A bound for Delaunay flip algorithms on flat tori

International audienceWe are interested in triangulations of flat tori. A Delaunay flip algorithm performs Delaunay flips on the edges of an input triangulation T until it reaches a Delaunay triangulation. We prove that no sequence of Delaunay flips is longer than C_Γ • n^2 • Λ(T) where Λ(T) is the maximum length of an edge of T , n is the number of vertices of T , and C_Γ > 0 depends only on the flat torus. The bound improves on the preexisting upper bound in three ways: the dependency in the "quality" of the input triangulation is linear instead of quadratic, the bound is tight, and the "quality parameter" is simpler

Two lower bounds for pp-centered colorings

Given a graph $G$ and an integer $p$, a coloring $f : V(G) \to \mathbb{N}$ is \emph{$p$-centered} if for every connected subgraph $H$ of $G$, either $f$ uses more than $p$ colors on $H$ or there is a color that appears exactly once in $H$. The notion of $p$-centered colorings plays a central role in the theory of sparse graphs. In this note we show two lower bounds on the number of colors required in a $p$-centered coloring. First, we consider monotone classes of graphs whose shallow minors have average degree bounded polynomially in the radius, or equivalently (by a result of Dvo\v{r}\'ak and Norin), admitting strongly sublinear separators. We construct such a class such that $p$-centered colorings require a number of colors super-polynomial in $p$. This is in contrast with a recent result of Pilipczuk and Siebertz, who established a polynomial upper bound in the special case of graphs excluding a fixed minor. Second, we consider graphs of maximum degree $\Delta$. D\k{e}bski, Felsner, Micek, and Schr\"{o}der recently proved that these graphs have $p$-centered colorings with $O(\Delta^{2-1/p} p)$ colors. We show that there are graphs of maximum degree $\Delta$ that require $\Omega(\Delta^{2-1/p} p \ln^{-1/p}\Delta)$ colors in any $p$-centered coloring, thus matching their upper bound up to a logarithmic factor.Comment: v3: final version with journal layout v2: revised following referees' comment

Les tensions entre esprit d’entreprendre émancipateur et esprit d’entreprise procédural : l’exemple des STAPS

En regroupant trois enquêtes sur la discipline universitaire STAPS (Sciences et techniques des activités physiques et sportives) traitant, d’une part, des divergences entre formateurs et, d’autre part, des carrières étudiantes et professionnelles dans le domaine du sport, nous montrons, de façon plus large, que la tension entre esprit d’entreprendre émancipateur et esprit d’entreprise procédural s’exprime sous des formes diverses. Chez les formateurs, elle recoupe les controverses entre conceptions de la professionnalisation des étudiants. Dans les carrières des jeunes se professionnalisant, elle s’exprime dans la difficile conciliation entre la passion pour le sport, la réussite dans les études et l’exercice pérenne d’un métier.By associating three surveys on the french Sport Sciences discipline dealing respectively with the divergences between trainers, student and professional careers in the field of sport, we argue that the global tension between the spirit of emancipatory entrepreneurship and the procedural spirit of enterprise takes various forms. Among the trainers it overlaps the controversies between conceptions of the professionalization of students. In the careers of these young peoples becoming professionals, it is expressed in the difficult articulation of the passion for sport, success in the studies and the perennial exercise of a trade.Spannungen zwischen emanzipatorischem und prozeduralem Unternehmergeist am Beispiel der STAPS. Auf Grundlage von drei gemeinsam betrachteten Untersuchungen, die im Studienfach STAPS (Sciences et techniques des activités physiques et sportives, Sportwissenschaft und -technik) durchgeführt wurden und sich mit den Divergenzen zwischen Ausbildern einerseits und den studentischen und beruflichen Laufbahnen im Bereich Sport andererseits befassen, wird im weiteren Sinne gezeigt, dass die Spannung zwischen emanzipatorischem und prozeduralem Unternehmergeist in verschiedenen Formen zum Ausdruck kommt. Bei den Ausbildern entspricht sie den Kontroversen zwischen den Auffassungen zur Professionalisierung. Bei den Berufswegen der sich professionalisierenden jungen Leute zeigt sie sich in der schwierigen Vereinbarung von Sportbegeisterung, erfolgreichem Studium und langfristiger Ausübung des Berufs.Al agrupar tres investigaciones sobre la disciplina universitaria STAPS (Sciences et techniques des activités physiques et sportives - Ciencias y técnicas de las actividades físicas y deportivas) que tratan sobre las divergencias entre formadores por una parte, y por otra, sobre carreras estudiantiles y profesionales en el ámbito deportivo, mostramos, de manera más general, que la tensión entre espíritu emprendedor emancipador y espíritu empresarial procesual se expresa en formas diversas. Entre los formadores, coincide con las controversias entre concepciones de la profesionalización de los estudiantes. En las carreras de los jóvenes que se profesionalizan, se expresa en la difícil conciliación de la pasión por el deporte, el éxito en los estudios y el ejercicio perenne de una profesión

