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116 results on '"ANR-10-LABX-0070"'

1. Connected perimeter of planar sets

Author: Marco Pozzetta, Matteo Novaga, François Dayrens, Simon Masnou, Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Dipartimento di Matematica [Pisa], University of Pisa - Università di Pisa, Simon Masnou and François Dayrens acknowledge support from the French National Research Agency (ANR) research grants MIRIAM (ANR-14-CE27-0019) and GEOMETRYA (ANR-12-BS01-0014), and from the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program 'Investissements d’Avenir' (ANR-11-IDEX-0007). Matteo Novaga and Marco Pozzetta acknowledge support from the INdAM-GNAMPA Project 2019 Problemi geometrici per strutture singolari., ANR-14-CE27-0019,MIRIAM,Restauration Multi-Images: des Mathématiques Appliqueés à l'Industrie de l'Imagerie.(2014), ANR-12-BS01-0014,GEOMETRYA,Théorie géométrique de la mesure et applications(2012), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), ANR-16-IDEX-0005,IDEXLYON,IDEXLYON(2016), Dayrens, Françoi, Masnou, Simon, Novaga, Matteo, Pozzetta, Marco, Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), ANR: ANR-10_LABX-0070,LABEX MILYON (ANR-10-LABX-0070) of Universit ́e de Lyon within the program 'Investissements d’Avenir (ANR-11-IDEX-0007)' operated by the French National Research Agency (ANR)., and ANR: 16-IDEX-0005,IDEXLYON,IDEXLYON(2016)
Subjects: Computer Science::Computational Geometry, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, Steiner tree problem, Perimeter, symbols.namesake, Planar, TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY, Simply connected space, FOS: Mathematics, Hardware_INTEGRATEDCIRCUITS, Mathematics::Metric Geometry, 0101 mathematics, Representation (mathematics), Geometry and topology, Mathematics, Discrete mathematics, Computer Science::Information Retrieval, Applied Mathematics, 010102 general mathematics, Minimization problem, ComputerSystemsOrganization_COMPUTER-COMMUNICATIONNETWORKS, Functional Analysis (math.FA), Mathematics - Functional Analysis, 010101 applied mathematics, symbols, Analysis, Envelope (motion), MathematicsofComputing_DISCRETEMATHEMATICS
Abstract: We introduce a notion of connected perimeter for planar sets defined as the lower semi-continuous envelope of perimeters of approximating sets which are measure-theoretically connected. A companion notion of simply connected perimeter is also studied. We prove a representation formula which links the connected perimeter, the classical perimeter, and the length of suitable Steiner trees. We also discuss the application of this notion to the existence of solutions to a nonlocal minimization problem., Advances in Calculus of Variations, In press
Published: 2020

2. An introduction to the homogenization modeling of non-Newtonian and electrokinetic flows in porous media

Author: Andro Mikelić, Mikelic, Andro, Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID, Springer, Elvira Mascolo, Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), MOCOMIPOC project (Modélisation multiéchelles des écoulements complexes en présence de gaz dans les milieux chargés), NEEDS program (Projet fédérateur Milieux Poreux MIPOR), CNRS, France et LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program 'Investissements d’Avenir' (ANR-11-IDEX-0007), and ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010)
Subjects: Physics, [SPI.MECA.MEFL] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], 010103 numerical & computational mathematics, Mechanics, 01 natural sciences, Homogenization (chemistry), Non-Newtonian fluid, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], 010101 applied mathematics, Physics::Fluid Dynamics, Electrokinetic phenomena, Monotone polygon, Compressibility, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Porous medium, Pressure gradient, Complex fluid
Abstract: International audience; The flow of complex fluids through porous media is common to many engineering applications. The upscaling is a powerful tool for modeling nonhomo-geneous media and we consider homogenization of quasi-Newtonian and electroki-netic flows through porous media. For the quasi-Newtonian polymeric fluids, the incompressible Navier-Stokes equations with the invariants dependent viscosity is supposed to hold the pore scale level. The 2-scale asymptotic expansions and the two-scale convergence of the monotone operators are applied to derive the reservoir level filtration law, given as a monotone relation between the filtration velocity and the pressure gradient. The second problem, we consider, is the quasi-static transport of an electrolyte through an electrically charged medium. The physical chemistry modeling is presented and used to get a dimensionless form of the problem. Next the equilibrium solutions are constructed through solving the Poisson-Boltzmann equation. For the solutions being close to the equilibrium, the two-scale convergence is applied to obtain the Onsager relations linking gradients of the pressure and of the chemical potentials to the filtration velocity and the ionic fluxes.
Published: 2017

3. Global existence of weak solutions to dissipative transport equations with nonlocal velocity

Author: Hantaek Bae, Rafael Granero-Belinchón, Omar Lazar, Ulsan National Institute of Science and Technology (UNIST), Équations aux dérivées partielles, analyse (EDPA), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Instituto de Ciencias Matematicas (ICMAT), Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC), This work was supported by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program 'Investissements d'Avenir' (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR)., ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Granero-Belinchon, Rafael, Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID, Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Function space, General Physics and Astronomy, 01 natural sciences, Multiplier (Fourier analysis), symbols.namesake, Operator (computer programming), Mathematics - Analysis of PDEs, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Mathematical Physics, Mathematics, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Statistical and Nonlinear Physics, Functional Analysis (math.FA), 010101 applied mathematics, Mathematics - Functional Analysis, Fourier transform, Dissipative system, symbols, Vector field, Hilbert transform, Analysis of PDEs (math.AP)
Abstract: We consider 1D dissipative transport equations with nonlocal velocity field: \[ \theta_t+u\theta_x+\delta u_{x} \theta+\Lambda^{\gamma}\theta=0, \quad u=\mathcal{N}(\theta), \] where $\mathcal{N}$ is a nonlocal operator given by a Fourier multiplier. Especially we consider two types of nonlocal operators: $\mathcal{N}=\mathcal{H}$, the Hilbert transform, $\mathcal{N}=(1-\partial_{xx} )^{-\alpha}$. In this paper, we show several global existence of weak solutions depending on the range of $\gamma$ and $\delta$. When $0, Comment: 28 pages, improved and extended version (some extra assumptions have been removed, new cases are treated)
Published: 2016

4. SUPPRESSION OF BLOW UP BY A LOGISTIC SOURCE IN 2D KELLER-SEGEL SYSTEM WITH FRACTIONAL DISSIPATION

Author: Burczak, Jan, Granero-Belinchón, Rafael, Institut of Mathematics - Polish Academy of Sciences (PAN), Polska Akademia Nauk = Polish Academy of Sciences (PAN), Équations aux dérivées partielles, analyse (EDPA), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), This work was supported by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program 'Investissements d'Avenir' (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR)., ANR-11-IDEX-0007,Avenir L.S.E.,PROJET AVENIR LYON SAINT-ETIENNE(2011), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Granero-Belinchon, Rafael, PROJET AVENIR LYON SAINT-ETIENNE - - Avenir L.S.E.2011 - ANR-11-IDEX-0007 - IDEX - VALID, and Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID
Subjects: Mathematics - Analysis of PDEs, Mathematics::Analysis of PDEs, FOS: Mathematics, 35R11, 35B65, 92C17, 35A01, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Quantitative Biology::Cell Behavior, Analysis of PDEs (math.AP)
Abstract: We consider a two dimensional parabolic-elliptic Keller-Segel equation with a logistic forcing and a fractional diffusion of order $\alpha$. We obtain existence of global in time regular solution for arbitrary initial data with no size restrictions and $c
Published: 2016

5. COSIMIA : Combiner Simulation et Apprentissage Automatique pour Optimiser la Configuration des Réseaux IoT

Author: Si-Mohammed, Samir, Begin, Thomas, Lassous, Isabelle, Vicat-Blanc, Pascale, Holistic Wireless Networks (hownet), Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), and LABEX MILYON (ANR-10-LABX-0070), Université de Lyon (ANR-11-IDEX-0007)
Subjects: [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI], Internet des Objets, Évaluation de Performance, Optimisation, Apprentissage automatique, Simulation
Abstract: International audience; L'internet des objets (IoT) couvre un large éventail d'applications qui s'appuient sur une ou plusieurs technologies réseau pour échanger des données entre les différents dispositifs IoT et les applications utilisateur. Ces technologies sont très hétérogènes et sont caractérisées par un ensemble de paramètres de configuration spécifiques à chacune. Les architectes IoT peuvent avoir recours à la simulation pour sélectionner une configuration réseau qui permette d'obtenir les meilleurs performances pour une application et un contexte cibles. Mais cette approche peut s'avérer coûteuse en temps de calcul et donc en énergie. Dans cet article, nous proposons COSIMIA, une méthode s'appuyant sur la combinaison de la Simulation et de l'Apprentissage automatique afin d'accélerer la recherche d'une configuration optimisée pour un scénario IoT donné. La méthode proposée est appliquée à deux études de cas inspirées de situations industrielles réelles, utilisant des technologies IoT différentes. Nous montrons que cette méthode permet de déterminer de bonnes configurations réseau avec un nombre réduit de simulations.
Published: 2023

6. Orthogonalization of Positive Operator Valued Measures

Author: de La Salle, Mikael, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), ANR-16-CE40-0022,AGIRA,Actions de Groupes, Isométries, Rigidité et Aléa(2016), ANR-19-CE40-0002,ANCG,Analyse non commutative sur les groupes et les groupes quantiques(2019), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), de la salle, mikael, Actions de Groupes, Isométries, Rigidité et Aléa - - AGIRA2016 - ANR-16-CE40-0022 - AAPG2016 - VALID, Analyse non commutative sur les groupes et les groupes quantiques - - ANCG2019 - ANR-19-CE40-0002 - AAPG2019 - VALID, and Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID
Subjects: Quantum Physics, Mathematics::Operator Algebras, General Mathematics, [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA], [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], Mathematics - Operator Algebras, FOS: Physical sciences, Computer Science::Computational Complexity, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], FOS: Mathematics, [MATH.MATH-OA] Mathematics [math]/Operator Algebras [math.OA], Operator Algebras (math.OA), Quantum Physics (quant-ph), [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]
Abstract: We show that a partition of the unity (or POVM) on a Hilbert space that is almost orthogonal is close to an orthogonal POVM in the same von Neumann algebra. This generalizes to infinite dimension previous results in matrix algebras by Kempe-Vidick and Ji-Natarajan-Vidick-Wright-Yuen. Quantitatively, our result are also finer, as we obtain a linear dependance, which is optimal. We also generalize to infinite dimension a duality result between POVMs and minimal majorants of finite subsets in the predual of a von Neumann algebra., Comment: 14 pages; v2: improvements in the presentation and small mistakes corrected. To appear in the open access journal Comptes Rendus - Math\'ematique
Published: 2022
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7. A System of Interaction and Structure III: The Complexity of BV and Pomset Logic

