513 citations
- Centre National de la Recherche ScientifiqueFR688 papers
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- Université Paris DiderotFR274 papers
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- École Normale Supérieure - PSLFR49 papers
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2,224 papers
Absence of gelation and regularity for coagulation-fragmentation-diffusion equations with critical coagulation rate in low dimension
Hector Bouton
We consider a discrete coagulation-fragmentation-diffusion system on a bounded domain of . In dimension , we prove mass conservation (that is absence of gela…
N{é}ron models of G\_m
Christophe Cornut
We construct ''N{é}ron models'' of Gm over any base scheme S.
Robustness Cannot be Reduced to Regularization: Studying Adversarial Training Beyond the Linear Case
David A. R. Robin, Rafael Pinot, Yann Chevaleyre
The vulnerability of ML models to adversarial examples has recently emerged as a major concern. While adversarial training is one of the most effective countermeasures to this issu…
Simple proofs for the existence of smooth solutions to a reaction-diffusion system modeling reversible chemistry
Hector Bouton, Laurent Desvillettes, Helge Dietert
We present in this work a very short proof for the existence, uniqueness and smoothness in dimensions of the system of reaction diffusion $ \partial\_t a\_i - d\_i Δa\_i…
Nonlinear Kinetic Diffusion Equations with -Growth
Helge Dietert, Lukas Niebel, Rico Zacher
We establish the local boundedness of (sub-)solutions to nonlinear kinetic diffusion equations with -growth, where the kinetic p-Laplace equation is a prototypical example. A ke…
Topology, forcing, and graph colourings
Noam Greenberg, Dominique Lecomte, Dan Turetsky +1
We introduce a family of forcing notions that are helpful in showing that certain graphs do not have countable colourings of (additive) Borel class alpha. We construct graphs that…