Experimental analysis of Delaunay flip algorithms on genus two hyperbolic surfaces

Guided by insights on the mapping class group of a surface, we give experimental evidence that the upper bound recently proven on the diameter of the flip graph of a surface by Despré, Schlenker, and Teillaud (SoCG'20) is largely overestimated. To obtain this result, we propose a set of techniques allowing us to actually perform experiments. We solve arithmetic issues by proving a density result on rationally described genus two hyperbolic surfaces, and we rely on a description of surfaces allowing us to propose a data structure on which flips can be efficiently implemented

Experimental analysis of Delaunay flip algorithms on genus two hyperbolic surfaces

International audienceWe give experimental evidence that the only known upper bound on the diameter of the flip graph of a hyperbolic surface recently proven by Despré, Schlenker, and Teillaud (SoCG'20), is largely overestimated. To this aim, we develop an experimental framework for the storage of triangulations of hyperbolic surfaces and modifications through twists. We show that the computations with algebraic numbers can be overcome, and we propose ways to generate surfaces that are meaningful for the experiments

Les oncoprotéines FET remodèlent l'épissage alternatif des sarcomes en détournant le complexe LASR

The FET (FUS, EWSR1, TAF15) genes are commonly involved in chromosomal translocations resulting in their fusion with various transcription factors (TF) genes. These genomic abnormalities are hallmarks of several sarcomas and leukemias, and are found along few other alterations in these neoplasms. The chimeric proteins encoded by these fusion genes share a similar architecture, with a strong aminoterminal transactivation domain derived from FET proteins, and a carboxyterminal DNA-binding domain derived from the TF partner. As this structure is reminiscent of that of a TF, the oncogenic potential of FET fusion proteins has been first attributed to their ability to reprogram transcription. However, this transcriptional role is not sufficient to fully explain how these oncoproteins single-handedly drive various cancers. Indeed, growing evidence points towards novel post-transcriptional roles for FET fusions, notably in the alternative splicing of pre-mRNA. Such a function has previously been studied for the prototypical FET fusion EWSR1::FLI1, the main driver of Ewing sarcoma. Interestingly, RBFOX2, an RNA-binding protein (RBP) governing alternative splicing as part of a large assembly of splicing regulators (LASR) complex, has been identified as a key functional partner of EWSR1::FLI1. In this project, we aim to determine whether the pre-mRNA alternative splicing function observed for EWSR1::FLI1 could be a shared mechanism promoting FET fusion-driven oncogenesis. RNA-sequencing of various FET-translocated sarcoma cell lines showed that thousands of alternative splicing events are induced when the expression of the corresponding fusion is prevented. This suggests that FET fusions inforce a specific splicing landscape in their corresponding sarcoma. In addition, we showed that a representative panel of FET fusions promoted exon inclusion of a reporter minigene, but only when directly tethered onto its pre-mRNA, suggesting that the control of splicing by FET fusions might be direct and might rely on its recruitment onto pre-mRNA. As FET fusions lack canonical RNA-binding domains, we hypothesized that endogenous recruitment could be mediated indirectly via an RBP. By performing luciferase-based protein complementation assays, we demonstrated that almost all FET fusions could interact with RBFOX2. Surprisingly, RBFOX2 appeared to preferentially interact with the C-terminal domains of the fusions, which are derived from a wide range of unrelated TFs. RBFOX2 is known to function as part of a hetero-multimeric splicing complex called LASR. Based on our genome-wide splicing analysis analysis, we found that RNA-binding motifs of RBFOX2 and other members of the LASR complex were found enriched in the proximity of differentially regulated cassette exons. We further validated that members of LASR co-immunoprecipitated with FET fusions. Finally, we confirmed the importance of RBFOX2 and other LASR components in the modulation of splicing of endogenous and cancer-related gene targets of FET fusions. Altogether, our work provided evidence supporting a direct role in splicing for FET fusions by interacting with the LASR complex. Although the mechanisms by which the oncoproteins and LASR collaborate to promote oncogenesis remain unclear, we have established a moonlighting function for these driver fusion proteins that could be crucial in our understanding of the tumorigenesis of multiple neoplasms

A Brownian particle in a microscopic periodic potential

We study a model for a massive test particle in a microscopic periodic potential and interacting with a reservoir of light particles. In the regime considered, the fluctuations in the test particle's momentum resulting from collisions typically outweigh the shifts in momentum generated by the periodic force, and so the force is effectively a perturbative contribution. The mathematical starting point is an idealized reduced dynamics for the test particle given by a linear Boltzmann equation. In the limit that the mass ratio of a single reservoir particle to the test particle tends to zero, we show that there is convergence to the Ornstein-Uhlenbeck process under the standard normalizations for the test particle variables. Our analysis is primarily directed towards bounding the perturbative effect of the periodic potential on the particle's momentum.Comment: 60 pages. We reorganized the article and made a few simplifications of the conten