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1. Hörmander functional calculus on UMD lattice valued Lp spaces under generalised Gaussian estimates

Author: Deleaval , Luc, Kemppainen , Mikko, Kriegler , Christoph, Laboratoire d'Analyse et de Mathématiques Appliquées ( LAMA ), Université Paris-Est Marne-la-Vallée ( UPEM ) -Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 ( UPEC UP12 ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques Blaise Pascal ( LMBP ), Université Blaise Pascal - Clermont-Ferrand 2 ( UBP ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Centre National de la Recherche Scientifique (CNRS), Université Clermont Auvergne (UCA), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM), and Université Clermont Auvergne [2017-2020] (UCA [2017-2020])
Subjects: Mathematics - Functional Analysis, Mathematics::Functional Analysis, [ MATH.MATH-CA ] Mathematics [math]/Classical Analysis and ODEs [math.CA], Mathematics - Classical Analysis and ODEs, 42A45, 42B25, 47A60, 47A80, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], [ MATH.MATH-FA ] Mathematics [math]/Functional Analysis [math.FA], [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]
Abstract: We consider self-adjoint semigroups $T_t = \exp(-tA)$ acting on $L^2(\Omega)$ and satisfying (generalised) Gaussian estimates, where $\Omega$ is a metric measure space of homogeneous type of dimension $d$. The aim of the article is to show that $A \otimes \mathrm{Id}_Y$ admits a H\"ormander type $\mathcal{H}^\beta_2$ functional calculus on $L^p(\Omega;Y)$ where $Y$ is a UMD lattice, thus extending the well-known H\"ormander calculus of $A$ on $L^p(\Omega)$. We show that if $T_t$ is lattice positive (or merely admits an $H^\infty$ calculus on $L^p(\Omega;Y)$) then this is indeed the case. Here the derivation exponent has to satisfy $\beta > \alpha \cdot d + \frac12$, where $\alpha \in (0,1)$ depends on $p$, and on convexity and concavity exponents of $Y$. A part of the proof is the new result that the Hardy-Littlewood maximal operator is bounded on $L^p(\Omega;Y)$. Moreover, our spectral multipliers satisfy square function estimates in $L^p(\Omega;Y)$. In a variant, we show that if $e^{itA}$ satisfies a dispersive $L^1(\Omega) \to L^\infty(\Omega)$ estimate, then $\beta > \frac{d+1}{2}$ above is admissible independent of convexity and concavity of $Y$. Finally, we illustrate these results in a variety of examples., Comment: accepted for publication in Journal d'Analyse Math\'ematique
Published: 2018

2. A bi-projection method for incompressible Bingham flows with variable density, viscosity and yield stress

Author: Chalayer, Rénald, Chupin, Laurent, Dubois, Thierry, Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Blaise Pascal ( LMBP ), Université Blaise Pascal - Clermont-Ferrand 2 ( UBP ) -Centre National de la Recherche Scientifique ( CNRS ), and ANR-16-CE03-0002,RAVEX,Développement d'une approche intégrée pour la réduction des Risques Associés au Volcanisme EXplosif, de la recherche sur l'aléa aux outils de gestion de crise : le cas de la Martinique(2016)
Subjects: [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Abstract: International audience; A new numerical scheme for solving incompressible Bingham flows with variable density, plastic viscosity and yield stress is proposed. The mathematical and computational difficulties due to the non-differentiable definition of the stress tensor in the plug regions, i.e. where the strain-rate tensor vanishes, is overcome by using a projection formulation as in the Uzawa-like method for viscoplastic flows. This projection definition of the plastic tensor is coupled with a fractional time-stepping scheme designed for Newtonian incompressible flows with variable density. The plastic tensor is treated implicitly in the first sub-step of the fractional time-stepping scheme and a fixed-point iterative procedure is used for its computation. A pseudo-time relaxation term is added into the Bingham projection whose effect is to ensure a geometric convergence of the fixed-point algorithm. This is a key feature of the bi-projection scheme which provides a fast and accurate computation of the plastic tensor. Stability and error analyses of the bi-projection scheme are provided. The use of the discrete divergence-free velocity to convect the density in the mass conservation equation allows us to derive lower and upper bounds for the discrete density. The error induced by the pseudo-time relaxation term is controlled by a prescribed numerical parameter so that a first-order estimate of the time error is derived for the velocity field and the density, as well as the dependent parameters that are the plastic viscosity and the yield stress.
Published: 2018

3. Some theoretical results concerning diphasic flows in thin films

Author: Guy Bayada, Bérénice Grec, Laurent Chupin, 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 ), Laboratoire de Mathématiques Blaise Pascal ( LMBP ), Université Blaise Pascal - Clermont-Ferrand 2 ( UBP ) -Centre National de la Recherche Scientifique ( CNRS ), Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National des Sciences Mathématiques et de leurs Interactions-Centre National de la Recherche Scientifique ( CNRS ), Modélisation mathématique, calcul scientifique (MMCS), 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), Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Centre National de la Recherche Scientifique (CNRS), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS), 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), 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), and 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)
Subjects: [ MATH ] Mathematics [math], Coupling, Applied Mathematics, Mathematical properties, Mechanics, Reynolds equation, Physics::Fluid Dynamics, Chemical effects, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Statistical physics, Limit (mathematics), [MATH]Mathematics [math], Thin film, Cahn–Hilliard equation, Analysis, Mathematics
Abstract: International audience; We are interested in a model for diphasic fluids in thin flows taking into account both the hydrodynamical and the chemical effects at the interface between the two fluids. A limit problem in "thin films" is introduced heuristically. It is a system coupling the Reynolds equation and the hydrodynamical Cahn-Hilliard equation. We study the mathematical properties of this system, and prove an existence result under some smallness condition on the data.
Published: 2015

4. Regression trees to identify combinations of farming practices that achieve the best overall intrinsic quality of milk

Author: L. Rey-Cadilhac, A. Ferlay, M. Gelé, S. Léger, C. Laurent, Unité Mixte de Recherche sur les Herbivores - UMR 1213 (UMRH), VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Institut de l'élevage (IDELE), Laboratoire de Mathématiques Blaise Pascal (LMBP), and Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)
Subjects: note de qualité, les produits laitiers, vache laitière, [SDV]Life Sciences [q-bio], tank à lait, Genetics, Animal Science and Zoology, analyse de régression, Food Science
Abstract: International audience; De nombreuses études au cours des 30 dernières années ont montré les effets des pratiques agricoles sur les composés du lait. Des combinaisons de pratiques peuvent avoir des effets antagonistes ou synergiques sur les composés du lait, mais ces effets combinés restent sous-étudiés. La recherche doit se concentrer sur la qualité intrinsèque globale du lait (incluant les dimensions sensorielles, technologiques, sanitaires et nutritionnelles) et identifier les combinaisons qui peuvent l'optimiser. L'objectif de cette étude était d'identifier quelles combinaisons de pratiques d'élevage obtenaient les meilleurs scores pour les dimensions sensorielles, technologiques, sanitaires, nutritionnelles et pour la qualité intrinsèque globale du lait. Quatre-vingt-dix-neuf fermes privées ont été visitées une fois chacune pour échantillonner leur lait en vrac et étudier leurs pratiques agricoles. Les pratiques enquêtées concernaient les caractéristiques du troupeau, la gestion de l'alimentation, les conditions d'hébergement, et les conditions de traite et de stockage du lait le jour de l'essai. Des analyses de lait de tank ont été conçues pour évaluer la qualité intrinsèque globale du lait pour 2 produits cibles : le fromage au lait cru et le lait demi-écrémé UHT. Des arbres de régression ont ensuite été utilisés pour identifier les combinaisons de pratiques agricoles qui ont obtenu les meilleurs scores sur chaque dimension et sur la qualité intrinsèque globale du lait. La race et le régime alimentaire (type de fourrage) étaient les facteurs les plus influents pour les dimensions sensorielles et sanitaires et pour les scores des dimensions technologiques et nutritionnelles, respectivement, dans l'évaluation du fromage. La qualité globale du fromage était fortement corrélée positivement avec ces scores à 4 dimensions. Par conséquent, la race et le régime alimentaire sont apparus comme les pratiques les plus influentes dans l'arbre de régression pour la qualité globale du fromage. Cependant, les combinaisons de pratiques ayant abouti aux meilleurs scores de qualité diffèrent selon la dimension étudiée et le produit visé. Cela suggère que les conseils sur les pratiques d'élevage pour améliorer la qualité intrinsèque du lait doivent être adaptés en fonction de la destination finale du lait collecté. Cette approche innovante combinant des données à la ferme et des arbres de régression fournit aux gestionnaires d'exploitations un outil précieux et pratique pour hiérarchiser les pratiques en fonction de leur rôle dans l'élaboration de la qualité du lait, et pour identifier les combinaisons de pratiques qui favorisent une bonne qualité du lait et les seuils ou modalités de pratique. nécessaires pour y parvenir. Cela suggère que les conseils sur les pratiques d'élevage pour améliorer la qualité intrinsèque du lait doivent être adaptés en fonction de la destination finale du lait collecté. Cette approche innovante combinant des données à la ferme et des arbres de régression fournit aux gestionnaires d'exploitations un outil précieux et pratique pour hiérarchiser les pratiques en fonction de leur rôle dans l'élaboration de la qualité du lait, et pour identifier les combinaisons de pratiques qui favorisent une bonne qualité du lait et les seuils ou modalités de pratique. nécessaires pour y parvenir. Cela suggère que les conseils sur les pratiques d'élevage pour améliorer la qualité intrinsèque du lait doivent être adaptés en fonction de la destination finale du lait collecté. Cette approche innovante combinant des données à la ferme et des arbres de régression fournit aux gestionnaires d'exploitations un outil précieux et pratique pour hiérarchiser les pratiques en fonction de leur rôle dans l'élaboration de la qualité du lait, et pour identifier les combinaisons de pratiques qui favorisent une bonne qualité du lait et les seuils ou modalités de pratique. nécessaires pour y parvenir.
Published: 2023

5. Stationary Oldroyd model with diffusive stress in thin pipes

Author: Chupin, Laurent, Ichim, Andrei, Martin, Sébastien, Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Centre National de la Recherche Scientifique (CNRS), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Blaise Pascal ( LMBP ), Université Blaise Pascal - Clermont-Ferrand 2 ( UBP ) -Centre National de la Recherche Scientifique ( CNRS ), Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National des Sciences Mathématiques et de leurs Interactions-Centre National de la Recherche Scientifique ( CNRS ), and Martin, Sébastien
Subjects: Physics::Fluid Dynamics, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Mechanics of the fluids [physics.class-ph], [ PHYS.MECA.MEFL ] Physics [physics]/Mechanics [physics]/Mechanics of the fluids [physics.class-ph], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [PHYS.MECA.MEFL] Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]
Abstract: The aim of this paper is to study the stationary flow of an Oldroyd fluid with particular diffusive stress, flowing through a thin 3D pipe. An asymptotic expansion with respect to a small parameter describing the ratio between the diameter of the cross section and the length is calculated and rigorously justified. The result obtained is compared against a numerical solution in the particular case of axisymmetric geometries.
Published: 2017

6. On the exact boundary controllability of semilinear wave equations

Author: Claret, Sue, Lemoine, Jerome, Munch, Arnaud, Laboratoire de Mathématiques Blaise Pascal (LMBP), and Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)
Subjects: Mathematics - Analysis of PDEs, AMS Classifications: 35L71, 93B05, Semilinear wave equation, Fixed point, Exact boundary controllability, [MATH]Mathematics [math], Carleman estimates, Mathematics - Optimization and Control
Abstract: We address the exact boundary controllability of the semilinear wave equation $\partial_{tt}y-\Delta y + f(y)=0$ posed over a bounded domain $\Omega$ of $\mathbb{R}^d$. Assuming that $f$ is continuous and satisfies the condition $\limsup_{\vert r\vert\to \infty} \vert f(r)\vert /(\vert r\vert \ln^p\vert r\vert)\leq \beta$ for some $\beta$ small enough and some $p\in [0,3/2)$, we apply the Schauder fixed point theorem to prove the uniform controllability for initial data in $L^2(\Omega)\times H^{-1}(\Omega)$. Then, assuming that $f$ is in $\mathcal{C}^1(\mathbb{R})$ and satisfies the condition $\limsup_{\vert r\vert\to \infty} \vert f^\prime(r)\vert/\ln^p\vert r\vert\leq \beta$, we apply the Banach fixed point theorem and exhibit a strongly convergent sequence to a state-control pair for the semilinear equation.
Published: 2023

