On the Number of Balanced Words of Given Length and Height over a Two-Letter Alphabet

We exhibit a recurrence on the number of discrete line segments joining two integer points in the plane using an encoding of such segments as balanced words of given length and height over the two-letter alphabet $\{0,1\}$. We give generating functions and study the asymptotic behaviour. As a particular case, we focus on the symmetrical discrete segments which are encoded by balanced palindromes.Comment: 24 page

Minimal arithmetic thickness connecting discrete planes

International audienceWhile connected arithmetic discrete lines are entirely characterized, only partial results exist for the more general case of arithmetic discrete hyperplanes. In the present paper, we focus on the $3$-dimensional case, that is on arithmetic discrete planes. Thanks to arithmetic reductions on a vector \vect{n}, we provide algorithms either to determine whether a given arithmetic discrete plane with \vect{n} as normal vector is connected, or to compute the minimal thickness for which an arithmetic discrete plane with normal vector \vect{n} is connected

The distance to the C component of I Zw 18 and its star formation history: A probabilistic approach

We analyzed the resolved stellar population of the C component of the extremely metal-poor dwarf galaxy Izw18 in order to evaluate its distance and star formation history as accurately as possible. In particular, we aimed at answering the question of whether this stellar population is young. We developed a probabilistic approach to analyzing high-quality photometric data obtained with the Advanced Camera for Surveys of the Hubble Space Telescope. This approach gives a detailed account of the various stochastic aspects of star formation. We carried out two successive models of the stellar population of interest, paying attention to how our assumptions could affect the results. We found a distance to the C component of I Zw 18 as high as 27 Mpc, a significantly higher value than those cited in previous works. The star formation history we inferred from the observational data shows various interesting features: a strong starburst that lasted for about 15 Myr, a more moderate one that occurred approx 100 Myr ago, a continuous process of star formation between both starbursts, and a possible episode of low level star formation at ages over 100 Myr. The stellar population studied is likely approx 125 Myr old, although ages of a few Gyr cannot be ruled out. Furthermore, nearly all the stars were formed in the last few hundreds of Myr.Comment: 13 pags., 17 (low-resolution) Figs. Accepted by A&

Discrete Circles: an arithmetical approach with non-constant thickness

International audienceIn the present paper, we introduce an arithmetical definition of discrete circles with a non-constant thickness and we exhibit different classes of them depending on the arithmetical discrete lines. On the one hand, it results in the characterization of regular discrete circles with integer parameters as well as J. Bresenham's circles. As far as we know, it is the first arithmetical definition of the latter one. On the other hand, we introduce new discrete circles, actually the thinnest ones for the usual discrete connectedness relations

On the topology of discrete hyperplanes

https://sites.google.com/site/numeration2012/DamienJamet-abstract.pdf?attredirects=0International audienc

Mapping domain junctions using 4D-STEM: toward controlled properties of epitaxially grown transition metal dichalcogenide monolayers

Epitaxial growth has become a promising route to achieve highly crystalline continuous two-dimensional layers. However, high-quality layer production with expected electrical properties is still challenging due to the defects induced by the coalescence between imperfectly aligned domains. In order to control their intrinsic properties at the device scale, the synthesized materials should be described as a patchwork of coalesced domains. Here, we report multi-scale and multistructural analysis on highly oriented epitaxial WS$_2$ and WSe$_2$ monolayers using scanning transmission electron microscopy (STEM) techniques. Characteristic domain junctions are first identified and classified based on the detailed atomic structure analysis using aberration corrected STEM imaging. Mapping orientation, polar direction and phase at the micrometer scale using four-dimensional STEM enabled to access the density and the distribution of the specific domain junctions. Our results validate a readily applicable process for the study of highly oriented epitaxial transition metal dichalcogenides, providing an overview of synthesized materials from large scale down to atomic scale with multiple structural information.Comment: 22 pages, 6 figures and Supplementary Informatio

Revisiting the Effects of Gender Diversity in Small Groups on Divergent Thinking: A Large-Scale Study Using Synchronous Electronic Brainstorming

Numerous studies have examined the effects of gender diversity in groups on creative performance, and no clear effect has been identified. Findings depend on situational cues making gender diversity more or less salient in groups. A large-scale study on two cohorts (N = 2,261) was conducted among business students to examine the impact of the gender diversity in small groups on divergent thinking in an idea-generation task performed by synchronous electronic brainstorming. Participants were automatically randomized in three- or four-member groups to generate ideas during 10 min on a gendered or neutral task. Then, five categories of groups where the proportion of men/women in groups varied from three/four men to three/four women were compared to examine creative performance on three divergent thinking measures (fluency, flexibility, and originality). A Multivariate Generalized Linear Mixed Model (mGLMM) showed greater fluency in all-women groups than in other groups (except mixed-gender groups composed of two men and two women), and more specifically “solo” groups composed of a single woman/man among a majority of men/women. For flexibility and originality, the superiority of all-women groups was found only in comparison to “solo” groups composed of a single woman. As gender differences are more salient in “solo” groups than in other groups faultlines may appear in groups, leading to a deleterious impact on creative performance

A REFORMA DA FORMAÇÃO DOS PROFESSORES: UMA ORIENTAÇÃO EUROPEIA AFIRMADA / Teacher training reform: a strongly-marked european orientation / La réforme de la formation des enseignants: une orientation européenne affirmée

A União Europeia interessa-se, particularmente, na reforma da formação dos professores. Uma análise comparativa dos elementos notáveis e comuns dos conteúdos das reformas, de um lado, nos levará a notar a difícil emergência do estabelecimento formador. Por outro lado, a síntese destes trabalhos porá em evidência que a reforma europeia da formação dos professores se insere em uma nova lógica da profissionalização. The European Union is taking particular interest in the teacher training reform. On the one hand, a comparative analysis of the salient and common features of their contents will lead us to notice the difficult emergence of the training institution. On the other hand, the synthesis of this research will highlight the fact that the European reform in teacher training is to be seen in a new logic of professionalisation.L'Union Européenne s'intéresse particulièrement à la réforme de la formation des enseignants. Une analyse comparative des éléments saillants et communs de leurs contenus nous conduira, d'une part, à constater la difficile émergence de l'établissement formateur. D'autre part, la synthèse de ces travaux mettra en évidence que la réforme européenne de la formation des enseignants s'insère dans une logique nouvelle de la professionnalisation

La région HII géante NGC 588 (Un laboratoire pour l'étude des populations stellaires et des nébuleuses ionisées)

PARIS7-Bibliothèque centrale (751132105) / SudocSudocFranceF

On the Connectedness of Rational Arithmetic Discrete Hyperplanes

Abstract. While connected arithmetic discrete lines are entirely characterized by their arithmetic thickness, only partial results exist for arithmetic discrete hyperplanes in any dimension. In the present paper, we focus on 0-connected rational arithmetic discrete planes in Z 3. Thanks to an arithmetic reduction on a given integer vector n, we provide an algorithm which computes the thickness of the thinnest 0-connected arithmetic plane with normal vector n.