Author: Nguyễn, Lê Thành Dũng, Straßburger, Lutz, Straßburger, Lutz, une expédition cartographique entre le lambda-calcul, la logique, et la combinatoire - - LambdaComb2021 - ANR-21-CE48-0017 - AAPG2021 - VALID, Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID, Preuves et Langages (PLUME), Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Automatisation et ReprésenTation: fOndation du calcUl et de la déducTion (PARTOUT), Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), ANR-21-CE48-0017,LambdaComb,une expédition cartographique entre le lambda-calcul, la logique, et la combinatoire(2021), and ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010)
Subjects: FOS: Computer and information sciences, Computer Science - Logic in Computer Science, [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], system BV, dicographs, relation webs, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], deep inference, proof nets, pomset logic, cographs, seriesparallel orders, Logic in Computer Science (cs.LO)
Abstract: Pomset logic and BV are both logics that extend multiplicative linear logic (with Mix) with a third connective that is self-dual and non-commutative. Whereas pomset logic originates from the study of coherence spaces and proof nets, BV originates from the study of series-parallel orders, cographs, and proof systems. Both logics enjoy a cut-admissibility result, but for neither logic can this be done in the sequent calculus. Provability in pomset logic can be checked via a proof net correctness criterion and in BV via a deep inference proof system. It has long been conjectured that these two logics are the same. In this paper we show that this conjecture is false. We also investigate the complexity of the two logics, exhibiting a huge gap between the two. Whereas provability in BV is NP-complete, provability in pomset logic is $\Sigma_2^p$-complete. We also make some observations with respect to possible sequent systems for the two logics.
Published: 2022

8. On the homology growth and the $\ell^2$-Betti numbers of $\mathrm{Out}(W_n)$

Author: Gaboriau, Damien, Guerch, Yassine, Horbez, Camille, Centre National de la Recherche Scientifique (CNRS), École normale supérieure de Lyon (ENS de Lyon), Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), ANR-11-IDEX-0007,Avenir L.S.E.,PROJET AVENIR LYON SAINT-ETIENNE(2011), ANR-10-LABX-0059,CARMIN,Centers of Hosting and International Mathematical Encounters(2010), ANR-22-ERCS-0011,Artin-Out-ME-OA,Groupes d'Artin, groupes modulaires et Out(Fn) : de la géométrie aux algèbres d'opérateurs via l'équivalence mesurée(2022), European Project: 101040507,Artin-Out-ME-OA, Horbez, Camille, Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID, PROJET AVENIR LYON SAINT-ETIENNE - - Avenir L.S.E.2011 - ANR-11-IDEX-0007 - IDEX - VALID, Centers of Hosting and International Mathematical Encounters - - CARMIN2010 - ANR-10-LABX-0059 - LABX - VALID, Groupes d'Artin, groupes modulaires et Out(Fn) : de la géométrie aux algèbres d'opérateurs via l'équivalence mesurée - - Artin-Out-ME-OA2022 - ANR-22-ERCS-0011 - T-ERC - VALID, and Artin groups, mapping class groups and Out(Fn): from geometry to operator algebras via measure equivalence - Artin-Out-ME-OA - 101040507 - INCOMING
Subjects: Geometric Topology (math.GT), [MATH.MATH-AT] Mathematics [math]/Algebraic Topology [math.AT], Group Theory (math.GR), [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], 57M07, 20J05, 20F28, 20E08, 20E26, 06A07, Mathematics - Geometric Topology, [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT], [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT], FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, Mathematics - Group Theory, [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR], [MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]
Abstract: Let $n\ge 3$, and let $\mathrm{Out}(W_n)$ be the outer automorphism group of a free Coxeter group $W_n$ of rank $n$. We study the growth of the dimension of the homology groups (with coefficients in any field $\mathbb{K}$) along Farber sequences of finite-index subgroups of $\mathrm{Out}(W_n)$. We show that, in all degrees up to $\lfloor\frac{n}{2}\rfloor-1$, these Betti numbers grow sublinearly in the index of the subgroup. When $\mathbb{K}=\mathbb{Q}$, through L\"uck's approximation theorem, this implies that all $\ell^2$-Betti numbers of $\mathrm{Out}(W_n)$ vanish up to degree $\lfloor\frac{n}{2}\rfloor-1$. In contrast, in top dimension equal to $n-2$, an argument of Gaboriau and No\^us implies that the $\ell^2$-Betti number does not vanish. We also prove that the torsion growth of the integral homology is sublinear. Our proof of these results relies on a recent method introduced by Ab\'ert, Bergeron, Fr\k{a}czyk and Gaboriau. A key ingredient is to show that a version of the complex of partial bases of $W_n$ has the homotopy type of a bouquet of spheres of dimension $\lfloor\frac{n}{2}\rfloor-1$.
Published: 2022

9. Bottom-Up Sequentialization of Unit-Free MALL Proof Nets

Author: Di Guardia, Rémi, Laurent, Olivier, Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Preuves et Langages (PLUME), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), ANR-20-CE48-0005,QuaReMe,Méthodes de raisonnement quantitative pour les logiques probabilistiques(2020), Di Guardia, Rémi, Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID, and Méthodes de raisonnement quantitative pour les logiques probabilistiques - - QuaReMe2020 - ANR-20-CE48-0005 - AAPG2020 - VALID
Subjects: [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], [INFO]Computer Science [cs], [INFO] Computer Science [cs]
Abstract: International audience; We propose a new proof of sequentialization for the proof nets of unit-free multiplicative-additive linear logic of Hughes & Van Glabbeek. This is done by adapting a method from unit-free multiplicative linear logic, showing the robustness of this approach.
Published: 2022

10. Types for Complexity of Parallel Computation in Pi-Calculus

Author: Patrick Baillot, Alexis Ghyselen, Preuves et Langages (PLUME), Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Baillot, Patrick, and Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID
Subjects: [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], Implicit Computational Complexity, Computer science, Process calculus, Computation, 0102 computer and information sciences, 02 engineering and technology, Parallel computing, Type (model theory), 01 natural sciences, Operational semantics, Article, Pi-calculus, Size Types, 0202 electrical engineering, electronic engineering, information engineering, Time complexity, Functional programming, Type Systems, Process (computing), [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], 020207 software engineering, 16. Peace & justice, Process Calculi, Complexity Analysis, 010201 computation theory & mathematics, Parallelism (grammar), Software
Abstract: Type systems as a technique to analyse or control programs have been extensively studied for functional programming languages. In particular some systems allow to extract from a typing derivation a complexity bound on the program. We explore how to extend such results to parallel complexity in the setting of the pi-calculus, considered as a communication-based model for parallel computation. Two notions of time complexity are given: the total computation time without parallelism (the work) and the computation time under maximal parallelism (the span). We define operational semantics to capture those two notions, and present two type systems from which one can extract a complexity bound on a process. The type systems are inspired both by size types and by input/output types, with additional temporal information about communications.
Published: 2021

11. Analyse de stabilité d'une équation à deux retards et application à la production des plaquettes sanguines

Author: Jacques Bélair, Laurent Pujo-Menjouet, Loïs Boullu, Multi-scale modelling of cell dynamics : application to hematopoiesis (DRACULA), Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Département de Mathématiques et de Statistiques [UdeM- Montréal], Université de Montréal (UdeM), Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan (ICJ), Université Claude Bernard Lyon 1 - Faculté des sciences (UCBL FS), Université de Lyon-Université de Lyon, Région Rhône-Alpes (Explo'RA Doc), France Canada Research Fund, NSERC, MITACS, ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Institut Camille Jordan [Villeurbanne] (ICJ), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Université Claude Bernard Lyon 1 - Faculté des sciences et technologies (UCBL FST), and LABEX MILYON (ANR-10-LABX-0070) of Universiyé de Lyon, within the program 'Investissements d’Avenir' (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR)
Subjects: Platelets, Differential equation, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Population, centre manifold analysis, Space (mathematics), Stability (probability), two delays, Combinatorics, 03 medical and health sciences, symbols.namesake, 0302 clinical medicine, Discrete Mathematics and Combinatorics, education, Bifurcation, 030304 developmental biology, Physics, Hopf bifurcation, 0303 health sciences, education.field_of_study, Applied Mathematics, Torus, stability, D-decomposition, 030220 oncology & carcinogenesis, oscillations, symbols, Production (computer science), Analysis
Abstract: International audience; We analyze the stability of a differential equation with two delays originating from a model for a population divided into two subpopulations, immature and mature, and we apply this analysis to a model for platelet production. The dynamics of mature individuals is described by the following nonlinear differential equation with two delays: x'(t) = −γx(t) + g(x(t − τ1)) − g(x(t − τ1 − τ2))e(−γ τ2). The method of D-decomposition is used to compute the stability regions for a given equilibrium. The centre manifold theory is used to investigate the steady-state bifurcation and the Hopf bifurcation. Similarly, analysis of the centre manifold associated with a double bifurcation is used to identify a set of parameters such that the solution is a torus in the pseudo-phase space. Finally, the results of the local stability analysis are used to study the impact of an increase of the death rate γ or of a decrease of the survival time τ2 of platelets on the onset of oscillations. We show that the stability is lost through a small decrease of survival time (from 8.4 to 7 days), or through an important increase of the death rate (from 0.05 to 0.625 1/day).; Nous analysons la stabilité d’une équation différentielle à deux retards issue de la dynamique de populations structurées en deux catégories, immatures et matures, puis nous appliquons cette analyse à un modèle pour la production des plaquettes. La dynamique du nombre d’individus matures est alors décrite par une équation à deux retards non-linéaire de la forme x'(t) = −γx(t) + g(x(t − τ1)) − g(x(t − τ1 − τ2))e(−γ τ2) . La méthode de la D-décomposition est utilisée pour procéder numériquement à une exploration exhaustive des configurations que peut prendre la région de stabilité dans les plans (A,B) et (τ,B). L’analyse de la variété centre est utilisée pour étudier la bifurcation "steady-state" et les bifurcations de Hopf. De manière similaire, l'analyse de la variété centre associée aux doubles bifurcations permet d'identifier un jeu de paramètres auquel correspond une solution prenant la forme d’un tore dans l’espace de pseudo-phase. Enfin, les résultats de l’analyse de stabilité locale est utilisé pour étudier l’impact d’une augmentation du taux de mort des plaquettes γ ainsi que celui d’une diminution du temps de survie des plaquettes τ2 sur l’apparition d’oscillations. Nous montrons alors que la stabilité peut être perdue à la suite d’une diminution légère du temps de survie (de 8.4 jours à 7 jours), ou par une forte augmentation du taux de mort (de 0.05 à 0.6/jour).
Published: 2020
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12. Work-in-Progress: Evaluating Task Dropping Strategies for Overloaded Real-Time Systems