7. On edge-colorings of bicubic planar graphs

Author: Robert, Louis-Hadrien, Laboratoire de Mathématiques Blaise Pascal (LMBP), and Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)
Subjects: FOS: Mathematics, Mathematics - Combinatorics, 55A15, 05C15, Combinatorics (math.CO), [MATH]Mathematics [math]
Abstract: In the first part, we introduce a notion a degree of edge-colorings of bicubic plane graphs and proves some local formula of the graded number of colorings. In the second part, we give a new proof of a result of Fisk saying that any two edge-3-colorings of a planar bicubic graph are Kempe equivalent. Additionaly we show that the degree of colorings behaves well with respect to Kempe equivalence., Comment: 11 pages, 7 figures, comments welcome
Published: 2023

8. Necessary and sufficient symmetries in Event-Chain Monte Carlo with generalized flows and Application to hard dimers

Author: Guyon, Tristan, Guillin, Arnaud, Michel, Manon, Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Institut Universitaire de FranceMésocentre Clermont Auvergne., and ANR-20-CE46-0007,SuSa,Développer des algorithmes stochastiques scalables par non-réversibilité, parallélisation et schémas adaptifs(2020)
Subjects: Statistical Mechanics (cond-mat.stat-mech), FOS: Physical sciences, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], Event-Chain Monte Carlo, Particle systems, Anisotropic particle systems, Rotations, Dimers, Piecewise Deterministic Markov Processes, Probability flow conservation conditions, Markov-chain Monte Carlo, Non-reversible Markov Processes, Condensed Matter - Statistical Mechanics
Abstract: Event-Chain Monte Carlo methods generate continuous-time and non-reversible Markov processes which often display important accelerations compared to their reversible counterparts. However their generalization to any system may appear less straightforward. In this work, we build on the recent analytical characterization of such methods as generating Piecewise Deterministic Markov Processes (PDMP) to clearly decipher the necessary symmetries the PDMP must obey from the sufficient ones which may prove to be too restrictive in a general setting. Thus, we derive a necessary rotational invariance of the probability flows and the minimum event rate, which identifies with the corresponding infinitesimal rejection rate. Such conditions always yield a correct ECMC scheme. We then generalize such results to the case of more general deterministic flows than the translational ones. In particular, we define two classes of interest of general flows, the ideal and uniform-ideal ones, which respectively suppresses or reduces the event rates. From there, we implement a complete non-reversible sampling of a systems of hard dimers, thanks to the introduction of rotational flows, which are uniform-ideal and shows a speed-up of up to ~3 compared to the state-of-the-art ECMC/Metropolis hybrid scheme.
Published: 2023

9. A survey on algebraic dilatations

Author: Dubouloz, Adrien, Mayeux, Arnaud, dos Santos, Joao Pedro, Mayeux, Arnaud, Institut de Mathématiques de Bourgogne [Dijon] (IMB), Université de Bourgogne (UB)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), Institut Montpelliérain Alexander Grothendieck (IMAG), and Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)
Subjects: torsors, affine modifications, differential Galois groups, formal blowups, Néron blowups, [MATH] Mathematics [math], Commutative Algebra (math.AC), shtukas, Mathematics - Algebraic Geometry, affine blowups, FOS: Mathematics, algebraic dilatations, [MATH]Mathematics [math], Algebraic Geometry (math.AG), multi-centered dilatations, dilatations of schemes, A 1 -homotopy theory, Kaliman-Zaidenberg modifications, level structures, Moy-Prasad isomorphism, representations of p-adic groups, Mathematics - Commutative Algebra, mono-centered dilatations, localizations of rings, congruent isomorphisms, Tannakian groups, affine geometry
Abstract: In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and theoretical aspects and the other applications to existing theories., arXiv admin note: text overlap with arXiv:2303.07712
Published: 2023

10. Essential norms of composition operators and multipliers acting between different Hardy spaces

Author: Bayart, Frédéric, Laboratoire de Mathématiques Blaise Pascal (LMBP), and Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS)
Subjects: Mathematics - Functional Analysis, FOS: Mathematics, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], Functional Analysis (math.FA)
Abstract: We compute the essential norm of inclusion operators, composition operators and multipliers acting from a closed subspace of some $L^p$-space into a subspace of some $L^q$-space, with $p > q.$
Published: 2023

11. Free post-groups, post-groups from group actions, and post-Lie algebras

Author: Al-Kaabi, Mahdi Jasim Hasan, Ebrahimi-Fard, Kurusch, Manchon, Dominique, Al-Mustansiriyah University, Norwegian University of Science and Technology (NTNU), Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), and ANR-20-CE40-0007,CARPLO,Combinatoire Algébrique, Renormalisation, Probabilités libres et Opérades(2020)
Subjects: post-group, Mathematics - Quantum Algebra, braided group, FOS: Mathematics, crossed homomorphism, [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA], Quantum Algebra (math.QA), post-Hopf algebra, post-Lie algebra, 20E05, 20N99, 17B38, 17D99
Abstract: After providing a short review on the recently introduced notion of post-group by Bai, Guo, Sheng and Tang, we exhibit post-group counterparts of important post-Lie algebras in the literature, including the infinite-dimensional post-Lie algebra of Lie group integrators. The notion of free post-group is examined, and a group isomorphism between the two group structures associated to a free post-group is explicitly constructed.
Published: 2023

12. Jamming pair of general run-and-tumble particles: Exact results and universality classes

Author: Hahn, Léo, Guillin, Arnaud, Michel, Manon, Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Institut Universitaire de France, ANR-20-CE46-0007,SuSa,Développer des algorithmes stochastiques scalables par non-réversibilité, parallélisation et schémas adaptifs(2020), and ANR-17-CE40-0030,EFI,Entropie, flots, inégalités(2017)
Subjects: Steady states, Statistical Mechanics (cond-mat.stat-mech), Universality Classes, Probability (math.PR), FOS: Physical sciences, Piecewise deterministic Markov Processes, Generator, Run-and-Tumble particles, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Markovian processes, FOS: Mathematics, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], PACS 05.40.-a, PACS 02.50.Ga, Condensed Matter - Statistical Mechanics, Mathematics - Probability, Active matter, Non-reversible processes
Abstract: We consider a general system of two run-and-tumble particles interacting by hardcore jamming on the unidimensional torus. RTP are a paradigmatic active matter model, typically modeling the evolution of bacteria. By directly modeling the system at the continuous-space and -time level thanks to piecewise deterministic Markov processes (PDMP), we derive the conservation conditions which sets the invariant distribution and explicitly construct the two universality classes for the steady state, the detailed-jamming and the global-jamming classes. They respectively identify with the preservation or not of a detailed symmetry at the level of the dynamical internal states between probability flows entering and exiting jamming configurations. Thanks to a spectral analysis of the tumble kernel, we give explicit expressions for the invariant measure in the general case. The non-equilibrium features exhibited by the steady state includes positive mass for the jammed configurations and, for the global-jamming class, exponential decay and growth terms, potentially modulated by polynomial terms. Interestingly, we find that the invariant measure follows, away from jamming configurations, a catenary-like constraint, which results from the interplay between probability conservation and the dynamical skewness introduced by the jamming interactions, seen now as a boundary constraint. This work shows the powerful analytical approach PDMP provide for the study of the stationary behaviors of RTP sytems and motivates their future applications to larger systems, with the goal to derive microscopic conditions for motility-induced phase transitions.
Published: 2023

13. Viscoelastic flows in a rough channel: a multiscale analysis

Author: Laurent Chupin, Sébastien Martin, Laboratoire de Mathématiques Blaise Pascal ( LMBP ), Université Blaise Pascal - Clermont-Ferrand 2 ( UBP ) -Centre National de la Recherche Scientifique ( CNRS ), Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National des Sciences Mathématiques et de leurs Interactions-Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Centre National de la Recherche Scientifique (CNRS), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), and Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Scale (ratio), Truncation error (numerical integration), Applied Mathematics, 010102 general mathematics, Mathematical analysis, Surface finish, 01 natural sciences, Domain (mathematical analysis), Viscoelasticity, Physics::Fluid Dynamics, 010101 applied mathematics, Boundary layer, Mathematics - Analysis of PDEs, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Asymptotic expansion, Mathematical Physics, Analysis, Mathematics, Communication channel, Analysis of PDEs (math.AP)
Abstract: We investigate the influence of the rough boundaries on viscoelastic flows, described by the diffusive Oldroyd model. The fluid domain has a rough wall modeled by roughness patterns of size e ≪ 1 . We present and rigorously justify an asymptotic expansion with respect to e, at any order, based upon the definition of elementary problems: Oldroyd-type problems at the global scale defined on a smoothened domain and boundary-layer corrector problems. The resulting analysis guarantees optimality with respect to the truncation error and leads to a numerical algorithm which allows us to build the approximation of the solution at any required precision.
Published: 2016

14. Les biomarqueurs d’un muscle pour predire la tendrete et la teneur en lipides des carcasses de l’aop maine anjou

Author: Brigitte Picard, Marwa Al-Jammas, Sébastien Couvreur, Pécot, M., Aminot, G., Stéphanie Léger, Leanne de Koning, Valais, A., Muriel Bonnet, Unité Mixte de Recherches sur les Herbivores ( UMR 1213 Herbivores ), VetAgro Sup ( VAS ) -AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement-Institut National de la Recherche Agronomique ( INRA ), Unité de Recherche sur les Systèmes d’Elevage (URSE), Université Bretagne Loire ( UBL ), S.I.C.A. Rouge des Prés, Laboratoire de Mathématiques Blaise Pascal ( LMBP ), Université Blaise Pascal - Clermont-Ferrand 2 ( UBP ) -Centre National de la Recherche Scientifique ( CNRS ), Plateforme RPPA, Institut Curie, Unité Mixte de Recherches sur les Herbivores - UMR 1213 (UMRH), VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement-Institut National de la Recherche Agronomique (INRA), Université Bretagne Loire (UBL), Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Centre National de la Recherche Scientifique (CNRS), Unité Mixte de Recherche sur les Herbivores - UMR 1213 (UMRH), VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Institut National de la Recherche Agronomique (INRA)-AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement, Institut National de la Recherche Agronomique (INRA)-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS), Unité de Recherche sur les Systèmes d'Elevage (URSE), Ecole supérieure d'Agricultures d'Angers (ESA), ProdInra, Archive Ouverte, and Institut National de la Recherche Agronomique (INRA)-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement
Subjects: [SDV] Life Sciences [q-bio], musculoskeletal diseases, tenderness, [ SDV ] Life Sciences [q-bio], muscle, [SDV]Life Sciences [q-bio], carcasse, teneur en lipides, biomarker, oil content, biomarqueur, tendrete, carcass
Abstract: The aim of this study was to predict tenderness and intramuscular fat (IMF) content of the French PDO Maine Anjou by themeasure of the relative abundance of accurate candidate biomarkers of these traits. Another objective was to choose amongfive muscles, one on which the abundance of biomarkers could be measured in order to predict the tenderness and the IMF ofthe others. The results show that the abundance of 4 proteins of the Triceps brachii combined with data on slaughter age andfinishing period duration, allowed an accurate prediction of the affiliation group of tenderness and IMF.
Published: 2016

15. Poincaré and Logarithmic Sobolev Inequalities for Nearly Radial Measures

Author: Cattiaux, Patrick, Guillin, Arnaud, Wu, Liming, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Mathematics - Functional Analysis, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], logconcave measure, Poincaré inequality, radial measure, Applied Mathematics, General Mathematics, Super-Poincaré inequality, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], logarithmic Sobolev inequality, Mathematics - Probability
Abstract: If Poincar{\'e} inequality has been studied by Bobkov for radial measures, few is known about the logarithmic Sobolev inequalty in the radial case. We try to fill this gap here using different methods: Bobkov's argument and super-Poincar{\'e} inequalities, direct approach via L1-logarithmic Sobolev inequalities. We also give various examples where the obtained bounds are quite sharp. Recent bounds obtained by Lee-Vempala in the logconcave bounded case are refined for radial measures.
Published: 2022

16. Learning doubly stochastic and nearly idempotent affinity matrix for graph-based clustering

Author: Julien Ah-Pine, Entrepôts, Représentation et Ingénierie des Connaissances (ERIC), Université Lumière - Lyon 2 (UL2)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), Centre d'Études et de Recherches sur le Développement International (CERDI), and Institut de Recherche pour le Développement (IRD)-Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)
Subjects: [SHS.STAT]Humanities and Social Sciences/Methods and statistics, Information Systems and Management, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], General Computer Science, Modeling and Simulation, Machine learning, Idempotent matrix ADMM, Doubly stochastic affinity matrix, Management Science and Operations Research, Graph-based clustering, Industrial and Manufacturing Engineering, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract: International audience; In graph-based clustering, a relevant affinity matrix is crucial for good results. Double stochasticity of the affinity matrix has been shown to be an important condition, both in theory and in practice. In this paper, we emphasize idempotency as another key condition. In fact, a theorem from Sinkhorn, R. (1968) allows us to exhibit the bijective relationship between the set of doubly stochastic and idempotent matrices of order (modulo permutation of rows and columns) on the one hand, and the set of possible partitions of a set of objects on the other hand. Thereby, both properties are necessary and sufficient conditions for properly modeling the clustering or graph partitioning tasks using matrices. Yet, this leads to a NP-hard discrete optimization problem. In this context, our main contribution is the introduction of a new relaxed model that efficiently learns a double stochastic and nearly idempotent affinity matrix for graph-based clustering. Our approach leverages existing properties between doubly stochastic and idempotent matrices on the one hand, and their associated Laplacian matrices on the other hand. The resulting optimization problem is bi-convex and can be addressed by an Alternating Direction Method of Multipliers scheme. Furthermore, our model requires less parameters to set in contrast to most of recent works. The experimental results we obtained using several real-world benchmarks, exhibit the interest of our method and the importance of taking into account idempotency in graph-based clustering.
Published: 2022

