arXiv subjects

Samuel Nicolay

Publications and source records attributed to Samuel Nicolay.

11 recordsLinked to original sources

arXiv2026

A Functorial Approach to Multi-Space Interpolation with Function Parameters

We introduce an extension of interpolation theory to more than two spaces by employing a functional parameter, while retaining a fully functorial and systematic framework. This approach allows for the construction of generalized intermediate spaces and ensures stability under natural operations such as powers and convex combinations. As a significant application, we demonstrate that the interpolation of multiple generalized Sobolev spaces yields a generalized Besov space. Our framework provides explicit tools for handling multi-parameter interpolation, highlighting both its theoretical robustness and practical relevance.

math.FA↗

arXiv2025

The Thomae Function: Fractal Insights

This article examines the Thomae function, a paradigmatic example of a function that is continuous on the irrationals and discontinuous elsewhere. Defined for a parameter $\theta>0$, it exhibits a rich self-similar structure and intriguing regularity properties. After revisiting its fundamental characteristics, we analyze its H\"older continuity, emphasizing the interplay between its discrete spikes and its behavior on dense subsets of the real line. This study provides a refined perspective on the irregularity of the Thomae function, using classical analytical tools to elucidate its fractal nature.

math.GM↗

arXiv2019

Generalized spaces of pointwise regularity: To a general framework for the WLM

In this work we generalize the spaces T^{p}_{u} introduced by Calderón and Zygmund using a pointwise version of conditions defining the generalized Besov spaces and give conditions binding the functions belonging to these spaces and the wavelet coefficients of such functions. Next, we propose a multifractal formalism based on the new spaces wich generalize the so-called wavelet leaders method and show that it is satisfied on a prevalent set.

math.FA↗

arXiv2014

Monofractal nature of air temperature signals reveals their climate variability

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 obtained in this way are richer than previous works studying long range correlations in meteorological stations. The approach presented here allows to bind the Hölder exponents with the climate variability. We also establish that such a link does not exist with methods previously carried out.

physics.data-an↗

arXiv2014

Building Cantor's Bijection

Cantor's first idea to build a one-to-one mapping from the unit interval to the unit square did not work since, as pointed out by Dedekind, the so-obtained function is not surjective. Here, we start from this function and modify it (on a negligible set) in order to obtain the desired result: a one-to-one correspondance between the unit interval and the unit square.

math.HO↗

arXiv2014

About the multifractal nature of Cantor's bijection

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 explore the fractal nature of this map by showing that its Hölder regularity lies between 0.35 and 0.72 almost everywhere (with respect to the Lebesgue measure).

math.FA↗

arXiv2013

Generalized pointwise Hölder spaces

In this paper, we introduce 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 generalized Hölder exponent.

math.FA↗

arXiv2011

A weak local irregularity property in S^νspaces

Although it has been shown that, from the prevalence point of view, the elements of the S^ νspaces are almost surely multifractal, we show here that they also almost surely satisfy a weak uniform irregularity property.

math.FA↗

arXiv2011

Wavelets techniques for pointwise anti-Holderian irregularity

In this paper, we introduce a notion of weak pointwise Holder regularity, starting from the de nition of the pointwise anti-Holder irregularity. Using this concept, a weak spectrum of singularities can be de ned as for the usual pointwise Holder regularity. We build a class of wavelet series satisfying the multifractal formalism and thus show the optimality of the upper bound. We also show that the weak spectrum of singularities is disconnected from the casual one (denoted here strong spectrum of singularities) by exhibiting a multifractal function made of Davenport series whose weak spectrum di ers from the strong one.

math.FA↗

arXiv2007

From DNA sequence analysis to modeling replication in the human genome

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 positioned replication origins and random terminations that accounts for the observed characteristic serrated skew profiles. We succeed in identifying 287 pairs of putative adjacent replication origins with an origin spacing approximately 1-2 Mbp that are likely to correspond to replication foci observed in interphase nuclei and recognized as stable structures that persist throughout subsequent cell generations.

q-bio.GN↗

arXiv2005

Functional modes of proteins are among the most robust ones

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 different protein models. This result should prove helpful in the context of several applications proposed recently, like for solving difficult molecular replacement problems or for fitting atomic structures into low-resolution electron density maps. Moreover, it may also pave the way for the development of methods allowing to predict such motions accurately.

q-bio.BM↗