Author: Gao, Yiqin, Pallez, Guillaume, Robert, Yves, Vivien, Frédéric, École normale supérieure de Lyon (ENS de Lyon), Optimisation des ressources : modèles, algorithmes et ordonnancement (ROMA), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Topology-Aware System-Scale Data Management for High-Performance Computing (TADAAM), Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), The work of Yiqin Gao was supported by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program 'Investissements d’Avenir' (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR)., École normale supérieure - Lyon (ENS Lyon), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), and Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Inria Bordeaux - Sud-Ouest
Subjects: [INFO.INFO-PF]Computer Science [cs]/Performance [cs.PF], real-time system, [INFO]Computer Science [cs], overloaded system, task dropping
Abstract: International audience; This paper discusses evaluation criteria and scheduling strategies for the analysis of overloaded real-time systems. This work builds upon techniques from queueing theory and proposes a new approach for real-time systems.
Published: 2021
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13. Well-posedness and decay to equilibrium for the Muskat problem with discontinuous permeability

Author: Rafael Granero-Belinchón, Steve Shkoller, Équations aux dérivées partielles, analyse (EDPA), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), University of California [Davis] (UC Davis), University of California, This work was supported by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program 'Investissements d'Avenir' (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR)., and ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010)
Subjects: Pointwise, Applied Mathematics, General Mathematics, 010102 general mathematics, Mathematical analysis, Classification of discontinuities, Singular integral, Curvature, 01 natural sciences, 010101 applied mathematics, Permeability (earth sciences), Mathematics - Analysis of PDEs, Step function, FOS: Mathematics, Fluid dynamics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Porous medium, Analysis of PDEs (math.AP), Mathematics
Abstract: We first prove local-in-time well-posedness for the Muskat problem, modeling fluid flow in a two-dimensional inhomogeneous porous media. The permeability of the porous medium is described by a step function, with a jump discontinuity across the fixed-in-time curve ( x 1 , − 1 + f ( x 1 ) ) (x_1,-1+f(x_1)) , while the interface separating the fluid from the vacuum region is given by the time-dependent curve ( x 1 , h ( x 1 , t ) ) (x_1,h(x_1,t)) . Our estimates are based on a new methodology that relies upon a careful study of the PDE system, coupling Darcy’s law and incompressibility of the fluid, rather than the analysis of the singular integral contour equation for the interface function h h . We are able to develop an existence theory for any initial interface given by h 0 ∈ H 2 h_0 \in H^2 and any permeability curve-of-discontinuity that is given by f ∈ H 2.5 f \in H^{2.5} . In particular, our method allows for both curves to have (pointwise) unbounded curvature. In the case that the permeability discontinuity is the set f = 0 f=0 , we prove global existence and decay to equilibrium for small initial data. This decay is obtained using a new energy-energy dissipation inequality that couples tangential derivatives of the velocity in the bulk of the fluid with the curvature of the interface. To the best of our knowledge, this is the first global existence result for the Muskat problem with discontinuous permeability.
Published: 2019
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14. Coinductive Algorithms for Büchi Automata

Author: Denis Kuperberg, Laureline Pinault, Damien Pous, Preuves et Langages (PLUME), Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Plume, ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), European Project: 678157,H2020,ERC-2015-STG,CoVeCe(2016), Pous, Damien, Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID, Coinduction for Verification and Certification - CoVeCe - - H20202016-04-01 - 2021-03-31 - 678157 - VALID, Centre National de la Recherche Scientifique (CNRS)-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École normale supérieure - Lyon (ENS Lyon), Université de Lyon-École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Claude Bernard Lyon 1 (UCBL), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), and Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL)
Subjects: 050101 languages & linguistics, Algebra and Number Theory, [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], Computer science, 05 social sciences, Coinduction, Structure (category theory), Büchi automaton, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], 02 engineering and technology, 0102 computer and information sciences, 01 natural sciences, Theoretical Computer Science, Automaton, Computational Theory and Mathematics, 010201 computation theory & mathematics, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, 0501 psychology and cognitive sciences, Equivalence (formal languages), Algorithm, Equivalence (measure theory), Computer Science::Formal Languages and Automata Theory, Information Systems
Abstract: International audience; We propose a new algorithm for checking language equivalence of non-deterministic Büchi automata. We start from a construction proposed by Calbrix, Nivat and Podelski, which makes it possible to reduce the problem to that of checking equivalence of automata on finite words. Although this construction generates large and highly non-deterministic automata, we show how to exploit their specific structure and apply state-of-the art techniques based on coinduction to reduce the state-space that has to be explored. Doing so, we obtain algorithms which do not require full determinisation or complementation.
Published: 2021
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15. Click and coLLecT An Interactive Linear Logic Prover

Author: Callies, Etienne, Laurent, Olivier, Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Preuves et Langages (PLUME), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), ANR-11-IDEX-0007,Avenir L.S.E.,PROJET AVENIR LYON SAINT-ETIENNE(2011), Centre National de la Recherche Scientifique (CNRS)-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École normale supérieure - Lyon (ENS Lyon), Université de Lyon-École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Claude Bernard Lyon 1 (UCBL), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Gouat, Isabelle, Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID, and PROJET AVENIR LYON SAINT-ETIENNE - - Avenir L.S.E.2011 - ANR-11-IDEX-0007 - IDEX - VALID
Subjects: [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO]
Abstract: International audience; We describe the 'Click and coLLecT' system, an interactive tool for building linear logic proofs online.
Published: 2021

16. Most rigid representation and Cayley index of finitely generated groups

Author: Leemann, Paul-Henry, de La Salle, Mikael, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), ANR-16-CE40-0022,AGIRA,Actions de Groupes, Isométries, Rigidité et Aléa(2016), ANR-19-CE40-0002,ANCG,Analyse non commutative sur les groupes et les groupes quantiques(2019), de la salle, mikael, Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID, Actions de Groupes, Isométries, Rigidité et Aléa - - AGIRA2016 - ANR-16-CE40-0022 - AAPG2016 - VALID, and Analyse non commutative sur les groupes et les groupes quantiques - - ANCG2019 - ANR-19-CE40-0002 - AAPG2019 - VALID
Subjects: Applied Mathematics, [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA], [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], Group Theory (math.GR), [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], Theoretical Computer Science, Mathematics::Group Theory, Computational Theory and Mathematics, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), Geometry and Topology, [MATH.MATH-OA] Mathematics [math]/Operator Algebras [math.OA], Mathematics - Group Theory, [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]
Abstract: If $G$ is a group and $S$ a generating set, $G$ canonically embeds into the automorphism group of its Cayley graph and it is natural to try to minimize, over all generating sets, the index of this inclusion. This infimum is called the Cayley index of the group. In a recent series of works, we have characterized the infinite finitely generated groups with Cayley index $1$. We complement this characterization by showing that the Cayley index is $2$ in the remaining cases and is attained for a finite generating set., 9 pages
Published: 2021

17. A duality operators/Banach spaces

Author: De la Salle, Mikael, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), ANR-16-CE40-0022,AGIRA,Actions de Groupes, Isométries, Rigidité et Aléa(2016), ANR-19-CE40-0002,ANCG,Analyse non commutative sur les groupes et les groupes quantiques(2019), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), de la salle, mikael, Actions de Groupes, Isométries, Rigidité et Aléa - - AGIRA2016 - ANR-16-CE40-0022 - AAPG2016 - VALID, Analyse non commutative sur les groupes et les groupes quantiques - - ANCG2019 - ANR-19-CE40-0002 - AAPG2019 - VALID, Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID, and École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Mathematics - Functional Analysis, Mathematics::Functional Analysis, [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA], FOS: Mathematics, [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], [MATH.MATH-OA] Mathematics [math]/Operator Algebras [math.OA], [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], Functional Analysis (math.FA), [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]
Abstract: Given a set $B$ of operators between subspaces of $L_p$ spaces, we characterize the operators between subspaces of $L_p$ spaces that remain bounded on the $X$-valued $L_p$ space for every Banach space on which elements of the original class $B$ are bounded. This is a form of the bipolar theorem for a duality between the class of Banach spaces and the class of operators between subspaces of $L_p$ spaces, essentially introduced by Pisier. The methods we introduce allow us to recover also the other direction --characterizing the bipolar of a set of Banach spaces--, which had been obtained by Hernandez in 1983., Comment: 34 pages. Old project, already announced at several occasions in 2016, and that took a long time to be completed. Comments welcome v2: 37 pages. Section 5 added on the duality between Banach spaces and operators on full Lp spaces. A few references added
Published: 2021

18. Inverting the Ray-Knight identity on the line

Author: Titus Lupu, Pierre Tarrès, Christophe Sabot, Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI), Laboratoire de Probabilités, Statistiques et Modélisations (LPSM (UMR_8001)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Sorbonne Université (SU), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon, NYU–ECNU Institute of Mathematical Sciences at NYU Shanghai, Courant Institute of Mathematical Sciences [New York] (CIMS), New York University [New York] (NYU), NYU System (NYU)-NYU System (NYU), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zurich Foundation, National Science Foundation of China (NSFC), grant No. 11771293, Australian Research Council (ARC), grant No. DP180100613, ANR-16-CE93-0003,MALIN,Marches aléatoires en interaction(2016), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), LABEX MILYON (ANR-10-LABX-0070), Laboratoire de Probabilités, Statistique et Modélisation (LPSM (UMR_8001)), Université Paris Dauphine-PSL-Centre National de la Recherche Scientifique (CNRS), and ANR-16-CE93-0003,MALIN,Marches aléatoires en interaction(2017)
Subjects: Statistics and Probability, 60G15, 60J60, 60K35, 60K37(primary), and 60J55, 81T25, 81T60(secondary), 01 natural sciences, Identity (music), 010104 statistics & probability, Mathematics::Probability, local time, Gaussian free field, FOS: Mathematics, isomorphism theorems, 0101 mathematics, Diffusion (business), Mathematics, 010102 general mathematics, Mathematical analysis, Probability (math.PR), self-interacting diffusion, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Flow (mathematics), Isomorphism theorem, Local time, Line (geometry), Jump, Statistics, Probability and Uncertainty, Mathematics - Probability
Abstract: Using a divergent Bass-Burdzy flow we construct a self-repelling one-dimensional diffusion. Heuristically, it can be interpreted as a solution to an SDE with a singular drift involving a derivative of the local time. We show that this self-repelling diffusion inverts the second Ray-Knight identity on the line. The proof goes through an approximation by a self-repelling jump processes that has been previously shown by the authors to invert the Ray-Knight identity in the discrete., Comment: 24 pages
Published: 2021
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19. On the continuity of Fourier multipliers on $\dot{W}^{l,1}\left( \mathbb{R}^{d}\right)$ and $\dot{W}^{l,\infty }\left( \mathbb{R}^{d}\right) $