17. Algebraic Magnetism

Author: Mayeux, Arnaud, Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), and European Project: RedLang
Subjects: Nonlinear Sciences::Chaotic Dynamics, Mathematics - Algebraic Geometry, Mathematics::Rings and Algebras, FOS: Mathematics, [MATH]Mathematics [math], Algebraic Geometry (math.AG)
Abstract: For a diagonalizable monoid scheme $A(M)_S$ acting on an algebraic space $X$, we introduce for any submonoid $N$ of $M$ an attractor space $X^N$. We then investigate and study various aspects of attractors associated to monoids., Comment: With an appendix by Matthieu Romagny
Published: 2023

18. Null controllability of quasilinear parabolic equations with gradient dependent coefficients

Author: Cindea, Nicolae, Lacour, Geoffrey, Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)
Subjects: Quasilinear parabolic equations, Numerical approximation, Mathematics - Analysis of PDEs, MSC: 35Q93, 35K59, 93B05, 93C20, Optimization and Control (math.OC), FOS: Mathematics, Exact controllability, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Approximate controllability, Hilbert Uniqueness Method, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Optimization and Control, Analysis of PDEs (math.AP)
Abstract: The aim of this paper is to study the null controllability of a large class of quasilinear parabolic equations. In a first step we prove that the associated linear parabolic equations with non-constant diffusion coefficients are approximately null controllable by the means of regular controls and that these controls depend continuously to the diffusion coefficient. A fixed-point strategy is employed in order to prove the null approximate controllability for the considered quasilinear parabolic equations. We also show the exact null controllability in arbitrary small time for a class of parabolic equations including the parabolic $p$-Laplacian with $\frac{3}{2} < p < 2$. The theoretical results are numerically illustrated combining a fixed point algorithm and a reformulation of the controllability problem for linear parabolic equation as a mixed-formulation which is numerically solved using a finite elements method.
Published: 2023

19. Disjoint frequent hypercyclicity of composition operators

Author: Frédéric Bayart, Laboratoire de Mathématiques Blaise Pascal (LMBP), and Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS)
Subjects: Mathematics - Functional Analysis, General Mathematics, FOS: Mathematics, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], Functional Analysis (math.FA)
Abstract: We give a sufficient condition for two operators to be disjointly frequently hypercyclic. We apply this criterion to composition operators acting on $H(\mathbb D)$ or on the Hardy space $H^2(\mathbb D)$. We simplify a result on disjoint frequent hypercyclicity of pseudo shifts of a recent paper of Martin et al. and we exhibit two disjointly frequently hypercyclic weighted shifts.
Published: 2023

20. ε-hypercyclic operators that are not δ-hypercyclic for δ < ε

Author: Bayart, Frédéric, Laboratoire de Mathématiques Blaise Pascal (LMBP), and Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS)
Subjects: MSC 47A16, 47B37, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]
Abstract: For every fixed ε ∈ (0, 1), we construct an operator on the separable Hilbert space which is δ-hypercyclic for all δ ∈ (ε, 1) and which is not δ-hypercyclic for all δ ∈ (0, ε).
Published: 2023

21. Multi-centered dilatations and congruent isomorphisms

Author: Mayeux, Arnaud, Laboratoire de Mathématiques Blaise Pascal (LMBP), and Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)
Subjects: [MATH]Mathematics [math]
Abstract: We introduce a multi-centered formalism in the context of dilatations of schemes and algebraic spaces. In particular, this provides new results on the behavior of [MRR20] dilatations. Furthermore, we use our new formalism to deduce some refined congruent isomorphisms. Contents 1 Introduction 1 2 Dilatations of semirings 5 3 Multi-centered dilatations in the absolute setting 14 4 Iterated multi-centered dilatations 21 5 Multi-centered dilatations along multiples of a single divisor 24 6 Some flatness and smoothness results 26 7 Néron blowups 27 8 Congruent isomorphisms 29 References 30 Acknowledgement.
Published: 2023

22. Koszul duality for Coxeter groups

Author: Riche, Simon, Vay, Cristian, Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), Universidad Nacional de Córdoba [Argentina], Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires] (CONICET), and European Project: RedLang
Subjects: FOS: Mathematics, Representation Theory (math.RT), [MATH]Mathematics [math], Mathematics - Representation Theory
Abstract: We construct a "Koszul duality" equivalence relating the (diagrammatic) Hecke category attached to a Coxeter system and a given realization to the Hecke category attached to the same Coxeter system and the dual realization. This extends a construction of Beilinson-Ginzburg-Soergel and Bezrukavnikov-Yun in a geometric context, and of the first author with Achar, Makisumi and Williamson. As an application, we show that the combinatorics of the "tilting perverse sheaves" considered in arXiv:1802.07651 is encoded in the combinatorics of the canonical basis of the Hecke algebra of $(W,S)$ attached to the dual realization.
Published: 2023

23. EXIT TIME AND PRINCIPAL EIGENVALUE OF NON-REVERSIBLE ELLIPTIC DIFFUSIONS

Author: Peutrec, Dorian Le, Michel, Laurent, Nectoux, Boris, Institut Denis Poisson (IDP), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), and ANR-19-CE40-0010,QuAMProcs,Analyse Quantitative de Processus Metastables(2019)
Subjects: Mathematics - Spectral Theory, Eyring-Kramers type formulas, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Metastability, MSC: 60J60, 35P15, 35Q82, 47F05, 60F10, principal eigenvalue, Probability (math.PR), mean exit time, FOS: Mathematics, Spectral Theory (math.SP), non-reversible processes, Mathematics - Probability, [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP]
Abstract: In this work, we analyse the metastability of non-reversible diffusion processes $$dX_t=\boldsymbol{b}(X_t)dt+\sqrt h\,dB_t$$ on a bounded domain $\Omega$ when $\mathbf{b}$ admits the decomposition $\mathbf{b}=-(\nabla f+\mathbf{\ell})$ and $\nabla f \cdot \mathbf{\ell}=0$. In this setting, we first show that, when $h\to 0$, the principal eigenvalue of the generator of $(X_t)_{t\ge 0}$ with Dirichlet boundary conditions on the boundary $\partial\Omega$ of $\Omega$ is exponentially close to the inverse of the mean exit time from $\Omega$, uniformly in the initial conditions $X_0=x$ within the compacts of $\Omega$. The asymptotic behavior of the law of the exit time in this limit is also obtained. The main novelty of these first results follows from the consideration of non-reversible elliptic diffusions whose associated dynamical systems $\dot X=\mathbf{b}(X)$ admit equilibrium points on $\partial\Omega$. In a second time, when in addition $\div \mathbf{\ell} =0$, we derive a new sharp asymptotic equivalent in the limit $h\to 0$ of the principal eigenvalue of the generator of the process and of its mean exit time from $\Omega$. Our proofs combine tools from large deviations theory and from semiclassical analysis, and truly relies on the notion of quasi-stationary distribution.
Published: 2023

24. Local Convex Hull density and level set estimation

Author: Aaron, Catherine, Garrido, Myriam, Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), and INRAE, Université Clermont Auvergne
Subjects: [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]
Abstract: Let X n = {X 1 ,. .. , X n } ⊂ R D be an iid sample drawn with a unknown distribution P X associated to a density f and supported by S. We study the problem of estimating the density f. When the density is continuous with regard to the Lebesgue measure and under wide hypotheses, the proposed density estimator has a minimax local asymptotic behaviour when D ≤ 7, but also offers global warranties (whatever the dimension is). It allows to estimate the level sets of the density consistently, even for level sets that intersects the boundary. It is also easy to adapt it to the case of a distribution supported by a d-dimensional, smooth enough, sub-manifold of R D with similar convergence rates (depending on d instead of D). The paper is dedicated to the study of the asymptotical behaviour of the proposed estimator based on local behaviour and is concluded by numerical experiments.
Published: 2023

25. Le site de référence du Partenariat européen d’innovation pour un vieillissement actif et en bonne santé MACVIA-LR (contre les maladies chroniques pour un vieillissement en bonne santé en Languedoc-Roussillon)

