysis to modeling replication in the human genome. *Physical Review Letters, 94*, 248103. doi:10.1103/PhysRevLett.94.248103

We explore the large-scale behavior of nucleotide compositional strand asymmetries along hum
chromosomes. As we observe for 7 of 9 origins of replication experimentally identified so far, the (TA
...

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Touchon, M., Nicolay, S., Audit, B., Brodie of Brodie, E. B., d'Aubenton-Carafa, Y., Arneodo, A., & Thermes, C. (2005). Replication-associated strand asymmetries in mammalian genomes: Toward detection of replication origins. *Proceedings of the National Academy of Sciences of the United States of America, 102* (28), 9836-9841. doi:10.1073/pnas.0500577102

In the course of evolution, mutations do not affect both strands of
genomic DNA equally. This imbalance mainly results from asym-
metric DNA mutation and repair processes associated with repli-
cat...

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Bastin, F., & Nicolay, S. (2004). A note on moments of scaling functions. *Rocky Mountain Journal of Mathematics, 34* (4, Winter), 1197-1206. doi:10.1216/rmjm/1181069795

In this note we give a proof of a reproducing formula for polynomials using natural decay hypothesis. This leads to a new exact formula for computation of moments of even order.

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Nicolay, S., Argoul, F., Touchon, M., d'Aubenton-Carafa, Y., Thermes, C., & Arneodo, A. (2004). Low frequency rythms in human DNA sequences: A key to the organization of gene location and orientation? *Physical Review Letters, 93* (10), 108101. doi:10.1103/PhysRevLett.93.108101

We explore large-scale nucleotide compositional fluctuations of the human genome using multi-
resolution techniques. Analysis of the GC content and of the AT and GC skews reveals the existence of
r...

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Nicolay, S., Brodie of Brodie, E. B., Touchon, M., d'Aubenton-Carafa, Y., Thermes, C., & Arneodo, A. (2004). From scale invariance to deterministic chaos in DNA sequences: towards a deterministic description of gene organisation in the human genome. *Physica A. Statistical Mechanics and its Applications, 342*, 270-280. doi:10.1016/j.physa.2004.04.088

We use the continuous wavelet transform to perform a space-scale analysis of the AT and GC
skews (strand asymmetries) in human genomic sequences, which have been shown to correlate
with gene transc...

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Nicolay, S., & Sanejouand, Y. H. (2004). Functional modes of proteins are among the most robust. *Physical Review Letters, 96*, 078104. doi:10.1103/PhysRevLett.96.078104

It is shown that a small subset of modes which are likely to be involved in protein functional motions of
large amplitude can be determined by retaining the most robust normal modes obtained using ...

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Bastin, F., & Nicolay, S. (2003). A general recurrence relation between the moments of a scaling function. In *Group 24 : Physical and Mathematical Aspects of Symmetries* (pp. 921-924). Bristol, United Kingdom: Iop Publishing Ltd.

Under natural and weak hypotheses, we prove a reproducing formula for polynomials. Then we obtain a new recurrence relation between the moments of a scaling function and a new exact formula for the...

Bastin, F., & Nicolay, S. (2003). A general recurrence relation between the moments of a scaling function. *Institute of Physics Conference Series, 173*, 921-924.

Under natural and weak hypotheses, we prove a reproducing formula for polynomials. Then we obtain a new recurrence relation between the moments of a scaling function and a new exact formula for the...

Touchon, M., Nicolay, S., Arneodo, A., d'Aubenton-Carafa, Y., & Thermes, C. (2003). Transcription-coupled TA and GC strand asymmetries in the human genome. *FEBS Letters, 555*, 579-582. doi:10.1016/S0014-5793(03)01306-1

Abstract Analysis of the whole set of human genes reveals that
most of them present TA and GC skews, that these biases are
correlated to each other and are speci¢c to gene sequences,
exhibiting sha...

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