Author: Curcă, Eduard, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Faculty of Computer Science [Iaşi, Roumania], Universitatea Alexandru Ioan Cuza [Lasi], ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Curca, Eduard-Valentin, and Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID
Subjects: 42B05, [MATH] Mathematics [math], Fourier multipliers, [MATH]Mathematics [math], Sobolev spaces. MSC 2020 classification: 42B15
Abstract: Kazaniecki and Wojciechowskiproved in 2013 that every Fourier multiplier on $\dot{W}^{1,1}\left( \mathbb{R}^{d}\right) $ is a bounded continuous function on $\mathbb{R}^{d}$. This is a generalization of a previous result of Bonami and Poornima (1987)concerning homogeneous multipliers of degree zero. We further generalize the resultof Kazaniecki and Wojciechowski. We prove that, given an integer $l\geq1$,every multiplier on $\dot{W}^{l,1}\left( \mathbb{R}^{d}\right) $ or on $\dot{W}^{l,\infty}\left( \mathbb{R}^{d}\right) $ is a bounded continuous functionon $\mathbb{R}^{d}$. We obtain these results via a substantial simplification of the Riesz products technique used by Kazaniecki and Wojciechowski.
Published: 2021

20. Minimiser la consommation d’énergie pour des tâches en temps réel sur des plateformes hétérogènes avec contraintes de délais et de fiabilité

Author: Gao, Yiqin, Han, Li, Liu, Jing, Robert, Yves, Vivien, Frédéric, Optimisation des ressources : modèles, algorithmes et ordonnancement (ROMA), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de l'Informatique du Parallélisme (LIP), Centre National de la Recherche Scientifique (CNRS)-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École normale supérieure - Lyon (ENS Lyon), East China Normal University [Shangaï] (ECNU), Innovative Computing Laboratory [Knoxville] (ICL), The University of Tennessee [Knoxville], This paper is partially supported by the National Key Research and Development under Project 2019YFA0706404, NSFC 61972150, and a JORISS grant from ENS de Lyon and ECNU. The work of Yiqin Gao was supported by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program 'Investissements d’Avenir' (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). First two authors contributed equally to this work., Inria - Research Centre Grenoble – Rhône-Alpes, ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), ANR-11-IDEX-0007,Avenir L.S.E.,PROJET AVENIR LYON SAINT-ETIENNE(2011), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), and Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL)
Subjects: Systèmes en temps réel, reliability, plates-formes hétérogènes, systèmes sensibles à l’énergie, [INFO]Computer Science [cs], scheduling, fiabilité, heterogeneous platforms, energy-aware systems, Real-time systems, ordonnancement
Abstract: Low energy consumption and high reliability are widely identified as increasingly relevant issues in real-time systems on heterogeneous platforms. In this paper, we propose a multi-criteria optimization strategy to minimize the expected energy consumption while enforcing the reliability threshold and meeting all task deadlines. The tasks arrive periodically. Each instance of a task is replicated to ensure a prescribed reliability threshold. The platform is composed of processors with different (and possibly unrelated) characteristics, including speed profile, energy cost and failure rate. We provide several mapping and scheduling heuristics to solve this challenging optimization problem. Specifically, a novel approach is designed to control (i) how many replicas to use for each task, (ii) on which processor to map each replica and (iii) when to schedule each replica for eachtask instance on its assigned processor. Different mappings achieve different levels of reliability and consume different amounts of energy. Scheduling matters because once a task replica is successful, the other replicas of that task instance are canceled, which calls for minimizing the amount of temporal overlap between any replica pair. The experiments are conducted for a comprehensive set of execution scenarios, with a wide range of processor speed profiles and failure rates. The comparison results reveal that our strategies perform better than the random baseline, with a gain in energy consumption of more than 40% for nearly all cases. The absolute performance of the heuristics is assessed by a comparison with a lower-bound; the best heuristics achieve an excellent performance. It saves only 2% less energy than the lower-bound.; La faible consommation d’énergie et la haute fiabilité sont identifiées comme des problèmes de plus en plus pertinents dans les systèmes en temps réel sur des plateformes hétérogènes. Dans ce rapport, nous proposons une stratégie d’optimisation multi-critère pour minimiser l’espérance de laconsommation d’énergie tout en respectant le seuil de fiabilité et toutes les échéances des tâches. Les tâches arrivent périodiquement. Chaque instance d’une tâche est répliquée pour garantir un seuil de fiabilité prescrit. La plateforme est composée de processeurs avec des caractéristiques différentes (et éventuellement sans corrélation), y compris la vitesse, le coût énergétique et le taux de panne. Nous fournissons plusieurs heuristiques de placement et d’ordonnancement pour ce problème d’optimisation difficile. Plus précisément, une nouvelle solution est conçue pour contrôler (i) le nombre de répliques à utiliser pour chaque tâche, (ii) sur quel processeur doit-on placer chaque réplique et (iii) comment ordonnancer chaque réplique de chaque instance de tâche sur le processeur qui lui est affecté. Différents placements atteignent différents niveaux de fiabilité et consomment différentes quantités d’énergie. L’ordonnancement est important car une fois qu’une réplique de tâche réussit, les autres répliques de cette instance sont annulées, ce qui demande de minimiser le recouvrement en temps entre toute paire de répliques. Les expériences sont exécutées pour un grand ensemble de scénarios, avec une large gamme de vitesses et de taux d’échec pour les processeurs. Les résultats montrent que nos stratégies fonctionnent mieux que la référence de base aléatoire, avec un gain de 40 % en consommation d’énergie, dans presque tous les cas. La performance absolue de l’heuristique est évaluée en la comparant avec une borne inférieure. La meilleure heuristique atteint une excellente performance, avec une valeur moyenne supérieure de seulement 2% à la borne inférieure.
Published: 2021

21. Zeta-like multiple zeta values in positive characteristic

Author: Le, Huy Hung, Ngo Dac, Tuan, Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU), Centre National de la Recherche Scientifique (CNRS), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), ANR-19-CE40-0015,COLOSS,Cohomologie des espaces localement symétriques(2019), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), and ANR: ANR-10_LABX-0070,LABEX MILYON (ANR-10-LABX-0070) of Universit ́e de Lyon within the program 'Investissements d’Avenir (ANR-11-IDEX-0007)' operated by the French National Research Agency (ANR).
Subjects: t-motives, General Mathematics, Mathematics::Number Theory, multiple zeta values, Function field arithmetic, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], Drinfeld and Anderson modules
Abstract: We study multiple zeta values (MZV's) over the rational function field over Fq which were introduced by Thakur as analogues of classical multiple zeta values of Euler. In this paper we affirmatively solve a conjecture of Lara Rodriguez and Thakur which gives a full list of zeta-like MZV's of weight at most q^2 and depth 2. Further, we completely determine all zeta-like MZV's of weight at most q^2 and arbitrary depth. Our method is based on a criterion which is derived from the Anderson-Thakur motivic interpretation of MZV's and the Anderson-Brownawell-Papanikolas criterion for linear independence in positive characteristic.
Published: 2021

22. On the Northcott property for special values of L-functions

Author: Pazuki, Fabien, Pengo, Riccardo, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), and ANR: ANR-10_LABX-0070,LABEX MILYON (ANR-10-LABX-0070) of Universit ́e de Lyon within the program 'Investissements d’Avenir (ANR-11-IDEX-0007)' operated by the French National Research Agency (ANR).
Subjects: abelian varieties. Mathematics Subject Classification: 11G40, 11G50, L-functions, motives, heights, 11F67, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], Northcott property, 14K05, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
Abstract: 28 pages. Comments are very welcome!; We propose an investigation on the Northcott, Bogomolov and Lehmer properties for special values of L-functions. We first introduce an axiomatic approach to these three properties. We then focus on the Northcott property for special values of L-functions. We prove that such a property holds for the special value at zero of Dedekind zeta functions of number fields. In the case of $L$-functions of pure motives, we prove a Northcott property for special values located at the left of the critical strip, assuming the validity of the functional equation.; On propose une étude de las propriétés de Northcott, Bogomolov et Lehmer pour les valeurs spéciales des fonctions L. Tout d'abord, on introduit des nouvelles définitions axiomatiques de ces propriétés. Deuxièmement, nous nous concentrons sûr la propriété de Northcott, pour les valeurs spéciales des fonctions L. Nous montrons que telle propriété est valide pour la valeur spéciale en zéro de les fonctions zêta des corps de nombres. Enfin, nous démontrons une propriété de Northcott pour les valeurs à la gauche de la bande critique des fonctions L des motifs pures, en assument la validité de l'équation fonctionnelle.
Published: 2021