Author: Miren David, Ariane Sultan, Guillaume Pandraud, Benoît G. Bardy, Jacques Morel, Giacomo Cavalli, Sylvain Jacquemin, Christine Rolland, Cyril Breuker, Philippe Boulet, Gregoire Mercier, Stéphane Bouly, Valérie Bruguière, Gwen Mathieu, Marc Meissonnier, Hervé Tassery, Vincent Marmelat, Michel Dauzat, Hubert Blain, Gérard Dray, Cyril Laurent, Christine Viarouge-Reunier, Marie Virginie Calmels, François Rivier, Gérard Dupeyron, Gérard Bourrel, Jacquie Berthe, Philippe Domy, Béatrice Lognos, Martine Aoustin, Davide Caimmi, Michel Kaczorek, Mélanie Badin, Pierre Nicolas, Alain Le Quellec, Sylvie Boichot, Vincent Le Moing, C. Boegner, Jérôme Fernandes, Michel Amouyal, Matthieu Desplan, Jean Paul Cristol, T. Camuzat, Karima Bakhti, Jean Michel Verdier, Paule Adnet, Christophe Jorgensen, Denis Sablot, Jean Ribstein, Henriette Dhivert-Donnadieu, Céline Vergne-Richard, Emilie Porte, Christine Azevedo, Isabelle Quéré, Dominique Jakovenko, Marion Gellerat-Rogier, Michel Tanfin, Karen Ritchie, Flavia Oana Coroian, Bernard Guillot, Fabrice Nouvel, J. Pelissier, Anna Bedbrook, Daniel Laune, Jean-Luc Bourrain, Yves Marie Pers, Jean Luc Savy, Chantal Marion, Cherif Heroum, Marianna Danko, Grégoire Vergotte, Françoise Radier-Pontal, Jean Luc Pasquié, Olivier Bénézet, Bernard Combe, Sylvain Richard, Liliane Landreau, Valérie Cros, Isabelle Rédini-Martinez, Emilie Viollet, David Guiraud, François Roubille, Jérôme Froger, Bertrand Coulet, Laurent Journot, Marie Suzanne Léglise, Sylvie Arnavieilhe, Isabel Tavares, Samir Jaber, Olivier Jonquet, David Morquin, Philippe Van de Perre, Roland Sicard, Raphaël Chiron, Vincent Tribout, Pierre Senesse, Xavier Quantin, Jacques Touchon, Kevin Mandrick, Alain Uziel, Vincent Bouix, Marie Christine Picot, Philippe Augé, Martine Lapierre, Antoine Avignon, Eric Pastor, Pascal Demoly, Kjerstin Torre, Jacques Mercier, Jean-Marie Robine, Dominique Larrey, D. J. Costa, Grégory Ninot, Laurent Schifano, Baya Soua, Anne Wojtusciszyn, Jean-Christophe Gris, Didier Delignières, Florence Gressard, Marie Pierre Pasdelou, Fabienne Portejoie, Michel Mondain, Philippe Nérin, Olivier Hantkié, Xavier Bobia, Delphine Paccard, Pierre Géraud Claret, Maxime Villiet, Jacques Burille, Christian Hérisson, Guillaume Tallon, V. Attalin, Jean Emmanuel de la Coussaye, William Camu, Didier Hoa, Chokri Boubakri, Jacques Reynes, Michel Enjalbert, Pascal Kouyoumdjian, Anthony Gellis, Jean Marc Lussert, Jean Philippe Pin, Christian Bourquin, Jean-Marc Lemaitre, Rodolphe Bourret, Isabelle Laffont, Claudine Berr, Marie Christine Courrouy-Michel, Nicolas Giraudeau, Trias Asteriou, Catherine Leblond, Cyril Meunier, Sylvain Lehmann, M. Nogues, Denise Strubel, Raul Punta-Morales, Alain Makinson, Jacques Bringer, Stéphane Perrey, Nathalie Pinto, Yannick Stephan, Charles Fattal, Jean Marc Davy, Arnaud Bourdin, Emilie Royère, Arnaud Dupeyron, Claire Daien, François Vialla, Frédéric Viart, Joël Bockaert, Arnaud Yves Goucham, Pierre Aubas, Huei Yune Bonnin, Fares Gouzi, Véronique Carre, Nicolas Best, Jean Pierre Riso, Jérome Cottalorda, Max Villain, Philippe Dauenhauer, Patrick Messner, Amélie Matheron, Claude Jeandel, Roxana Taddei-Ologeanu, Bernard Alomène, Sylvie Albert, Stéphane Cade, Gérard Canovas, Pauline Coignard, Karine Patte, Sofiane Ramdani, Frédéric Abecassis, Maurice Hayot, Marc Ychou, Anne Laure Coupet, Nathalie Raffort, D. Heve, Philippe Gabrion, Pierre Mares, Pierre Labauge, Marie Pierre Battesti, Denis Mottet, Philippe Fraisse, Jean Bousquet, Jean Louis Pujol, Emilie Galano, Pierre Fesler, Vincent Dufour, Gregory Baptista, Pierre Louis Bernard, Mireille Fouletier, Pierre Dujol, Xavier Vasquez, Jean Paul Ortiz, Pierre Martin-Gousset, Philippe Courtet, Oude Engberink, Valérie Handweiler, S. Granier, Laurence Vian, Françoise Leclercq, Frédéric Cuisinier, Pierre Costa, Guillaume Cayla, Centre Hospitalier Régional Universitaire [Montpellier] (CHRU Montpellier), Contre les MAladies Chroniques pour un VIeillissement Actif en Languedoc-Roussillon (MACVIA-LR), Université Montpellier 1 (UM1)-Centre Hospitalier Régional Universitaire [Montpellier] (CHRU Montpellier)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre Hospitalier Régional Universitaire de Nîmes (CHRU Nîmes)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-European Innovation Partnership on Active and Healthy Ageing Reference Site (EIP on AHA), Commission Européenne-Commission Européenne-Organisation Mondiale de la Santé / World Health Organization Office (OMS / WHO), Département d'anesthésie-réanimation[Montpellier], Université Montpellier 1 (UM1)-Centre Hospitalier Régional Universitaire [Montpellier] (CHRU Montpellier)-Hôpital Gui de Chauliac [Montpellier], Centre Hospitalier Régional Universitaire de Nîmes (CHRU Nîmes), Caractéristiques féminines des dysfonctions des interfaces cardio-vasculaires (EA 2992), Université Montpellier 1 (UM1)-Université de Montpellier (UM), Physiologie & médecine expérimentale du Cœur et des Muscles [U 1046] (PhyMedExp), Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Department of Geriatrics - Efficiency and Deficiency Laboratory, Hadassah Hebrew University Medical Center [Jerusalem], IMT - MINES ALES (IMT - MINES ALES), Institut Mines-Télécom [Paris] (IMT), Département de Biostatistiques, Agence Régionale de Santé Languedoc Roussillon (ARS), Institut de Recherche en Infectiologie de Montpellier (IRIM), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), Roche Pharma Research and Early Development [Basel] (pRED), F. Hoffmann-La Roche [Basel], Service de gynécologie-obstétrique, Mécanismes adaptatifs : des organismes aux communautés (MAOAC), Centre National de la Recherche Scientifique (CNRS)-Collège de France (CdF)-Muséum national d'Histoire naturelle (MNHN), Laboratoire de Géochimie Isotopique Environnementale (GIS) / Université de Nîmes (GIS), Université de Nîmes (UNIMES)-Centre National de la Recherche Scientifique (CNRS), Institut de Recherche en Cancérologie de Montpellier (IRCM - U1194 Inserm - UM), CRLCC Val d'Aurelle - Paul Lamarque-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Montpellier (UM), Agence nationale de sécurité sanitaire de l'alimentation, de l'environnement et du travail (ANSES), Genre (LARHRA GENRE), LAboratoire de Recherche Historique Rhône-Alpes - UMR5190 (LARHRA), Centre National de la Recherche Scientifique (CNRS)-Université Jean Moulin - Lyon 3 (UJML), Université de Lyon-Université de Lyon-Université Lumière - Lyon 2 (UL2)-École normale supérieure - Lyon (ENS Lyon)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Jean Moulin - Lyon 3 (UJML), Université de Lyon-Université de Lyon-Université Lumière - Lyon 2 (UL2)-École normale supérieure - Lyon (ENS Lyon)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Grenoble Alpes (UGA), Département de Médecine générale, Université Montpellier 1 (UM1)-Centre Hospitalier Régional Universitaire [Montpellier] (CHRU Montpellier), Control of Artificial Movement and Intuitive Neuroprosthesis (CAMIN), Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-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), Département de médecine générale, Université de Montpellier (UM), Euromov (EuroMov), Centre Européen de Réalité Virtuelle (CERV), École Nationale d'Ingénieurs de Brest (ENIB), Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Centre National de la Recherche Scientifique (CNRS), Pathologies du système nerveux : recherche épidémiologique et clinique, Université Montpellier 1 (UM1)-IFR76-Institut National de la Santé et de la Recherche Médicale (INSERM), Institut de Génomique Fonctionnelle (IGF), Université de Montpellier (UM)-Université Montpellier 1 (UM1)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Montpellier 2 - Sciences et Techniques (UM2)-Centre National de la Recherche Scientifique (CNRS), CERFRANCE Nord Est - Ile de France, Réseau de Vigilance en Dermato-Allergologie - Groupe d'Etudes et de Recherches en DERmato-Allergologie (Revidal-Gerda), Réseau de Vigilance en Dermato-Allergologie (Revidal), Centre Mutualiste de Rééducation et de Réadaptation Fonctionnelles de KERPAPE [Ploemeur] (CMRRF), Centre Mutualiste de Rééducation et de Réadaptation Fonctionnelles de Kerpape, Laboratoire de Bioingénierie et NanoSciences (LBN), Institut de Génétique Moléculaire de Montpellier (IGMM), Dynamique des capacités humaines et des conduites de santé (EPSYLON), Université Montpellier 1 (UM1)-Université Paul-Valéry - Montpellier 3 (UM3)-Université de Montpellier (UM), Laboratory of Cardio-Vascular Physiology (LCVP), Université Montpellier 1 (UM1), Institut Pierre Louis d'Epidémiologie et de Santé Publique (iPLESP), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut National de la Santé et de la Recherche Médicale (INSERM), Département de Rééducation et Réadaptation Neuro Orthopédique [Nîmes] (Pôle NACRRE), Hôpital Universitaire Carémeau [Nîmes], Centre Mutualiste de Réeducation Neurologique Propara (PROPARA), Languedoc Mutualité, Oc Santé Montpellier, Artificial movement and gait restoration (DEMAR), Unité de Rééducation Neurologique, Centre Hélio-Marin CHU Nîmes, Department de Dermatologie, Médecine physique et de réadaptation, Hôpital Lapeyronie [Montpellier] (CHU), Institut de Génomique Fonctionnelle - Montpellier GenomiX (IGF MGX), Université de Montpellier (UM)-Université Montpellier 1 (UM1)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Montpellier 2 - Sciences et Techniques (UM2)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Université Montpellier 1 (UM1)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Montpellier 2 - Sciences et Techniques (UM2)-Centre National de la Recherche Scientifique (CNRS), Service de Chirurgie Orthopédique, Département de neurologie [Montpellier], Université Montpellier 1 (UM1)-Centre Hospitalier Régional Universitaire [Montpellier] (CHRU Montpellier)-Hôpital Gui de Chauliac [Montpellier]-Université de Montpellier (UM), Centre Bouffard-Vercelli, Laboratoire de Mécanique et Technologie (LMT), École normale supérieure - Cachan (ENS Cachan)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Cellules Souches, Plasticité Cellulaire, Médecine Régénératrice et Immunothérapies (IRMB), Centre Hospitalier Régional Universitaire [Montpellier] (CHRU Montpellier)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Montpellier (UM), Plateforme de Protéomique Clinique, CHU Saint-Eloi, Recherches Translationnelles sur le VIH et les maladies infectieuses (TransVIHMI), Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Recherche pour le Développement (IRD)-Université Montpellier 1 (UM1)-Université Cheikh Anta Diop [Dakar, Sénégal] (UCAD)-Universtié Yaoundé 1 [Cameroun]-Université de Montpellier (UM), Département Conception et conduite des véhicules Aéronautiques et Spatiaux (DCAS), Institut Supérieur de l'Aéronautique et de l'Espace (ISAE-SUPAERO), Lab-STICC_TB_CID_TOMS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de recherche souterrain de Meuse/Haute-Marne, Agence Nationale de gestion des Déchets Radioactifs, Aix-Marseille Université - Faculté des Sciences du Sport (AMU FSS), Aix Marseille Université (AMU), HORIBA Medical (HORIBA ABX SAS), HORIBA Scientific [France], Unité Mathématique, Informatique et Génome (MIG), Institut National de la Recherche Agronomique (INRA), Interactions, Corpus, Apprentissages, Représentations (ICAR), École normale supérieure - Lyon (ENS Lyon)-Université Lumière - Lyon 2 (UL2)-INRP-Ecole Normale Supérieure Lettres et Sciences Humaines-Centre National de la Recherche Scientifique (CNRS), Unité clinique d'Immuno-Rhumatologie & Thérapeutique des maladies ostéo-articulaires, Centre Hospitalier Régional Universitaire [Montpellier] (CHRU Montpellier)-Hôpital Lapeyronie, Institut de Chimie des Substances Naturelles (ICSN), Centre National de la Recherche Scientifique (CNRS), UNICANCER - Institut régional du Cancer [Montpellier] (ICM), CRLCC Val d'Aurelle - Paul Lamarque, Biocommunication en Cardio-Métabolique (BC2M), Neuropsychiatrie : recherche épidémiologique et clinique, Université Montpellier 1 (UM1)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Montpellier (UM), Département d'oncologie médicale et digestive, Centre de cancérologie Val d'Aurelle, Complexité, Innovation, Activités Motrices et Sportives (CIAMS), Université d'Orléans (UO)-Université Paris-Sud - Paris 11 (UP11), Cognition, Action, et Plasticité Sensorimotrice [Dijon - U1093] (CAPS), Université de Bourgogne (UB)-Institut National de la Santé et de la Recherche Médicale (INSERM), Physiopathologie et thérapie des déficits sensoriels et moteurs, Université Montpellier 2 - Sciences et Techniques (UM2)-IFR76-Institut National de la Santé et de la Recherche Médicale (INSERM), Centre de recherche et de Diagnostic sur le Sida (CeDreS), CHU Treichville, Interaction entre Systèmes Protéiques et Différenciation dans la Cellule Tumorale (ISPDCT), Université de la Méditerranée - Aix-Marseille 2-Centre National de la Recherche Scientifique (CNRS), Dynamiques du droit (DD), Université de Montpellier (UM)-Université Montpellier 1 (UM1)-Centre National de la Recherche Scientifique (CNRS), Centre de pharmacologie et innovation dans le diabète (CPID), Université Montpellier 1 (UM1)-Centre Hospitalier Régional Universitaire [Montpellier] (CHRU Montpellier)-Centre National de la Recherche Scientifique (CNRS), Recherche en épidémiologie et biostatistique, Université Paris-Sud - Paris 11 ( UP11 ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ), Centre Hospitalier Régional Universitaire [Montpellier] ( CHRU Montpellier ), Université Montpellier 1 ( UM1 ) -Centre Hospitalier Régional Universitaire [Montpellier] ( CHRU Montpellier ) -Hôpital Gui de Chauliac, Physiologie & médecine expérimentale du Cœur et des Muscles [U 1046] ( PhyMedExp ), Centre National de la Recherche Scientifique ( CNRS ) -Université de Montpellier ( UM ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ), IMT - Mines Alès Ecole Mines - Télécom ( IMT - MINES ALES ), Agence Régionale de Santé Languedoc Roussillon ( ARS ), Institut de Recherche en Infectiologie de Montpellier ( IRIM ), Centre National de la Recherche Scientifique ( CNRS ) -Université de Montpellier ( UM ), Roche Pharma Research and Early Development [Basel] ( pRED ), Centre Hospitalier Régional Universitaire de Nîmes ( CHRU Nîmes ), Mécanismes adaptatifs : des organismes aux communautés ( MAOAC ), Muséum National d'Histoire Naturelle ( MNHN ) -Collège de France ( CdF ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Géochimie Isotopique Environnementale (GIS) / Université de Nîmes ( GIS ), Centre National de la Recherche Scientifique ( CNRS ) -Université de Nîmes ( UNIMES ), Institut de recherche en cancérologie de Montpellier ( IRCM ), Université Montpellier 1 ( UM1 ) -CRLCC Val d'Aurelle - Paul Lamarque-Institut National de la Santé et de la Recherche Médicale ( INSERM ) -Université de Montpellier ( UM ), Contre les MAladies Chroniques pour un VIeillissement Actif en Languedoc-Roussillon ( MACVIA-LR ), Université Montpellier 1 ( UM1 ) -World Health Organization ( WHO/OMS ) -Centre Hospitalier Régional Universitaire [Montpellier] ( CHRU Montpellier ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ) -Centre Hospitalier Régional Universitaire de Nîmes ( CHRU Nîmes ) -Université de Montpellier ( UM ) -Centre National de la Recherche Scientifique ( CNRS ) -European Innovation Partnership on Active and Healthy Ageing Reference Site, Agence Nationale de Sécurité Sanitaire, de l'Alimentation, de l'environnement et du Travail ( ANSES ), ANSES, Genre ( LARHRA GENRE ), LAboratoire de Recherche Historique Rhône-Alpes - UMR5190 ( LARHRA ), Centre National de la Recherche Scientifique ( CNRS ) -Université Jean Moulin - Lyon III-Université Lumière - Lyon 2 ( UL2 ) -École normale supérieure - Lyon ( ENS Lyon ) -Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Grenoble Alpes ( UGA ) -Centre National de la Recherche Scientifique ( CNRS ) -Université Jean Moulin - Lyon III-Université Lumière - Lyon 2 ( UL2 ) -École normale supérieure - Lyon ( ENS Lyon ) -Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Grenoble Alpes ( UGA ), Université Montpellier 1 ( UM1 ), Artificial movement and gait restoration ( DEMAR ), Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier ( LIRMM ), Université de Montpellier ( UM ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Montpellier ( UM ) -Centre National de la Recherche Scientifique ( CNRS ) -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 ), Université de Montpellier ( UM ), Euromov ( EuroMov ), Centre Hospitalier Régional Universitaire [Montpellier] ( CHRU Montpellier ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ) -Université de Montpellier ( UM ), Centre Européen de Réalité Virtuelle ( CERV ), École Nationale d'Ingénieurs de Brest ( ENIB ), Laboratoire de Mathématiques Blaise Pascal ( LMBP ), Université Blaise Pascal - Clermont-Ferrand 2 ( UBP ) -Centre National de la Recherche Scientifique ( CNRS ), Université Montpellier 1 ( UM1 ) -IFR76-Institut National de la Santé et de la Recherche Médicale ( INSERM ), Institut de Génomique Fonctionnelle ( IGF ), Centre National de la Recherche Scientifique ( CNRS ) -Université Montpellier 2 - Sciences et Techniques ( UM2 ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ) -Université Montpellier 1 ( UM1 ) -Université de Montpellier ( UM ), Réseau de Vigilance en Dermato-Allergologie - Groupe d'Etudes et de Recherches en DERmato-Allergologie ( Revidal-Gerda ), Réseau de Vigilance en Dermato-Allergologie ( Revidal ), Centre Mutualiste de Rééducation et de Réadaptation Fonctionnelles de KERPAPE [Ploemeur] ( CMRRF ), Laboratoire de Bioingénierie et NanoScience-UM, Université Montpellier 1 ( UM1 ) -Université de Montpellier ( UM ), Institut de Génétique Moléculaire de Montpellier ( IGMM ), Université de Montpellier ( UM ) -Centre National de la Recherche Scientifique ( CNRS ), Dynamique des capacités humaines et des conduites de santé ( EPSYLON ), Université Paul-Valéry - Montpellier 3 ( UM3 ) -Université Jean Monnet [Saint-Étienne] ( UJM ) -Université Montpellier 1 ( UM1 ) -Université de Montpellier ( UM ), Laboratory of Cardio-Vascular Physiology ( LCVP ), Institut Pierre Louis d'Epidémiologie et de Santé Publique ( iPLESP ), Université Pierre et Marie Curie - Paris 6 ( UPMC ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ), Département de Rééducation et Réadaptation Neuro Orthopédique [Nîmes] ( Pôle NACRRE ), Centre Mutualiste de Réeducation Neurologique Propara ( PROPARA ), Hôpital Lapeyronie [Montpellier] ( CHU ), Institut de Génomique Fonctionnelle - Montpellier GenomiX ( IGF MGX ), Laboratoire de Mécanique et Technologie ( LMT ), École normale supérieure - Cachan ( ENS Cachan ) -Université Pierre et Marie Curie - Paris 6 ( UPMC ) -Centre National de la Recherche Scientifique ( CNRS ), CHU Saint-Eloi-Centre Hospitalier Régional Universitaire [Montpellier] ( CHRU Montpellier ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ) -Université de Montpellier ( UM ), Recherches Translationnelles sur le VIH et les maladies infectieuses ( TransVIHMI ), Université Montpellier 1 ( UM1 ) -Université Cheikh Anta Diop ( UCAD ) -Universtié Yaoundé 1 (Cameroun)-Université de Montpellier ( UM ), Département Conception et conduite des véhicules Aéronautiques et Spatiaux ( DCAS ), Institut Supérieur de l'Aéronautique et de l'Espace ( ISAE-SUPAERO ), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance ( Lab-STICC ), École Nationale d'Ingénieurs de Brest ( ENIB ) -Université de Bretagne Sud ( UBS ) -Université de Brest ( UBO ) -Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques ( IBNM ), Université de Brest ( UBO ) -Université européenne de Bretagne ( UEB ) -ENSTA Bretagne-Institut Mines-Télécom [Paris]-Centre National de la Recherche Scientifique ( CNRS ) -École Nationale d'Ingénieurs de Brest ( ENIB ) -Université de Bretagne Sud ( UBS ) -Université de Brest ( UBO ) -Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques ( IBNM ), Université de Brest ( UBO ) -Université européenne de Bretagne ( UEB ) -ENSTA Bretagne-Institut Mines-Télécom [Paris]-Centre National de la Recherche Scientifique ( CNRS ), Aix-Marseille Université - Faculté des Sciences du Sport ( AMU FSS ), Aix Marseille Université ( AMU ), HORIBA Medical ( HORIBA ABX SAS ), Unité Mathématique, Informatique et Génome ( MIG ), Institut National de la Recherche Agronomique ( INRA ), Interactions, Corpus, Apprentissages, Représentations ( ICAR ), École normale supérieure - Lyon ( ENS Lyon ) -Université Lumière - Lyon 2 ( UL2 ) -INRP-Ecole Normale Supérieure Lettres et Sciences Humaines-Centre National de la Recherche Scientifique ( CNRS ), Centre Hospitalier Régional Universitaire [Montpellier] ( CHRU Montpellier ) -Hôpital Lapeyronie, Institut de Chimie des Substances Naturelles ( ICSN ), Centre National de la Recherche Scientifique ( CNRS ), UNICANCER - Institut régional du Cancer [Montpellier] ( ICM ), Efficience Déficience Motrice [Montpellier] ( EDM ), Centre de pharmacologie et innovation dans le diabète ( CPID ), Université Montpellier 1 ( UM1 ) -Centre Hospitalier Régional Universitaire [Montpellier] ( CHRU Montpellier ) -Centre National de la Recherche Scientifique ( CNRS ), Complexité, Innovation, Activités Motrices et Sportives ( CIAMS ), Université Paris-Sud - Paris 11 ( UP11 ) -Université d'Orléans ( UO ), Cognition, Action, et Plasticité Sensorimotrice [Dijon - U1093] ( CAPS ), Université de Bourgogne ( UB ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ), Université Montpellier 2 - Sciences et Techniques ( UM2 ) -IFR76-Institut National de la Santé et de la Recherche Médicale ( INSERM ), Centre de recherche et de Diagnostic sur le Sida ( CeDreS ), Interaction entre Systèmes Protéiques et Différenciation dans la Cellule Tumorale ( ISPDCT ), Université de la Méditerranée - Aix-Marseille 2-Centre National de la Recherche Scientifique ( CNRS ), Dynamiques du droit ( DD ), Centre National de la Recherche Scientifique ( CNRS ) -Université Montpellier 1 ( UM1 ) -Université de Montpellier ( UM ), Centre Hospitalier Régional Universitaire [Montpellier] (CHRU Montpellier)-Université Montpellier 1 (UM1)-Centre Hospitalier Universitaire de Nîmes (CHU Nîmes)-European Innovation Partnership on Active and Healthy Ageing Reference Site (EIP on AHA), Commission Européenne-Commission Européenne-Organisation Mondiale de la Santé / World Health Organization Office (OMS / WHO)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Montpellier (UM), Centre Hospitalier Universitaire de Nîmes (CHU Nîmes), CERMES3 - Centre de recherche Médecine, sciences, santé, santé mentale, société (CERMES3 - UMR 8211 / U988 / UM 7), École des hautes études en sciences sociales (EHESS)-Université Paris Descartes - Paris 5 (UPD5)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Université de Montpellier (UM)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Génie Informatique et Ingénierie de Production (LGI2P), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Agence Régionale de la Santé (ARS), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Université Pierre Mendès France - Grenoble 2 (UPMF)-École normale supérieure - Lyon (ENS Lyon)-Université Lumière - Lyon 2 (UL2)-Université Jean Moulin - Lyon 3 (UJML), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-École normale supérieure - Lyon (ENS Lyon)-Université Lumière - Lyon 2 (UL2)-Université Jean Moulin - Lyon 3 (UJML), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Inria Sophia Antipolis - Méditerranée (CRISAM), Neuropsychiatrie : recherche épidémiologique et clinique (PSNREC), Université Montpellier 1 (UM1)-Université Paul-Valéry - Montpellier 3 (UPVM)-Université de Montpellier (UM), Hôpital Universitaire Carémeau [Nîmes] (CHU Nîmes), Centre Hospitalier Universitaire de Nîmes (CHU Nîmes)-Centre Hospitalier Universitaire de Nîmes (CHU Nîmes), Oc Santé [Montpellier], Interactive Digital Humans (IDH), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), Hôpital Gui de Chauliac [Montpellier]-Centre Hospitalier Régional Universitaire [Montpellier] (CHRU Montpellier)-Université Montpellier 1 (UM1)-Université de Montpellier (UM), Université de Montpellier (UM)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre Hospitalier Régional Universitaire [Montpellier] (CHRU Montpellier), Recherches Translationnelles sur le VIH et les maladies infectieuses endémiques er émergentes (TransVIHMI), Université Cheikh Anta Diop [Dakar, Sénégal] (UCAD)-Institut de Recherche pour le Développement (IRD)-Université de Yaoundé I-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Montpellier (UM)-Université Montpellier 1 (UM1), Service de Rhumatologie [CHRU Montpellier], École normale supérieure - Lyon (ENS Lyon)-Université Lumière - Lyon 2 (UL2)-INRP-Ecole Normale Supérieure Lettres et Sciences Humaines (ENS LSH)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Institut de Chimie du CNRS (INC), Institut du Cancer de Montpellier (ICM), Université Paris-Sud - Paris 11 (UP11)-Université d'Orléans (UO), Centre de recherche et de Diagnostic sur le Sida [Abidjan, Côte d'Ivoire] (CeDreS), Centre Hospitalier Universitaire de Treichville [Abidjan, Côte d'Ivoire] (CHU de Treichville), École pratique des hautes études (EPHE), Université Paris sciences et lettres (PSL), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université Montpellier 1 (UM1), Centre National de la Recherche Scientifique (CNRS)-Centre Hospitalier Régional Universitaire [Montpellier] (CHRU Montpellier)-Université Montpellier 1 (UM1), Muséum national d'Histoire naturelle (MNHN)-Collège de France (CdF)-Centre National de la Recherche Scientifique (CNRS), and CRLCC Val d'Aurelle - Paul Lamarque-Université de Montpellier (UM)-Institut National de la Santé et de la Recherche Médicale (INSERM)
Subjects: Aging, [ SDV ] Life Sciences [q-bio], business.industry, [SDV]Life Sciences [q-bio], General Medicine, MESH: Accidental Falls, 3. Good health, 03 medical and health sciences, 0302 clinical medicine, [ SDV.MHEP ] Life Sciences [q-bio]/Human health and pathology, Medicine, 030211 gastroenterology & hepatology, Accidental Falls, MESH: Aging, 030212 general & internal medicine, business, Humanities, ComputingMilieux_MISCELLANEOUS, [SDV.MHEP]Life Sciences [q-bio]/Human health and pathology
Abstract: International audience; Le site de référence du Partenariat européen d'innovation pour un vieillissement actif et en bonne santé MACVIA-LR (contre les maladies chroniques pour un vieillissement en bonne santé en Languedoc-Roussillon)
Published: 2015

