À venir

Résumé : Résumé : Le groupe pro-unipotent DMR0, qui sous-tend le schéma des relations de double mélange satisfaites par les nombres zêtas multiples (Racinet 2002), est un sous-groupe de celui des automorphismes de l'algèbre de Lie libre en deux générateurs e0 et e1, envoyant e1 sur lui-même et e0 sur un conjugué. Nous montrons que DMR0 est en fait contenu dans le sous-groupe des automorphismes spéciaux, c'est-à-dire envoyant également einfty:=-e0-e1 sur un conjugué, et est globalement invariant sous l'involution du groupe des automorphismes spéciaux induit par l'échange de e0 et einfty (travail commun avec H. Furusho).

Résumé : Exposés d'entrainement avant JAVA (où on donnera ces exposés la semaine suivante). Les exposés seront auto-contenus et dureront une heure. On laissera une pause entre les deux ainsi qu’une pause avant le pré-séminaire (s’il aura lieu).

Résumé : Exposés d'entrainement avant JAVA (où on donnera ces exposés la semaine suivante). Les exposés seront auto-contenus et dureront une heure. On laissera une pause entre les deux ainsi qu’une pause avant le pré-séminaire (s’il aura lieu).

Résumé : Exposés d'entrainement avant JAVA (où on donnera ces exposés la semaine suivante). Les exposés seront auto-contenus et dureront une heure. On laissera une pause entre les deux ainsi qu’une pause avant le pré-séminaire (s’il aura lieu).

Résumé : The talk starts with a brief overview of Marcello's current research topics and collaborations. Then, the approximation capabilities of deep perceptron networks with piecewise-polynomial computational units are investigated in terms of the influence of depth, type of activation functions, and number of parameters. Probabilistic bounds on approximation errors are derived by using concentration-of-measure inequalities applicable to sufficiently smooth functions of the random variables. Conditions are presented, under which approximation of random classifiers behaves almost deterministically. It is shown that such behavior arises when networks are "reasonably small" with respect to the size of the domain, in particular when the number of input-output functions grows polynomially with its size. To study properties of deep perceptron networks that approximate random classifiers, estimates of growth functions - studied in Statistical Learning Theory in connection with VC-dimension - are employed. Conditions for concentration of approximation errors are derived in terms of network depth, effective depth, total number of parameters, and degrees and numbers of pieces of piecewise polynomial activation functions. The results are illustrated on networks with widespread activation functions: Heaviside, ramp sigmoid,rectified linear, and rectified power.

Résumé :

Dans ce sem’in, nous présenterons OPLA, un générateur de pages personnelles à destination du personnel de recherche. OPLA transforme simplement un fichier Markdown en une page web personnelle. L’outil intègre automatiquement vos publications scientifiques depuis des fichiers BibTeX ou directement depuis HAL.

Au programme :

• Démonstration de la création et de l’édition d’une page OPLA

• Présentation de deux méthodes de publication :

  1. Via gitlab.math.unistra.fr avec GitLab Pages
  2. En ligne de commande vers le répertoire public_html sur file.math.unistra.fr

Que vous souhaitiez créer votre première page web ou moderniser une page existante, ce sem’in est fait pour vous !

Résumé : In this work, we are interested in the mathematical modeling of the impact of apoptosis on the dynamics of cellular tissues, and in particular on cell tissue fluidity. Indeed, cell apoptosis corresponds to the programmed cell death: when they leave the tissue, they induce local contractions but also enable cells rearrangements.

We first propose an individual-based model that provides the dynamics of the positions, velocities and polarities of the cells, idealized as hard spheres. Cells interact with each other through contact forces, smooth attraction, and polarity alignment. The model also involves a microscopic description of apoptotic and proliferation events. The present work is an extension of the model proposed in [3] and validated by experiments on cellular rings. Numerical simulations are performed and several indicators of fluidity are analyzed.

Next, we derive a macroscopic description, following the methodology proposed in [1], [2]. We start from a mean-field dynamics of the kinetic distribution function in phase-space (position, polarity, radius), where contact forces have been replaced with repulsion forces. We then introduce a specific time and space rescaling and identify the equilibria distribution functions, which are parameterized by two macroscopic quantities: the density and the mean polarity. Based on the Generalized Collision Invariant (GCI) method [2], we are then able to identify their dynamics: the resulting description can be seen as a modified Self-Organized Hydrodynamics (SOH) model. We finally discuss the obtained model and highlight the effect of the apoptotic events on the dynamics.

This is a joint work with Laurent Navoret (Université de Strasbourg) and Marcela Szopos (Université Paris Cité). It has also been carried out in collaboration with Romain Levayer (Institut Pasteur) and Daniel Riveline (IGBMC, Université de Strasbourg) in the context of the ANR project MAPEFLU.

References

[1] Degond, P., Dimarco, G., Mac, T. B. N., and Wang, N. Macroscopic models of collective motion with repulsion. Communications in Mathematical Sciences, 13(6), 1615–1638 (2015).

[2] Degond, P., and Motsch, S. Continuum limit of self-driven particles with orientation interaction. Mathematical Models and Methods in Applied Sciences, 18(supp01), 1193–1215 (2008).

[3] Vecchio, S. L., Pertz, O., Szopos, M., Navoret, L., and Riveline, D. Spontaneous rotations in epithelia as an interplay between cell polarity and boundaries. Nature Physics (2024).

Résumé : In the past 10 to 20 years, representation theory of associative algebras has been permeating many areas of mathematics and mathematical physics. At its core, representation theory is the translation of abstract problems into linear algebra. While it might sound like once the translation is achieved all problems are easily solved, this is not the case! In recent years through the advent of cluster theory as well as through the connection with (homological) mirror symmetry, combinatorial surface geometry has provided powerful tools to advance important problems in representation theory as well as in areas of application. I will give an overview of some of the recent developments illustrated by many examples.

Résumé : TBA

Résumé : Online