23. Covert Cycle Stealing in a Single FIFO Server

Author: Philippe Nain, Don Towsley, Bo Jiang, Shangaï Jiao Tong University [Shangaï], Dynamic Networks : Temporal and Structural Capture Approach (DANTE), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Institut Rhône-Alpin des systèmes complexes (IXXI), Université Grenoble Alpes (UGA)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Lumière - Lyon 2 (UL2)-Université Jean Moulin - Lyon 3 (UJML), Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École normale supérieure - Lyon (ENS Lyon)-Université Grenoble Alpes (UGA)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Lumière - Lyon 2 (UL2)-Université Jean Moulin - Lyon 3 (UJML), Université de Lyon, University of Massachusetts [Amherst] (UMass Amherst), University of Massachusetts System (UMASS), The research of Don Towsley was supported by the US NSF grant CNS-1564067 and the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program 'Investissements d’Avenir' (ANR-11-IDEX- 0007) operated by the French National Research Agency (ANR)., ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), ANR-11-IDEX-0007,Avenir L.S.E.,PROJET AVENIR LYON SAINT-ETIENNE(2011), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), École normale supérieure de Lyon (ENS de Lyon)-Université Lumière - Lyon 2 (UL2)-Université Jean Moulin - Lyon 3 (UJML), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Université Lumière - Lyon 2 (UL2)-Université Jean Moulin - Lyon 3 (UJML), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Centre National de la Recherche Scientifique (CNRS)-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), and Université de Lyon-École normale supérieure - Lyon (ENS Lyon)-Institut Rhône-Alpin des systèmes complexes (IXXI)
Subjects: FOS: Computer and information sciences, Covert communication, Computer Networks and Communications, FIFO (computing and electronics), Computer science, Cycle stealing, Throughput, 02 engineering and technology, 01 natural sciences, Upper and lower bounds, 010104 statistics & probability, [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI], Queue, 0202 electrical engineering, electronic engineering, information engineering, Media Technology, Computer Science (miscellaneous), FOS: Mathematics, 0101 mathematics, Safety, Risk, Reliability and Quality, Time complexity, computer.programming_language, Computer Science - Performance, business.industry, Probability (math.PR), 020206 networking & telecommunications, Performance (cs.PF), Hardware and Architecture, Covert, business, Alice (programming language), computer, Mathematics - Probability, Software, Information Systems, Computer network
Abstract: Consider a setting where Willie generates a Poisson stream of jobs and routes them to a single server that follows the first-in first-out discipline. Suppose there is an adversary Alice, who desires to receive service without being detected. We ask the question: What is the number of jobs that she can receive covertly, i.e., without being detected by Willie? In the case where both Willie and Alice jobs have exponential service times with respective rates μ 1 and μ 2 , we demonstrate a phase-transition when Alice adopts the strategy of inserting a single job probabilistically when the server idles: over n busy periods, she can achieve a covert throughput, measured by the expected number of jobs covertly inserted, of O (√ n ) when μ 1 < 2 μ 2 , O (√ n log n ) when μ 1 = 2μ 2 , and O ( n μ 2 /μ 1 ) when μ 1 > 2μ 2 . When both Willie and Alice jobs have general service times, we establish an upper bound for the number of jobs Alice can execute covertly. This bound is related to the Fisher information. More general insertion policies are also discussed.
Published: 2021
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24. A generalized method for Sparse Partial Least Squares (Dual-SPLS): theory and applications

Author: Alsouki, Louna, Wahl, Francois, Duval, Laurent, Marteau, Clément, El-Haddad, Rami, Alsouki, Louna, Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon, IFP Energies nouvelles (IFPEN), Université Saint-Joseph de Beyrouth (USJ), and ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010)
Subjects: [STAT]Statistics [stat], dual norm, sparsity, regression, [STAT.OT]Statistics [stat]/Other Statistics [stat.ML], Partial Least Squares, lasso algorithm, [STAT.OT] Statistics [stat]/Other Statistics [stat.ML], [STAT] Statistics [stat]
Abstract: National audience; In data analysis, high dimensionality is often a delicate obstacle to overcome which can be solved by representing the data in a lower dimensional space using projection methods like the Partial Least Squares regression (PLS) or by resorting to variable selection methods like the lasso approach. The Sparse Partial Least Squares (SPLS) combines the two latter in order to better interpret the results due to the sparsity imposed on the new directions. Several implementations have been proposed. However, problems of accuracy of predictions and correct interpretation of regression coefficients arise in these approaches. Hence we developed the Dual Sparse Partial Least Squares, a flexible method that results in more accurate predictions and better interpre- tation of the coefficients due to their sparsity. In this paper we present the theory behind Dual-SPLS and some applicative results on petroleum data sets.
Published: 2021

25. ONE-ENDED SPANNING SUBFORESTS AND TREEABILITY OF GROUPS

Author: Conley, Clinton, Gaboriau, Damien, Marks, Andrew, Tucker-Drob, Robin, Gaboriau, Damien, Appel à projets générique - Groupes, Actions, Métriques, Mesures et théorie Ergodique - - GAMME2014 - ANR-14-CE25-0004 - Appel à projets générique - VALID, Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), ANR-14-CE25-0004,GAMME,Groupes, Actions, Métriques, Mesures et théorie Ergodique(2014), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), and École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)
Subjects: 05C10) ergodic and Borel equivalence relations, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA], ergodic dimension, locally compact groups, [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], trees, ergodic and Borel equivalence relations, [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], planar graphs, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], treeability, [MATH.MATH-LO]Mathematics [math]/Logic [math.LO], probability measure preserving and Borel actions of groups, elementarily free groups, 37A20 (03E15, [MATH.MATH-LO] Mathematics [math]/Logic [math.LO], 22F10, measure equivalence, [MATH.MATH-OA] Mathematics [math]/Operator Algebras [math.OA], 37A20 (03E15, 22F10, 05C10), cost of groups, [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]
Abstract: 42 pages, 2 x 2 figures; We show that several new classes of groups are measure strongly treeable. In particular, finitely generated groups admitting planar Cayley graphs, elementarily free groups, and Isom(H^2) and all its closed subgroups. In higher dimensions, we also prove a dichotomy that the fundamental group of a closed aspherical 3-manifold is either amenable or has strong ergodic dimension 2. Our main technical tool is a method for finding measurable treeings of Borel planar graphs by constructing one-ended spanning subforests in their planar dual. Our techniques for constructing one-ended spanning subforests also give a complete classification of the locally finite p.m.p. graphs which admit Borel a.e. one-ended spanning subforests.
Published: 2021

26. Interpretable Dual Sparse Partial Least Squares (DS-PLS) regression; Application to NMR/NIR petroleum data sets

Author: Alsouki, Louna, Wahl, Francois, Duval, Laurent, Marteau, Clément, El-Haddad, Rami, Alsouki, Louna, Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon, IFP Energies nouvelles (IFPEN), Université Saint-Joseph de Beyrouth (USJ), and ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010)
Subjects: dual norm, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], sparsity, regression, [STAT.OT]Statistics [stat]/Other Statistics [stat.ML], Partial Least Squares, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], [STAT.OT] Statistics [stat]/Other Statistics [stat.ML], ComputingMilieux_MISCELLANEOUS
Abstract: National audience
Published: 2021

27. Real structures on nilpotent orbit closures

Author: Bulois, Michael, Moser-Jauslin, Lucy, Terpereau, Ronan, Terpereau, Ronan, APPEL À PROJETS GÉNÉRIQUE 2018 - Fibrations et actions de groupes algébriques - - FIBALGA2018 - ANR-18-CE40-0003 - AAPG2018 - VALID, Ingénierie et Innovation par les sciences physiques, les savoir-faire technologiques et l'interdisciplinarité - - EIPHI2017 - ANR-17-EURE-0002 - EURE - VALID, and Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID
Subjects: Mathematics - Algebraic Geometry, real form, 14R20, 14M17, 14P99, 11S25, 20G20, homogeneous space, Mathematics::Rings and Algebras, real structure, Galois cohomology, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], FOS: Mathematics, Nilpotent orbit, Mathematics::Representation Theory, Algebraic Geometry (math.AG)
Abstract: We determine the equivariant real structures on nilpotent orbits and the normalizations of their closures for the adjoint action of a complex semisimple algebraic group on its Lie algebra., Comment: 16 pages, final version, to appear in Journal of Lie Theory (Volume 32)
Published: 2021
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28. On the Orbits of Automaton Semigroups and Groups

Author: D'Angeli, Daniele, Francoeur, Dominik, Rodaro, Emanuele, Wächter, Jan Philipp, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), Francoeur, Dominik, and Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID
Subjects: reversible, FOS: Computer and information sciences, Algebra and Number Theory, Formal Languages and Automata Theory (cs.FL), orbits, Computer Science - Formal Languages and Automata Theory, automaton semigroups, [MATH] Mathematics [math], Group Theory (math.GR), Nonlinear Sciences::Cellular Automata and Lattice Gases, orbital graphs, FOS: Mathematics, Discrete Mathematics and Combinatorics, automaton groups, [MATH]Mathematics [math], Schreier graphs, F.4.m, Mathematics - Group Theory, Computer Science::Formal Languages and Automata Theory, 20E99 20F10 20M30 20M35 68Q70
Abstract: We investigate the orbits of automaton semigroups and groups to obtain algorithmic and structural results, both for general automata but also for some special subclasses. First, we show that a more general version of the finiteness problem for automaton groups is undecidable. This problem is equivalent to the finiteness problem for left principal ideals in automaton semigroups generated by complete and reversible automata. Then, we look at $\omega$-word (i.e. right infinite words) with a finite orbit. We show that every automaton yielding an $\omega$-word with a finite orbit already yields an ultimately periodic one, which is not periodic in general, however. On the algorithmic side, we observe that it is not possible to decide whether a given periodic $\omega$-word has an infinite orbit and that we cannot check whether a given reversible and complete automaton admits an $\omega$-word with a finite orbit, a reciprocal problem to the finiteness problem for automaton semigroups in the reversible case. Finally, we look at automaton groups generated by reversible but not bi-reversible automata and show that many words have infinite orbits under the action of such automata., Comment: arXiv admin note: substantial text overlap with arXiv:1903.00222
Published: 2020

29. ON THE STABILISERS OF POINTS IN GROUPS WITH MICRO-SUPPORTED ACTIONS

Author: Dominik Francoeur, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Francoeur, Dominik, Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID, and École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Algebra and Number Theory, 20E07, 20F65, Group (mathematics), 010102 general mathematics, Hausdorff space, Neighbourhood (graph theory), Mathematics::General Topology, [MATH] Mathematics [math], Group Theory (math.GR), Thompson groups, 01 natural sciences, Action (physics), Homeomorphism, Combinatorics, 0103 physical sciences, FOS: Mathematics, 010307 mathematical physics, 0101 mathematics, [MATH]Mathematics [math], Mathematics - Group Theory, Mathematics
Abstract: Given a group $G$ of homeomorphism of a first-countable Hausdorff space $\mathcal{X}$, we prove that if the action of $G$ on $\mathcal{X}$ is minimal and has rigid stabilisers that act locally minimally, then the neighbourhood stabilisers of any two points in $\mathcal{X}$ are conjugated by a homeomorphism of $\mathcal{X}$. This allows us to study stabilisers of points in many classes of groups, such as topological full groups of Cantor minimal systems, Thompson groups, branch groups, and groups acting on trees with almost prescribed local actions., Comment: 12 pages
Published: 2020