26. Stationary Oldroyd model with diffusive stress: mathematical analysis of the model and vanishing diffusion process

Author: Sébastien Martin, Laurent Chupin, Laboratoire de Mathématiques Blaise Pascal ( LMBP ), Université Blaise Pascal - Clermont-Ferrand 2 ( UBP ) -Centre National de la Recherche Scientifique ( CNRS ), Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National des Sciences Mathématiques et de leurs Interactions-Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Centre National de la Recherche Scientifique (CNRS), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), and Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)
Subjects: General Chemical Engineering, diffusive stress, 01 natural sciences, 010305 fluids & plasmas, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Stress (mechanics), [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], 0103 physical sciences, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], General Materials Science, Point (geometry), Statistical physics, 0101 mathematics, Diffusion (business), Link (knot theory), Physics, Applied Mathematics, Mechanical Engineering, Mathematical analysis, Viscoelastic fluid, Condensed Matter Physics, Oldroyd model, 010101 applied mathematics, Diffusion process, viscoelastic fluid, [ SPI.MECA.MEFL ] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph]
Abstract: International audience; In this paper we address the stationary Oldroyd model with diffusive stress in two ways: first we present the mathematical analysis of the model. Second, as the link between the diffusive model and the standard one is questionable from the mathematical point of view, we discuss, by means of numerical simulations, the behaviour of the model with respect to vanishing diffusion. In particular, numerical results in 2D or 3D suggest that the solution of the diffusive model converges to the solution of the non-diffusive model at order 1 in the $L^2-$norm and $H^1-$norm.
Published: 2015

