Abstract numeration systems on bounded languages and multiplication by a constant

A set of integers is $S$-recognizable in an abstract numeration system $S$ if the language made up of the representations of its elements is accepted by a finite automaton. For abstract numeration systems built over bounded languages with at least three letters, we show that multiplication by an integer $\lambda\ge2$ does not preserve $S$-recognizability, meaning that there always exists a $S$-recognizable set $X$ such that $\lambda X$ is not $S$-recognizable. The main tool is a bijection between the representation of an integer over a bounded language and its decomposition as a sum of binomial coefficients with certain properties, the so-called combinatorial numeration system

Multidimensional Generalized Automatic Sequences and Shape-symmetric Morphic Words

An infinite word is S-automatic if, for all n>=0, its (n + 1)st letter is the output of a deterministic automaton fed with the representation of n in the considered numeration system S. In this extended abstract, we consider an analogous definition in a multidimensional setting and present the connection to the shape-symmetric infinite words introduced by Arnaud Maes. More precisely, for d>=2, we state that a multidimensional infinite word x : N^d \to \Sigma over a finite alphabet \Sigma is S-automatic for some abstract numeration system S built on a regular language containing the empty word if and only if x is the image by a coding of a shape-symmetric infinite word

Asymptotic properties of free monoid morphisms

Motivated by applications in the theory of numeration systems and recognizable sets of integers, this paper deals with morphic words when erasing morphisms are taken into account. Cobham showed that if an infinite word $w =g(f^\omega(a))$ is the image of a fixed point of a morphism $f$ under another morphism $g$, then there exist a non-erasing morphism $\sigma$ and a coding $\tau$ such that $w =\tau(\sigma^\omega(b))$. Based on the Perron theorem about asymptotic properties of powers of non-negative matrices, our main contribution is an in-depth study of the growth type of iterated morphisms when one replaces erasing morphisms with non-erasing ones. We also explicitly provide an algorithm computing $\sigma$ and $\tau$ from $f$ and $g$.Comment: 25 page

Acousto-optical coherence tomography with a digital holographic detection scheme

Acousto-optical coherence tomography (AOCT) consists in using random phase jumps on ultrasound and light to achieve a millimeter resolution when imaging thick scattering media. We combined this technique with heterodyne off-axis digital holography. Two-dimensional images of absorbing objects embedded in scattering phantoms are obtained with a good signal-to-noise ratio. We study the impact of the phase modulation characteristics on the amplitude of the acousto-optic signal and on the contrast and apparent size of the absorbing inclusion

Structural properties of bounded languages with respect to multiplication by a constant

peer reviewedWe consider the preservation of recognizability of a set of integers after multiplication by a constant for numeration systems built over a bounded language. As a corollary we show that any nonnegative integer can be written as a sum of binomial coefficients with some prescribed properties

Activités parascolaires et climat de classe, quels liens ?

Le climat de classe a une grande influence sur les apprentissages, le bien-être des élèves et des enseignants. Il contient plusieurs composants qui peuvent se travailler ensemble et simultanément ; le climat relationnel, le climat éducatif, le climat d’appartenance, le climat de justice et le climat de sécurité. Ces composants regroupent plusieurs caractéristiques. Prendre connaissance de ces dernières permet d’acquérir de bonnes bases pour celui qui souhaite bénéficier d’un bon climat de classe. Plusieurs auteurs décrivent le climat de classe comme une variable subjective, puisqu’elle est perçue de façon différente par chacun. Néanmoins, ce concept peut se travailler et se développer. Le climat de classe peut évoluer positivement en fonction des éléments mis en place pour le favoriser et en prenant en compte chaque individu de la classe. Il est imbriqué dans le climat scolaire, qui lui est régit par l’école dans son ensemble. En effet, l’ambiance générale de l’école peut aussi entrainer celle de la classe. Ce travail se concentre sur un levier influençant le climat de classe, en particulier celui des sorties scolaires. Ma recherche auprès de 6 enseignants et leurs 95 élèves a permis de mettre en évidence les sorties et les camps effectués ainsi que leurs conséquences en classe. Quelques enseignants ont partagé ce qu’ils mettent en place pour soutenir leur climat de classe et leurs élèves ont été questionnés sur leur perception de l’école en général

Heterodyne holographic microscopy of gold particles

We report experimental results on heterodyne holographic microscopy of subwavelength-sized gold particles. The apparatus uses continuous green laser illumination of the metal beads in a total internal reflection configuration for dark-field operation. Detection of the scattered light at the illumination wavelength on a charge-coupled device array detector enables 3D localization of brownian particles in wate