30. Concentration estimates for random subspaces of a tensor product, and application to Quantum Information Theory

Author: Felix Parraud, Benoit Collins, Department of Mathematics, Kyoto University (Kyoto), Kyoto University [Kyoto], Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Kyoto University, École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), Parraud, Felix, and Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID
Subjects: [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Quantum Physics, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA], Mathematics - Operator Algebras, Statistical and Nonlinear Physics, [MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph], [MATH.MATH-OA] Mathematics [math]/Operator Algebras [math.OA], Mathematics - Probability, Mathematical Physics, [PHYS.QPHY] Physics [physics]/Quantum Physics [quant-ph]
Abstract: Given a random subspace H n chosen uniformly in a tensor product of Hilbert spaces V n ⊗ W, we consider the collection K n of all singular values of all norm one elements of H n with respect to the tensor structure. A law of large numbers has been obtained for this random set in the context of W fixed and the dimension of H n, V n tending to infinity at the same speed by Belinschi, Collins, and Nechita [Commun. Math. Phys. 341(3), 885–909 (2016)]. In this paper, we provide measure concentration estimates in this context. The probabilistic study of K n was motivated by important questions in quantum information theory and allowed us to provide the smallest known dimension for the dimension of an ancilla space, allowing for Minimum Output Entropy (MOE) violation. With our estimates, we are able, as an application, to provide actual bounds for the dimension of spaces where the violation of MOE occurs.
Published: 2020

31. On the operator norm of non-commutative polynomials in deterministic matrices and iid Haar unitary matrices

Author: Felix Parraud, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics, Kyoto University (Kyoto), Kyoto University [Kyoto], ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), Kyoto University, Parraud, Felix, and Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID
Subjects: Statistics and Probability, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Mathematics::Operator Algebras, [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA], Mathematics - Operator Algebras, Statistics, Probability and Uncertainty, [MATH.MATH-OA] Mathematics [math]/Operator Algebras [math.OA], Mathematics - Probability, Analysis
Abstract: Let $U^N = (U_1^N,\dots, U^N_p)$ be a d-tuple of $N\times N$ independent Haar unitary matrices and $Z^{NM}$ be any family of deterministic matrices in $\mathbb{M}_N(\mathbb{C})\otimes \mathbb{M}_M(\mathbb{C})$. Let $P$ be a self-adjoint non-commutative polynomial. In 1998, Voiculescu showed that the empirical measure of the eigenvalues of this polynomial evaluated in Haar unitary matrices and deterministic matrices converges towards a deterministic measure defined thanks to free probability theory. Let now $f$ be a smooth function, the main technical result of this paper is a precise bound of the difference between the expectation of $$ \frac{1}{MN} \text{Tr}\left( f(P(U^N\otimes I_M,Z^{NM})) \right) , $$ and its limit when $N$ goes to infinity. If $f$ is seven times differentiable, we show that it is bounded by $M^2 \left\Vert f\right\Vert_{\mathcal{C}^7} N^{-2}$. As a corollary we obtain a new proof with quantitative bounds of a result of Collins and Male which gives sufficient conditions for the operator norm of a polynomial evaluated in Haar unitary matrices and deterministic matrices to converge almost surely towards its free limit. Actually we show that if $U^N$ and $Y^{M_N}$ are independent and $M_N = o(N^{1/3})$, then almost surely, the norm of any polynomial in $(U^N\otimes I_{M_N}, I_N\otimes Y^{M_N})$ converges almost surely towards its free limit., Comment: arXiv admin note: text overlap with arXiv:1912.04588
Published: 2020

32. Autour de la propriété de Northcott pour les valeurs spéciales des fonctions L

Author: Pazuki, Fabien, Pengo, Riccardo, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), ANR: ANR-10_LABX-0070,LABEX MILYON (ANR-10-LABX-0070) of Universit ́e de Lyon within the program 'Investissements d’Avenir (ANR-11-IDEX-0007)' operated by the French National Research Agency (ANR)., École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), and ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010)
Subjects: 11G50, Mathematics - Number Theory, heights, 11F67, Northcott property, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], abelian varieties. Mathematics Subject Classification: 11G40, Mathematics - Algebraic Geometry, L-functions, motives, FOS: Mathematics, Number Theory (math.NT), [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], Algebraic Geometry (math.AG), 11G40, 11G50, 14K05, 11F67, 14K05
Abstract: We propose an investigation on the Northcott, Bogomolov and Lehmer properties for special values of $L$-functions. We first introduce an axiomatic approach to these three properties. We then focus on the Northcott property for special values of $L$-functions. In the case of $L$-functions of pure motives, we prove a Northcott property for special values located at the left of the critical strip, assuming that the $L$-functions in question satisfy some expected properties. Inside the critical strip, focusing on the Dedekind zeta function of number fields, we prove that such a property does not hold for the special value at one, but holds for the special value at zero, and we give a related quantitative estimate in this case., 44 pages. Comments are very welcome!
Published: 2020

33. Asymptotic expansion of smooth functions in polynomials in deterministic matrices and iid GUE matrices

Author: Felix Parraud, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics, Kyoto University (Kyoto), Kyoto University [Kyoto], ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Parraud, Felix, Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID, École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), and Kyoto University
Subjects: [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], High Energy Physics::Theory, Mathematics::Probability, Probability (math.PR), [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA], FOS: Mathematics, Mathematics - Operator Algebras, Statistical and Nonlinear Physics, Operator Algebras (math.OA), [MATH.MATH-OA] Mathematics [math]/Operator Algebras [math.OA], Mathematical Physics, Mathematics - Probability
Abstract: Let $X^N$ be a family of $N\times N$ independent GUE random matrices, $Z^N$ a family of deterministic matrices, $P$ a self-adjoint non-commutative polynomial, that is for any $N$, $P(X^N)$ is self-adjoint, $f$ a smooth function. We prove that for any $k$, if $f$ is smooth enough, there exist deterministic constants $\alpha_i^P(f,Z^N)$ such that $$ \mathbb{E}\left[\frac{1}{N}\text{Tr}\left( f(P(X^N,Z^N)) \right)\right]\ =\ \sum_{i=0}^k \frac{\alpha_i^P(f,Z^N)}{N^{2i}}\ +\ \mathcal{O}(N^{-2k-2}) .$$ Besides the constants $\alpha_i^P(f,Z^N)$ are built explicitly with the help of free probability. In particular, if $x$ is a free semicircular system, then when the support of $f$ and the spectrum of $P(x,Z^N)$ are disjoint, for all $i$, $\alpha_i^P(f,Z^N)=0$. As a corollary, we prove that given $\alpha
Published: 2020

34. Cayley graphs with few automorphisms: the case of infinite groups

Author: Paul-Henry Leemann, Mikael de la Salle, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), ANR-16-CE40-0022,AGIRA,Actions de Groupes, Isométries, Rigidité et Aléa(2016), ANR-19-CE40-0002,ANCG,Analyse non commutative sur les groupes et les groupes quantiques(2019), de la salle, mikael, Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID, Actions de Groupes, Isométries, Rigidité et Aléa - - AGIRA2016 - ANR-16-CE40-0022 - AAPG2016 - VALID, Analyse non commutative sur les groupes et les groupes quantiques - - ANCG2019 - ANR-19-CE40-0002 - AAPG2019 - VALID, and École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)
Subjects: [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA], [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], Ocean Engineering, Group Theory (math.GR), [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 05E18, 05E30, 20B27, 05C25, 05C63, [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], Mathematics::Group Theory, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), [MATH.MATH-OA] Mathematics [math]/Operator Algebras [math.OA], Mathematics - Group Theory, [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]
Abstract: We characterize the finitely generated groups that admit a Cayley graph whose only automorphisms are the translations, confirming a conjecture by Watkins from 1976. The proof relies on random walk techniques. As a consequence, every finitely generated group admits a Cayley graph with countable automorphism group. We also treat the case of directed graphs., v1: 17 pages v2: 19 pages, improvements in the presentation, Section 6 added. To appear in Annales Henri Lebesgue
Published: 2020

35. Large deviations for the largest eigenvalues and eigenvectors of spiked random matrices

Author: Biroli, Giulio, Guionnet, Alice, Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon), Centre National de la Recherche Scientifique (CNRS), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Guionnet, Alice, Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID, and École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS)
Subjects: [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Statistical Mechanics (cond-mat.stat-mech), Probability (math.PR), FOS: Physical sciences, Mathematics - Statistics Theory, Disordered Systems and Neural Networks (cond-mat.dis-nn), Mathematical Physics (math-ph), Statistics Theory (math.ST), Condensed Matter - Disordered Systems and Neural Networks, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], FOS: Mathematics, Mathematics - Probability, Condensed Matter - Statistical Mechanics, Mathematical Physics
Abstract: International audience; We consider matrices formed by a random $N\times N$ matrix drawn from the Gaussian Orthogonal Ensemble (or Gaussian Unitary Ensemble) plus a rank-one perturbation of strength $\theta$, and focus on the largest eigenvalue, $x$, and the component, $u$, of the corresponding eigenvector in the direction associated to the rank-one perturbation. We obtain the large deviation principle governing the atypical joint fluctuations of $x$ and $u$. Interestingly, for $\theta>1$, in large deviations characterized by a small value of $u$, i.e. $u
Published: 2020

36. A NOTE ON THE BOOLEAN DIMENSION OF A GRAPH AND OTHER RELATED PARAMETERS

Author: Maurice, Pouzet, Si Kaddour, Hamza, Thatte, Bhalchandra, Université Claude Bernard Lyon 1 (UCBL), Université de Lyon, University of Calgary, Université Fédérale du Minas Gerais, université fédérale du Minas Gerais, ANR-10-LABX-0070, and Miguel Couceiro, Pierre Monnin, Amedeo Napoli
Subjects: graphs, Boolean dimension, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Abstract: an expanded version of this paper will be submitted to Discrete mathematics and computer science; International audience; Abstract. We consider Boolean, binary and symplectic dimensions of a graph. We obtain an exact formula for the Boolean dimension of a tree in terms of a certain star decomposition. We relate the binary dimension to the mrank2 of a graph.
Published: 2020

37. Non axiomatisability of positive relation algebras with constants, via graph homomorphisms

Author: Doumane, Amina, Pous, Damien, Preuves et Langages (PLUME), Laboratoire de l'Informatique du Parallélisme (LIP), Centre National de la Recherche Scientifique (CNRS)-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École normale supérieure - Lyon (ENS Lyon), Plume, ANR: ANR-10_LABX-0070,LABEX MILYON (ANR-10-LABX-0070) of Universit ́e de Lyon within the program 'Investissements d’Avenir (ANR-11-IDEX-0007)' operated by the French National Research Agency (ANR)., European Project: 678157,H2020,ERC-2015-STG,CoVeCe(2016), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Igor Konnov, Laura Kovács, École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), and Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL)
Subjects: Mathematics of computing → Discrete mathematics, Relation algebra, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], graph homomorphisms, (in)equational theories
Abstract: International audience; We study the equational theories of composition and intersection on binary relations, with or without their associated neutral elements (identity and full relation). Without these constants, the equational theory coincides with that of semilattice-ordered semigroups. We show that the equational theory is no longer finitely based when adding one or the other constant, refuting a conjecture from the literature. Our proofs exploit a characterisation in terms of graphs and homomorphisms, which we show how to adapt in order to capture standard equational theories over the considered signatures.
Published: 2020
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38. Fine mesh limit of the VRJP in dimension one and Bass-Burdzy flow