27. Homogenization of ferrofluid flow models in porous media with Langevin magnetization law

Author: Amirat, Youcef, Hamdache, Kamel, Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), and Pôle Universitaire Léonard de Vinci (PULV)
Subjects: Ferrofluid flow in porous media, Applied Mathematics, Darcy law, homogenization, Stokes equations, Langevin magnetization law, two-scale convergence, [MATH]Mathematics [math], Analysis
Abstract: International audience; The paper is concerned with the homogenization of the equations describing the flow of a ferrofluid through a heterogeneous porous medium $\Omega$ in the presence of an applied magnetic field. We discuss two models where the magnetization $M$ is parallel to the magnetic field $H$. In the first one $M$ and $H$ satisfy the relation$M=\lambda_0 \, {1}_{\Omega_f} H\, \mbox{ in } \Omega,$where $\lambda_0$ is a positive constant and ${1}_{\Omega_f}$ is the characteristic function of $\Omega_f$ (the pore space). In the second model, $M$ and $H$ satisfy the Langevin magnetization law$M= M_s \frac{L(b_1\, |H|)}{|H|} {1}_{\Omega_f} \, H,$where ${L}$ is the Langevin function given by $L(x)= \frac{1}{\tanh x} - \frac{1}{ x}$,$M_s$ is the saturation magnetization and $b_1$ is a positive physical constant.The velocity and the pressure satisfy the Stokes equation with a Kelvin magnetic force. We perform the homogenization of the equations of each of the two models. Using the two-scale convergence method, we rigorously derive the homogenized equation for the magnetic potential and determine the asymptotic limit of the magnetization. Then we rigorously derive a Darcy law.
Published: 2023

28. Asymptotics of twisted Alexander polynomials and hyperbolic volume

Author: Bénard, Léo, Dubois, Jérôme, Heusener, Michael, Porti, Joan, Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Centre National de la Recherche Scientifique (CNRS), Departament de Matemàtiques [Barcelona] (UAB), Universitat Autònoma de Barcelona (UAB), Heusener, Michael, Laboratoire de Mathématiques Blaise Pascal - Clermont Auvergne (LMBP), Université Clermont Auvergne (UCA)-Centre National de la Recherche Scientifique (CNRS), Departament de Matemàtiques [Barcelona], and Universitat Autònoma de Barcelona [Barcelona] (UAB)
Subjects: Mathematics - Geometric Topology, [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT], General Mathematics, [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG], Mathematics::Geometric Topology, [MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]
Abstract: For a hyperbolic knot and a natural number n, we consider the Alexander polynomial twisted by the n-th symmetric power of a lift of the holonomy. We establish the asymptotic behavior of these twisted Alexander polynomials evaluated at unit complex numbers, yielding the volume of the knot exterior. More generally, we prove the asymptotic behavior for cusped hyperbolic manifolds of finite volume. The proof relies on results of M\"uller, and Menal-Ferrer and the last author. Using the uniformity of the convergence, we also deduce a similar asymptotic result for the Mahler measures of those polynomials., Comment: 51 pages, comments welcome
Published: 2022

29. PDMP Characterisation of Event-Chain Monte Carlo Algorithms for Particle Systems

Author: Athina Monemvassitis, Arnaud Guillin, Manon Michel, Michel, Manon, Développer des algorithmes stochastiques scalables par non-réversibilité, parallélisation et schémas adaptifs - - SuSa2020 - ANR-20-CE46-0007 - AAPG2020 - VALID, Entropie, flots, inégalités - - EFI2017 - ANR-17-CE40-0030 - AAPG2017 - VALID, CAP 20-25 - - CAP 20-252016 - ANR-16-IDEX-0001 - IDEX - VALID, Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), ANR-20-CE46-0007,SuSa,Développer des algorithmes stochastiques scalables par non-réversibilité, parallélisation et schémas adaptifs(2020), ANR-17-CE40-0030,EFI,Entropie, flots, inégalités(2017), and ANR-16-IDEX-0001,CAP 20-25,CAP 20-25(2016)
Subjects: [PHYS]Physics [physics], Particle systems, Statistical Mechanics (cond-mat.stat-mech), Event-chain algorithm, Probability (math.PR), Ergodicity, FOS: Physical sciences, Markov-chain Monte Carlo, Statistical and Nonlinear Physics, [MATH] Mathematics [math], [PHYS] Physics [physics], Piecewise deterministic Markov Process, FOS: Mathematics, [MATH]Mathematics [math], Condensed Matter - Statistical Mechanics, Mathematics - Probability, Mathematical Physics
Abstract: International audience; Monte Carlo simulations of systems of particles such as hard spheres or soft spheres with singular kernels can display around a phase transition prohibitively long convergence times when using traditional Hasting-Metropolis reversible schemes. Efficient algorithms known as event-chain Monte Carlo were then developed to reach necessary accelerations. They are based on non-reversible continuoustime Markov processes. Proving invariance and ergodicity for such schemes cannot be done as for discrete-time schemes and a theoretical framework to do so was lacking, impeding the generalisation of ECMC algorithms to more sophisticated systems or processes. In this work, we characterize the Markov processes generated in ECMC as piecewise deterministic Markov processes. It first allows us to propose more general schemes, for instance regarding the direction refreshment. We then prove the invariance of the correct stationary distribution. Finally, we show the ergodicity of the processes in soft-and hard-sphere systems, with a density condition for the latter.
Published: 2023

30. Free Rota-Baxter Family Algebras and Free (tri)dendriform Family Algebras

Author: Yuanyuan Zhang, Xing Gao, Dominique Manchon, Department of Mathematics and Statistics [Lanzhou], Lanzhou University, Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), and Manchon, Dominique
Subjects: Rings and Algebras (math.RA), Mathematics::Quantum Algebra, General Mathematics, Mathematics::Rings and Algebras, [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA], FOS: Mathematics, [MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA], Mathematics - Rings and Algebras, 16W99, 16S10, 13P10, 08B20
Abstract: In this paper, we first construct the free Rota-Baxter family algebra generated by some set $X$ in terms of typed angularly $X$-decorated planar rooted trees. As an application, we obtain a new construction of the free Rota-Baxter algebra only in terms of angularly decorated planar rooted trees (not forests), which is quite different from the known construction via angularly decorated planar rooted forests by K. Ebrahimi-Fard and L. Guo. We then embed the free dendriform (resp. tridendriform) family algebra into the free Rota-Baxter family algebra of weight zero (resp. one). Finally, we prove that the free Rota-Baxter family algebra is the universal enveloping algebra of the free (tri)dendriform family algebra., Reference precised in the introduction. This text uses in an essential way the description of the free dendriform and tridendriform family algebras given in arXiv:1909.08946
Published: 2023

31. Fixed-kinetic Neural Hamiltonian Flows for enhanced interpretability and reduced complexity

Author: Souveton, Vincent, Guillin, Arnaud, Jasche, Jens, Lavaux, Guilhem, Michel, Manon, Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Oskar Klein Centre [Stockholm], Stockholm University, Institut d'Astrophysique de Paris (IAP), and Institut national des sciences de l'Univers (INSU - CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, Generative models, [INFO]Computer Science [cs], Sampling, Normalizing flows, Hamiltonian flows, Machine Learning (cs.LG)
Abstract: Normalizing Flows (NF) are Generative models which are particularly robust and allow for exact sampling of the learned distribution. They however require the design of an invertible mapping, whose Jacobian determinant has to be computable. Recently introduced, Neural Hamiltonian Flows (NHF) are based on Hamiltonian dynamics-based Flows, which are continuous, volume-preserving and invertible and thus make for natural candidates for robust NF architectures. In particular, their similarity to classical Mechanics could lead to easier interpretability of the learned mapping. However, despite being Physics-inspired architectures, the originally introduced NHF architecture still poses a challenge to interpretability. For this reason, in this work, we introduce a fixed kinetic energy version of the NHF model. Inspired by physics, our approach improves interpretability and requires less parameters than previously proposed architectures. We then study the robustness of the NHF architectures to the choice of hyperparameters. We analyze the impact of the number of leapfrog steps, the integration time and the number of neurons per hidden layer, as well as the choice of prior distribution, on sampling a multimodal 2D mixture. The NHF architecture is robust to these choices, especially the fixed-kinetic energy model. Finally, we adapt NHF to the context of Bayesian inference and illustrate our method on sampling the posterior distribution of two cosmological parameters knowing type Ia supernovae observations.
Published: 2023

32. A NOTE ON FIXED POINT THEORY FOR MULTIVALUED MAPPINGS

Author: Al-Izeri, Abdul-Majeed, Latrach, Khalid, Laboratoire de Mathématiques Blaise Pascal (LMBP), and Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)
Subjects: weakly sequentially upper semicontinuous multivalued map, Fixed point theorem, measure of weak noncompactness, upper semicontinuous multivalued map, multivalued maps, [MATH]Mathematics [math]
Abstract: International audience; In this paper, we establish two fixed point theorems of Himmelberg's type for multivalued maps. Using abstract measures of weak noncompactness, these results are applied to derive some fixed point theorems of Sadovskii's type.
Published: 2023

33. The graph embedded topic model

Author: Liang, Dingge, Corneli, Marco, Bouveyron, Charles, Latouche, Pierre, Modèles et algorithmes pour l’intelligence artificielle (MAASAI), 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)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Scalable and Pervasive softwARe and Knowledge Systems (Laboratoire I3S - SPARKS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Université Côte d'Azur (UCA), Laboratoire Jean Alexandre Dieudonné (LJAD), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Université Clermont Auvergne (UCA), Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), Université Paris Cité (UPCité), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), and Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)
Subjects: Deep latent variable models, Graph neural networks Topic modeling Deep latent variable models Clustering Network analysis, Network analysis, [MATH]Mathematics [math], Clustering, Graph neural networks, Topic modeling
Abstract: Most of existing graph neural networks (GNNs) developed for the prevalent text-rich networks typically treat texts as node attributes. This kind of approach unavoidably results in the loss of important semantic structures and restricts the representational power of GNNs. In this work, we introduce a document similarity-based graph convolutional network (DS-GCN) encoder to combine graph convolutional networks and embedded topic models for text-rich network representation. Then, a latent position-based decoder is used to reconstruct the graph while preserving the network topology. Similarly, the document matrix is rebuilt using a decoder that takes both topic and word embeddings into account. By including a cluster membership variable for each node in the network, we thus develop an end-to-end clustering technique relying on a new deep probabilistic model called the graph embedded topic model (GETM). Numerical experiments on three simulated scenarios emphasize the ability of GETM in fusing the graph topology structure and the document embeddings, and highlight its node clustering performance. Moreover, an application on the Cora-enrich citation network is conducted to demonstrate the e↵ectiveness and interest of GETM in practice.
Published: 2023

34. Faithful flatness of Hopf algebras over coideal subalgebras with a conditional expectation

Author: Bichon, Julien, Laboratoire de Mathématiques Blaise Pascal (LMBP), and Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)
Subjects: 16T05, Rings and Algebras (math.RA), [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA], Mathematics - Quantum Algebra, FOS: Mathematics, [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA], Quantum Algebra (math.QA), Mathematics - Rings and Algebras
Abstract: Let $H$ be a Hopf algebra and let $A\subset H$ be a right coideal subalgebra. We show that if $A$ is a direct summand in $H$ as a right $A$-module, then $H$ is faithfully flat as a right $A$-module.
Published: 2023

35. Global boundary null-controllability of one-dimensional semilinear heat equations

Author: Bhandari, Kuntal, Lemoine, Jérôme, Munch, Arnaud, Institute of Mathematics of the Czech Academy of Science (IM / CAS), Czech Academy of Sciences [Prague] (CAS), Université Clermont Auvergne (UCA), Laboratoire de Mathématiques Blaise Pascal (LMBP), and Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Fixed point arguments, [MATH]Mathematics [math], Mathematics Subject Classification: 35K58, Boundary null-controllability, Carleman estimates, Mathematics Subject Classification: 35K58 93B05 Semilinear heat equation Boundary null-controllability Carleman estimates Fixed point arguments, 93B05 Semilinear heat equation
Abstract: This paper addresses the boundary null-controllability of the semi-linear heat equation ∂ty − ∂xxy + f (y) = 0, (x, t) ∈ (0, 1) × (0, T). Assuming that the nonlinear function f is locally Lipschitz and satisfies lim sup |r|→+∞ |f (r)|/(|r| ln 3/2 |r|) β for some β > 0 small enough and that the initial datum belongs to L ∞ (0, 1), we prove the global null-controllability using the Schauder fixed point theorem and a linearization for which the term f (y) is seen as a right side of the equation. Then, assuming that f is C 1 over R and satisfies lim sup |r|→∞ |f (r)|/ ln 3/2 |r| β for some β small enough, we show that the fixed point application is contracting yielding a constructive method to approximate boundary controls for the semilinear equation. The crucial technical point is a regularity property of a state-control pair for a linear heat equation with L 2 right hand side obtained by using a global Carleman estimate with boundary observation. Numerical experiments illustrate the results. The arguments developed can notably be extended to the multi-dimensional case.
Published: 2023

36. Bioclimatic inference based on mammal community using machine learning regression models: perspectives for paleoecological studies

Author: Linchamps, Pierre, Stoetzel, Emmanuelle, Robinet, François, Hanon, Raphaël, Latouche, Pierre, Cornette, Raphaël, Institut de Systématique, Evolution, Biodiversité (ISYEB ), Muséum national d'Histoire naturelle (MNHN)-École Pratique des Hautes Études (EPHE), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université des Antilles (UA), Histoire naturelle de l'Homme préhistorique (HNHP), Muséum national d'Histoire naturelle (MNHN)-Université de Perpignan Via Domitia (UPVD)-Centre National de la Recherche Scientifique (CNRS), Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg [Luxembourg], University of the Witwatersrand [Johannesburg] (WITS), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), and Muséum national d'Histoire naturelle (MNHN)
Subjects: machine learning, mammal communities, paleoenvironments, palaeoclimates, methodology, [SDV.EE.BIO]Life Sciences [q-bio]/Ecology, environment/Bioclimatology, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, climate modeling, random forest, ecological inference, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract: Climate has played a significant role in shaping the distribution of mammal species across the world. Mammal community composition can therefore be used for inferring modern and past climatic conditions. Here, we develop a novel approach for bioclimatic inference using machine learning (ML) algorithms, which allows for accurate prediction of a set of climate variables based on the composition of the faunal community. The automated dataset construction process aggregates bioclimatic variables with modern species distribution maps, and includes multiple taxonomic ranks as explanatory variables for the predictions. This yields a large dataset that can be used to produce highly accurate predictions. Various ML algorithms that perform regression have been examined. To account for spatial dependence in our data, we employed a geographical block validation approach for model validation and selection. The random forest (RF) outperformed the other evaluated algorithms. Ultimately, we used unseen modern mammal surveys to assess the high predictive performances and extrapolation abilities achieved by our trained models. This contribution introduces a framework and methodology to construct models for developing models based on neo-ecological data, which could be utilized for paleoclimate applications in the future. The study aimed to satisfy specific criteria for interpreting both modern and paleo faunal assemblages, including the ability to generate reliable climate predictions from faunal lists with varying taxonomic resolutions, without the need for published wildlife inventory data from the study area. This method demonstrates the versatility of ML techniques in climate modeling and highlights their promising potential for applications in the fields of archaeology and paleontology.
Published: 2023

37. Identification of fog Particle Size Distribution by a radiative transfer equation inversion

Author: ALI KRAYEM, Frédéric Bernardin, Arnaud Münch, BERNARDIN, Frédéric, Centre d'Etudes et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement - Equipe-projet STI (Cerema Equipe-projet STI), Centre d'Etudes et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement (Cerema), Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), and This work was supported by the International Research Center 'Innovation Transportation and Production Systems' of the I-SITE CAP 20-25.
Subjects: fog, radiative transfer equation, Lorenz-Mie scattering theory, Optical properties, droplet size distribution, inverse problem, [MATH] Mathematics [math], [MATH]Mathematics [math]
Abstract: We investigate the identification problem of the fog Droplet Size Distribution (DSD) by an inverse method of the 1D radiative transfer equation thanks to spectral radiation measurements in the range 350 nm-2500 nm. This distribution together with Lorenz-Mie scattering theory allow to compute the optical properties (scattering coefficient, absorption coefficient, and phase function). We prove the well-posedness of the underlying inverse problem then we perform some numerical experiments using synthetic data. The numerical results suggest that the method allows to identify the DSD with different modellings of the radiative transfer (Beer-Lambert, isotropic and anisotropic collision operator).
Published: 2023
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38. Constructive exact control of semilinear 1D heat equations

Author: Lemoine, Jérôme, Munch, Arnaud, Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), Université Clermont Auvergne (UCA), Université Blaise Pascal - Clermont-Ferrand 2 (UBP)-Centre National de la Recherche Scientifique (CNRS), and Munch, Arnaud
Subjects: Null controllability, Least-squares approach, Mathematics::Analysis of PDEs, AMS Classifications: 35K58, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Optimization and Control, 93B05 Semilinear heat equation
Abstract: The exact distributed controllability of the semilinear heat equation $\partial_{t}y-\Delta y + g(y)=f \,1_{\omega}$ posed over multi-dimensional and bounded domains, assuming that $g\in C^1(\mathbb{R})$ satisfies the growth condition $\limsup_{r\to \infty} g(r)/(\vert r\vert \ln^{3/2}\vert r\vert)=0$ has been obtained by Fern\'andez-Cara and Zuazua in 2000. The proof based on a non constructive fixed point arguments makes use of precise estimates of the observability constant for a linearized heat equation. In the one dimensional setting, assuming that $g^\prime$ does not grow faster than $\beta \ln^{3/2}\vert r\vert$ at infinity for $\beta>0$ small enough and that $g^\prime$ is uniformly H\"older continuous on $\mathbb{R}$ with exponent $p\in [0,1]$, we design a constructive proof yielding an explicit sequence converging to a controlled solution for the semilinear equation, at least with order $1+p$ after a finite number of iterations., Comment: arXiv admin note: text overlap with arXiv:2008.12656, arXiv:2101.06446
Published: 2023

39. Loi des grands nombres pour un réseau de neurones bayésien à deux couches entraîné par inférence variationnelle

Author: Descours, Arnaud, Huix, Tom, Guillin, Arnaud, Michel, Manon, Moulines, Éric, Nectoux, Boris, Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), École polytechnique (X), and Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS)
Subjects: FOS: Computer and information sciences, mean-field, Probability (math.PR), Bayesian neural networks, law of large numbers, Mathematics - Statistics Theory, Machine Learning (stat.ML), Statistics Theory (math.ST), [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], infinite-width neural networks, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Statistics - Machine Learning, FOS: Mathematics, Mathematics - Probability, variational inference
Abstract: We provide a rigorous analysis of training by variational inference (VI) of Bayesian neural networks in the two-layer and infinite-width case. We consider a regression problem with a regularized evidence lower bound (ELBO) which is decomposed into the expected log-likelihood of the data and the Kullback-Leibler (KL) divergence between the a priori distribution and the variational posterior. With an appropriate weighting of the KL, we prove a law of large numbers for three different training schemes: (i) the idealized case with exact estimation of a multiple Gaussian integral from the reparametrization trick, (ii) a minibatch scheme using Monte Carlo sampling, commonly known as Bayes by Backprop, and (iii) a new and computationally cheaper algorithm which we introduce as Minimal VI. An important result is that all methods converge to the same mean-field limit. Finally, we illustrate our results numerically and discuss the need for the derivation of a central limit theorem.
Published: 2023
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40. The Deep Latent Position Topic Model for Clustering and Representation of Networks with Textual Edges

Author: Boutin, Rémi, Latouche, Pierre, Bouveyron, Charles, Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), Modèles et algorithmes pour l’intelligence artificielle (MAASAI), 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)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Scalable and Pervasive softwARe and Knowledge Systems (Laboratoire I3S - SPARKS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (LJAD), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: Social and Information Networks (cs.SI), FOS: Computer and information sciences, Computer Science - Machine Learning, Computer Science - Computation and Language, embedded topic model, Computer Science - Social and Information Networks, unsupervised learning, Machine Learning (cs.LG), [STAT]Statistics [stat], Methodology (stat.ME), graph convolutional network, [INFO]Computer Science [cs], deep latent position model, Computation and Language (cs.CL), Statistics - Methodology
Abstract: Numerical interactions leading to users sharing textual content published by others are naturally represented by a network where the individuals are associated with the nodes and the exchanged texts with the edges. To understand those heterogeneous and complex data structures, clustering nodes into homogeneous groups as well as rendering a comprehensible visualisation of the data is mandatory. To address both issues, we introduce Deep-LPTM, a model-based clustering strategy relying on a variational graph auto-encoder approach as well as a probabilistic model to characterise the topics of discussion. Deep-LPTM allows to build a joint representation of the nodes and of the edges in two embeddings spaces. The parameters are inferred using a variational inference algorithm. We also introduce IC2L, a model selection criterion specifically designed to choose models with relevant clustering and visualisation properties. An extensive benchmark study on synthetic data is provided. In particular, we find that Deep-LPTM better recovers the partitions of the nodes than the state-of-the art ETSBM and STBM. Eventually, the emails of the Enron company are analysed and visualisations of the results are presented, with meaningful highlights of the graph structure., Comment: 44 pages including the appendix, 11 figures, 6 tables, journal paper
Published: 2023
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41. Some extensions of the modular method and Fermat equations of signature (13,13,n)

Author: Billerey, Nicolas, Chen, Imin, Dembélé, Lassina, Dieulefait, Luis, Freitas, Nuno, Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), Department of Mathematics Simon Fraser University, University of Luxembourg [Luxembourg], Departament d'Algebra i Geometria, Facultat de Matematiques, Universitat de Barcelona, Instituto de Ciencias Matemàticas [Madrid] (ICMAT), Universidad Carlos III de Madrid [Madrid] (UC3M)-Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)-Universidad Autónoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC), and Billerey, Nicolas
Subjects: Mathematics - Number Theory, 11D41, 11G10, 11F80, Galois representations, Modularity, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], Fermat equations, 2022. 2010 Mathematics Subject Classification. Primary 11D41, abelian surfaces, 11F80 Fermat equations, FOS: Mathematics, Secondary 11G10, Number Theory (math.NT), Abelian surfaces, March 7, modularity, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
Abstract: We provide several extensions of the modular method which were motivated by the problem of completing previous work to prove that, for any integer $n \geq 2$, the equation \[ x^{13} + y^{13} = 3 z^n \] has no non-trivial solutions. In particular, we present four elimination techniques which are based on: (1) establishing reducibility of certain residual Galois representations over a totally real field; (2) generalizing image of inertia arguments to the setting of abelian surfaces; (3) establishing congruences of Hilbert modular forms without the use of often impractical Sturm bounds; and (4) a unit sieve argument which combines information from classical descent and the modular method. The extensions are of broader applicability and provide further evidence that it is possible to obtain a complete resolution of a family of generalized Fermat equations by remaining within the framework of the modular method. As a further illustration of this, we complete a theorem of Anni-Siksek to show that, for $\ell, m\ge 5$, the only solutions to the equation $x^{2\ell} + y^{2m} = z^{13}$ are the trivial ones., Several modifications after the referees' comments. To appear in Publicacions Matem\`atiques
Published: 2023

42. A generic deep-learning based defect segmentation model for electron micrographs for automatic defect inspection

Author: Julien Baderot, Ali Hallal, Martin Jacob, Vincent Barra, Arnaud Guillin, Sergio Martinez, Johann Foucher, BARRA, Vincent, POLLEN METROLOGY, Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)-Institut national polytechnique Clermont Auvergne (INP Clermont Auvergne), Université Clermont Auvergne (UCA)-Université Clermont Auvergne (UCA), Laboratoire de Mathématiques Blaise Pascal (LMBP), and Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)
Subjects: [INFO.INFO-AI] Computer Science [cs]/Artificial Intelligence [cs.AI], [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Published: 2023