Author: Titus Lupu, Christophe Sabot, Pierre Tarrès, Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI), Laboratoire de Probabilités, Statistiques et Modélisations (LPSM (UMR_8001)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), NYU–ECNU Institute of Mathematical Sciences at NYU Shanghai, NYU Shanghai, LABEX MILYON (ANR-10-LABX-0070)projet ANR MALIN (ANR-16-CE93-0003)Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zurich FoundationNational Science Foundation of China (NSFC), grant No. 11771293., ANR-16-CE93-0003,MALIN,Marches aléatoires en interaction(2016), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Laboratoire de Probabilités, Statistique et Modélisation (LPSM (UMR_8001)), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Université Paris Dauphine-PSL-Centre National de la Recherche Scientifique (CNRS), and ANR-16-CE93-0003,MALIN,Marches aléatoires en interaction(2017)
Subjects: Statistics and Probability, Vertex (graph theory), MSC(2010): 60J60, 60K35, 60K37(primary), and 60J55(secondary), Space (mathematics), 01 natural sciences, 010104 statistics & probability, Dimension (vector space), local time, FOS: Mathematics, diffusion in random environment, Limit (mathematics), 0101 mathematics, Computer Science::Databases, Mathematics, reinforcement, Discrete space, 010102 general mathematics, Mathematical analysis, Probability (math.PR), Random walk, self-interacting diffusion, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Flow (mathematics), Statistics, Probability and Uncertainty, Jump process, Analysis, Mathematics - Probability
Abstract: We introduce a continuous space limit of the Vertex Reinforced Jump Process (VRJP) in dimension one, which we call Linearly Reinforced Motion (LRM) on $\R$. It is constructed out of a convergent Bass-Burdzy flow. The proof goes through the representation of the VRJP as a mixture of Markov jump processes. As a by-product this gives a representation in terms of a mixture of diffusions of the LRM and of the Bass-Burdzy flow itself. We also show that our continuous space limit can be obtained out of the Edge Reinforced Random Walk (ERRW), since the ERRW and the VRJP are known to be closely related. Compared to the discrete space processes, the LRM has an additional symmetry in the initial local times (initial occupation profile): changing them amounts to a deterministic change of the space and time scales., 26 pages, 1 figure. Originally called ''Scaling limit of the VRJP in dimension one and Bass-Burdzy flow''
Published: 2020
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39. Minimal $BV$-liftings of $W^{1,1}\left( \Omega ,\mathbb{S}^{1}\right)$maps in 2D are 'often' unique

Author: Curcă, Eduard, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon, ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Curca, Eduard-Valentin, and Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID
Subjects: [MATH] Mathematics [math], [MATH]Mathematics [math]
Abstract: Let $\mathbb{S}^{1}$ bethe unit circle, $\Omega $ a smooth, bounded and simplyconnected domain in $\mathbb{R}^{2}$, and $k$ a positive integer. We provethat the set of configurations $a=\left( a_{1},...,a_{k}\right) \in \Omega ^{k}$for which each $u\in W^{1,1}\left( \Omega ,\mathbb{S}^{1}\right) \cap C(\Omega\backslash \left\{ a_{1},...,a_{k}\right\} )$ admits a unique ($mod\,2\pi $)minimal $BV$-lifting $\varphi\in BV (\Omega, \mathbb{R})$ is of full measure in $\Omega ^{k}$. In particular, this implies that the set of those $u\in W^{1,1}\left( \Omega,\mathbb{S}^{1}\right)$ that admit a unique ($mod\, 2\pi $)minimal $BV$-lifting is dense in $W^{1,1}$ $\left(\Omega,\mathbb{S}^{1}\right)$. Thisanswers a question of Brezis and Mironescu.
Published: 2020

40. Large deviations for the largest eigenvalue of Rademacher matrices

Author: Alice Guionnet, Jonathan Husson, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS), HUSSON, Jonathan, and Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID
Subjects: Statistics and Probability, Wishart distribution, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Gaussian, Diagonal, 01 natural sciences, large deviations, Combinatorics, 010104 statistics & probability, symbols.namesake, FOS: Mathematics, 0101 mathematics, Eigenvalues and eigenvectors, Mathematics, 60B20, Laplace transform, Probability (math.PR), 010102 general mathematics, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], symbols, Large deviations theory, Statistics, Probability and Uncertainty, Random matrices, Random matrix, Rate function, Mathematics - Probability, 60F10
Abstract: In this article, we consider random Wigner matrices, that is symmetric matrices such that the subdiagonal entries of Xn are independent, centered, and with variance one except on the diagonal where the entries have variance two. We prove that, under some suitable hypotheses on the laws of the entries, the law of the largest eigenvalue satisfies a large deviation principle with the same rate function as in the Gaussian case. The crucial assumption is that the Laplace transform of the entries must be bounded above by the Laplace transform of a centered Gaussian variable with same variance. This is satisfied by the Rademacher law and the uniform law on [sqrt{3}, sqrt{3}]. We extend our result to complex entries Wigner matrices and Wishart matrices., Comment: 30 pages
Published: 2020

41. The divergence equation with L ∞ source

Author: Curcă, Eduard, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon, ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Curca, Eduard-Valentin, and Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID
Subjects: [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH] Mathematics [math], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], [MATH]Mathematics [math]
Abstract: A well-known fact is that there exists $g\inL^{\infty}(\mathbf{T}^{2})$ with zero integral, such that the equation \begin{equation}div f=g \tag{$\ast$}\end{equation}has no solution $f=(f_{1},f_{2})\in W^{1,\infty}(\mathbf{T}^{2})$. This wasproved by Preiss (1997), using an involved geometric argument, and, independently, by McMullen (1998), via Ornstein's non-inequality. Weimprove this result: roughly speaking, we prove that, there exists $g\inL^{\infty}$ for which ($\ast$) has no solution such that $%\partial_{2}f_{2}\in L^{\infty}$ and $f$ is "slightly better" than $L^{1}$.Our proof relies on Riesz products in the spirit of the approach ofWojciechowski (1998) for the study of ($\ast$) with source $g\in L^{1}$. Theproof we give is elementary, self-contained and completely avoids the use ofOrnstein's non-inequality.
Published: 2020

42. Siblings of countable cographs

Author: Hahn, Gena, Pouzet, Maurice, Woodrow, Robert, Laboratoire de Probabilités, Combinatoire et Statistique (LAPCS), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), University of Calgary, Werklund School of Education, Calgary, Canada, ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Pouzet, Maurice, and Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID
Subjects: graphs, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Computer Science::Discrete Mathematics, FOS: Mathematics, Mathematics - Combinatorics, equimorphy, cographs, trees, Combinatorics (math.CO), [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], isomorphy, Computer Science::Data Structures and Algorithms, well quasi ordering
Abstract: We show that every countable cograph has either one or infinitely many siblings. This answers, very partially, a conjecture of Thomass\'e. The main tools are the notion of well quasi ordering and the correspondence between cographs and some labelled ordered trees., Comment: Dedicated to the memory of Ivo G. Rosenberg, Three figures, 27 pages
Published: 2020
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43. On the Representation of References in the pi-calculus

Author: Hirschkoff, Daniel, Prebet, Enguerrand, Sangiorgi, Davide, Prebet, Enguerrand, Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID, Coinduction for Verification and Certification - CoVeCe - - H20202016-04-01 - 2021-03-31 - 678157 - VALID, Differential Program Semantics - DIAPASoN - - H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)2019-03-01 - 2024-02-29 - 818616 - VALID, École normale supérieure - Lyon (ENS Lyon), Alma Mater Studiorum Università di Bologna [Bologna] (UNIBO), Foundations of Component-based Ubiquitous Systems (FOCUS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Dipartimento di Informatica - Scienza e Ingegneria [Bologna] (DISI), Alma Mater Studiorum Università di Bologna [Bologna] (UNIBO)-Alma Mater Studiorum Università di Bologna [Bologna] (UNIBO), École normale supérieure de Lyon (ENS de Lyon), Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Preuves et Langages (PLUME), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), MIUR-PRIN project ‘Analysis of Program Analyses’ (ASPRA, ID: 201784YSZ5_004), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), European Project: 678157,H2020,ERC-2015-STG,CoVeCe(2016), European Project: 818616,H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC),DIAPASoN(2019), and European Project: 818616,DIAPASoN
Subjects: Imperative programming 26, and phrases Process calculus, [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], Asynchrony, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], phrases Process calculus, Bisimulation, Imperative programming, Process calculus
Abstract: International audience; The π-calculus has been advocated as a model to interpret, and give semantics to, languages with higher-order features. Often these languages make use of forms of references (and hence viewing a store as set of references). While translations of references in π-calculi (and CCS) have appeared, the precision of such translations has not been fully investigated. In this paper we address this issue. We focus on the asynchronous π-calculus (Aπ), where translations of references are simpler. We first define π ref , an extension of Aπ with references and operators to manipulate them, and illustrate examples of the subtleties of behavioural equivalence in π ref. We then consider a translation of π ref into Aπ. References of π ref are mapped onto names of Aπ belonging to a dedicated "reference" type. We show how the presence of reference names affects the definition of barbed congruence. We establish full abstraction of the translation w.r.t. barbed congruence and barbed equivalence in the two calculi. We investigate proof techniques for barbed equivalence in Aπ, based on two forms of labelled bisimilarities. For one bisimilarity we derive both soundness and completeness; for another, more efficient and involving an inductive 'game' on reference names, we derive soundness, leaving completeness open. Finally, we discuss examples of uses of the bisimilarities.
Published: 2020
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44. Global solutions for a hyperbolic–parabolic system of chemotaxis