43. A combinatorial characterisation of d-Koszul and (D,A)-stacked monomial algebras that satisfy (Fg)

Author: Jawad, Ruaa, Snashall, Nicole, Taillefer, Rachel, Middle Technical University, Technical Instructors Training Institute, University of Leicester, School of Computing and Mathematical Sciences, Laboratoire de Mathématiques Blaise Pascal (LMBP), Université Clermont Auvergne [2017-2020] (UCA [2017-2020])-Centre National de la Recherche Scientifique (CNRS), and The Higher Committee For Education Development in Iraq (HCED) Reference D1201116
Subjects: (D, [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT], [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA], K-Theory and Homology (math.KT), Mathematics - Rings and Algebras, Hochschild cohomology, Ext algebra, Rings and Algebras (math.RA), Mathematics - K-Theory and Homology, finiteness condition, [MATH.MATH-KT]Mathematics [math]/K-Theory and Homology [math.KT], FOS: Mathematics, d-Koszul, A)-stacked, 16G20, 16E40, 16S37, 16E65, 16E30, Representation Theory (math.RT), Mathematics - Representation Theory
Abstract: Condition (Fg) was introduced in [6] to ensure that the theory of support varieties of a finite dimensional algebra, established by Snashall and Solberg, has some similar properties to that of a group algebra. In this paper we give some easy to check combinatorial conditions that are equivalent to (Fg) for monomial d-Koszul algebras. We then extend this to monomial (D, A)-stacked algebras. We also extend the description of the Yoneda algebra of a d-Koszul algebra in [11] to (D, A)-stacked monomial algebras.
Published: 2023
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44. Non-isochoric stable granular models taking into account fluidisation by pore gas pressure

Author: Chupin, Laurent, Dubois, Thierry, Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), and This is contribution of the ClerVolc program of the International Research Center for Disaster Sciences and Sustainable Development of the University of Clermont Auvergne.
Subjects: pore gas pressure, FOS: Physical sciences, [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph], stability, fluidisation, modelisation, dense granular flows, Geophysics (physics.geo-ph), Physics - Geophysics, Mathematics - Analysis of PDEs, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], rheology, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], dilatation, Analysis of PDEs (math.AP)
Abstract: In this paper, we study non-isochoric models for mixtures of solid particles, at high volume concentration, and a gas. One of the motivations of this work concerns geophysics and more particularly the pyroclastic density currents which are precisely mixtures of pyroclast and lithic fragments and air. They are extremely destructive phenomena, capable of devastating urbanised areas, and are known to propagate over long distances, even over almost flat topography. Fluidisation of these dense granular flows by pore gas pressure is one response that could explain this behaviour and must therefore be taken into account in the models. Starting from a gas-solid mixing model and invoking the compressibility of the gas, through a law of state, we rewrite the conservation of mass equation of the gas phase into an equation on the pore gas pressure whose net effect is to reduce the friction between the particles. The momentum equation of the solid phase is completed by generic constitutive laws, specified as in Schaeffer et al (2019, Journal of Fluid Mechanics, 874, 926-951) by a yield function and a dilatancy function. Therefore, the divergence of the velocity field, which reflects the ability of the granular flow to expand or compress, depends on the volume fraction, pressure, strain rate and inertial number. In addition, we require the dilatancy function to describe the rate of volume change of the granular material near an isochoric equilibrium state, i.e. at constant volume. This property ensures that the volume fraction, which is the solution to the conservation of mass equation, is positive and finite at all times. We also require that the non-isochoric fluidised model is linearly stable and dissipates energy (over time). In this theoretical framework, we derive the dilatancy models corresponding to classical rheologies such as Drucker-Prager and $\mu$(I) (with or without expansion effects). The main result of this work is to show that it is possible to obtain non-isochoric and fluidised granular models satisfying all the properties necessary to correctly account for the physics of granular flows and being well-posed, at least linearly stable.
Published: 2023
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45. The Topological Quandles up to Four Elements

Author: Ayadi, Mohamed, Laboratoire de Mathématiques Blaise Pascal (LMBP), and Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)
Subjects: Finite topological spaces, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], FOS: Mathematics, Mathematics - Combinatorics, 57K12, 54A10, Finite topological quandles, Combinatorics (math.CO), [MATH]Mathematics [math], Quandles
Abstract: The finite topological quandles can be represented as $n\times n$ matrices, recently defined by S. Nelson and C. Wong. In this paper, we first study the finite topological quandles and we show how to use these matrices to distinguish all isomorphism classes of finite topological quandles for a given cardinality $n$. As an application, we classify finite topological quandles with up to 4 elements.
Published: 2023
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46. Twisted separability for adjoint functors

Author: Bichon, Julien, Laboratoire de Mathématiques Blaise Pascal (LMBP), and Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)
Subjects: Mathematics - Quantum Algebra, [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA], FOS: Mathematics, Quantum Algebra (math.QA), Mathematics - Category Theory, Category Theory (math.CT), [MATH.MATH-CT]Mathematics [math]/Category Theory [math.CT]
Abstract: Twisted separable functors generalize the separable functors of Nastasescu, Van den Bergh and Van Oystaeyen, and provide a convenient tool to compare various projective dimensions. We discuss when an adjoint functor is twisted separable, obtaining a version of Rafael's Theorem in the twisted case. As an application, we show that if $R$ is Hopf-Galois object over a Hopf algebra $A$, then their Hochschild cohomological dimension coincide, provided that the cohomological dimension of $A$ is finite and that $R$ has a unital twisted trace with respect to a semi-colinear automorphism.
Published: 2023
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47. Fixed points under pinning-preserving automorphisms of reductive group schemes

Author: Achar, Pramod, Richarz, Timo, Riche, Simon, Lourenço, João, Department of Mathematics Louisiana State University, Louisiana State University (LSU), Technische Universität Darmstadt - Technical University of Darmstadt (TU Darmstadt), Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), Westfälische Wilhelms-Universität Münster = University of Münster (WWU), and European Project: RedLang
Subjects: Mathematics - Algebraic Geometry, [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT], FOS: Mathematics, Representation Theory (math.RT), Algebraic Geometry (math.AG), Mathematics - Representation Theory
Abstract: In this paper we determine the scheme-theoretic fixed points of pinned reductive group schemes acted upon by a group of pinning-preserving automorphisms. The results are used in a companion paper to establish a ramified geometric Satake equivalence with integral or modular coefficients., Comments welcome!
Published: 2022

48. Quelques théorèmes de points fixes pour des applications univoques et multivoques et applications

Author: Yassin Abdallah, Mohamed, Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), Université Clermont Auvergne, and Khalid Latrach
Subjects: Nonlinear integral equations of Volterra, Fixed point theorem, Équations statinnaires de transport neutronique, Équations intégrales non linéaires de Volterra, Dunford-Pettis operators, Stationary neutron transport equations, Opérateurs de Dunford-Pettis, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], Countably condensing mappings, Upper semicontinuous multivalued mappings, [MATH.MATH-GN]Mathematics [math]/General Topology [math.GN], Applications multivoques semi-continues supérieurement, Théorèmes de point fixe, Mesure de non-compacité et de non faible compacité, Measure of noncompactness and weak noncompactness, Applications dénombrablement condensantes, Condensing mappings
Abstract: N this thesis, we present some fixed point theorems for single and multivalued mappings in Banach spaces. In the first part, fixed point theorems of the Altman, Sadovskii, Leray-Schauder and Krasnosel’skii type have been established for countably condensing maps. Further, some fixed point results involving two or three maps were presented. These results are based on the concepts of ws-compact and ww-compact maps. For multivalued mapping, many fixed point results of Krasnosel'skii’s type have been established for various kind of perturbations (singlevalued and multivalued maps). In the last part of this work, we present applications of our results to solve nonlinear integral Volterra equations and two models of stationary neutron transport equations.; On présente dans cette thèse quelques théorèmes de points fixes pour des applications univoques et multivoques dans les espaces de Banach. Dans la première, des théorèmes de points fixes de type Altman, Sadovskii, Leray-Schauder et Krasnosel’skii ont été établis pour les applications dénombrablement condensantes. Ensuite des résultats de points fixes faisant intervenir deux ou trois applications ont été présentés. Ces résultats reposent sur les concepts d’applications ws-compactes et ww-compactes. Pour les applications multivoques on a établi de nombreux résultats de points fixes de type Krasnosel’skii en considérant divers types de perturbations (applications univoques et mutivoques). Dans la dernière partie, on a présenté des applications de ces résultats aux équations non linéaires intégrales de Volterra et à deux modèles d’équations de transport neutronique stationnaires.
Published: 2022

49. Une méthode opérationnelle d'évaluation multicritère des élevages laitiers par l'utilisation de la spectroscopie du lait et de l'outil d'évaluation CAP'2ER®

Author: Lepoivre, M., Martin, Bruno, Grollemund, P-M., Laurent, C., Botreau, Raphaëlle, Monsallier, F., Hulin, S., Gerber, P., Chassard, Christophe, Coppa, M., Unité Mixte de Recherche sur le Fromage (UMRF), VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Université Clermont Auvergne (UCA), Unité Mixte de Recherche sur les Herbivores - UMR 1213 (UMRH), VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), CHAMBRE D'AGRICULTURE DU CANTAL, Partenaires IRSTEA, Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA), Pôle Fromager AOP Massif Central, Institut de l'Elevage, and INRAE
Subjects: [SDV]Life Sciences [q-bio]
Abstract: Séance : Qualité des produits; International audience; This study proposes an adaptation of the methodologies of Botreau et al. (2018) and Rey-Cadilhac et al. (2021) forthe multi-criteria assessment of milk intended for the manufacture of raw milk cheese, concerning the environmentalimpacts of milk production and the quality of the milk obtained. A main contribution is to rely on rapid and operationalanalysis methods on a larger scale: mid-infrared and fluorescence spectroscopies milk analyzes and CAP'2ER®diagnostic results of the farm. On 15 grassland dairy farms located in Cantal, representative of three types ofadaptation to the territorial context, the multi-criteria evaluation model tested in this study proved to be sensitive.Among the 4 components of milk quality and the 5 components of environmental performance analyzed, only thehealth component of quality showed significant differences between the different farm profiles. A significant andpositive correlation is found between the risk of eutrophication and risk for health. Other trending correlations areanalyzed between the components of milk quality and environmental performance, in association with agronomicpractices.; La présente étude propose une adaptation des méthodologies de Botreau et al. (2018) et Rey-Cadilhac et al. (2021)pour l’évaluation multicritère du lait destiné à la fabrication de fromage au lait cru, concernant les impactsenvironnementaux de la production du lait et la qualité du lait obtenu. Une des contributions de ce travail est lerecours à des méthodes d’analyse rapides et opérationnelles à large échelle : analyses du lait en spectroscopies enmoyen infra-rouge et fluorescence, et résultats de diagnostic CAP'2ER® de l'exploitation. Sur 15 fermes laitièresherbagères situées dans le Cantal, représentatives de trois types d’adaptation au contexte territorial, le modèled’évaluation multicritère testé dans cette étude s’est avéré sensible. Parmi les 4 composantes de la qualité du lait etles 5 composantes de la performance environnementale analysées, seule la composante santé de la qualité du laitprésente des différences significatives entre les différents types de fermes. Une corrélation significative et positiveest établie entre risque d’eutrophisation et risque pour la santé. D’autres corrélations en tendance sont analyséesentre les composantes de la qualité du lait et de la performance environnementale, en association avec les pratiquesagronomiques.
Published: 2022

50. Homogenization of MHD flows in porous media

Author: Youcef Amirat, Kamel Hamdache, Vladimir V. Shelukhin, Laboratoire de Mathématiques Blaise Pascal (LMBP), Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA), Pôle Universitaire Léonard de Vinci, Lavrentyev Institute of Hydrodynamics (LIH), and SBRAS
Subjects: [SPI.ELEC]Engineering Sciences [physics]/Electromagnetism, Maxwell equations, Applied Mathematics, Magnetohydrodynamic (MHD) flow in porous media, homogenization, Stokes equations, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], two-scale convergence, two-scale equations, Analysis, averaging of a nonlinear differential system, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph]
Abstract: International audience; The paper is concerned with the homogenization of a nonlinear differential system describing the flow of an electrically conducting, incompressible and viscous Newtonian fluid through a periodic porous medium, in the presence of a magnetic field. We introduce a variational formulation of the differential system equipped with boundary conditions. We show the existence of a solution of the variational problem, and derive uniform estimates of the solutions depending on the characteristic parameters of the flow. Using the two-scale convergence method, we rigorously derive a two-scale equation for the two-scale current density, and a two-pressure Stokes system. We derive, in the case of constant magnetic permeability, an explicit relation expressing the macroscopic velocity as a function of the macroscopic Lorentz force, the pressure gradient, the external body force, and the macroscopic current density, via two permeability filtration tensors. When the magnetic field is absent, this relation reduces to the Darcy law.
Published: 2022

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