Author: Rafael Granero-Belinchón, Équations aux dérivées partielles, analyse (EDPA), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), This work was supported by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program 'Investissements d'Avenir' (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR)., ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), and ANR-11-IDEX-0007,Avenir L.S.E.,PROJET AVENIR LYON SAINT-ETIENNE(2011)
Subjects: Tumor angiogenesis, Quantitative Biology::Tissues and Organs, Applied Mathematics, 010102 general mathematics, Chemotaxis, Dissipation, 01 natural sciences, Quantitative Biology::Cell Behavior, 010101 applied mathematics, Parabolic system, Mathematics - Analysis of PDEs, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Applied mathematics, 0101 mathematics, Fractional Laplacian, Analysis, Analysis of PDEs (math.AP), Mathematics
Abstract: We study a hyperbolic–parabolic model of chemotaxis related to tumor angiogenesis in dimensions one and two. We consider diffusions given by the fractional Laplacian and, in particular, we prove the global existence of classical solutions in certain dissipation regimes.
Published: 2017
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45. Implicit Computational Complexity of Subrecursive Definitions and Applications to Cryptographic Proofs

Author: Ugo Dal Lago, Gilles Barthe, Patrick Baillot, Preuves et Langages (PLUME), Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Institute IMDEA Software [Madrid], Dipartimento di Scienze dell'Informazione [Bologna] (DISI), Alma Mater Studiorum Università di Bologna [Bologna] (UNIBO), Foundations of Component-based Ubiquitous Systems (FOCUS), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Dipartimento di Informatica - Scienza e Ingegneria [Bologna] (DISI), Alma Mater Studiorum Università di Bologna [Bologna] (UNIBO)-Alma Mater Studiorum Università di Bologna [Bologna] (UNIBO), ANR-14-CE25-0005,ELICA,Élargir les idées logiques pour l'analyse de complexité(2014), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Baillot, Patrick, Appel à projets générique - Élargir les idées logiques pour l'analyse de complexité - - ELICA2014 - ANR-14-CE25-0005 - Appel à projets générique - VALID, Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID, Centre National de la Recherche Scientifique (CNRS)-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École normale supérieure - Lyon (ENS Lyon), Barthe, Gille, and Dal Lago, Ugo
Subjects: [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], Effect system, Mathematics::General Topology, 0102 computer and information sciences, 02 engineering and technology, [INFO] Computer Science [cs], Type (model theory), Mathematical proof, 01 natural sciences, Upper and lower bounds, Theoretical Computer Science, [INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR], Mathematics::Probability, Mathematics::Category Theory, 0202 electrical engineering, electronic engineering, information engineering, Mathematics::Metric Geometry, [INFO]Computer Science [cs], ComputingMilieux_MISCELLANEOUS, Mathematics, Discrete mathematics, Computer Science (all), Type inference, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], 020207 software engineering, Function (mathematics), Abstract machine, Mathematics::Logic, 010201 computation theory & mathematics, Linear independence, Algorithm
Abstract: We define a call-by-value variant of Godel's System $$\mathsf {T} $$ with references, and equip it with a linear dependent type and effect system, called $$\mathsf {d}\ell \mathsf {T} $$, that can estimate the complexity of programs, as a function of the size of their inputs. We prove that the type system is intentionally sound, in the sense that it over-approximates the complexity of executing the programs on a variant of the CEK abstract machine. Moreover, we define a sound and complete type inference algorithm which critically exploits the subrecursive nature of $$\mathsf {d}\ell \mathsf {T} $$. Finally, we demonstrate the usefulness of $$\mathsf {d}\ell \mathsf {T} $$ for analyzing the complexity of cryptographic reductions by providing an upper bound for the constructed adversary of the Goldreich-Levin theorem.
Published: 2019
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46. Calculating the Euler characteristic of the moduli space of curves

Author: Lass, Bodo, Combinatoire, théorie des nombres (CTN), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Lass, Bodo, and Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID
Subjects: Computational Mathematics, Discrete Mathematics and Combinatorics, [MATH] Mathematics [math], [MATH]Mathematics [math]
Abstract: The orbifold Euler characteristic of the moduli space M g;1 of genus g smoth curves with one marked point (g ≥ 1) was calculated by Harer and Zagier: χ(M g;1) = ζ(1 − 2g) = −B 2g /(2g), where ζ is the Riemann zeta function and B 2g is the (2g)th Bernoulli number. We want to make their proof shorter and more combinatorial.
Published: 2019

47. Modulated equations of Hamiltonian PDEs and dispersive shocks

Author: Sylvie Benzoni-Gavage, Colin Mietka, L. Miguel Rodrigues, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS), ANR-13-BS01-0009,BoND,Frontières, numérique, dispersion.(2013), ANR: 10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2011), Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), ANR-10-LABX-0070 ANR-13-BS01-0009-0, Agence Nationale de la Recherche, Institut Universitaire de France, ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), and Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)
Subjects: Shock wave, Integrable system, 35B10, periodic traveling waves, soliton asymptotics, Hamiltonian dynam- ics, generalized Korteweg-de Vries equations, General Physics and Astronomy, 35B35, 01 natural sciences, Instability, symbols.namesake, Mathematics - Analysis of PDEs, 37K05, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, abbreviated action integral, Nonlinear Sciences::Pattern Formation and Solitons, Mathematical Physics, dispersive shock, Mathematics, Hamiltonian mechanics, 35B10, 35B35, 35Q35, 35Q51, 35Q53, 37K05, 37K45, modulational instability, Whitham modulated equations, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Statistical and Nonlinear Physics, 37K45, 010101 applied mathematics, Euler-Korteweg systems, Modulational instability, Wavelength, Nonlinear Sciences::Exactly Solvable and Integrable Systems, 35Q53, 35Q51, symbols, AMS Subject Classifications:35B10, 35Q35, Parametrization, Hamiltonian (control theory), harmonic limit, Analysis of PDEs (math.AP)
Abstract: Motivated by the ongoing study of dispersive shock waves in non integrable systems, we propose and analyze a set of wave parameters for periodic waves of a large class of Hamiltonian partial differential systems -- including the generalized Korteweg de Vries equations and the Euler-Korteweg systems -- that are well-behaved in both the small amplitude and small wavelength limits. We use this parametrization to determine fine asymptotic properties of the associated modulation systems, including detailed descriptions of eigenmodes. As a consequence, in the solitary wave limit we prove that modulational instability is decided by the sign of the second derivative -- with respect to speed, fixing the endstate -- of the Boussinesq moment of instability; and, in the harmonic limit, we identify an explicit modulational instability index, of Benjamin--Feir type., 65 pages
Published: 2019
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48. Event structures for mixed choice

Author: De Visme, Marc, Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Preuves et Langages (PLUME), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), de Visme, Marc, and Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID
Subjects: nondeterminism, 000 Computer science, knowledge, general works, [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], TheoryofComputation_COMPUTATIONBYABSTRACTDEVICES, probability, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], CCS, TheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS, Computer Science::Logic in Computer Science, Computer Science, Computer Science::Programming Languages, concurrency, Computer Science::Formal Languages and Automata Theory, event structures
Abstract: International audience; In the context of models with mixed nondeterministic and probabilistic choice, we present a concurrent model based on partial orders, more precisely Winskel's event structures. We study its relationship with the interleaving-based model of Segala's probabilistic automata. Lastly, we use this model to give a truly concurrent semantics to an extension of CCS with probabilistic choice, and relate this concurrent semantics to the usual interleaving semantics, thus generalising existing results on CCS, event structures and labelled transition systems.
Published: 2019

49. Mathematical Theory of Nonlinear Single-Phase Poroelasticity

Author: Van Duijn, Cornelis, Mikelic, Andro, Eindhoven University of Technology [Eindhoven] (TU/e), Darcy Center, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Mikelic, Andro, and Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID
Subjects: [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]
Abstract: In this paper we study the equations of nonlinear poroelasticity derived from mixture theory. They describe the quasi-static mechanical behaviour of a fluid saturated porous medium. The nonlinearity arises from the compressibility of the fluid and from the dependence of porosity and permeability on the divergence of the displacement. We point out analytical difficulties with the model. In our approach we discretize the quasi-static formulation in time and first consider the corresponding incremental problem. For this, we prove existence of a solution using Brézis' theory of pseudo-monotone operators. Generalizing Biot's free energy to the nonlinear setting we construct a Lyapunov functional for the model and prove stability. It allows constructing bounds that are uniform with respect to the time step. In the case when dissipative interface effects between the fluid and the solid are taken into account, we consider the continuous time case in the limit when the time step tends to zero. This yields existence of a weak free energy solution.
Published: 2019

50. On the representation as exterior differentials of closed forms with L 1 -coefficients

Author: Curcă, Eduard, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon, Équations aux dérivées partielles, analyse (EDPA), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Curca, Eduard-Valentin, and Community of mathematics and fundamental computer science in Lyon - - MILYON2010 - ANR-10-LABX-0070 - LABX - VALID
Subjects: [MATH] Mathematics [math], [MATH]Mathematics [math]
Abstract: Let $N\ge 2$. If $g\in L^{1}_{c}(\textbf{R}^{N})$ has zero integral, then the equation $div X=g$ need not have a solution $X\in W^{1,1}_{loc}(\textbf{R}^{N} ; \textbf{R}^{N})$ (Wojciechowski 1999) or even $X\in L^{N/(N-1)}_{loc}$ $(\textbf{R}^{N} ; \textbf{R}^{N})$ (Bourgain and Brezis 2003). Using these results, we prove that, whenever $N\geq3$ and $2\le \ell\le N-1$, there exists some $\ell$-form $f\in L^{1}_{c}(\textbf{R}^{N} ; \Lambda^{\ell})$ such that $df=0$ and the equation $d\lambda=f$ has no solution $\lambda\in W^{1,1}_{loc}(\textbf{R}^{N} ; \Lambda^{\ell-1})$. This provides a negative answer to a question raised by Baldi, Bruno and Pansu (2019)., Soit $N\geq 2$. Si $g\in L_{c}^{1}(\mathbf{R}^{N})$ est d'integrale nulle, alors en général il n'est pas possible de résoudre l'équation $div X=g$ avec $X\in W_{loc}^{1,1}(\mathbf{R}^{N};%\mathbf{R}^{N})$ (Wojciechowski 1999), ou même $X\in L^{N/(N-1)}_{loc}$ $(\textbf{R}^{N} ; \textbf{R}^{N})$ (Bourgain et Brezis 2003).En utilisant ces résultats, nous prouvons que, pour $N\geq 3$ et $2\leq \ell \leq N-1$, il existe une $\ell$-forme $f\in L_{c}^{1}(%\mathbf{R}^{N};\Lambda ^{\ell })$ avec $df=0$ et telle que l'équation $%d\lambda =f$ \ n'ait pas de solution $\lambda \in W_{loc}^{1,1}(\mathbf{R}%^{N};\Lambda ^{\ell -1})$. Ceci donne une réponse négative à une question posée parBaldi, Bruno et Pansu (2019).
Published: 2019

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